Chap002金融机构管理课后题答案
金融机构管理第九章中文版课后习题答案(1、2、3、6、11、12、13、16)
金融机构管理第九章课后习题部分答案(1、2、3、6、11、12、13、16)1. 有效期限衡量的是经济定义中资产和负债的平均期限。
有效期限的经济含义是资产价值对于利率变化的利率敏感性(或利率弹性)。
有效期限的严格定义是一种以现金流量的相对现值为权重的加权平均到期期限。
有效期限与到期期限的不同在于,有效期限不仅考虑了资产(或负债)的期限,还考虑了期间发生的现金流的再投资利率。
2.息票债券面值价值= $1,00利率= 0.10 每年付一次息到期收益率=0.08 期限= 2时间现金流PVIF PV ofCF PV*CF *T1 $100.00 0.92593$92.59 $92.592 $1,100.00 0.85734$943.07 $1,886.15价格=$1,035.67分子= $1,978.74有效期限=1.9106= 分子/价格到期收益率=0.10时间现金流PVIF PV ofCF PV*CF *T1 $100.00 0.90909$90.91 $90.912 $1,100.00 0.82645$909.09 $1,818.18价格=$1,000.00分子= $1,909.09有效期限=1.9091= 分子/价格到期收益率=0.12时间现金流PVIF PV ofCF PV*CF *T1 $100.00 0.892$89.29 $89.292 $1,100.00 0.79719$876.91 $1,753.83价格=$966.20分子= $1,843.11有效期限=1.9076= 分子/价格b. 到期收益率上升时,有限期限减少。
c.零息债券面值价值= $1,00利率= 0.00到期收益率=0.08 期限= 2时间现金流PVIF PV ofCF PV*CF *T1 $0.00 0.92593$0.00 $0.002 $1,000.00 0.85734$857.34 $1,714.68价格=$857.34分子= $1,714.68有效期限=2.000= 分子/价格到期收益率=0.10时间现金流PVIF PV ofCF PV*CF *T1 $0.00 0.90909$0.00 $0.002 $1,000.00 0.82645$826.45 $1,652.89价格=$826.45分子= $1,652.89有效期限=2.000= 分子/价格到期收益率=0.12时间现金流PVIF PV ofCF PV*CF *T1 $0.00 0.892$0.00 $0.002 $1,000.00 0.79719 $797.19 $1,594.39价格 = $797.19分子 =$1,594.39有效期限 =2.0000= 分子/价格d.到期收益率的变化不影响零息债券的有效期限。
风险管理与金融机构第二版课后习题答案+修复的)
1.15假定某一投资预期回报为8%,标准差为14%;另一投资预期回报为12%,标准差为20%。
两项投资相关系数为0.3,构造风险回报组合情形。
1.16投资人在有效边界上构造了一个资产组合,预期回报为10%,另外一个构造,预期回报20%,求两个资产组合各自的标准差。
解:由资本市场线可得:p m fm f p r r r r δδ-+=,当%,10%,15%,7,12.0====p m f m r r r δ则%9%)7%12/(%15*%)7%10()/(*)(=--=--=f m m f p p r r r r δδ同理可得,当%20=p r ,则标准差为:%39=p δ 1.17一家银行在下一年度的盈利服从正太分布,其期望值及标准差分别为资产的0.8%及2%.股权资本为正,资金持有率为多少。
在99% 99.9%的置信度下,为使年终时股权资本为正,银行的资本金持有率(分母资产)分别应为多少(1)设 在99%置信度下股权资本为正的当前资本金持有率为A ,银行在下一年的盈利占资产的比例为X ,由于盈利服从正态分布,因此银行在99%的置信度下股权资本为正的当前资本金持有率的概率为:()P X A >-,由此可得0.8%0.8%()1()1()()99%2%2%A A P X A P X A N N --+>-=-<-=-==查表得0.8%2%A +=2.33,解得A=3.85%,即在99%置信度下股权资本为正的当前资本金持有率为3.85%。
(2)设 在99.9%置信度下股权资本为正的当前资本金持有率为B ,银行在下一年的盈利占资产的比例为Y ,由于盈利服从正态分布,因此银行在99.9%的置信度下股权资本为正的当前资本金持有率的概率为:()P Y B >-,由此可得0.8%0.8%()1()1()()99.9%2%2%B B P Y B P Y B N N --+>-=-<-=-==查表得0.8%2%B +=3.10,解得B=5.38% 即在99.9%置信度下股权资本为正的当前资本金持有率为5.38%。
金融机构管理习题答案025
Chapter Twenty FiveOptions, Caps, Floors, and CollarsChapter Outline IntroductionBasic Features of Options∙Buying a Call Option on a Bond∙Writing a Call Option on a Bond∙Buying a Put Option on a Bond∙Writing a Put Option on a BondWriting versus Buying Options∙Economic Reasons for Not Writing Options∙Regulatory Reasons∙Futures versus Options HedgingThe Mechanics of Hedging a Bond or Bond Portfolio∙Hedging with Bond Options Using the Binomial Model Actual Bond OptionsUsing Options to Hedge Interest Rate Risk on the Balance Sheet Using Options to Hedge Foreign Exchange RiskHedging Credit Risk with OptionsHedging Catastrophe Risk with Call Spread OptionsCaps, Floors, and Collars∙Caps∙Floors∙Collars∙Caps, Floors, Collars, and Credit RiskSummarySolutions to End-of-Chapter Questions and Problems: Chapter Twenty Five1.How does using options differ from using forward or futures contracts?Both options and futures contracts are useful in managing risk. Other than the pure mechanics, the primary difference between these contracts lies in the requirement of what must be done on or before maturity. Futures and forward contracts require that the buyer or seller of the contracts must execute some transaction. The buyer of an option has the choice to execute the option or to let it expire without execution. The writer of an option must perform a transaction only if the buyer chooses to execute the option.2.What is a call option?A call option is an instrument that allows the owner to buy some underlying asset at a prespecified price on or before a specified maturity date.3.What must happen to interest rates for the purchaser of a call option on a bond to makemoney? How does the writer of the call option make money?The call option on a bond allows the owner to buy a bond at a specific price. For the owner of the option to make money, he should be able to immediately sell the bond at a higher price. Thus, for the bond price to increase, interest rates must decrease between the time the option is purchased and the time it is executed. The writer of the call option makes a premium from the sale of the option. If the option is not exercised, the writer maximizes profit in the amount of the premium. If the option is exercised, the writer stands to lose a portion or the entire premium, and may lose additional money if the price on the underlying asset moves sufficiently far.4.What is a put option?A put option is an instrument that allows the owner to sell some underlying asset at a prespecified price on or before a specified maturity date.5.What must happen to interest rates for the purchaser of a put option on a bond to makemoney? How does the writer of the put option make money?The put option on a bond allows the owner to sell a bond at a specific price. For the owner of the option to make money, he should be able to buy the bond at a lower price immediately prior to exercising the option. Thus, for the bond price to decrease, interest rates must increase between the time the option is purchased and the time it is executed. The writer of the put option makes a premium from the sale of the option. If the option is not exercised, the writer maximizes profit in the amount of the premium. If the option is exercised, the writer stands to lose a portion or the entire premium, and may lose additional money if the price on the underlying asset moves sufficiently far.6. Consider the following:a. What are the two ways to use call and put options on T-bonds to generate positive cashflows when interest rates decline? Verify your answer with a diagram.The FI can either (a) buy a call option, or (b) sell a put option on interest rate instruments, such as T-bonds, to generate positive cash flows in the event that interest rates decline. In the case of a call option, positive cash flows will increase as long as interest rates continue to decrease. See Figure 25-1 in the text as an example of positive cash flows minus the premium paid for the option. Although not labeled in this diagram, interest rates areassumed to be decreasing as you move from left to right on the x-axis. Thus bond prices are increasing.The sale of a put option generates positive cash flows from the premium received. Figure 25-4 shows that the payoff will decrease as the price of the bond falls. Of course this can only happen if interest rates are increasing. Again, although not labeled in this diagram, interest rates are assumed to be increasing as you move from right to left on the x-axis.b. Under what balance sheet conditions can an FI use options on T-bonds to hedge itsassets and/or liabilities against interest rate declines?An FI can use call options on T-bonds to hedge an underlying cash position that decreases in value as interest rates decline. This would be true if, in the case of a macrohedge, the FI's duration gap is negative and the repricing gap is positive. In the case of a microhedge, the FI can hedge a single fixed-rate liability against interest rate declines.c. Is it more appropriate for FIs to hedge against a decline in interest rates with long callsor short puts?An FI is better off purchasing calls as opposed to writing puts for two reasons. First,regulatory restrictions limit an FI's ability to write naked short options. Second, since the potential positive cash inflow on the short put option is limited to the size of the putpremium, there may be insufficient cash inflow in the event of interest rate declines tooffset the losses in the underlying cash position.7. In each of the following cases, identify what risk the manager of an FI faces and whetherthe risk should be hedged by buying a put or a call option.a. A commercial bank plans to issue CDs in three months.The bank faces the risk that interest rates will increase. The FI should buy a put option. If rates rise, the CDs can be purchased at a lower price and sold immediately by exercising the option. The gain will offset the higher interest rate the FI must pay in the spot market.b. An insurance company plans to buy bonds in two months.The insurance company (IC) is concerned that interest rates will fall, and thus the price of the bonds will rise. The IC should buy call options that allow the bond purchase at thelower price. The bonds purchased with the options can be sold immediately for a gain that can be applied against the lower yield realized in the market. Or the bonds can be kept and placed in the IC’s portfolio if they are the desired type of asset.c. A thrift plans to sell Treasury securities next month.The thrift is afraid that rates will rise and the value of the bonds will fall. The thrift should buy a put option that allows the sale of the bonds at or near the current price.d. A U.S. bank lends to a French company with a loan payable in francs.The U.S. bank is afraid that the dollar will appreciate (francs will depreciate). Thus the bank should buy a put to sell francs at or near the current exchange rate.e. A mutual fund plans to sell its holding of stock in a British company.The fund is afraid that the dollar will appreciate (£ will depreciate). Thus the fund should buy a put to sell £ at or near the current exchange rate.f. A finance company has assets with a duration of six years and liabilities with a durationof 13 years.The FI is concerned that interest rates will fall, causing the value of the liabilities to rise more than the value of the assets which would cause the value of the equity to decrease.Thus the bond should buy a call option on interest rates (bonds).8. Consider an FI that wishes to use bond options to hedge the interest rate risk in the bondportfolio.a. How does writing call options hedge the risk when interest rates decrease?In the case where the FI is long the bond, writing a call option will provide extra cash flow in the form of a premium. But falling interest rates will cause the value of the bond toincrease, and eventually the option will be exercised at a loss to the writer. But the loss is offset by the increase in value of the long bond. Thus the initial goal of maintaining the interest rate return on the long bond can be realized.b. Will writing call options fully hedge the risk when interest rates increase? Explain.Writing call options provides a premium that can be used to offset the losses in the bond portfolio caused by rising rates up to the amount of the premium. Further losses are not protected.c. How does buying a put option reduce the losses on the bond portfolio when interestrates rise?When interest rates increase, the value of the bond falls, but the put allows the sale of the bond at or near the original price. Thus the profit potential increases as interest ratescontinue to increase, although it is tempered by the amount of premium that was paid for the put.d. Diagram the purchase of a bond call option against the combination of a bondinvestment and the purchase of a bond put option.The profit payoff of a bond call option is given in Figure 25-1. If the price of the bond falls below the exercise price, the purchaser of the call loses the premium. As the price of the bond increases beyond the exercise price, the purchaser recovers the premium and thenrealizes a net profit. Figures 25-6 and 25-7 give the individual and net profit payoff ofholding a bond long and the purchase of a put option. The put option allows a profit ifbond prices drop. This profit will offset the loss on the long bond caused by the decrease in the bond value. If bond prices increase, the option will not be exercised and the investor will realize a gain from the increase in the bonds value. Thus the call option or thecombination of long bond and put option give the same value.9. What are the regulatory reasons that FIs seldom write options?Regulators often prohibit the writing of options because of the unlimited loss potential.10.What are the problems of using the Black-Scholes option pricing model to value bondoptions? What is meant by the term pull to par?The Black-Scholes model assumes unrealistically that short-term interest rates are constant. Second, the model assumes that the variance of returns on the bond is constant over time. In fact, the variance may increase in the initial life of a bond, but it must decrease during the final stages of the bond’s li fe because the bond must trade at par at maturity. The decrease in variance of returns over the final portion of a bond’s life is called the pull-to-par.11. An Fi has purchased a two-year, $1,000 par value zero-coupon bond for $867.43. The FIwill hold the bond to maturity unless it needs to sell the bond at the end of one year forliquidity purposes. The current one-year interest rate is 7 percent, and the one-year rate in one year is forecast to be either 8.04 percent or 7.44 percent with equal likelihood. The FI wishes to buy a put option to protect itself against a capital loss in the event the bond needs to be sold in one year.a. What was the yield on the bond at the time of purchase?PV0 = FV*PVIF n=2,i=?⇒ $867.43 = $1,000* PVIF n=2,i=?⇒ i = 7.37 percentb. What is the market-determined, implied one-year rate one year before maturity?E(r1) = 0.5*0.0804 + 0.5*0.0744 = 0.0774c. What is the expected sale price if the bond has to be sold at the end of one year?E(P1) = $1,000/(1.0774) = $928.16d.e. If the bank buys a put option with an exercise price equal to your answer in part (c),what will be its value at the end of one year?Put Option Value of WeightedExercise Bond Price Put Option Probability Value$928.16 - $925.58 = $2.58 * 0.5 = $1.29$928.16 - $930.75 = $0.00 * 0.5 = $0.00Total value = $1.29f. What should be the premium on the put option today?PV = $1.29/1.07 = $1.2056.g. Diagram the values for the put option on the 2-year zero-coupon bond.h.end of one year were expected to be 8.14 percent and 7.34 percent?The bond prices for the respective interest rates are $924.73 and $931.62. The expected one-year rate and the expected one-year bond price are the same. Further, the call price of the option is the same.Put Option Value of WeightedExercise Bond Price Put Option Probability Value$928.16 - $924.73 = $3.43 * 0.5 = $1.715$928.16 - $931.62 = $0.00 * 0.5 = $0.000Total value = $1.715 PV = $1.715/1.07 = $1.61.12. A pension fund manager anticipates the purchase of a 20-year, 8 percent coupon Treasurybond at the end of two years. Interest rates are assumed to change only once every year at year-end, with an equal probability of a 1 percent increase or a 1 percent decrease. TheTreasury bond, when purchased in two years, will pay interest semiannually. Currently, the Treasury bond is selling at par.a. What is the pension fund manager's interest rate risk exposure?The pension fund manager is exposed to interest rate declines (price increases).b. How can the pension fund manager use options to hedge that interest rate risk exposure?This interest rate risk exposure can be hedged by buying call options on either financialsecurities or financial futures.c. What prices are possible on the 20-year T-bonds at the end of year 1 and year 2?Currently, the bond is priced at par, $1,000 per $1,000 face value. At the end of the first year, either of two interest rates will occur.(a) Interest rates will increase 1 percent to 9 percent (50 percent probability of eitheroccurrence). The 20-year 8 percent coupon Treasury bond's price will fall to $907.9921 per $1,000 face value.(b) Interest rates will decrease 1 percent to 7 percent (50 percent probability ofoccurrence). The 20-year 8 percent coupon Treasury bond's price will increase to$1,106.7754 per $1,000 face value.At the end of two years, one of three different interest rate scenarios will occur.(a) Interest rates will increase another 1 percent to 10 percent (25 percent probability ofoccurrence). The 20 year 8 percent coupon Treasury bond's price will fall to $828.4091 per $1,000 face value.(b) Interest rates will decrease 1 percent to 8 percent or increase 1 percent to 8 percent(50 percent probability of occurrence). The 20-year 8 percent coupon Treasury bond'sprice will return to $1,000 per $1,000 face value.(c) Interest rates will decrease another 1 percent to 6 percent (25 percent probability ofoccurrence). The 20-year 8% coupon Treasury bond's price will increase to$1,231.1477 per $1,000 face value.Note: The diagram for part (d) is on the next page.e. If options on $100,000, 20-year, 8 percent coupon Treasury bonds (both puts and calls)have a strike price of 101, what are the possible (intrinsic) values of the option positionat the end of year 1 and year 2?The call option's intrinsic value at the end of one year will be either:(a) Zero if the price of a $100,000 20-year Treasury bond is $90,799.21 (in the scenariothat interest rates rise to 9 percent); or(b) $110,677.54 - $101,000 (strike price) = $9,677.54 if the price of a $100,000 20-yearTreasury bond is $110,677.54 (in the scenario that interest rates fall to 7 percent).The call option's intrinsic value at the end of two years will be either:(a) Zero if the price of a $100,000 20-year Treasury bond is $82,840.91 (in the scenariothat interest rates rise to 10 percent); or(b) Zero if the price of a $100,000 20-year Treasury bond is $100,000 (in the scenariothat interest rates stay at 8 percent); or(c ) $123,114.77 - $101,000 (strike price) = $22,114.77 if the price of a $100,000 20-year Treasury bond is $123,114.77 (in the scenario that interest rates fall to 6 percent).d.f.g.PV = $9,677.54/1.08 + $22,114.17/(1.08)2 = $10,773.25.13. Why are options on interest rate futures contracts preferred to options on cash instrumentsin hedging interest rate risk?Futures options are preferred to options on the underlying bond because they are more liquid, have less credit risk, are homogeneous, and have the benefit of mark-to-market features common in futures contracts. At the same time, the futures options offer the same asymmetric payoff functions of regular puts and calls.14. Consider Figure 25-12. What are the prices paid for the following futures options:a. June T-bond calls at 116. ⇒ $1,703.125 per $100,000 contract.b. June T-note puts at 116. ⇒ $1,468.750 per $100,000 contract.c. June Eurodollar calls at 9900 (99.00). ⇒ $1,000.000 per $1,000,000 contract.15. Consider Figure 25-12 again. What happens to the price of the following?a. A call when the exercise price increases? ⇒ The call value decreases.b. A call when the time until expiration increases? ⇒ The call value increases.c. A put when the exercise price increases? ⇒ The put value increases.d. A put when the time to expiration increases? ⇒ The put value increases.16. An FI manager writes a call option on a T-bond futures contract with an exercise price of114 at a quoted price of 0-55.a. What type of opportunities or obligations does the manager have?The manager is obligated to sell the interest rate futures contract to the call option buyer at the price of $114,000 per $100,000 contract, if the buyer chooses to exercise the option. If the writer does not own the bond at the time of exercise, the bond must be purchased in the market. The call writer received a premium of $859.38 from the sale of the option.b. In what direction must interest rates move to encourage the call buyer to exercise theoption?Interest rates must decrease so the market price of the bond increases.17. What is the delta of an option (δ)?The delta of an option measures the change in the option value for a $1 change in the value of the underlying asset. The delta of a call option always will be between 0 and 1.0, and the delta of a put option always will be between –1.0 and 0.18. An FI has a $100 million portfolio of six-year Eurodollar bonds that have an 8 percentcoupon. The bonds are trading at par and have a duration of five years. The FI wishes to hedge the portfolio with T-bond options that have a delta of -0.625. The underlying long-term Treasury bonds for the option have a duration of 10.1 years and trade at a market value of $96,157 per $100,000 of par value. Each put option has a premium of $3.25. a. How many bond put options are necessary to hedge the bond portfolio?contracts D B Value Portfolio Bond N p 82474.823157,96$*1.10*625.0000,000,100$**≈=--==δb. If interest rates increase 100 basis points, what is the expected gain or loss on the putoption hedge? A $100,000 20-year, eight percent bond selling at $96,157 implies a yield of 8.4 percent. ∆P = ∆p * N p = 824 * -0.625 * -10.1/1.084 * $96,157 * 0.01 = $4,614,028.00 gain c. What is the expected change in market value on the bond portfolio? ∆PV Bond = -5 * .01/1.08 * $100,000,000 = -$4,629,629.63 d. What is the total cost of placing the hedge?The price quote of $3.25 is per $100 of face value. Therefore the cost of one put contract is $3,250, and the cost of the hedge = 824 contracts * $3,250 per contract = $2,678,000. e. Diagram the payoff possibilities.The diagram of this portfolio position and the corresponding hedge is given in Figures 25-6 and 25-7.f. How far must interest rates move before the payoff on the hedge will exactly offset the cost of placing the hedge? Solving for the change in interest rates gives ∆R = ($3,250*1.084)/(0.625*10.1*$96,157) = 0.005804 or .58 percent.g. How far must interest rates move before the gain on the bond portfolio will exactly offset the cost of placing the hedge? Again solving for ∆R = ($3,250*824*1.08)/(5*$100,000,000) = .0057844 or .58 percent. h. Summarize the gain, loss, cost conditions of the hedge on the bond portfolio in terms of changes in interest rates.If rates increase 0.58 percent, the portfolio will decrease in value approximately equal to the gain on the hedge. This position corresponds to the intersection of the payoff function from the put and the X-axis in Figure 25-6. The FI is out the cost of the hedge, which alsowill be the case for any other increase in interest rates. In effect the cost of the hedge is the insurance premium to assure the yield on the portfolio at the time the hedge is placed.If rates decrease approximately 0.58 percent, the gain on the portfolio will offset the cost of the hedge, and the put option will not be exercised. This position is shown by theintersection of the X-axis and the net payoff function in Figure 25-7. Any increase in rates beyond 0.58 percent will generate positive profits for the portfolio in excess of the cost of the hedge.19. Corporate Bank has $840 million of assets with a duration of 12 years and liabilities worth$720 million with a duration of 7 years. The bank is concerned about preserving the value of its equity in the event of an increase in interest rates and is contemplating a macrohedge with interest rate options. The call and put options have a delta (δ) of 0.4 and –0.4,respectively. The price of an underlying T-bond is 104-34, and its modified duration is 7.6 years. a. What type of option should Corporate Bank use for the macrohedge? The duration gap for the bank is [12 – (720/840)7] = 6. Therefore the bank is concernedthat interest rates may increase, and it should purchase put options. As rates rise, the value of the bonds underlying the put options will fall, but they will be puttable at the higher put option exercise price. b. How many options should be purchased? The bonds underlying the put options have a market value of $104,531.25. Assuming an 8percent bond, these bonds are trading at a yield to maturity of 7.56 percent. Given a modified duration of 7.6, the duration of these bonds is MD*1.0756 = 8.17 years. Thuscontracts or B D A DGAP N p 754,1475.753,1425.531,104$*17.8*)4.(000,000,840$*6***=-==δc. What is the effect on the economic value of the equity if interest rates rise 50 basispoints?Assuming R for the assets is similar to R for the underlying bonds, the change in equityvalue is –DGAP*A*(∆R/(1+R)) = -6($840,000,000)(.005/1.0756) = -$23,428,784. d. What will be the effect on the hedge if interest rates rise 50 basis points? ∆P = N p (δ*-MD*B*∆R) = 14,754*-.4*-7.6*$104,531.25*0.005 = $23,442,262 gain e. What will be the cost of the hedge if each option has a premium of $0.875?A price quote of $0.875 is per $100 face value of the put contract. Therefore, the cost percontract is $875, and the cost of the hedge is $875*14,754 = $12,909,750.f. Diagram the economic conditions of the hedge.The diagram of this portfolio position and the corresponding hedge is given in Figures 25-6 and 25-7. In this particular case, the payoff function for the net long position of the bank (DGAP = 6) should be considered as the payoff function of the bond in Figure 25-6.g. How much must interest rates move against the hedge for the increased value of thebank to offset the cost of the hedge?Let ∆E = $12,909,750, and solve the equation in part (c) above for ∆R. Then∆R = $12,909,750*1.0756/($840,000,000*-6) = -0.002755 or -0.2755 percent.h. How much must interest rates move in favor of the hedge, or against the balance sheet,before the payoff from the hedge will exactly cover the cost of the hedge?Use the equation in part (d) above and solve for ∆R. Then∆R = $12,909,750/[14,754*-.4*-7.6*$104,531.25] = 0.002755 or 0.2755 percent.i. Formulate a management decision rule regarding the implementation of the hedge.If rates increase 0.2755 percent, the equity will decrease in value approximately equal to the gain on the hedge. This position corresponds to the intersection of the payoff function from the put and the X-axis in Figure 25-6. The FI is out the cost of the hedge, which also will be the case for any other increase in interest rates. In effect the cost of the hedge is the insurance premium to assure the value of the equity at the time the hedge is placed.If rates decrease approximately 0.2755 percent, the gain on the equity value will offset the cost of the hedge, and the put option will not be exercised. This position is shown by the intersection of the X-axis and the net payoff function in Figure 25-7. Any increase in rates beyond 0.2755 percent will generate positive increases in value for the equity in excess of the cost of the hedge.20. An FI has a $200 million asset portfolio that has an average duration of 6.5 years. Theaverage duration of its $160 million in liabilities is 4.5 years. The FI uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta (δ) of the put options has been estimated at -0.3, and the average duration of the T-bonds is 7 years. The current market value of the T-Bonds is $96,000.a. What is the modified duration of the T-bonds if the current level of interest rates is 10percent?MD = D/1+.10 = 7/1.10 = 6.3636 yearsb. How many put option contracts should it purchase to hedge its exposure against rising interest rates? The face value of the T-bonds is $100,000.B * D * A * ]D k - D [ = N L A p-δ = [6.5 - 4.5(.80)]*$200,000,000/[(-.3)*(-7.0)*(96,000)] = 2,876.98 or 2,877 contractsc. If interest rates increase 50 basis points, what will be the change in value of the equity of the FI? Assuming R for the assets is similar to R for the underlying bonds, the change in equity value is –DGAP*A*(∆R/(1+R)) = -2.9($200,000,000)(.005/1.10) = -$2,636,363.64.d. What will be the change in value of the T-bond option hedge position? ∆P = N p (δ*-MD*B*∆R) = 2,877*-.3*-6.3636*$96,000*0.005 = $2,636,363.12 gaine. If put options on T-bonds are selling at a premium of $1.25 per face value of $100, what is the total cost of hedging using options on T-bonds? Premium on the put options = 2,877 x $1.25 x 1,000 = $3,596,250.f. Diagram the spot market conditions of the equity and the option hedge.The diagram of this portfolio position and the corresponding hedge is given in Figures 25-6 and 25-7. In this particular case, the payoff function for the net long position of the bank (DGAP = 2.9) should be considered as the payoff function of the bond in Figure 25-6. g. What must be the change in interest rates before the change in value of the balance sheet (equity) will offset the cost of placing the hedge? Let ∆E = $3,596,250, and solve the equation in part (c) above for ∆R. Then ∆R = $3,596,250*1.10/($200,000,000*-2.9) = -0.00682 or -0.68 percent.h. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? Use the equation in part (d) above and solve for ∆R. Then∆R = $3,596,250/[2,877*-.3*-6.3636*$96,000] = 0.00682 or 0.68 percent. i. Given your answer in part (g), what will be the net gain or loss to the FI?If rates decrease by 0.68 percent, the increase in value of the equity will exactly offset the cost of placing the hedge. The options will be allowed to expire unused since the price of the bonds will be higher in the market place than the exercise price of the option.21. A mutual fund plans to purchase $10,000,000 of 20-year T-bonds in two months. Thesebonds have a duration of 11 years. The mutual fund is concerned about interest rateschanging over the next four months and is considering a hedge with a two-month option on a T-bond futures contract. Two-month calls with a strike price of 105 are priced at 1-25, and puts of the same maturity and exercise price are quoted at 2-09. The delta of the call is .5 and the delta of the put is -.7. The current price of a deliverable T-bond is 103-08 per $100 of face value, and its modified duration is nine years. a. What type of option should the mutual fund purchase? The mutual fund is concerned about interest rates falling which would imply that bondprices would increase. Therefore the FI should buy call options to guarantee a certain purchase price. b. How many options should it purchase?options call or B * MD * A* D = N p23775.236250,103$*9*5.000,000,10$*11==-δ c. What is the cost of these options? The quote for T-bond options is 1-25, or 1 + 25/64 =1.390625 per $100 face value. Thisconverts to $1,390.625 per $100,000 option contract. The total cost of the hedge is 237 * $1,390.625 = $329,578.125. d. If rates change +/-50 basis points, what will be the impact on the price of the desired T-bonds? The price on a deliverable T-bond is $103,250 which implies that the yield to maturity inthe market on a 20-year, 8 percent bond is 7.68 percent. Therefore, for a rate increase, the ∆Bond value = -11(0.005)$10,000,000/1.0768 = -$510,772.66. If rates decrease, the valueof the bonds will increase by $510,772.66. e. What will be the effect on the value of the hedge if rates change +/- 50 basis points? If rates decrease, the value of the underlying bonds, and thus the hedge, increases. ∆P = N c (δ*-MD*B*∆R) = 237*0.5*-9*$103,250*(-0.005) = $550,580.62. This occursbecause the FI can buy the bonds at the exercise price and sell them at the higher market price. If rates rise, the options will expire without value because the bonds will be priced lower in the market. f. Diagram the effects of the hedge and the spot market value of the desired T-bonds. The payoff profile of the call option hedge is given in Figure 25-1, and the profile of a longbond is shown in Figure 25-5. The payoff profile of the call option is less than the bond by the amount of the premium, but the call option profile illustrates less opportunity for loss.。
风险管理与金融机构第二版课后习题答案.doc
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金融机构管理习题答案020
