Question

Consider the following probability distribution for stocks A and B: State probability return on stock A return on stock B 1 0.10 10% 8% 2 0.20 13% 7% 3 0.20 12% 6% 4 0.30 14% 9% 5 0.20 15% 8% 1)

1. Let G be the global minimum variance portfolio. The weights of A and B in G are __________ and __________, respectively.

Answer 1

The expected rates of return of stocks A and B are 13.2% and 7.7%,respectively.

E(RA) = 0.1 (10%) + 0.2 (13%) + 0.2 (12%) + 0.3 (14%) + 0.2 (15%)= 13.2%

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E(RB) = 0.1 (8%) + 0.2 (7%) + 0.2 (6%) + 0.3 (9%) + 0.2 (8%)= 7.7%

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The standard deviation of stocks A and B are 1.5% and 1.1%,respectively.

Var(RA) = [0.1 (10%-13.2%)2 + 0.2 (13%-13.2%)2 + 0.2 (12%-13.2%)2 + 0.3 (14%-13.2%)2 + 0.2 (15%-13.2%)2 ] 1/2 = 1.5%

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Var(RB) = [0.1 (8%-7.7%)2 + 0.2 (7%-7.7%)2 + 0.2 (6%-7.7%)2 + 0.3(9%-7.7%)2 + 0.2 (8%-7.7%)2 ] 1/2 = 1.1%

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Cov(RA,RB) =0.1 (8%-7.7%)(10%-13.2%) + 0.2 (7%-7.7%)(13%-13.2%)+ 0.2 (6%-7.7%)(12%-13.2%) + 0.3 (9%-7.7%)(14%-13.2%)+ 0.2 (8%-7.7%)(15%-13.2%)

=0.76

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Coefficient of correlation between A and B= 0.76/(1.1*1.5)=0.46.

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If G be the global minimum variance portfolio. The weights of A and B in G are 0.23 and 0.77, respectively.

WA = [(1.1)^2 -(1.5)(1.1)(0.46)]/[ (1.5)^2 +(1.1)^2-(2)(1.5)(1.1)(0.46)]=0.23

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WB = 1-0.23=0.77

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