Performance+Evaluation+Solution

Performance+Evaluation+Solution - FINA 3104 Practice...

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1 FINA 3104 Practice Problems Fall 2011 Portfolio Performance Evaluation (Suggested Solution) 1. True or False (a) 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 . 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. (b) Investors should avoid funds with negative information ratio. Solution: False. Investors should short sell funds with negative information ratio. Funds with negative information ratio generate negative abnormal returns relative to the CAPM, and if investors short sell these funds, they can earn positive abnormal returns. (c) If the CAPM holds, the Jensen measures of all securities and portfolios are zero, and the Treynor measures of all securities and portfolios are the same. Solution: True. If the CAPM holds, all securities and portfolios lie on the Security Market Line (SML). The Jensen measures, which represent the deviation from the SML, should be zero. The Treynor measures should be also be the same for all securities and portfolios because they are all equal to the slope of the SML. (d) If a multifactor APT holds, the Jensen measure of all securities and portfolios is zero, and the Treynor measure of all securities and portfolios are the same. Solution: False. The Jensen measures and the Treynor measures are defined relative to the CAPM. If securities returns in fact follow a multifactor model, the returns will generally not lie on the SML line of the CAPM. It is possible to have positive or negative Jensen alphas, and different Treynor measures.
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2 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: r i r f = i1 ( r M r f ) + i2 r SMB + i3 r HML + e i (a) Use the above notations and write down the formula of the modified information ratio.
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Performance+Evaluation+Solution - FINA 3104 Practice...

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