Ec1723-Fall2018-PSet3-Solutions.pdf - Ec1723 Fall 2018...

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Ec1723, Fall 2018: Problem Set 3 Solutions1. The riskless interest rate is 1%. You hold a portfolio consisting of short-term safe assetsand the market portfolio of risky assets, which has a mean return of 12% and a standarddeviation of 25%.You are considering the stock of Microsoft that you believe to have abeta of 1.4 with the market portfolio, and a standard deviation of return of 50%.a) What is the standard deviation of the idiosyncratic component of Microsoft’s return(the residual in the market model regression)?What is the correlation of Microsoft’s returnwith the market’s return?
7b) If the CAPM holds, what must be the mean excess return on Microsoft over theriskfree rate?What must be Microsoft’s alpha?What must be its Sharpe ratio?Is theSharpe ratio on Microsoft higher or lower than the Sharpe ratio on the market?Explain,and generalize to other stocks.
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c) Suppose that Microsoft stock has a lower alpha than the CAPM implies.Explainhow to change its weight in your portfolio in such a way as to increase the mean return onyour portfolio without increasing its variance. (Do this in words, or write down a relevantequation if you can.)

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