Stock pricing The market price of a security is $20. Its expected rate of return is ten percent. The risk free rate is two percent and the expected excess return on the market portfolio is six percent. What will be the market price of the security if the correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Suppose 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.
1) 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?
2) What happens to beta when the correlation coefficient doubles?
3) What was the security's beta before the change in the correlation coefficient?
4) What happens to the expected surplus return of the security? What will be the new expected total return of the security?
5) Using the Gordon model, the fact that dividends are constant, and your result from part
6) 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?