Question

a.)A portfolio consists of four assets in equal weights. Asset 1 has a beta of 0.90. Asset 2 has a beta of 1.00. Asset 3 has a beta of 1.40. Asset 4 has a beta of 1.10. If the portfolio's required return is 7.50% and the risk-free rate is 3.60%, what is Asset 2's required return?

b.) Suppose the risk-free rate is 5.90% and the market portfolio has an expected return of 15.75%. A portfolio is invested equally in three securities with betas of 0.83, 1.58, and 1.63 respectively. What is the expected return on this portfolio?

Answer 1

Answer a.

Weight of Asset 1 = 0.25
Weight of Asset 2 = 0.25
Weight of Asset 3 = 0.25
Weight of Asset 4 = 0.25

Portfolio Beta = Weight of Asset 1 * Beta of Asset 1 + Weight of Asset 2 * Beta of Asset 2 + Weight of Asset 3 * Beta of Asset 3 + Weight of Asset 4 * Beta of Asset 4
Portfolio Beta = 0.25 * 0.90 + 0.25 * 1.00 + 0.25 * 1.40 + 0.25 * 1.10
Portfolio Beta = 1.10

Portfolio Required Return = Risk-free Rate + Portfolio Beta * Market Risk Premium
7.50% = 3.60% + 1.10 * Market Risk Premium
1.10 * Market Risk Premium = 3.90%
Market Risk Premium = 3.55%

Required Return of Asset 2 = Risk-free Rate + Beta of Asset 2 * Market Risk Premium
Required Return of Asset 2 = 3.60% + 1.00 * 3.55%
Required Return of Asset 2 = 7.15%

Answer b.

Weight of Security 1 = 1/3
Weight of Security 2 = 1/3
Weight of Security 3 = 1/3

Portfolio Beta = Weight of Security 1 * Beta of Security 1 + Weight of Security 2 * Beta of Security 2 + Weight of Security 3 * Beta of Security 3
Portfolio Beta = (1/3) * 0.83 + (1/3) * 1.58 + (1/3) * 1.63
Portfolio Beta = 1.3467

Portfolio Required Return = Risk-free Rate + Portfolio Beta * (Market Return - Risk-free Rate)
Portfolio Required Return = 5.90% + 1.3467 * (15.75% - 5.90%)
Portfolio Required Return = 5.90% + 1.3467 * 9.85%
Portfolio Required Return = 19.16%