T6+2011 - Fina 3104 L2 T6 Homework 2 Practice Problems on...

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Fina 3104 1 Fina 3104 L2 T6 § Homework 2 § Practice Problems on Portfolio Performance Evaluation
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Fina 3104 2 Q1: Practice Problem 1(3 mins) 1. True or False Suppose two portfolios have the same average return, the same standard deviation of returns, but portfolio A has a higher beta than portfolio B . According to the Sharpe measure, the performance of portfolio A is the same as the performance of portfolio B .
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Fina 3104 3 Solution True. The Sharpe measure only looks at the average excess return and the standard deviation of returns. If these are the same, different betas will not give different Sharpe measures.
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Fina 3104 4 Q2:Practice Problem 2(6 mins) 2. Information Ratio The original information ratio measure is based on the CAPM. You want to modify the measure so that it is based on the following APT model: ri rf = bi1 ( rM rf ) + bi2 rSMB + bi3 rHML + ei (a) Use the above notations and write down the formula of the modified information ratio. (b) Using the original measure, Portfolio P has an information ratio of 0.2; but using the
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Fina 3104 5 Solution (a) The modified information ratio is where σ( ei ) is the standard deviation of ei and denotes the arithmetic average of x .
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Fina 3104 6 (b) The original information ratio of Portfolio P is where σ(ep) is the residual from a CAPM regression. It is possible that the original information ratio of 0.2 comes from some small stocks and high book-to-market stocks,
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T6+2011 - Fina 3104 L2 T6 Homework 2 Practice Problems on...

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