Question
In: Finance
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(rP) = 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 2 years agoRelated Solutions
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