金融机构风险管理练习题1

1.What is the process of asset transformation performed by a financial institution? Whydoes this process often lead to the creation of interest rate risk? What is interest rate risk?Asset transformation by an FI involves purchasing primary assets and issuing secondary assets as a source of funds. The primary securities purchased by the FI often have maturity and liquidity characteristics that are different from the secondary securities issued by the FI. For example, a bank buys medium- to long-term bonds and makes medium-term l oans with funds raised by issuing short-term deposits.Interest rate risk occurs because the prices and reinvestment income characteristics oflong-term assets react differently to changes in market interest rates than the prices and interest expense characteristics of short-term deposits. Interest rate risk is the risk incurred by an FI when the maturities of its assets and liabilities are mismatched.2.The sales literature of a mutual fund claims that the fund has no riskexposure since it invests exclusively in federal government securities that are free of default risk. Is this claim true? Explain why or why not. Although the fund's asset portfolio is comprised of securities with no default risk, the securities are exposed to interest rate risk. For example, if interest rates increase, the market value of the fund's Treasury security portfolio will decrease. Further, if interest rates decrease, the realized yield on these securities will be less than the expected rate of return because of reinvestment risk. In either case, investors who liquidate their positions in the fund may sell at a Net Asset Value (NAV) that is lower than the purchase price.3. What is market risk? How do the results of this risk surface in the operating performanceof financial institutions? What actions can be taken by FI management to minimize the effects of this risk?Market risk is the risk incurred from assets and liabilities in an FI’s trading book due to changes in interest rates, exchange rates, and other prices. Market risk affects any firm that trades assets and liabilities. The risk can surface because of changes in interest rates, exchange rates, or any other prices of financial assets that are traded rather than held on the balance sheet. Market risk can be minimized by using appropriate hedging techniques such as futures, options, and swaps, and by implementing controls that limit the amount of exposure taken by market makers.4. What is credit risk? Which types of FIs are more susceptibl e to this type of risk?Why?Credit risk is the risk that promised cash flows from loans and securities held by FIs may not be paid in full. FIs that lend money for long periods of time, whether as loans or by buying bonds, are more susceptible to this risk than those FIs that have short investment horizons. For example, life insurance companies and depository institutions generally must wait a longer time for returns to be realized than money market mutual funds and property-casualty insurance companies.5. What is foreign exchange risk? What does it mean for an FI to be net long in foreignassets? What d oes it mean for an FI to be net short in foreign assets? In each case, what must happen to the foreign exchange rate to cause the FI to suffer losses? Foreign e xchange risk is the risk that exchange rate changes can affect the value of an FI’s assets and liabilities denominated in non-domestic currencies. An FI is net long inforeign assets when the foreign currency-denominated assets exceed the foreigncurrency denominated liabilities. In this case, an FI will suffer potential losses if thedomestic currency strengthens relative to the foreign currency when repayment ofthe assets will occur in the foreign currency. An FI is net short in foreign assetswhen the foreign currency-denominated liabilities exceed the foreign currencydenominated assets. In this case, an FI will suffer potential losses if the domesticcurrency weakens relative to the foreign currency when repayment of the liabilitieswill occur in the domestic currency.6. What is the repricing gap? In using this model to