Problem 10-4 Suppose that there are two independent economic factors, F1 and F2.

Question

Problem 10-4 Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 10%, and all stocks have independent firm- specific components with a standard deviation of 50%. Portfolios A and B are both well-diversified with the following properties: Expected Beta on F2Return 28% 23% Portfolio Beta on Fi 1.2 3.1 2.0 -0.20 What is the expected return-beta relationship in this economy? Calculate the risk-free rate, rs and the factor risk premiums, RP1 and RP2, to complete the equation below. (Do not round intermediate calculations. Round your answers to two decimal places.) rf RP1 RP2

Explanation / Answer

This is more of a mathematics question than Finance.

You just have to simultaneously solve two equations and find the co-efficients.

Given two economic factors F1 and F2, the equation will be structured as,

Expected Return = Riskfree rate + Betaf1 * RP1 + Betaf2 * RP2

Substituting values from portfolio A,

28% = 10% + 1.2 * RP1 + 2* RP2 ------Eqn 1

Substituting values from portfolio B,

23% = 10% + 3.1 * RP1 -0.2 * RP2 ------Eqn 2

Multiplying eqn 2 by 10 and adding Eqn 1 + Eqn 2, we get

258% = 110% + 32.2 RP1

RP1 = 4.596%

RP2 = 6.242%

Equation will be given by E(rp) = 10% + 4.596% Betaf1 + 6.242% Betaf2

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