ProblemSet06

3 3. CAPM Suppose that CAPM holds, the riskfree rate is r f = 2% and the expected return on the market portfolio is E [ r m ] = 12%. The standard deviation of the market return is 0.2 or 20%. (a) What is the expected return on an asset that has β = 1 . 5 with respect to the market return? (b) What is the beta of a portfolio that has E [ r p ] = 11%? (c) A security return r i has a covariance of σ i,m = 0 . 1 with the market return. What is the expected excess return E [ r i ] - r f ? 4. Stock pricing The market price of a security is $20. Its expected rate of return is 10%. The risk-free rate is 2% and the expected excess return on the market portfolio is 6%. What will be the market price of the security if the correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity, and that the CAPM holds. To answer this question, let us go through the following steps. (a) Consider the security before the correlation coefficient doubles. Given the price, the expected return (discount rate) and the fact that g = 0, what are the expected dividend payments for this security? (b) What was the security’s beta before the change in the correlation coefficient? (c) What happens to beta when the correlation coefficient doubles? (d) What happens to the expected excess return of the security? What will be the new expected total return of the security? (e) Using the Gordon model, the fact that dividends are constant, and your result from part (d) about the expected return (i.e., the discount rate), what will be the new market price of the security? In which direction did the stock price change? Why?