evaluate interest rate risk, what is meantby rate sensitivity? On what financial performance variable does the repricing modelfocus? Explain.The repricing gap is a measure of the difference between the dollar value of assetsthat will reprice and the dollar value of liabilities that will reprice within a specifictime period, where reprice means the potential to receive a new interest rate. Rate sensitivity represents the time interval where repricing can occur. The modelfocuses on the potential changes in the net interest income variable. In effect, if interest rates change, interest income and interest expense will change as the various assets and liabilities are repriced, that is, receive new interest rates.e the following information about a hypothetical government security dealer named M.P. Jorgan. Marketyields are in parenthesis, and amounts are in millions. 8.11Assets Liabilities and EquityCash $10 Overnight Repos $1701 month T-bills (7.05%) 75 Subordinated debt3 month T-bills (7.25%) 75 7-year fixed rate (8.55% 1502 year T-notes (7.50%) 508 year T-notes (8.96%) 1005 year munis (floating rate)(8.20% reset every 6 months) 25 Equity 15Total Assets $335 Total Liabilities & Equity $335a. What is the funding or repricing gap if the planning period is 30 days? 91 days?2 years? Recall that cash is a noninterest-earning asset.Funding or repricing gap using a 30-day planning period = 75 - 170 = -$95million.Funding gap using a 91-day planning period = (75 + 75) - 170 = -$20 million.Funding gap using a two-year planning period = (75 + 75 + 50 + 25) - 170 =+$55 million.b. What is the impact over the next 30 days on net interest income if all interestrates rise 50 basis points? Decrease 75 basis points?Net interest income will decline by $475,000. ∆NII = FG(∆R) = -95(.005) = $0.475m.Net interest income will increase by $712,500. ∆NII = FG(∆R) = -95(.0075) = $0.7125m.c.The following one-year runoffs are expected: $10 million for two-yearT-notes, and $20 million for eight-year T-notes. What is the one-yearrepricing gap?Funding or repricing gap over the 1-year planning period = (75 + 75 + 10 + 20 +25) - 170 = +$35 million.d. If runoffs are considered, what is the effect on net interest income atyear-end if interest rates rise 50 basis points? Decrease 75 basis points?Net interest income will increase by $175,000. ∆NII = FG(∆R) = 35(0.005) = $0.175m.Net interest income will decrease by $262,500, ∆NII = FG(∆R) = 35(-0.0075) = -$0.2625m.8. Consumer Bank has $20 million in cash and a $180 million loan portfolio. Theassets are funded with demand deposits of $18 million, a $162 million CD and $20 million in equity. The loan portfolio has a maturity of 2 years, earnsinterest at the annual rate of 7 percent, and is amortized monthly. The bankpays 7 percent annual interest on the CD, but the interest will not be paid until the CD matures at the end of 2 years.a. What is the maturity gap for Consumer Bank?M A = [0*$20 + 2*$180]/$200 = 1.80 yearsM L = [0*$18 + 2*$162]/$180 = 1.80 yearsMGAP = 1.80 – 1.80 = 0 years.b. Is Consumer Bank immunized or protected against changes in interest rates?Why or why not?It is tempting to conclude that the bank is immunized because the maturity gap is zero. However, the cash flow stream for the loan and the cash flow stream for the CD are different because the loan amortizes monthly and the CD paysannual interest on the CD. Thus any change in interest rates will affect theearning power of the loan more than the interest cost of the CD.c. Does Consumer Bank face interest rate risk? That is, if market interestrates increase or decrease 1 percent, what happens to the value of the equity?The bank does face interest rate risk. If market rates increase 1 percent, thevalue of the cash and demand deposits does not change. However, the value ofthe loan will decrease to $178.19, and the value of the CD will fall to $159.01.Thus the value of the equity will be ($178.19 + $20 - $18 - $159.01) = $21.18.In this case the increase in interest rates causes the market value of equity toincrease because of the reinvestment opportunities on the loan payments.If market rates decrease 1 percent, the