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S10 - HAAS SCHOOL OF BUSINESS UNIVERSITY OF CALIFORNIA AT...

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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY UGBA 103 A VINASH V ERMA S OLUTION TO H OMEWORK 10 1. Assume that the CAPM holds. E p R f σ p M (Market Portfolio) Security i Portfolio a Portfolio q Security j Securityk [4 points each for a total of 44 points for (a) through (k) in 1.1 and 1.2] 1.1. Indicate whether the following statements are true or false based on what you can infer from the graph above without scaling it . (a). Portfolio q has no diversifiable risk. True. Portfolio q is on the CML. Therefore, it is a portfolio of the risk free asset and the market portfolio. The risk free asset has no risk, and the market portfolio has no diversifiable risk. Therefore, portfolio q has no diversifiable risk. (b). 1 = aM β . False. If β aM were equal to one, then by CAPM, E a would have to EQUAL E M . However we can see from the graph that E a > E M . (c). Portfolio q is a portfolio in which we have invested positive amounts both in the risk free asset and in the market portfolio. True. Portfolio q is on the CML. Therefore, ( E q R f ) / σ q = ( E M R f ) / σ M . Since Portfolio q is a portfolio of the risk free asset and the market portfolio, σ q = x M * σ M . We can see from the graph that σ q < σ M x M * σ M < σ M 0< x M < 1, and since the two portfolio weights sum up to one, 0< x Rf < 1. (d). Security i has no systematic risk. True. We can see from the graph that E i , the expected return on Security i , equals the risk free rate. Given CAPM and E i = R f , β iM , = 0. By definition, systematic risk is given by β iM 2 * σ M 2 , which is zero given that β iM , = 0. (e). M a aM σ σ σ * = . True. Since Portfolio a is on the CML, ( E a R f ) / σ a = ( E M R f ) / σ M ( E a R f ) = ( σ a / σ M )*( E M R f ). Also by CAPM, ( E a R f ) = β aM *( E M R f ). Therefore, ( σ a / σ M ) = β aM . By using the definition of beta, β aM = σ aM / σ M 2 . Therefore, ( σ a / σ M ) = β aM = σ aM / σ M 2 . Cross-multiplying, we get σ aM = σ a * σ M . (f). 2 M kM σ σ False. We can see from the graph that E k , the expected return on Security k , equals E M , the expected return on the market portfolio. Given CAPM, and the fact that E k = E M , β kM , = 1. By using the definition of beta, β kM = σ kM / σ M 2 = 1 σ kM = σ M 2 . (g). 0< ρ qM <1 False. Since Portfolio q is on the CML, ( E q R f ) / σ q = ( E M R f ) / σ M ( E q R f ) = ( σ q / σ M )*( E M R f ). Also by CAPM, ( E q R f ) = β qM *( E M R f ). Therefore, ( σ q / σ M ) = β qM . By using the definition of beta, β qM = σ qM / σ M 2 .
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