金融学(第二版)陈学彬课后答案

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《金融学(第二版)》讲义大纲及课后习题答案详解第15章

CHAPTER 15OPTIONS AND CONTINGENT CLAIMSObjectives•How to use options to modify one’s exposure to investment risk.•To understand the pricing relationships that exist among calls, puts, stocks and bonds.•To explain the binomial and Black-Scholes option-pricing models and apply them to the valuation of corporate bonds and other contingent claims.•To explore the range of financial decisions that can be fruitfully analyzed in terms of options.Outline15.1 How Options Work15.2 Investing with Options15.3 The Put-Call Parity Relation15.4 Volatility and Option Prices15.5 Two-State (Binomial) Option-Pricing15.6 Dynamic Replication and the Binomial Model15.7 The Black-Scholes Model15.8 Implied Volatility15.9 Contingent Claims Analysis of Corporate Debt and Equity15.10 Credit Guarantees15.11 Other Applications of Option-Pricing Methodologythe maturity of the option, and C the price of the call.•One can create a synthetic option from the underlying stock and the risk-free asset through a dynamic replication strategy that is self-financing after the initial investment. By the Law of One Price, the option’s price is given by the formula:where:C = price of the callS = price of the stockE = exercise pricer = risk-free interest rate (the annualized continuously compounded rate on a safe asset with the same maturity as the option)T = time to maturity of the option in yearsσ= standard deviation of the annualized continuously compounded rate of return on the stockd = continuous dividend yield on the stockln = natural logarithme = the base of the natural log function (approximately 2.71828)N(d1) = the probability that a random draw from a standard normal distribution will be less than d1.•The same methodology used to price options can be used to value many other contingent claims, including corporate stocks and bonds, loan guarantees, and the “real options” imbedded in investments in research and development and flexible manufacturing technology.Solutions to Problems at End of ChapterPayoff Diagrams1. Graph the payoff for a European put option with exercise price E, written on a stock with value S, when:a. You hold a long position (i.e., you buy the put)b. You hold a short position (i.e., you sell the put)SOLUTION: a.b.2.Graph the payoff to a portfolio holding one European call option and one European put option, each with the same expiration date and each with exercise price E, when both options are on a stock with value S.Investing with options3. The risk-free one –year rate of interest is 4%, and the Globalex stock index is at 100. The price of one-year European call options on the Globalex stock index with an exercise price of 104 is 8% of the current price of the index. Assume that the expected dividend yield on the stocks in the Globalex index is zero. You have $1million to invest for the next year. You plan to investenough of your money in one-year T-bills to insure that you will at least get back your original $1 million, and you will use the rest of your money to buy Globalex call options.a. Assuming that you can invest fractional amounts in Globalex options,show the payoff diagram for your investment. Measure the Globalex index on the horizontal axis and the portfolio rate of return on the vertical axis. What is the slope of the payoff line to the right of an index value of 104? b. If you think that there is a probability of .5 that the Globalex index a year from now will be up 12%, a probability of .25 that it will be up 40%, and a probability of .25 that it will be down 20%, what is the probability distribution of your portfolio rate of return?SOLUTION:a.To insure that you will at least get back your original $1 million, you need toinvestin T-bills.You can buy46.538,961$04.1000,000,1$1000,000,1$=+=+f r 69.4807854.461,38$10008.46.538,961$000,000,1$==⨯-options.The slope of the payoff line to the right of an index value of 104 is 4807.69, as seen from the graph:b.Put-Call Parity4.a.Show how one can replicate a one-year pure discount bond with a facevalue of $100 using a share of stock, a put and a call.b.Suppose that S=$100, P=$10, and C=$15. What must be the one-year interest rate?c.Show that if the one-year risk-free interest rate is lower than in youranswer to part b, there would be an arbitrage opportunity. (Hint: The price of the pure discount bond would be too high).SOLUTION:a.To replicate a one-year pure discount bond with a face value of $100, buy ashare of stock, and a European put with exercise price $100, and sell aEuropean call with an exercise price $100.b.S = $100, P = $10, and C = $15.E/(1+r) = S + P- C$100/(1+r) = $100 + $10 - $15 = $95r = 100/95 -1 = .053 or 5.3%c.If r = 4%, then one could make risk-free arbitrage profits by borrowing at 4%and investing in synthetic 1-year pure discount bonds consisting of a share of stock, a European put with exercise price $100, and a short position in aEuropean call with an exercise price $100. The synthetic bond would cost $95 and pay off $100 at maturity in 1 year. The principal and interest on the $95 it costs to buy this synthetic bond would be $95 x 1.04 = $98.8. Thus there would be a pure arbitrage profit of $1.20 per bond a year from now with zero initial outlay of funds.5. A 90-day European call option on a share of the stock of Toshiro Corporation is currently trading at 2,000 yen whereas the current price of the share itself is 2, 400 yen. 90-day zero-coupon securities issued by the government of Japan are selling for 9, 855 yen per 10, 000 yen face value. Infer the price of a 90-day European put option on this stock if both the call and put have a common exercise price of 500 yen.SOLUTION:Using the expression for put-call parity, P =-S + E/(1+r)T + CS is the share price, P is the price of the put, C is the price of the call and E is the common exercise price.Since government bonds are selling at . 9855 per 1 yen of face value, this is thediscount factor for computing the PV of the exercise price. There is no need to compute the riskless rate, r.Substituting in the parity equation we get:P = -2,400 + 500 x .9855 +2,000 = 92.75 yen6. Gordon Gekko has assembled a portfolio consisting of ten 90-day US Treasury bills, each having a face value of $1, 000 and a current price of $990.10, and 200 90-day European call options, each written on a share of Paramount stock and having an exercise price of $50.00. Gekko is offering to trade you this portfolio for 300 shares of Paramount stock, which is currently valued at $215.00 a share.If 90-day European put options on Paramount stock with a $50.00 exercise price are currently valued at $25.00,a.Infer the value of the calls in Gekko’s portfolio.b.Determine whether you should accept Gekko’s offer.SOLUTION:ing put-call parity, the current price of a call is found to be approximately$190.50 as follows:C =S - E/(1+r)T + P= $215 - $50 x .9901 + $25 = $190.495b.The v alue of Gekko’s portfolio is 10 x $990.10 + 200 x $190.495 = $48,000But the value of 300 shares is $64,500. We should reject Gekko’s offer.7. The stock of Kakkonen, Ltd., a hot tuna distributor, currently lists for $500.00 a share, whereas one-year European call options on this stock, with an exercise price of $200.00, sell for $400.00 and European put options with a similar expiration date and exercise price sell for $84.57.a.Infer the yield on a one-year, zero-coupon U.S. government bond soldtoday.b.If this yield is actually at 9%, construct a profitable trade to exploit thepotential for arbitrage.SOLUTION:ing put-call parity, we can infer the riskless yield to be approximately 8.36%as follows:A portfolio consisting of a share of the stock, a put, and a short position in acall is equivalent to a 1-year T-bill with a face value of E. Therefore the price of such a T-bill would have to be $184.57:E/(1+r)T = S + P- C = $500.00 +$84.57 -$400.00 = $184.571+r= 200/184.57 = 1.0836r= .0836 or 8.36%b.There are many ways to exploit the violation of the Law of One Price to makearbitrage profits. Since the risk-free interest rate is 9%, and the implied interest rate on the replicating portfolio is 8.36%, we could go short the replicating portfolio and invest the proceeds in T-bills. For example, at current prices,short-sell a “unit” portfolio, which consists of long positions in one put and one share and writing one call, to earn immediate revenue of $184.57. The portfolio you sold short requires payment of $200 one year from now. If you invest the $184.57 in one-year T-bills you will have 1.09x $184.57 = $201.18 a year from now. Thus you will earn a risk-free arbitrage profit of $1.18 with no outlay of your own money.Two-State Option Pricing8. Derive the formula for the price of a put option using the two-state model. SOLUTION:To price the put option, we create a synthetic option by selling short a fraction (denote the fraction “a”) and len d $b in risk-free asset. Denote the price of the stock S, the price of the put option P, the stock price when the next period is an “up” to be uS, the stock price when the next period is a “down” to be dS, the payoffs of the put option in each state Pu and Pd, and the risk-free interest r.We solve for (a, b) in 1) and 2) We find:andSo that the price of the put optionuP b r a S u =⨯++⨯⨯-)1(d P b r a S d =⨯++⨯⨯-)1(Sd u P P a d u ⨯---=)()1()(r d u P d P u b u d +⨯-⨯-⨯=⎥⎦⎤⎢⎣⎡⨯⎪⎭⎫ ⎝⎛---+⨯⎪⎭⎫ ⎝⎛--+⨯+=+⨯-=d u P d u r u P d u d r r b S a P 1)1)1(19. The share value of Drummond, Griffin and McNabb, a New Orleanspublishing house, is currently trading at $100.00 but is expected, 90 days from today, to rise to $150.00 or to decline to $50.00, depending on critical reviews of its new biography of Ezra Pound. Assuming the risk-free interest rate over the next 90 days is 1%, can you value a European call option written on a share of DGM stock if the option carries an exercise price of $85.00?SOLUTION:Should the value of DBM stock rise to $150 in 90 days, the call will be worth $65.00 at that date, but if DBM stock falls to $50.00 the call will be worthless at expiration. Using the 2-state option pricing model, we find that the call is worth $32.82:To replicate the call using the stock and risk-free borrowing we buy x shares ofstock and borrow y. We findthe values for x and y by setting up two equations, one for each of the possible payoffs of the call at expiration:The solution to this set of two equations is x = .65 and y = $32.50/1.01 = $32.18 Thus, we can replicate the call option by buying .65 of a share of stock (at a cost of $65) and borrowing $32.18.The price of the call option is $32.82: C = .65 x $100 - $32.18 = $32.82The Black-Scholes Formula 10.a. Use the Black-Scholes formula to find the price of a 3-month European call option on a non-dividend- paying stock with a current price of $50.Assume the exercise price is $51, the continuously compounded risk-free interest rate is 8% per year, and σ is .4.b. What is the composition of the initial replicating portfolio for this call option?c. Use the put-call parity relation to find the Black-Scholes formula for the price of the corresponding put option.SOLUTION:a. The price of the call is $3.987. Since the present value of the exercise price is01.1506501.1150=⨯-⨯=⨯-⨯y x y x 4$5.504.4.4.=⨯⨯⨯=⨯⨯⨯=T S C σapproximately equal to the current stock price, we could use the linearapproximation to the Black-Scholes formula:b.The hedge ratio, which is the number of shares of stock you must buy, equalsN(d1), and the amount to borrow is N(d2) times the PV of the exercise price.To find N(d1) and N(d2) you must compute d1 and d2 and then apply the N( ) function (i.e., the standard normal cumulative density function). You can either use NORMDIST in Excel or use a statistical table to do this. The hedge ratio is .54, which means you would buy .54 of a share of stock for $27. The amount to borrow is $23.c. From put-call parity: P = -S + E e0.02 + C = -$50 + $51.01 + $4 = $5.0111. As a financial analyst at Yew and Associates, a Singaporean investment house, you are asked by a client if she should purchase European call options on Rattan, Ltd. stock, which are currently selling in U.S. dollars for $30.00. These options have an exercise price of $50.00. Rattan stock currently exhibits a share price of $55.00, and the estimated rate of return variance of the stock is .04.If these options expire in 25 days and the risk-free interest rate over that period is 5% per year, what do you advise your client to do?SOLUTION:We can apply the Black-Scholes formula, where S = $55, E = $50, σ = .2, T =25/365, r = .05. We find thatC = $5.20. This is a lot less than $30, so clearly the options are not worth buying.Valuation of Corporate Securities with the Two-State Model12. Lorre and Greenstreet, Inc., a purveyor of antique statues, currently has corporate assets valued at$100,000 and must repay $50, 000, the aggregate face value of zero-coupon bonds sold to private investors, in 90 days. An independent appraisal of a newly acquired antique falcon from Malta will be publicly released at that time, and the value of the firm’s assets is expected to increase to $170,000 if the falcon is certified as genuine, but to decline to a mere $45, 000 if the antique is found to be a fake. The firm will declare bankruptcy in this latter circumstance and shareholders will surrender the assets of the firm to its creditors.a.Can you express the current aggregate value of equity in Lorre andGreenstreet as a contingent expression of the value of the firm’s assets and the face value of its outstanding debt?b.Is there a relation between the expression you have derived for equity anda 90-day European call option written upon the aggregate value of thefirm’s assets?c.Can you express the current aggregate value of the bonds issued by Lorreand Greenstreet in terms of the value of the firm’s assets and the facevalue of its outstanding debt?d.Is there a relation among the current value of the bonds the firm hasissued, the current value of riskless bonds with the same term to maturity and face value, and a European put option written on the aggregate value of the firm’s assets? What would the implication of such a relationship be for expressing the value of risky debt in terms of risk-free debt andcollateral?SOLUTION:a.The aggregate value of the firm’s equity in 90 d ays is E1 = max (V1 -B, 0)where E1 and V1 are, respectively, the aggregate values in 90 days of thefirm’s equity and assets, and where B is the aggregate face value of the firm’s debt.The current value of the equity can be expressed as:E = xV - ywhere x is the fraction of the value of the firm that one must purchase toreplicate the payoffs from the equity, and y is the amount that must beborrowed. We find the values for x and y by setting up two equations, one for each of the possible payoffs of the equity 90 days from now:170000x - y(1+r) = 120,00045000x - y(1+r) = 0The solution to this set of two equations is x = 120/125 = .96 and y =$43,200/(1+r), where r is the risk-free 90-day interest rate. Thus, we canreplicate the equity by buying 96% of the firm’s assets (at a cost of $96,000) and borrowing the present value of $43,200. The current value of the equity is therefore:E = $96,000 -$43,200/(1+r)b.They are exactly analogous. The call value is analogous to the aggregate valueof equity, the share price is analogous to the aggregate value of the firm’sassets, and the exercise price is analogou s to the face value of the firm’s debt.In effect, the firm’s shareholders hold a call option on the firm’s assets, which they can exercise by repaying the face value of the debt.c.In the presence of limited corporate liability, the realized aggregate payoff tothe firm’s creditors in 90 days, D1, can be written as:D1 = min (V1,B).d.The difference in value between the firm’s bonds and the correspondingdefault-free bonds equals the value of a European put on the firm’s assets. This relation implies the limit ed liability that stockholders have to sell the firm’s assets at the debt’s face value, which also implies that the value of risk-free debt equals the sum of the value of the risky debt and the value of collateral.13. Gephardt, Army and Gore, a vaudeville booking agency, has issued zero-coupon corporate debt this week, consisting of 80 bonds, each with a face value of $1,000 and a term to maturity of one year. Industry analysts predict that the value of GAG assets will be $160,000 in one year if Rupert Murdoch succeeds in purchasing and converting the Washington Press Club into a comedy venue, $130,000 if Murdoch buys the club but retains its current scheduling, and $20,000 if Murdoch builds an alternative comedy venue in Washington. Industry analysts also predict that aggregate value of the assets of a second firm in the field of comedy entertainment, Yelstin Yuks, Ltd., will have the values of $100,000, $100,000, and $40,000 in these respective circumstances. Assuming that investors can purchase portfolios comprised of shares of the assets of GAG and YY Ltd., as well as buying or short –selling one-year, zero-coupon, government bonds at the risk-free annual rate of .10, thena.Infer the three alternative values for aggregate equity in GAG, one yearfrom today.b.Devise a portfolio that is a perfect substitute for the payoffs given by aportfolio composed only of equity in GAG.c.Determine the current market value of a share of equity in GAG, assuming10,000 shares of GAG stock are outstanding, the current market value of GAG assets is $120,000, and the current market value of YY Ltd., assets is $85,725.d.Determine the current market value of a bond issued by GAG, assuming80 bonds are issued, under these circumstances. What of the yield tomaturity on each such bond?SOLUTION:a.In the first circumstance, the value of aggregate equity in GAG is $160,000-$80,000=$80,000.In the second circumstance, the value of aggregate equity in GAG is $130,000-$80,000=$50,000.In the third circumstance, the value of aggregate equity in GAG is 0.b.Suppose that the replicating portfolio consists of buying x units of the GAGasset, y units of the YY asset, and z units of the government bond (with a face value of $100,000). The payoff of this portfolio will exactly match that of the GAG equity, that gives:160,000x + 100,000y + 100,000z = 80,000130,000x + 100,000y + 100,000z = 50,00020,000x + 40,000y +100,000z = 0solving the equations, we have x = 1, y = -1, z = 0.2c.We define three types of pure contingent claims: at the end of one year, AD1will pay off $1 if and only if Rupert Murdoch succeeds in purchasing andconverting the Washington Press Club into a comedy venue; AD2 will pay off $1 if and only if Murdoch buys the club but retains its current scheduling; AD3 will pay off $1 if and only if Murdoch builds an alternative comedy venue in Washington. Denote the prices as of today of the three pure contingent claims as p1, p2 and p3, respectively.From the value equation of the GAG asset, YY asset and the government bond, we have:GAG: 160,000p1 + 130,000p2 + 20,000p3 = 120,000YY: 100,000p1 + 100,000p2 + 40,000p3 = 85,725Government bond: 100,000p1 + 100,000p2 + 100,000p3 = 100,000/(1+10%) = 90,909Solve the equations, we have p1 = 0.3774, p2=0.4453, p3=0.0864The total value of GAG equity is80,000p1 + 50,000p2 = $52457The per share price of equity is $5.25.d.The value of the bond and the value of the equity add up to the value of theasset, so,V bond = V asset– V equity = 120,000 – 52547 = $67543The yield-to-maturity of bond is (80,000-67543)/67543 = 18.4%。

