Question

Stock A has a market beta of 0.8 and a required rate of return of 6%. The return on the overall stock market is 7%. [Show the work leading to your answers] a. Determine the risk-free rate, rRF. b. Assume that the overall market return increases to 10% and that Stock A’s beta and the riskfree rate remain unchanged. What is Stock A’s new required return after the change in the market return? c. The overall market return remains at 10%. An investor forms a two-stock investment portfolio with $6 million invested in Stock A and $4 million invested in Stock B. Stock B’ beta is twice as high as the beta of the overall market. What is the beta of the investor’s two-stock portfolio? d. What is the required rate of return on the investor’s two-stock portfolio?

Answer 1

A) As per CAPM,

Required Rate of Return = Risk free Rate + Beta x (Return on Market - Risk free Rate)

6% = Rf + 0.8 (7% - Rf)

6% = Rf + 5.6% - 0.8Rf

6% - 5.6% = 0.20 Rf

Risk free Rate Rf = 2%

B) Given, Market Return = 10%, Stock Beta = 0.8 and Risk free Rate = 2%

New Required Return = Risk free Rate + Beta x (Return on Market - Risk free Rate)

New Required Return = 2% + 0.8 x (10% - 2%)

New Required Return = 8.40%

C) Given, Market Return = 10%, investment in stock A = $6million and investment in stock B =$4million

Weight of Stock A in portfolio =6/(6+4) = 60%

Weight of Stock B in portfolio = 4/(6+4) = 40%

Beta of Stock B = 2 x Beta of overall market

We know that Beta of Market is 1, Therefore, Beta of Stock B = 2 x 1 = 2

Beta of Portfolio, is weighted average beta of individual stock's beta, Therefore,

Beta of Portfolio = Beta of Stock A x Weight of Stock A + Beta of Stock B x Weight of Stock B

Beta of Portfolio = 0.8 x 60% + 2 x 40%

Beta of Portfolio = 1.28

D) Required Rate of Return on two stock portfolio = Risk free Rate + Beta of portfolio x (Market Rate - Risk free Rate)

Required Rate of Return = 2% + 1.28 (10% - 2%)

Required Rate of Return =12.24%

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