Question

A portfolio consists of four assets in equal weights. Asset 1 has a beta of 1.00. Asset 2 has a beta of 1.00. Asset 3 has a beta of 1.50. Asset 4 has a beta of 1.20. If the portfolio's required return is 8.00% and the risk-free rate is 3.80%, what is Asset 2's required return?

a) 6.82%

B) 7.01%

C) 7.19%

D) 7.37%

E)7.56%

Answer 1

Beta of a portfolio is weighted average of the beta of constituents of portfolio. In this case, since all the assets are equally weighted. Beta of portfolio would be simple average of beta of constituents

Beta of portfolio = (1 + 1 + 1.50 + 1.20)/4 = 1.175

Based on CAPM,

Required return on asset = Risk free rate + Beta * Market risk premium

8% = 3.80% + 1.175 * Market risk premium

4.20% = 1.175 * Market risk premium

Market risk premium = 3.57%

For Asset 2,

Required return = 3.80% + 1 * 3.57% = 7.37%