Suppose your expectations regarding the rate of return of stocks A and B are as

Question

Suppose your expectations regarding the rate of return of stocks A and B are as follows State of the economy Probability Return A Return B Boom 30% 20% 10% Recession 70% -5% -2% If you decide to invest 40% in stock A and the remaining part in stock B, what would be your portfolio expected return and standard deviation? The expected return is -2.10% and standard deviation is -9.06% The expected return is 1.9% and standard deviation is 0.62% The expected return is 1.9% and standard deviation is 7.88% The expected return is 3.9% and standard deviation is -9.06% None of the above

Explanation / Answer

A Return in % Prob Expected return Boom 20 30 6 Recession -5 70 -3.5 2.5 B Return Prob Expected return Boom 10 30 3 Recession -2 70 -1.4 1.6 Expected Return of portfolio= 2.5*40%+1.6*60% 1.96% Calculation of Standard deviation A Given return Exp. Returr D d^2 Prob. Value Boom 20 2.5 17.5 306.25 0.3 91.875 Recession -5 2.5 -7.5 56.25 0.7 39.375 362.5 131.25 std deviation= underroot 131.25 11.46 Calculation of Standard deviation B Given return Exp. Returr D d^2 Prob. Value Boom 10 1.6 8.4 70.56 0.3 21.168 Recession -2 1.6 -3.6 12.96 0.7 9.072 83.52 30.24 std deviation= underroot 30.24 5.49 Since corelation is not given it is assumed that it is + 1 Std deviation of Portfoloi= 11.46*40%+5.49*60% 7.88% Therefore answer C is correct

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