Solution to H9

Solution to H9 - H AAS S CHOOL OF B USINESS U NIVERSITY OF...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 9 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 ....
View Full Document

This note was uploaded on 02/12/2012 for the course UGBA 101A taught by Professor Mccullough during the Spring '08 term at Berkeley.

Page1 / 4

Solution to H9 - H AAS S CHOOL OF B USINESS U NIVERSITY OF...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online