《金融学(第二版)》讲义大纲及课后习题答案详解第四章

CHAPTER 4THE TIME VALUE OF MONEY AND DISCOUNTED CASH FLOW ANALYSISObjectives•To explain the concepts of compounding and discounting, future value and present value.•To show how these concepts are applied to making financial decisions.Outline4.1 Compounding4.2 The Frequency of Compounding4.3 Present Value and Discounting4.4 Alternative Discounted Cash Flow Decision Rules4.5 Multiple Cash Flows4.6 Annuities4.7 Perpetual Annuities4.8 Loan Amortization4.9 Exchange Rates and Time Value of Money4.10 Inflation and Discounted Cash Flow Analysis4.11 Taxes and Investment DecisionsSummary•Compounding is the process of going from present value (PV) to future value (FV). The future value of $1 earning interest at rate i per period for n periods is (1+i)n.•Discounting is finding the present value of some future amount. The present value of $1 discounted at rate i per period for n periods is 1/(1+i)n.•One can make financial decisions by comparing the present values of streams of expected future cash flows resulting from alternative courses of action. The present value of cash inflows less the present value of cash outflows is called net present value (NPV). If a course of action has a positive NPV, it is worth undertaking. •In any time value of money calculation, the cash flows and the interest rate must be denominated in the same currency.•Never use a nominal interest rate when discounting real cash flows or a real interest rate when discounting nominal cash flows.How to Do TVM Calculations in MS ExcelAssume you have the following cash flows set up in a spreadsheet:Move the cursor to cell B6 in the spreadsheet. Click the function wizard f x in the tool bar and when a menu appears, select financial and then NPV. Then follow the instructions for inputting the discount rate and cash flows. You can input the column of cash flows by selecting and moving it with your mouse. Ultimately cell B6should contain the following:=NPV(0.1,B3:B5)+B2The first variable in parenthesis is the discount rate. Make sure to input the discount rate as a decimal fraction (i.e., 10% is .1). Note that the NPV function in Excel treats the cash flows as occurring at the end of each period, and therefore the initial cash flow of 100 in cell B2 is added after the closing parenthesis. When you hit the ENTER key, the result should be $47.63.Now move the cursor to cell B7to compute IRR. This time select IRR from the list of financial functions appearing in the menu. Ultimately cell B7 should contain the following:=IRR(B2:B5)When you hit the ENTER key, the result should be 34%.Your spreadsheet should look like this when you have finished:Solutions to Problems at End of Chapter1. If you invest $1000 today at an interest rate of 10% per year, how much will you have 20 years from now,assuming no withdrawals in the interim?2. a. If you invest $100 every year for the next 20 years, starting one year from today and you earninterest of 10% per year, how much will you have at the end of the 20 years?b. How much must you invest each year if you want to have $50,000 at the end of the 20 years?3. What is the present value of the following cash flows at an interest rate of 10% per year?a. $100 received five years from now.b. $100 received 60 years from now.c. $100 received each year beginning one year from now and ending 10 years from now.d. $100 received each year for 10 years beginning now.e. $100 each year beginning one year from now and continuing forever.e. PV = $100 = $1,000.104. You want to establish a “wasting” fund which will provide you with $1000 per year for four years, at which time the fund will be exhausted. How much must you put in the fund now if you can earn 10% interest per year?SOLUTION:5. You take a one-year installment loan of $1000 at an interest rate of 12% per year (1% per month) to be repaid in 12 equal monthly payments.a. What is the monthly payment?b. What is the total amount of interest paid over the 12-month term of the loan?SOLUTION:b. 12 x $88.85 - $1,000 = $66.206. You are taking out a $100,000 mortgage loan to be repaid over 25 years in 300 monthly payments.a.If the interest rate is 16% per year what is the amount of the monthly payment?b.If you can only afford to pay $1000 per month, how large a loan could you take?c.If you can afford to pay $1500 per month and need to borrow $100,000, how many months would it taketo pay off the mortgage?d.If you can pay $1500 per month, need to borrow $100,000, and want a 25 year mortgage, what is thehighest interest rate you can pay?SOLUTION:a.Note: Do not round off the interest rate when computing the monthly rate or you will not get the same answerreported here. Divide 16 by 12 and then press the i key.b.Note: You must input PMT and PV with opposite signs.c.Note: You must input PMT and PV with opposite signs.7. In 1626 Peter Minuit purchased Manhattan Island from the Native Americans for about $24 worth of trinkets. If the tribe had taken cash instead and invested it to earn 6% per year compounded annually, how much would the Indians have had in 1986, 360 years later?SOLUTION:8. You win a $1 million lottery which pays you $50,000 per year for 20 years, beginning one year from now. How much is your prize really worth assuming an interest rate of 8% per year?SOLUTION:9. Your great-aunt left you $20,000 when she died. You can invest the money to earn 12% per year. If you spend $3,540 per year out of this inheritance, how long will the money last?SOLUTION:10. You borrow $100,000 from a bank for 30 years at an APR of 10.5%. What is the monthly payment? If you must pay two points up front, meaning that you only get $98,000 from the bank, what is the true APR on the mortgage loan?SOLUTION:If you must pay 2 points up front, the bank is in effect lending you only $98,000. Keying in 98000 as PV and computing i, we get:11. Suppose that the mortgage loan described in question 10 is a one-year adjustable rate mortgage (ARM), which means that the 10.5% interest applies for only the first year. If the interest rate goes up to 12% in the second year of the loan, what will your new monthly payment be?SOLUTION:Step 2 is to compute the new monthly payment at an interest rate of 1% per month:12. You just received a gift of $500 from your grandmother and you are thinking about saving this money for graduation which is four years away. You have your choice between Bank A which is paying 7% for one-year deposits and Bank B which is paying 6% on one-year deposits. Each bank compounds interest annually. What is the future value of your savings one year from today if you save your money in Bank A? Bank B? Which is the better decision? What savings decision will most individuals make? What likely reaction will Bank B have? SOLUTION:$500 x (1.07) = $535Formula:$500 x (1.06) = $530a.You will decide to save your money in Bank A because you will have more money at the end of the year. Youmade an extra $5 because of your savings decision. That is an increase in value of 1%. Because interestcompounded only once per year and your money was left in the account for only one year, the increase in value is strictly due to the 1% difference in interest rates.b.Most individuals will make the same decision and eventually Bank B will have to raise its rates. However, it isalso possible that Bank A is paying a high rate just to attract depositors even though this rate is not profitable for the bank. Eventually Bank A will have to lower its rate to Bank B’s rate in order to make money.13.Sue Consultant has just been given a bonus of $2,500 by her employer. She is thinking about using the money to start saving for the future. She can invest to earn an annual rate of interest of 10%.a.According to the Rule of 72, approximately how long will it take for Sue to increase her wealth to $5,000?b.Exactly how long does it actually take?SOLUTION:a.According to the Rule of 72: n = 72/10 = 7.2 yearsIt will take approximately 7.2 years for Sue’s $2,500 to double to $5,000 at 10% interest.b.At 10% interestn i PV FV PMTSolve10 - $2,500 $5,0007.27 YearsFormula:$2,500 x (1.10)n = $5,000Hence, (1.10)n = 2.0n log 1.10 = log 2.0n = .693147 = 7.27 Years.095310rry’s bank account has a “floating” interest rate on certa in deposits. Every year the interest rate is adjusted. Larry deposited $20,000 three years ago, when interest rates were 7% (annual compounding). Last year the rate was only 6%, and this year the rate fell again to 5%. How much will be in his account at the end of this year?SOLUTION:$20,000 x 1.07 x 1.06 x 1.05 = $23,818.2015.You have your choice between investing in a bank savings account which pays 8% compounded annually (BankAnnual) and one which pays 7.5% compounded daily (BankDaily).a.Based on effective annual rates, which bank would you prefer?b.Suppose BankAnnual is only offering one-year Certificates of Deposit and if you withdraw your moneyearly you lose all interest. How would you evaluate this additional piece of information when making your decision?SOLUTION:a.Effective Annual Rate: BankAnnual = 8%.Effective Annual Rate BankDaily = [1 + .075]365 - 1 = .07788 = 7.788%365Based on effective annual rates, you would prefer BankAnnual (you will earn more money.)b.If BankAnnual’s 8% annual return i s conditioned upon leaving the money in for one full year, I would need tobe sure that I did not need my money within the one year period. If I were unsure of when I might need the money, it might be safer to go for BankDaily. The option to withdraw my money whenever I might need it will cost me the potential difference in interest:FV (BankAnnual) = $1,000 x 1.08 = $1,080FV (BankDaily) = $1,000 x 1.07788 = $1,077.88Difference = $2.12.16.What are the effective annual rates of the following:a.12% APR compounded monthly?b.10% APR compounded annually?c.6% APR compounded daily?SOLUTION:Effective Annual Rate (EFF) = [1 + APR] m - 1ma.(1 + .12)12 - 1 = .1268 = 12.68%12b.(1 + .10)- 1 = .10 = 10%1c.(1 + .06)365 - 1 = .0618 = 6.18%36517.Harry promises that an investment in his firm will double in six years. Interest is assumed to be paid quarterly and reinvested. What effective annual yield does this represent?EAR=(1.029302)4-1=12.25%18.Suppose you know that you will need $2,500 two years from now in order to make a down payment on a car.a.BankOne is offering 4% interest (compounded annually) for two-year accounts, and BankTwo is offering4.5% (compounded annually) for two-year accounts. If you know you need $2,500 two years from today,how much will you need to invest in BankOne to reach your goal? Alternatively, how much will you need to invest in BankTwo? Which Bank account do you prefer?b.Now suppose you do not need the money for three years, how much will you need to deposit today inBankOne? BankTwo?SOLUTION:PV = $2,500 = $2,311.39(1.04)2PV = $2,500 = $2,289.32(1.045)2You would prefer BankTwo because you earn more; therefore, you can deposit fewer dollars today in order to reach your goal of $2,500 two years from today.b.PV = $2,500 = $2,222.49(1.04)3PV = $2,500 = $2,190.74(1.045)3Again, you would prefer BankTwo because you earn more; therefore, you can deposit fewer dollars today in order to reach your goal of $2,500 three years from today.19.Lucky Lynn has a choice between receiving $1,000 from her great-uncle one year from today or $900 from her great-aunt today. She believes she could invest the $900 at a one-year return of 12%.a.What is the future value of the gift from her great-uncle upon receipt? From her great-aunt?b.Which gift should she choose?c.How does your answer change if you believed she could invest the $900 from her great-aunt at only 10%?At what rate is she indifferent?SOLUTION:a. Future Value of gift from great-uncle is simply equal to what she will receive one year from today ($1000). Sheearns no interest as she doesn’t receive the money until next year.b. Future Value of gift from great-aunt: $900 x (1.12) = $1,008.c. She should choose the gift from her great-aunt because it has future value of $1008 one year from today. Thegift from her great-uncle has a future value of $1,000. This assumes that she will able to earn 12% interest on the $900 deposited at the bank today.d. If she could invest the money at only 10%, the future value of her investment from her great-aunt would only be$990: $900 x (1.10) = $990. Therefore she would choose the $1,000 one year from today. Lucky Lynn would be indifferent at an annual interest rate of 11.11%:$1000 = $900 or (1+i) = 1,000 = 1.1111(1+i) 900i = .1111 = 11.11%20.As manager of short-term projects, you are trying to decide whether or not to invest in a short-term project that pays one cash flow of $1,000 one year from today. The total cost of the project is $950. Your alternative investment is to deposit the money in a one-year bank Certificate of Deposit which will pay 4% compounded annually.a.Assuming the cash flow of $1,000 is guaranteed (there is no risk you will not receive it) what would be alogical discount rate to use to determine the present value of the cash flows of the project?b.What is the present value of the project if you discount the cash flow at 4% per year? What is the netpresent value of that investment? Should you invest in the project?c.What would you do if the bank increases its quoted rate on one-year CDs to 5.5%?d.At what bank one-year CD rate would you be indifferent between the two investments?SOLUTION:a.Because alternative investments are earning 4%, a logical choice would be to discount the project’s cash flowsat 4%. This is because 4% can be considered as your opportunity cost for taking the project; hence, it is your cost of funds.b.Present Value of Project Cash Flows:PV = $1,000 = $961.54(1.04)The net present value of the project = $961.54 - $950 (cost) = $11.54The net present value is positive so you should go ahead and invest in the project.c.If the bank increased its one-year CD rate to 5.5%, then the present value changes to:PV = $1,000 = $947.87(1.055)Now the net present value is negative: $947.87 - $950 = - $2.13. Therefore you would not want to invest in the project.d.You would be indifferent between the two investments when the bank is paying the following one-year interestrate:$1,000 = $950 hence i = 5.26%(1+i)21.Calculate the net present value of the following cash flows: you invest $2,000 today and receive $200 one year from now, $800 two years from now, and $1,000 a year for 10 years starting four years from now. Assume that the interest rate is 8%.SOLUTION:Since there are a number of different cash flows, it is easiest to do this problem using cash flow keys on the calculator:22.Your cousin has asked for your advice on whether or not to buy a bond for $995 which will make one payment of $1,200 five years from today or invest in a local bank account.a.What is the internal rate of return on the bond’s cash flows? What additional information do you need tomake a choice?b.What advice would you give her if you learned the bank is paying 3.5% per year for five years(compounded annually?)c.How would your advice change if the bank were paying 5% annually for five years? If the price of thebond were $900 and the bank pays 5% annually?SOLUTION:a.$995 x (1+i)5 = $1,200.(1+i)5 = $1,200$995Take 5th root of both sides:(1+i) =1.0382i = .0382 = 3.82%In order to make a choice, you need to know what interest rate is being offered by the local bank.b.Upon learning that the bank is paying 3.5%, you would tell her to choose the bond because it is earning a higherrate of return of 3.82% .c.If the bank were paying 5% per year, you would tell her to deposit her money in the bank. She would earn ahigher rate of return.5.92% is higher than the rate the bank is paying (5%); hence, she should choose to buy the bond.23.You and your sister have just inherited $300 and a US savings bond from your great-grandfather who had left them in a safe deposit box. Because you are the oldest, you get to choose whether you want the cash or the bond. The bond has only four years left to maturity at which time it will pay the holder $500.a.If you took the $300 today and invested it at an interest rate 6% per year, how long (in years) would ittake for your $300 to grow to $500? (Hint: you want to solve for n or number of periods. Given these circumstances, which are you going to choose?b.Would your answer change if you could invest the $300 at 10% per year? At 15% per year? What otherDecision Rules could you use to analyze this decision?SOLUTION:a.$300 x (1.06)n = $500(1.06)n = 1.6667n log 1.06 = log 1.6667n = .510845 = 8.77 Years.0582689You would choose the bond because it will increase in value to $500 in 4 years. If you tookthe $300 today, it would take more than 8 years to grow to $500.b.You could also analyze this decision by computing the NPV of the bond investment at the different interest rates:In the calculations of the NPV, $300 can be considered your “cost” for acquiring the bond since you will give up $300 in cash by choosing the bond. Note that the first two interest rates give positive NPVs for the bond, i.e. you should go for the bond, while the last NPV is negative, hence choose the cash instead. These results confirm the previous method’s results.24.Suppose you have three personal loans outstanding to your friend Elizabeth. A payment of $1,000 is due today, a $500 payment is due one year from now and a $250 payment is due two years from now. You would like to consolidate the three loans into one, with 36 equal monthly payments, beginning one month from today. Assume the agreed interest rate is 8% (effective annual rate) per year.a.What is the annual percentage rate you will be paying?b.How large will the new monthly payment be?SOLUTION:a.To find the APR, you must first compute the monthly interest rate that corresponds to an effective annual rate of8% and then multiply it by 12:1.08 = (1+ i)12Take 12th root of both sides:1.006434 = 1+ ii = .006434 or .6434% per monthOr using the financial calculator:b.The method is to first compute the PV of the 3 loans and then compute a 36 month annuity payment with thesame PV. Most financial calculators have keys which allow you to enter several cash flows at once. This approach will give the user the PV of the 3 loans.Note: The APR used to discount the cash flows is the effective rate in this case, because this method is assuming annual compounding.25.As CEO of ToysRFun, you are offered the chance to participate, without initial charge, in a project that produces cash flows of $5,000 at the end of the first period, $4,000 at the end of the next period and a loss of $11,000 at the end of the third and final year.a.What is the net present value if the relevant discount rate (the company’s cost of capital) is 10%?b.Would you accept the offer?c.What is the internal rate of return? Can you explain why you would reject a project which has aninternal rate of return greater than its cost of capital?SOLUTION:At 10% discount rate:Net Present Value = - 0 + $5,000 + $4,000 - $11,000 = - 413.22(1.10) (1.10)2 (1.10)3c.This example is a project with cash flows that begin positive and then turn negative--it is like a loan. The 13.6% IRR is therefore like an interest rate on that loan. The opportunity to take a loan at 13.6% when the cost of capital is only 10% is not worthwhile.26.You must pay a creditor $6,000 one year from now, $5,000 two years from now, $4,000 three years from now, $2,000 four years from now, and a final $1,000 five years from now. You would like to restructure the loan into five equal annual payments due at the end of each year. If the agreed interest rate is 6% compounded annually, what is the payment?SOLUTION:Since there are a number of different cash flows, it is easiest to do the first step of this problem using cash flow keys on the calculator. To find the present value of the current loan payments:27.Find the future value of the following ordinary annuities (payments begin one year from today and all interest rates compound annually):a.$100 per year for 10 years at 9%.b.$500 per year for 8 years at 15%.c.$800 per year for 20 years at 7%.d.$1,000 per year for 5 years at 0%.e.Now find the present values of the annuities in a-d.f.What is the relationship between present values and future values?SOLUTION:Future Value of Annuity:e.f.The relationship between present value and future value is the following:nbeginning three years from today in an account that yields 11% compounded annually. How large should the annual deposit be?SOLUTION:You will be making 7 payments beginning 3 years from today. So, we need to find the value of an immediate annuity with 7 payments whose FV is $50,000:29.Suppose an investment offers $100 per year for five years at 5% beginning one year from today.a.What is the present value? How does the present value calculation change if one additional payment isadded today?b.What is the future value of this ordinary annuity? How does the future value change if one additionalpayment is added today?SOLUTION:$100 x [(1.05)5] - 1 = $552.56.05If you were to add one additional payment of $100 today, the future value would increase by:$100 x (1.05)5 = $127.63. Total future value = $552.56 + $127.63 = $680.19.Another way to do it would be to use the BGN mode for 5 payments of $100 at 5%, find the future value of that, and then add $100. The same $680.19 is obtained.30.You are buying a $20,000 car. The dealer offers you two alternatives: (1) pay the full $20,000 purchase price and finance it with a loan at 4.0% APR over 3 years or (2) receive $1,500 cash back and finance the rest at a bank rate of 9.5% APR. Both loans have monthly payments over three years. Which should you choose? SOLUTION:31.You are looking to buy a sports car costing $23,000. One dealer is offering a special reduced financing rate of 2.9% APR on new car purchases for three year loans, with monthly payments. A second dealer is offering a cash rebate. Any customer taking the cash rebate would of course be ineligible for the special loan rate and would have to borrow the balance of the purchase price from the local bank at the 9%annual rate. How large must the cash rebate be on this $23,000 car to entice a customer away from the dealer who is offering the special 2.9% financing?SOLUTION:of the 2.9% financing.32.Show proof that investing $475.48 today at 10% allows you to withdraw $150 at the end of each of the next 4 years and have nothing remaining.SOLUTION:You deposit $475.48 and earn 10% interest after one year. Then you withdraw $150. The table shows what happensAnother way to do it is simply to compute the PV of the $150 annual withdrawals at 10% : it turns out to be exactly $475.48, hence both amounts are equal.33.As a pension manager, you are considering investing in a preferred stock which pays $5,000,000 per year forever beginning one year from now. If your alternative investment choice is yielding 10% per year, what is the present value of this investment? What is the highest price you would be willing to pay for this investment? If you paid this price, what would be the dividend yield on this investment?SOLUTION:Present Value of Investment:PV = $5,000,000 = $50,000,000.10Highest price you would be willing to pay is $50,000,000.Dividend yield = $5,000,000 = 10%.$50,000,00034. A new lottery game offers a choice for the grand prize winner. You can receive either a lump sum of $1,000,000 immediately or a perpetuity of $100,000 per year forever, with the first payment today. (If you die, your estate will still continue to receive payments). If the relevant interest rate is 9.5% compounded annually, what is the difference in value between the two prizes?SOLUTION:The present value of the perpetuity assuming that payments begin at the end of the year is:$100,000/.095 = $1,052,631.58If the payments begin immediately, you need to add the first payment. $100,000 + 1,052,632 = $1,152,632.So the annuity has a PV which is greater than the lump sum by $152,632.35.Find the future value of a $1,000 lump sum investment under the following compounding assumptions:a.7% compounded annually for 10 yearsb.7% compounded semiannually for 10 yearsc.7% compounded monthly for 10 yearsd.7% compounded daily for 10 yearse.7% compounded continuously for 10 yearsa.$1,000 x (1.07)10 = $1,967.15b.$1,000 x (1.035)20 = $1,989.79c.$1,000 x (1.0058)120 = $2,009.66d.$1,000 x (1.0019178)3650 = $2,013.62e.$1,000 x e.07x10 = $2,013.7536.Sammy Jo charged $1,000 worth of merchandise one year ago on her MasterCard which has a stated interest rate of 18% APR compounded monthly. She made 12 regular monthly payments of $50, at the end of each month, and refrained from using the card for the past year. How much does she still owe? SOLUTION:Sammy Jo has taken a $1,000 loan at 1.5% per month and is paying it off in monthly installments of $50. We could work out the amortization schedule to find out how much she still owes after 12 payments, but a shortcut on the financial calculator is to solve for FV as follows:37.Suppose you are considering borrowing $120,000 to finance your dream house. The annual percentage rate is 9% and payments are made monthly,a.If the mortgage has a 30 year amortization schedule, what are the monthly payments?b.What effective annual rate would you be paying?c.How do your answers to parts a and b change if the loan amortizes over 15 years rather than 30?EFF = [1 + .09]1238.Suppose last year you took out the loan described in problem #37a. Now interest rates have declined to 8% per year. Assume there will be no refinancing fees.a.What is the remaining balance of your current mortgage after 12 payments?b.What would be your payment if you refinanced your mortgage at the lower rate for 29 years? SOLUTION:Exchange Rates and the Time Value of Money39.The exchange rate between the pound sterling and the dollar is currently $1.50 per pound, the dollar interest rate is 7% per year, and the pound interest rate is 9% per year. You have $100,000 in a one-year account that allows you to choose between either currency, and it pays the corresponding interest rate.a.If you expect the dollar/pound exchange rate to be $1.40 per pound a year from now and are indifferentto risk, which currency should you choose?b.What is the “break-even” value of the dollar/pound exchange rate one year from now?SOLUTION:a.You could invest $1 today in dollar-denominated bonds and have $1.07 one year from now. Or you couldconvert the dollar today into 2/3 (i.e., 1/1.5) of a pound and invest in pound-denominated bonds to have .726667(i.e., 2/3 x 1.09) pounds one year from now. At an exchange rate of $1.4 per pound, this would yield 0.726667(1.4) = $1.017 (this is lower than $1.07), so you would choose the dollar currency.b.For you to break-even the .726667 pounds would have to be worth $1.07 one year from now, so the break-evenexchange rate is $1.07/.726667 or $1.4725 per pound. So for exchange rates lower than $1.4725 per pound one year from now, the dollar currency will give a better return.。

金融学讲义(陈学彬主编)

金融机构的分类
按照业务性质的不同，金融机构可分为银行类金融机构和非银行类金融机构；按照是否接受公众存款，可分为存款性金融机构和非存款性金融机构。
金融机构的作用
金融机构在现代经济中发挥着信用中介、支付中介、金融服务、风险管理等重要功能。
金融市场与金融机构的关系
相互依存关系
金融市场和金融机构是相互依存的，金融市场为金融机构提供了交易场所和交易工具，而金融机构则是金融市场的参与者和推动者。
金融学的研究方法
01
实证研究方法
实证研究方法是通过收集和分析实际数据来验证理论假设的方法。在金
融学中，实证研究方法被广泛应用于金融市场、金融机构等领域的研究。
02
规范研究方法
规范研究方法是通过逻辑推理和演绎分析来研究金融问题的方法。这种
方法强调理论分析和逻辑推理，注重从一般到特殊的推导过程。
03
案例研究方法
货币政策工具
法定存款准备金率
再贴现政策
中央银行通过调整法定存款准备金率，影响商业银行的信贷扩张能力，从而调节市场中的货币供应量。
中央银行通过调整再贴现率，影响商业银行从中央银行获得资金的成本，进而调节市场利率和货币供应量。
公开市场操作
利率政策
中央银行在公开市场上买卖有价证券，从而调节市场中的流动性，影响市场利率和货币供应量。
和评估等。
金融风险与金融监管的关系
金融风险是金融监管的前提
正是由于金融风险的存在，才需要金融监管来防范和化解风险。
金融监管是控制金融风险的重要手段
通过有效的监管措施，可以及时发现和处置金融风险，维护金融市场的稳定和秩序。
金融风险与金融监管相互促进
在应对金融风险的过程中，金融监管不断完善和创新，同时金融风险的演变也促使金融监管不断改进和完善。