Chapter TwentyCapital AdequacyChapter OutlineIntroductionCapital and Insolvency Risk∙Capital∙The Market Value of Capital∙The Book Value of Capital∙The Discrepancy between the Market and Book Values of Equity∙Arguments against Market Value AccountingCapital Adequacy in the Commercial Banking and Thrift Industry∙Actual Capital Rules∙The Capital-Assets Ratio (or Leverage Ratio)∙Risk-Based Capital Ratios∙Calculating Risk-Based Capital RatiosCapital Requirements for Other Fis∙Securities Firms∙Life Insurance∙Property-Casualty InsuranceSummaryAppendix 20A: Internal Ratings Based Approach to Measuring Credit Risk-Adjusted AssetsSolutions for End-of-Chapter Questions and Problems: Chapter Twenty1. Identify and briefly discuss the importance of the five functions of an FI’s capital?Capital serves as a primary cushion against operating losses and unexpected losses in the value of assets (such as the failure of a loan). FIs need to hold enough capital to provide confidence to uninsured creditors that they can withstand reasonable shocks to the value of their assets. In addition, the FDIC, which guarantees deposits, is concerned that sufficient capital is held so that their funds are protected, because they are responsible for paying insured depositors in the event of a failure. This protection of the FDIC funds includes the protection of the FI owners against increases in insurance premiums. Finally, capital also serves as a source of financing to purchase and invest in assets.2. Why are regulators concerned with the levels of capital held by an FI compared to a non-financial institution?Regulators are concerned with the levels of capital held by an FI because of its special role in society. A failure of an FI can have severe repercussions to the local or national economy unlike non-financial institutions. Such externalities impose a burden on regulators to ensure that these failures do not impose major negative externalities on the economy. Higher capital levels will reduce the probability of such failures.3. What are the differences between the economic definition of capital and the book valuedefinition of capital?The book value definition of capital is the value of assets minus liabilities as found on the balance sheet. This amount often is referred to as accounting net worth. The economic definition of capital is the difference between the market value of assets and the market value of liabilities.a. How does economic value accounting recognize the adverse effects of credit andinterest rate risk?The loss in value caused by credit risk and interest rate risk is borne first by the equityholders, and then by the liability holders. In market value accounting, the adjustments to equity value are made simultaneously as the losses due to these risk elements occur. Thus economic insolvency may be revealed before accounting value insolvency occurs.b. How does book value accounting recognize the adverse effects of credit and interestrate risk?Because book value accounting recognizes the value of assets and liabilities at the timethey were placed on the books or incurred by the firm, losses are not recognized until the assets are sold or regulatory requirements force the firm to make balance sheet accounting adjustments. In the case of credit risk, these adjustments usually occur after all attempts tocollect or restructure the loans have occurred. In the case of interest rate risk, the change in interest rates will not affect the recognized accounting value of the assets or the liabilities.4. A financial intermediary has the following balance sheet (in millions) with all assets andliabilities in market values:Assets Liabilities and Equity6 percent semiannual 4-year 5 percent 2-year subordinated debtTreasury notes (par value $12) $10 (par value $25) $207 percent annual 3-yearAA-rated bonds (par=$15) $159 percent annual 5-yearBBB rated bonds (par=$15) $15 Equity capital $20 Total Assets $40 Total Liabilities & Equity $40a. Under FASB Statement No. 115, what would be the effect on equity capital (net worth)if interest rates increase by 30 basis points? The T-notes are held for trading purposes,the rest are all classified as held to maturity.Only assets that are classified for trading purposes or available-for-sale are to be reported at market values. Those classified as held-to-maturity are reported at book values. Thechange in value of the T-notes for a 30 basis points change in interest rates is:$10 = PVA n=8,k=?($0.36) + PV n=8,k=?($12) k = 5.6465 x 2 = 11.293%If k =11.293% + 0.30% =11.593/2 = 5.7965%, the value of the notes will decline to:PVA n=8,k=5.7965($0.36) + PV n=3,k=5.7965($12) = $9.8992. And the change in value is $9.8992 - $10 = -0.1008 x $1,000,000 = $100,770.39The remainder of the balance sheet remains the same:6% semiannual 4-year 5% 2-year subordinated T-notes (par value $12) $9.8992 debt (par value $25) $20.0000 7% annual 3-yearAA-rated bonds (par=$15) $15.0000 Equity capital $20.0000 9% annual 5-yearBBB rated bonds (par=$15) $15.0000 Adj. To equity -0.1008 Total $39.8992$39.8992b. Under FASB Statement No. 115, how are the changes in the market value of assetsadjusted in the income statements and balance sheets of FIs?Under FASB Statement No. 115 assets held till maturity will be kept in book value. Assets available for sale and for trading purposes will always be reported in market values except by securities firms, which will have all assets and liabilities reported in market values. Also, all unrealized and realized income gains and losses will be reflected in both incomestatements and balance sheets for trading purposes. Adjustments to assets available for sale will be reflected only through equity adjustments.5. Why is the market value of equity a better measure of a bank's ability to absorb losses thanbook value of equity?The market value of equity is more relevant than book value because in the event of a bankruptcy, the liquidation (market) values will determine the FI's ability to pay the various claimants.6. State Bank has the following year-end balance sheet (in millions):Assets Liabilities and EquityCash $10 Deposits $90Loans $90 Equity $10Total Assets $100 $100The loans primarily are fixed-rate, medium-term loans, while the deposits are either short-term or variable-rate. Rising interest rates have caused the failure of a key industrialcompany, and as a result, 3 percent of the loans are considered to be uncollectable and thus have no economic value. One-third of these uncollectable loans will be charged off.Further, the increase in interest rates has caused a 5 percent decrease in the market value of the remaining loans.a. What is the impact on the balance sheet after the necessary adjustments are madeaccording to book value accounting? According to market value accounting?Under book value accounting, the only adjustment is to charge off 1 percent of the loans.Thus the loan portfolio will decrease by $0.90 and a corresponding adjustment will occur in the equity account. The new book value of equity will be $9.10. We assume no tax affects since the tax rate is not given.Under market value accounting, the 3 percent decrease in loan value will be recognized, as will the 5 percent decrease in market value of the remaining loans. Thus equity willdecrease by 0.03 x $90 + 0.05 x $90(1 – 0.03) = $7.065. The new market value of equity will be $2.935.b. What is the new market to book value ratio if State Bank has $1 million sharesoutstanding?The new market to book value ratio is $2.935/$9.10 = 0.3225.7. What are the arguments for and against the use of market value accounting for FIs? Market values produce a more accurate picture of the bank’s current financial position for both stockholders and regulators. Stockholders can more easily see the effects of changes in interest rates on the bank’s equity, and they can evaluate more clearly the liquidation value of a distressed bank. Among the arguments against market value accounting are that market values sometimes are difficult to estimate, particularly for small banks with non-traded assets. Thisargument is countered by the increasing use of asset securitization as a means to determine value of even thinly traded assets. In addition, some argue that market value accounting can produce higher volatility in the earnings of banks. A significant issue in this regard is that regulators may close a bank too quickly under the prompt corrective action requirements of FDICIA.8. How is the leverage ratio for an FI defined?The leverage ratio is the ratio of book value of core capital to the book value of total assets, where core capital is book value of equity plus qualifying cumulative perpetual preferred stock plus minority interests in equity accounts of consolidated subsidiaries.9. What is the significance of prompt corrective action as specified by the FDICIA legislation?The prompt corrective action provision requires regulators to appoint a receiver for the bank when the leverage ratio falls below 2 percent. Thus even though the bank is technically not insolvent in terms of book value of equity, the institution can be placed into receivorship.10. Identify and discuss the weaknesses of the leverage ratio as a measure of capital adequacy.First, closing a bank when the leverage ratio falls below 2 percent does not guarantee that the depositors are adequately protected. In many cases of financial distress, the actual market value of equity is significantly negative by the time the leverage ratio reaches 2 percent. Second, using total assets as the denominator does not consider the different credit and interest rate risks of the individual assets. Third, the ratio does not capture the contingent risk of the off-balance sheet activities of the bank.11. What is the Basel Agreement?The Basel Agreement identifies the risk-based capital ratios agreed upon by the member countries of the Bank for International Settlements. The ratios are to be implemented for all commercial banks under their jurisdiction. Further, most countries in the world now have accepted the guidelines of this agreement for measuring capital adequacy.12. What is the major feature in the estimation of credit risk under the Basel I capitalrequirements?The major feature of the Basel Agreement is that the capital of banks must be measured as an average of credit-risk-adjusted total assets both on and off the balance sheet.13. What is the total risk-based capital ratio?The total risk-based capital ratio divides total capital by the total of risk-adjusted assets. This ratio must be at least 8 percent for a bank to be considered adequately capitalized. Further, at least 4 percent of the risk-based assets must be supported by core capital.14. Identify the five zones of capital adequacy and explain the mandatory regulatory actionscorresponding to each zone.Zone 1: Well capitalized. The total risk-based capital ratio (RBC) ratio exceeds 10 percent. No regulatory action is required.Zone 2: Adequately capitalized. The RBC ratio exceeds 8 percent, but is less than 10 percent.Institutions may not use brokered deposits except with the permission of the FDIC. Zone 3: Undercapitalized. The RBC ratio exceeds 6 percent, but is less than 8 percent.Requires a capital restoration plan, restricts asset growth, requires approval foracquisitions, branching, and new activities, disallows the use of brokered deposits, andsuspends dividends and management fees.Zone 4: Significantly undercapitalized. The RBC ratio exceeds 2 percent, but is less than 6 percent. Same as zone 3 plus recapitalization is mandatory, places restrictions ondeposit interest rates, interaffiliate transactions, and the pay level of officers.Zone 5: Critically undercapitalized. The RBC ratio is less than 2 percent. Places the bank in receivorship within 90 days, suspends payment on subordinated debt, and restricts other activities at the discretion of the regulator.The mandatory provisions for each of the zones described above include the penalties for any of the zones prior to the specific zone.15. What are the definitional differences between Tier I and Tier II capital?Tier I capital is comprised of the most junior (subordinated) securities issued by the firm. These include equity and qualifying perpetual preferred stock. Tier II capital is senior to Tier I, but subordinated to deposits and the deposit insurer's claims. These include preferred stock with fixed maturities and long-term debt with minimum maturities over 5 years. Tier II capital often is called supplementary or secondary capital.16. What components are used in the calculation of credit risk-adjusted assets?The two components are credit risk-adjusted on-balance-sheet assets and credit risk-adjusted off-balance-sheet assets.17. Explain the process of calculating credit risk-adjusted on-balance-sheet assets.Balance sheet assets are assigned to four categories of credit risk exposure. The dollar amount of assets in each category is multiplied by an appropriate weight of 0 percent, 20 percent, 50 percent, and 100 percent respectively for the categories representing no risk to full credit risk respectively. The weighted dollar amounts of each category are added together to get the total risk-adjusted on-balance-sheet assets.a. What assets are included in the four (five) categories of credit risk exposure underBasel I (Basel II)?Category 1 includes cash, United States Treasury bills, notes and bonds, mortgage-backed securities, and Federal Reserve Bank balances. Category 2 includes U.S. agency-backed securities, municipal issued general obligation bonds, FHLMC and FNMA mortgage-backed securities, and interbank deposits. Category 3 includes other municipal revenuebonds and regular residential mortgage loans. All other commercial, consumer, and credit card loans, real assets and any other asset not included above are included in category 4.Basel II attempts to align capital requirements more closely with the banking risk of the FI.In addition to the above classifications, the Basel II categories include the following: Category 1: Loans to sovereigns with an S&P rating of AA- or better.Category 2: Loans to sovereigns with an S&P rating between A- and A+ inclusive, and loans to banks and corporates with an S&P rating of AA- or better.Category 3: Loans to sovereigns with an S&P rating between BBB- and BBB+inclusive, and loans to banks and corporates with an S&P rating betweenAA- and A+ inclusive.Category 4: Loans to sovereigns with an S&P rating of B- to BB+. Loans to bankswith an S&P rating of B- to BBB+. Loans to corporates with a creditrating of BB- to BBB+.Category 5: This is a new category introduced by Basel II. Loans to sovereigns, banks, and securities firms with an S&P credit rating below B-. Loans tocorporates with a credit rating below BB-.b. What are the appropriate risk-weights for each category?Category 1 has a risk weight of 0 percent, category 2 has a risk weight of 20 percent,category 3 has a risk weight of 50 percent, and category 4 has a risk weight of 100 percent.In addition for Basel II, category 5 has a risk weight of 150 percent.18. National Bank has the following balance sheet (in millions) and has no off-balance-sheetactivities:Assets Liabilities and EquityCash $20 Deposits $980Treasury bills $40 Subordinated debentures $40Residential mortgages $600 Common stock $40Other loans $430 Retained earnings $30 Total Assets $1,090 Total Liabilities and Equity $1,090a.The leverage ratio is ($40 + $30)/$1,090 = 0.06422 or 6.422 percent.b. What is the Tier I capital ratio?Risk-adjusted assets = $20x0.0 + $40x0.0 + $600x0.5 + $430x1.0 = $730.Tier I capital ratio = ($40 + $30)/$730 = 0.09589 or 9.59 percent.c. What is the total risk-based capital ratio?The total risk-based capital ratio = ($40 + $40 + $30)/$730 = 0.150685 or 15.07 percent.d. In what capital category would the bank be placed?The bank would be place in the well-capitalized category.19. Onshore Bank has $20 million in assets, with risk-adjusted assets of $10 million. Tier Icapital is $500,000, and Tier II capital is $400,000. How will each of the followingtransactions affect the value of the Tier I and total capital ratios? What will be the newvalue of each ratio?The current value of the Tier I ratio is 0.05 and the total ratio is 0.09.a. The bank repurchases $100,000 of common stock.Tier I decreases to 0.04, and the total ratio decreases to 0.08.b. The bank issues $2,000,000 of CDs and uses the proceeds for loans to homeowners.Tier I decreases to $500,000/$11 million = 0.0454, and the total ratio decreases to 0.0818.c. The bank receives $500,000 in deposits and invests them in T-bills.Both ratios remain unchanged.d. The bank issues $800,000 in common stock and lends it to help finance a new shoppingmall.Tier I increases to $1.3/$10.8 = 0.1204, and the total ratio increases to 0.1574.e. The bank issues $1,000,000 in nonqualifying perpetual preferred stock and purchasesgeneral obligation municipal bonds.Tier I decreases to $500,000/$10.2 million = 0.0490, and the total ratio decreases to 0.0882.f. Homeowners pay back $4,000,000 of mortgages, and the bank uses the proceeds tobuild new ATMs.Tier I decreases to $500,000/$12 million = 0.041667, and the total ratio decreases to 0.075.20. Explain the process of calculating risk-adjusted off-balance-sheet contingent guarantycontracts?The first step is to convert the off-balance-sheet items to credit equivalent amounts of an on-balance-sheet item by multiplying the notional amounts by an appropriate conversion factor as given in Table 20-14. The converted amounts then are multiplied by the appropriate risk weights as if they were on-balance-sheet items.a. What is the basis for differentiating the credit equivalent amounts of contingentguaranty contracts?The factors used in the conversion are arbitrary selections from the list of choices approved by the regulators. While a subjective relationship undoubtedly exists between the factors and the respective credit risks to the bank, no theoretical valuation models were utilized to determine the specific weights that are used.b. On what basis are the risk weights for the credit equivalent amounts differentiated?The appropriate risk weights depend on the counterparty source to off-balance-sheetactivity.21. Explain how off-balance-sheet market contracts, or derivative instruments, differ fromcontingent guaranty contracts?Off-balance-sheet contingent guaranty contracts in effect are forms of insurance that banks sell to assist customers in the financial management of the customers businesses. Bank management typically uses market contracts, or derivative instruments, to assist in the management of the bank’s assets and liability risks. For example, a loan commitment or a standby letter of credit may be provided to help a customer with another source of financing, while an over-the-counter interest rate swap likely would be used by the bank to help manage interest rate risk.a. What is counterparty credit risk?Counterparty credit risk is the risk that the other party in a contract may default on their payment obligations.b. Why do exchange-traded derivative security contracts have no capital requirements?Counterparty obligations of exchange-traded contracts are guaranteed by the exchange on which they are traded. Thus there is no counterparty risk to the bank.c. What is the difference between the potential exposure and the current exposure of over-the-counter derivative contracts?The potential exposure is the portion of the credit equivalent amount that would be at risk if the counterparty to the contract defaulted in the future. The current exposure is the cost of replacing the contract if the counterparty defaulted today.d. Why are the credit conversion factors for the potential exposure of foreign exchangecontracts greater than they are for interest rate contracts?The credit conversion factors for the potential exposure of foreign exchange contracts are greater than they are for interest rate contracts because research indicates that foreignexchange rates are more volatile than interest rates.e. Why do regulators not allow banks to benefit from positive current exposure values?Regulators fear that allowing banks to gain from a counterparty default would create risk-taking incentives that would not be in the best interests of the bank or the financial services industry.22. What is the process of netting off-balance-sheet derivative contracts under Basel I? Whatrequirement is necessary to allow a bank to calculate this exposure? How is net currentexposure defined? How does net potential exposure differ from net current exposure?A large commercial bank may have exposure from many derivative contracts at any given time, and thus it may be desirable to net or combine the various positive and negative exposures to determine one total net exposure. The Fed allows this netting or combining of exposures under the condition that the bank has a bilateral netting contract that clearly establishes a legal obligation by the counterparty to pay or receive a single net amount on the contracts. The bank must estimate the net current exposure and the net potential exposure of the positions included in the bilateral netting contract.The net current exposure is the net sum of all positive and negative replacement costs. If the value is positive, the net current exposure is equal to the amount. If the net sum is negative, the net exposure is zero.The net potential exposure is determined by calculating a weighted average of the sum of the potential exposures of each contract and the product of the sum of the potential exposures multiplied times the ratio of the net current exposure to gross current exposure (NGR). The weights are 0.4 and 0.6 respectively. Thus the equation to determine the net potential exposure is A net = (0.4 x A gross) + (0.6 x NGR x A gross).23. How does the risk-based capital measure attempt to compensate for the limitations of thestatic leverage ratio?The RBC ratio (1) more systematically accounts for credit risk differences between assets, (2) incorporates off-balance-sheet risk exposures, and (3) applies similar capital requirements across all of the major banks.24. Identify and discuss the problems in the risk-based capital approach to measuring capitaladequacy.First the risk weights may not be true representations of the correct or necessary weights, or they may not be in the correct proportion to each other. For example, does a weight of 100 percent imply twice as much risk as a weight of 50 percent? Second, the fact that the exact weighting process is know by bankers as well as regulators may give bankers an incentive to manipulate the balance sheet assets to achieve desired RBC ratios. Third, the RBC ratio does not consider the effects of portfolio risk diversification. In effect, RBC assumes the correlation between assets is one. Fourth, rating all commercial loans with the highest credit risk may cause banks to reduce lending in this area, an action that could have negative effects on the monitoring function performed by the financial services industry. Fifth, all commercial loans are given equal weight, even in the case where the otherwise credit ratings of two companies may be significantly different. Sixth, the BIS plan does not include factors to measure interest rate risk, foreign exchange risk, operating risk, etc. Finally, tax and accounting differences across different banking systems probably will preclude the BIS plan from being perfectly successful in creatinga level playing field for comparison purposes in an international or global environment.25. What is the contribution to the credit risk-adjusted asset base of the following items underthe Basel I requirements? Under Basel II requirements? Under the U.S. capital-assets ratio?Basel I Basel II U.S.a. $10 million cash reserves. $0 $0 $10 millionb. $50 million 91-day U.S. Treasury bills $0 $0 $50 millionc. $25 million cash items in the processof collection. $5 million $5 million $0d. $5 million U.K. government bonds,AAA rated $0 $0 $5 millione.$5 million Australian short-termgovernment bonds, AA-rated. $0 $1 million $5 millionf. $1 million general obligation municipalbonds $200,000 $200,000 $1 milliong. $40 million repurchase agreements(against U.S. Treasuries) $8 million $8 million $40 millionh. $500 million 1-4 family home mortgages $250 million $250 million $500 millioni. $500 million commercial and industrialloans BBB-rated $500 million $500 million $500 million j. $100,000 performance related standbyletters of credit to a AAA corporation $50,000 $10,000 $0 k. $100,000 performance related standbyletters of credit to a municipality issuinggeneral obligation bonds $10,000 $10,000 $0l. $7 million commercial letter of creditto a foreign A-rated corporation $1.4 million $700,000 $0 m. $3 million 5-year loan commitmentto an OECD government $0 $0 $0 n. $8 million banker’s acceptanceconveyed to a AA-rated corporation $1.6 million $320,000 $0 o. $17 million 3-year loan commitmentto a private agent $8.5 million $8.5 million $0 p. $17 million 3-month loan commitmentto a private agent $0 $0 $0 q. $30 million standby letter of credit toback a corporate issue of commercialpaper $30 million $30 million $0 r. $4 million 5-year interest rate swapwith no current exposure (the counterparty is a private agent) $20,000 $20,000 $0 s. $4 million 5-year interest rate swapwith no current exposure (the counterparty is a municipality) $4,000 $20,000 $0 t. $6 million 2-year currency swap with$500,000 current exposure (the counterparty is a low credit-risk entity) $400,000 $800,000 $0The bank balance sheet information below is for questions 26-29.Used for answers to 26-29 On Balance Sheet Items Category Face Value Weight Value Cash 1 $121,600 0% $0 Short term government securities (<92 days) 1 5,400 0% $0 Long term government securities (>92 days) 1 414,400 0% $0 Federal Reserve Stock 1 9,800 0% $0 Repos secured by Federal Agencies 2 159,000 20% $31,800 Claims on U.S. Depository Institutions 2 937,900 20% $187,580 Short term (<1yr) claims on foreign banks 2 1,640,000 20% $328,000 General Obligations Municipals 2 170,000 20% $34,000 Claims on or guaranteed by Federal agencies 2 26,500 20% $5,300 Municipal Revenue Bonds 3 112,900 50% $56,450 Commercial Loans, BB+ rated 4 6,645,700 100% $6,645,700 Claims on Foreign banks (>1yr.) 4 5,800 100% $5,800Basel IConversion Face Credit-Equivalent Risk-Adjusted Off Balance Sheet Items: Factor Value Amount Asset Value U.S. Government counterpartyLoan Commitments, AAA rated:< 1 year 0% $300 $0 $0 1-5 year 50% $1,140 $570 $0Standby Letters of Credit, AA rated:Performance Related 50% $200 $100 $0 Direct credit substitute 100% $100 $100 $0 U.S. depository institution counterpartyLoan Commitments, BBB+ rated:< 1 year 0% $1,000 $0 $0 > 1 year 50% $3,000 $1,500 $300 Standby Letters of Credit, AA- rated:Performance Related 50% $200 $100 $20 Direct credit substitute 100% $56,400 $56,400 $11,280 Commercial Letters of Credit, BBB+ rated 20% $400 $80 $16 State and local government counterpartyLoan Commitments, BBB- rated:>1 year 50% $100 $50 $25 Standby Letters of Credit, AAA ratedPerformance-Related 50% $135,400 $67,700 $33,850 Corporate customer counterpartyLoan Commitments, CCC rated:< 1 year 0% $2,980,000 $0 $0 >1 year 50% $3,046,278 $1,523,139 $1,523,139 Standby Letters of Credit, BBB rated:Performance Related 50% $101,543 $50,772 $50,772 Direct credit substitute 100% $485,000 $485,000 $485,000 Commercial Letters of Credit, AA- rated: 20% $78,978 $15,796 $15,796 Note Issuance Facilities 50% $20,154 $10,077 $10,077 Forward Agreements 100% $5,900 $5,900 $5,900 Category II Interest Rate Market Contracts:(Current exposure assumed to be zero.)< 1 year (Notional Amount) 0% $2,000 $0 $0 > 1-5 year (Notional Amount) 0.5% $5,000 $25 $12.5 26. What is the bank's risk-adjusted asset base under Basel I? Under Basel II?In this particular case, the risk-adjusted asset base under Basel II is greater than for Basel I.Basel I Basel II On-balance-sheet risk-adjusted asset base $7,294,630 $7,294,630 Off-balance-sheet risk-adjusted asset base $2,136,188 $2,898,957 Total risk-adjusted asset base $9,430,818 $10,193,587 Under Basel II, the on-balance-sheet risk-adjusted assets are the same as for Basel I. However, the OBS risk-adjusted assets are adjusted upward in two areas. First, the U.S. depository institution counterparty BBB+rated loan commitments > 1 year have a risk factor of 100%, which gives a risk-adjusted asset value of $1,500. Second, the corporate customer。
金融机构管理习题答案022
