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FBE441_Homework_3_solutions

# FBE441_Homework_3_solutions - USC MARSHALL SCHOOL OF...

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USC - MARSHALL SCHOOL OF BUSINESS FBE 441 Investments – P. Matos – Spring 2010 Homework Assignment #3 – Solutions 1. Suppose CAPM is true. You are considering investing in an equally weighted portfolio of two stocks, A and B. The betas of these stocks to the market factor are 1.10 and 0.80, respectively. The total return volatilities of stocks A and B are A =0.20 and B =0.18, and the standard deviation of the factor’s return is 0.15. 1.a. What is the beta of your portfolio? SOLUTION: Beta = 0.95. The beta of the portfolio is the average beta of the two stocks. 95 . 0 80 . 0 5 . 0 1 . 1 5 . 0 β β , i B A i i p w 1.b. What is the portfolio’s systematic risk (stated as a variance)? SOLUTION: Systematic risk =0.020306 . The portfolio’s systematic risk is: 020306 . 0 (0.1425) 15 . 0 95 . 0 σ β σ 2 2 2 2 2 2 , m p systematic p 1.c. What is your portfolio’s total risk (stated as a variance), assuming the idiosyncratic risks of the stocks A and B are uncorrelated? SOLUTION: Total risk of the portfolio can be decomposed into systematic and non-systematic risk: 2 systematic non 2 systematic 2 p σ σ σ . From part 3.b. the systematic variance is 0.020306. The idiosyncratic risks of each stock are: 012775 . 0 ) 15 . 0 * 1 . 1 ( 20 . 0 σ σ σ 2 2 2 systematic 2 A 2 systematic non 018 . 0 ) 15 . 0 * 8 . 0 ( 10 . 0 σ σ σ 2 2 2 systematic 2 B 2 systematic non So the non-systematic variance of the portfolio is given by: 007694 . 0 018 . 0 ) 5 (. 012775 . 0 ) 5 (. σ w σ 2 2 2 i 2 i 2 systematic non Hence the sum of systematic variance and non-systematic variance is 2 2 systematic non 2 systematic 2 p ) 1674 . 0 ( 028 . 0 007694 . 0 020306 . 0 σ σ σ

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2. Assume the CAPM holds and refer to the following graph. 2.a. What can we say about the betas of stocks A, B and C? i) All have betas greater than 1 because stocks have more risk than the market (M). ii) Beta of A is below 1, Beta of B is 1 and Beta of C is above 1. iii) Beta of A is below 0, Beta of B is between 0 and 1 and Beta of C is above 1. iv) Cannot tell from the information that is given in the graph. SOLUTION: iii) Beta of A is below zero, Beta of B is between zero and one and C are is above one. In equilibrium, stock prices are such that expected returns E(R) are only determined by the systematic risk of assets (measured by the market Beta). So assets line up vertically according
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FBE441_Homework_3_solutions - USC MARSHALL SCHOOL OF...

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