《金融学(第二版)》讲义大纲及课后习题答案详解十四章

CHAPTE R 14FORWARD AND FUTURE S PRICE SObjectives∙ To explain the economic role of futures markets∙To show what information can and cannot be inferred from forward and futures prices.Outline14.1 Distinctions Between Forward and Futures Contracts14.2 The Economic Function of Futures Markets14.3 The Role of Speculators14.4 Relation Between Commodity Spot and Futures Prices14.5 Extracting Information from Commodity Futures Prices14.6 Spot-Futures Price Parity for Gold14.7 Financial Futures14.8 The Implied Risk-Free Rate14.9 The Forward Price Is Not a Forecast of the Spot Price14.10 Forward-Spot Parity with Cash Payouts14.11 Implied Dividends14.12 The Foreign-Exchange Parity Relation14.13 The Role of Expectations in Determining Exchange RatesSummary∙ Futures contracts make it possible to separate the decision of whether to physically store a commodity from thedecision to have financial exposure to its price changes.∙ Speculators in futures markets improve the informational content of futures prices and make futures marketsmore liquid than they would otherwise be.∙ The futures price of wheat cannot exceed the spot price by more than the cost of carry:∙ The forward-spot price parity relation for gold is that the forward price equals the spot price times the cost ofcarry:This relation is maintained by the force of arbitrage . ∙One can infer the implied cost of carry and the implied storage costs from the observed spot and forward prices and the risk-free interest rate. ∙ The forward-spot parity relation for stocks is that the forward price equals the spot price times 1 plus the risk-free rate less the expected cash dividend.This relation can therefore be used to infer the implied dividend from the observed spot and forward prices and the risk-free interest rate.∙ The forward-spot price parity relation for the dollar/yen exchange rate involves two interest rates:where F is the forward price of the yen, S is the current spot price, r Y is the yen interest rate, and r $ is the dollarinterest rate.∙If the forward dollar/yen exchange rate is an unbiased forecast of the future spot exchange rate, then one can infer that forecast either from the forward rate or from the dollar-denominated and yen-denominated risk-free interest rates. F S C-≤F S r s =++()1F S r D=+-()1F r S r Y11+=+$Solutions to Problems at End of ChapterForward Contracts and Forward-Spot Parity.1. Suppose that you are planning a trip to E ngland. The trip is a year from now, and you have reserved a hotel room in London at a price of ₤ 50 per day. You do not have to pay for the room in advance. The exchange rate is currently $1.50 to the pound sterling.a.E xplain several possible ways that you could completely hedge the exchange rate risk in this situation.b.Suppose that r₤=.12 and r$=.08. Because S=$1.50, what must the forward price of the pound be?c.Show that if F is $0.10 higher than in your answer to part b, there would be an arbitrage opportunity. SOLUTION:a.Ways to hedge the exchange rate risk:Pay for the room in advanceBuy the pounds you will need in the forward market.Invest the present value of the rental payments in a pound-denominated riskless asset.b. F = S (1+r$)/(1+r£) = $1.50 x 1.08/1.12 = $1.4464 per poundc.If F is $1.55 then arbitrage profits can be made by borrowing dollars, investing in pounds and selling themforward at the inflated forward price. After paying off principle and interest on the dollars borrowed, you would have pure arbitrage profits left over. For example,Borrow $1.50,Convert it into 1 pound,Invest it in pound-denominated bonds to have 1.12 pounds a year from now,Sell 1.12 pounds forward at $1.55 per pound to have $1.736 a year from now,After 1 year, pay off the principle and interest on the loan ($1.50x 1.08 = $1.62).This series of transactions leaves you with $.116 a year from now with no initial outlay of your money.Forward-Spot Parity Relation with Known Cash Payouts2. Suppose that the Treasury yield curve is flat at an interest rate of 7% per year (compounded semiannually).a.What is the spot price of a 30-year Treasury bond with an 8% coupon rate assuming coupons are paidsemiannually?b.What is the forward price of the bond for delivery six months from now?c.Show that if the forward price is $1 lower than in your answer to part b, there should be an arbitrageopportunity.SOLUTION:b. The forward price for delivery six months from now is $1,124.089:F = S(1+r) - C = $1,124.724 x 1.035 - 40 =$1,124.089c. If the forward price is only $1,123.089, then arbitrage profits can be made by selling the bond short and buying itforward at the low forward price. It can be described as follows:Sell short a bond at $1,124.724; buy it forward at $1,123.089; invest the proceeds of the short sale to earn 3.5% for6 monthsAfter 6 months, take delivery of the bond and cover your short saleForward-Spot Parity Relation with Uncertain Dividends3. A stock has a spot price of $100; the riskless interest rate is 7% per year (compounded annually), and the expected dividend on the stock is $3, to be received a year from now.a.What should be the one-year futures price?b.If the futures price is $1 higher than your answer to part a, what might that imply about the expected dividend? SOLUTION:a.S = $100, r = .07, D = $3. F = S ( 1+r) - D = $104b.If F is $105, that might imply that D is really only $2.Storage Costs versus Dividend Yield4. Compare the forward-spot price-parity relation for gold to the one for stocks. Is it fair to say that stocks have a negative storage cost equal to the dividend yield?SOLUTIONOne could definitely say that stocks have a negative storage cost equal to the dividend.5. Suppose you are a distributor of canola seed and you observe the spot price of canola to be $7.45 per bushel while the futures price for delivery one month from today is $7.60. Assuming a $.10 per bushel carrying cost, what would you do to hedge your price uncertainty?SOLUTIONWe see that F> S+C. If you short the futures contract, you can sell your seed at $7.60 per bushel.6. Infer the spot price of an ounce of gold if you observe the price of one ounce of gold for forward delivery in three months is $435.00, the interest rate on a 91-day Treasury bill is 1% and the quarterly carrying cost as a percentage of the spot price is .2%.SOLUTIONDeduce from the futures price parity condition for gold that F = S0 (1 + r + s) so that S0 = $429.84.7. You are a dealer in kryptonite and are contemplating a trade in a forward contract. You observe that the current spot price per ounce of kryptonite is $180.00, the forward price for delivery of one ounce of kryptonite in one year is $205.20, and annual carrying costs of the metal are 4% of the current spot price.a.Can you infer the annual return on a riskless zero-coupon security implied by the Law of One Price?b.Can you describe a trading strategy that would generate arbitrage profits for you if the annual return on theriskless security is only 5%? What would your arbitrage profit be, per ounce of kryptonite?SOLUTIONa.By no-arbitrage, we require that the riskless rate r satisfy:F = S0 (1 + r + s)205.2 = 180 (1 +r +.04) = 187.2 + 180rr = 18/180 = .10 or 10%b.The implicit risk-free rate that you can earn by buying kryptonite, storing it, and selling it forward at $205.2 perounce is 10%. If the riskless borrowing rate is five percent, you should borrow at that rate and invest in hedged kryptonite. If you buy an ounce of kryptonite for $180, you will get $205.2 for it for sure a year from now. If you borrow the $180, you will have to pay principal and interest of $180 x 1.05 plus another .04 x $180 in storage costs.This totals $196.2, thus leaving you with $9 in arbitrage profits.8. Calculate the implicit cost of carrying an ounce of gold and the implied storage cost per ounce of gold if the current spot price of gold per ounce is $425.00, the forward price of an ounce of gold for delivery in 273 days is $460.00, the yield over 91 days on a zero-coupon Treasury bill is 2% and the term structure of interest rates is flat. SOLUTIONFirst, we solve it assuming a simple compounding method for the risk free interest rate. Over 273 days, the Risk free rate is 2%*3=6%. Therefore we have,F = S (1 + r + s )460 = 425 (1.06 + s)s = (460 - 450.5)/425 = 9.5/425 = .02235 for 273 daysThus the carrying costs are roughly 8.24% for 273 days or 10.98% per year.Second, we solve it assuming we need to compound the interest rates. The risk free rate over 273 days will be(1+2%)3-1=6.12%.plug in the above formulae we get s=.021145 for 273 days.Thus the carrying costs are roughly 8.23% for 273 days or 11.13% per year.9. The forward price for a share of stock to be delivered in 182 days is $410.00, whereas the current yield on a 91-day T-bill is 2%. If the term structure of interest rates is fiat, what spot price for the stock is implied by the Law of One Price?SOLUTIONF = $410; r = .02 per quarter.S = F/(1+r)2 = $394.0810. You observe that the one-year forward price of a share of stock in Kramer,Inc.,a New York tour-bus company and purveyor of fine clothing, is $45.00 while the spot price of a share is $41.00. If the riskless yield on a one-year zero-coupon government bond is 5%:a.What is the forward price implied by the Law of One Price?b.Can you devise a trading strategy to generate arbitrage profits? How much would you earn per share?SOLUTIONa.The no-arbitrage value of the forward price is F = $43.05.b.The observed forward price is excessive. Consider short-selling a forward contract and taking a long position ina portfolio consisting of one stock and the sale of a bond with face value of F. Future liabilities for this positionare zero, while the current cash inflow is $1.86.11. Infer the yield on a 273-day, zero-coupon Japanese government security if the spot price of a share of stock in Mifune and Associates is 4,750 yen whereas the forward price for delivery of a share in 273 days is 5,000 yen.SOLUTIONThe implied yield over the 273 day term is r = 5.26%.12. On your first day of trading in Vietnamese forward contracts, you observe that the share price of Giap Industries is currently 54, 000 dong while the one-year forward price is 60, 000 dong. If the yield on a one-year riskless security is fifteen percent, are arbitrage profits possible in this market? If not, explain why not. If so, devise an appropriate trading strategy.SOLUTIONArbitrage profits would seem to be possible, since the no-arbitrage forward price implied by these parameters isF = $62,100.The futures contract is underpriced, relative to this no-arbitrage value. Consider taking a long position in the forward contract and simultaneously selling a share of Giap stock and buying a riskless bond with a face value equal to the observed forward price. The liabilities from these joint positions are zero, while the current cash inflow is $1826.09.13. The share price of Schleifer and Associates, a financial consultancy in Moscow, is currently 10, 000 roubles whereas the forward price for delivery of a share in 182 days is 11,000 roubles. If the yield on a riskless zero-coupon security with term to maturity of 182 days is 15%, infer the expected dividend to be paid by Schleifer and Associates over the next six months.SOLUTIONThe implied dividend is 500 roubles.14. The spot rate of exchange of yen for Canadian dollars is currently 113 yen per dollar but the one-year forward rate is 110 yen per dollar. Determine the yield on a one-year zero-coupon Canadian government security if the corresponding yield on a Japanese government security is 2.21%.SOLUTIONThe implied Canadian rate over this term is approximately 5.00%.。

金融学陈学彬课后答案

金融学陈学彬课后答案【篇一：金融学第一章(讲稿)】t>教案2013～2014学年第一学期系(部、中心) 理工系教研室数学教研室课程名称金融学课程学时 68 授课方式课堂讲授授课对象数学1101 授课教师侯致武职称职务助教使用教材《金融学》高等教育出版社二〇一三年九月- 1 -（3）货币的价值取决于什么时候得到它——今天得到的1元钱比未来得到的1元钱更值钱；（4）不是每个人都知道相同的事情——金融市场上不同的参与者所持有的信息存在差别（信息不对称）。

2.如何界定目前的金融学？可见国内外学者对于金融和金融学的理解存在一定的偏差，考虑到目前国内学科发展的现状，我们的金融学在内容设置中将两部分兼顾，即以货币银行学的内容为基础，适度加入国外金融研究的基本知识点。

金融学就是研究金融系统的组织、结构、运行规律及其与经济系统的相互影响的科学。

金融学的主要研究对象是货币、信用、银行、金融调控的运动规律及其应用，研究范围是与经济发展紧密相关的金融领域，包括货币及货币制度、信用、利息与利率、金融机构与金融市场、商业银行、中央银行、金融监管、通货膨胀与通货紧缩、货币政策、金融与经济发展等内容。

二、《金融学》课程简介1.金融的重要性“大家都知道有那么回事，但不知道是怎么一回事。

”——旧约全书。

邓小平在1991年视察上海时指出：“金融很重要，是现代经济的核心。

金融搞好了，一着棋活，全盘皆活。

”再比如：（1）从普通的货币到引人入胜甚至眩目的股票债券市场、期货市场、各种神秘的衍生证券交易；（2）从纳斯达克一夜暴富的神话到认识金融危机的巨大破坏性和传染性。

例如，1997年爆发的亚洲金融危机：泰国、韩国、马来西亚；（3）从索罗斯量子基金掀起的金融风暴到国际金融市场上来去匆匆hot money（热钱）以及基金交易背后的黑幕揭露；（4）从人民币是否该升值的争论到巨额外汇储备的评判；（5）从倒金字塔形交易结构探究虚拟经济与实体经济。

金融学第二版课后习题答案

金融学第二版课后习题答案金融学第二版课后习题答案金融学是一门研究金融市场、金融机构和金融工具的学科，它对于理解和解决现代金融问题具有重要意义。

而课后习题则是帮助学生巩固所学知识、提高解决问题能力的重要工具。

本文将为读者提供金融学第二版课后习题的答案，以帮助读者更好地理解金融学的概念和理论。

第一章：金融的基本概念和职能1. 金融的基本概念是指金融的定义和范围。

金融的定义是指金融活动和金融制度的总称。

金融的范围包括金融市场、金融机构和金融工具等。

2. 金融的职能是指金融对于经济发展和社会进步的作用。

金融的主要职能包括储蓄和融资、支付和结算、风险管理和信息中介等。

第二章：金融市场1. 金融市场的分类包括货币市场、资本市场和衍生品市场等。

货币市场是指短期资金融通的市场，资本市场是指长期资金融通的市场，衍生品市场是指金融衍生品交易的市场。

2. 金融市场的功能包括资源配置、风险管理和信息传递等。

资源配置是指将资金从供给者转移给需求者的过程，风险管理是指通过金融市场进行风险的转移和分散，信息传递是指金融市场通过价格和交易信息传递经济信息。

第三章：金融机构1. 金融机构的分类包括银行、非银行金融机构和金融市场机构等。

银行是最重要的金融机构，它包括商业银行、中央银行和政策性银行等。

2. 金融机构的职能包括储蓄和融资、支付和结算、风险管理和信息中介等。

储蓄和融资是指金融机构接受存款并提供贷款的过程，支付和结算是指金融机构提供支付和结算服务的过程，风险管理是指金融机构通过风险评估和风险转移来管理风险，信息中介是指金融机构通过收集、加工和传递信息来提供金融服务。

第四章：金融工具1. 金融工具的分类包括货币工具、债券、股票和衍生品等。

货币工具是指短期借贷和短期投资的金融工具，债券是指借款人向债权人发行的债务凭证，股票是指公司向股东发行的所有权凭证，衍生品是指衍生自其他金融资产的金融工具。

2. 金融工具的特点包括流动性、收益性和风险性等。

金融学第二版讲义大纲及课后习题答案详解第十章

CHAPTER 10AN OVERVIEW OF RISK MANAGEMENTObjectives« To explore how risk affects finan cial decisi on-mak ing.« To provide a con ceptual framework for the man ageme nt of risk.«To explain how the financial system facilitates the efficient allocation of risk-bearing.Outline10.1 What Is Risk?10.2 Risk and Econo mic Decisi ons10.3 The Risk Ma nageme nt Process10.4 The Three Dime nsions of Risk Tran sfer10.5 Risk Tran sfer and Econo mic Efficie ncy10.6 In stituti ons for Risk Man ageme nt10.7 Portfolio Theory: Quan titative An alysis for Optimal Risk Man ageme nt10.8 Probability Distributions of ReturnsSummary* Risk is defined as uncertainty that matters to people. Risk management is the process of formulating the benefit- cost trade-offs of risk-reduction and deciding on a course of action to take. Portfolio theory is the quantitative analysis of those trade-offs to find an optimal course of action.* All risks are ultimately borne by people in their capacity as consumers, stakeholders of firms and other econo mic orga ni zati ons, or taxpayers.* The risk in ess of an asset or a tra nsacti on cannot be assessed in isolati on or in the abstract; it depe nds on the specific frame of refere nee. In on e con text, the purchase or sale of a particular asset may add to one ' s risk exposure; in another, the same transaction may be risk-reducing.* Speculators are in vestors who take positi ons that in crease their exposure to certa in risks in the hope of in creas ing their wealth. In con trast, hedgers take positi ons to reduce their exposures. The same pers on can be a speculator on some exposures and a hedger on others.* Many resource-allocation decisions, such as saving, investment, and financing decisions, are significantly in flue need by the prese nee of risk and therefore are partly risk-ma nageme nt decisi ons.* We disti nguish among five major categories of risk exposures for households: sick ness, disability, and death job loss; consumer-durable asset risk ; liability risk ; and financial asset risk .* Firms face several categories of risks: production risk , price risk of outputs , and price risk of in puts .* There are five steps in the risk-management process: risk identification, risk assessment, selection of riskman ageme nt tech ni ques, impleme ntati on, review.* There are four techniques of risk management: r isk avoidanee, loss prevention and control, risk retention, risk tra nsfer.* There are three dimensions of risk transfer: hedging , insuring , and diversifying .* Diversificati on improves welfare by spread ing risks among many people, so that the existi ng un certa inty matters less. * From society ' s perspective-n^ageme nt in stituti ons con tribute to econo mic efficie ncy in two importa nt ways. First, they shift risk away from those who are least willing or able to bear it to those who are most willing to bear it. Second, they cause a reallocation of resources to production and consumption in accordance with the new distribution of risk-bearing.By allowing people to reduce their exposure to the risk of undertaking certain bus in ess ven tures, they may en courage en trepre neurial behavior that can have a ben efit to society.* Over the cen turies, various econo mic orga ni zati ons and con tractual arra ngeme nts have evolved to facilitate a more efficient allocation of risk-bearing by expanding the scope of diversification and the types of risk that are shifted.* Among the factors limit ing the efficie nt allocati on of risks are tra nsacti ons costs and problems of adverse selecti on and moral hazard.Solutions to Problems at End of ChapterOn the Nature of Risk and Risk Management1. Suppose that you and a friend have decided to go to a movie together next Saturday. You will select any movie for which tickets are available when you get to the theater. Is this a risky situation for you? Explain. Now suppose that your friend has already purchased a ticket for a movie that is going to be released this Saturday. Why is this a risky situation? How would you deal with the risk?SOLUTION:No, the uncertainty doesn ' t represienncteriysokusdo not care which movie you see. However, if your friend has a ticket already, and if you wait till Saturday to buy yours, the show may be sold out. To eliminate the risk that you may not be able to sit with your friend and see the same movie, you might buy your ticket in advance.2. Suppose you are aware of the following investment opportunity: You could open a coffee shop around the corner from your home for $25,000. If business is strong, you could net $15,000 in after-tax cash flows each year over the next 5 years.a. If you knew for certain the business would be a success, would this be a risky investment?b. Now assume this is a risky venture and that there is a 50% chance it is a success and a 50% chance you gobankrupt within 2 years. You decide to go ahead and invest. If the business subsequently goes bankrupt, did you make the wrong decision based on the information you had at the time? Why or why not?SOLUTION:a. No, this investment would not be risky.b. No, you did not make a “ wrong ” decision. When you made your decision, you did not know for certain that thecompany would go bankrupt. You decided to invest for many reasons, including the possibility of making a lot of money.Given your tolerance for risk and the fact that you based our decision on the information available at the time, your decision was not wrong and may have been optimal at the time.3. Suppose you are a pension fund manager and you know today that you need to make a $100,000 payment in 3 months.a. What would be a risk-free investment for you?b. If you had to make that payment in 20 years instead, what would be a risk free investment?c. What do you conclude from your answers to Parts a and b of this question?SOLUTION:a. A risk-free investment for you would be a Treasury Bill (default risk free) which matures in exactly 3 months.b. A risk-free investment would be a zero coupon U.S. Treasury security maturing in 20 years and which would have thesame single payment of $100,000.c. Because risk is dependent upon circumstances, what is risk-free for one individual may be risky for another too. There canbe any number of risk-free investments depending upon circumstances. Your investment time horizon is critical tochoosing the best risk-free investment (so payments in can exactly match payments out so that you are left with no risk).4. Is it riskier to make a loan denominated in dollars or in yen?SOLUTION:It depends on the context. For people whose income and expenses are denominated in dollars (perhaps because they live in the U.S), denominating a loan in yen would be riskier than denominating it in dollars. But for someone whose income and expenses are denominated in yen, denominating the loan in yen would be less risky than in dollars.5. Which risk management technique has been chosen in each of the following situations?« Installing a smoke detector in your home« Investing savings in T-bills rather than in stocks« Deciding not to purchase collision insurance on your car« Purchasing a life insurance policy for yourselfSOLUTION:« Loss preve nti on and con trol.・Risk avoida nee« Risk rete nti on・Risk tran sfer6. You are considering a choice between investing $1,000 in a conventional one-year T-Bill offering an interest rate of 8% and a one-year Index 丄inked Inflation Plus T-Bill offering 3% plus the rate of inflation.a. Which is the safer investment?b. Which offers the higher expected return?c. What is the real return on the Index 丄inked Bond?SOLUTION:a. The inflation-indexed T-Bill offers a fixed real rate of return of 3% over the life of the investment. The realreturn on the conventional T- Bill ' s real return depends upon the expected rate of inflation over the life of thein vestme nt. The safer in vestme nt is the In flati on Plus T-Bill.b. The real rate of return on the conventional T-Bill depends upon the expected rate of inflation over the life of thein vestme nt. You do not know which expected retur n is higher unl ess you know what in flati on is expected to be.c. The real retur n on the in dex-l in ked T-Bill is 3%.Hedging and Insurance7. Suppose you are interested in financing your new home purchase. You have your choice of a myriad financing options. You could enter into any one of the following agreements: 8% fixed rate for 7 years, 8.5% fixed rate for 15 years, 9% fixed for 30 years. In addition, you could finance with a 30-year variable rate that begins at 5% and increases and decreases with the prime rate, or you could finance with a 30year variable rate that begins at 6% with ceilings of 2% per year to a maximum of 12% and no minimum.a. Suppose you believe that interest rates are on the rise. If you want to completely eliminate your risk of risinginterest rates for the longest period of time, which option should you choose?b. Would you consider that hedging or insuring? Why?c. What does you r risk management decision “ cost ” you in terms of quoted interest rates during the firstyear?SOLUTION:a. You would choose the 30-year fixed rate at 9%.b. That would be a hedge because you have elim in ated both the upside (decli ning rates) or dow nside ( rising rates).c. This costs me at least 4% since I could get a variable rate loa n at 5%.8. Referring to the information in problem 7, answer the following:a. Suppose you believe interest rates are going to fall, which option should you choose?b. What risk do you face in that transaction?c. How might you insure against that risk? What does that cost you (in terms of quoted interest rates?). SOLUTION:a. You would want one of the variable rate options, in particular the variable loan tied to the prime rate, currently equal to5%.b. You face the risk of rising rates.c. You could in sure aga inst that risk by purchas ing the opti on to have a 12% ceil ing on the rate (2% in crease per year.This option cost you 1% (the difference between 6% and 5%).9. Suppose you are thinking of investing in real estate. How might you achieve a diversified real estate investment?SOLUTION:« You could own several differe nt build ings in the same gen eral area.« You could own several differe nt build ings in differe nt geographic areas.« You could sell some of your equity own ership to other owners to lower your own in dividual exposure to decli ning market values.10. Suppose the following represents the historical returns for Microsoft and Lotus Development Corporation:Historical ReturnsYear MSFT LOTS110%9%215%12%3-12%-7%420%18%57%5%a. What is the mean return for Microsoft? For Lotus?b. What is the standard deviation of returns for Microsoft? For Lotus?c. Suppose the returns for Microsoft and Lotus have normally distributed returns with means and standarddeviations calculated above. For each stock, determine the range of returns within one expected standard deviation of the mean and within two standard deviations of the mean.SOLUTION:a. Mea n return Microsoft: 8.0%; Lotus: 7.4%b. If you use the formula for the sta ndard deviati on based on a sample of size n:You find that the standard deviations are: MSFT: 10.94%; Lotus: 8.357%.However, if you use the formula for the population standard deviation:You find that the standard deviations are: MSFT 12.23% and LOTS 9.34%.c. Range of returns within 1 standard deviation Microsoft: -2.94% to +18.94% Range of returns within 1 standarddeviation Lotus: -0.957% to + 15.76% Range of returns within 2 standard deviations Microsoft: -13.88% to+29.88% Range of returns within 1 standard deviation Lotus: -9.31% to + 24.11%。

