Beta and required rate of return A stock has a required return of 11%; the risk-

Question

Beta and required rate of return A stock has a required return of 11%; the risk-free rate is 2.5%; and the market risk premium is 6%. What is the stock's beta? Round your answer to two decimal places. If the market risk premium increased to 8%, what would happen to the stock's required rate of return? Assume the risk-free rate and the beta remain unchanged. If the stock's beta is equal to 1.0. then the change in required rate of return will be less than the change in the market risk premium. If the stock's beta is greater than 1.0. then the change in required rate of return will be greater than the change in the market risk premium. If the stock's beta is less than 1.0. then the change in required rate of return will be greater than the change in the market risk premium. If the stock's beta is greater than 1.0. then the change in required rate of return will be less than the change in the market risk premium. If the stock's beta is equal to 1.0. then the change in required rate of return will be greater than the change in the market risk premium. New stock's required rate of return will be %. Round your answer to two decimal places. Stocks X and Y have the following probability distributions of expected future returns: Calculate the expected rate of return, rY, for Stock Y (rX = 14.30%.) Round your answer to two decimal places. % Calculate the standard deviation of expected returns, sigma_X, for Stock X (sigma_Y = 19.78%.) Round your answer to two decimal places. % Now calculate the coefficient of variation for Stock Y. Round your answer to two decimal places. Is it possible that most investors might regard Stock Y as being less risky than Stock X?

Explanation / Answer

8.5 a: As per capital asset pricing model (CAPM), expected return on a stock = risk free rate + (beta*market risk premium).

Using this formula, 11% = 2.5%+(beta*6%)

or 11-2.5% = (beta*6%)

or 8.5% = (beta*6%) or beta = 8.5%/6% = 1.42%

b. The option II is applicable i.e if a stock's beta is greater than 1, then the change in required rate of return will be greater than the change in market risk premium. This is because the market risk premium gets multiplied by beta which is a number which is greater than 1, thus increasing the change in required rate of return.

Now, required rate of return = 2.5%+(1.42%*8%) [Using the CAPM formula as shown in "a" above].

= 2.5%+11.33% = 13.83%

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