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# hw-2-sol - INVESTMENT ANALYSIS 70-492 Fall 2009 Suggested...

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INVESTMENT ANALYSIS 70-492 Fall 2009 Suggested Solution to Problem Set 2 Let ω be the proportion of wealth invested in Apple and (1 - ω ) the proportion invested in Banana. The expected return and the standard deviation of the return on a portfolio of the two risky assets is E ( r P ) = ωE ( r A ) + (1 - ω ) E ( r B ) (1) σ P = q ω 2 σ 2 A + (1 - ω ) 2 σ 2 B + 2 ω (1 - ω ) ρ AB σ A σ B (2) a) ρ AB = - 0 . 5. Solve (2) for ω and substitute the value of ω into (1) to obtain E ( r P ). This gives ω = 0 . 252 , E ( r P ) = 0 . 072. b) ρ AB = 0. ω = 0 . 291 , E ( r P ) = 0 . 0697. c) ρ AB = 0 . 5. ω = 1 , E ( r P ) = 0 . 02. d) Target standard deviation = 0.05. The expected return that he can obtain for each choice of the correlation coefficient is ρ AB = - 0 . 5 E ( r P ) = 0 . 0723 ρ AB = 0 E ( r P ) = 0 . 0697 ρ AB = 0 . 5 E ( r P ) = 0 . 0663 Hence he chooses ρ AB = - 0 . 5 because that choice gives him the highest expected return (the benefits of diversification are greater when two assets are negatively correlated). e) If two assets are perfectly negatively correlated, it is possible to form a portfolio that is riskless, i.e., σ P = 0.

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