《金融学（第二版）》讲义大纲及课后习题答案详解十三章

《⾦融学（第⼆版）》讲义⼤纲及课后习题答案详解⼗三章CHAPTER 13THE CAPITAL ASSET PRICING MODELObjectivesExplain the theory behind the CAPM.Explain how to use the CAPM to establish benchmarks for measuring the performance of investment portfolios. Explain how to infer from the CAPM the correct risk-adjusted discount rate to use in discounted-cash-flow valuation models. Explain the APT and its relationship to the CAPM.Outline13.1 The Capital Asset Pricing Model in Brief13.2 Determinants of the Risk Premium on the Market Portfolio13.3 Beta and Risk Premiums on Individual Securities13.4 Using the CAPM in Portfolio Selection13.5 Valuation and Regulating Rates of Return13.6 Extensions, Modifications, and Alternatives to the CAPMSummaryThe CAPM has three main implications:In equilibrium, ev eryone’s relative holding of risky assets are the same as in the market portfolio.The size of the risk-premium of the market portfolio is determined by the risk-aversion of investors.The risk premium on any asset is equal to its beta times the risk premium on the market portfolio.Whether or not the CAPM is strictly true, it provides a rationale for a very simple passive portfolio strategy: Diversify your holdings of risky assets in the proportions of the market portfolio, andMix this portfolio with the risk-free asset to achieve a desired risk-reward combination.The CAPM is used in portfolio management primarily in two ways:To establish a logical and convenient starting point in asset allocation and security selectionTo establish a benchmark for evaluating portfolio management ability on a risk-adjusted basis.In corporate finance the CAPM is used to determine the appropriate risk-adjusted discount rate in valuation models of the firm and in capital budgeting decisions. The CAPM is also used to establish a “fair” rate of return on invested capital for regulated firms and in cost-plus pricing.Today few financial scholars consider the CAPM in its simplest form to be an accurate model for explaining or predicting risk premiums on risky assets. However, modified versions of the model are still a central feature of the theory and practice of finance.The APT gives a rationale for the expected return-beta relationship that relies on the condition that there be no arbitrage profit opportunities; the CAPM requires that investors be portfolio optimizers. The APT and CAPM are not incompatible; rather, they complement each other.Solutions to Problems at End of ChapterComposition of the Market Portfolio1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a risklessgovernment security. Evaluated at current prices in US dollars, the total market values of these assets are, respectively, $24 billion, $36 billion, $24 billion and $16 billion.a. Determine the relative proportions of each asset in the market portfolio.b. If one trader with a $100,000 portfolio holds $40,000 in the riskless security, $15,000 in X, $12,000 in Y, and$33,000 in Z, determine the holdings of the three risky assets of a second trader who invests $20, 000 of a $200, 000 portfolio in the riskless security.SOLUTION:The total value of all assets in the economy is 100 billion dollars. a. The proportions of each asset relative to the value of all assets are, respectively, .24 (X), .36 (Y),b. .24 (Z) and .16 (riskless bond.) The proportions of each risky asset to the total value of all risky assets are, respectively, (2/7) (X), (3/7) (Y) and (2/7) (Z).c. . Ignore the question as it appears in the First Edition of the textbook. Instead, the question should be: If aninvestor has $100,000 with $30,000 invested in the riskless asset, how much is invested in securities X, Y, and Z? The answer to this question is $20,000 in X and Z, and $30,000 in Y.Implications of CAPM2. The riskless rate of interest is .06 per year, and the expected rate of return on the market portfolio is .15 per year.a. According to the CAPM , what is the efficient way for an investor to achieve an expected rate of returnof .10 per year?b. If the standard deviation of the rate of return on the market portfolio is .20, what is the standarddeviation on the above portfolio?c. Draw the CML and locate the foregoing portfolio on the same graph.d. Draw the SML and locate the foregoing portfolio on the same graph.e. Estimate the value of a stock with an expected dividend per share of $5 this coming year, an expecteddividend growth rate of 4% per year forever, and a beta of .8. If its market price is less than the value you have estimated, i.e., if it is under-priced, what is true of its mean rate of return?SOLUTION: a.So one would hold a portfolio that is 4/9 invested in the market portfolio and 5/9 in the riskless asset. b.c. The formula for the CML is9415.)1(06.10.)()1()(=+-=?+-?=x xx x r E x r r E M f 08889.)20(.94==?=M x σσσσσ45.06.)()(+=-+=MfM f r r E r r Ed. The formula for the SML ise. Use constant growth rate DDM and find r using the SML relationIf the market price of the stock is less than this, then its expected return is higher than the 13.2% required rate.()ββ09.06.)()(+=-+=f M f r r E r r E 35.54$04.132.504.510=-=-=-=r g r D P 132.8.09.06.09.06.=?+=+=βr3. If the CAPM is valid, which of the following situations is possible? Explain. Consider each situation independently. a.PortfolioExpected ReturnBeta A 0.20 1.4B 0.25 1.2b.PortfolioExpected ReturnStandard DeviationA 0.300.35B 0.400.25c.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A 0.160.12d.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A0.200.22SOLUTION:a. Impossible. Since the risk premium on the market portfolio is positive, a security with a higher beta must have ahigher expected return.b. Possible. Since portfolios A & B are not necessarily efficient, A can have a higher standard deviation and alower expected return than B.c. Impossible. Portfolio A lies above the CML, implying that the CML is not efficient. If the standard deviation ofA is .12, then according to the CML its expected return cannot be greater than .14.d. Impossible. Portfolio A has a lower standard deviation and a higher mean return than the market portfolio,implying that the market portfolio is not efficient.4. If the Treasury bill rate is currently 4% and the expected return to the market portfolio over the same period is 12%, determine the risk premium on the market. If the standard deviation of the return on the market is .20, what is the equation of the Capital Market Line?SOLUTION: The risk premium on the market portfolio is .08. The slope of the CML is .08/.2 = .4. Thus, the equation of the CML is:Determinants of the Market Risk Premium5. Consider an economy in which the expected return on the market portfolio over a particular period is .25, the standard deviation of the return to the market portfolio over this same period is .25, and the averagedegree of risk aversion among traders is 3. If the government wishes to issue risk-free zero-coupon bonds with a term to maturity of one period and a face value per bond of $100,000, how much can the government expect to receive per bond? []σσσ4.04.)()(+=++=MfMf r rE r r ESOLUTION:According to the CAPM, E(r M) - r f = Aσ2, so that r f = E(r M) - Aσ2.Substituting into this formula we find: r f = .25 – 3 x .252 = .0625Therefore the revenue raised by the government per bond issued is $100,000 = $94,117.651.06256. . Norma Swanson has invested 40% of her wealth in MGM stock and 60% in Industrial Light and Magic stock. Norma believes the returns to these stocks have a correlation of .06 and that their respective means and standard deviations are: MGM ILMExpected Return (%) 10 15Standard Deviation (%) 15 25a.Determine the expected value and standard deviation of the return on Norma’s portfolio.b.Would a risk-averse investor such as Norma prefer a portfolio composed entirely of only MGM stock? Ofonly ILM stock? Why or why not?SOLUTION:a.The expected return is .13, and the standard deviation is .1649.b. A risk averse investor will not want to hold a portfolio composed entirely of MGM or of ILM stock, becauseone can, in general, achieve the same expected return with a lower standard deviation by combining a portfolio of MGM and ILM with the risk-free asset.7. Consider a portfolio exhibiting an expected return of 20% in an economy in which the riskless interest rate is 8%, the expected return to the market portfolio is thirteen percent, and the standard deviation of the return to the market portfolio is .25. Assuming this portfolio is efficient, determine:a.its beta.b.the standard deviation of its return.c.its correlation with the market return.SOLUTION:/doc/ad5801fd700abb68a982fb59.html e the security market line to infer that the beta of this portfolio is 2.4:.20 = .08 + β(.13 - .08)β = (.20 - .08)/(.13 - .08) = .12/.05 = 2.4/doc/ad5801fd700abb68a982fb59.html e the capital market line to infer that the standard deviation of the yield to this portfolio is .6:.20 = .08+ (.13 - .08) σ = .08+ .2 σ.25σ = .12/.2 = .6c.By definition the following relationships hold:β = cov/σ2Mρ = covσiσMwhere ρ denotes the correlation coefficient. We know that β = 2.4, σM = .25, and σi = .6.So from the definition of β, we get that the cov is 2.4 x .252 = .15. Substituting this into the definition of ρ: ρ = cov = .15 __ = 1σiσM .6 x .25Application of CAPM to Corporate Finance8. . The Suzuki Motor Company is contemplating issuing stock to finance investment in producing a new sports-utility vehicle, the Seppuku. Financial analysts within Suzuki forecast that this investment will have precisely the same risk as the market portfolio, where the annual return to the market portfolio is expected to be 15% and the current risk-free interest rate is 5%. The analysts further believe that the expected return to the Seppuku project will be 20% annually. Derive the maximal beta value that would induce Suzuki to issue the stock.SOLUTION:The project would be on the borderline if its required return were 20% per year. Since the risk-free rate is 5% and the risk premium on the market portfolio is 10%, the required return would be 20% if the beta were 1.5.9. . Roobel and Associates, a firm of financial analysts specializing in Russian financial markets, forecasts that the stock of the Yablonsky Toy Company will be worth 1,000 roubles per share one year from today. If the riskless interest rate on Russian government securities is 10% and the expected return to the market portfolio is 18% determine how much you would pay for a share of Yablonsky stock today if:a.the beta of Yablonsky is 3.b.the beta of Yablonsky is 0.5.SOLUTION:Use the security market line in each case to determine a required rate of return, then infer the current price from the forecasted price of 1,000 roubles and the required rate of return you have determined.a.If beta is 3, the required return is .10+ 3x.08 = .34. You would pay 1,000/1.34 = 746.27 roubles;b.If beta is .5, the required return is .10+ .5x.08 = .14. You would pay 1,000/1.14 = 877.19 roubles.Application of CAPM to Portfolio Management10. Suppose that the stock of the new cologne manufacturer, Eau de Rodman, Inc., has been forecast to havea return with standard deviation .30 and a correlation with the market portfolio of .9. If the standard deviation of the yield on the market is .20, determine the relative holdings of the market portfolio and Eau de Rodman stock to form a portfolio with a beta of 1.8.SOLUTION: By definition:β = cov/σ2Mρ = covσrσMTherefore, β = ρσr/σM. The beta of Rodman stock is therefore .9x.3/.2 = 1.35.The beta of a portfolio is a weighted average of the betas of the component securities. Let A be a fraction of the portfolio invested in Rodman stock to produce a beta of 1.8. Then we have:1.35A + (1-A) = 1.8.35A = .8A = 2.286So the portfolio would have to have 228.6% invested in Rodman stock and a short position in the market portfolio equal to 128.6%.11. The current price of a share of stock in the Vo Giap Clothing Company of Vietnam is 50 dong and its expected yield over the year is 14%. The market risk premium in Vietnam is 8% and the riskless interest rate 6%. What would happen to the stock’s current price if its expected future payout remains co nstant while the covariance of its rate of return with the market portfolio falls by 50%?SOLUTION:Deduce that the expected future price of a share of Vo Giap is 57 dong, so that a reduction in this stock’s beta of 50% implies, by the security market relation, that the required yield on Vo Giap is now 10%, so that its current share price rises by 3.64% toa new value of 51.82 dong.12. Suppose that you believe that the price of a share of IBM stock a year from today will be equal to the sumof the price of a share of General Motors stock plus the price of a share of Exxon, and further you believethat the price of a share of IBM stock in one year will be $100 whereas the price of a share of General Motors today is $30. If the annualized yield on 91-day T-bills (the riskless rate you use) is 5%, the expected yield on the market is 15%, the variance of the market portfolio is 1, and the beta of IBM is 2, what price would you be willing to pay for one share of Exxon stock today?SOLUTION:Expected return = .05 + 2(.15 - .05) = 25%; (100 - x)/x = .25 → x = $80Deduce that the current price of a share of IBM stock is $80, so that the upper bound on the price of a share of Exxon is ($80 -$30 = $50).13. Ascertain whether the following quotation is true or false, and state why:“When arbitrage is absent from financial markets, and investors are each concerned with only the risk and return to their portfolios, then each investor can eliminate all the riskiness of his investments through diversification, and as a consequence the expected yield on each available asset will depend only on the covariance of its yield with the covariance of the yield on the diversified portfolio of risky assets each investor holds.”SOLUTION:False. You cannot eliminate all risk through diversification, only the unsystematic risk.Application of CAPM to Measuring Portfolio Performance14. During the most recent 5-year period, the Pizzaro mutual fund earned an average annualized rate of return of 12% and had an annualized standard deviation of 30%. The average risk-free rate was 5% per year. The average rate of return in the market index over that same period was 10% per year and the standard deviation was 20%. How well did Pizzaro perform on a risk-adjusted basis?SOLUTION:Compute the ratio of average excess return to standard deviation for Pizzaro and compare it to that of the market portfolio: Pizzaro risk-adjusted performance ratio = (.12-.05)/.30 = .233Market portfolio risk-adjusted performance ratio = (.1-.05)/.2 = .250So, on a risk-adjusted basis, Pizzaro did worse than the market index.Challenge ProblemCAPM with only 2 Risky Assets15. There are only two risky assets in the economy: stocks and real estate and their relative supplies are 50% stocks and 50% real estate. Thus, the market portfolio will be half stocks and half real estate. The standard deviations are .20 for stocks, .20 for real estate, and the correlation between them is 0. The coefficient of relative risk aversion of the average market participant (A) is 3. r f is .08 per year.a.According to the CAPM what must be the equilibrium risk premium on the market portfolio, on stocks,and on real estate?b.Draw the Capital Market Line. What is its slope? Where is the point representing stocks located relativeto the CML?c.Draw the SML. What is its formula? Where is the point representing stocks located relative to the SML? SOLUTION: a.The market portfolio consists of half stocks and half real estate. It has a standard deviation of .1414, computedas follows:σ2M = w2σ2s + (1-w)2σ2r+ 2 w(1-w) cov s,rσ2M = 2 x (1/2)2 .22 = .02σM = .1414The equilibrium risk premium on the market portfolio is E(r M)-r f = Aσ2M = 3x.02 = .06.The market portfolio’s expected rate of return is also a weighted average of the expected rates of return on stocks and real estate, where the weights are each 1/2. Stocks and real estate must have the same risk premiumbecause they have the same standard deviation and correlation with the market. Therefore the risk premium on stocks and real estate must be .06, the same as the market portfolio’s risk premium.b.The slope of the CML is .06/.1414 = .424. The point representing stocks is M, it is to the right of the CML.equaling to 1.The formula is: E(r) = r f + (E(r M) –r f).。

