The market price of a security is $40. Its expected rate of return is 10%. The risk-free rate is 3% and the expected excess return on the market portfolio is 8%. What will be the market price of the security if the correlation coefficient with the market portfolio becomes half of what it is now (and all other variables remain unchanged)? Assume that the stock's dividend is expected to be growing at a constant growth rate, and that CAPM holds. To answer this question, let us go through the following steps.
a) Consider the security before the correlation coefficient becomes half. Given the price, the expected return (discount rate) and the fact that g = 2%, 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 becomes half?
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?