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Investment Theory Thesis

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Investment Theory
(Master course, ABS) Final Exam 2013
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Remark: In all the questions of this exam we assume that there is no transaction cost and investors can take long and short positions in any asset without margin requirement. Part I (8 questions, 5 points each; circle one and only on choice that you think is the best. No penalty for the wrong choice.) 1. The excess return on any stock can be seen as a zero-cost gamble because a. it is highly risky, and risk averse people don’ like it. t b. its expected value is zero provided there is no arbitrage. *c. it is priced at zero when there is no arbitrage. d. all the above are correct. e. both b) and c). 2. The stochastic discount factor (SDF) a. is unique when the capital market is mean-variance e¢ cient. b. is a random variable that is used for pricing all other risky assets. c. has an expected value equal to the present value of 1: d. is unique when the capital market is complete. *e. satis…es all above descriptions except a). 3. Consider a trinomial model of capital market in which there are three possible states of economy in one year with equal probability of occurrence. Let s denote the price of the Arrow-Debreu security that pays $1 in state s and zero otherwise. Suppose 1 = 0:2; 2 = 0:45; and 3 = 0:33: Suppose a stock is currently priced at 33:5; and its payo¤ will be 20; 30; 50 in state 1; 2; and 3 respectively. Then *a. there is an arbitrage opportunity because the stock is too cheap. b. there is an arbitrage opportunity because the stock is too expensive. c. there is no arbitrage opportunity because the stock is fairly priced. d. the stock is too expensive because it has a negative expected excess return. e. both b) and d). Answer: Fair price of the stock is 0:2 20 + 0:45 30 + 0:33 50 = 34:0: 4. In the trinomial model above, what is the risk neutral probability ps

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