Question

2. Using the CAPM, answer the following problems: a. A stock has a beta of 1.2, the expected return on the market is 17 percent, and the risk-free rate is 8 percent. What must the expected return on this stock be? b. A stock has an expected return of 14 percent, the risk-free rate is 4 percent, and the market risk premium is 6 percent. What must the beta of this stock be? c. A stock has an expected return of 15 percent, its beta is 0.9, and the risk-free rate is 6 percent. What must the expected return on the market be? d. A stock has an expected return of 22 percent and a beta of 1.6, and the expected return on the market is 16 percent. What must the risk-free rate be?
step by step solutions please. no excel solutions

Answer 1

Part a:
Expected return=Risk free rate + Beta*(Market return-Risk free rate)
Substituting the values, we get;
Expected return=8% + 1.2*(17%-8%)
=8% + 10.80%
=18.80%

Part b:
Expected return=Risk free rate + Beta*(Market risk premium)
Market risk premium=Market return-Risk free rate
Substituting the values, we get;
14%=4% + Beta*(6%)
=>14%-4%=Beta*(6%)
=>10.0%=Beta*(6%)
=>Beta=10.0%/6%=1.6667

Part c:
Expected return=Risk free rate + Beta*(Market return-Risk free rate)
Substituting the values, we get;
15%=6% + 0.9*(Market return-6%)
=>15%-6%=0.9*(Market return-6%)
=>9.00%=0.9*(Market return-6%)
=>9%/0.9=(Market return-6%)
=>10.00%+6%=Market return
=>Market return=16%

Part d:
Expected return=Risk free rate + Beta*(Market return-Risk free rate)
Substituting the values, we get;
22%=Risk free rate + 1.6*(16%-Risk free rate)
=>22%=Risk free rate + 1.6*16%-1.6*Risk free rate
=>22%=Risk free rate +25.60%-1.6*Risk free rate
=>22%-25.60%=Risk free rate -1.6*Risk free rate
=>-3.60%=Risk free rate*(1-1.6)
=>-3.60%=Risk free rate*(-0.6)
Risk free rate=(-3.60%)/(-0.6)=6.00%

Answer 2

We have $25,000 invested in ABC stock with a beta of 1.6; $50,000 on DEF stock with a beta of 0.7; and $15,000 in GHI stock with a beta of 1.2. What is the portfolio's beta? b) Long term government bonds are returning 4%. The equity risk premium is 5%. If XYZ stock has beta of 0.6, what is the expected return?