Question

Stock A has a beta of 0.7, whereas Stock B has a beta of 1.3. Portfolio P has 50% invested in both A and B. Which of the following would occur if the market risk premium increased by 1% but the risk-free rate remained constant?a. The required return on Portfolio P would increase by 1%.b. The required return on both stocks would increase by 1%.c. The required return on Portfolio P would remain unchanged.d. The required return on Stock A would increase by more than 1%, while the return on Stock B would increase by less than 1%.

Answer 1

Answer:

a. The required return on Portfolio P would increase by 1%

Explanation:

Assume that in the given question, the Market risk premium is 7% while the risk free return is 5%, then according to the Capital asset pricing model(CAPM), the expected return of stock A and B will be calculated as follows:

CAPM=Risk free return+Beta(Market risk premium)

Expected Return on stock A=5%+0.70*7%=9.9%

Expected Return on stock B=5%+1.30*7%=14.1%

Since the equal amount of 50% of portfolio P has been invested in the stock A and B, therefore, the return on the portfolio P shall be calculated as follows

Expected return on portfolio P=0.50*9.9%+0.50*14.1%=12%

If the market risk premium is increased by 1% i.e. from 7% to 8%, then the expected return of the Stock A and B shall be calculated as follows:

Expected Return on stock A=5%+0.70*8%=10.6%

Expected Return on stock B=5%+1.30*8%=15.4%

Expected return on portfolio P=0.50*10.6%+0.50*15.4%=13%

So the expected return on portfolio P has been increased by 1% i.e. from 12% to 13% when the market risk premium has been increased by 1%.

Based on the above calculations, the answer shall be a. The required return on Portfolio P would increase by 1%