Chapter Twenty TwoGeographic Diversification: DomesticChapter OutlineIntroductionDomestic ExpansionsRegulatory Factors Impacting Geographic Expansion∙Insurance Companies∙Thrifts∙Commercial BanksCost and Revenue Synergies Impacting Geographic Expansion by Merger or Acquisition ∙Cost Synergies∙Revenue SynergiesOther Market- and Firm-Specific Factors Impacting Geographic Expansion Decisions The Success of Geographic Expansions∙Investor Reaction∙Postmerger PerformanceSummarySolutions for End-of-Chapter Questions and Problems: Chapter Twenty Two1.How do limitations on geographic diversification affect an FI’s profitability?Limitations on geographic diversification increase FI profitability by creating locally uncompetitive markets. FIs in these markets earn monopoly rents that are protected by limitations on geographic expansion by potential competitors. Limitations on geographic diversification reduce FI profitability by preventing the FI from exploiting any economies of scale and/or scope or revenue synergies that may be available.2.How are insurance companies able to offer services in states beyond their state ofincorporation?Insurance companies are state-regulated firms that are not prohibited from establishing subsidiaries and offices in other states. Further, the capital requirements are kept low by state regulators.3.In what way did the Garn-St Germain Act and FIRREA provide incentives for theexpansion of interstate branching?Both legislative acts provided for sound banks and thrifts to acquire failing banks and thrifts across state lines. These acquisitions could be operated either as separate subsidiaries or as branches of the acquiring institution.4.Why were unit and money center banks opposed to bank branching in the early 1900s?Smaller unit banks were afraid of losing retail business to the larger branching banks, and the larger money center banks were afraid of losing correspondent business such as check clearing and other payment services.5.In what ways did the banking industry continuously succeed in maintaining interstatebanking activities during the 50-year period beginning in the early 1930s? What legislative efforts did regulators use to respond to each foray by banks into previously prohibitedbanking and commercial activities?The McFadden Act of 1927 restricted the branching activity of nationally chartered banks to the same extent allowed for state-chartered banks that generally were disallowed from such activity. As a result, the banking industry attempted to circumvent the prohibition of interstate banking by establishing subsidiaries rather than branches under the holding company organizational form. The Douglas Amendment to the Bank Holding Company Act restricted the acquisition of banking units to the state-allowed activities. However, the law did not prohibit one-bank holding companies from acquiring nonbank subsidiaries that sold financial products. Thus the path to geographic expansion continued as banks searched for loopholes to circumvent the legislative restrictions placed on their activities.6. What is the difference between an MBHC and an OBHC?A multibank holding company is a parent organization that owns more than one bank subsidiary, and a one-bank holding company is a parent organization that owns only one bank subsidiary. Each organization may own other subsidiaries that provide services closely related to banking as allowed by regulatory authorities.7. What is an interstate banking pact? How did the three general types of interstate bankingpacts differ in their encouragement of interstate banking?An interstate banking pact is an agreement between states defining the conditions under which out-of-state banks can acquire in-state subsidiaries. A major feature of these pacts normally was the reciprocity conditions awarded each state involved. A nationwide pact allowed out-of-state banks to purchase target banks even if the acquirer’s state did not allow such activity. A nationwide reciprocal pact allowed purchase only if the acquirer’s state allowed the same activity. Third, a regional pact allowed out-of-state acquisitions within a small number of states only under conditions of reciprocity.8. What significant economic events during the 1980s provided the incentive for the Garn-StGermain Act and FIRREA to allow further expansion of interstate banking?The bankruptcy of the FSLIC and the depletion of the FDIC’s insurance reserves provided incentives to allow out-of-state acquisitions to resolve bank failures. The Garn-St Germain Act allowed banks to acquire failing thrifts across state lines. Finally, FIRREA allows for the purchase across state lines of healthy thrifts.9. What is a nonbank bank? What legislation allowed the creation of nonbank banks? Whatrole did nonbank banks play in the further development of interstate banking activities?A nonbank bank is a financial institution that did not meet the requirement of (1) making commercial loans and (2) accepting demand deposits as defined in the 1956 Bank Holding Company Act. By purchasing an out-of-state bank and divesting its commercial loans, a large bank or bank holding company could create a nonbank bank that could be used to provide retailor consumer finance banking activities. This loophole was not closed until the Competitive Equality Banking Act of 1987.10. How did the development of the nonbank bank competitive strategy further clarify themeaning of the term activities closely related to banking? In a more general sense, how has this strategy assisted the banking industry in their attempts to provide services and products outside the strictly banking environment?The Bank Holding Company Amendments of 1970 specified that nonbank activities had to be closely related to banking. As the growth rate of nonbank acquisitions increased, so too did the pressure on the Federal Reserve to expand the list of these acceptable activities. The nonbank subsidiaries eventually were allowed to provide more than 60 different types of financial products. Thus banks learned how to replicate full-scale (or nearly) banking institutions without having a legally defined bank.11. How did the provisions of the Riegle-Neal Interstate Banking and Branching EfficiencyAct of 1994 allow for full interstate banking? What are the expected profit performance effects of interstate banking? What has been the impact on the structure of the banking and financial services industry?The main feature of the Riegle-Neal Act of 1995 is the removal of barriers to interstate banking. In September 1995, bank holding companies were allowed to acquire banks in other states. In 1997, banks were allowed to convert out-of-state subsidiaries into branches of a single interstate bank. The act has resulted in significant consolidations and acquisitions, with the emergence of very large banks with branches all over the country, as currently practiced in the rest of the world. The law, as of now, does not allow the establishment of de novo branches unless allowed by the individual states. As expected, profit performance of the largest banks has been very good over the period 1995 to 1999.12. Bank mergers often produce hard to quantify benefits called X efficiencies and costs calledX inefficiencies. Give an example of each.An X efficiency is a cost saving that is difficult to measure and whose source is difficult to identify. One common example is the reduction in expenses thought to be derived from greater managerial efficiency of an acquiring bank. X inefficiencies occur when a merger results in cost incr eases that are usually attributed to management’s inability to control costs.13. What does the Berger and Humphrey study reveal about the cost savings from bankmergers? What differing results are revealed by the Rhoades study?Berger and Humphrey found that (1) the managerial efficiency of the acquirer is greater than that of the acquiree, (2) the X efficiency gains were small, and (3) the cost savings of mergers with geographic overlap were no greater than those for mergers with no geographic or market share overlap. Rhoades reviewed nine megamergers and found large cost savings. In those cases where cost efficiency gains were not realized, the problems were from integrating data processing and operating systems.14. What are the three revenue synergies that may be obtained by an FI from expandinggeographically?The three revenue synergies that an FI may obtain by expanding geographically are as follows:(a) Opportunities to increase revenue because of growing market share.(b) Different credit risk, interest rate risk and other risks that allow for diversification benefitsand the stabilization of revenues.(c) Expansion into less-than-competitive markets, which provides opportunities to reap someeconomic rents that may not be available in competitive markets.15. What is the Herfindahl-Hirschman Index? How is it calculated and interpreted?The Herfindahl-Hirschman Index (HHI) is a measure of market concentration whose value can be 0 to 10,000. The index is measured by adding the squares of the percentage market share ofthe individual firms in the market. An index value greater than 1,800 indicates a concentrated market, a value between 1,000 and 1,800 indicates a moderately concentrated market, and an unconcentrated market would have a value less than 1,000.16. City Bank currently has 60 percent market share in banking services, followed byNationsBank with 20 percent and State Bank with 20 percent.a. What is the concentration ratio as measured by the Herfindahl-Hirschman Index (HHI)?HHI = (60)2 + (20)2 + (20)2 = 4,400b. If City Bank acquires State Bank, what will be the new HHI?HHI = (80)2 + (20)2 = 6,800c. Assume the Justice department will allow mergers as long as the changes in HHI do notexceed 1,400. What is the minimum amount of assets that City Bank will have todivest after it merges with State Bank?This is a little tricky. For City Bank to complete the merger, its maximum HHI should besuch that when it disposes of part of its assets, the HHI will be X 2 + Y 2 + Z 2 = 5,800. Since Z = 20 percent, we need to solve the following: X 2 + Y 2 = 5,400; that is, 5,800 less the share of Z 2 which is 202 or 400.If the merger stands with no adjustment, then X = 80 and Y = 0. But some portion of Xmust be liquidated. Therefore we need to solve the equation (80 – Q)2 + Q 2 = 5,400 where Q is the amount of disinvestment. This requires solving the quadratic equation of the form: Q 2 + (80 - Q)2 = 5,400 which expands and simplifies to 2Q 2 – 160Q + 1,000 = 0.Using the formula: Q = 2a4ac) - b ( b -2 , we get Q = 73.1662 percent, which means City Bank has to dispose of 6.8338 percent of total banking assets. To verify, we can check the total relationship: (73.1662)2 + (6.8338)2 + (20)2 = 5,800.17. The Justice Department has been asked to review a merger request for a market with thefollowing four FI's.Bank AssetsA $12 millionB $25 millionC $102 millionD $3 milliona. What is the HHI for the existing market?Bank Assets Market ShareA $12 m 8.45 %B $25 m 17.61%C $102 m 71.83%D $3 m 2.11%100.00%The HHI = (8.45)2 + (17.61)2 + (71.83)2 + (2.11)2 = 5,545.5b. If Bank A acquires Bank D, what will be the impact on the market's level ofconcentration?Bank Assets Market ShareA $12 m 10.56%B $25 m 17.61%C $102 m 71.83%100.00%The HHI = (10.56)2 + (17.61)2 + (71.83)2 = 5,581c. If Bank C acquires Bank D, what will be the impact on the market's level ofconcentration?Bank Assets Market ShareA $12 m 8.45 %B $25 m 17.61%C $102 m 73.94%100.00%The HHI = (8.45)2 + (17.61)2 + (73.94)2 + (2.11)2 = 5,848.6d. What is likely to be the Justice Department's response to the two merger applications?The Justice Department may challenge Bank C’s application to acquire Bank D since it significantly increases market concentration (HHI = 5,848.6). On the other hand, the Justice Department would most likely approve Bank A's application since the merger causes only a small increase in market concentration (HHI = 5,581).18. The Justice Department measures market concentration using the HHI of market share.What problems does this measure have for (a) multiproduct FIs and (b) FIs with global operations?(a) The Herfindahl-Hirschman Index (HHI) for multiproduct firms is calculated either on thebasis of total assets or one particular product (say, deposits). Neither solution is entirely appropriate. Use of total assets distorts market share calculations since different FIs have different product mixes. Moreover, an HHI based on total assets will not be accurate if there are different market concentration levels in each product market.(b) Since the calculation of the Herfindahl-Hirschman Index specifies a market area, results aredependent upon the assumption of the appropriate geographic market. Global FIs willundoubtedly have activities outside of the specified market area. If these are omitted in the calculation of market shares, the FIs’ market share may be understated. However, if they are included, this may overstat e the global FIs’ market share and make the market appear to be more concentrated than it is in actuality.19. What factors, other than market concentration, does the Justice Department consider indetermining the acceptability of a merger?Other factors considered by the Justice Department include ease of entry, the nature of the product, the terms of sale of the product, market information about specific transactions, buyer market characteristics, conduct of firms in the market, and market performance.20. What are some plausible reasons for the percentage of assets of small banks decreasing andthe percentage of assets of large banks increasing while the percentage of assets ofintermediate banks has stayed constant since 1984?One reason for the decreasing share of small bank assets is the wave of mergers that has taken place over the 13 year time period. If two small banks merge, the merged bank may have assets that move it into the next higher asset category. The changes in the interstate banking laws have encouraged this wave of mergers. Finally, the growth of the national economy has been unprecedented during this time, which has caused the entire banking industry to perform well since the late 1980s.21. According to empirical studies, what factors have the highest impact on merger premiumsas defined by the ratio of a target bank’s purchase price to book value?Premiums appear to be higher in states with the most restrictive regulations and for target banks with high-quality loan portfolios. Interestingly, the growth rate of the target bank seems to have little effect on bid premiums, and profitability and capital adequacy give mixed signals of importance.22. What are the results of studies that have examined the mergers of banks, including post-merger performance? How do they differ from the studies examining mergers of nonbanks? Most studies examining mergers between banks show that both bidding and target banks realize an increase in market value. These results contrast with those of nonbanks studies where only target firms benefit by an increase in stock prices (market value). Bidding firms experience either no gains or in some cases, a decline in market value declines. In addition, studies have also shown that post-merger banks increase their efficiency through reduced operating costs, increased productivity, and enhanced asset growth.23. What are some of the important firm-specific financial factors that influence the acquisitionof an FI?Some of the important factors are the leverage ratio, the amount of loss reserves, the loan to deposit ratio, and the amount of nonperforming loans.24. How has the performance of merged banks compared to that of bank industry averages?Cornett and Tehranian found that merged banks tend to outperform the industry with significant improvements in the ability to attract loans and deposits, increased employee productivity, and enhanced asset growth. Spong and Shoenhair found that acquired banks maintain or increase profits and become more active lenders. Boyd and Graham found that banks formed from the merger of small banks also outperformed the industry.25. What are some of the benefits for banks engaging in geographic expansion?The benefits to geographic diversification are:(a) Economies of scale: If there are efficiency gains to growth, geographic diversification canreduce costs and increase profitability.(b) Risk reduction: Overall risk reduction via diversification.(c) Survival: As nonbank financial firms have increasingly eroded bank s’ market share, banks’campaign to expand geographically can be viewed as a competitive response. That is, as global FIs dominate the financial environment, larger institutions with presence in many regions may better position the FI to compete.(d) Managerial welfare maximization: Empirical evidence suggests that larger institutions offermore lucrative compensation packages with greater amounts of perquisites for managers.Growth via geographic diversification may therefore be in the interests of managers, but not in the interests of stockholders unless the activities increase firm value.。
风险管理与金融机构第二版课后习题答案
第七章7.1大约有50亿期限超过一年的贷款是由期限小于一年的存款所支撑,换句话说,大约有50亿期限小于一年期限的负债(存款)是用于支撑期限大于一年的资产(贷款)。
当利率增长时,存款利息增加,但贷款利息却没有增加,净利息溢差收入受到压力。
7.2 S&Ls的长期固定利息的房屋贷款是由短期存款支持因此在利率迅速增长时,S&Ls会有所损失。
7.3这是利率不匹配为100亿美元,在今后3年,银行的净利息收入会每年下降1亿美元。
7.4因为如果长期利率仅仅反映了预期短期利率,我们会看到长期利率低于短期利率的情况和长期利率高于短期利率的情况一样频繁(因为投资人假设利率未来上涨和下降的概率相同),流动性偏好理论认为长期利率高于将来预期短期利率,这意味着长期利率在多数时间会高于短期利率,当市场认为利率会下跌时,长期利率低于短期利率。
7.5金融机构一般是将LIBOR互换利率曲线作为无风险利率,市场通常认为国债利率低于无风险利率,这是因为:(1)金融机构为满足一定的监管要求,必须买入一定的长期及短期国债,而这一需求造成国债收益率的降低;(2)通持与其他类似的低风险的投资相比,持有国债所需要的资本金要少;(3)在美国,对于国债的税务规定要比其他定息投资更为有利,投资政府国债而获益无需缴纳州税。
7.6久期信息用以描述了收益率小的平行移动对于债券价格的影响,交易组合价格减小的百分比等于组合久期乘以小的平行移动的数量;局限性是这一方法只适应于小的平行移动。
7.7(a)令该5年期债券的票面价格为m=100美元,根据债券价格公式,p=*e-y*ti + m* e-y*t得到,p1=86.80美元。
(b)根据债券久期公式,D=- *=-(8*e-0.11+16*e-0.22+24*e-0.33+32*e-0.44+40*e-0.55)-5*100*e-0.55=-369.42,D=-*(-369.42)=4.256得到,债券久期D=4.256。
金融机构管理 课后习题答案
Chapter OneWhy Are Financial Intermediaries Special?Chapter OutlineIntroductionFinancial Intermediaries’ Specialness•Information Costs•Liquidity and Price Risk•Other Special ServicesOther Aspects of Specialness•The Transmission of Monetary Policy•Credit Allocation•Intergenerational Wealth Transfers or Time Intermediation •Payment Services•Denomination IntermediationSpecialness and Regulation•Safety and Soundness Regulation•Monetary Policy Regulation•Credit Allocation Regulation•Consumer Protection Regulation•Investor Protection Regulation•Entry RegulationThe Changing Dynamics of Specialness•Trends in the United States•Future Trends•Global IssuesSummarySolutions for End-of-Chapter Questions and Problems: Chapter One1. Identify and briefly explain the five risks common to financial institutions.Default or credit risk of assets, interest rate risk caused by maturity mismatches between assets and liabilities, liability withdrawal or liquidity risk, underwriting risk, and operating cost risks.2. Explain how economic transactions between household savers of funds and corporate users of funds would occur in a world without financial intermediaries (FIs).In a world without FIs the users of corporate funds in the economy would have to approach directly the household savers of funds in order to satisfy their borrowing needs. This process would be extremely costly because of the up-front information costs faced by potential lenders. Cost inefficiencies would arise with the identification of potential borrowers, the pooling of small savings into loans of sufficient size to finance corporate activities, and the assessment of risk and investment opportunities. Moreover, lenders would have to monitor the activities of borrowers over each loan's life span. The net result would be an imperfect allocation of resources in an economy.3. Identify and explain three economic disincentives that probably would dampen the flow offunds between household savers of funds and corporate users of funds in an economic world without financial intermediaries.Investors generally are averse to purchasing securities directly because of (a) monitoring costs, (b) liquidity costs, and (c) price risk. Monitoring the activities of borrowers requires extensive time, expense, and expertise. As a result, households would prefer to leave this activity to others, and by definition, the resulting lack of monitoring would increase the riskiness of investing in corporate debt and equity markets. The long-term nature of corporate equity and debt would likely eliminate at least a portion of those households willing to lend money, as the preference of many for near-cash liquidity would dominate the extra returns which may be available. Third, the price risk of transactions on the secondary markets would increase without the information flows and services generated by high volume.4. Identify and explain the two functions in which FIs may specialize that enable the smoothflow of funds from household savers to corporate users.FIs serve as conduits between users and savers of funds by providing a brokerage function and by engaging in the asset transformation function. The brokerage function can benefit both savers and users of funds and can vary according to the firm. FIs may provide only transaction services, such as discount brokerages, or they also may offer advisory services which help reduce information costs, such as full-line firms like Merrill Lynch. The asset transformation function is accomplished by issuing their own securities, such as deposits and insurance policies that are more attractive to household savers, and using the proceeds to purchase the primary securities ofcorporations. Thus, FIs take on the costs associated with the purchase of securities.5. In what sense are the financial claims of FIs considered secondary securities, while thefinancial claims of commercial corporations are considered primary securities? How does the transformation process, or intermediation, reduce the risk, or economic disincentives, to the savers?The funds raised by the financial claims issued by commercial corporations are used to invest in real assets. These financial claims, which are considered primary securities, are purchased by FIs whose financial claims therefore are considered secondary securities. Savers who invest in the financial claims of FIs are indirectly investing in the primary securities of commercial corporations. However, the information gathering and evaluation expenses, monitoring expenses, liquidity costs, and price risk of placing the investments directly with the commercial corporation are reduced because of the efficiencies of the FI.6. Explain how financial institutions act as delegated monitors. What secondary benefitsoften accrue to the entire financial system because of this monitoring process?By putting excess funds into financial institutions, individual investors give to the FIs the responsibility of deciding who should receive the money and of ensuring that the money is utilized properly by the borrower. In this sense the depositors have delegated the FI to act as a monitor on their behalf. The FI can collect information more efficiently than individual investors. Further, the FI can utilize this information to create new products, such as commercial loans, that continually update the information pool. This more frequent monitoring process sends important informational signals to other participants in the market, a process that reduces information imperfection and asymmetry between the ultimate sources and users of funds in the economy.7. What are five general areas of FI specialness that are caused by providing various servicesto sectors of the economy?First, FIs collect and process information more efficiently than individual savers. Second, FIs provide secondary claims to household savers which often have better liquidity characteristics than primary securities such as equities and bonds. Third, by diversifying the asset base FIs provide secondary securities with lower price-risk conditions than primary securities. Fourth, FIs provide economies of scale in transaction costs because assets are purchased in larger amounts. Finally, FIs provide maturity intermediation to the economy which allows the introduction of additional types of investment contracts, such as mortgage loans, that are financed with short-term deposits.8. How do FIs solve the information and related agency costs when household savers investdirectly in securities issued by corporations? What are agency costs?Agency costs occur when owners or managers take actions that are not in the best interests of the equity investor or lender. These costs typically result from the failure to adequately monitor theactivities of the borrower. If no other lender performs these tasks, the lender is subject to agency costs as the firm may not satisfy the covenants in the lending agreement. Because the FI invests the funds of many small savers, the FI has a greater incentive to collect information and monitor the activities of the borrower.9. What often is the benefit to the lenders, borrowers, and financial markets in general of thesolution to the information problem provided by the large financial institutions?One benefit to the solution process is the development of new secondary securities that allow even further improvements in the monitoring process. An example is the bank loan that is renewed more quickly than long-term debt. The renewal process updates the financial and operating information of the firm more frequently, thereby reducing the need for restrictive bond covenants that may be difficult and costly to implement.10. How do FIs alleviate the problem of liquidity risk faced by investors who wish to invest inthe securities of corporations?Liquidity risk occurs when savers are not able to sell their securities on demand. Commercial banks, for example, offer deposits that can be withdrawn at any time. Yet the banks make long-term loans or invest in illiquid assets because they are able to diversify their portfolios and better monitor the performance of firms that have borrowed or issued securities. Thus individual investors are able to realize the benefits of investing in primary assets without accepting the liquidity risk of direct investment.11. How do financial institutions help individual savers diversify their portfolio risks? Whichtype of financial institution is best able to achieve this goal?Money placed in any financial institution will result in a claim on a more diversified portfolio. Banks lend money to many different types of corporate, consumer, and government customers, and insurance companies have investments in many different types of assets. Investment in a mutual fund may generate the greatest diversification benefit because of the fund’s investment in a wide array of stocks and fixed income securities.12. How can financial institutions invest in high-risk assets with funding provided by low-riskliabilities from savers?Diversification of risk occurs with investments in assets that are not perfectly positively correlated. One result of extensive diversification is that the average risk of the asset base of an FI will be less than the average risk of the individual assets in which it has invested. Thus individual investors realize some of the returns of high-risk assets without accepting the corresponding risk characteristics.13. How can individual savers use financial institutions to reduce the transaction costs ofinvesting in financial assets?By pooling the assets of many small investors, FIs can gain economies of scale in transaction costs. This benefit occurs whether the FI is lending to a corporate or retail customer, or purchasing assets in the money and capital markets. In either case, operating activities that are designed to deal in large volumes typically are more efficient than those activities designed for small volumes.14. What is maturity intermediation? What are some of the ways in which the risks ofmaturity intermediation are managed by financial intermediaries?If net borrowers and net lenders have different optimal time horizons, FIs can service both sectors by matching their asset and liability maturities through on- and off-balance sheet hedging activities and flexible access to the financial markets. For example, the FI can offer the relatively short-term liabilities desired by households and also satisfy the demand for long-term loans such as home mortgages. By investing in a portfolio of long-and short-term assets that have variable- and fixed-rate components, the FI can reduce maturity risk exposure by utilizing liabilities that have similar variable- and fixed-rate characteristics, or by using futures, options, swaps, and other derivative products.15. What are five areas of institution-specific FI specialness, and which types of institutions aremost likely to be the service providers?First, commercial banks and other depository institutions are key players for the transmission of monetary policy from the central bank to the rest of the economy. Second, specific FIs often are identified as the major source of finance for certain sectors of the economy. For example, S&Ls and savings banks traditionally serve the credit needs of the residential real estate market. Third, life insurance and pension funds commonly are encouraged to provide mechanisms to transfer wealth across generations. Fourth, depository institutions efficiently provide payment services to benefit the economy. Finally, mutual funds provide denomination intermediation by allowing small investors to purchase pieces of assets with large minimum sizes such as negotiable CDs and commercial paper issues.16. How do depository institutions such as commercial banks assist in the implementation andtransmission of monetary policy?The Federal Reserve Board can involve directly the commercial banks in the implementation of monetary policy through changes in the reserve requirements and the discount rate. The open market sale and purchase of Treasury securities by the Fed involves the banks in the implementation of monetary policy in a less direct manner.17. What is meant by credit allocation regulation? What social benefit is this type ofregulation intended to provide?Credit allocation regulation refers to the requirement faced by FIs to lend to certain sectors of the economy, which are considered to be socially important. These may include housing and farming. Presumably the provision of credit to make houses more affordable or farms moreviable leads to a more stable and productive society.18. Which intermediaries best fulfill the intergenerational wealth transfer function? What isthis wealth transfer process?Life insurance and pension funds often receive special taxation relief and other subsidies to assist in the transfer of wealth from one generation to another. In effect, the wealth transfer process allows the accumulation of wealth by one generation to be transferred directly to one or more younger generations by establishing life insurance policies and trust provisions in pension plans. Often this wealth transfer process avoids the full marginal tax treatment that a direct payment would incur.19. What are two of the most important payment services provided by financial institutions?To what extent do these services efficiently provide benefits to the economy?The two most important payment services are check clearing and wire transfer services. Any breakdown in these systems would produce gridlock in the payment system with resulting harmful effects to the economy at both the domestic and potentially the international level.20. What is denomination intermediation? How do FIs assist in this process?Denomination intermediation is the process whereby small investors are able to purchase pieces of assets that normally are sold only in large denominations. Individual savers often invest small amounts in mutual funds. The mutual funds pool these small amounts and purchase negotiable CDs which can only be sold in minimum increments of $100,000, but which often are sold in million dollar packages. Similarly, commercial paper often is sold only in minimum amounts of $250,000. Therefore small investors can benefit in the returns and low risk which these assets typically offer.21. What is negative externality? In what ways do the existence of negative externalities justifythe extra regulatory attention received by financial institutions?A negative externality refers to the action by one party that has an adverse affect on some third party who is not part of the original transaction. For example, in an industrial setting, smoke from a factory that lowers surrounding property values may be viewed as a negative externality. For financial institutions, one concern is the contagion effect that can arise when the failure of one FI can cast doubt on the solvency of other institutions in that industry.22. If financial markets operated perfectly and costlessly, would there be a need forfinancial intermediaries?To a certain extent, financial intermediation exists because of financial market imperfections. If information is available costlessly to all participants, savers would not need intermediaries to act as either their brokers or their delegated monitors. However, if there are social benefits tointermediation, such as the transmission of monetary policy or credit allocation, then FIs would exist even in the absence of financial market imperfections.23. What is mortgage redlining?Mortgage redlining occurs when a lender specifically defines a geographic area in which it refuses to make any loans. The term arose because of the area often was outlined on a map with a red pencil.24. Why are FIs among the most regulated sectors in the world? When is netregulatory burden positive?FIs are required to enhance the efficient operation of the economy. Successful financial intermediaries provide sources of financing that fund economic growth opportunity that ultimately raises the overall level of economic activity. Moreover, successful financial intermediaries provide transaction services to the economy that facilitate trade and wealth accumulation.Conversely, distressed FIs create negative externalities for the entire economy. That is, the adverse impact of an FI failure is greater than just the loss to shareholders and other private claimants on the FI's assets. For example, the local market suffers if an FI fails and other FIs also may be thrown into financial distress by a contagion effect. Therefore, since some of the costs of the failure of an FI are generally borne by society at large, the government intervenes in the management of these institutions to protect society's interests. This intervention takes the form of regulation.However, the need for regulation to minimize social costs may impose private costs to the firms that would not exist without regulation. This additional private cost is defined as a net regulatory burden. Examples include the cost of holding excess capital and/or excess reserves and the extra costs of providing information. Although they may be socially beneficial, these costs add to private operating costs. To the extent that these additional costs help to avoid negative externalities and to ensure the smooth and efficient operation of the economy, the net regulatory burden is positive.25. What forms of protection and regulation do regulators of FIs impose to ensuretheir safety and soundness?Regulators have issued several guidelines to insure the safety and soundness of FIs:a. FIs are required to diversify their assets. For example, banks cannot lend morethan 10 percent of their equity to a single borrower.b. FIs are required to maintain minimum amounts of capital to cushion anyunexpected losses. In the case of banks, the Basle standards require a minimum core and supplementary capital of 8 percent of their risk-adjusted assets.c. Regulators have set up guaranty funds such as BIF for commercial banks, SIPCfor securities firms, and state guaranty funds for insurance firms to protectindividual investors.d. Regulators also engage in periodic monitoring and surveillance, such as on-siteexaminations, and request periodic information from the FIs.26. In the transmission of monetary policy, what is the difference between insidemoney and outside money? How does the Federal Reserve Board try to control the amount of inside money? How can this regulatory position create a cost for the depository financial institutions?Outside money is that part of the money supply directly produced and controlled by the Fed, for example, coins and