Use the information in the table below to answer the next seven multiple choice

Question

Use the information in the table below to answer the next seven multiple choice questions. State of Nature Probability Return on A Return on B I 0.2 7% 11% II 0.2 9% 7% III 0.6 13% 14% The correlation between A and B is 0.35. The portfolio weight of A is 30%. The portfolio weight of B is 70%.

The expected return in percent for investment A is

The standard deviation of returns for investment A is

The expected return in percent for investment B is

The standard deviation of returns for investment B is

The expected return in percent for a portfolio of 30% investment A and 70% investment B is

The covariance between investment A and investment B is

The return standard deviation for a portfolio of 30% investment A and 70% investment B is

Explanation / Answer

INVESTMENT A: state of deviations nature probability (p) return ® r*p from mean (d) d^2 p*d^2 i 0.2 7 1.4 -4 16 3.2 II 0.2 9 1.8 -2 4 0.8 III 0.6 13 7.8 2 4 2.4 11.0 6.4 Expected return = r*p = 11% Std. deviation = p*d^2 = 6.4 = 2.53% INVESTMENT B: state of deviations nature probability (p) return ® r*p from mean (d) d^2 p*d^2 i 0.2 11 2.2 -1 1 0.2 II 0.2 7 1.4 -5 25 5 III 0.6 14 8.4 2 4 2.4 12.0 7.6 Expected return = r*p = 12% Std. deviation = p*d^2 = 7.6 = 2.76% Expected return of portfolio: is the weighted average of returns of individual securities = 11*0.3 +12*0.7 = 11.70% Covariance between A & B: state of dA dB nature probability (p) return A return B A - Mean of A B - Mean of B dA*dB*p i 0.2 7 11 -4 -1 0.8 II 0.2 9 7 -2 -5 2 III 0.6 13 14 2 2 2.4 5.2 Covariance of returns = 5.2% Std deviation of portfolio: Portfolio Variance = w^2A*^2(RA) + w^2B*^2(RB) + 2*(wA)*(wB)*Cov(RA, RB) Where: wA and wB are portfolio weights, ^2(RA) and ^2(RB) are variances and Cov (RA, RB) is the covariance =0.3^2*2.53^2 + 0.7^2*2.76^2 + 2*0.3*0.7*5.2 6.49 % Standard deviation of portfolio =6.49 2.55 %

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