《金融学(第二版)》讲义大纲及课后习题答案详解第五章

CHAPTER 5LIFE-CYCLE FINANCIAL PLANNINGObjectivesIn this chapter you will learn how to analyze:•How much to save for retirement.•Whether to defer taxes or pay them now.•Whether to get a professional degree.•Whether to buy or rent an apartment.•How to minimize estate taxes.Outline5.1 A Life-Cycle Model of Saving5.2 Taking Account of Social Security5.3 Deferring Taxes Through Voluntary Retirement Plans5.4 Should You Invest in a Professional Degree?5.5 Should You Buy or Rent?Summary•In making lifetime saving/consumption decisions:(1) Do the analysis in real terms (constant dollars) to simplify the calculations and to avoid having toforecast inflation.(2) Start by computing the present value of your lifetime resources. The present value of your lifetimespending cannot exceed this amount.•Social security or any other forced saving program will offset voluntary saving. It may have a positive or a negative effect on the present value of your total lifetime resources.•Tax-deferred retirement accounts are advantageous because they allow you to earn a before-tax rate of return until money is withdrawn from the account. They are advantageous if you are in the same tax bracket before and after you retire, and even more so if your tax bracket is lower after you retire. •Getting a professional degree can be evaluated as an investment in human capital. As such, it should be undertaken if the present value of the benefits (such as increase in your earnings) exceeds the present value of the costs (such as tuition and forgone salary.)•In deciding whether to buy or rent an apartment or a consumer durable, choose the alternative with the lower present value of costsSolutions to Problems at End of ChapterSaving for Retirement1. Assume that you are 40 years old and wish to retire at age 65. You expect to be able to average a 6% annual rate of interest on your savings over your lifetime (both prior to retirement and after retirement). You would like to save enough money to provide $8,000 per year beginning at age 66 in retirement income to supplement other sources (social security, pension plans, etc.). Suppose you decide that the extra income needs to be provided for only 15 years (up to age 80). Assume that your first contribution to the savings plan will take place one year from NOW.a.How much must you save each year between now and retirement to achieve your goal?b.If the rate of inflation turns out to be 6% per year between now and retirement, how much willyour first $8000 withdrawal be worth in terms of today’s purchasing power?SOLUTION:a. Age 40 41 65 66 80Time 0 1 25 26 40. . . .X X 8,000 8,000It is a 2 part computation. First compute the amount needed at age 65 to finance the $8,000 per year annuityin terms of today’s purchasing power.2. You are saving for retirement and you come across the following table. It shows the percentage of your current salary that you should save for your retirement in order to retire with an annuity equal to 70% of your salary if you have not yet saved anything. It assumes that your annual salary will remain constant in real terms until retirement, and that you will live for 25 years after retiring. For instance, if you have 35 years left before you retire and earn3.5% per year on your investments, then you should save 17.3% of your current salary.a. Fill in the missing number in Table A.SOLUTION:The method for computing how much saving is needed to reach the desired target (70%) consists of two steps:First compute the amount you need to have accumulated in your personal retirement account when you reach the retirement age. (We’ll do the calculations as percentages of real salary)Then compute the annual amount of saving needed to reach that future value59.79% if you have 15 years to retire29.62% if you have 25 years to retire17.30% if you have 35 years to retireb. Now fill in Table B. It assumes that instead of targeting a 70% replacement rate of preretirement income, your goal is to maintain the same level of consumption spending both before and after retirement.First compute the amount you need to have accumulated in your personal retirement account when you reach the retirement age. (We’ll do the calculations as percentages of real salary)Then compute the annual amount of saving needed to reach that future value85.41% if you have 15 years to retire42.31% if you have 25 years to retire24.72% if you have 35 years to retire3. You are saving for retirement and you come across the following the table. It shows the increase in the annual benefit you can receive in retirement per dollar that you increase your annual retirement saving in the years before retirement. It assumes that you will live for 20 years after retiring. For instance, if you have 30 years left before you retire and earn an interest rate of 3% per year, then you will obtain an increase of $3.20 in your annual retirement benefit for every $1 per year increase in annual saving. Fill in the missing table values.4. George Thriftless is 45 years old, earns $50,000 per year, and expects that his future earnings will keep pace with inflation, but will not exceed inflation. He has not yet saved anything towards his retirement. His company does not offer any pension plan. George pays Social Security taxes equal to 7.5% of his salary, and he assumes that when he retires at age 65, he will receive $12,000 per year in inflation-adjusted Social Security benefits for the rest of his life. His life expectancy is age 85.George buys a book on retirement planning that recommends saving enough so that when private savings and Social Security are combined, he can replace 80% of his preretirement salary. George buys a financial calculator and goes through the following calculations:First, he computes the amount he will need to receive in each year of retirement to replace 80% of his salary: .8 x $50,000 = $40,000.Since he expects to receive $12,000 per year in Social Security benefits, he calculates that he will have to provide the other $28,000 per year from his own retirement fund.Using the 8% interest rate on long-term default-free bonds, George computes the amount he will need to have at age 65 as $274,908 (the present value of $28,000 for 20 years at 8% per year). Then he computes the amount he will have to save in each of the next 20 years to reach that future accumulation as $6,007 (the annual payment that will produce a future value of $274,908 at an interest rate of 8% per year). George feels pretty confident that he can save 12% of his salary (i.e., $6,007/$50,000) in order to insure a comfortable retirement.a.If the expected long-term real interest rate is 3% per year, approximately what is the long-term expected rate of inflation?b.Has George correctly taken account of inflation in his calculations? If not, how would youcorrect him?c.How much should George save in each of the next 20 years (until age 65) if he wants tomaintain a constant level of consumption over the remaining 40 years of his life (from age 45 to age 85)?Ignore income taxes.SOLUTION:a. The long-term expected rate of inflation can be approximated by subtracting the expected real rate ofinterest (3% per year) from the long-term nominal interest rate (8% per year). The expected rate of inflation is therefore approximately 5% per year.The exact value can be calculated using:1+nom= (1+real)(1+inf)hence, the inflation rate is 4.854% per year.b. George has used the nominal interest rate to discount real cash flows. As a result, he has seriouslyunderestimated how much saving he must do to achieve an 80% replacement rate. The time line for this problem is:Age 45 46 65 66 85Time 0 1 20 21 40. . . .X X 28,000 28,000Using the real rate of 3% per year in the calculations results in a needed accumulation at age 65 of $416,569.30:The annual saving needed to achieve this accumulation at a 3% real rate is $15,502.92:So instead of $6,007 per year, George must save $15,502.92 per year. This is 31% of his salary rather than 12%.c. The time line for this problem is:Age 45 46 65 66 85Time 0 1 20 21 40. . . .Inflows 46,250 46,250 12,000 12,000Outflows C CIf George wants to maintain a constant level of consumption both before and after retirement, he must find C , where C is the solution to the following equation:∑∑∑===+=40140212010310001203125046031t t tt t t .,.,.C Equation 1 says that the present value of consumption spending over the next 40 years equals the present value of labor income over the next 20 years (after paying Social Security taxes) plus the present value of Social Security benefits received after retirement.First we find the value on the right side of the equation, the PV of George’s lifetime resources:Step 4: Find PV of lifetime resources as of age 45:688,083.21 + 98,847.56 = 786,930.78So each year between the ages of 46 and 65 George must save $12,205.50, the difference between his income after SS tax ($46,250) and his consumption spending ($34,044.50).Now let us check to make sure that by saving this amount George will indeed have enough to provide the same constant level of consumption spending after retirement as before.Thus, by saving $12,205.50 per year for 20 years earning a real rate of 3% per year, he will have at age 65 an accumulation of $327,966.36.Adding this annuity to the SS benefit we get:$22,044.50 + $12,000 = $34,044.505. George’s company has a defined-benefit pension plan. Suppose the plan pays a benefit equal to 1% of final salary per year of service. George is 40 years old and has worked for the company for 15 years. His last year’s salary was $50,000 and is expected to remain so in real terms until retirement. The expected rate of inflation is 4%.a.If normal retirement age is 65, the interest rate is 8%, and Geor ge’s life expectancy is 80, what isthe present value of his accrued pension benefit?b.What effect should his pension benefit have on George’s planned saving assuming he has a 75%target replacement rate?SOLUTION:a.George’s last year salary $50,000 has a r eal growth rate of 0%, hence it will keep up with inflation untilretirement but not beat it. At retirement, he would have worked for the company for a total of forty years. Hence his annual pension benefit will be equal to 1% x (50,000x 1.0425) x 40 = $53,316.73. We must first find the value of those annual payments in the year when he retires, then discount that back to today.PV65 = $456,363.4140b.For a 75% replacement rate, George expects to have an annual income of 0.75 x 50,000 =$37,500 inreal terms after retirement. Since his pension benefit is providing him with part of his financial needs after retirement, he would only need to worry about the difference between his target income and what the pension is providing him, hence decreasing his planned savings before retirement.6.Analyze the “expert’s” responses to the following questions:Question: How early do you recommend people begin saving for retirement? Would it be too early for my 14-year-old to start saving?Expert: It’s never too early.Question: For a college student , what would you suggest for a savings plan?Expert: I’d suggest deciding on a specific a mount to set aside each month, then making sure you do it, no matter the temptations not to.SOLUTION:a.Because of the time value of money, obviously, the earlier you start saving for retirement the morevalue you’ll have for each dollar saved.Suppose you save $1 at age 15 and you expect to retire at age 65, this dollar will be worth at 8% interest rate $46.9. Of course there’s a trade-off because you’ll also be postponing your spending (enjoying life) to your retirement.b.Again, because of the time value of money, each dollar you save as a college student will earn youmore than a dollar saved later on in your life. That’s why, you must decide on a certain amount you can afford to save and stick with it.Investing in Human Capital7. You are 30 years old and are considering full-time study for an MBA degree. Tuition and other direct costs will be $15,000 per year for two years. In addition you will have to give up a job with a salary of $30,000 per year. Assume tuition is paid and salary received at the end of the year. By how much does your salary have to increase (in real terms) as a result of getting your MBA degree to justify the investment? Assume a real interest rate of 3% per year and ignore taxes. Also assume that the salary increase is a constant real amount that starts after you complete your degree (at the end of the year following graduation) and lasts until retirement at age 65.SOLUTION:Buy or Rent?8. Suppose you currently rent an apartment and have an option to buy it for $200,000. Property taxes are $2,000 per year and are deductible for income tax purposes. Annual maintenance costs on the property are $1,500 per year and are not tax deductible. You expect property taxes and maintenance costs to increase at the rate of inflation. Your income tax rate is 40%, you can earn an after-tax real interest rate of 2% per year, and you plan to keep the apartment forever. What is the “break-even” annual rent such that you would buy it if the rent exceeds this amount? SOLUTION:The after-tax annual outlay if you buy is:$1,500 + .6 x $2,000 = $2,700The PV of this is $2700/.02 = $135,000.The PV of the costs of owning are $135,000 + $200,000 = $335,000.The break-even rent is .02 x $335,000 = $6,700 per year.Buy or lease a car9. You have decided to acquire a new car which costs $30,000. You are considering whether to lease it for 3 years or to purchase it and finance the purchase with a 3-year installment loan. The lease requires no down payment and lasts for 3 years. Lease payments are $400 monthly starting immediately, whereas the installment loan will require monthly payments starting a month from now at an annual percentage rate (APR) of 8%.a.If you expect the resale value of the car to be $20,000 3 years from now, should you buy or leaseit?b.What is the break-even resale price of the car 3 years from now, such that you would beindifferent between buying and leasing it?SOLUTION:a.We have to compare the NPVs of the two alternatives:Since in this case, the car is costing me more, I should choose the first alternative of leasing the car.b. In order to be indifferent among the two alternatives, their respective NPV must be equal, i.e. –12,850.Hence, the PV of the resale price is 30,000-12,850=17,15010. Analyze the following newspaper column:“Many of us who started families late share a nightmare image: having to pay huge college bills just as we’re giving up paychecks and shouldering the ste ep costs of retirement. In fact, the double whammy might not be so bad, assuming the parents have prepared properly. On the plus side, older parents are likely to have enjoyed their best earnings years before the college costs begin, allowing them to put a side more than younger parents can. They’ve also had more years for investments to compound. In the ideal situation, older parents can avoid borrowing to meet college costs, taking the preferred route of earning interest on investments rather than paying i t on student loans.” (Excerpted from Jeff Brown’s Personal Finance column in the Philadelphia Inquirer, May 11, 1998.) SOLUTION:As it is mentioned in the newspaper column, ideally older parents can avoid borrowing to meet college costs provided that they had prepared properly and started saving early in their lives.However, one can argue that with no children in the household, parents have less incentive to save (and enjoy their younger years) and might in fact be faced with this nightmare image of having to pay huge college bills just as they are giving up paychecks.11. Analyze the following newspaper column:“What’s the best age for a person to start collecting Social Security benefits? According to conventional wisdom, retirement starts at age 65. I t’s true that full benefits don’t start until age 65, but 62 year olds can retire and collect 80% of their benefits.Take the hypothetical cases of John and Mary, who have the same birthday and who are both slated to start drawing $1,000 a month in Social Security benefits at age 65. On his 62nd birthday, John decides to go ahead and start claiming his benefits of $800 a month (80% of $1000). Mary decides to wait until she’s 65, when she can claim the full $1000. Three years later, Mary turns 65 and begins receiving $1,000 a month from the Social Security Administration. John continues to receive $800 a month. But he has already been paid $28,800 while Mary received nothing.Five years go by, with Mary drawing $1,000 a month and John $800 a month. At 70, John has received $76,800, compared to Mary’s $60,000. When they reach 77, Mary will pull ahead. So, it seems if a person doesn’t live past 76, it would better to start collecting Social Security benefits at 62. For those who reach their upper 70’s, it pays to wait until they are 65 to collect Social Security. (adapted from 1998, Atlanta Business Chronicle, Gary Summer Contributing writer, June 29, 1998.) SOLUTION:The analysis in this newspaper column ignores the time value of money. The best way to look at this situation is to assume an interest rate, say 5%.The FV at age 65 of the $800 payments that John was taking is:At age 65, when Mary decides to start receiving the benefits from SSA, John has been paid $31,003. Not $28,800 as mentioned in the article.Now, in order to see when Mary will pull ahead, we have to see how many $200 payments (=1000-800) are the $31,003 worth.After 250 month, i.e. at age 85 and 10 months, Mary will eventually pull ahead.Personal Balance Sheets12. Using the finance concepts presented in this chapter, construct a personal balance sheet showing your assets, liabilities and net worth.a.Did you value your assets at cost or at current market value? Why?b.Did you include your human capital as an asset? Why?c.Did you include deferred taxes as a liability? Why?a.I valued my assets at current market value because their cost is irrelevant to me.b.Even though human capital is probably anyone’s biggest asset, I didn’t include it in the balance sheetbecause it’s uncert ain, hard to quantify and I will need to make too many assumptions concerning the PV of my future earnings.c.Once again, I haven’t.Home ownership Over the Life Cycle13. Suppose you buy a house for $200,000 when you are 35 years old. You make a 20% down payment and borrow the other 80% from a mortgage lender. The mortgage loan is at a fixed interest rate of 8% per year for 30 years and requires level annual payments. At age 65, you plan to take out a “reverse-mortgage” loan which will allow you to borrow a constant annual amount for the rest of your life to be paid off by the sale of your house when you die. Your life expectancy is age 85. The interest rate on both the original mortgage loan and the reverse mortgage will be 8% per year.a.Suppose that you expect the inflation rate to be 3% per year and you can rent an equivalenthouse for $10,000 per year. Is it worth buying the house?b.Show how buying the house will affect your assets, liabilities and cash flow over the next 50 years.c.In Making the Most of your money, JB Quinn has written: “ Over the long run, the value ofhomes should follow the inflation rate. But over the time that you won your particular house, its value might rise or fall or stall. You can’t predict. But there are reasons other than profit for owning a house.•Mortgage payments force to save, while rental payments don’t.•You get tax deductions, and can tax-shelter your capital gains.•You’re landlord free.•You know the deep contentment of holding a spot of ground that others can enter by invitation only.•You won’t lose your lease.•You can renovate to suit.• A house is collateral for a loan.Comment.SOLUTION:a.In order to compare the two alternatives, we have to compare their NPVs.Buy Alternative:Basically, this alternative consists of buying the house now at $200,000 and selling it 50 years from now at its market value, accounting for inflation:The FV of the house is:The house will be worth : $876,781 when you are 85.Now, to calculate the NPV of this alternative, we have to discount at 8% to account for the mortgage and the reverse mortgage.Hence the NPV of this option is: -200,000 + 18,694 = -181,306Rent Alternative:We assume that rent will be $10,000 in real terms and hence must be discounted at the real interest rate = 4.854%Hence, it is more economical to buy the house.c. Most of the points mentioned by JB Quinn were discussed in this exercise, namely the fact thatmortgage payments force you to save and that a house can serve as collateral for a loan. She also presents in his discussion some “intangible” benefits from owning a house such as not having a landlord and renovating to suit.。

《金融学(第二版)》(高等教育出版社)名词解释及课后习题答案

第一章货币概述货币量层次划分：货币量层次划分，即是把流通中的货币量，主要按照其流动性的大小进行相含排列，分成若干层次并用符号代表的一种方法。

价值尺度：货币在表现商品的价值并衡量商品价值量的大小时，发挥价值尺度的职能。

这是货币最基本、最重要的职能。

价格标准：指包含一定重量的贵金属的货币单位。

在历史上，价格标准和货币单位曾经是一致的，随着商品经济的发展，货币单位名称和货币本身重量单位名称分离了。

货币制度：货币制度简称“币制”，是一个国家以法律形式确定的该国货币流通的结构、体系与组织形式。

它主要包括货币金属，货币单位，货币的铸造、发行和流通程序，准备制度等。

金本位制：金本位制又称金单本位制，它是以黄金作为本位货币的一种货币制度。

其形式有三种金币本位制、金块本位制和金汇兑本位制。

无限法偿：即在货币收付中无论每次支付的金额多大，用本位币支付时，受款人不得拒绝接受，也即本位币具有无限的法定支付能力，即无限法偿。

有限法偿：有限法偿是指，货币在每一次支付行为中使用的数量受到限制，超过限额的部分，受款人可以拒绝接受。

格雷欣法则：即所谓“劣币驱逐良币”的规律。

就是在两种实际价值不同而面额价值相同的通货同时流通的情况下，实际价值较高的通货（所谓良币）必然会被人们熔化、输出而退出流通领域；而实际价值较低的通货（所谓劣币）反而会充斥市场。

6．什么是货币量层次划分，我国划分的标准和内容如何？（1）所谓货币量层次划分，即是把流通中的货币量，主要按照其流动性的大小进行相含排列，分成若干层次并用符号代表的一种方法。

（2）货币量层次划分的目的是把握流通中各类货币的特定性质、运动规律以及它们在整个货币体系中的地位，进而探索货币流通和商品流通在结构上的依存关系和适应程度，以便中央银行拟订有效的货币政策。

（3）我国货币量层次指标的划分标准主要为货币的流动性。

所谓流动性是指一种资产具有可以及时变为现实的购买力的性质。

流动性程度不同，所形成的购买力也不一样，因而对社会商品流通的影响程度也就不同。

金融学陈学彬课后答案

金融学陈学彬课后答案金融学陈学彬课后答案【篇一：金融学第一章(讲稿)】t>教案2013～2014学年第一学期系(部、中心) 理工系教研室数学教研室课程名称金融学课程学时 68 授课方式课堂讲授授课对象数学1101 授课教师侯致武职称职务助教使用教材《金融学》高等教育出版社二〇一三年九月- 1 -（3）货币的价值取决于什么时候得到它——今天得到的1元钱比未来得到的1元钱更值钱；（4）不是每个人都知道相同的事情——金融市场上不同的参与者所持有的信息存在差别（信息不对称）。