value of the loan increases to $181.84,and the value of the CD increases to $165.07. Thus the value of the equitydecreases to $18.77.d. How can a decrease in interest rates create interest rate risk?The amortized loan payments would be reinvested at lower rates. Thus eventhough interest rates have decreased, the different cash flow patterns of the loanand the CD have caused interest rate risk.9. You have discovered that the price of a bond rose from $975 to $995 when theYTM fell from 9.75 percent to 9.25 percent. What is the duration of the bond? We know years D years R R P P D 5.45.40975.1005.97520)1(=⇒-=-=+∆∆=- 10. If you use only duration to immunize your portfolio, what three factors affectchanges in the net worth of a financial institution when interest rates change?The change in net worth for a given change in interest rates is given by the followingequation:[]AL k where R R A k D D E L A =+∆--=∆1**Thus, three factors are important in determining ∆E.1) [D A - D L k ] or the leveraged adjusted duration gap. The larger this gap, the more exposed is the FI to changes in interest rates.2) A, or the size of the FI. The larger is A , the larger is the exposure to interest rate changes.3) ΔR /1 + R , or interest rate shocks. The larger is the shock, the larger is the interest rate risk exposure.11. What is meant by daily earnings at risk (DEAR )? What are the three measurablecomponents? What is the price volatility component?DEAR or Daily Earnings at Risk is defined as the estimated potential loss of a portfolio's value over a one-day unwind period as a result of adverse moves in market conditions, such as changes in interest rates, foreign exchange rates, and market volatility. DEAR is comprised of (a) the dollar value of the position, (b) the price sensitivity of the assets to changes in the risk factor, and (c) the adverse move in the yield. The product of the price sensitivity of the asset and the adverse move in the yield provides the price volatility component.12. Bank Two has a portfolio of bonds with a market value of $200 million. The bonds have anestimated price volatility of 0.95 percent. What are the DEAR and the 10-day VAR for these bonds?Daily earnings at risk (DEAR) =($ Value of position) x (Price volatility)= $200 million x .0095= $1.9million, or $1,900,000Value at risk (VAR) = DEAR x √N = $1,900,000 x √10= $1,900,000 x 3.1623 = $6,008,327.5513. The following are the foreign currency positions of an FI, expressed in dollars.15.5 Currency Assets Liabilities FX Bought FX Sold Swiss franc (SF) $125,000 $50,000 $10,000 $15,000British pound (£) 50,000 22,000 15,000 20,000Japanese yen (¥) 75,000 30,000 12,000 88,000a. W hat is the FI’s net exposure in Swiss francs?Net exposure in Swiss francs = $70,000.b. What is the FI’s net exposure in British pounds?Net exposure in British pounds = $23,000.c. What is the FI’s net exposure in Japanese yen?Net exposure in Japanese yen = -$31,000d. What is the expected loss or gain if the SF exchange rate appreciates by 1percent?If assets are greater than liabilities, then an appreciation of the foreign exchange rates will generate a gain = $70,000 x 0.01 = $7,000.e. What is the expected loss or gain if the £ exchange rate appreciates by 1percent?Gain = $23,000 x 0.01 = $230f. What is the expected loss or gain if the ¥ exchange rate appreciates by 2 percent?Loss = -$31,000 x 0.02 = -$6,200⏹练习1：⏹Calculate the repricing gap and the impact on net interest income of a 1 percent increasein interest rates for each of the following positions:⏹⏹Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.Repricing gap = RSA RSL = $200 $100 million = +$100 million.NII = ($100 million)(.01) = +$1.0 million, or $1,000,000.⏹Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.Repricing gap = RSA RSL = $100 $150 million = -$50 million.NII = (-$50 million)(.01) = -$0.5 million, or -$500,000.⏹Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.Repricing gap = RSA RSL = $150 $140 million = +$10 million.NII = ($10 million)(.01) = +$0.1 million, or $100,000.⏹练习2：⏹Which of the following assets or liabilities fit the one-year rate or repricing sensitivitytest?