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03-PS7-PT_sol

03-PS7-PT_sol - MIT Sloan School of Management J Wang...

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MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Problem Set 7: Portfolio Choice Solution 1. (BKM) Which statement(s) about portfolio diversification is correct? (a) False. Systematic risk cannot be diversified. (b) False. Suppose you have two stocks with the same return. Buying a combination of two could reduce the risk you’re facing, but never lower your return. (c) True. As more and more securities are added, systematic risk becomes dominant. (d) False. Diversification starts when you add the first stock. 2. The information given in this question is not quite sufficient. The solution below will assume that all stock has insignificant weight in the tangent portfolio: (a) Since all the covariance are 0 . 01 = 10% 2 , the systematic risk has to be 10%. The risk of each individual stock disappears. (b) From (a), all stocks have the same beta, and therefore must have the same expected return. Consider a case where some stock has a higher return, then the tangent portfolio will hold a significant weight in the stock such that the beta is higher. But that is a contradiction to the assumption made. 3. (a) Although both return of B is lower than A and has a higher volatility, some people still may want to invest in B because it is not perfectly correlated to A.
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