Stock A has a beta of 0.8,Stock B has a beta of 1.0,and Stock C has a beta of 1.2.Portfolio P has equal amounts invested in each of the three stocks.Each of the stocks has a standard deviation of 25%.The returns on the three stocks are independent of one another (i.e.,the correlation coefficients all equal zero).Assume that there is an increase in the market risk premium,but the risk-free rate remains unchanged.Which of the following statements is correct?
A)The required return of all stocks will remain unchanged since there was no change in their betas.
B)The required return on Stock A will increase by less than the increase in the market risk premium, while the required return on Stock C will increase by more than the increase in the market risk premium.
C)The required return on the average stock will remain unchanged, but the returns of riskier stocks (such as Stock C) will increase while the returns of safer stocks (such as Stock A) will decrease.
D)The required return on the average stock will remain unchanged, but the returns of riskier stocks (such as Stock C) will decrease while the returns on safer stocks (such as Stock A) will increase.

Question

Quizplus · Accepted Answer

According to the capital asset pricing model (CAPM), the required return on a stock is equal to the risk-free rate plus the market risk premium multiplied by the stock's beta. Since the betas of the three stocks are different, an increase in the market risk premium will result in different changes in the required returns of each stock.

Stock A has a beta of 0.8, which means it is less sensitive to market fluctuations compared to the average stock. Therefore, its required return will increase by less than the increase in the market risk premium.

Stock C, on the other hand, has a beta of 1.2, which means it is more sensitive to market fluctuations compared to the average stock. Therefore, its required return will increase by more than the increase in the market risk premium.

Portfolio P has equal amounts invested in each of the three stocks, so its required return will be the weighted average of the required returns of the individual stocks. Since Stock A and Stock C have opposite effects on the required return, the required return of Portfolio P will increase by an amount between the required returns of Stock A and Stock C.

Stock a Has a Beta of 0