課程名稱︰投資學 課程性質︰必修 課程教師︰陳其美 開課學院：管理學院 開課系所︰財金系 考試日期（年月日）︰97年6月20日 考試時限（分鐘）：180 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Part I, True-False Questions. (40%) 1. Recent studies of stock market prices using US data found that long-horizon returns are positively serially correlated, while short- or intermediate-horizon returns are negatively serially correlated. 2. The yield to maturity of a bond diers from the current yield of the bond; the latter is the bond's annual coupon payment divided by the bond price. 3. Advocates of the liquidity preference theory of the term struc- ture believe that short-term investors dominate the market so that the foward rate will generally fall short of the expected short rate. 4. According to James Tobin, the ratio of market price of a rm's equity to the replacement cost of its assets less its liabilities, or the Tobin's q, will tend toward 1 in the long run. 5. A short straddle is established by buying a call and a put on a stock, each with the same exercise price and the same expiration date. A strap is a variation of a straddle, involving two calls and one put. 6. The Black-Scholes option pricing formula has a surprising feature: the option value does not depend on the expected rate of return on the underlying asset (the stock). 7. The open interest on a futures contract is the number of contracts outstanding, where long and short positions are counted separately, but the clearinghouse's position is not counted in the computation of open interest. 8. Since 2002 OneChicago has operated an entirely electronic market in single-stock futures, but trading volume in this market has to date been disappointing. 9. Sharpe's and Treynor's measures both give excess return per unit of risk on a mutual fund, but the former considers only the systematic risk. 10. Convergence arbitrage means to buy one security and sell the other, with the belief that at a given date the pricing discrepencies between the two securities almost necessarily must disappear. This was a strategy extensively used by Long-Term Capital Management. Part II, Computations. (Important Instruction: You must (i) detail all the computations and (ii) give a precise solution to each problem. You will not receive any credit if you simply write down an equation without obtaining the nal result.) 1. (30%) Consider a three-date (dates 0, 1 and 2) economy with perfect nancial markets. There are four possible states ( = w1; w2; w3; w4). At date 0, investors only know that the true state is an element of , and the true state will be revealed perfectly at date 2. At date 1, the occurrence or non-occurrence of the event E = w1; w2 becomes publicly known. This is the standard event tree that we considered in Lecture 5A. We assume that markets are dynamically complete. The following table gives the price process of asset 1, denoted by p1, and the forward price process for the delivery of one unit of asset 1 at date 2, which is denoted by G. Asset price/(Date,Event) (0;omega ) (1;E) (1;Ec) (2; w1) (2; w2) (2; w3) (2; w4) p1 100 110 90 150 114 134 100 G 624/5 132 117 150 114 134 100 At date 0, two default-free coupon bonds, referred to as X and Y, are traded, and their data are summarized in the following table (where the date-0 bond prices are obtained after the date-0 coupon payments are made; see Lecture 7, Part I): bond maturity coupon payment face value date-0 price X date 1 50 1000 x Y date 2 200 1000 y (i) Compute x and y. (ii) Mr. B is endowed with 1 million dollars (a sure income!) at date 2. He only wants to consume at date 1, and he wants to consume the same amount in event E and in event Ec. Suppose that he is allowed to trade the above two bonds X and Y only, and he is allowed to trade only at date 0. At date 0, how many units of bond X should Mr. B buy or sell, and how many units of bond Y should Mr. B buy or sell? How much can Mr. B consume at date 1? (iii) At date 0, what is the futures price for the delivery of one unit of asset 1 at date 2? 2. (30%) Consider a three-date economy with the same event tree as de- scribed in Problem 1 above; that is, markets are dynamcially complete, with the following table giving the price process p1 of asset 1 and the forward price process G for the delivery of one unit of asset 1 at date 2. Asset price/(Date,Event) (0;omega ) (1;E) (1;Ec) (2; w1) (2; w2) (2; w3) (2; w4) p1 100 110 90 150 114 134 100 G 624/5 132 117 150 114 134 100 Consider a European call option (with price denoted by c) written on one unit of asset 1 with date 2 being the expiration date and exercise price being 126. Assume that one-period deposit (the riskless one- period money market account) is available for trading at both dates 0 and 1. (i) Find c(0), c(1;E) and c(1;Ec); and (ii) Suppose that the date-0 option price prevailing in the market is actually greater than the c(0) that you computed in part (i). Find a dynamic arbitrage strategy that involves trading only in asset 1, the riskless one-period money market account, and the call option. --

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