⏹⏹91-day U.S. Treasury bills Yes⏹1-year U.S. Treasury notes Yes⏹20-year U.S. Treasury bonds No⏹20-year floating-rate corporate bonds with annual repricing Yes⏹30-year floating-rate mortgages with repricing every two years No⏹30-year floating-rate mortgages with repricing every six months Yes⏹Overnight fed funds Yes⏹9-month fixed rate CDs Yes⏹1-year fixed-rate CDs Yes⏹5-year floating-rate CDs with annual repricing Yes⏹Common stock No⏹练习3：Consider the following balance sheet for WatchoverU Savings, Inc. (in millions): Assets Liabilities and EquityFloating-rate mortgages Demand deposits(currently 10% annually) $50 (currently 6% annually) $70 30-year fixed-rate loans Time deposits(currently 7% annually) $50 (currently 6% annually $20Equity $10 Total Assets $100 Total Liabilities & Equity $100a. What is WatchoverU’s expected net interest income at year-end?Current expected interest income: $5m + $3.5m = $8.5m.Expected interest expense: $4.2m + $1.2m = $5.4m.Expected net interest income: $8.5m - $5.4m = $3.1m.b. What will be the net interest income at year-end if interest rates rise by 2 percent?After the 200 basis point interest rate increase, net interest income declines to:50(0.12) + 50(0.07) - 70(0.08) - 20(.06) = $9.5m - $6.8m = $2.7m, a decline of$0.4m.c. Using the cumulative repricing gap model, what is the expected net interestincome for a 2 percent increase in interest rates?Wachovia’s' repricing or funding gap is $50m - $70m = -$20m. The change innet interest income using the funding gap model is (-$20m)(0.02) = -$.4m.练习4：M A = [0*20 + 5*60 + 200*30]/320 = 19.69 years, and M L = [0*140 + 1*160]/300 = 0.533. Therefore the maturity gap = MGAP = 19.69 – 0.533 = 19.16 years. Nearby bank is exposed to an increase in interest rates. If rates rise, the value of assets will decrease much more than the value of liabilities.练习5M A = [0*20 + 15*160 + 30*300]/480 = 23.75 years.M L = [0*100 + 5*210 + 20*120]/430 = 8.02 years.MGAP = 23.75 – 8.02 = 15.73 years.Five-year BondPar value = $1,000 Coupon rate = 15% Annual paymentsR = 9% Maturity = 5 yearsTime Cash Flow PV of CF PV of CF x t1 $150 $137.62 $137.622 $150 $126.25 $252.503 $150 $115.83 $347.484 $150 $106.26 $425.065 $1,150 $747.42 $3,737.10$1,233.38 $4,899.76 Duration = $4899.76/1,233.38= 3.97 ≈ 4 years⏹ 练习The duration of the capital note is 1.8975 years.Two-year Capital Note (values in thousands of $s)Par value = $900 Coupon rate = 7.25% Semiannual paymentsR = 7.25% Maturity = 2 years Time Cash Flow PV of CF PV of CF x t0.5 $32.625 $31.48 $15.741 $32.625 $30.38 $30.381.5 $32.625 $29.32 $43.982 $932.625 $808.81 $1,617.63$900.00 $1,707.73 Duration = $1,707.73/$900.00 =1.8975The leverage-adjusted duration gap can be found as follows:[]years k D D gap duration adjusted Leverage L A 23.8000,000,1$000,900$8975.194.9=-=-=-⏹ Follow Bank has a $1 million position in a five-year, zero-coupon bond with a face valueof $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. Thehistorical mean change in daily yields is 0.0 percent, and the standard deviation is 12basis points.⏹⏹ a. W hat is the modified duration of the bond?MD = 5 ÷ (1.07) = 4.6729 years⏹ b. W hat is the maximum adverse daily yield move given that we desire no more than a5 percent chance that yield changes will be greater than this maximum?Potential adverse move in yield at 5 percent = 1.65 = 1.65 x 0.0012 = .001980⏹ c. What is the price volatility of this bond?Price volatility = -MD x potential adverse move in yield= -4.6729 x .00198 = -0.009252 or -0.9252 percent⏹ d. W hat is the daily earnings at risk for this bond?DEAR = ($ value of position) x (price volatility)= $1,000,000 x 0.009252 = $9,252⏹The DEAR for a bank is $8,500. What is the VAR for a 10-day period? A 20-day period?Why is the VAR for a 20-day period not twice as much as that for a 10-day period?For the 10-day period: VAR = 8,500 x [10]½ = 8,500 x 3.1623 = $26,879.36For the 20-day period: VAR = 8,500 x [20]½= 8,500 x 4.4721 = $38,013.16The reason that VAR20 (2 x VAR10) is because *20+½ (2 x *10+½). The interpretation is that the daily effects of an adverse event become less as time moves farther away from the event.。