currency. Inside money refers to bank deposits not directly controlled by the Fed. The Fed can influence this amount of money by reserve requirement and discount rate policies. In cases where the level of required reserves exceeds the level considered optimal by the FI, the inability to use the excess reserves to generate revenue may be considered a tax or cost of providing intermediation.27. What are some examples of credit allocation regulation? How can this attemptto create social benefits create costs to the private institution?The qualified thrift lender test (QTL) requires thrifts to hold 65 percent of their assets in residential mortgage-related assets to retain the thrift charter. Some states have enacted usury laws that place maximum restrictions on the interest rates that can be charged on mortgages and/or consumer loans. These types of restrictions often create additional operating costs to the FI and almost certainly reduce the amount of profit that could be realized without such regulation.28. What is the purpose of the Home Mortgage Disclosure Act? What are thesocial benefits desired from the legislation? How does the implementation of this legislation create a net regulatory burden on financial institutions?The HMDA was passed by Congress to prevent discrimination in mortgage lending. The social benefit is to ensure that everyone who qualifies financially is provided the opportunity to purchase a house should they so desire. The regulatory burden has been to require a written statement indicating the reasons why credit was or was not granted. Since 1990, the federal regulators have examined millions of mortgage transactions from more than 7,700 institutions each calendar quarter.29. What legislation has been passed specifically to protect investors who use investment banksdirectly or indirectly to purchase securities? Give some examples of the types of abuses for which protection is provided.The Securities Acts of 1933 and 1934 and the Investment Company Act of 1940 were passed byCongress to protect investors against possible abuses such as insider trading, lack of disclosure, outright malfeasance, and breach of fiduciary responsibilities.30. How do regulations regarding barriers to entry and the scope of permitted activities affectthe charter value of financial institutions?The profitability of existing firms will be increased as the direct and indirect costs of establishing competition increase. Direct costs include the actual physical and financial costs of establishing a business. In the case of FIs, the financial costs include raising the necessary minimum capital to receive a charter. Indirect costs include permission from regulatory authorities to receive a charter. Again in the case of FIs this cost involves acceptable leadership to the regulators. As these barriers to entry are stronger, the charter value for existing firms will be higher.31. What reasons have been given for the growth of investment companies at the expense of“traditional” banks and insurance companies?The recent growth of investment companies can be attributed to two major factors: a. Investors have demanded increased access to direct securities markets.Investment companies and pension funds allow investors to take positions indirect securities markets while still obtaining the risk diversification, monitoring, and transactional efficiency benefits of financial intermediation. Some experts would argue that this growth is the result of increased sophistication on the part of investors; others would argue that the ability to use these markets has caused the increased investor awareness. The growth in these assets is inarguable.b. Recent episodes of financial distress in both the banking and insuranceindustries have led to an increase in regulation and governmental oversight,thereby increasing the net regulatory burden of “traditional” companies. Assuch, the costs of intermediation have increased, which increases the cost ofproviding services to customers.32. What are some of the methods which banking organizations have employed to reduce thenet regulatory burden? What has been the effect on profitability?Through regulatory changes, FIs have begun changing the mix of business products offered to individual users and providers of funds. For example, banks have acquired mutual funds, have expanded their asset and pension fund management businesses, and have increased the security underwriting activities. In addition, legislation that allows banks to establish branches anywhere in the United States has caused a wave of mergers. As the size of banks has grown, an expansion of possible product offerings has created the potential for lower service costs. Finally, the emphasis in recent years has been on products that generate increases in fee income, and the entire banking industry has benefited from increased profitability in recent years.33. What characteristics of financial products are necessary for financial markets to becomeefficient alternatives to financial intermediaries? Can you give some examples of the commoditization of products which were previously the sole property of financial institutions?Financial markets can replace FIs in the delivery of products that (1) have standardized terms, (2) serve a large number of customers, and (3) are sufficiently understood for investors to be comfortable in assessing their prices. When these three characteristics are met, the products often can be treated as commodities. One example of this process is the migration of over-the-counter options to the publicly traded option markets as trading volume grows and trading terms become standardized.34. In what way has Regulation 144A of the Securities and Exchange Commission provided anincentive to the process of financial disintermediation?Changing technology and a reduction in information costs are rapidly changing the nature of financial transactions, enabling savers to access issuers of securities directly. Section 144A of the SEC is a recent regulatory change that will facilitate the process of disintermediation. The private placement of bonds and equities directly by the issuing firm is an example of a product that historically has been the domain of investment bankers. Although historically private placement assets had restrictions against trading, regulators have given permission for these assets to trade among large investors who have assets of more than $100 million. As the market grows, this minimum asset size restriction may be reduced.Chapter TwoThe Financial Services Industry: Depository InstitutionsChapter OutlineIntroductionCommercial Banks•Size, Structure, and Composition of the Industry•Balance Sheet and Recent Trends•Other Fee-Generating Activities•Regulation•Industry PerformanceSavings Institutions•Savings Associations (SAs)•Savings Banks•Recent Performance of Savings Associations and Savings BanksCredit Unions•Size, Structure, and Composition of the Industry and Recent Trends•Balance Sheets•Regulation•Industry PerformanceGlobal Issues: Japan, China, and GermanySummaryAppendix 2A: Financial Statement Analysis Using a Return on Equity (ROE) FrameworkAppendix 2B: Depository Institutions and Their RegulatorsAppendix 3B: Technology in Commercial BankingSolutions for End-of-Chapter Questions and Problems: Chapter Two1.What are the differences between community banks, regional banks, andmoney-center banks? Contrast the business activities, location, and markets of each of these bank groups.Community banks typically have assets under $1 billion and serve consumer and small business customers in local markets. In 2003, 94.5 percent of the banks in the United States were classified as community banks. However, these banks held only 14.6 percent of the assets of the banking industry. In comparison with regional and money-center banks, community banks typically hold a larger percentage of assets in consumer and real estate loans and a smaller percentage of assets in commercial and industrial loans. These banks also rely more heavily on local deposits and less heavily on borrowed and international funds.Regional banks range in size from several billion dollars to several hundred billion dollars in assets. The banks normally are headquartered in larger regional cities and often have offices and branches in locations throughout large portions of the United States. Although these banks provide lending products to large corporate customers, many of the regional banks have developed sophisticated electronic and branching services to consumer and residential customers. Regional banks utilize retail deposit bases for funding, but also develop relationships with large corporate customers and international money centers.Money center banks rely heavily on nondeposit or borrowed sources of funds. Some of these banks have no retail branch systems, and most regional banks are major participants in foreign currency markets. These banks compete with the larger regional banks for large commercial loans and with international banks for international commercial loans. Most money center banks have headquarters in New York City.e the data in Table 2-4 for the banks in the two asset size groups (a) $100million-$1 billion and (b) over $10 billion to answer the following questions.a. Why have the ratios for ROA and ROE tended to increase for both groupsover the 1990-2003 period? Identify and discuss the primary variables thataffect ROA and ROE as they relate to these two size groups.The primary reason for the improvements in ROA and ROE in the late 1990smay be related to the continued strength of the macroeconomy that allowedbanks to operate with a reduced regard for bad debts, or loan charge-offproblems. In addition, the continued low interest rate environment hasprovided relatively low-cost sources of funds, and a shift toward growth in fee income has provided additional sources of revenue in many product lines.。
金融机构管理习题答案024
Chapter Twenty FourFutures and ForwardsChapter Outline IntroductionForward and Futures Contracts•Spot Contracts•Forward Contracts•Futures ContractsForward Contracts and Hedging Interest Rate Risk Hedging Interest Rate Risk with Futures Contracts •Microhedging•Macrohedging•Routine Hedging versus Selective Hedging•Macrohedging with Futures•The Problem of Basis RiskHedging Foreign Exchange Risk•Forwards•Futures•Estimating the Hedge RatioHedging Credit Risk with Futures and Forwards •Credit Forward Contracts and Credit Risk Hedging•Futures Contracts and Catastrophe Risk•Futures and Forward Policies of Regulators SummarySolutions for End-of-Chapter Questions and Problems: Chapter Twenty Four1.What are derivative contracts? What is the value of derivative contracts to the managers ofFIs? Which type of derivative contracts had the highest volume among all U.S. banks as of September 2003?Derivatives are financial assets whose value is determined by the value of some underlying asset. As such, derivative contracts are instruments that provide the opportunity to take some action at a later date based on an agreement to do so at the current time. Although the contracts differ, the price, timing, and extent of the later actions usually are agreed upon at the time the contracts are arranged. Normally the contracts depend on the activity of some underlying asset.The contracts have value to the managers of FIs because of their aid in managing the various types of risk prevalent in the institutions. As of September 2003 the largest category of derivatives in use by commercial banks was swaps, which was followed by options, and then by futures and forwards.2.What has been the regulatory result of some of the misuses by FIs of derivative products?In many cases the accounting requirements for the use of derivative contracts have been tightened. Specifically, FASB now requires that all derivatives be marked to market and that all gains and losses immediately be identified on financial statements.3.What are some of the major differences between futures and forward contracts? How dothese contracts differ from a spot contract?A spot contract is an exchange of cash, or immediate payment, for financial assets, or any other type of assets, at the time the agreement to transact business is made, i.e., at time 0. Futures and forward contracts both are agreements between a buyer and a seller at time 0 to exchange the asset for cash (or some other type of payment) at a later time in the future. The specific grade and quantity of asset is identified, as is the specific price and time of transaction.One of the differences between futures and forward contracts is the uniqueness of forward contracts because they are negotiated between two parties. On the other hand, futures contracts are standardized because they are offered by and traded on an exchange. Futures contracts are marked to market daily by the exchange, and the exchange guarantees the performance of the contract to both parties. Thus the risk of default by the either party is minimized from the viewpoint of the other party. No such guarantee exists for a forward contract. Finally, delivery of the asset almost always occurs for forward contracts, but seldom occurs for futures contracts. Instead, an offsetting or reverse transaction occurs through the exchange prior to the maturity of the contract.4.What is a naive hedge? How does a naïve hedge protect the FI from risk?A hedge involves protecting the price of or return on an asset from adverse changes in price or return in the market. A naive hedge usually involves the use of a derivative instrument that hasthe same underlying asset as the asset being hedged. Thus if a change in the price of the cash asset results in a gain, the same change in market value will cause the derivative instrument to generate a loss that will offset the gain in the cash asset.5.An FI holds a 15-year, par value, $10,000,000 bond that is priced at 104 with a yield tomaturity of 7 percent. The bond has a duration of eight years, and the FI plans to sell it after two months. The FI’s market analyst predicts that interest rates will be 8 percent at the time of the desired sale. Because most other analysts are predicting no change in rates, two-month forward contracts for 15-year bonds are available at 104. The FI would like to hedge against the expected change in interest rates with an appropriate position in aforward contract. What will be this position? Show that if rates rise 1 percent as forecast, the hedge will protect the FI from loss.The expected change in the spot position is –8 x $10,400,000 x (1/1.07) = -$777,570. This would mean a price change from 104 to 96.2243 per $100 face value of bonds. By entering into a two-month forward contract to sell $10,000,000 of 15-year bonds at 104, the FI will have hedged its spot position. If rates rise by 1 percent, and the bond value falls by $777,570, the FI can close out its forward position by receiving 104 for bonds that are now worth 96.2243 per $100 face value. The profit on the forward position will offset the loss in the spot market.The actual transaction to close the forward contract may involve buying the bonds in the market at 96.2243 and selling the bonds to the counterparty at 104 under the terms of the forward contract. Note that if a futures contract were used, closing the hedge position would involve buying a futures contract through the exchange with the same maturity date and dollar amount as the initial opening hedge contract.6.Contrast the position of being short with that of being long in futures contracts.To be short in futures contracts means that you have agreed to sell the underlying asset at a future time, while being long means that you have agreed to buy the asset at a later time. In each case, the price and the time of the future transaction are agreed upon when the contracts are initially negotiated.7. Suppose an FI purchases a Treasury bond futures contract at 95.a. What is the FI’s obligation at the time the futures contra ct was purchased?You are obligated to take delivery of a $100,000 face value 20-year Treasury bond at aprice of $95,000 at some predetermined later date.b. If an FI purchases this contract, in what kind of hedge is it engaged?This is a long hedge undertaken to protect the FI from falling interest rates.c. Assume that the Treasury bond futures price falls to 94. What is the loss or gain?The FI will lose $1,000 since the FI must pay $95,000 for bonds that have a market value of only $94,000.d. Assume that the Treasury bond futures price rises to 97. Mark-to-market the position.In this case the FI gains $2,000 since the FI pays only $95,000 for bonds that have a market value of $97,000.8. Long Bank has assets that consist mostly of 30-year mortgages and liabilities that are short-term time and demand deposits. Will an interest rate futures contract the bank buys add to or subtract from the bank’s risk?The purchase of an interest rate futures contract will add to the risk of the bank. If rates increase in the market, the value of the bank’s assets will decrease more than the value of the liabilities. In addition, the value of the futures contract also will decrease. Thus the bank will suffer decreases in value both on and off the balance sheet. If the bank had sold the futures contract, the increase in rates would have allowed the futures position to reflect a gain that would offset (at least partially) the losses in value on the balance sheet.9.In each of the following cases, indicate whether it would be appropriate for an FI to buy orsell a forward contract to hedge the appropriate risk.a. A commercial bank plans to issue CDs in three months.The bank should sell a forward contract to protect against an increase in interest rates.b. An insurance company plans to buy bonds in two months.The insurance company should buy a forward contract to protect against a decrease ininterest rates.c. A thrift is going to sell Treasury securities next month.The thrift should sell a forward contract to protect against an increase in interest rates.d. A U.S. bank lends to a French company; the loan is payable in francs.The bank should sell francs forward to protect against a decrease in the value of the franc, or an increase in the value of the dollar.e. A finance company has assets with a duration of six years and liabilities with a durationof 13 years.The finance company should buy a forward contract to protect against decreasing interest rates that would cause the value of liabilities to increase more than the value of assets, thus causing a decrease in equity value.10. The duration of a 20-year, 8 percent coupon Treasury bond selling at par is 10.292 years.The bond’s interest is paid semiannually, and the bond qu alifies for delivery against the Treasury bond futures contract.a. What is the modified duration of this bond?The modified duration is 10.292/1.04 = 9.896 years.b. What is the impact on the Treasury bond price if market interest rates increase 50 bps?∆P = -MD(∆R)$100,000 = -9.896 x 0.005 x $100,000 = -$4,948.08.c. If you sold a Treasury bond futures contract at 95 and interest rates rose 50 basis points,what would be the change in the value of your futures position?=P-9.(0.005)9P∆∆==-MDR(-000700.70,,4$958)6$d. If you purchased the bond at par and sold the futures contract, what would be the netvalue of your hedge after the increase in interest rates?Decrease in market value of the bond purchase -$4,948.08Gain in value from the sale of futures contract $4,700.70Net gain or loss from hedge -$247.3811. What are the differences between a microhedge and a macrohedge for a FI? Why is itgenerally more efficient for FIs to employ a macrohedge than a series of microhedges?A microhedge uses a derivative contract such as a forward or futures contract to hedge the risk exposure of a specific transaction, while a macrohedge is an attempt to hedge the duration gap of the entire balance sheet. FIs that attempt to manage their risk exposure by hedging each balance sheet position will find that hedging is excessively costly, because the use of a series of microhedges ignores the FI’s internal hedges that are already on the balance sheet. That is, if a long-term fixed-rate asset position is exposed to interest rate increases, there may be a matching long-term fixed-rate liability position that also is exposed to interest rate decreases. Putting on two microhedges to reduce the risk exposures of each of these positions fails to recognize that the FI has already hedged much of its risk by taking matched balance sheet positions. The efficiency of the macrohedge is that it focuses only on those mismatched positions that are candidates for off-balance-sheet hedging activities.12. What are the reasons an FI may choose to hedge selectively its portfolio?Selective hedging involves an explicit attempt to not minimize the risk on the balance sheet. An FI may choose to hedge selectively in an attempt to improve profit performance by accepting some risk on the balance she et, or to arbitrage profits between a spot asset’s price movements and the price movements of the futures price. This latter situation often occurs because of changes in basis caused in part by cross-hedging.13. Hedge Row Bank has the following balance sheet (in millions):Assets $150 Liabilities $135Equity $15Total $150 Total $150The duration of the assets is six years, and the duration of the liabilities is four years. The bank is expecting interest rates to fall from 10 percent to 9 percent over the next year.a. What is the duration gap for Hedge Row Bank?DGAP = D A– k x D L = 6 – (0.9)(4) = 6 – 3.6 = 2.4 yearsb. What is the expected change in net worth for Hedge Row Bank if the forecast isaccurate?Expected ∆E = -DGAP[∆R/(1 + R)]A = -2.4(-0.01/1.10)$150 = $3.272.c. What will be the effect on net worth if interest rates increase 100 basis points?Expected ∆E = -DGAP[∆R/(1 + R)]A = -2.4(0.01/1.10)$150 = -$3.272.d. If the existing interest rate on the liabilities is 6 percent, what will be the effect on networth of a 1 percent increase in interest rates?Solving for the impact on the change in equity under this assumption involves finding the impact of the change in interest rates on each side of the balance sheet, and thendetermining the difference in these values. The analysis is based on the original equation:Expected ∆E = ∆A - ∆L∆A = -D A[∆R A/(1 + R A)]A = -6[0.01/1.10]$150 = -$8.1818and ∆L = -D L[∆R L/(1 + R L)]L = -4[0.01/1.06]$135 = -$5.0943Therefore, ∆E = ∆A - ∆L = -$8.1818 – (-$5.0943) = - $3.0875.14. For a given change in interest rates, why is the sensitivity of the price of a Treasury bondfutures contract greater than the sensitivity of the price of a Treasury bill futures contract?The price sensitivity of a futures contract depends on the duration of the asset underlying the contract. In the case of a T-bill contract, the duration is 0.25 years. In the case of a T-bond contract, the duration is much longer.15. What is the meaning of the Treasury bond futures price quote 101-13?A bid-ask quote of 101 - 13 = $101 13/32 per $100 face value. Since the Treasury bond futures contracts are for $100,000 face value, the quoted price is $101,406.25.16. What is meant by fully hedging the balance sheet of an FI?Fully hedging the balance sheet involves using a sufficient number of futures contracts so that any gain (or loss) of net worth on the balance sheet is just offset by the loss (or gain) from off-balance-sheet use of futures for given changes in interest rates.17. Tree Row Bank has assets of $150 million, liabilities of $135 million, and equity of $15million. The asset duration is six years, and the duration of the liabilities is four years. Market interest rates are 10 percent. Tree Row Bank wishes to hedge the balance sheet with Treasury bond futures contracts, which currently have a price quote of $95 per $100 face value for the benchmark 20-year, 8 percent coupon bond underlying the contract.a. Should the bank go short or long on the futures contracts to establish the correctmacrohedge?The bank should sell futures contracts since an increase in interest rates would cause thevalue of the equity and the futures contracts to decrease. But the bank could buy back the futures contracts to realize a gain to offset the decreased value of the equity.b. How many contracts are necessary to fully hedge the bank?If the market value of the underlying 20-year, 8 percent benchmark bond is $95 per $100,the market rate is 8.525 percent (using a calculator) and the duration is 10.05 as shown on the last page of this chapter solutions. The number of contracts to hedge the bank is:contracts x m P x D A kD D N F F L A F 06.377750,954$000,000,360$000,95$05.10150)$4)9.0(6()(==-=-=c. Verify that the change in the futures position will offset the change in the cash balancesheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points.For an increase in rates of 100 basis points, the change in the cash balance sheet position is:Expected ∆E = -DGAP[∆R/(1 + R)]A = -2.4(0.01/1.10)$150 = -$3,272,727.27. Thechange in bond value = -10.05(0.01/1.08525)$95,000 = -$8,797.51, and the change in 377 contracts is -$8,797.51 x 377 = -$3,316,662.06. Since the futures contracts were sold, they could be repurchased for a gain of $3,316,662.06. The difference between the two values is a net gain of $43,934.79.For a decrease in rates of 50 basis points, the change in the cash balance sheet position is: Expected ∆E = -DGAP[∆R/(1 + R)]A = -2.4(-0.005/1.10)$150 = $1,636,363.64. Thechange in each bond value = -10.05(-0.005/1.08525)$95,000 = $4,398.76 and the change in 377 contracts is $4,398.76 x 377 = $1,658,331.03. Since the futures contracts were sold, they could be repurchased for a loss of $1,658,331.03. The difference between the two values is a loss of $21,967.39.d. If the bank had hedged with Treasury bill futures contracts that had a market value of $98 per $100 of face value, how many futures contracts would have been necessary to hedge fully the balance sheet?If Treasury bill futures contracts are used, the duration of the underlying asset is 0.25 years, the face value of the contract is $1,000,000, and the number of contracts necessary to hedge the bank is: contracts x m P x D A kD D N F F L A F 39.469,1000,245$000,000,360$000,980$25.0150)$4)9.0(6()(==-=-=e. What additional issues should be considered by the bank in choosing between T-bonds or T-bills futures contracts?In cases where a large number of Treasury bonds are necessary to hedge the balance sheetwith a macrohedge, the FI may need to consider whether a sufficient number of deliverable Treasury bonds are available. Although the number of Treasury bill contracts necessary to hedge the balance sheet is greater than the number of Treasury bonds, the bill market is much deeper and the availability of sufficient deliverable securities should be less of a problem.18. Reconsider Tree Row Bank in problem 17 but assume that the cost rate on the liabilities is6 percent.a. How many contracts are necessary to fully hedge the bank?In this case, the bank faces different average interest rates on both sides of the balancesheet, and further, the yield on the bonds underlying the futures contracts is a third interest rate. Thus the hedge also has the effects of basis risk. Determining the number of futures contracts necessary to hedge this balance sheet must consider separately the effect of a change in rates on each side of the balance sheet, and then consider the combined effect on equity. Estimating the number of contracts can be determined with the modified general equation shown on the next page.b. Verify that the change in the futures position will offset the change in the cash balancesheet position for a change in market interest rates of plus 100 basis points and minus 50 basis points.For an increase in rates of 100 basis points, ∆E = 0.01[(4/1.06)$135 m – (6/1.10)$150 m] =-$3,087,478.56. The change in the bond value is –10.05(.01/1.08525)$95,000 = -$8,797.51, and the change for 351 contracts = -$3,087,926.74. Since the futures contracts were sold, they could be repurchased for a gain of $3,087,926.74. The difference between the two values is a net gain of $448.18.For a decrease in rates of 50 basis points, ∆E = -0.005[(4/1.06)$135 m – (6/1.10)$150 m] =$1,543,739.28. The change in the bond value is –10.05(-.005/1.08525)$95,000 = $4,398.75,and the change for 351 contracts = $1,543,963.01. Since the futures contracts were sold, they could be repurchased for a loss of $1,543,963.01. The difference between the two values is a net loss of $223.73.Modified Equation Model for part (a): contractsor MD P LMD A MD MD P A MD L MD N A MD L MD MD P N A MD L MD R P N D A R R D L R R D L R R D A R R D R R P N D LA F EF FF L A F F A L F A L F F F A L F F F F A A L L L L A A F F F F 35195.35021.751,879$92.855,747,308$21.751,879$26.962,433,509$18.818,181,818$08525.105.10*000,95000,000,135*06.14000,000,150*10.16******)**(*1*)**(*)1()*(**)1(**)1(*)1(**)1(*)1(*)*(==-=-=-=+-=--=-+=-∆+-∆++=⎥⎦⎤⎢⎣⎡+∆--+∆-=+∆-∆-∆=∆∆=∆c. If the bank had hedged with Treasury bill futures contracts that had a market value of $98 per $100 of face value, how many futures contracts would have been necessary to fully hedge the balance sheet?A market value of $98 per $100 of face value implies a discount rate of 8 percent on theunderlying T-bills. Therefore the equation developed above in part (a) to determine thenumber of contracts necessary to hedge the bank can be adjusted as follows for the use of T-bill contracts:contractsor MD P L MD A MD N FF L A F 361,101.361,185.851,226$92.855,747,308$85.851,226$26.962,433,509$18.818,181,818$08.125.0*000,980000,000,135*06.14000,000,150*10.16***==-=-=-=19. What is basis risk? What are the sources of basis risk?Basis risk is the lack of perfect correlation between changes in the yields of the on-balance-sheet assets and the changes in interest rates on the futures contracts. The reason for this difference is that the cash assets and the futures contracts are traded in different markets.20. How would your answers for part (b) in problem 17 change if the relationship of the pricesensitivity of futures contracts to the price sensitivity of underlying bonds were br = 0.92?The number of contracts necessary to hedge the bank would increase to 410 contracts. This can be found by dividing $360,000,000 by ($954,750 * 0.92).21. A mutual fund plans to purchase $500,000 of 30-year Treasury bonds in four months.These bonds have a duration of 12 years and are priced at 96-08\32. The mutual fund is concerned about interest rates changing over the next four months and is considering a hedge with T-bond futures contracts that mature in six months. The T-bond futurescontracts are selling for 98-24\32 and have a duration of 8.5 years.a. If interest rate changes in the spot market exactly match those in the futures market,what type of futures position should the mutual fund create?The mutual fund needs to enter into a contract to buy Treasury bonds at 98-24 in fourmonths. The fund manager fears a fall in interest rates and by buying a futures contract, the profit from a fall in rates will offset a loss in the spot market from having to pay more for the securities.b. How many contracts should be used?The number of contracts can be determined by using the following equation:contracts P D P D N F F F 88.6750,98$*5.8250,481$*12**===Rounding this up to the nearest whole number is 7.0 contracts.c. If the implied rate on the deliverable bond in the futures market moves 12 percent more than the change in the discounted spot rate, how many futures contracts should be used to hedge the portfolio? In this case the value of br = 1.12, and the number of contracts is 6.88/1.12 = 6.14 contracts. This may be adjusted downward to 6 contracts.d. What causes futures contracts to have different price sensitivity than the assets in the spot markets? One reason for the difference in price sensitivity is that the futures contracts and the cash assets are traded in different markets.22. Consider the following balance sheet (in millions) for an FI:Assets LiabilitiesDuration = 10 years $950 Duration = 2 years $860Equity $90 a. What is the FI's duration gap?The duration gap is 10 - (860/950)(2) = 8.19 years. b. What is the FI's interest rate risk exposure?The FI is exposed to interest rate increases. The market value of equity will decrease ifinterest rates increase.c. How can the FI use futures and forward contracts to put on a macrohedge? The FI can hedge its interest rate risk by selling future or forward contracts.d. What is the impact on the FI's equity value if the relative change in interest rates is an increase of 1 percent? That is, ∆R/(1+R) = 0.01. ∆E . - 8.19(950,000)(.01) . -$77,805e. Suppose that the FI in part (c) macrohedges using Treasury bond futures that are currently priced at 96. What is the impact on the FI's futures position if the relative change in all interest rates is an increase of 1 percent? That is, ∆R/(1+R) = 0.01. Assume that the deliverable Treasury bond has a duration of nine years.