{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

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 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}