金融学就是研究金融系统的组织、结构、运行规律及其与经济系统的相互影响的科学。

二、《金融学》课程简介1.金融的重要性“大家都知道有那么回事，但不知道是怎么一回事。

”——旧约全书。

邓小平在1991年视察上海时指出：“金融很重要，是现代经济的核心。

金融搞好了，一着棋活，全盘皆活。

《金融学（第二版）》讲义大纲及课后习题答案详解十二章

《⾦融学（第⼆版）》讲义⼤纲及课后习题答案详解⼗⼆章CHAPTER 12CHOOSING AN INVESTMENT PORTFOLIOObjectivesTo understand the process of personal investing in theory and in practice.To build a quantitative model of the tradeoff between risk and reward.Outline12.1 The Process of Personal Portfolio Selection12.2 The Trade-off between Expected Return and Risk12.3 Efficient Diversification with Many Risky AssetsSummaryThere is no single portfolio selection strategy that is best for all people.Stage in the life cycle is an imp ortant determinant of the optimal composition of a person’s optimal portfolio of assets and liabilities.Time horizons are important in portfolio selection. We distinguish among three time horizons: the planning horizon, the decision horizon, and the trading horizon.In making portfolio selection decisions, people can in general achieve a higher expected rate of return only by exposing themselves to greater risk.One can sometimes reduce risk without lowering expected return by diversifying more completely either withina given asset class or across asset classes.The power of diversification to reduce the riskiness of an investor’s portfolio depends on the correlations among the assets that make up the portfolio. In practice, the vast majority of assets are positively correlated with each other because they are all affected by common economic factors. Consequently, one’s ability to reduce risk through diversification among risky assets without lowering expected return is limited.Although in principle people have thousands of assets to choose from, in practice they make their choices from a menu of a few final products offered by financial intermediaries such as bank accounts, stock and bond mutual funds, and real estate. In designing and producing the menu of assets to offer to their customers theseintermediaries make use of the latest advances in financial technology.Solutions to Problems at End of Chapter1. Suppose that your 58-year-old father works for the Ruffy Stuffed Toy Company and has contributed regularly to his company-matched savings plan for the past 15 years. Ruffy contributes $0.50 for every $1.00 your father puts into the savings plan, up to the first 6% of his salary. Participants in the savings plan can allocate their contributions among four different investment choices: a fixed-income bond fund, a “blend” option that invests in large companies, small companies, and the fixed-income bond fund, a growth-income mutual fund whose investments do not include other toy companies, and a fund whose sole investment is stock in the Ruffy Stuffed Toy Company. Over Thanksgiving vacation, Dad realizes that you have been majoring in finance and decides to reap some early returns on that tuition money he’s been investing in your education. He shows you the most recent quarterly statement for his savings plan, and you see that 98% of its current value is in the fourth investment option, that of the Ruffy Company stock..a.Assume that your Dad is a typical risk-averse person who is considering retirement in five years. Whenyou ask him why he has made the allocation in this way, he responds that the company stock has continually performed quite well, except for a few declines that were caused by problems in a division that the company has long since sold off. Inaddition, he says, many of his friends at work have done the same. What advice would you give your dad about adjustments to his plan allocations? Why?b.If you consider the fact that your dad works for Ruffy in addition to his 98% allocation to the Ruffy stockfund, does this make his situation more risky, less risky, or does it make no difference? Why? SOLUTION:a.Dad has exposed himself to risk by concentrating almost all of his plan money in the Ruffy Stock fund. This is analogous to taking 100% of the money a family has put aside for investment and investing it in a single stock.First, Dad needs to be shown that just because the company stock has continually performed quite well is no guarantee that it will do so indefinitely. The company may have sold off the divisions which produced price declines in the past, but future problems are unpredictable, and so is the movement of the stock price. “Past performance is no guarantee of future results” is the lesson.Second, Dad needs to hear about diversification. He needs to be counseled that he can reduce his risk by allocating his money among several of the options available to him. Indeed, he can reduce his risk considerably merely by moving all of his money into the “blend” fund because it is diversifi ed by design: it has a fixed-income component, a large companies component, and a small companies component. Diversification isachieved not only via the three differing objectives of these components, but also via the numerous stocks that comprise each of the three components.Finally, Dad’s age and his retirement plans need to be considered. People nearing retirement age typically begin to shift the value of their portfolios into safer investments. “Safer” normally connotes less variability, so that the risk of a large decline in the value of a portfolio is reduced. This decline could come at any time, and it would be very unfortunate if it were to happen the day before Dad retires. In this example, the safest option would be the fixed-income bond fund because of its diversified composition and interest-bearing design, but there is still risk exposure to inflation and the level of interest rates. Note that the tax-deferred nature of the savings plan encourages allocation to something that produces interest or dividends. As it stands now, Dad is very exposed to a large decline in the value of his savings plan because it is dependent on the value of one stock.Individual equities over time have proven to produce the most variable of returns, so Dad should definitely move some, probably at least half, of his money out of the Ruffy stock fund. In fact, a good recommendation given his retirement horizon of five years would be to re-align the portfolio so that it has 50% in the fixed- income fund and the remaining 50% split between the Ruffy stock fund (since Dad insists) and the “blend” fund.Or, maybe 40% fixed-income, 25% Ruffy, 15% growth-income fund, and 20% “blend” fund. This latterallocation has the advantage of introducing another income-producing component that can be shielded by the tax-deferred status of the plan.b.The fact that Dad is employed by the Ruffy Company makes his situation more risky. Let’s say that the companyhits a period of slowed business activities. If the stock price declines, so will th e value of Dad’s savings plan. If the company encounters enough trouble, it may consider layoffs. Dad’s job may be in jeopardy. At the same time that his savings plan may be declining in value, Dad may also need to look for a job or go onunemployment. Thus, Dad is exposed on two fronts to the same risk. He has invested both his human capital and his wealth almost exclusively in one company.2. Refer to Table 12.1.a.Perform the calculations to verify that the expected returns of each of the portfolios (F, G, H, J, S) in thetable (column 4) are correct.b.Do the same for the standard deviations in column 5 of the table.c.Assume that you have $1million to invest. Allocate the money as indicated in the table for each of the fiveportfolios and calculate the expected dollar return of each of the portfolios.d.Which of the portfolios would someone who is extremely risk tolerant be most likely to select? SOLUTION:d.An extremely risk tolerant person would select portfolio S, which has the largest standard deviation but also thelargest expected return.3. A mutual fund company offers a safe money market fund whose current rate is4.50% (.045). The same company also offers an equity fund with an aggressive growth objective which historically has exhibited an expected return of 20% (.20) and a standard deviation of .25.a.Derive the equation for the risk-reward trade-off line.b.How much extra expected return would be available to an investor for each unit of extra risk that shebears?c.What allocation should be placed in the money market fund if an investor desires an expected return of15% (.15)?SOLUTION:a.E[r] = .045 + .62b.0.62c.32.3% [.15 = w*(.045) + (1-w)*(.020) ]4. If the risk-reward trade-off line for a riskless asset and a risky asset results in a negative slope, what does that imply about the risky asset vis-a-vis the riskless asset?SOLUTION:A trade-off line wit h a negative slope indicates that the investor is “rewarded” with less expected return for taking on additional risk via allocation to the risky asset.5. Suppose that you have the opportunity to buy stock in AT&T and Microsoft.a.stocks is 0? .5? 1? -1? What do you notice about the change in the allocations between AT&T andMicrosoft as their correlation moves from -1 to 0? to .5? to +1? Why might this be?b.What is the variance of each of the minimum-variance portfolios in part a?c.What is the optimal combination of these two securities in a portfolio for each value of the correlation,assuming the existence of a money market fund that currently pays 4.5% (.045)? Do you notice any relation between these weights and the weights for the minimum variance portfolios?d.What is the variance of each of the optimal portfolios?e.What is the expected return of each of the optimal portfolios?f.Derive the risk-reward trade-off line for the optimal portfolio when the correlation is .5. How much extraexpected return can you anticipate if you take on an extra unit of risk?SOLUTION:a.Minimum risk portfolios if correlation is:-1: 62.5% AT&T, 37.5% Microsoft0: 73.5% AT&T, 26.5% Microsoft.5: 92.1% AT&T, 7.9% Microsoft1: 250% AT&T, short sell 150% MicrosoftAs the correlation moves from -1 to +1, the allocation to AT&T increases. When two stocks have negativec orrelation, standard deviation can be reduced dramatically by mixing them in a portfolio. It is to the investors’benefit to weight more heavily the stock with the higher expected return since this will produce a high portfolio expected return while the standard deviation of the portfolio is decreased. This is why the highest allocation to Microsoft is observed for a correlation of -1, and the allocation to Microsoft decreases as the correlationbecomes positive and moves to +1. With correlation of +1, the returns of the two stocks will move closely together, so you want to weight most heavily the stock with the lower individual standard deviation.b. Variances of each of the minimum variance portfolios:62.5% AT&T, 37.5% Microsoft Var = 073.5% AT&T, 26.5% Microsoft Var = .016592.1% AT&T, 7.9% Microsoft Var = .0222250% AT&T, short 150% Microsoft Var = 0c. Optimal portfolios if correlation is:-1: 62.5% AT&T, 37.5% Microsoft0: 48.1% AT&T, 51.9% Microsoft.5: 11.4% AT&T, 88.6% Microsoft1: 250% AT&T, short 150% Microsoftd. Variances of the optimal portfolios:62.5% AT&T, 37.5% Microsoft Var = 048.1% AT&T, 51.9% Microsoft Var = .022011.4% AT&T, 88.6% Microsoft Var = .0531250% AT&T, short 150% Microsoft Var = 0e. Expected returns of the optimal portfolios:62.5% AT&T, 37.5% Microsoft E[r] = 14.13%48.1% AT&T, 51.9% Microsoft E[r] = 15.71%11.4% AT&T, 88.6% Microsoft E[r] = 19.75%250% AT&T, short 150% Microsoft E[r] = -6.5%f.Risk-reward trade-off line for optimal portfolio with correlation = .5:E[r] = .045 + .66/doc/31dbf23b580216fc700afd59.html ing the optimal portfolio of AT&T and Microsoft stock when the correlation of their price movements is 0.5, along with the results in part f of question 12-5, determine:a.the expected return and standard deviation of a portfolio which invests 100% in a money market fundreturning a current rate of 4.5%. Where is this point on the risk-reward trade-off line?b.the expected return and standard deviation of a portfolio which invests 90% in the money market fundand 10% in the portfolio of AT&T and Microsoft stock.c.the expected return and standard deviation of a portfolio which invests 25% in the money market fundand 75% in the portfolio of AT&T and Microsoft stock.d.the expected return and standard deviation of a portfolio which invests 0% in the money market fundand 100% in the portfolio of AT&T and Microsoft stock. What point is this?SOLUTION:a.E[r] = 4.5%, standard deviation = 0. This point is the intercept of the y (expected return) axis by the risk-rewardtrade-off line.b.E[r] = 6.03%, standard deviation = .0231c.E[r] = 15.9%, standard deviation = .173d.E[r] = 19.75%, standard deviation = .2306. This point is the tangency between the risk-reward line from 12-5part f and the risky asset risk-reward curve (frontier) for AT&T and Microsoft.7. Again using the optimal portfolio of AT&T and Microsoft stock when the correlation of their price movements is 0.5, take $ 10,000 and determine the allocations among the riskless asset, AT&T stock, and Microsoft stock for:a. a portfolio which invests 75% in a money market fund and 25% in the portfolio of AT&T and Microsoftstock. What is this portfolio’s expected return?b. a portfolio which invests 25% in a money market fund and 75% in the portfolio of AT&T and Microsoftstock. What is this portfolio’s expect ed return?c. a portfolio which invests nothing in a money market fund and 100% in the portfolio of AT&T andMicrosoft stock. What is this portfolio’s expected return?SOLUTION:a.$7,500 in the money-market fund, $285 in AT&T (11.4% of $2500), $2215 in Microsoft. E[r] = 8.31%, $831.b.$2,500 in the money-market fund, $855 in AT&T (11.4% of $7500), $6645 in Microsoft. E[r] = 15.94%, $1,594.c.$1140 in AT&T, $8860 in Microsoft. E[r] = 19.75%, $1,975.8. What strategy is implied by moving further out to the right on a risk-reward trade-off line beyond the tangency point between the line and the risky asset risk-reward curve? What type of an investor would be most likely to embark on this strategy? Why?SOLUTION:This strategy calls for borrowing additional funds and investing them in the optimal portfolio of AT&T and Microsoft stock. A risk-tolerant, aggressive investor would embark on this strategy. This person would be assuming the risk of the stock portfolio with no risk-free component; the money at risk is not onl y from this person’s own wealth but also represents a sum that isowed to some creditor (such as a margin account extended by the investor’s broker).9. Determine the correlation between price movements of stock A and B using the forecasts of their rate of return and the assessments of the possible states of the world in the following table. The standard deviations for stock A and stock B are0.065 and 0.1392, respectively. Before doing the calculation, form an expectation of whether that correlation will be closer to1 or -1 by merely inspecting the numbers.SOLUTION:Expectation: correlation will be closer to +1.E[r A] = .05*(-.02) + .15*(-.01) + .60*(.15) + .20*(.15) = .1175, or, 11.75%E[r B] = .05*(-.20) + .15*(-.10) + .60*(.15) + .20*(.30) = .1250, or, 12.50%Covariance = .05*(-.02-.1175)*(-.20-.125) + .15*(-.01-.1175)*(-.10-.125) +.60*(.15-.1175)*(.15-.125) + .20*(.15-.1175)*(.30-.125) =.008163Correlation = .008163/(.065)*(.1392) = .90210.Analyze the “expert’s” answers to the following questions:a.Question:I have approx. 1/3 of my investments in stocks, and the rest in a money market. What do you suggestas a somewhat “safer” place to invest another 1/3? I like to keep 1/3 accessible for emergencies.Expert’s answer:Well, you could try 1 or 2 year Treasury bonds. You’d get a little bit more yie ld with no risk.b.Question:Where would you invest if you were to start today?Expert’s answer:That depends on your age and short-term goals. If you are very young – say under 40 –and don’tneed the money you’re investing for a home or college tuition or such, you would put it in a stockfund. Even if the market tanks, you have time to recoup. And, so far, nothing has beaten stocks overa period of 10 years or more. But if you are going to need money fairly soon, for a home or for yourretirement, you need to play it safer.SOLUTION:a.You are not getting a little bit more yield with no risk. The real value of the bond payoff is subject to inflationrisk. In addition, if you ever need to sell the Treasury bonds before expiration, you are subject to the fluctuation of selling price caused by interest risk.b.The expert is right in pointing out that your investment decision depends on your age and short-term goals. In addition, the investment decision also depends on other characteristics of the investor, such as the special character of the labor income (whether it is highly correlated with the stock market or not), and risk tolerance.Also, the fact that over any period of 10 years or more the stock beats everything else cannot be used to predict the future.。

《金融学(第二版)》讲义大纲及课后习题答案详解第13章

CHAPTER 13THE CAPITAL ASSET PRICING MODELObjectives•Explain the theory behind the CAPM.•Explain how to use the CAPM to establish benchmarks for measuring the performance of investment portfolios. •Explain how to infer from the CAPM the correct risk-adjusted discount rate to use in discounted-cash-flow valuation models.•Explain the APT and its relationship to the CAPM.Outline13.1 The Capital Asset Pricing Model in Brief13.2 Determinants of the Risk Premium on the Market Portfolio13.3 Beta and Risk Premiums on Individual Securities13.4 Using the CAPM in Portfolio Selection13.5 Valuation and Regulating Rates of Return13.6 Extensions, Modifications, and Alternatives to the CAPMSummary•The CAPM has three main implications:•In equilibrium, ev eryone’s relative holding of risky assets are the same as in the market portfolio.•The size of the risk-premium of the market portfolio is determined by the risk-aversion of investors.•The risk premium on any asset is equal to its beta times the risk premium on the market portfolio. •Whether or not the CAPM is strictly true, it provides a rationale for a very simple passive portfolio strategy: •Diversify your holdings of risky assets in the proportions of the market portfolio, and•Mix this portfolio with the risk-free asset to achieve a desired risk-reward combination.•The CAPM is used in portfolio management primarily in two ways:•To establish a logical and convenient starting point in asset allocation and security selection•To establish a benchmark for evaluating portfolio management ability on a risk-adjusted basis.•In corporate finance the CAPM is used to determine the appropriate risk-adjusted discount rate in valuation models of the firm and in capital budgeting decisions. The CAPM is also used to establish a “fair” rate of return on invested capital for regulated firms and in cost-plus pricing.•Today few financial scholars consider the CAPM in its simplest form to be an accurate model for explaining or predicting risk premiums on risky assets. However, modified versions of the model are still a central feature of the theory and practice of finance.•The APT gives a rationale for the expected return-beta relationship that relies on the condition that there be no arbitrage profit opportunities; the CAPM requires that investors be portfolio optimizers. The APT and CAPM are not incompatible; rather, they complement each other.Solutions to Problems at End of ChapterComposition of the Market Portfolio1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a risklessgovernment security. Evaluated at current prices in US dollars, the total market values of these assets are, respectively, $24 billion, $36 billion, $24 billion and $16 billion.a. Determine the relative proportions of each asset in the market portfolio.b. If one trader with a $100,000 portfolio holds $40,000 in the riskless security, $15,000 in X, $12,000 in Y, and$33,000 in Z, determine the holdings of the three risky assets of a second trader who invests $20, 000 of a $200, 000 portfolio in the riskless security.SOLUTION:The total value of all assets in the economy is 100 billion dollars. a. The proportions of each asset relative to the value of all assets are, respectively, .24 (X), .36 (Y),b. .24 (Z) and .16 (riskless bond.) The proportions of each risky asset to the total value of all risky assets are,respectively, (2/7) (X), (3/7) (Y) and (2/7) (Z). c. . Ignore the question as it appears in the First Edition of the textbook. Instead, the question should be: If aninvestor has $100,000 with $30,000 invested in the riskless asset, how much is invested in securities X, Y, and Z? The answer to this question is $20,000 in X and Z, and $30,000 in Y.Implications of CAPM2. The riskless rate of interest is .06 per year, and the expected rate of return on the market portfolio is .15 per year.a. According to the CAPM , what is the efficient way for an investor to achieve an expected rate of returnof .10 per year?b. If the standard deviation of the rate of return on the market portfolio is .20, what is the standarddeviation on the above portfolio?c. Draw the CML and locate the foregoing portfolio on the same graph.d. Draw the SML and locate the foregoing portfolio on the same graph.e. Estimate the value of a stock with an expected dividend per share of $5 this coming year, an expecteddividend growth rate of 4% per year forever, and a beta of .8. If its market price is less than the value you have estimated, i.e., if it is under-priced, what is true of its mean rate of return?SOLUTION: a.So one would hold a portfolio that is 4/9 invested in the market portfolio and 5/9 in the riskless asset. b.c. The formula for the CML is9415.)1(06.10.)()1()(=+-=⨯+-⨯=x xx x r E x r r E M f 08889.)20(.94==⨯=M x σσσσσ45.06.)()(+=-+=MfM f r r E r r Ed. The formula for the SML ise. Use constant growth rate DDM and find r using the SML relationIf the market price of the stock is less than this, then its expected return is higher than the 13.2% required rate.()ββ09.06.)()(+=-+=f M f r r E r r E 35.54$04.132.504.510=-=-=-=r g r D P 132.8.09.06.09.06.=⨯+=+=βr3. If the CAPM is valid, which of the following situations is possible? Explain. Consider each situation independently.a.PortfolioExpected ReturnBeta A 0.20 1.4B 0.25 1.2b.PortfolioExpected ReturnStandard DeviationA 0.300.35B 0.400.25c.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A 0.160.12d.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A0.200.22SOLUTION:a. Impossible. Since the risk premium on the market portfolio is positive, a security with a higher beta must have ahigher expected return.b. Possible. Since portfolios A & B are not necessarily efficient, A can have a higher standard deviation and alower expected return than B.c. Impossible. Portfolio A lies above the CML, implying that the CML is not efficient. If the standard deviation ofA is .12, then according to the CML its expected return cannot be greater than .14.d. Impossible. Portfolio A has a lower standard deviation and a higher mean return than the market portfolio,implying that the market portfolio is not efficient.4. If the Treasury bill rate is currently 4% and the expected return to the market portfolio over the same period is 12%, determine the risk premium on the market. If the standard deviation of the return on the market is .20, what is the equation of the Capital Market Line?SOLUTION: The risk premium on the market portfolio is .08. The slope of the CML is .08/.2 = .4. Thus, the equation of theCML is:Determinants of the Market Risk Premium5. Consider an economy in which the expected return on the market portfolio over a particular period is .25, the standard deviation of the return to the market portfolio over this same period is .25, and the averagedegree of risk aversion among traders is 3. If the government wishes to issue risk-free zero-coupon bonds with a term to maturity of one period and a face value per bond of $100,000, how much can the government expect to receive per bond?[]σσσ4.04.)()(+=++=MfMf r rE r r ESOLUTION:According to the CAPM, E(r M) - r f = Aσ2, so that r f = E(r M) - Aσ2.Substituting into this formula we find: r f = .25 – 3 x .252 = .0625Therefore the revenue raised by the government per bond issued is $100,000 = $94,117.651.06256. . Norma Swanson has invested 40% of her wealth in MGM stock and 60% in Industrial Light and Magic stock. Norma believes the returns to these stocks have a correlation of .06 and that their respective means and standard deviations are:MGM ILMExpected Return (%) 10 15Standard Deviation (%) 15 25a.Determine the expected value and standard deviation of the return on Norma’s portfolio.b.Would a risk-averse investor such as Norma prefer a portfolio composed entirely of only MGM stock? Ofonly ILM stock? Why or why not?SOLUTION:a.The expected return is .13, and the standard deviation is .1649.b. A risk averse investor will not want to hold a portfolio composed entirely of MGM or of ILM stock, becauseone can, in general, achieve the same expected return with a lower standard deviation by combining a portfolio of MGM and ILM with the risk-free asset.7. Consider a portfolio exhibiting an expected return of 20% in an economy in which the riskless interest rate is 8%, the expected return to the market portfolio is thirteen percent, and the standard deviation of the return to the market portfolio is .25. Assuming this portfolio is efficient, determine:a.its beta.b.the standard deviation of its return.c.its correlation with the market return.SOLUTION:e the security market line to infer that the beta of this portfolio is 2.4:.20 = .08 + β(.13 - .08)β = (.20 - .08)/(.13 - .08) = .12/.05 = 2.4e the capital market line to infer that the standard deviation of the yield to this portfolio is .6:.20 = .08+ (.13 - .08) σ = .08+ .2 σ.25σ = .12/.2 = .6c.By definition the following relationships hold:β = cov/σ2Mρ = covσiσMwhere ρ denotes the correlation coefficient. We know that β = 2.4, σM = .25, and σi = .6.So from the definition of β, we get that the cov is 2.4 x .252 = .15. Substituting this into the definition of ρ: ρ = cov = .15 __ = 1σiσM .6 x .25Application of CAPM to Corporate Finance8. . The Suzuki Motor Company is contemplating issuing stock to finance investment in producing a new sports-utility vehicle, the Seppuku. Financial analysts within Suzuki forecast that this investment will have precisely the same risk as the market portfolio, where the annual return to the market portfolio is expected to be 15% and the current risk-free interest rate is 5%. The analysts further believe that the expected return to the Seppuku project will be 20% annually. Derive the maximal beta value that would induce Suzuki to issue the stock.SOLUTION:The project would be on the borderline if its required return were 20% per year. Since the risk-free rate is 5% and the risk premium on the market portfolio is 10%, the required return would be 20% if the beta were 1.5.9. . Roobel and Associates, a firm of financial analysts specializing in Russian financial markets, forecasts that the stock of the Yablonsky Toy Company will be worth 1,000 roubles per share one year from today. If the riskless interest rate on Russian government securities is 10% and the expected return to the market portfolio is 18% determine how much you would pay for a share of Yablonsky stock today if:a.the beta of Yablonsky is 3.b.the beta of Yablonsky is 0.5.SOLUTION:Use the security market line in each case to determine a required rate of return, then infer the current price from the forecasted price of 1,000 roubles and the required rate of return you have determined.a.If beta is 3, the required return is .10+ 3x.08 = .34. You would pay 1,000/1.34 = 746.27 roubles;b.If beta is .5, the required return is .10+ .5x.08 = .14. You would pay 1,000/1.14 = 877.19 roubles.Application of CAPM to Portfolio Management10. Suppose that the stock of the new cologne manufacturer, Eau de Rodman, Inc., has been forecast to havea return with standard deviation .30 and a correlation with the market portfolio of .9. If the standard deviation of the yield on the market is .20, determine the relative holdings of the market portfolio and Eau de Rodman stock to form a portfolio with a beta of 1.8.SOLUTION: By definition:β = cov/σ2Mρ = covσrσMTherefore, β = ρσr/σM. The beta of Rodman stock is therefore .9x.3/.2 = 1.35.The beta of a portfolio is a weighted average of the betas of the component securities. Let A be a fraction of the portfolio invested in Rodman stock to produce a beta of 1.8. Then we have:1.35A + (1-A) = 1.8.35A = .8A = 2.286So the portfolio would have to have 228.6% invested in Rodman stock and a short position in the market portfolio equal to 128.6%.11. The current price of a share of stock in the Vo Giap Clothing Company of Vietnam is 50 dong and its expected yield over the year is 14%. The market risk premium in Vietnam is 8% and the riskless interest rate 6%. What would happen to the stock’s current price if its expected future payout remains co nstant while the covariance of its rate of return with the market portfolio falls by 50%?SOLUTION:Deduce that the expected future price of a share of Vo Giap is 57 dong, so that a reduction in this stock’s beta of 50% implies, by the security market relation, that the required yield on Vo Giap is now 10%, so that its current share price rises by 3.64% to a new value of 51.82 dong.12. Suppose that you believe that the price of a share of IBM stock a year from today will be equal to the sumof the price of a share of General Motors stock plus the price of a share of Exxon, and further you believethat the price of a share of IBM stock in one year will be $100 whereas the price of a share of General Motors today is $30. If the annualized yield on 91-day T-bills (the riskless rate you use) is 5%, the expected yield on the market is 15%, the variance of the market portfolio is 1, and the beta of IBM is 2, what price would you be willing to pay for one share of Exxon stock today?SOLUTION:Expected return = .05 + 2(.15 - .05) = 25%; (100 - x)/x = .25 → x = $80Deduce that the current price of a share of IBM stock is $80, so that the upper bound on the price of a share of Exxon is ($80 - $30 = $50).13. Ascertain whether the following quotation is true or false, and state why:“When arbitrage is absent from financial markets, and investors are each concerned with only the risk and return to their portfolios, then each investor can eliminate all the riskiness of his investments through diversification, and as a consequence the expected yield on each available asset will depend only on the covariance of its yield with the covariance of the yield on the diversified portfolio of risky assets each investor holds.”SOLUTION:False. You cannot eliminate all risk through diversification, only the unsystematic risk.Application of CAPM to Measuring Portfolio Performance14. During the most recent 5-year period, the Pizzaro mutual fund earned an average annualized rate of return of 12% and had an annualized standard deviation of 30%. The average risk-free rate was 5% per year. The average rate of return in the market index over that same period was 10% per year and the standard deviation was 20%. How well did Pizzaro perform on a risk-adjusted basis?SOLUTION:Compute the ratio of average excess return to standard deviation for Pizzaro and compare it to that of the market portfolio:Pizzaro risk-adjusted performance ratio = (.12-.05)/.30 = .233Market portfolio risk-adjusted performance ratio = (.1-.05)/.2 = .250So, on a risk-adjusted basis, Pizzaro did worse than the market index.Challenge ProblemCAPM with only 2 Risky Assets15. There are only two risky assets in the economy: stocks and real estate and their relative supplies are 50% stocks and 50% real estate. Thus, the market portfolio will be half stocks and half real estate. The standard deviations are .20 for stocks, .20 for real estate, and the correlation between them is 0. The coefficient of relative risk aversion of the average market participant (A) is 3. r f is .08 per year.a.According to the CAPM what must be the equilibrium risk premium on the market portfolio, on stocks,and on real estate?b.Draw the Capital Market Line. What is its slope? Where is the point representing stocks located relativeto the CML?c.Draw the SML. What is its formula? Where is the point representing stocks located relative to the SML? SOLUTION:a.The market portfolio consists of half stocks and half real estate. It has a standard deviation of .1414, computedas follows:σ2M = w2σ2s + (1-w)2σ2r+ 2 w(1-w) cov s,rσ2M = 2 x (1/2)2 .22 = .02σM = .1414The equilibrium risk premium on the market portfolio is E(r M)-r f = Aσ2M = 3x.02 = .06.The market portfolio’s expected rate of return is also a weighted average of the expected rates of return on stocks and real estate, where the weights are each 1/2. Stocks and real estate must have the same risk premiumbecause they have the same standard deviation and correlation with the market. Therefore the risk premium on stocks and real estate must be .06, the same as the market portfolio’s risk premium.b.The slope of the CML is .06/.1414 = .424. The point representing stocks is M, it is to the right of the CML.equaling to 1.The formula is: E(r) = r f + (E(r M) –r f).。