∆E . - 9(96,000)(.01) . -$8,640 per futures contract. Since the macrohedge is a short hedge, this will be a profit of $8,640 per contract.f. If the FI wanted a perfect macrohedge, how many Treasury bond futures contracts does it need?To perfectly hedge, the Treasury bond futures position should yield a profit equal to the loss in equity value (for any given increase in interest rates). Thus, the number of futures contracts must be sufficient to offset the $77,805 loss in equity value. This will necessitate the sale of $77,805/8,640 = 9.005 contracts. Rounding down, to construct a perfect macrohedge requires the FI to sell 9 Treasury bond futures contracts.23. Refer again to problem 22. How does consideration of basis risk change your answers toproblem 22?In problem 22, we assumed that basis risk did not exist. That allowed us to assert that the percentage change in interest rates (∆R/(1+R)) would be the same for both the futures and underlying cash positions. If there is basis risk, then (∆R/(1+R)) is not necessarily equal to(∆R f /(1+R f )). If the FI wants to fully hedge its interest rate risk exposure in an environment with basis risk, the required number of futures contracts must reflect the disparity in volatilities between the futures and cash markets. a. Compute the number of futures contracts required to construct a perfect macrohedge if [∆R f /(1+R f ) ÷ ∆R/(1+R)] = br = 0.90If br = 0.9, then: contracts 10 = )(.90)(9)(96,00000)8.19(950,0= b P D A )D k - D ( = N FF L A f b. Explain what is meant by br = 0.90. br = 0.90 means that the implied rate on the deliverable bond in the futures market movesby 0.9 percent for every 1 percent change in discounted spot rates (∆R/(1+R)). c. If br = 0.90, what information does this provide on the number of futures contractsneeded to construct a perfect macrohedge?If br = 0.9 then the percentage change in cash market rates exceeds the percentage changein futures market rates. Since futures prices are less sensitive to interest rate shocks than cash prices, the FI must use more futures contracts to generate sufficient cash flows to offset the cash flows on its balance sheet position.24. An FI is planning to hedge its $100 million bond instruments with a cross hedge usingEuromark interest rate futures. How would the FI estimatebr = [∆R f /(1+R f ) ÷ ∆R/(1+R)]to determine the exact number of Euromark futures contracts to hedge?One way of estimating br (or the ratio of changes in yields of futures to the underlying rates) involves regressing the changes in bond yields against Euromark futures. The estimated slope of the line br provides the exact number of contracts to hedge. Note that historical estimation of the basis is not a guarantee that it will remain the same in the future.25. Village Bank has $240 million of assets with a duration of 14 years and liabilities worth$210 million with a duration of 4 years. In the interest of hedging interest rate risk, Village Bank is contemplating a macrohedge with interest rate futures contracts now selling for 102-21\32. If the spot and futures interest rates move together, how many futures contracts must Village Bank sell to fully hedge the balance sheet?contracts or x m P x D A kD D N F F L A F 27375.272656,102$9240)$4)875..0(14()(=-=-=26. Assume an FI has assets of $250 million and liabilities of $200 million. The duration of theassets is six years, and the duration of the liabilities is three years. The price of the futures contract is $115,000, and its duration is 5.5 years. a. What number of futures contracts is needed to construct a perfect hedge if br = 1.10?contracts b) P D ()A D k - D (= N f f L A f 57.293,1750,695$000,000,900$10.1*000,115$*5.5000,000,250)]$8.0*3(6[==-= b. If ∆R f /(1+R f ) = 0.0990, what is the expected ∆R/(1+R)?∆R/(1 + R) = (∆R f /(1+R f ))/br = 0.0990/1.10 = 0.0927. Suppose an FI purchases a $1 million 91-day Eurodollar futures contract trading at 98.50. a. If the contract is reversed two days later by purchasing the contract at 98.60, what is thenet profit?Profit = 0.9860 - 0.9850 x 91/360 x 1,000,000 = $252.78 b. What is the loss or gain if the price at reversal is 98.40? Loss = 0.9840 - 0.9850 x 91/360 x 1,000,000 = -$252.7828. What factors may make the use of swaps or forward contracts preferable to the use offutures contracts for the purpose of hedging long-term foreign exchange positions?A primary factor is that futures contracts may not be available on the day the hedge is desired, or the desired maturity may not be available. If the maturity of the available contract is less than the desired hedge maturity, the FI will incur additional transaction costs from rolling the futures。
Chap009金融机构管理课后题答案
Chapter NineInterest Rate Risk IIChapter Outline IntroductionDurationA General Formula for Duration∙The Duration of Interest Bearing Bonds∙The Duration of a Zero-Coupon Bond∙The Duration of a Consol Bond (Perpetuities)Features of Duration∙Duration and Maturity∙Duration and Yield∙Duration and Coupon InterestThe Economic Meaning of Duration∙Semiannual Coupon BondsDuration and Immunization∙Duration and Immunizing Future Payments∙Immunizing the Whole Balance Sheet of an FI Immunization and Regulatory ConsiderationsDifficulties in Applying the Duration Model∙Duration Matching can be Costly∙Immunization is a Dynamic Problem∙Large Interest Rate Changes and ConvexitySummaryAppendix 9A: Incorporating Convexity into the Duration Model ∙The Problem of the Flat Term Structure∙The Problem of Default Risk∙Floating-Rate Loans and Bonds∙Demand Deposits and Passbook Savings∙Mortgages and Mortgage-Backed Securities∙Futures, Options, Swaps, Caps, and Other Contingent ClaimsSolutions for End-of-Chapter Questions and Problems: Chapter Nine1. What are the two different general interpretations of the concept of duration, and what isthe technical definition of this term? How does duration differ from maturity?Duration measures the average life of an asset or liability in economic terms. As such, durationhas economic meaning as the interest sensitivity (or interest elasticity) of an asset’s value to changes in the interest rate. Duration differs from maturity as a measure of interest ratesensitivity because duration takes into account the time of arrival and the rate of reinvestment ofall cash flows during the assets life. Technically, duration is the weighted-average time to maturity using the relative present values of the cash flows as the weights.2. Two bonds are available for purchase in the financial markets. The first bond is a 2-year,$1,000 bond that pays an annual coupon of 10 percent. The second bond is a 2-year,$1,000, zero-coupon bond.a. What is the duration of the coupon bond if the current yield-to-maturity (YTM) is 8percent? 10 percent? 12 percent? (Hint: You may wish to create a spreadsheetprogram to assist in the calculations.)Coupon BondPar value = $1,000 Coupon = 0.10 Annual payments YTM = 0.08 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T1 $100.00 0.92593 $92.59 $92.592 $1,100.00 0.85734 $943.07 $1,886.15Price = $1,035.67Numerator = $1,978.74 Duration = 1.9106 = Numerator/Price YTM = 0.10Time Cash Flow PVIF PV of CF PV*CF*T1 $100.00 0.90909 $90.91 $90.912 $1,100.00 0.82645 $909.09 $1,818.18Price = $1,000.00Numerator = $1,909.09 Duration = 1.9091 = Numerator/Price YTM = 0.12Time Cash Flow PVIF PV of CF PV*CF*T1 $100.00 0.89286 $89.29 $89.292 $1,100.00 0.79719 $876.91 $1,753.83Price = $966.20Numerator = $1,843.11 Duration = 1.9076 = Numerator/Priceb. How does the change in the current YTM affect the duration of this coupon bond?Increasing the yield-to-maturity decreases the duration of the bond.c. Calculate the duration of the zero-coupon bond with a YTM of 8 percent, 10 percent,and 12 percent.Zero Coupon BondPar value = $1,000 Coupon = 0.00YTM = 0.08 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T1 $0.00 0.92593 $0.00 $0.002 $1,000.00 0.85734 $857.34 $1,714.68Price = $857.34Numerator = $1,714.68 Duration = 2.0000 = Numerator/Price YTM = 0.10Time Cash Flow PVIF PV of CF PV*CF*T1 $0.00 0.90909 $0.00 $0.002 $1,000.00 0.82645 $826.45 $1,652.89Price = $826.45Numerator = $1,652.89 Duration = 2.0000 = Numerator/Price YTM = 0.12Time Cash Flow PVIF PV of CF PV*CF*T1 $0.00 0.89286 $0.00 $0.002 $1,000.00 0.79719 $797.19 $1,594.39Price = $797.19Numerator = $1,594.39 Duration = 2.0000 = Numerator/Priced. How does the change in the current YTM affect the duration of the zero-coupon bond?Changing the yield-to-maturity does not affect the duration of the zero coupon bond.e. Why does the change in the YTM affect the coupon bond differently than the zero-coupon bond?Increasing the YTM on the coupon bond allows for a higher reinvestment income that more quickly recovers the initial investment. The zero-coupon bond has no cash flow untilmaturity.3. A one-year, $100,000 loan carries a market interest rate of 12 percent. The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year. a. What is the duration of this loan?Cash flow in 6 months = $100,000 x .12 x .5 + $50,000 = $56,000 interest and principal. Cash flow in 1 year = $50,000 x 1.06 = $53,000 interest and principal. Time Cash Flow PVIF CF*PVIF T*CF*CVIF1 $56,000 0.943396 $52,830.19 $52,830.192 $53,000 0.889996 $47,169.81 $94,339.62Price = $100,000.00$147,169.81 = Numerator735849.02100.000,100$81.169,147$==x D yearsb. What will be the cash flows at the end of 6 months and at the end of the year? Cash flow in 6 months = $100,000 x .12 x .5 + $50,000 = $56,000 interest and principal. Cash flow in 1 year = $50,000 x 1.06 = $53,000 interest and principal.c. What is the present value of each cash flow discounted at the market rate? What is thetotal present value? $56,000 ÷ 1.06 = $52,830.19 = PVCF 1$53,000 ÷ (1.06)2 = $47,169.81 = PVCF 2=$100,000.00 = PV Total CFd. What proportion of the total present value of cash flows occurs at the end of 6 months?What proportion occurs at the end of the year? Proportion t=.5 = $52,830.19 ÷ $100,000 x 100 = 52.830 percent. Proportion t=1 = $47,169.81 ÷ $100,000 x 100 = 47.169 percent. e. What is the weighted-average life of the cash flows on the loan?D = 0.5283 x 0.5 years + 0.47169 x 1.0 years = 0.26415 + 0.47169 = 0.73584 years. f. How does this weighted-average life compare to the duration calculated in part (a)above? The two values are the same.4. What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannualcoupon selling at par? Selling with a YTM of 12 percent? 14 percent? What can youconclude about the relationship between duration and yield to maturity? Plot therelationship. Why does this relationship exist?Five-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.95238 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.90703 $45.35 $45.351.5 $50.00 0.86384 $43.19 $64.792 $50.00 0.8227 $41.14 $82.272.5 $50.00 0.78353 $39.18 $97.943 $50.00 0.74622 $37.31 $111.933.5$50.00 0.71068 $35.53 $124.374$50.00 0.67684 $33.84 $135.374.5 $50.00 0.64461 $32.23 $145.045 $1,050.00 0.61391 $644.61 $3,223.04Price = $1,000.00Numerator = $4,053.91 Duration = 4.0539 = Numerator/Price Five-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.12 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.9434 $47.17 $23.58 Duration YTM1 $50.00 0.89 $44.50 $44.50 4.0539 0.101.5 $50.00 0.83962 $41.98 $62.97 4.0113 0.122 $50.00 0.79209 $39.60 $79.21 3.9676 0.142.5 $50.00 0.74726 $37.36 $93.413 $50.00 0.70496 $35.25 $105.743.5$50.00 0.66506 $33.25 $116.384$50.00 0.62741 $31.37 $125.484.5 $50.00 0.5919 $29.59 $133.185 $1,050.00 0.55839 $586.31 $2,931.57 .Price = $926.40Numerator = $3,716.03 Duration = 4.0113 = Numerator/PriceFive-year Treasury Bond Par value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.14 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T 0.5 $50.00 0.93458 $46.73 $23.36 1 $50.00 0.87344 $43.67 $43.67 1.5 $50.00 0.8163 $40.81 $61.22 2 $50.00 0.7629 $38.14 $76.29 2.5 $50.00 0.71299 $35.65 $89.12 3 $50.00 0.66634 $33.32 $99.95 3.5 $50.00 0.62275 $31.14 $108.98 4 $50.00 0.58201 $29.10 $116.40 4.5 $50.00 0.54393 $27.20 $122.39 5 $1,050.00 0.50835 $533.77 $2,668.83 Price = $859.53Numerator = $3,410.22 Duration = 3.9676 = Numerator/Price5. Consider three Treasury bonds each of which has a 10 percent semiannual coupon and trades at par.a. Calculate the duration for a bond that has a maturity of 4 years, 3 years, and 2 years? Please see the calculations on the next page.a. Four-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 4Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.952381 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.907029 $45.35 $45.351.5 $50.00 0.863838 $43.19 $64.792 $50.00 0.822702 $41.14 $82.272.5 $50.00 0.783526 $39.18 $97.943 $50.00 0.746215 $37.31 $111.933.5$50.00 0.710681 $35.53 $124.374$1,050.00 0.676839 $710.68 $2,842.73Price = $1,000.00Numerator = $3,393.19 Duration = 3.3932 = Numerator/Price Three-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 3Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.952381 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.907029 $45.35 $45.351.5 $50.00 0.863838 $43.19 $64.792 $50.00 0.822702 $41.14 $82.272.5 $50.00 0.783526 $39.18 $97.943 $1,050.00 0.746215 $783.53 $2,350.58Price = $1,000.00Numerator = $2,664.74 Duration = 2.6647 = Numerator/Price Two-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.952381 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.907029 $45.35 $45.351.5 $50.00 0.863838 $43.19 $64.792 $1,050.00 0.822702 $863.84 $1,727.68Price = $1,000.00Numerator = $1,861.62 Duration = 1.8616 = Numerator/Priceb. What conclusions can you reach about the relationship of duration and the time tomaturity? Plot the relationship.As maturity decreases, duration decreases at a decreasing rate. Although the graph below does not illustrate with great precision, the change in duration is less than the cha nge in time to maturity.6. A six-year, $10,000 CD pays 6 percent interest annually. What is the duration of the CD? What would be the duration if interest were paid semiannually? What is the relationship of duration to the relative frequency of interest payments?Six-year CDPar value = $10,000 Coupon = 0.06 Annual payments YTM = 0.06 Maturity = 6Time Cash Flow PVIF PV of CF PV*CF*T 1 $600.00 0.94340 $566.04 $566.04 PVIF = 1/(1+YTM)^(Time) 2 $600.00 0.89000 $534.00 $1,068.00 3 $600.00 0.83962 $503.77 $1,511.31 4 $600.00 0.79209 $475.26 $1,901.02 5 $600.00 0.74726 $448.35 $2,241.77 6 $10,600 0.70496 $7,472.58 $44,835.49Price = $10,000.00Numerator = $52,123.64 Duration = 5.2124 = Numerator/PriceSix-year CDPar value = $10,000 Coupon = 0.06 Semiannual payments YTM = 0.06 Maturity = 6Time Cash Flow PVIF PV of CF PV*CF*T 0.5 $300.00 0.970874 $291.26 $145.63 PVIF = 1/(1+YTM/2)^(Time*2) 1 $300.00 0.942596 $282.78 $282.78 1.5 $300.00 0.915142 $274.54$411.812 $300.00 0.888487 $266.55 $533.092.5 $300.00 0.862609 $258.78 $646.963 $300.00 0.837484 $251.25 $753.743.5$300.00 0.813092 $243.93 $853.754$300.00 0.789409 $236.82 $947.294.5 $300.00 0.766417 $229.93 $1,034.665 $300.00 0.744094 $223.23 $1,116.145.5 $300.00 0.722421 $216.73 $1,192.006 $10,300 0.701380 $7,224.21 $43,345.28Price = $10,000.00Numerator = $51,263.12 Duration = 5.1263 = Numerator/Price Duration decreases as the frequency of payments increases. This relationship occurs because (a) cash is being received more quickly, and (b) reinvestment income will occur more quickly from the earlier cash flows.7. What is the duration of a consol bond that sells at a YTM of 8 percent? 10 percent? 12percent? What is a consol bond? Would a consol trading at a YTM of 10 percent have agreater duration than a 20-year zero-coupon bond trading at the same YTM? Why?A consol is a bond that pays a fixed coupon each year forever. A consol Consol Bond trading at a YTM of 10 percent has a duration of 11 years, while a zero- YTM D = 1 + 1/R coupon bond trading at a YTM of 10 percent, or any other YTM, has a 0.08 13.50 years duration of 20 years because no cash flows occur before the twentieth 0.10 11.00 years year. 0.12 9.33 years8. Maximum Pension Fund is attempting to balance one of the bond portfolios under itsmanagement. The fund has identified three bonds which have five-year maturities andwhich trade at a YTM of 9 percent. The bonds differ only in that the coupons are 7 percent,9 percent, and 11 percent.a. What is the duration for each bond?Five-year BondPar value = $1,000 Coupon = 0.07 Annual payments YTM = 0.09 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $70.00 0.917431 $64.22 $64.22 PVIF = 1/(1+YTM)^(Time)2 $70.00 0.841680 $58.92 $117.843 $70.00 0.772183 $54.05 $162.164 $70.00 0.708425 $49.59 $198.365 $1,070.00 0.649931 $695.43 $3,477.13Price = $922.21Numerator = $4,019.71 Duration = 4.3588 = Numerator/PriceFive-year BondPar value = $1,000 Coupon = 0.09 Annual payments YTM = 0.09 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $90.00 0.917431 $82.57 $82.57 PVIF = 1/(1+YTM)^(Time)2 $90.00 0.841680 $75.75 $151.503 $90.00 0.772183 $69.50 $208.494 $90.00 0.708425 $63.76 $255.035 $1,090.00 0.649931 $708.43 $3,542.13Price = $1,000.00Numerator = $4,239.72 Duration = 4.2397 = Numerator/Price Five-year BondPar value = $1,000 Coupon = 0.11 Annual payments YTM = 0.09 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $110.00 0.917431 $100.92 $100.92 PVIF = 1/(1+YTM)^(Time)2 $110.00 0.841680 $92.58 $185.173 $110.00 0.772183 $84.94 $254.824 $110.00 0.708425 $77.93 $311.715 $1,110.00 0.649931 $721.42 $3,607.12Price = $1,077.79Numerator = $4,459.73 Duration = 4.1378 = Numerator/Priceb. What is the relationship between duration and the amount of coupon interest that is paid?Plot the relationship.9. An insurance company is analyzing three bonds and is using duration as the measure ofinterest rate risk. All three bonds trade at a YTM of 10 percent and have $10,000 parvalues. The bonds differ only in the amount of annual coupon interest that they pay: 8, 10, or 12 percent.a. What is the duration for each five-year bond?Five-year BondPar value = $10,000 Coupon = 0.08 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $800.00 0.909091 $727.27 $727.27 PVIF = 1/(1+YTM)^(Time)2 $800.00 0.826446 $661.16 $1,322.313 $800.00 0.751315 $601.05 $1,803.164 $800.00 0.683013 $546.41 $2,185.645 $10,800.00 0.620921 $6,705.95 $33,529.75Price = $9,241.84Numerator = $39,568.14 Duration = 4.2814 = Numerator/Price Five-year BondPar value = $10,000 Coupon = 0.10 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $1,000.00 0.909091 $909.09 $909.09 PVIF = 1/(1+YTM)^(Time)2 $1,000.00 0.826446 $826.45 $1,652.893 $1,000.00 0.751315 $751.31 $2,253.944 $1,000.00 0.683013 $683.01 $2,732.055 $11,000.00 0.620921 $6,830.13 $34,150.67Price = $10,000.00Numerator = $41,698.65 Duration = 4.1699 = Numerator/Price Five-year BondPar value = $10,000 Coupon = 0.12 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $1,200.00 0.909091 $1,090.91 $1,090.91 PVIF = 1/(1+YTM)^(Time)2 $1,200.00 0.826446 $991.74 $1,983.473 $1,200.00 0.751315 $901.58 $2,704.734 $1,200.00 0.683013 $819.62 $3,278.465 $11,200.00 0.620921 $6,954.32 $34,771.59Price = $10,758.16Numerator = $43,829.17 Duration = 4.0740 = Numerator/Priceb. What is the relationship between duration and the amount of coupon interest that is paid?10. You can obtain a loan for $100,000 at a rate of 10 percent for two years. You have a choiceof either paying the principal at the end of the second year or amortizing the loan, that is, paying interest and principal in equal payments each year. The loan is priced at par. a. What is the duration of the loan under both methods of payment?Two-year loan: Principal and interest at end of year two. Par value = 100,000 Coupon = 0.00 No annual payments YTM = 0.10 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T 1 $0.00 0.90909 $0.00 $0.00 PVIF = 1/(1+YTM)^(Time) 2 $121,000 0.82645 $100,000.0 200,000.00 Price = $100,000.0 Numerator = 200,000.00 Duration = 2.0000 = Numerator/Price Two-year loan: Interest at end of year one, P & I at end of year two. Par value = 100,000 Coupon = 0.10 Annual payments YTM = 0.10 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 $10,000 0.909091 $9,090.91 $9,090.91 PVIF = 1/(1+YTM)^(Time) 2 $110,000 0.826446 $90,909.09 181,818.18 Price = $100,000.0 Numerator = 190,909.09 Duration = 1.9091 = Numerator/Price Two-year loan: Amortized over two years. Amortized payment of $57.619.05 Par value = 100,000 Coupon = 0.10 YTM = 0.10 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 $57,619.05 0.909091 $52,380.95 $52,380.95 PVIF = 1/(1+YTM)^(Time) 2 $57,619.05 0.826446 $47,619.05 $95,238.10 Price = $100,000.0Numerator = 147,619.05 Duration = 1.4762 = Numerator/Priceb. Explain the difference in the two results?11. How is duration related to the interest elasticity of a fixed-income security? What is therelationship between duration and the price of the fixed-income security?Taking the first derivative of a bond’s (or any fixed -income security) price (P) with respect to the yield to maturity (R) provides the following:D R dRPdP-=+)1( The economic interpretation is that D is a measure of the percentage change in price of a bond for a given percentage change in yield to maturity (interest elasticity). This equation can be rewritten to provide a practical application:P R dR D dP ⎥⎦⎤⎢⎣⎡+-=1In other words, if duration is known, then the change in the price of a bond due to small changes in interest rates, R, can be estimated using the above formula.12. You have discovered that the price of a bond rose from $975 to $995 when the YTM fellfrom 9.75 percent to 9.25 percent. What is the duration of the bond?We know years D years R RPPD 5.45.40975.1005.97520)1(=⇒-=-=+∆∆=-13. Calculate the duration of a 2-year, $1,000 bond that pays an annual coupon of 10 percentand trades at a yield of 14 percent. What is the expected change in the price of the bond if interest rates decline by 0.50 percent (50 basis points)?Two-year Bond Par value = $1,000 Coupon = 0.10 Annual payments YTM = 0.14 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 $100.00 0.87719 $87.72 $87.72 PVIF = 1/(1+YTM)^(Time) 2 $1,100.00 0.76947 $846.41 $1,692.83 Price = $934.13Numerator = $1,780.55 Duration = 1.9061 = Numerator/PriceExpected change in price = 81.7$13.934$14.1005.9061.11=--=+∆-P RR D. This implies a newprice of $941.94. The actual price using conventional bond price discounting would be $941.99. The difference of $0.05 is due to convexity, which was not considered in this solution.14. The duration of an 11-year, $1,000 Treasury bond paying a 10 percent semiannual couponand selling at par has been estimated at 6.9 years. a. What is the modified duration of the bond (Modified Duration = D/(1 + R))? MD = 6.9/(1 + .10/2) = 6.57 years b. What will be the estimated price change of the bond if market interest rates increase0.10 percent (10 basis points)? If rates decrease 0.20 percent (20 basis points)?Estimated change in price = -MD x ∆R x P = -6.57 x 0.001 x $1,000 = -$6.57. Estimated change in price = -MD x ∆R x P = -6.57 x -0.002 x $1,000 = $13.14. c. What would be the actual price of the bond under each rate change situation in part (b)using the traditional present value bond pricing techniques? What is the amount of error in each case?Rate Price Actual Change Estimated Price Error + 0.001 $993.43 $993.45 $0.02 - 0.002 $1,013.14 $1,013.28 -$0.1415. Suppose you purchase a five-year, 13.76 percent bond that is priced to yield 10 percent. a. Show that the duration of this annual payment bond is equal to four years.Five-year Bond Par value = $1,000 Coupon = 0.1376 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $137.60 0.909091 $125.09 $125.09 PVIF = 1/(1+YTM)^(Time)2 $137.60 0.826446 $113.72 $227.443 $137.60 0.751315 $103.38 $310.144 $137.60 0.683013 $93.98 $375.935 $1,137.60 0.620921 $706.36 $3,531.80Price = $1,142.53Numerator = $4,570.40 Duration = 4.0002 = Numerator/Priceb. Show that, if interest rates rise to 11 percent within the next year and that if yourinvestment horizon is four years from today, you will still earn a 10 percent yield onyour investment.Value of bond at end of year four: PV = ($137.60 + $1,000) ÷ 1.11 = $1,024.86.Future value of interest payments at end of year four: $137.60*FVIF n=4, i=11% = $648.06.Future value of all cash flows at n = 4:Coupon interest payments over four years $550.40Interest on interest at 11 percent 97.66Value of bond at end of year four $1,024.86Total future value of investment $1,672.92Yield on purchase of asset at $1,142.53 = $1,672.92*PVIV n=4, i=?% ⇒ i = 10.002332%.c. Show that a 10 percent yield also will be earned if interest rates fall next year to 9percent.Value of bond at end of year four: PV = ($137.60 + $1,000) ÷ 1.09 = $1,043.67.Future value of interest payments at end of year four: $137.60*FVIF n=4, i=9% = $629.26.Future value of all cash flows at n = 4:Coupon interest payments over four years $550.40Interest on interest at 9 percent 78.86Value of bond at end of year four $1,043.67Total future value of investment $1,672.93Yield on purchase of asset at $1,142.53 = $1,672.93*PVIV n=4, i=?% ⇒ i = 10.0025 percent. 16. Consider the case where an investor holds a bond for a period of time longer than theduration of the bond, that is, longer than the original investment horizon.a. If market interest rates rise, will the return that is earned exceed or fall short of theoriginal required rate of return? Explain.In this case the actual return earned would exceed the yield expected at the time ofpurchase. The benefits from a higher reinvestment rate would exceed the price reductioneffect if the investor holds the bond for a sufficient length of time.b. What will happen to the realized return if market interest rates decrease? Explain.If market rates decrease, the realized yield on the bond will be less than the expected yield because the decrease in reinvestment earnings will be greater than the gain in bond value.c. Recalculate parts (b) and (c) of problem 15 above, assuming that the bond is held for allfive years, to verify your answers to parts (a) and (b) of this problem.The case where interest rates rise to 11 percent, n = five years:Future value of interest payments at end of year five: $137.60*FVIF n=5, i=11% = $856.95.Future value of all cash flows at n = 5:Coupon interest payments over five years $688.00Interest on interest at 11 percent 168.95Value of bond at end of year five $1,000.00Total future value of investment $1,856.95Yield on purchase of asset at $1,142.53 = $1,856.95*PVIF n=5, i=?%The case where interest rates fall to 9 percent, n = five years:Future value of interest payments at end of year five: $137.60*FVIF n=5, i=9% = $823.50.Future value of all cash flows at n = 5:Coupon interest payments over five years $688.00Interest on interest at 9 percent 135.50Value of bond at end of year five $1,000.00Total future value of investment $1,823.50Yield on purchase of asset at $1,142.53 = $1,823.50*PVIV n=5, i=?% ⇒ i = 9.8013 percent.d. If either calculation in part (c) is greater than the original required rate of return, whywould an investor ever try to match the duration of an asset with his investment horizon?The answer has to do with the ability to forecast interest rates. Forecasting interest rates isa very difficult task, one that most financial institution money managers are unwilling to do.For most managers, betting that rates would rise to 11 percent to provide a realized yield of10.20 percent over five years is not a sufficient return to offset the possibility that ratescould fall to 9 percent and thus give a yield of only 9.8 percent over five years.17. Two banks are being examined by the regulators to determine the interest rate sensitivity oftheir balance sheets. Bank A has assets composed solely of a 10-year, 12 percent, $1million loan. The loan is financed with a 10-year, 10 percent, $1 million CD. Bank B has assets composed solely of a 7-year, 12 percent zero-coupon bond with a current (market)value of $894,006.20 and a maturity (principal) value of $1,976,362.88. The bond isfinanced with a 10-year, 8.275 percent coupon, $1,000,000 face value CD with a YTM of10 percent. The loan and the CDs pay interest annually, with principal due at maturity.a. If market interest rates increase 1 percent (100 basis points), how do the market valuesof the assets and liabilities of each bank change? That is, what will be the net affect onthe market value of the equity for each bank?For Bank A, an increase of 100 basis points in interest rate will cause the market values of assets and liabilities to decrease as follows:Loan: $120*PVIVA n=10,i=13% + $1,000*PVIV n=10,i=13% = $945,737.57.CD: $100*PVIVA n=10,i=11% + $1,000*PVIV n=10,i=11% = $941,107.68.Therefore, the decrease in value of the asset was $4,629.89 less than the liability.For Bank B:Bond: $1,976,362.88*PVIV n=7,i=13% = $840,074.08.CD: $82.75*PVIVA n=10,i=11% + $1,000*PVIV n=10,i=11% = $839,518.43.The bond value decreased $53,932.12, and the CD value fell $54,487.79. Therefore,the decrease in value of the asset was $555.67 less than the liability.b. What accounts for the differences in the changes of the market value of equity betweenthe two banks?The assets and liabilities of Bank A change in value by different amounts because thedurations of the assets and liabilities are not the same, even though the face values andmaturities are the same. For Bank B, the maturities of the assets and liabilities are different, but the current market values and durations are the same. Thus the change in interest rates causes the same (approximate) change in value for both liabilities and assets.c. Verify your results above by calculating the duration for the assets and liabilities ofeach bank, and estimate the changes in value for the expected change in interest rates.Summarize your results.Ten-year CD:Bank B (Calculation in millions)Par value = $1,000 Coupon = 0.08 Annual payments YTM = 0.10 Maturity = 10Time Cash Flow PVIF PV of CF PV*CF*T1 $82.75 0.909091 $75.23 $75.23 PVIF = 1/(1+YTM)^(Time)2 $82.75 0.826446 $68.39 $136.783 $82.75 0.751315 $62.17 $186.514 $82.75 0.683013 $56.52 $226.085 $82.75 0.620921 $51.38 $256.916 $82.75 0.564474 $46.71 $280.267 $82.75 0.513158 $42.46 $297.258 $82.75 0.466507 $38.60 $308.839 $82.75 0.424098 $35.09 $315.8510 $1,082.75 0.385543 $417.45 $4,174.47Price = $894.006Numerator = $6,258.15 Duration = 7.0001 = Numerator/PriceThe duration for the CD of Bank B is calculated above to be 7.001 years. Since the bond is a zero-coupon, the duration is equal to the maturity of 7 years. Using the duration formula to estimate the change in value: Bond:∆Value = 39.875,55$20.006,894$12.101.0.71-=-=+∆-P R R DCD: ∆Value = 43.899,56$22.006,894$10.101.0001.71-=-=+∆-P RR DThe difference in the change in value of the assets and liabilities for Bank B is $1,024.04 using the duration estimation model. The small difference in this estimate and the estimate found in part a above is due to the convexity of the two financial assets.The duration estimates for the loan and CD for Bank A are presented below:Ten-year Loan: Bank A (Calculation in millions)Par value = $1,000 Coupon = 0.12 Annual payments YTM = 0.12 Maturity = 10Time Cash Flow PVIF PV of CF PV*CF*T 1 $120.00 0.892857 $107.14 $107.14 PVIF = 1/(1+YTM)^(Time) 2 $120.00 0.797194 $95.66 $191.33 3 $120.00 0.711780 $85.41 $256.24 4 $120.00 0.635518 $76.26 $305.05 5 $120.00 0.567427 $68.09 $340.46 6 $120.00 0.506631 $60.80 $364.77 7 $120.00 0.452349 $54.28 $379.97 8 $120.00 0.403883 $48.47 $387.73 9 $120.00 0.360610 $43.27 $389.46 10 $1,120.00 0.321973 $360.61 $3,606.10 Price = $1,000.00Numerator = $6,328.25 Duration = 6.3282 = Numerator/PriceTen-year CD: Bank A (Calculation in millions) Par value = $1,000 Coupon = 0.10 Annual payments YTM = 0.10 Maturity = 10 Time Cash Flow PVIF PV of CF PV*CF*T 1 $100.00 0.909091 $90.91 $90.91 PVIF = 1/(1+YTM)^(Time) 2 $100.00 0.826446 $82.64 $165.29 3 $100.00 0.751315 $75.13 $225.39 4 $100.00 0.683013 $68.30 $273.21 5 $100.00 0.620921 $62.09 $310.46。
