Question

Assume that in recent years both expected inflation and the market risk premium (r M − r RF) have declined. Assume also that all stocks have positive betas. Which of the following would be most likely to have occurred as a result of these changes?a. Required returns have increased for stocks with betas greater than 1.0 but have declined for stocks with betas less than 1.0.b. The required returns on all stocks have fallen, but the decline has been greater for stocks with lower betas.c. The required returns on all stocks have fallen by the same amount.d. The average required return on the market, rM, has remained constant, but the required returns have fallen for stocks that have betas greater than 1.0.e. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.

Answer 1

Answer: e. The required returns on all stocks have fallen, but the fall has been greater for stocks with higher betas.

Explanation:

The beta of a stock reflects the stock's sensitivity to a movement in market returns. Used in the Capital Asset Pricing Model, it can be used to calculate Required Return by the formula;

Required return = Risk free rate + Beta * Market risk Premium.

This formula shows that if market risk premium were to decrease, the decrease in required returns will be more for stocks with higher betas.

For instance, Assume two stocks. Stock A has a beta of 4 and Stock B has a beta of 2.

Assuming that the risk free rate is 4% and the Market premium went from 10% to 6%, the stock required return will be;

Stock A

Initial required return = 4% + 4 * 10% = 44%

Return after fall in Market premium = 4% + 4 * 6% = 28%

Return fell by = 44 - 28 = 16%

Stock B

Initial required return = 4% + 2 * 10% = 24%

Return after fall in Market premium = 4% + 2 * 6% = 16%

Return fell by = 24 - 16 = 8%

Stock A required return fell more than Stock B's because it had a higher beta.