Problem -1 [50 Points] Short Questions. Explain or prove your answer in the space provided. a) [5 Points] Explain how event studies assess market efficient market hypothesis. Use a CAR (Cumulative Abnormal Return) of a negative event with leakage to explain your answer. b) [5 Points] Mutual fund performance is used to test for the efficient market hypothesis (EMH). Detail how? To get full mark for this question you need to detail how the performance is measured, what the expected performance under EMH is, and what the empirical results show. c) [7 Points] Analytically show that the Arrow-Debreu state pricing is in fact Risk Neutral valuation. Now suppose a stock is currently selling for 100 . In the next period it is either 120 or 90 with a probability of 50%. The risk free rate is 5%. Use the Arrow-Debreu state pricing to price a binary option that gives you $10 when the stock is less than 100 and zero otherwise. d) [5 Points] Two years ago at this time, you allocated your entire portfolio among the three 0-coupon bonds below, and at that time: BOND A had 8 years to maturity and the annual YTM was 9% \& face value of $1000 BOND B had 6 years to maturity and the annual YTM was 7% \& face value of $1000 BOND C had 4 years to maturity and the annual YTM was 6% \& face value of $1000. You allocated 60% of your portfolio to Bond A,40% to Bond B, and 0% to Bond C. If the yield curve has experienced a parallel shift up by 1.5% during the past 2 years [this means that all spot rates rose by 1.5% during the past 2 years], what return did you earn on your portfolio? e) [6 points] Fill the missing entries in the following table, assuming that the CAPM holds. [Make sure you show your calculation for each entry]. Expected return and standard deviation are expressed in percentage points. If you do not have enough information to fill a specific entry, state so. f) [7 points] Suppose the entire stock market has only two securities in it, stock S1 and S2. Assume the market value of stock 1 is three times the market value of stock 2 , so that M=.75S1+.25S2. The following table shows the expected return and standard deviation of the two stocks. The correlation coefficient between the returns of stocks S1 and S2 is 0.25. The risk-free rate is 5%. Find the expected return on the market portfolio E(RM) and the variance of the market portfolio V(RM). Find the beta of stocks S1 and S2. Write down the equation of the security market line as a function of beta