金融机构管理习题答案
Chapter NineInterest Rate Risk IIChapter Outline IntroductionDurationA General Formula for Duration•The Duration of Interest Bearing Bonds•The Duration of a Zero-Coupon Bond•The Duration of a Consol Bond (Perpetuities)Features of Duration•Duration and Maturity•Duration and Yield•Duration and Coupon InterestThe Economic Meaning of Duration•Semiannual Coupon BondsDuration and Immunization•Duration and Immunizing Future Payments•Immunizing the Whole Balance Sheet of an FI Immunization and Regulatory ConsiderationsDifficulties in Applying the Duration Model•Duration Matching can be Costly•Immunization is a Dynamic Problem•Large Interest Rate Changes and ConvexitySummaryAppendix 9A: Incorporating Convexity into the Duration Model •The Problem of the Flat Term Structure•The Problem of Default Risk•Floating-Rate Loans and Bonds•Demand Deposits and Passbook Savings•Mortgages and Mortgage-Backed Securities•Futures, Options, Swaps, Caps, and Other Contingent ClaimsSolutions for End-of-Chapter Questions and Problems: Chapter Nine1. What are the two different general interpretations of the concept of duration, and what isthe technical definition of this term? How does duration differ from maturity?Duration measures the average life of an asset or liability in economic terms. As such, duration has economic meaning as the interest sensitivity (or interest elasticity) of an asset’s value to changes in the interest rate. Duration differs from maturity as a measure of interest ratesensitivity because duration takes into account the time of arrival and the rate of reinvestment ofall cash flows during the assets life. Technically, duration is the weighted-average time to maturity using the relative present values of the cash flows as the weights.2. Two bonds are available for purchase in the financial markets. The first bond is a 2-year,$1,000 bond that pays an annual coupon of 10 percent. The second bond is a 2-year,$1,000, zero-coupon bond.a. What is the duration of the coupon bond if the current yield-to-maturity (YTM) is 8percent? 10 percent? 12 percent? (Hint: You may wish to create a spreadsheetprogram to assist in the calculations.)Coupon BondPar value = $1,000 Coupon = 0.10 Annual payments YTM = 0.08 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T1 $100.00 0.92593 $92.59 $92.592 $1,100.00 0.85734 $943.07 $1,886.15Price = $1,035.67Numerator = $1,978.74 Duration = 1.9106 = Numerator/Price YTM = 0.10Time Cash Flow PVIF PV of CF PV*CF*T1 $100.00 0.90909 $90.91 $90.912 $1,100.00 0.82645 $909.09 $1,818.18Price = $1,000.00Numerator = $1,909.09 Duration = 1.9091 = Numerator/Price YTM = 0.12Time Cash Flow PVIF PV of CF PV*CF*T1 $100.00 0.89286 $89.29 $89.292 $1,100.00 0.79719 $876.91 $1,753.83Price = $966.20Numerator = $1,843.11 Duration = 1.9076 = Numerator/Priceb. How does the change in the current YTM affect the duration of this coupon bond?Increasing the yield-to-maturity decreases the duration of the bond.c. Calculate the duration of the zero-coupon bond with a YTM of 8 percent, 10 percent,and 12 percent.Zero Coupon BondPar value = $1,000 Coupon = 0.00YTM = 0.08 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T1 $0.00 0.92593 $0.00 $0.002 $1,000.00 0.85734 $857.34 $1,714.68Price = $857.34Numerator = $1,714.68 Duration = 2.0000 = Numerator/Price YTM = 0.10Time Cash Flow PVIF PV of CF PV*CF*T1 $0.00 0.90909 $0.00 $0.002 $1,000.00 0.82645 $826.45 $1,652.89Price = $826.45Numerator = $1,652.89 Duration = 2.0000 = Numerator/Price YTM = 0.12Time Cash Flow PVIF PV of CF PV*CF*T1 $0.00 0.89286 $0.00 $0.002 $1,000.00 0.79719 $797.19 $1,594.39Price = $797.19Numerator = $1,594.39 Duration = 2.0000 = Numerator/Priced. How does the change in the current YTM affect the duration of the zero-coupon bond?Changing the yield-to-maturity does not affect the duration of the zero coupon bond.e. Why does the change in the YTM affect the coupon bond differently than the zero-coupon bond?Increasing the YTM on the coupon bond allows for a higher reinvestment income that more quickly recovers the initial investment. The zero-coupon bond has no cash flow untilmaturity.3. A one-year, $100,000 loan carries a market interest rate of 12 percent. The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year. a. What is the duration of this loan?Cash flow in 6 months = $100,000 x .12 x .5 + $50,000 = $56,000 interest and principal. Cash flow in 1 year = $50,000 x 1.06 = $53,000 interest and principal. Time Cash Flow PVIF CF*PVIF T*CF*CVIF1 $56,000 0.943396 $52,830.19 $52,830.192 $53,000 0.889996 $47,169.81 $94,339.62Price = $100,000.00 $147,169.81 = Numerator735849.02100.000,100$81.169,147$==x D yearsb. What will be the cash flows at the end of 6 months and at the end of the year? Cash flow in 6 months = $100,000 x .12 x .5 + $50,000 = $56,000 interest and principal. Cash flow in 1 year = $50,000 x 1.06 = $53,000 interest and principal.c. What is the present value of each cash flow discounted at the market rate? What is the total present value? $56,000 ÷ 1.06 = $52,830.19 = PVCF 1$53,000 ÷ (1.06)2 = $47,169.81 = PVCF 2=$100,000.00 = PV Total CFd. What proportion of the total present value of cash flows occurs at the end of 6 months? What proportion occurs at the end of the year? Proportion t=.5 = $52,830.19 ÷ $100,000 x 100 = 52.830 percent. Proportion t=1 = $47,169.81 ÷ $100,000 x 100 = 47.169 percent.e. What is the weighted-average life of the cash flows on the loan?D = 0.5283 x 0.5 years + 0.47169 x 1.0 years = 0.26415 + 0.47169 = 0.73584 years. f. How does this weighted-average life compare to the duration calculated in part (a) above? The two values are the same.4. What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannualcoupon selling at par? Selling with a YTM of 12 percent? 14 percent? What can youconclude about the relationship between duration and yield to maturity? Plot therelationship. Why does this relationship exist?Five-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.95238 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.90703 $45.35 $45.351.5 $50.00 0.86384 $43.19 $64.792 $50.00 0.8227 $41.14 $82.272.5 $50.00 0.78353 $39.18 $97.943 $50.00 0.74622 $37.31 $111.933.5$50.00 0.71068 $35.53 $124.374$50.00 0.67684 $33.84 $135.374.5 $50.00 0.64461 $32.23 $145.045 $1,050.00 0.61391 $644.61 $3,223.04Price = $1,000.00Numerator = $4,053.91 Duration = 4.0539 = Numerator/Price Five-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.12 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.9434 $47.17 $23.58 Duration YTM1 $50.00 0.89 $44.50 $44.50 4.0539 0.101.5 $50.00 0.83962 $41.98 $62.97 4.0113 0.122 $50.00 0.79209 $39.60 $79.21 3.9676 0.142.5 $50.00 0.74726 $37.36 $93.413 $50.00 0.70496 $35.25 $105.743.5$50.00 0.66506 $33.25 $116.384$50.00 0.62741 $31.37 $125.484.5 $50.00 0.5919 $29.59 $133.185 $1,050.00 0.55839 $586.31 $2,931.57 .Price = $926.40Numerator = $3,716.03 Duration = 4.0113 = Numerator/PriceFive-year Treasury Bond Par value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.14 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T 0.5 $50.00 0.93458 $46.73 $23.36 1 $50.00 0.87344 $43.67 $43.67 1.5 $50.00 0.8163 $40.81 $61.22 2 $50.00 0.7629 $38.14 $76.29 2.5 $50.00 0.71299 $35.65 $89.12 3 $50.00 0.66634 $33.32 $99.95 3.5 $50.00 0.62275 $31.14 $108.98 4 $50.00 0.58201 $29.10 $116.40 4.5 $50.00 0.54393 $27.20 $122.39 5 $1,050.00 0.50835 $533.77 $2,668.83 Price = $859.53Numerator = $3,410.22 Duration = 3.9676 = Numerator/Price5. Consider three Treasury bonds each of which has a 10 percent semiannual coupon and trades at par.a. Calculate the duration for a bond that has a maturity of 4 years, 3 years, and 2 years? Please see the calculations on the next page.a. Four-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 4Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.952381 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.907029 $45.35 $45.351.5 $50.00 0.863838 $43.19 $64.792 $50.00 0.822702 $41.14 $82.272.5 $50.00 0.783526 $39.18 $97.943 $50.00 0.746215 $37.31 $111.933.5$50.00 0.710681 $35.53 $124.374$1,050.00 0.676839 $710.68 $2,842.73Price = $1,000.00Numerator = $3,393.19 Duration = 3.3932 = Numerator/Price Three-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 3Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.952381 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.907029 $45.35 $45.351.5 $50.00 0.863838 $43.19 $64.792 $50.00 0.822702 $41.14 $82.272.5 $50.00 0.783526 $39.18 $97.943 $1,050.00 0.746215 $783.53 $2,350.58Price = $1,000.00Numerator = $2,664.74 Duration = 2.6647 = Numerator/Price Two-year Treasury BondPar value = $1,000 Coupon = 0.10 Semiannual payments YTM = 0.10 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T0.5 $50.00 0.952381 $47.62 $23.81 PVIF = 1/(1+YTM/2)^(Time*2)1 $50.00 0.907029 $45.35 $45.351.5 $50.00 0.863838 $43.19 $64.792 $1,050.00 0.822702 $863.84 $1,727.68Price = $1,000.00Numerator = $1,861.62 Duration = 1.8616 = Numerator/Priceb. What conclusions can you reach about the relationship of duration and the time tomaturity? Plot the relationship.As maturity decreases, duration decreases at a decreasing rate. Although the graph below does not illustrate with great precision, the change in duration is less than the change in time to maturity.6. A six-year, $10,000 CD pays 6 percent interest annually. What is the duration of the CD? What would be the duration if interest were paid semiannually? What is the relationship of duration to the relative frequency of interest payments?Six-year CDPar value = $10,000 Coupon = 0.06 Annual payments YTM = 0.06 Maturity = 6 Time Cash Flow PVIF PV of CF PV*CF*T 1 $600.00 0.94340 $566.04 $566.04 PVIF = 1/(1+YTM)^(Time) 2 $600.00 0.89000 $534.00 $1,068.00 3 $600.00 0.83962 $503.77 $1,511.31 4 $600.00 0.79209 $475.26 $1,901.02 5 $600.00 0.74726 $448.35 $2,241.77 6 $10,600 0.70496 $7,472.58 $44,835.49Price = $10,000.00Numerator = $52,123.64 Duration = 5.2124 = Numerator/PriceSix-year CDPar value = $10,000 Coupon = 0.06 Semiannual payments YTM = 0.06 Maturity = 6Time Cash Flow PVIF PV of CF PV*CF*T 0.5 $300.00 0.970874 $291.26 $145.63 PVIF = 1/(1+YTM/2)^(Time*2) 1 $300.00 0.942596 $282.78 $282.78 1.5 $300.00 0.915142 $274.54$411.812 $300.00 0.888487 $266.55 $533.092.5 $300.00 0.862609 $258.78 $646.963 $300.00 0.837484 $251.25 $753.743.5$300.00 0.813092 $243.93 $853.754$300.00 0.789409 $236.82 $947.294.5 $300.00 0.766417 $229.93 $1,034.665 $300.00 0.744094 $223.23 $1,116.145.5 $300.00 0.722421 $216.73 $1,192.006 $10,300 0.701380 $7,224.21 $43,345.28Price = $10,000.00Numerator = $51,263.12 Duration = 5.1263 = Numerator/Price Duration decreases as the frequency of payments increases. This relationship occurs because (a) cash is being received more quickly, and (b) reinvestment income will occur more quickly from the earlier cash flows.7. What is the duration of a consol bond that sells at a YTM of 8 percent? 10 percent? 12percent? What is a consol bond? Would a consol trading at a YTM of 10 percent have agreater duration than a 20-year zero-coupon bond trading at the same YTM? Why?A consol is a bond that pays a fixed coupon each year forever. A consol Consol Bond trading at a YTM of 10 percent has a duration of 11 years, while a zero- YTM D = 1 + 1/R coupon bond trading at a YTM of 10 percent, or any other YTM, has a 0.08 13.50 years duration of 20 years because no cash flows occur before the twentieth 0.10 11.00 years year. 0.12 9.33 years 8. Maximum Pension Fund is attempting to balance one of the bond portfolios under itsmanagement. The fund has identified three bonds which have five-year maturities andwhich trade at a YTM of 9 percent. The bonds differ only in that the coupons are 7 percent,9 percent, and 11 percent.a. What is the duration for each bond?Five-year BondPar value = $1,000 Coupon = 0.07 Annual payments YTM = 0.09 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $70.00 0.917431 $64.22 $64.22 PVIF = 1/(1+YTM)^(Time)2 $70.00 0.841680 $58.92 $117.843 $70.00 0.772183 $54.05 $162.164 $70.00 0.708425 $49.59 $198.365 $1,070.00 0.649931 $695.43 $3,477.13Price = $922.21Numerator = $4,019.71 Duration = 4.3588 = Numerator/PriceFive-year BondPar value = $1,000 Coupon = 0.09 Annual payments YTM = 0.09 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $90.00 0.917431 $82.57 $82.57 PVIF = 1/(1+YTM)^(Time)2 $90.00 0.841680 $75.75 $151.503 $90.00 0.772183 $69.50 $208.494 $90.00 0.708425 $63.76 $255.035 $1,090.00 0.649931 $708.43 $3,542.13Price = $1,000.00Numerator = $4,239.72 Duration = 4.2397 = Numerator/Price Five-year BondPar value = $1,000 Coupon = 0.11 Annual payments YTM = 0.09 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $110.00 0.917431 $100.92 $100.92 PVIF = 1/(1+YTM)^(Time)2 $110.00 0.841680 $92.58 $185.173 $110.00 0.772183 $84.94 $254.824 $110.00 0.708425 $77.93 $311.715 $1,110.00 0.649931 $721.42 $3,607.12Price = $1,077.79Numerator = $4,459.73 Duration = 4.1378 = Numerator/Priceb. What is the relationship between duration and the amount of coupon interest that is paid?Plot the relationship.9. An insurance company is analyzing three bonds and is using duration as the measure ofinterest rate risk. All three bonds trade at a YTM of 10 percent and have $10,000 parvalues. The bonds differ only in the amount of annual coupon interest that they pay: 8, 10, or 12 percent.a. What is the duration for each five-year bond?Five-year BondPar value = $10,000 Coupon = 0.08 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $800.00 0.909091 $727.27 $727.27 PVIF = 1/(1+YTM)^(Time)2 $800.00 0.826446 $661.16 $1,322.313 $800.00 0.751315 $601.05 $1,803.164 $800.00 0.683013 $546.41 $2,185.645 $10,800.00 0.620921 $6,705.95 $33,529.75Price = $9,241.84Numerator = $39,568.14 Duration = 4.2814 = Numerator/Price Five-year BondPar value = $10,000 Coupon = 0.10 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $1,000.00 0.909091 $909.09 $909.09 PVIF = 1/(1+YTM)^(Time)2 $1,000.00 0.826446 $826.45 $1,652.893 $1,000.00 0.751315 $751.31 $2,253.944 $1,000.00 0.683013 $683.01 $2,732.055 $11,000.00 0.620921 $6,830.13 $34,150.67Price = $10,000.00Numerator = $41,698.65 Duration = 4.1699 = Numerator/Price Five-year BondPar value = $10,000 Coupon = 0.12 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $1,200.00 0.909091 $1,090.91 $1,090.91 PVIF = 1/(1+YTM)^(Time)2 $1,200.00 0.826446 $991.74 $1,983.473 $1,200.00 0.751315 $901.58 $2,704.734 $1,200.00 0.683013 $819.62 $3,278.465 $11,200.00 0.620921 $6,954.32 $34,771.59Price = $10,758.16Numerator = $43,829.17 Duration = 4.0740 = Numerator/Priceb. What is the relationship between duration and the amount of coupon interest that is paid?10. You can obtain a loan for $100,000 at a rate of 10 percent for two years. You have a choiceof either paying the principal at the end of the second year or amortizing the loan, that is, paying interest and principal in equal payments each year. The loan is priced at par. a. What is the duration of the loan under both methods of payment?Two-year loan: Principal and interest at end of year two. Par value = 100,000 Coupon = 0.00 No annual payments YTM = 0.10 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T 1 $0.00 0.90909 $0.00 $0.00 PVIF = 1/(1+YTM)^(Time) 2 $121,000 0.82645 $100,000.0 200,000.00 Price = $100,000.0 Numerator = 200,000.00 Duration = 2.0000 = Numerator/Price Two-year loan: Interest at end of year one, P & I at end of year two. Par value = 100,000 Coupon = 0.10 Annual payments YTM = 0.10 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 $10,000 0.909091 $9,090.91 $9,090.91 PVIF = 1/(1+YTM)^(Time) 2 $110,000 0.826446 $90,909.09 181,818.18 Price = $100,000.0 Numerator = 190,909.09 Duration = 1.9091 = Numerator/Price Two-year loan: Amortized over two years. Amortized payment of $57.619.05 Par value = 100,000 Coupon = 0.10 YTM = 0.10 Maturity = 2 Time Cash Flow PVIF PV of CF PV*CF*T 1 $57,619.05 0.909091 $52,380.95 $52,380.95 PVIF = 1/(1+YTM)^(Time) 2 $57,619.05 0.826446 $47,619.05 $95,238.10 Price = $100,000.0Numerator = 147,619.05 Duration = 1.4762 = Numerator/Priceb. Explain the difference in the two results?11. How is duration related to the interest elasticity of a fixed-income security? What is therelationship between duration and the price of the fixed-income security?Taking the first derivative of a bond’s (or any fixed -income security) price (P) with respect to the yield to maturity (R) provides the following:D R dR P dP-=+)1( The economic interpretation is that D is a measure of the percentage change in price of a bond for a given percentage change in yield to maturity (interest elasticity). This equation can be rewritten to provide a practical application:P R dR D dP ⎥⎦⎤⎢⎣⎡+-=1 In other words, if duration is known, then the change in the price of a bond due to small changes in interest rates, R, can be estimated using the above formula.12. You have discovered that the price of a bond rose from $975 to $995 when the YTM fellfrom 9.75 percent to 9.25 percent. What is the duration of the bond?We know years D years R R P PD 5.45.40975.1005.97520)1(=⇒-=-=+∆∆=-13. Calculate the duration of a 2-year, $1,000 bond that pays an annual coupon of 10 percentand trades at a yield of 14 percent. What is the expected change in the price of the bond if interest rates decline by 0.50 percent (50 basis points)?Two-year Bond Par value = $1,000 Coupon = 0.10 Annual payments YTM = 0.14 Maturity = 2Time Cash Flow PVIF PV of CF PV*CF*T 1 $100.00 0.87719 $87.72 $87.72 PVIF = 1/(1+YTM)^(Time) 2 $1,100.00 0.76947 $846.41 $1,692.83 Price = $934.13Numerator = $1,780.55 Duration = 1.9061 = Numerator/PriceExpected change in price = 81.7$13.934$14.1005.9061.11=--=+∆-P R R D . This implies a newprice of $941.94. The actual price using conventional bond price discounting would be $941.99. The difference of $0.05 is due to convexity, which was not considered in this solution.14. The duration of an 11-year, $1,000 Treasury bond paying a 10 percent semiannual couponand selling at par has been estimated at 6.9 years. a. What is the modified duration of the bond (Modified Duration = D/(1 + R))? MD = 6.9/(1 + .10/2) = 6.57 years b. What will be the estimated price change of the bond if market interest rates increase0.10 percent (10 basis points)? If rates decrease 0.20 percent (20 basis points)?Estimated change in price = -MD x ∆R x P = -6.57 x 0.001 x $1,000 = -$6.57. Estimated change in price = -MD x ∆R x P = -6.57 x -0.002 x $1,000 = $13.14. c. What would be the actual price of the bond under each rate change situation in part (b)using the traditional present value bond pricing techniques? What is the amount of error in each case?Rate Price Actual Change Estimated Price Error + 0.001 $993.43 $993.45 $0.02 - 0.002 $1,013.14 $1,013.28 -$0.1415. Suppose you purchase a five-year, 13.76 percent bond that is priced to yield 10 percent. a. Show that the duration of this annual payment bond is equal to four years.Five-year Bond Par value = $1,000 Coupon = 0.1376 Annual payments YTM = 0.10 Maturity = 5Time Cash Flow PVIF PV of CF PV*CF*T1 $137.60 0.909091 $125.09 $125.09 PVIF = 1/(1+YTM)^(Time)2 $137.60 0.826446 $113.72 $227.443 $137.60 0.751315 $103.38 $310.144 $137.60 0.683013 $93.98 $375.935 $1,137.60 0.620921 $706.36 $3,531.80Price = $1,142.53Numerator = $4,570.40 Duration = 4.0002 = Numerator/Priceb. Show that, if interest rates rise to 11 percent within the next year and that if yourinvestment horizon is four years from today, you will still earn a 10 percent yield onyour investment.Value of bond at end of year four: PV = ($137.60 + $1,000) ÷ 1.11 = $1,024.86.Future value of interest payments at end of year four: $137.60*FVIF n=4, i=11% = $648.06.Future value of all cash flows at n = 4:Coupon interest payments over four years $550.40Interest on interest at 11 percent 97.66Value of bond at end of year four $1,024.86Total future value of investment $1,672.92Yield on purchase of asset at $1,142.53 = $1,672.92*PVIV n=4, i=?% ⇒ i = 10.002332%.c. Show that a 10 percent yield also will be earned if interest rates fall next year to 9percent.Value of bond at end of year four: PV = ($137.60 + $1,000) ÷ 1.09 = $1,043.67.Future value of interest payments at end of year four: $137.60*FVIF n=4, i=9% = $629.26.Future value of all cash flows at n = 4:Coupon interest payments over four years $550.40Interest on interest at 9 percent 78.86Value of bond at end of year four $1,043.67Total future value of investment $1,672.93Yield on purchase of asset at $1,142.53 = $1,672.93*PVIV n=4, i=?% ⇒ i = 10.0025 percent. 16. Consider the case where an investor holds a bond for a period of time longer than theduration of the bond, that is, longer than the original investment horizon.a. If market interest rates rise, will the return that is earned exceed or fall short of theoriginal required rate of return? Explain.In this case the actual return earned would exceed the yield expected at the time ofpurchase. The benefits from a higher reinvestment rate would exceed the price reductioneffect if the investor holds the bond for a sufficient length of time.b. What will happen to the realized return if market interest rates decrease? Explain.If market rates decrease, the realized yield on the bond will be less than the expected yield because the decrease in reinvestment earnings will be greater than the gain in bond value.c. Recalculate parts (b) and (c) of problem 15 above, assuming that the bond is held for allfive years, to verify your answers to parts (a) and (b) of this problem.The case where interest rates rise to 11 percent, n = five years:Future value of interest payments at end of year five: $137.60*FVIF n=5, i=11% = $856.95.Future value of all cash flows at n = 5:Coupon interest payments over five years $688.00Interest on interest at 11 percent 168.95Value of bond at end of year five $1,000.00Total future value of investment $1,856.95Yield on purchase of asset at $1,142.53 = $1,856.95*PVIF n=5, i=?%The case where interest rates fall to 9 percent, n = five years:Future value of interest payments at end of year five: $137.60*FVIF n=5, i=9% = $823.50.Future value of all cash flows at n = 5:Coupon interest payments over five years $688.00Interest on interest at 9 percent 135.50Value of bond at end of year five $1,000.00Total future value of investment $1,823.50Yield on purchase of asset at $1,142.53 = $1,823.50*PVIV n=5, i=?% ⇒ i = 9.8013 percent.d. If either calculation in part (c) is greater than the original required rate of return, whywould an investor ever try to match the duration of an asset with his investment horizon?The answer has to do with the ability to forecast interest rates. Forecasting interest rates isa very difficult task, one that most financial institution money managers are unwilling to do.For most managers, betting that rates would rise to 11 percent to provide a realized yield of10.20 percent over five years is not a sufficient return to offset the possibility that ratescould fall to 9 percent and thus give a yield of only 9.8 percent over five years.17. Two banks are being examined by the regulators to determine the interest rate sensitivity oftheir balance sheets. Bank A has assets composed solely of a 10-year, 12 percent, $1million loan. The loan is financed with a 10-year, 10 percent, $1 million CD. Bank B has assets composed solely of a 7-year, 12 percent zero-coupon bond with a current (market) value of $894,006.20 and a maturity (principal) value of $1,976,362.88. The bond isfinanced with a 10-year, 8.275 percent coupon, $1,000,000 face value CD with a YTM of10 percent. The loan and the CDs pay interest annually, with principal due at maturity.a. If market interest rates increase 1 percent (100 basis points), how do the market valuesof the assets and liabilities of each bank change? That is, what will be the net affect onthe market value of the equity for each bank?For Bank A, an increase of 100 basis points in interest rate will cause the market values of assets and liabilities to decrease as follows:Loan: $120*PVIVA n=10,i=13% + $1,000*PVIV n=10,i=13% = $945,737.57.CD: $100*PVIVA n=10,i=11% + $1,000*PVIV n=10,i=11% = $941,107.68.Therefore, the decrease in value of the asset was $4,629.89 less than the liability.For Bank B:Bond: $1,976,362.88*PVIV n=7,i=13% = $840,074.08.CD: $82.75*PVIVA n=10,i=11% + $1,000*PVIV n=10,i=11% = $839,518.43.The bond value decreased $53,932.12, and the CD value fell $54,487.79. Therefore,the decrease in value of the asset was $555.67 less than the liability.b. What accounts for the differences in the changes of the market value of equity betweenthe two banks?The assets and liabilities of Bank A change in value by different amounts because thedurations of the assets and liabilities are not the same, even though the face values andmaturities are the same. For Bank B, the maturities of the assets and liabilities are different, but the current market values and durations are the same. Thus the change in interest rates causes the same (approximate) change in value for both liabilities and assets.c. Verify your results above by calculating the duration for the assets and liabilities ofeach bank, and estimate the changes in value for the expected change in interest rates.Summarize your results.Ten-year CD:Bank B (Calculation in millions)Par value = $1,000 Coupon = 0.08 Annual payments YTM = 0.10 Maturity = 10Time Cash Flow PVIF PV of CF PV*CF*T1 $82.75 0.909091 $75.23 $75.23 PVIF = 1/(1+YTM)^(Time)2 $82.75 0.826446 $68.39 $136.783 $82.75 0.751315 $62.17 $186.514 $82.75 0.683013 $56.52 $226.085 $82.75 0.620921 $51.38 $256.916 $82.75 0.564474 $46.71 $280.267 $82.75 0.513158 $42.46 $297.258 $82.75 0.466507 $38.60 $308.839 $82.75 0.424098 $35.09 $315.8510 $1,082.75 0.385543 $417.45 $4,174.47Price = $894.006Numerator = $6,258.15 Duration = 7.0001 = Numerator/PriceThe duration for the CD of Bank B is calculated above to be 7.001 years. Since the bond is a zero-coupon, the duration is equal to the maturity of 7 years.Using the duration formula to estimate the change in value:Bond: ∆Value = 39.875,55$20.006,894$12.101.0.71-=-=+∆-P R R DCD:∆Value = 43.899,56$22.006,894$10.101.0001.71-=-=+∆-P R R DThe difference in the change in value of the assets and liabilities for Bank B is $1,024.04using the duration estimation model. The small difference in this estimate and the estimate found in part a above is due to the convexity of the two financial assets.The duration estimates for the loan and CD for Bank A are presented below:Ten-year Loan: Bank A (Calculation in millions)Par value = $1,000 Coupon = 0.12 Annual payments YTM = 0.12 Maturity = 10Time Cash Flow PVIF PV of CF PV*CF*T 1 $120.00 0.892857 $107.14 $107.14 PVIF = 1/(1+YTM)^(Time) 2 $120.00 0.797194 $95.66 $191.33 3 $120.00 0.711780 $85.41 $256.24 4 $120.00 0.635518 $76.26 $305.05 5 $120.00 0.567427 $68.09 $340.46 6 $120.00 0.506631 $60.80 $364.77 7 $120.00 0.452349 $54.28 $379.97 8 $120.00 0.403883 $48.47 $387.73 9 $120.00 0.360610 $43.27 $389.46 10 $1,120.00 0.321973 $360.61 $3,606.10 Price = $1,000.00Numerator = $6,328.25 Duration = 6.3282 = Numerator/PriceTen-year CD: Bank A (Calculation in millions) Par value = $1,000 Coupon = 0.10 Annual payments YTM = 0.10 Maturity = 10 Time Cash Flow PVIF PV of CF PV*CF*T 1 $100.00 0.909091 $90.91 $90.91 PVIF = 1/(1+YTM)^(Time) 2 $100.00 0.826446 $82.64 $165.29 3 $100.00 0.751315 $75.13 $225.39 4 $100.00 0.683013 $68.30 $273.21 5 $100.00 0.620921 $62.09 $310.46。
金融机构管理第十章中文版课后习题答案(1-8、19)
金融机构管理第十章中文版课后习题答案(1-8、19)1.市场风险是指由于市场条件,例如资产价值、利率、市场波动性与市场流动性的变化而给金融机构交易资产组合的盈利所带来的不确定性风险。
2.市场风险测量的重要性:a.管理信息,市场风险测量能向高级管理人员提供交易员所承担的风险敞口的信息。
b.设定限额,市场风险测量可以在每个交易领域设定每位交易员在经济上合理的头寸限额。
c.资源分配,市场风险测量可以识别每单位风险有着最大潜在的回报的领域,从而向这个领域导入更多的资本与资源。
d.业绩评估,市场风险测量可以计算交易员的风险回报比率,提供一个更合理的奖惩制度。
e.监管,市场风险测量能够指出由于谨慎监管而导致的潜在的资源配置不当。
3 .日风险收益是指一日内,在利率变化、汇率变化、市场波动等不利环境下对投资组合估计的潜在损失。
日风险收益=头寸的美元市值*该头寸的价格敏感性*收益率潜在的不利变动=头寸的美元市值*价格波动性。
价格波动性即价格敏感性乘以收益率的不利变动。
4. a. MD = 5 ÷ (1.07) = 4.6729 年b . 收益率的不利变动= 1.65σ = 1.65 x 0.0012 = .001980c. 价格波动性= -MD x 收益率的不利变动= -4.6729 x .00198 = -0.009252 或-0.9252 %d. DEAR = 头寸的美元市值x价格波动性= $1,000,000 x 0.009252 = $9,2525. 风险价值是指一段时间内累积的日风险收益。
V AR = DEAR x [N]½.=$9,252 x3.1623 = $29,257.39.这个公式假设收益率的冲击式独立的,即这一天发生的损失不会影响到下一天的收益,但这种假设是不严谨的。
事实上,市场上每天的变动都是相互联系的。
6. 10天的:VAR = 8,500 x [10]½ = 8,500 x 3.1623 = $26,879.3620天的V AR = 8,500 x [20]½= 8,500 x 4.4721 = $38,013.16V AR20≠ (2 x VAR10) 的原因:随着时间的推移,一件不利的事情对每天的影响是逐渐减少的。
金融机构管理第八章答案中文版
第8章利率风险I 课后习题答案(1-10)自己边做题边翻译的,仅供参考….1.利率波动程度比1979-1982年采用非借入准备金制度时显著降低。
2. 金融市场一体化加速了利率的变化,以及各个国家利率波动之间的传递;与过去相比,利率水平更难控制,不确定性也更大;另外,由于金融机构越来越全球化,任何利率水平的波动都会更迅速地引起公司额外的利率风险问题。
3. 再定价缺口指在一定时期内,需要再定价的资产价值和负债价值之间的差额,再定价即意味着面临一个新的利率。
利率敏感性意味着金融机构的管理者在改变每项资产或负债所公布的利率之前需等待的时间。
再定价模型关注净利息收入变量的潜在变化。
事实上,当利率变化时,资产和负债将被重新定价,利息收入和利息支出都将发生改变,这就是所谓的“面临一个新的利率”。
4. 期限等级是指衡量资产和负债的时间期,投资组合中的证券是否有利率敏感性取决于其再定价期限时间的长短。
再定价期限越长,到期或需要重新定价的证券就越多,利率风险就越大。
5. a.(1)再定价缺口= RSA - RSL = $200 - $100 million = +$100 million.净利息收入= ($100 million)(.01) = +$1.0 million, 或$1,000,000.(2)再定价缺口= RSA - RSL = $100 - $150 million = -$50 million.净利息收入= (-$50 million)(.01) = -$0.5 million, 或-$500,000.(3)再定价缺口= RSA - RSL = $150 - $140 million = +$10 million.净利息收入= ($10 million)(.01) = +$0.1 million, 或$100,000.b. (1)和(3)的情况下的金融机构在利率下降时面临风险(正的再定价缺口),(2)情况下的金融机构在利率上升时面临风险(负的再定价缺口)。
金融机构管理习题答案023