《金融学(第二版)》讲义大纲及课后习题答案详解第七章

《金融学〔第二版〕》讲义大纲及课后习题答案详解第七章CHAPTER 7PRINCIPLES OF ASSET VALUATIONObjectives? Understand why asset valuation is important in finance.? Explain the Law of One Price as the principle underlying all asset-valuation procedures. ? Explain the meaning and role of valuation models.? Explain how information gets reflected in security prices.Outline7.1 The Relation Between an Asset’s Value and Its Price 7.2 Value Maximization and Financial Decisions 7.3 The Law of One Price and Arbitrage7.4 Arbitrage and the Prices of Financial Assets 7.5 Exchange Rates and Triangular Arbitrage 7.6 Interest Rates and the Law of One Price 7.7 Valuation Using Comparables 7.8 Valuation Models7.9 Accounting Measures of Value7.10 How Information Gets Reflected in Security Prices 7.11 The Efficient Markets HypothesisSummary? In finance the measure of an asset’s value is the price it would fetch if it were sold in a competitive market. Theability to accurately value assets is at the heart of the discipline of finance because many personal and corporate financial decisions can be made by selecting the alternative that maximizes value.? The Law of One Price states that in a competitive market, if two assets are equivalent they will tend to have thesame price. The law is enforced by a process called arbitrage, the purchase and immediate sale of equivalent assets in order to earn a sure profit from a difference in their prices.? Even if arbitrage cannot be carried out in practice to enforce the Law of One Price, unknown asset values canstill be inferred from the prices of comparable assets whose prices are known.? The quantitative method used to infer an asset’s value from information about the prices of comparable assets iscalled a valuation model. The best valuation model to employ varies with the information available and the intended use of the estimated value. ? The book value of an asset or a liability as reported in a firm’s financial statements often differs from its currentmarket value.? In making most financial decisions, it is a good idea to start by assuming that for assets that are bought and soldin competitive markets, price is a pretty accurate reflection of fundamental value. This assumption is generally warranted precisely because there are many well-informed professionals looking for mispriced assets who profit by eliminating discrepancies between the market prices and the fundamental values of assets. The proposition that an asset’s current price fully reflects all publicly-available information about future economic fundamentals affecting the asset’s value is known as the Efficient Markets Hypothesis.? The prices of traded assets reflect information about the fundamental economic determinants of their value.Analysts are constantly searching for assets whose prices are different from their fundamental value in order to buy/sell these “bargains.〞 In deciding the best strategy for the purchase/sale of a “bargain,〞 theanalyst has to evaluate the accuracy of her information. The market price of an asset reflects the weighted average of all analysts opinions with heavier weights for analysts who control large amounts of money and for those analysts who have better than average information.Instructor’s ManualChapter 7 Page 106Solutions to Problems at End of ChapterLaw of One Price and Arbitrage1. IBX stock is trading for $35 on the NYSE and $33 on the Tokyo Stock Exchange. Assume that the costs of buying and selling the stock are negligible. a. How could you make an arbitrage profit?b. Over time what would you expect to happen to the stock prices in New York and Tokyo?c. Now assume that the cost of buying or selling shares of IBX is 1% per transaction. How does this affectyour answer?SOLUTION:a. Buy IBX stock in Tokyo and simultaneously sell them in NY. Your arbitrage profit is $2 per share.b. The prices would converge.c. Instead of the prices becoming exactly equal, there can remain a 2% discrepancy between them, roughly $.70 inthis case.2. Suppose you live in the state of Taxachusetts which has a 16% sales tax on liquor. A neighboring state called Taxfree has no tax on liquor. The price of a case of beer is $25 in Taxfree and it is $29 in Taxachusetts.a. Is this a violation of the Law of One Price?b. Are liquor stores in Taxachusetts near the border with Taxfree going to prosper?SOLUTION:a. This is not a violation of the Law of One Price because it is due to a tax imposed in one state but not in the other.Illegal arbitrage will probably occur, with lawbreakers buying large quantities of liquor in Taxfree and selling it in Taxachusetts without paying the tax.b. It is likely that liquor stores will locate in Taxfree near the border with Taxachusetts. Residents of both stateswill buy their liquor in the stores located in Taxfree, and liquor stores in Taxachusetts will go out of business.Triangular Arbitrage3. Suppose the price of gold is 155 marks per ounce.a. If the dollar price of gold is $100 per ounce, what should you expect the dollar price of a mark to be?b. If it actually only costs $0.60 to purchase one mark, how could one make arbitrage profits?SOLUTION:a. $100 buys the same amount of gold (1 ounce) as 155 DM, so 1 DM should cost 100/155 or $.645.b. The marks are “cheaper〞 than they should be, so the arbitrage transaction requires you to buy marks at thecheap price, use them to purchase gold, and sell the gold for dollars. Example:1. Start with $1 million, which you borrow for only enough time to carry out the arbitrage transaction.2. Use the million dollars to buy 1,666,667 marks (1,000,000 / 0.60)3. Buy 10,752.69 ounces of gold (1,666,667 / 155)4. Sell the gold for $1,075,269 (10752.69 x 100)Your risk-free arbitrage profit is $75,269.4. You observe that the dollar price of the Italian lira is $0.0006 and the dollar price of the yen is $0.01. What must be the exchange rate between lira and yen for there to be no arbitrage opportunity?SOLUTION:.0006$/lira?.06Yen/lira.01$/YenInstructor’s ManualChapter 7 Page 1075. Fill in the missing exchange rates in the following table: US dollar British pound German mark Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 German mark DM2.0 Japanese ￥100 Yen SOLUTION: US dollar British pound German mark Japanese Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 1 = .67 / 2 = .67 / 100 German mark DM2.0 = 2 / .67 1 = 2 / 100 Japanese ￥100 = 100 / .67 = 100 / 2 1 Yen US dollar British pound German mark Japanese Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 ￡1 ￡.33 ￡.0067 German mark DM2.0 DM3.0 DM1.0 DM.02 Japanese ￥100 ￥150 ￥50 ￥1 Yen Valuation Using Comparables6. Suppose you own a home that you purchased four years ago for $475,000. The tax assessor’s office has just informed you that they are increasing the taxable value of your home to $525,000. a. How might you gather information to help you appeal the new assessment?b. Suppose the house next door is comparable to yours except that it has one fewer bedroom. It just sold for$490,000. How might you use that information to argue your case? What inference must you make about the value of an additional bedroom?SOLUTION:a. You should retrieve as much information as you can about recent sales of comparable homes. If you canconvince the assessor’s office that your home is comparable (and the market value of the recent sales is less than $525,000) you should have a good case. You can gather the information about home sales from a real estate broker.b. The difference between your house’s assessed value and the actual market value of the home next door is$35,000 ($525,000 - $490,000). If you can convince the tax assessor’s office that the value of a bedroom is less than $35,000, then the assessor must agree that your home is worth less than $525,000. For example, if comparable sales figures show that one additional bedroom (all else reasonably equivalent) is worth only $10,000, then you should be able to argue that your home is worth $500,000 rather than $525,000.7. The P/E ratio of ITT Corporation is currently 6 while the P/E ratio of the S&P 500 is 10. What might account for the difference? SOLUTION: There are several possible reasons:? ITT may be riskier than the S&P500 either because it is in a relatively risky industry or has a relatively higherdebt ratio.? ITT’s reported earnings may be higher than they are expected to be in the future, or they may be inflated due tospecial accounting methods used by ITT.Instructor’s ManualChapter 7 Page 1088. Suppose you are chief financial officer of a private toy company. The chief executive officer has asked you to come up with an estimate for the company’s price per share. Your company’s earnings per share were $2.00 in the year just ended. You know that you should look at public company comparables, however, they seem to fall into two camps. Those with P/E ratios of 8x earnings and those with P/E ratios of 14x earnings. You are perplexed at the difference until you notice that on average, the lower P/E companies have higher leverage than the higher P/E group. The 8x P/E group has a debt/equity ratio of 2:1. The 14x P/E group has a debt/equityratio of 1:1. If your toy company has a debt/equity ratio of 1.5:1, what might you tell the CEO about your company’s equity value per share? SOLUTION:It would be reasonable to apply a P/E of 11x earnings (= (8 + 14) / 2) because your leverage is midway between the two groups. Hence, your company’s price per share would be: 11x $2.00 = $22.00 per share.9. Assume that you have operated your business for 15 years. Sales for the most recent fiscal year were $12,000,000. Net income for the most recent fiscal year was $1,000,000. Your book value is $10,500,000. A similar company recently sold for the following statistics: Multiple of Sales: 0.8x Multiple of Net Income 12x Multiple of Book Value 0.9xa. What is an appropriate range of value for your company?b. If you know that your company has future investment opportunities that are far more profitable than thecompany above, what does that say about your company’s likely valuation? SOLUTION:a. Multiple of Sales: .8x = $12 million x .8 Multiple of Net Income 12x = $1 million x 12 Multiple of Book Value .9x = $10.5 million x .9 An appropriate range might be 9 to 12 millionb. Higher end of the range = $9.6 million = $12 million = $9.45 millionEfficient Markets Hypothesis10. The price of Fuddy Co. stock recently jumped when the sudden unexpected death of its CEO was announced. What might account for such a market reaction?SOLUTION:Investors may believe that the company’s future prospects look better(i.e., either higher earnings or less risky) without the deceased CEO.11. Your analysis leads you to believe that the price of Outel’s stock should be $25 per share. Its current market price is $30.a. If you do not believe that you have access to special information about the company, what do you do?b. If you are an analyst with much better than average information, what do you do?SOLUTION:a. If you believe that the market for Outel stock is an informationally efficient one then the $30 market price(which is a weighted average of the valuations of all analysts) is the best estimate of the stock’s true value. You should question whether your own analysis is correct.b. You sell the stock because you think you have superior information. Real Interest Rate Parity12. Assume that the world-wide risk-free real rate of interest is 3% per year. Inflation in Switzerland is 2% per year and in the United States it is 5% per year. Assuming there is no uncertainty about inflation, what are the implied nominal interest rates denominated in Swiss francs and in US dollars?SOLUTION: Switzerland: (1.03 x 1.02) =1.0506 hence nominal interest rate = 5.06% US: (1.03 x 1.05) = 1 .0815 hence nominal interest rate = 8.15%Instructor’s ManualChapter 7 Page 109Integrative Problem13. Suppose an aunt has passed away and bequeathed to you and your siblings (one brother, one sister) a variety of assets. The original cost of these assets follows:ITEM COST WHEN PURCHASEDJewelry $500 by Grandmother 75 years ago House 1,200,000 10 years ago Stocks and Bonds 1,000,000 3 years ago Vintage (used) Car 200,000 2 months ago Furniture 15,000 various dates during last 40 yearsBecause you are taking a course in finance, your siblings put you in charge of dividing the assets fairly among the three of you. Before you start, your brother approaches you and says: “I’d really like the car for myself, so when you divide up the assets, just give me the car and deduct the $200,000 from my share.〞Hearing that, your sister says: “That sounds fair, because I really like the jewelry and you can assign that to me and deduct the $500 from my share.〞You have always loved your aunt’s house and its furnishings, so you would like to keep the house and the furniture.a. How do you respond to your brother and sister’s requests? Justify your responses.b. How would you go about determining appropriate values for each asset?SOLUTION:a. Because the market price of the car is close to the what your brother is willing to give up for it, your brother’srequest is reasonable. It is, however, quite possible (even likely), that the antique jewelry is worth much more today than what your relative’s grandmother paid for it in the past. Assigning only its acquisition cost to your sister’s share is quite likely a gross miscalculation. If she wants the jewelry, she should be “charged〞 an amount equal to today’s market value. It does not matter that your sister does not want to sell the jewelry for a profit, because the jewelry has VALUE even if you do not sell it. Fairness is all about equal VALUE.b. You would probably have to hire a professional appraiser for the furniture and the jewelry. You can look up thevalue of the stocks and bonds in a financial newspaper. You can estimate the value of the house by inquiring for how much similar houses in the same neighborhood have recently been sold. The car was purchased only twomonths ago, so it is probably reasonable to assume that the current market price is very close to what your distant relative paid for the car. Instructor’s ManualChapter 7 Page 110。

