FINAL EXAM - Studies2 - HEC Paris

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$Multifractality of US Dollar/Deutsche Mark Exchange Rates - Studies2$

Problem 1. (30 points) Decide whether the following statements are true or false. No explanations are necessary. (a) If the Capital Asset Pricing Model holds, no mutual fund manager can earn a higher return than the market. (False) (b) Over the long run, the stocks of small companies tend to outperform the stocks of larger companies. (True) (c) A credit default swap is a contract that provides insurance against the risk of default by a company. (True) (d) In the Capital Asset Pricing Model, investors are compensated for the firm-specific volatility of a stock. (False) (e) The Black-Scholes formula for a European call assumes that the logarithm of the price of the underlying stock has a normal distribution. (True) (f) It is never optimal to exercise an American call on a non-dividend paying stock prior to maturity. (True) (g) It is never optimal to exercise an American put on a non-dividend paying stock prior to maturity. (False) (h) A put is the obligation to sell an asset at a fixed price on a certain date. (False) (i) A put option on the S&P 500 index has a negative β. (True) (j) A straddle consists of a long position in a call and a put with the same strike price. (True) 2
Problem 2. (20 points) Consider an economy with two possible states of the world, which occur with equal probability. Stocks A and B yield the following returns in each state: Return on stock A Return on stock B State 1 +40% +25% State 2 -10% -5% (a) Compute the expected returns on stocks A and B. Solution: The expected returns on the stocks are: E[rA] = (40% − 10%)/2 = 15% E[rB] = (25% − 5%)/2 = 10% (b) Compute the standard deviation of returns on A and B. Solution: The variance of the return on stock A is: V ar(rA) = [(0.25) 2 + (0.25) 2 ]/2 = (0.25) 2 The standard deviation of stock A is therefore 25%. The variance of the return on stock B is: V ar(rB) = [(0.15) 2 + (0.15) 2 ]/2 = (0.15) 2 . The standard deviation of stock B is therefore σB = 15%. (c) Compute the covariance of the returns on A and B. Solution: The covariance is given by: Cov(rA, rB) = 0.5 × 0.25 × 0.15 + 0.5 × 0.25 × 0.15 = 0.25 × 0.15 = 0.0375. The above calculation implies that Cov(rA, rB) = σAσB. (d) Compute the correlation of the returns on A and B. Solution: Corr(rA, rB) = Cov(rA, rB) = 1. 3 σAσB
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FINAL EXAM - Studies2 - HEC Paris

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