Question

A) Using the CAPM, estimate the appropriate required rate of retun for the following three stocks, given that the risk-free rate is 5%, and the expected return for the market is 17%.

Stock A - Beta 0.75

Stock B- Beta 0.90

Stock C- Beta 1.40

B) If you are planning to buy an equally-weighted portfolio of these three stocks, what will e your required rate of return on the portfolio?

C) What is the beta of the portfolio?

D) Calculate the required rate of return on the portfolio again, using the portfolio beta.

Answer 1

According to the CAPM,

Required Return = Risk-free Rate + [Beta * (Expected Market Return - Risk-free Rate)]

a). Stock A's Required Return = 5% + [0.75 * (17% - 5%)] = 5% + 9% = 14%

Stock B's Required Return = 5% + [0.90 * (17% - 5%)] = 5% + 10.8% = 15.8%

Stock C's Required Return = 5% + [1.40 * (17% - 5%)] = 5% + 16.8% = 21.8%

b). Portfolio's Required Return = [Weight(i) * Return(i)]

i-1

= [(1/3) * 14%] + [(1/3) * 15.8%] + [(1/3) * 21.8%]

= 4.67% + 5.27% + 7.27% = 17.20%

c). Portfolio's Beta = [Weight(i) * Return(i)]

i-1

= [(1/3) * 0.75] + [(1/3) * 0.90] + [(1/3) * 1.40]

= 0.25 + 0.30 + 0.467 = 1.017

d). Portfolio's Required Return = 5% + [1.017 * (17% - 5%)] = 5% + 12.2% = 17.2%