Chapter Twenty ThreeGeographic Diversification: InternationalChapter OutlineIntroductionGlobal and International Expansions∙U.S. Banks Abroad∙Foreign Banks in the United States∙The International Banking Act of 1978Advantages and Disadvantages of International Expansion ∙Advantages∙DisadvantagesSummary272Solutions for End-of-Chapter Questions and Problems: Chapter Twenty Three1. What are three ways in which FI can establish a global or international presence?The three most common methods are (1) selling financial services from domestic offices to foreign customers, (2) selling financial services through a branch or representative office established in the foreign customer’s country, and (3) selling financial services to a foreign customer throu gh subsidiary companies in a foreign customer’s country.2. How did the Overseas Direct Investment Control Act of 1964 assist in the growth of globalbanking activities? How much growth in foreign assets occurred from 1980 to 2003?Which types of foreign assets saw the largest amount of growth?The Overseas Direct Investment Control Act of 1964 restricted the ability of U.S. banks to lend to U.S. corporations that wanted to make investments overseas. Although later repealed, the law created incentives for U.S. banks to establish offices offshore to serve the financial needs of their U.S. corporate clients. From 1980 to 2003, foreign assets of U.S. banks grew from $354 billion to $804 billion, growth in foreign assets of 127% in 23 years. The largest dollar increase and the largest percentage increase occurred in individual loans. These numbers are affected by the slow economic activity of the first 3 years of this decade. Table 23-2 clearly shows that C&I loans had shown the largest dollar increase through the end of 2000.3. What is a Eurodollar transaction? What are Eurodollars?Eurodollars are dollar-denominated claims at foreign or U.S. banks outside the United States. The Eurodollar transaction may be a liability or an asset transaction that is booked external to the boundaries of the United States.4. Identify and explain the impact of at least four factors that have encouraged global U.S.bank expansion.First, the growth of international trade with the dollar as the primary medium of exchange has encouraged the use of U.S. foreign bank subsidiaries to assist in these trade-related transactions. Second, the U.S. banks in strategic locations, such as the Cayman Islands and the Bahamas, became preferred depositories for funds that were flowing out of politically sensitive and risky countries. Third, the Federal Reserve Bank often allowed U.S. banks to participate in activities that were permitted in foreign countries, even though those same activities may not have been permitted in the U.S. Finally, the technological improvements in communications, and the development of an international payment system (CHIPS) provided banks with the control of overseas operations at a decreasing rate.5. What is the expected impact of the implementation of the revised BIS risk-based capitalrequirements on the international activities of some major U.S. banks?Several large banks may find it necessary to increase capital because only loans to OECD countries rated above AA- will require zero risk weight or zero capital set aside.2736. What effect have the problems of emerging-market economies in the late 1990s had on theglobal expansion of traditional banking activities by U.S. banks?Many U.S. banks have become more cautious in expanding outside the traditional overseas markets even though the regulatory environment seems more favorable.7. What factors gave the Japanese banks significant advantages in competing for internationalbusiness for an extended period of time through the mid-1990s? What are the advantages of size in a competitive market? Does size necessarily imply high profitability? Japanese banks had access to a large domestic savings base at relatively low cost, enjoyed a slow pace of deregulation in their domestic markets, and were very large in asset size. The size advantage gave these banks the ability to diversify across borders and attract business by aggressively cutting fees and spreads. The size advantage of the Japanese banks deteriorated as thin margins, an economic domestic recession, and increasing nonperforming assets weakened the Japanese financial structure.8. What is the European Community (EC) Second Banking Directive? What impact has theSecond Banking Directive had on the competitive banking environment of Europe?The EC Second Banking Directive created a single banking market in Europe wherein banks could branch and acquire banks throughout the entire European Community. As a result, a significant cross-border merger wave among European banks has occurred, as well as the development of strategic alliances that allow customers to utilize any of the branches of the members of the alliances to open accounts, access account information, and make payments to third parties. These actions obviously make a more competitive environment for U.S. banks. 9. Identify and discuss the various ways that foreign banks can enter the U.S. market. Whatare international banking facilities?First, a foreign bank subsidiary can be chartered with its own capital and access to both retail and wholesale markets. Second, branch bank can be established with capital support from the parent, but with access to both the retail and wholesale markets. Third, an agency organization is restricted in its access of funds to those available in the wholesale and money markets. Fourth, Edge Act Corporations specialize in international trade-related banking transactions. Fifth, a representative office serves as a loan production office that generates loans that are booked in the home country. International Banking Facilities are allowed to take deposits from and to make loans to foreign customers only, effectively operating as offshore banking units onshore, but without the effects of U.S. bank regulation and taxes.10. What factors affected the relative growth of the proportion of U.S. banking assets that arecontrolled by foreign banks during the 1990s into 2003?Several factors have led to this decline including the highly competitive wholesale market for banking in the United States, a decline in the quality of U.S. loans, capital constraints and poor lending performance on Japanese banks at home, and the introduction of FBSEA in 1991.27411. What was the fundamental philosophical focus of the International Banking Act (IBA) of1978?The IBA of 1978 and the Foreign Bank Supervision Enhancement Act of 1991 brought the regulation of foreign banks under the control of federal regulators with the intent of treating them under the same guidelines as domestic national banks.a. What advantages and disadvantages did foreign banks have relative to domestic banksprior to the passage of this legislation?As state-licensed organizations, they were not subject to reserve requirements, audits, or exams of the Federal Reserve System, interstate branching activities, or restrictions oncorporate securities underwiritng. At the same time, the international branches did nothave access to the Federal Reserve discount window, the fed funds market (Fedwire), or to FDIC deposit insurance.b. What requirements were placed on the foreign banks by the IBA?The foreign branches were required to meet reserve requirements if their worldwide assets exceeded $1 billion, made subject to Federal Reserve examinations, and made subject to both McFadden Act interstate branching restrictions and the Glass-Steagall Act securities underwriting restrictions.c. What was the likely effect of the IBA on the growth of foreign bank activities in theUnited States? Why?Although restrictive in nature, the IBA also provided access to the discount window, the Fedwire, and FDIC insurance. Thus foreign bank activities expanded in the United States.12. What events led to the passage of the Foreign Bank Supervision Enhancement Act (FBSEA)of 1991? What was the main objective of this legislation?The primary objective of FBSEA was to extend federal regulatory authority over foreign banking organizations in the United States. The three events that served as the catalyst for this legislation were the failure of the Bank of Credit and Commerce International (BCCI), the issuance of more than $1 billion of unauthorized letters of credit to Iraq by the Atlanta branch of Banca Nazionale del Lavoro, and the unauthorized use of deposit funds by the U.S. representative office of the Greek National Mortgage Bank of New York.13. What were the main features of FBSEA? How did FBSEA encourage cooperation with thehome country regulator? What was the effect of the FBSEA on the Federal Reserve and on the foreign banks?The five main features of FBSEA are identified and discussed below:275Entry. The Fed must approve the establishment of a subsidiary, branch, agency, or representative office in the United States. The two mandatory standards are (a) thecomprehensive supervision of the foreign bank on a consolidated basis by a home country regulator, and (b) the provision by the home country regulator of all of the necessaryinformation needed by the Fed to evaluate the application.Closure. The Fed has the power to close the foreign bank if (a) the home country supervision is inadequate, (b) the bank has violated U.S. laws, and (c) the bank is engaged in unsound and unsafe banking practices.Examination. The Fed has the power to examine each office of a foreign bank, and must examine at least annually each branch or agency.Deposit taking. Only foreign subsidiaries with access to FDIC insurance are allowed to take deposits under $100,000.Activity powers. Effective December 19, 1992, state-licensed branches and agencies of foreign banks could not engage in any activity not permitted to a federal branch.Clearly the authority of the Federal Reserve over the foreign banks was increased. Further, Further, the regulatory burden and the costs of entry by foreign banks into the United States also increased.14. What are the major advantages of international expansion to FIs? Explain how eachadvantage can affect the operating performance of FIs?First, an FI can benefit from significant risk diversification, especially if the economies of the world are not perfectly integrated, or if different countries allow different banking activities. Second, an FI may benefit from economies of scale. Third, the returns from new product innovations may be larger if the market is international rather than just domestic. Fourth, the risk and cost of sources of funds both should be reduced. Fifth, FIs should be able to maintain contact with, and thus provide better service to, their international customers. Sixth, an FI may be able to reduce its regulatory burden by selectively finding those countries that have lower regulatory restrictions.15. What are the difficulties of expanding globally? How can each of these difficulties createnegative effects on the operating performance of FIs?First, the difficulties of international expansion include the higher cost of information collection and monitoring in many countries. Because the level of customer specific information may not be as readily available as in the U.S., the absolute level of lending risk may be higher. Also, coordinating different regulatory rules and guidelines will increase the cost of regulation. Second, the political risk of nationalization or expropriation may increase the costs to an FI from the loss of fixed assets to the legal recovery of deposits in U.S. courts from such action. Third, the establishment of foreign offices may have large fixed costs.276。
金融机构管理 课后习题答案.
Chapter OneWhy Are Financial Intermediaries Special?Chapter OutlineIntroductionIntermediaries’’SpecialnessFinancial Intermediaries•Information Costs•Liquidity and Price Risk•Other Special ServicesOther Aspects of Specialness•The Transmission of Monetary Policy•Credit Allocation•Intergenerational Wealth Transfers or Time Intermediation•Payment Services•Denomination IntermediationSpecialness and Regulation•Safety and Soundness Regulation•Monetary Policy Regulation•Credit Allocation Regulation•Consumer Protection Regulation•Investor Protection Regulation•Entry RegulationThe Changing Dynamics of Specialness•Trends in the United States•Future Trends•Global IssuesSummarySolutions for End-of-Chapter Questions and Problems:Chapter One1.Identify and briefly explain the five risks common to financial institutions.Default or credit risk of assets,interest rate risk caused by maturity mismatches between assets and liabilities,liability withdrawal or liquidity risk,underwriting risk,and operating cost risks.2.Explain how economic transactions between household savers of funds and corporate users of funds would occur in a world without financial intermediaries (FIs).In a world without FIs the users of corporate funds in the economy would have to approach directly the household savers of funds in order to satisfy their borrowing needs.This process would be extremely costly because of the up-front information costs faced by potential lenders. Cost inefficiencies would arise with the identification of potential borrowers,the pooling of small savings into loans of sufficient size to finance corporate activities,and the assessment of risk and investment opportunities.Moreover,lenders would have to monitor the activities of borrowers over each loan's life span.The net result would be an imperfect allocation of resources in an economy.3.Identify and explain three economic disincentives that probably would dampen the flow offunds between household savers of funds and corporate users of funds in an economic world without financial intermediaries.Investors generally are averse to purchasing securities directly because of(a)monitoring costs,(b) liquidity costs,and(c)price risk.Monitoring the activities of borrowers requires extensive time, expense,and expertise.As a result,households would prefer to leave this activity to others,and by definition,the resulting lack of monitoring would increase the riskiness of investing in corporate debt and equity markets.The long-term nature of corporate equity and debt would likely eliminate at least a portion of those households willing to lend money,as the preference of many for near-cash liquidity would dominate the extra returns which may be available.Third,the price risk of transactions on the secondary markets would increase without the information flows and services generated by high volume.4.Identify and explain the two functions in which FIs may specialize that enable the smoothflow of funds from household savers to corporate users.FIs serve as conduits between users and savers of funds by providing a brokerage function and by engaging in the asset transformation function.The brokerage function can benefit both savers and users of funds and can vary according to the firm.FIs may provide only transaction services, such as discount brokerages,or they also may offer advisory services which help reduce information costs,such as full-line firms like Merrill Lynch.The asset transformation function is accomplished by issuing their own securities,such as deposits and insurance policies that are more attractive to household savers,and using the proceeds to purchase the primary securities ofcorporations.Thus,FIs take on the costs associated with the purchase of securities.5.In what sense are the financial claims of FIs considered secondary securities,while thefinancial claims of commercial corporations are considered primary securities?How does the transformation process,or intermediation,reduce the risk,or economic disincentives,to the savers?The funds raised by the financial claims issued by commercial corporations are used to invest in real assets.These financial claims,which are considered primary securities,are purchased by FIs whose financial claims therefore are considered secondary securities.Savers who invest in the financial claims of FIs are indirectly investing in the primary securities of commercial corporations. However,the information gathering and evaluation expenses,monitoring expenses,liquidity costs,and price risk of placing the investments directly with the commercial corporation are reduced because of the efficiencies of the FI.6.Explain how financial institutions act as delegated monitors.What secondary benefitsoften accrue to the entire financial system because of this monitoring process?By putting excess funds into financial institutions,individual investors give to the FIs the responsibility of deciding who should receive the money and of ensuring that the money is utilized properly by the borrower.In this sense the depositors have delegated the FI to act as a monitor on their behalf.The FI can collect information more efficiently than individual investors.Further, the FI can utilize this information to create new products,such as commercial loans,that continually update the information pool.This more frequent monitoring process sends important informational signals to other participants in the market,a process that reduces information imperfection and asymmetry between the ultimate sources and users of funds in the economy.7.What are five general areas of FI specialness that are caused by providing various services tosectors of the economy?First,FIs collect and process information more efficiently than individual savers.Second,FIs provide secondary claims to household savers which often have better liquidity characteristics than primary securities such as equities and bonds.Third,by diversifying the asset base FIs provide secondary securities with lower price-risk conditions than primary securities.Fourth,FIs provide economies of scale in transaction costs because assets are purchased in larger amounts.Finally, FIs provide maturity intermediation to the economy which allows the introduction of additional types of investment contracts,such as mortgage loans,that are financed with short-term deposits.8.How do FIs solve the information and related agency costs when household savers investdirectly in securities issued by corporations?What are agency costs?Agency costs occur when owners or managers take actions that are not in the best interests of the equity investor or lender.These costs typically result from the failure to adequately monitor the activities of the borrower.If no other lender performs these tasks,the lender is subject to agencycosts as the firm may not satisfy the covenants in the lending agreement.Because the FI invests the funds of many small savers,the FI has a greater incentive to collect information and monitor the activities of the borrower.9.What often is the benefit to the lenders,borrowers,and financial markets in general of thesolution to the information problem provided by the large financial institutions?One benefit to the solution process is the development of new secondary securities that allow even further improvements in the monitoring process.An example is the bank loan that is renewed more quickly than long-term debt.The renewal process updates the financial and operating information of the firm more frequently,thereby reducing the need for restrictive bond covenants that may be difficult and costly to implement.10.How do FIs alleviate the problem of liquidity risk faced by investors who wish to invest inthe securities of corporations?Liquidity risk occurs when savers are not able to sell their securities on mercial banks, for example,offer deposits that can be withdrawn at any time.Yet the banks make long-term loans or invest in illiquid assets because they are able to diversify their portfolios and better monitor the performance of firms that have borrowed or issued securities.Thus individual investors are able to realize the benefits of investing in primary assets without accepting the liquidity risk of direct investment.11.How do financial institutions help individual savers diversify their portfolio risks?Whichtype of financial institution is best able to achieve this goal?Money placed in any financial institution will result in a claim on a more diversified portfolio. Banks lend money to many different types of corporate,consumer,and government customers,and insurance companies have investments in many different types of assets.Investment in a mutual fund may generate the greatest diversification benefit because of the fund’s investment in a wide array of stocks and fixed income securities.12.How can financial institutions invest in high-risk assets with funding provided by low-riskliabilities from savers?Diversification of risk occurs with investments in assets that are not perfectly positively correlated. One result of extensive diversification is that the average risk of the asset base of an FI will be less than the average risk of the individual assets in which it has invested.Thus individual investors realize some of the returns of high-risk assets without accepting the corresponding risk characteristics.13.How can individual savers use financial institutions to reduce the transaction costs ofinvesting in financial assets?By pooling the assets of many small investors,FIs can gain economies of scale in transaction costs.This benefit occurs whether the FI is lending to a corporate or retail customer,or purchasing assets in the money and capital markets.In either case,operating activities that are designed to deal in large volumes typically are more efficient than those activities designed for small volumes.14.What is maturity intermediation?What are some of the ways in which the risks of maturityintermediation are managed by financial intermediaries?If net borrowers and net lenders have different optimal time horizons,FIs can service both sectors by matching their asset and liability maturities through on-and off-balance sheet hedging activities and flexible access to the financial markets.For example,the FI can offer the relatively short-term liabilities desired by households and also satisfy the demand for long-term loans such as home mortgages.By investing in a portfolio of long-and short-term assets that have variable-and fixed-rate components,the FI can reduce maturity risk exposure by utilizing liabilities that have similar variable-and fixed-rate characteristics,or by using futures,options,swaps,and other derivative products.15.What are five areas of institution-specific FI specialness,and which types of institutions aremost likely to be the service providers?First,commercial banks and other depository institutions are key players for the transmission of monetary policy from the central bank to the rest of the economy.Second,specific FIs often are identified as the major source of finance for certain sectors of the economy.For example,S&Ls and savings banks traditionally serve the credit needs of the residential real estate market.Third, life insurance and pension funds commonly are encouraged to provide mechanisms to transfer wealth across generations.Fourth,depository institutions efficiently provide payment services to benefit the economy.Finally,mutual funds provide denomination intermediation by allowing small investors to purchase pieces of assets with large minimum sizes such as negotiable CDs and commercial paper issues.16.How do depository institutions such as commercial banks assist in the implementation andtransmission of monetary policy?The Federal Reserve Board can involve directly the commercial banks in the implementation of monetary policy through changes in the reserve requirements and the discount rate.The open market sale and purchase of Treasury securities by the Fed involves the banks in the implementation of monetary policy in a less direct manner.17.What is meant by credit allocation regulation?What social benefit is this type of regulationintended to provide?Credit allocation regulation refers to the requirement faced by FIs to lend to certain sectors of the economy,which are considered to be socially important.These may include housing and farming. Presumably the provision of credit to make houses more affordable or farms more viable leads to a more stable and productive society.18.Which intermediaries best fulfill the intergenerational wealth transfer function?What isthis wealth transfer process?Life insurance and pension funds often receive special taxation relief and other subsidies to assist in the transfer of wealth from one generation to another.In effect,the wealth transfer process allows the accumulation of wealth by one generation to be transferred directly to one or more younger generations by establishing life insurance policies and trust provisions in pension plans. Often this wealth transfer process avoids the full marginal tax treatment that a direct payment would incur.19.What are two of the most important payment services provided by financial institutions?To what extent do these services efficiently provide benefits to the economy?The two most important payment services are check clearing and wire transfer services.Any breakdown in these systems would produce gridlock in the payment system with resulting harmful effects to the economy at both the domestic and potentially the international level.20.What is denomination intermediation?How do FIs assist in this process?Denomination intermediation is the process whereby small investors are able to purchase pieces of assets that normally are sold only in large denominations.Individual savers often invest small amounts in mutual funds.The mutual funds pool these small amounts and purchase negotiable CDs which can only be sold in minimum increments of$100,000,but which often are sold in million dollar packages.Similarly,commercial paper often is sold only in minimum amounts of $250,000.Therefore small investors can benefit in the returns and low risk which these assets typically offer.21.What is negative externality?In what ways do the existence of negative externalities justifythe extra regulatory attention received by financial institutions?A negative externality refers to the action by one party that has an adverse affect on some third party who is not part of the original transaction.For example,in an industrial setting,smoke from a factory that lowers surrounding property values may be viewed as a negative externality.For financial institutions,one concern is the contagion effect that can arise when the failure of one FI can cast doubt on the solvency of other institutions in that industry.22.If financial markets operated perfectly and costlessly,would there be a need forfinancial intermediaries?To a certain extent,financial intermediation exists because of financial market imperfections.If information is available costlessly to all participants,savers would not need intermediaries to act as either their brokers or their delegated monitors.However,if there are social benefits to intermediation,such as the transmission of monetary policy or credit allocation,then FIs wouldexist even in the absence of financial market imperfections.23.What is mortgage redlining?Mortgage redlining occurs when a lender specifically defines a geographic area in which it refuses to make any loans.The term arose because of the area often was outlined on a map with a red pencil.24.Why are FIs among the most regulated sectors in the world?When is netregulatory burden positive?FIs are required to enhance the efficient operation of the economy.Successful financial intermediaries provide sources of financing that fund economic growth opportunity that ultimately raises the overall level of economic activity.Moreover,successful financial intermediaries provide transaction services to the economy that facilitate trade and wealth accumulation.Conversely,distressed FIs create negative externalities for the entire economy.That is,the adverse impact of an FI failure is greater than just the loss to shareholders and other private claimants on the FI's assets.For example,the local market suffers if an FI fails and other FIs also may be thrown into financial distress by a contagion effect.Therefore,since some of the costs of the failure of an FI are generally borne by society at large,the government intervenes in the management of these institutions to protect society's interests.This intervention takes the form of regulation.However,the need for regulation to minimize social costs may impose private costs to the firms that would not exist without regulation.This additional private cost is defined as a net regulatory burden.Examples include the cost of holding excess capital and/or excess reserves and the extra costs of providing information.Although they may be socially beneficial,these costs add to private operating costs.To the extent that these additional costs help to avoid negative externalities and to ensure the smooth and efficient operation of the economy,the net regulatory burden is positive.25.What forms of protection and regulation do regulators of FIs impose to ensuretheir safety and soundness?Regulators have issued several guidelines to insure the safety and soundness of FIs:a.FIs are required to diversify their assets.For example,banks cannot lend morethan10percent of their equity to a single borrower.b.FIs are required to maintain minimum amounts of capital to cushion anyunexpected losses.In the case of banks,the Basle standards require a minimum core and supplementary capital of8percent of their risk-adjusted assets.c.Regulators have set up guaranty funds such as BIF for commercial banks,SIPCfor securities firms,and state guaranty funds for insurance firms to protectindividual investors.d.Regulators also engage in periodic monitoring and surveillance,such as on-siteexaminations,and request periodic information from the FIs.26.In the transmission of monetary policy,what is the difference between insidemoney and outside money?How does the Federal Reserve Board try to control the amount of inside money?How can this regulatory position create a cost for the depository financial institutions?Outside money is that part of the money supply directly produced and controlled by the Fed,for example,coins and currency.Inside money refers to bank deposits not directly controlled by the Fed.The Fed can influence this amount of money by reserve requirement and discount rate policies.In cases where the level of required reserves exceeds the level considered optimal by the FI,the inability to use the excess reserves to generate revenue may be considered a tax or cost of providing intermediation.27.What are some examples of credit allocation regulation?How can this attemptto create social benefits create costs to the private institution?The qualified thrift lender test(QTL)requires thrifts to hold65percent of their assets in residential mortgage-related assets to retain the thrift charter.Some states have enacted usury laws that place maximum restrictions on the interest rates that can be charged on mortgages and/or consumer loans. These types of restrictions often create additional operating costs to the FI and almost certainly reduce the amount of profit that could be realized without such regulation.28.What is the purpose of the Home Mortgage Disclosure Act?What are thesocial benefits desired from the legislation?How does the implementation of this legislation create a net regulatory burden on financial institutions?The HMDA was passed by Congress to prevent discrimination in mortgage lending.The social benefit is to ensure that everyone who qualifies financially is provided the opportunity to purchase a house should they so desire.The regulatory burden has been to require a written statement indicating the reasons why credit was or was not granted.Since1990,the federal regulators have examined millions of mortgage transactions from more than7,700institutions each calendar quarter.29.What legislation has been passed specifically to protect investors who use investment banksdirectly or indirectly to purchase securities?Give some examples of the types of abuses for which protection is provided.The Securities Acts of1933and1934and the Investment Company Act of1940were passed byCongress to protect investors against possible abuses such as insider trading,lack of disclosure, outright malfeasance,and breach of fiduciary responsibilities.30.How do regulations regarding barriers to entry and the scope of permitted activities affectthe charter value of financial institutions?The profitability of existing firms will be increased as the direct and indirect costs of establishing competition increase.Direct costs include the actual physical and financial costs of establishing a business.In the case of FIs,the financial costs include raising the necessary minimum capital to receive a charter.Indirect costs include permission from regulatory authorities to receive a charter. Again in the case of FIs this cost involves acceptable leadership to the regulators.As these barriers to entry are stronger,the charter value for existing firms will be higher.31.What reasons have been given for the growth of investment companies at the expense of“traditional”banks and insurance companies?The recent growth of investment companies can be attributed to two major factors: a.Investors have demanded increased access to direct securities markets.Investment companies and pension funds allow investors to take positions indirect securities markets while still obtaining the risk diversification,monitoring, and transactional efficiency benefits of financial intermediation.Some experts would argue that this growth is the result of increased sophistication on the part of investors;others would argue that the ability to use these markets has caused the increased investor awareness.The growth in these assets is inarguable.b.Recent episodes of financial distress in both the banking and insuranceindustries have led to an increase in regulation and governmental oversight,thereby increasing the net regulatory burden of“traditional”companies.Assuch,the costs of intermediation have increased,which increases the cost ofproviding services to customers.32.What are some of the methods which banking organizations have employed to reduce the netregulatory burden?What has been the effect on profitability?Through regulatory changes,FIs have begun