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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 8 1. Suppose the market portfolio is expected to earn a return a 12.5% with a standard deviation of 16%. The risk free asset yields a return of 4.5%. Investor X decides that she would want her portfolio to generate an expected return of at least 15%. What is the standard deviation of returns on her portfolio? What fraction of her wealth is invested in the risk free asset? 18 points Given: E M = 12.5% σ M = 16%, and R f = 4.5%. Also given: E p = 15%. Plugging these values into the CML, M f M p f p R E R E σ σ = (15% – 4.5%)/ σ p = (12.5% – 4.5%)/16%, or, 10.5%/ σ p = 0.5 σ p = 10.5%/0.5 = 21%. Let us denote the risk free asset as Security 1 , and the market portfolio as Security 2 . The portfolio variance is given by: σ σ σ ρ σ σ p x x x x 2 1 2 1 2 2 2 2 2 1 2 12 1 2 2 = + + . However, because Security 1 is risk free, σ 1 = 0 and ρ 12 = 0, and therefore σ p = x 2 * σ 2 x 2 = σ p / σ 2 = 21%/16% = 1.3125 the fraction invested in the risk free asset, x 1 = – 0.3125. 2. Suppose the parameters describing the market and the risk free asset are the same as in Problem 1 above. Investor Y does not want her portfolio returns to have a standard deviation higher than 5%. What is the highest return she can expect to earn? If she has $900,000 to invest, what would be the dollar amount she would invest in the market portfolio? she would invest in the market portfolio?...
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 Spring '08
 MCCULLOUGH
 Variance, Market Portfolio, HAAS SCHOOL OF BUSINESS, Avinash Verma

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