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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 % If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard deviation

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Answer:

The expected rates of return of stocks A and B:

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

E(RA) = 13.2%

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

E(RB) = 7.7%

The standard deviation of stocks A and B are:

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

Var(RA) = 1.5%

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

Var(RB) = 1.1%

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