changing the mix of business products offered to individual users and providers of funds.For example,banks have acquired mutual funds,have expanded their asset and pension fund management businesses,and have increased the security underwriting activities.In addition,legislation that allows banks to establish branches anywhere in the United States has caused a wave of mergers.As the size of banks has grown,an expansion of possible product offerings has created the potential for lower service costs.Finally,the emphasis in recent years has been on products that generate increases in fee income,and the entire banking industry has benefited from increased profitability in recent years.33.What characteristics of financial products are necessary for financial markets to becomeefficient alternatives to financial intermediaries?Can you give some examples of the commoditization of products which were previously the sole property of financial institutions?Financial markets can replace FIs in the delivery of products that(1)have standardized terms,(2) serve a large number of customers,and(3)are sufficiently understood for investors to be comfortable in assessing their prices.When these three characteristics are met,the products often can be treated as commodities.One example of this process is the migration of over-the-counter options to the publicly traded option markets as trading volume grows and trading terms become standardized.34.In what way has Regulation144A of the Securities and Exchange Commission provided anincentive to the process of financial disintermediation?Changing technology and a reduction in information costs are rapidly changing the nature of financial transactions,enabling savers to access issuers of securities directly. Section144A of the SEC is a recent regulatory change that will facilitate the process of disintermediation.The private placement of bonds and equities directly by the issuing firm is an example of a product that historically has been the domain of investment bankers.Although historically private placement assets had restrictions against trading,regulators have given permission for these assets to trade among large investors who have assets of more than$100million.As the market grows,this minimum asset size restriction may be reduced.Chapter TwoThe Financial Services Industry:Depository InstitutionsChapter OutlineIntroductionCommercial Banks•Size,Structure,and Composition of the Industry•Balance Sheet and Recent Trends•Other Fee-Generating Activities•Regulation•Industry PerformanceSavings Institutions•Savings Associations(SAs)•Savings Banks•Recent Performance of Savings Associations and Savings BanksCredit Unions•Size,Structure,and Composition of the Industry and Recent Trends•Balance Sheets•Regulation•Industry PerformanceGlobal Issues:Japan,China,and GermanySummaryAppendix2A:Financial Statement Analysis Using a Return on Equity(ROE) FrameworkAppendix2B:Depository Institutions and Their RegulatorsAppendix3B:Technology in Commercial BankingSolutions for End-of-Chapter Questions and Problems:Chapter Two1.What are the differences between community banks,regional banks,and money-center banks?Contrast the business activities,location,and markets of each of these bank groups.Community banks typically have assets under$1billion and serve consumer and small business customers in local markets.In2003,94.5percent of the banks in the United States were classified as community banks.However,these banks held only 14.6percent of the assets of the banking industry.In comparison with regional and money-center banks,community banks typically hold a larger percentage of assets in consumer and real estate loans and a smaller percentage of assets in commercial and industrial loans.These banks also rely more heavily on local deposits and less heavily on borrowed and international funds.Regional banks range in size from several billion dollars to several hundred billion dollars in assets.The banks normally are headquartered in larger regional cities and often have offices and branches in locations throughout large portions of the United States.Although these banks provide lending products to large corporate customers, many of the regional banks have developed sophisticated electronic and branching services to consumer and residential customers.Regional banks utilize retail deposit bases for funding,but also develop relationships with large corporate customers and international money centers.Money center banks rely heavily on nondeposit or borrowed sources of funds.Some of these banks have no retail branch systems,and most regional banks are major participants in foreign currency markets.These banks compete with the larger regional banks for large commercial loans and with international banks for international commercial loans.Most money center banks have headquarters in New York City.e the data in Table2-4for the banks in the two asset size groups(a)$100million-$1billion and(b)over$10billion to answer the following questions.a.Why have the ratios for ROA and ROE tended to increase for both groupsover the1990-2003period?Identify and discuss the primary variables thataffect ROA and ROE as they relate to these two size groups.The primary reason for the improvements in ROA and ROE in the late1990smay be related to the continued strength of the macroeconomy that allowedbanks to operate with a reduced regard for bad debts,or loan charge-offproblems.In addition,the continued low interest rate environment hasprovided relatively low-cost sources of funds,and a shift toward growth in fee income has provided additional sources of revenue in many product lines.。
风险管理与金融机构第二版课后习题答案
第六章交易组合价值减少10500美元。
一个交易组合的Vega是指交易组合价格变化与基础资产价格波动率变化的比率,所以当波动率变化2%时,交易组合价格增长200×2=400美元。
两种情形下的增长量均为*30*4=60美元Delta= 意味着在股票价格增加一个小的数量时,期权价格的上涨大约是股价增长的70%,同时当股价下跌一个小的数量时,期权价格的下跌大约是股价下跌的70%。
1000 份期权短头寸的Delta 等于-700,可以通过买入700 份股票的形式使交易组合达到Delta 中性。
的含义是在其他条件不变的情况下,交易组合的价值变化与时间变化的比率。
Theta为-100的含义是指在股价与波动率没有变化的情况下,期权价格每天下降100美元。
假如交易员认为股价及隐含波动率在将来不会改变,交易员可以卖出期权,并且Theta值越高越好。
答:期权的Gamma是期权的Delta同基础资产价格变化的比率,可视为期权价格和对基础资产价格的二阶偏导数。
当一个期权承约人的Gamma绝对值较大,Gamma本身为负,并且Delta等于0,在市场变化率较大的情况下,期权承约人会有较大损失。
为了对冲期权风险,我们有必要构造相反方向的合成期权交易,例如,为了对冲看跌期权长头寸,我们应该构造合成看跌期权的短头寸,构造人为期权交易的过程就是对冲期权风险的反过程。
看涨及看跌期权的长头寸都具备正的Gamma,由图可以看出,当Gamma为正时,对冲人在股票价格变化较大时会有收益,而在股票价格变化较小时会有损失,因此对冲人在(b)情形收益更好,当交易组合包含期权的短头寸时,对冲人在(a)情形收益会更好。
Delta的数值说明当欧元汇率增长时,银行交易价格会增加*30000=300美元,Gamma的数值说明,当欧元价格增长时,银行交易组合的Delta会下降*80000=800美元,为了做到Delta中性,我们应该卖出30000欧元,当汇率增长到时,我们期望交易组合的Delta下降为()*80000=24000,组合价值变为27600。
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Chapter TwoThe Financial Services Industry: Depository InstitutionsChapter OutlineIntroductionCommercial Banks∙Size, Structure, and Composition of the Industry∙Balance Sheet and Recent Trends∙Other Fee-Generating Activities∙Regulation∙Industry PerformanceSavings Institutions∙Savings Associations (SAs)∙Savings Banks∙Recent Performance of Savings Associations and Savings BanksCredit Unions∙Size, Structure, and Composition of the Industry and Recent Trends∙Balance Sheets∙Regulation∙Industry PerformanceGlobal Issues: Japan, China, and GermanySummaryAppendix 2A: Financial Statement Analysis Using a Return on Equity (ROE) Framework Appendix 2B: Depository Institutions and Their RegulatorsAppendix 3B: Technology in Commercial BankingSolutions for End-of-Chapter Questions and Problems: Chapter Two1.What are the differences between community banks, regional banks, and money-centerbanks? Contrast the business activities, location, and markets of each of these bank groups. Community banks typically have assets under $1 billion and serve consumer and small business customers in local markets. In 2003, 94.5 percent of the banks in the United States were classified as community banks. However, these banks held only 14.6 percent of the assets of the banking industry. In comparison with regional and money-center banks, community banks typically hold a larger percentage of assets in consumer and real estate loans and a smaller percentage of assets in commercial and industrial loans. These banks also rely more heavily on local deposits and less heavily on borrowed and international funds.Regional banks range in size from several billion dollars to several hundred billion dollars in assets. The banks normally are headquartered in larger regional cities and often have offices and branches in locations throughout large portions of the United States. Although these banks provide lending products to large corporate customers, many of the regional banks have developed sophisticated electronic and branching services to consumer and residential customers. Regional banks utilize retail deposit bases for funding, but also develop relationships with large corporate customers and international money centers.Money center banks rely heavily on nondeposit or borrowed sources of funds. Some of these banks have no retail branch systems, and most regional banks are major participants in foreign currency markets. These banks compete with the larger regional banks for large commercial loans and with international banks for international commercial loans. Most money center banks have headquarters in New York City.e the data in Table 2-4 for the banks in the two asset size groups (a) $100 million-$1billion and (b) over $10 billion to answer the following questions.a. Why have the ratios for ROA and ROE tended to increase for both groups over the1990-2003 period? Identify and discuss the primary variables that affect ROA andROE as they relate to these two size groups.The primary reason for the improvements in ROA and ROE in the late 1990s may berelated to the continued strength of the macroeconomy that allowed banks to operate with a reduced regard for bad debts, or loan charge-off problems. In addition, the continued low interest rate environment has provided relatively low-cost sources of funds, and a shifttoward growth in fee income has provided additional sources of revenue in many product lines. Finally, a growing secondary market for loans has allowed banks to control the size of the balance sheet by securitizing many assets. You will note some variance inperformance in the last three years as the effects of a softer economy were felt in thefinancial industry.b. Why is ROA for the smaller banks generally larger than ROA for the large banks?Small banks historically have benefited from a larger spread between the cost rate of funds and the earning rate on assets, each of which is caused by the less severe competition in the localized markets. In addition, small banks have been able to control credit risk moreefficiently and to operate with less overhead expense than large banks.c. Why is the ratio for ROE consistently larger for the large bank group?ROE is defined as net income divided by total equity, or ROA times the ratio of assets to equity. Because large banks typically operate with less equity per dollar of assets, netincome per dollar of equity is larger.d. Using the information on ROE decomposition in Appendix 2A, calculate the ratio ofequity-to-total-assets for each of the two bank groups for the period 1990-2003. Whyhas there been such dramatic change in the values over this time period, and why isthere a difference in the size of the ratio for the two groups?ROE = ROA x (Total Assets/Equity)Therefore, (Equity/Total Assets) = ROA/ROE$100 million - $1 Billion Over $10 BillionYear ROE ROA TA/Equity Equity/TA ROE ROA TA/Equity Equity/TA1990 9.95% 0.78% 12.76 7.84% 6.68% 0.38% 17.58 5.69%1995 13.48% 1.25% 10.78 9.27% 15.60% 1.10% 14.18 7.05%1996 13.63% 1.29% 10.57 9.46% 14.93% 1.10% 13.57 7.37%1997 14.50% 1.39% 10.43 9.59% 15.32% 1.18% 12.98 7.70%1998 13.57% 1.31% 10.36 9.65% 13.82% 1.08% 12.80 7.81%1999 14.24% 1.34% 10.63 9.41% 15.97% 1.28% 12.48 8.02%2000 13.56% 1.28% 10.59 9.44% 14.42% 1.16% 12.43 8.04%2001 12.24% 1.20% 10.20 9.80% 13.43% 1.13% 11.88 8.41%2002 12.85% 1.26% 10.20 9.81% 15.06% 1.32% 11.41 8.76%2003 12.80% 1.27% 10.08 9.92% 16.32% 1.42% 11.49 8.70% The growth in the equity to total assets ratio has occurred primarily because of theincreased profitability of the entire banking industry and the encouragement of theregulators to increase the amount of equity financing in the banks. Increased fee income, reduced loan loss reserves, and a low, stable interest rate environment have produced the increased profitability which in turn has allowed banks to increase equity through retained earnings.Smaller banks tend to have a higher equity ratio because they have more limited assetgrowth opportunities, generally have less diverse sources of funds, and historically have had greater profitability than larger banks.3.What factors have caused the decrease in loan volume relative to other assets on thebalance sheets of commercial banks? How has each of these factors been related to the change and development of the financial services industry during the 1990s and early2000s? What strategic changes have banks implemented to deal with changes in thefinancial services environment?Corporations have utilized the commercial paper markets with increased frequency rather than borrow from banks. In addition, many banks have sold loan packages directly into the capital markets (securitization) as a method to reduce balance sheet risks and to improve liquidity. Finally, the decrease in loan volume during the early 1990s and early 2000s was due in part to the recession in the economy.As deregulation of the financial services industry continued during the 1990s, the position of banks as the primary financial services provider continued to erode. Banks of all sizes have increased the use of off-balance sheet activities in an effort to generate additional fee income. Letters of credit, futures, options, swaps and other derivative products are not reflected on the balance sheet, but do provide fee income for the banks.4.What are the major uses of funds for commercial banks in the United States? What are theprimary risks to the bank caused by each use of funds? Which of the risks is most critical to the continuing operation of the bank?Loans and investment securities continue to be the primary assets of the banking industry. Commercial loans are relatively more important for the larger banks, while consumer, small business loans, and residential mortgages are more important for small banks. Each of these types of loans creates credit, and to varying extents, liquidity risks for the banks. The security portfolio normally is a source of liquidity and interest rate risk, especially with the increased use of various types of mortgage backed securities and structured notes. In certain environments, each of these risks can create operational and performance problems for a bank.5.What are the major sources of funds for commercial banks in the United States? How isthe landscape for these funds changing and why?The primary sources of funds are deposits and borrowed funds. Small banks rely more heavily on transaction, savings, and retail time deposits, while large banks tend to utilize large, negotiable time deposits and nondeposit liabilities such as federal funds and repurchase agreements. The supply of nontransaction deposits is shrinking, because of the increased use by small savers of higher-yielding money market mutual funds,6. What are the three major segments of deposit funding? How are these segments changingover time? Why? What strategic impact do these changes have on the profitable operation of a bank?Transaction accounts include deposits that do not pay interest and NOW accounts that pay interest. Retail savings accounts include passbook savings accounts and small, nonnegotiable time deposits. Large time deposits include negotiable certificates of deposits that can be resold in the secondary market. The importance of transaction and retail accounts is shrinking due to the direct investment in money market assets by individual investors. The changes in the deposit markets coincide with the efforts to constrain the growth on the asset side of the balance sheet.7. How does the liability maturity structure of a bank’s balance sheet compare with thematurity structure of the asset portfolio? What risks are created or intensified by thesedifferences?Deposit and nondeposit liabilities tend to have shorter maturities than assets such as loans. The maturity mismatch creates varying degrees of interest rate risk and liquidity risk.8. The following balance sheet accounts have been taken from the annual report for a U.S.bank. Arrange the accounts in balance sheet order and determine the value of total assets.Based on the balance sheet structure, would you classify this bank as a community bank, regional bank, or a money center bank?Assets Liabilities and EquityCash $ 2,660 Demand deposits $ 5,939Fed funds sold $ 110 NOW accounts $12,816Investment securities $ 5,334 Savings deposits $ 3,292Net loans $29,981 Certificates of deposit $ 9,853Intangible assets $ 758 Other time deposits $ 2,333Other assets $ 1,633 Short-term Borrowing $ 2,080Premises $ 1,078 Other liabilities $ 778Total assets $41,554 Long-term debt $ 1,191Equity $ 3,272Total liab. and equity $41,554This bank has funded the assets primarily with transaction and savings deposits. The certificates of deposit could be either retail or corporate (negotiable). The bank has very little ( 5 percent) borrowed funds. On the asset side, about 72 percent of total assets is in the loan portfolio, but there is no information about the type of loans. The bank actually is a small regional bank with $41.5 billion in assets, but the asset structure could easily be a community bank with $41.5 million in assets.9.What types of activities normally are classified as off-balance-sheet (OBS) activities?Off-balance-sheet activities include the issuance of guarantees that may be called into play at a future time, and the commitment to lend at a future time if the borrower desires.a. How does an OBS activity move onto the balance sheet as an asset or liability?The activity becomes an asset or a liability upon the occurrence of a contingent event,which may not be in the control of the bank. In most cases the other party involved with the original agreement will call upon the bank to honor its original commitment.b.What are the benefits of OBS activities to a bank?The initial benefit is the fee that the bank charges when making the commitment. If the bank is required to honor the commitment, the normal interest rate structure will apply to the commitment as it moves onto the balance sheet. Since the initial commitment does notappear on the balance sheet, the bank avoids the need to fund the asset with either deposits or equity. Thus the bank avoids possible additional reserve requirement balances anddeposit insurance premiums while improving the earnings stream of the bank.c.What are the risks of OBS activities to a bank?The primary risk to OBS activities on the asset side of the bank involves the credit risk of the borrower. In many cases the borrower will not utilize the commitment of the bank until the borrower faces a financial problem that may alter the credit worthiness of the borrower.Moving the OBS activity to the balance sheet may have an additional impact on the interest rate and foreign exchange risk of the bank.e the data in Table 2-6 to answer the following questions.a.What was the average annual growth rate in OBS total commitments over the periodfrom 1992-2003?$78,035.6 = $10,200.3(1+g)11 g = 20.32 percentb.Which categories of contingencies have had the highest annual growth rates?Category of Contingency or Commitment Growth RateCommitments to lend 14.04%Future and forward contracts 15.13%Notional amount of credit derivatives 52.57%Standby contracts and other option contracts 56.39%Commitments to buy FX, spot, and forward 3.39%Standby LCs and foreign office guarantees 7.19%Commercial LCs -1.35%Participations in acceptances -6.11%Securities borrowed 20.74%Notional value of all outstanding swaps 31.76%Standby contracts and other option contracts have grown at the fastest rate of 56.39 percent, and they have an outstanding balance of $214,605.3 billion. The rate of growth in thecredit derivatives area has been the second strongest at 52.57 percent, the dollar volumeremains fairly low at $1,001.2 billion at year-end 2003. Interest rate swaps grew at anannual rate of 31.76 percent with a change in dollar value of $41,960.7 billion. Clearly the strongest growth involves derivative areas.c.What factors are credited for the significant growth in derivative securities activities bybanks?The primary use of derivative products has been in the areas of interest rate, credit, andforeign exchange risk management. As banks and other financial institutions have pursuedthe use of these instruments, the international financial markets have responded byextending the variations of the products available to the institutions.11. For each of the following banking organizations, identify which regulatory agencies (OCC,FRB, FDIC, or state banking commission) may have some regulatory supervisionresponsibility.(a) State-chartered, nonmember, nonholding-company bank.(b)State-chartered, nonmember holding-company bank(c) State-chartered member bank(d)Nationally chartered nonholding-company bank.(e)Nationally chartered holding-company bankBank Type OCC FRB FDIC SBCom.(a) Yes Yes(b) Yes Yes Yes(c) Yes Yes Yes(d) Yes Yes Yes(e) Yes Yes Yes12. What factors normally are given credit for the revitalization of the banking industry duringthe decade of the 1990s? How is Internet banking expected to provide benefits in thefuture?The most prominent reason was the lengthy economic expansion in both the U.S. and many global economies during the entire decade of the 1990s. This expansion was assisted in the U.S. by low and falling interest rates during the entire period.The extent of the impact of Internet banking remains unknown. However, the existence of this technology is allowing banks to open markets and develop products that did not exist prior to the Internet. Initial efforts have focused on retail customers more than corporate customers. The trend should continue with the advent of faster, more customer friendly products and services, and the continued technology education of customers.13. What factors are given credit for the strong performance of commercial banks in the early2000s?The lowest interest rates in many decades helped bank performance on both sides of the balance sheet. On the asset side, many consumers continued to refinance homes and purchase new homes, an activity that caused fee income from mortgage lending to increase and remain strong. Meanwhile, the rates banks paid on deposits shrunk to all-time lows. In addition, the development and more comfortable use of new financial instruments such as credit derivatives and mortgage backed securities helped banks ease credit risk off the balance sheets. Finally, information technology has helped banks manage their risk more efficiently.14. What are the main features of the Riegle-Neal Interstate Banking and Branching EfficiencyAct of 1994? What major impact on commercial banking activity is expected from this legislation?The main feature of the Riegle-Neal Act of 1994 was the removal of barriers to inter-state banking. In September 1995 bank holding companies were allowed to acquire banks in other states. In 1997, banks were allowed to convert out-of-state subsidiaries into branches of a single interstate bank. As a result, consolidations and acquisitions have allowed for the emergence of very large banks with branches across the country.15. What happened in 1979 to cause the failure of many savings associations during the early1980s? What was the effect of this change on the operating statements of savingsassociations?The Federal Reserve changed its reserve management policy to combat the effects of inflation, a change which caused the interest rates on short-term deposits to increase dramatically more than the rates on long-term mortgages. As a result, the marginal cost of funds exceeded the average yield on assets that caused a negative interest spread for the savings associations. Further, because savings associations were constrained by Regulation Q on the amount of interest which could be paid on deposits, they suffered disintermediation, or deposit withdrawals, which led to severe liquidity pressures on the balance sheets.16. How did the two pieces of regulatory legislation, the DIDMCA in 1980 and the DIA in1982, change the operating profitability of savings associations in the early 1980s? What impact did these pieces of legislation ultimately have on the risk posture of the savingsassociation industry? How did the FSLIC react to this change in operating performance and risk?The two pieces of legislation allowed savings associations to offer new deposit accounts, such as NOW accounts and money market deposit accounts, in an effort to reduce the net withdrawal flow of deposits from the institutions. In effect this action was an attempt to reduce the liquidity problem. In addition, the savings associations were allowed to offer adjustable-rate mortgages and a limited amount of commercial and consumer loans in an attempt to improve the profitability performance of the industry. Although many savings associations were safer, more diversified, and more profitable, the FSLIC did not foreclose many of the savings associations which were insolvent. Nor did the FSLIC change its policy of assessing higher insurance premiums on companies that remained in high risk categories. Thus many savings associations failed, which caused the FSLIC to eventually become insolvent.17. How do the asset and liability structures of a savings association compare with the assetand liability structures of a commercial bank? How do these structural differences affect the risks and operating performance of a savings association? What is the QTL test?The savings association industry relies on mortgage loans and mortgage-backed securities as the primary assets, while the commercial banking industry has a variety of loan products, including mortgage products. The large amount of longer-term fixed rate assets continues to cause interestrate risk, while the lack of asset diversity exposes the savings association to credit risk. Savings associations hold considerably less cash and U.S. Treasury securities than do commercial banks. On the liability side, small time and saving deposits remain as the predominant source of funds for savings associations, with some reliance on FHLB borrowing. The inability to nurture relationships with the capital markets also creates potential liquidity risk for the savings association industry.The acronym QTL stands for Qualified Thrift Lender. The QTL test refers to a minimum amount of mortgage-related assets that a savings association must hold. The amount currently is 65 percent of total assets.18. How do savings banks differ from savings and loan associations? Differentiate in terms ofrisk, operating performance, balance sheet structure, and regulatory responsibility.The asset structure of savings banks is similar to the asset structure of savings associations with the exception that savings banks are allowed to diversify by holding a larger proportion of corporate stocks and bonds. Savings banks rely more heavily on deposits and thus have a lower level of borrowed funds. The banks are regulated at both the state and federal level, with deposits insured by t he FDIC’s BIF.19. How did the Financial Institutions Reform, Recovery, and Enforcement Act (FIRREA) of1989 and the Federal Deposit Insurance Corporation Improvement Act of 1991 reversesome of the key features of earlier legislation?FIRREA rescinded some of the expanded thrift lending powers of the DIDMCA of 1980 and the Garn-St Germain Act of 1982 by instituting the qualified thrift lender (QTL) test that requires that all thrifts must hold portfolios that are comprised primarily of mortgages or mortgage products such as mortgage-backed securities. The act also required thrifts to divest their portfolios of junk bonds by 1994, and it replaced the FSLIC with a new thrift deposit insurance fund, the Savings Association Insurance Fund, which was managed by the FDIC.The FDICA of 1991 amended the DIDMCA of 1980 by introducing risk-based deposit insurance premiums in 1993 to reduce excess risk-taking. FDICA also provided for the implementation of a policy of prompt corrective actions (PCA) that allows regulators to close banks more quickly in cases where insolvency is imminent. Thus the ill-advised policy of regulatory forbearance should be curbed. Finally, the act amended the International Banking Act of 1978 by expanding the regulatory oversight powers over foreign banks.20. What is the “common bond” membership qualification under which credit unions havebeen formed and operated? How does this qualification affect the operational objective ofa credit union?The common bond policy allows any one who meets a specific membership requirement to become a member of the credit union. The requirement normally is tied to a place of employment. Because the common bond policy has been loosely interpreted, implementation has allowed credit union membership and assets to grow at a rate that exceeds similar growth inthe commercial banking industry. Since credit unions are mutual organizations where the members are owners, employees essentially use saving deposits to make loans to other employees who need funds.21. What are the operating advantages of credit unions that have caused concern bycommercial bankers? What has been the response of the Credit Union NationalAssociation to the bank criticisms?Credit unions are tax-exempt organizations that often are provided office space by employers at no cost. As a result, because non-interest operating costs are very low, credit unions can lend money at lower rates and pay higher rates on savings deposits than can commercial banks. CUNA has responded that the cost to tax payers from the tax-exempt status is replaced by the additional social good created by the benefits to the members.22. How does the asset structure of credit unions compare with the asset structure ofcommercial banks and savings and loan associations? Refer to Tables 2-5, 2-9, and 2-12 to formulate your answer.The relative proportions of credit union assets are more similar to commercial banks than savings associations, with 20 percent in investment securities and 63 percent in loans. However, nonmortgage loans of credit unions are predominantly consumer loans. On the liability side of the balance sheet, credit unions differ from banks in that they have less reliance on large time deposits, and they differ from savings associations in that they have virtually no borrowings from any source. The primary sources of funds for credit unions are transaction and small time and savings accounts.23. Compare and contrast the performance of the U.S. depository institution industry withthose of Japan, China, and Germany.The entire Japanese financial system was under increasing pressure from the early 1990s as the economy suffered from real estate and other commercial industry pressures. The Japanese government has used several financial aid packages in attempts to avert a collapse of the Japanese financial system. Most attempts have not been successful.The deterioration in the banking industry in China in the early 2000s was caused by nonperforming loans and credits. The remedies include the opportunity for more foreign bank ownership in the Chinese banking environment primarily via larger ownership positions, less restrictive capital requirements for branches, and increased geographic presence.German banks also had difficulties in the early 2000s, but the problems were not universal. The large banks suffered from credit problems, but the small banks enjoyed high credit ratings and low cast of funds because of government guarantees on their borrowing. Thus while small banks benefited from growth in small business lending, the large banks became reliant on fee and trading income.。