《金融学(第二版)》讲义大纲及课后习题答案详解第九章

CHAPTER 9VALUATION OF COMMON STOCKSObjectives∙To explain the theory and application of the discounted cash flow valuation method as applied to the equity of a firm.Outline9.1 Reading Stock Listings9.2 The Discounted Dividend Model9.3 Earnings and Investment Opportunities9.4 A Reconsideration of the Price/Earnings Multiple Approach9.5 Does Dividend Policy Affect the Value of a Share?Summary∙The discounted cash flow (DCF) method of valuing assets consists of discounting expected future cash flows ata risk-adjusted discount rate.∙The discounted dividend model (DDM) for valuing shares of stock starts from the observation that an investor in common stock expects a rate of return (consisting of cash dividends and price appreciation) that is equal to the market capitalization rate. The resulting formula shows that the current price of a share is the present value of all expected future dividends.∙In the constant growth rate DDM, the growth rate of dividends is also the expected rate of price appreciation.∙Growth per se does not add value to a share’s current price. What adds value is the opportunity to invest in projects that yield a rate of return in excess of the market capitalization rate.∙In a “frictionless” financial envir onment, where there are no taxes and no transaction costs, the wealth of shareholders is the same no matter what dividend policy the firm adopts.∙In the real world there are a number of frictions that can cause dividend policy to have an effect on the wealth of shareholders. These include taxes, regulations, the costs of external finance, and the information content of dividends.Solutions to Problems at End of Chapter1.The DDM Corporation has just paid a cash dividend (D0) of $2 per share. It has consistently increased its cash dividends in the past by 5% per year, and you expect it to continue to do so. You estimate that the market capitalization rate for this stock should be 13% per year.a.What is your estimate of the intrinsic value of a share (derived using the DDM model)?b.Suppose that the actual price of a share is $20. By how much would you have to adjust each of thefollowing model parameters to “justify” this observed price:i.The growth rate of dividendsii.The market capitalization rateSOLUTION:a.P0 = D0(1+g)/(k-g) = 2(1+0.05)/(0.13-0.05) = $26.25b.If the actual price of the share is $20, then some of our input parameters might need some adjustments:i.Assuming all other parameters are left as given, then solving for g =(.13 x 20 – 2)/(2+20) = 0.0273= 2.73%ii.Similarly, solving for k = 2(1.05)/20 + 0.05 = 0.155 = 15.5%2.The Rusty Clipper Fishing Corporation is expected to pay a cash dividend of $5 per share this year. You estimate that the market capitalization rate for this stock should be 10% per year. If its current price is $25 per share, what can you infer about its expected growth rate of dividends?SOLUTION:D1 = $5; k = 10%; P0= $25Hence g = 0.1 - 5/25 = -0.1 = -10%3. The Constant Growth Corporation (CGC) has expected earnings per share (E1) of $5. It has a history of paying cash dividends equal to 20% of earnings. The market capitalization rate for CGC’s stock is 15% per year, and the expected ROE on the firm’s future investments is 17% per year? U sing the constant growth rate discounted dividend model,a. What is the expected growth rate of dividends?b. What is the model’s estimate of the present value of the stock?c. If the model is right, what is the expected price of a share a year from now?d.Suppose that the current price of a share is $50.By how much would you have to adjust each of the following model parameters to “justify” this observed price:i.The expected ROE on the firm’s future investments.ii.The market capitalization rateiii.The dividend payout ratio.SOLUTION:a. g = earnings retention ratio x ROE = .8 x .17 = .136 = 13.6%b. P0 = D1/(k-g)D1 = .2 x $5 = $1 per shareP0 = $1/(.15 -.136) = $1/.014 = $71.43c. The stock price grows at the same rate as dividends, i.e., 13.6% per year:P1 = P0 x (1 + g) = $71.43 x 1.136 = $81.14d.If the market is efficient then the $50 price represents the best estimate of the stock’s true value. To “justify” thisprice, one of the input parameters in the model needs to be adjusted:i.Assuming all other parameters are correct, if we were to adjust for the ROE:50 = D1/(k-g), where g = 0.8 x ROESolving for g, then for ROE: g = .15 – 1/50 = 0.13 = 13%,hence ROE is equal to 13/0.8 = 16.25%ii. If we were to adjust the market capitalization k then:k = 1/50 + .136 = .156 = 15.6%iii.Dividend payout ratio x E1 = 50 x (.15-.136) = 0.7,hence Dividend payout ratio = 0.7/5=0.14 = 14%4. The stock of Slogro Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2 per share. The company has a policy of paying out 60% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue forever.a. Assuming the current market price of the stock reflects its intrinsic value as computed using the constantgrowth rate DDM, what rate of return do Slogro’s investors require?b. By how much does its value exceed what it would be if all earnings were paid as dividends and nothingwere reinvested?c. If Slogro were to cut its dividend payout ratio to 25%, what would happen to its stock price? What ifSlogro eliminated the dividend altogether?d. Suppose that Slogro wishes to maintain its current 60% dividend payout policy but that it also wishes toinvest an amount each year equal to that year’s total earnings. All the money would be invested inprojects earning 20% per year. One way that Slogro could do so would be to issue an amount of new stock each year equal to one-half that year’s earnings. What do you think would be the effect of this policy on the current stock price?SOLUTION:a. P0 = $10, E1 = $2, b = .4, ROE = .2k = D1/P0 + gD1 = .6 x $2 = $1.20g = b x ROE = .4 x .2 = .08Therefore, k = $1.20/$10 + .08 = .12 + .08 = .2 or 20%b. If all earnings were paid as dividends its price would be:P0 = $2/.2 = $10Thus, its price is the same whether it reinvests or not. This is because k = ROE.c. Since k = ROE, the stock price would be unaffected by cutting the dividend and investing the additionalearnings.d.Again, this should have no impact on the stock’s price since the NPV of the investments would be zero (the IRRof those projects (20%) is equal to the investors’ required rate of return, hence the firm’s c ost of capital).5. The Corporation currently pays no cash dividends, and it is not expected to for the next 5 years. Its sales have been growing at 25% per year.a.Can you apply the constant growth rate DDM to estimate its intrinsic value? Explain.b.It is expected to pay its first cash dividend $1 per share 5 years from now. It its market capitalization rateis 20% and its dividends are expected to grow by 10% per year, what would you estimate its intrinsic value to be?c.If its current market price is $100 per share, what would you infer the expected growth rate of its futuredividends to be?SOLUTION:a.Yes, we can apply the DDM model even if the company doesn’t pay dividends for the first 5 years. Thecompany will eventually have to pay dividends in the future.b.P4 = D5/(k-g) = 1/(.2-.1) = $10P0 = 10/1.24 = $4.82c.If P0 = $100 then P4 = 100 x 1.24 = 207.36 and g = 0.2 – 1/207.36 = 19.518%6. The Digital Growth Corp. pays no cash dividends currently and is not expected to for the next 5 years. Its latest EPS was $10, all of which was reinvested in the company. The firm’s expected ROE for the next 5 years is 20% per year, and during this time it is expected to continue to reinvest all of its earnings. Starting 6 years from now, the firm’s ROE on new investments is expected to fall to 15%, and the company is expected to start paying out 40% of its earnings in cash dividends, which it will continue to do forever after. DG’s market capitalization rate is 15% per year.a. What is your estimate of DG’s int rinsic value per share?b. Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its priceover the next year? The year after?c. What effect would it have on your estimate of DG’s intrinsic value if you expecte d DG to pay out only20% of earnings starting in year 6?56P0 = P5/(1+k)5 = $180.82/1.155 = $89.90b.The price should rise by 15% per year until year 5 after which it will grow at the dividends’ growth rate g (=9%).c. Since ROE =k, the dividend payout ratio will have no effect on current price.7. The 2Stage Co. just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% per year for the next 3 years and then to level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year.a. What is your estimate of the intrinsic value of a share of the stock?b. If the market price of a share is equal to this intrinsic value, what is the expected dividend yield?c. What do you expect its price to be one year from now? Is the implied capital gain consistent with yourestimate of the dividend yield and the market capitalization rate?P 3 = D 4/(k – g) = 2.05078/(.20 -.05) = $13.67P 0 = D 1/(1+k) + D 2/(1+k)2 + (D 3 + P 3)/(1+k)3 = $1.25/1.2 + $1.5625/1.22 + ($1.953 + $13.67)/1.23 = $11.17 b. If the market price of a share is equal to this intrinsic value, the expected dividend yield is D 1/P 0, which is1.25/11.17 = .1119 or 11.2%c. Its price one year from now = P 1 = D 2/(1+k) + (D 3 + P 3)/(1+k)2 = $1.5625/1.2 + ($1.953 + $13.67)/1.22 =$12.15.The implied capital gain is $12.15 - $11.17 = $.98, which is 8.8% of the price P 0. Thus the dividend yield plusthe capital gain rate add up to 20%, which is k.8. The Bearded ladies’ Stock guide offers the following method for selecting stocks:Compute the stock’s PEG ratio by dividing its P/E mu ltiple by its growth rate of earnings. Select only those stocks whose PEG ratio is in the lowest quartile.a. If the stock is fairly priced according to the constant-growth-rate DDM, what should be its PEG ratio asa function of the following three variables: the stock’s market capitalization rate (k), the expectedprofitability of its future investments (ROE), and its plowback ratio (b)? (Assume the P/E ratio used in computing PEG is the ratio of the stock’s current price to its expected earnings per share, P 0/E 1)b. Assume the CAPM and the DDM are valid. The risk free rate is .04 and the risk premium on the marketportfolio is .06. What should be the relationship between the PEG for a stock whose ROE is .10 and a stock whose ROE is .15, assuming the two stocks have the same beta (equal to 1) and plowback ratio (equal to .6)?c. What do you think of the Bearded Ladies’ method?SOLUTION:a. If the DDM holds we know that P 0 = D 1 / (k-g), furthermore, we know that g = b x ROE and D 1=(1-b) E 1b(ROE)(k -b(ROE))b (ROE)b E k -b(ROE)E )b (g E P PEG -=⨯-==1111110b. The values of k for each of the stocks will be: k = .04 + .06 beta = .04 + .06 =.1PEG 1= (1-.6) / (.6 x .10 x (.1 - .6 x .10)) = 166.67PEG 2= (1-.6) / (.6 x .15 x (.1 - .6 x .15)) = 444.44PEG 1 < PEG 2c. As we can see in part b, the PEG rule would lead us to choose the stock with the lowest ROE.In general, if the stock market is informally efficient, then any stock will offer an expected rate of return that is commensurate with the stock’s perceived market risk, regardless of the stock’s PEG.Using the Internet for Stock Pricing9. Pick a company whose stock is traded on the NYSE. Use one of the stock valuation models discussed in this chapter together with information that you can find by searching the Internet to compute an intrinsic value for the s tock. Compare your estimate of intrinsic value with the stock’s actual price. Would you be willing to make an investment decision on the basis of your research? Why or why not?SOLUTION:One simple model that we can use to value a company is to find the average P/E multiple of the industry in which the company operates and multiply it by the expected earnings per share of that company. The difference between this intrinsic value and the actual market value of the stock can be explained by the difference between our assumptions regarding the company’s future investment opportunities and the market’s expectations. For example, if the market value of the stock is higher than the intrinsic value found, then this difference reflects the investors’ belief that the company will have a greater-than-average future investments opportunities with a rate of return greater than the market capitalization rate for this particular industry. If markets are efficient, then this market value is supposed to be the “real” value o f the company, and represents the view of the majority of investors, hence I would be reluctant to follow my own findings of the intrinsic value as a basis for an investment decision.Dividend Policy10. Divido Corporation is an all-equity financed firm with a total market value of $100 million. The company holds $10 million in cash-equivalents and has $90 million in other assets. There are 1,000,000 shares of Divido common stock outstanding, each with a market price of $100. What would be the impact on Di vido’s stock price and on the wealth of its shareholders of each of the following decisions? Consider each decision separately.a. The company pays a cash dividend of $10 per share.b. The company repurchases 100,000 shares.c. The company pays a 10% stock dividend.d. The company has a 2-for-1 stock split.e. The company invests $10 million in an expansion that has an expected IRR equal to the firm’s cost ofcapital.SOLUTION:a.The stock price falls by $10, but shareholder wealth remains the same in a frictionless world becauseshareholders receive $10 in cash on each share they own. In the real world, shareholder’s wealth may decline because personal taxes may have to be paid on the cash dividend.b.The stock price is unchanged and so is shareholder wealth. Some of the shareholders who sold their shares mayhave to pay taxes on their capital gains in the real world.c.The number of shares outstanding rises to 1,100,000, and the stock price falls to $90.909 (=$100MM/$1.1MM)per share. Shareholder wealth is unchanged: instead of having one share at $100, now the shareholder will have1.1 shares at $90.909/share (1.1 x 90.909 = 100)d.The number of shares outstanding rises to 2,000,000, and the stock price falls to $50 per share. Theoretically,shareholder wealth is unchanged.e.The composition of the firm’s assets changes. Cash falls by $10 million and other assets go up by the sameamount. There is no change in either the stock price or in shareholder wealth.11. It has been found empirically, that on average the total market value of their stock rises when firms announce a stock split. What hypotheses might you offer to explain this phenomenon?SOLUTION:Theoretically, when a firm announces a stock-split, the number of shares doubles (if 2-to-1 stock split) and the market value per share drops by half. Empirically, we have observed a small increase in market value of the stock after the announcement of a stock-split. This can be explained by the informational content of the split. Outside investors may interpret this stock dividend as a positive sign that the company is doing well, hence increasing the price of the stock. Another possible interpretation is that since the price per share is now lower after the split, it can become more affordable for some investors.12. Suppose that a company has had an extraordinarily profitable year, and it announces that it will use most of its net cash inflow to buy back shares of its stock in the market. Would you expect the price of its stock to rise or fall when the announcement is made? Explain.SOLUTION:Theoretically, the price of the stock should not change after a stock repurchase. But the announcement could send a positive signal to investors that the company has been doing very well and has enough cash to buy back shares as a form of dividends. This might increase the price of the stock after the announcement.。

国际金融学第2次答案

10秋金融陈斐国际金融学第一讲国际收支一、单项选择题1、在国际收支平衡表中，下列各项属于单方面转移的是（B ）A．保险赔偿金B．专利费C．投资收益D．政府间债务减免2、下列项目应记入贷方的是（C）A．从外国获得的商品与劳务B．向外国政府或私人提供的援助、捐赠C．国内私人国外资产的减少或国外负债的增加D．国内官方当局的国外资产的增加或国外负债的减少3、综合项目差额是指（B ）A．经常项目差额与资本与金融项目差额之与B．经常项目差额与资本与金融项目中扣除官方储备后差额之与C．经常项目差额与金融项目差额之与D．经常项目差额与资本项目差额之与4、最早论述“物价现金流动机制”理论的是（B ）A．马歇尔B．休谟·大卫C．弗里德曼D．凯恩斯5、主要研究货币贬值对贸易收支的影响的国际收支调节理论是（B ）A．物价现金流动机制B．弹性分析理论C．“米德冲突”与协调理论D．自动调节理论6、“马歇尔——勒纳条件”是指（ A ）A．进口需求弹性与出口需求弹性之与大于1B．进口需求弹性与出口需求弹性之与大于0C．进口需求弹性与出口需求弹性之与小于1D．进口需求弹性与出口需求弹性之与小于07、当处于通货膨胀与国际收支逆差的经济状况时，应采用下列政策搭配（D ）A．紧缩国内支出，本币升值B．扩张国内支出，本币贬值C．扩张国内支出，本币升值D．紧缩国内支出，本币贬值二、多项选择题1、从供给角度讲，调节国际收支的政策有（BC ）A．财政政策B．产业政策C．科技政策D．货币政策E．融资政策2、下列项目中属于自主性交易的是（ABC ）A．经常项目B．资本项目C．证券投资项目D．官方储备项目E．错误与遗漏项目三、判断题1、国际收支平衡表是反映一国在一定时期内实现外汇收支的对外经济交易的统计表。

（×）2、凡引起本国外汇收入的项目，记入借方，记为“—”。

（×）3、按IMF规定，在报告期内已发生所有权转移但并未实现外汇收支的项目，不需要登录在报告期的国际收支平衡表中。

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第三章货币的时间价值2、你现在有10000元资金准备存在银行5年，有3种存款方式可选择：存1年期存款，每年到期后连本代利转存4次；存3年期存款，到期后连本代利转存1年期存款2次；存5年期存款1期。

1年期、3年期5年期存款的年利率分别为2%、2.2%和3%。

请问3种方式5年后的终值各为多少？哪种方案最优？解：5110000(12%)11040.81FV =⨯+=2210000(1 2.2%3)(12%)11090.66FV =⨯+⨯⨯+=310000(13%5)11500FV =⨯+⨯=因此，方案3 最优3.你现在每个月存款1000元，年利率为3%，10年后你有多少钱？这10年存款的现值为多少钱？解：12013%1000(1)139741.42 ()12tt FV ==⨯+=∑元 11911000103561.75 ()3%(1)12t t PV ==⨯=+∑元 4.你准备购买价值40万元的住房一套，目前1年期存款利率为5%，贷款利率为6%，利息收入税为20%，预测未来5年房地产价格平均每年上涨3%。

你有3种方案可供选择，以A 方案所需的时间计算，各方案的净现值和内涵报酬率为多少？哪种方案最优？A ．你每个月存款5000元，多长时间你可以存储到可以一次性全额付款方式（一次性付清房款打九八折）购买该类住房所需的资金？B ．你现在贷款购买该住房，每月还款5000元，多长时间能够还清贷款？C ．如果你将贷款购买的住房出租，每月房租为1500元，一并用于归还贷款，多长时间能够还清贷款？解：方案A ：粗略估计50.98400000(13%)/600005⨯⨯+>年，所以在第六年起房价不上涨的假设下，付款的终值为50.98400000(13%)454435.44 ()⨯⨯+=元一年期存款实际利率为0.85%4%⨯=，设从现在起第n 月底可以一次性全额付款，则终值满足下列方程514%0.98400000(13%)5000(1)12nn tt -=⨯⨯+=⨯+∑ 得到80n =,也即第7年8月底可以一次性全额付款。

方案B ：每月月底还款5000元，则现值满足1140000050006%(1)12nt t ==⨯+∑ 得到103n =，也即第9年7月底可以还清贷款。

方案C ：加上每月月租1500，每月月底还款6500元，则现值满足1140000065006%(1)12nt t ==⨯+∑ 得到74n =，也即第7年2月底可以还清贷款。

以A 方案所需的时间80个月计算，各方案的净现值和内部收益率（IRR 的计算上，这里直接用excel 工具进行不断尝试，找到四位小数条件下净现值最接近零者。

当然，用IRR 函数也能计算之）分别为：方案A ：5808010.98400000(13%)150002378.53 ()4%4%(1)(1)1212t t NPV =⨯⨯+=-⨯=-++∑元0.351%IRR =方案B ：8011400000500049402.11 ()4%(1)12t t NPV ==-⨯=+∑元 0.00%IRR =方案C ：8011400000650055777.26 ()4%(1)12t t NPV ==-⨯=-+∑元 0.6803%IRR =5.你现在有10万元美元可进行投资，美元存款年利率为3%，日元存款年利率为1%，预测未来两年日元汇率将升值5%，哪种投资方案较优？解：美元存款在第二年末的终值为：2110(13%)10.609 ()FV =⨯+=万美元日元存款在第二年末的终值是：2210(11%)(1+5%)10.711 ()FV =⨯+⨯=万美元所以，存日元存款并与第二年结束兑换为美元的投资方案较优。

第四章资源的时间配置4、如果您2007年的可支配收入为80000元，消费支出为60000元，2008年的可支配收入为100000元，消费支出为65000元。

假定您的边际消费倾向不变，如果2009年您的可支配收入为120000元，根据绝对收入假说，您的消费和储蓄各为多少？平均消费和储蓄倾向有何变化？解：C a cY =+边际消费倾向 65000600000.2510000080000MPC -==- 消费函数常数600000.258000040000 ()a C cY =-=-⨯=元所以，消费函数是400000.25C Y =+2009年的消费2009400000.2512000070000 ()C =+⨯=元 2009年的储蓄2009200920091200007000050000 ()S Y C =-=-=元2007年-2009年平均消费倾向逐年下降：2007600000.7580000APC ==，2008650000.65100000APC ==，2009700000.58120000APC ==相应地，2007年-2009年平均储蓄倾向逐年递增：200710.750.25APS =-=，200810.650.35APS =-=，200910.580.42APS =-=5、假设一个人22岁大学毕业开始工作，父母给他10万元资金的支持1，第一年劳动收入为5万元，每年按5%的速度增长，60岁退休，预期寿命为80岁。

预测未来几十年的年平均通货膨胀率为2%，名义投资收益率为4%。

他希望实际消费水平也能够每年增长2%，还给子女留下遗产100万元。

不考虑所得税和养老金的影响。

请你给他做一个生命周期的消费储蓄规划。

解：考虑有遗产的生命周期规划：0(1)(1)(1)nmt t tt t tt T t TC B Y W i i i ==+=++++∑∑ 1(1)t t Y g Y -=+ 1(1)t t C k C π-=++ t t t S Y C =- 1(1)t t t W i W S -=++其中，22T =，60m =，80n =，4%i =，1000000t B =，0100000W =，5%g =，4%i =，2%k =，2%π=利用excel 可以生成生命周期内的消费支出情况如下表4-1和下图4-1：表4-1 修正的生命周期消费储蓄规划单位：元年龄T收入t Y 消费t C 储蓄t S 期末财富t W1这里，我们考虑父母的10万元支持源于22岁的期初。

21 100000.0022 50000.00 39891.46 10108.54 114108.5423 52500.00 41487.12 11012.88 129685.7624 55125.00 43146.60 11978.40 146851.5925 57881.25 44872.47 13008.78 165734.4426 60775.31 46667.37 14107.95 186471.7627 63814.08 48534.06 15280.02 209210.6528 67004.78 50475.42 16529.36 234108.4329 70355.02 52494.44 17860.58 261333.3530 73872.77 54594.22 19278.55 291065.2431 77566.41 56777.99 20788.42 323496.2832 81444.73 59049.11 22395.63 358831.7533 85516.97 61411.07 24105.90 397290.9234 89792.82 63867.51 25925.30 439107.8635 94282.46 66422.21 27860.24 484532.4236 98996.58 69079.10 29917.48 533831.1937 103946.41 71842.27 32104.14 587288.5838 109143.73 74715.96 34427.77 645207.9039 114600.92 77704.59 36896.32 707912.5440 120330.96 80812.78 39518.18 775747.2241 126347.51 84045.29 42302.22 849079.3342 132664.89 87407.10 45257.78 928300.2943 139298.13 90903.39 48394.74 1013827.0544 146263.04 94539.52 51723.52 1106103.6445 153576.19 98321.10 55255.09 1205602.8746 161255.00 102253.95 59001.05 1312828.0447 169317.75 106344.10 62973.64 1428314.8148 177783.63 110597.87 67185.77 1552633.1749 186672.82 115021.78 71651.03 1686389.5350 196006.46 119622.65 76383.80 1830228.9151 205806.78 124407.56 81399.22 1984837.2952 216097.12 129383.86 86713.26 2150944.0453 226901.97 134559.22 92342.76 2329324.5554 238247.07 139941.59 98305.49 2520803.0355 250159.43 145539.25 104620.18 2726255.3256 262667.40 151360.82 111306.58 2946612.1257 275800.77 157415.25 118385.52 3182862.1258 289590.81 163711.86 125878.95 3436055.5559 304070.35 170260.34 133810.01 3707307.7860 319273.86 177070.75 142203.12 3997803.2161 0.00 184153.58 -184153.58 3973561.7662 0.00 191519.72 -191519.72 3940984.5163 0.00 199180.51 -199180.51 3899443.3864 0.00 207147.73 -207147.73 3848273.3865 0.00 215433.64 -215433.64 3786770.6766 0.00 224050.99 -224050.99 3714190.5167 0.00 233013.03 -233013.03 3629745.1168 0.00 242333.55 -242333.55 3532601.3769 0.00 252026.89 -252026.89 3421878.5370 0.00 262107.96 -262107.96 3296645.7171 0.00 272592.28 -272592.28 3155919.2572 0.00 283495.97 -283495.97 2998660.0573 0.00 294835.81 -294835.81 2823770.6474 0.00 306629.25 -306629.25 2630092.2275 0.00 318894.42 -318894.42 2416401.4976 0.00 331650.19 -331650.19 2181407.3677 0.00 344916.20 -344916.20 1923747.4578 0.00 358712.85 -358712.85 1641984.5079 0.00 373061.36 -373061.36 1334602.5280 0.00 387983.82 -387983.82 1000002.80图4-1修正的生命周期消费储蓄规划（单位：元）第六章资产价值评估2、如果美元对欧元汇率伦敦市场为1:1.010，纽约市场为1:1.012，外汇交易成本为0.1%，你是否可以从中套利？如果可以，盈利率是多少？解：由于1.012 1.0100.182%0.1%1.010-=>,所以可以从中套利，盈利率为0.082%。

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