Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 5%, and...

Suppose there are two independent economic factors, M₁ and M₂. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 56%. Portfolios A and B are both well diversified.

Portfolio	Beta on M₁	Beta on M₂	Expected Return (%)
A	1.7	2.2	35
B	2.1	-0.8	8

What is the expected return–beta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected return–beta relationship E(r_P) = 5% + ____ ?_P1 + ____ ?_P2

Solutions

Expert Solution

Expected return on the portfolio = Risk free rate + Beta of portfolio 1 * (expected return on portfolio 1 - Risk free rate) + Beta of portfolio 2 * (expected return on portfolio 2 - Risk free rate)

35% = 5% + 1.7 * Risk premium for portfolio 1 + 2.2 * Risk premium for portfolio 2.................(1)

8% = 5% + 2.1 * Risk premium for portfolio 1 - 0.8 * Risk premium for portfolio 2.................(2)

Multiply eq. by 2.75 and add in eqn. 1

35% + 22% = 5% + 2.75 * 5% + 1.7 * Risk premium for portfolio 1 + 5.775 * Risk premium for portfolio 1 + 0

57% = 18.75% + 7.475 * Risk premium for portfolio 1

Risk premium for portfolio 1 = 5.12%

Put value of risk premium for portfolio 1 in equation 1

35% = 5% + 1.7 * 5.12% + 2.2 * Risk premium for portfolio 2

35% = 13.70% + 2.2 * Risk premium for portfolio 2

Risk premium for portfolio 2 = 21.30%/ 2.2

Risk premium for portfolio 2 = 9.68%

Expected return–beta relationship E(rP) = 5% + 5.12% * Beta of Portfolio 1 + 9.68% * Beta of Portfolio 2

jeff jeffy answered 1 year ago

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