_Sample_Midterm_Solutions

_Sample_Midterm_Solutions - Q1a We are given the standard...

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Q1a) We are given the standard deviation and expected return of B; now we need these values for A: E(rA) = 0.1(40-50)/50 + 0.8(55-50)/50 + 0.1(60-50)/50 = 0.08 SD(A) = 0.1(-0.2-0.08)^2 + 0.8(0.10-0.08)^2 + 0.1(0.20-0.08)^2 = 0.0979 E(rB) = 0.09 SD(B) = 0.12 b) E(rP) = 0.7*0.08 + 0.3*0.09 = 0.083 Var(P) = (0.7*0.0979)^2 + (0.3*0.12)^2 + 2*0.7*0.3*0.6*0.0979*0.12 = 0.0089 SD(P) = sqrt(0.0089) = 0.0946 c) We know that the beta of a portfolio is the weighted average of the assets in the portfolio. Let’s compute the betas for A and B: Beta(A) = corr(A,M)*sd(A)/sd(M) = 0.80*0.0979/0.10 = 0.78 Beta(B) = corr(B,M)*sd(B)/sd(M) = 0.20*0.12/0.10 = 0.24 Beta(P) = 0.7*0.78 + 0.3*0.24 = 0.62 A risk averse investor will prefer B, which has a return of 9% and a Beta of .24 over A. Q2a) Suppose that an investor had a portfolio consisting only of Sitwell. Then, the portfolio’s beta would be 1.25. Now suppose that the investor were to add Sleepwell to the portfolio. We know that the beta of the portfolio is the weighted average of the betas of Sleepwell and Sitwell.

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This note was uploaded on 12/05/2011 for the course ECON 134b taught by Professor Johnhartman during the Fall '11 term at UCSB.

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_Sample_Midterm_Solutions - Q1a We are given the standard...

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