# 3330 PS6 sol - Cornell University Fall 2010 Economics 3330:...

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Cornell University Fall 2010 Economics 3330: Problem Set 6 Solutions 1. True/False/Explain State whether each of the following is true or false and explain your answer. Please limit your explanations to no more than two sentences. a. For diversification to reduce risk, at least some of the assets must be negatively correlated. False. It suffices that the assets not be perfectly correlated. b. The optimal risky portfolio does not depend on the investor’s risk aversion. True. The optimal risky portfolio maximizes the Share ratio. Investor risk aversion determines the portfolio share invested in the risky portfolio. 2. Question 12 of Chapter 7 of Text Suppose that there are many stocks in the security market and that Stocks A and B are perfectly negatively correlated. Stock A has expected return 10% and standard deviation of 5%. Stock NB has expected return of 15% and standard deviation of 10%. What must be the value of the risk- free rate of return in the economy? Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio, in equilibrium, will be the risk-free rate. To find the proportions of this portfolio [with the proportion w A invested in Stock A and w B = (1 – w A ) invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation is: P = Absolute value [w A A w B B ] 0 = 5w A [10 (1 – w A )] w A = 0.6667 The expected rate of return for this risk-free portfolio is: E(r) = (0.6667 10) + (0.3333 15) = 11.667% Therefore, the risk-free rate is: 11.667% 3. Questions 9-13 of Chapter 8 of Text Suppose that the index model for stocks A and B is estimated from excess returns with the following results: R A = 3% + 0.7R M + e A R B = -2% + 1.2R M + e B σ M = 20%; R-square A = 0.20; R-square B =.12 a. What is the standard deviation of each stock?

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## This note was uploaded on 04/06/2011 for the course ECON 3330 taught by Professor Mbiekop during the Fall '08 term at Cornell University (Engineering School).

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3330 PS6 sol - Cornell University Fall 2010 Economics 3330:...

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