ABC Investment Corporation is considering a portfolio with 30% weighting in a cyclical stock and 70% weighting in a countercyclical stock. It is expected that there will be three economic states; Good, Average and Bad, each with equal probabilities of occurrence. The cyclical stock is expected to have returns of 12%, 5% and 1% in Good, Average and Bad economies respectively. The countercyclical stock is expected to have returns of -8%, 2% and 14% in Good, Average and Bad economies respectively. Given this information, calculate the portfolio standard deviation.

A) 4.97%
B) 5.97%
C) 6.97%
D) 7.97%
E) 8.97%

Question

Chris Martin · Accepted Answer

Final Answer : A, Explanation :  The correct answer is A.The portfolio standard deviation is calculated as the square root of the variance of the portfolio. The variance of the portfolio is calculated as the weighted average of the variances of the individual stocks, where the weights are the proportions of the portfolio invested in each stock.The variance of the cyclical stock is calculated as the weighted average of the squared deviations of the returns from the expected return. The expected return of the cyclical stock is (12% + 5% + 1%) / 3 = 6%. The variance of the cyclical stock is therefore:(12% - 6%)^2 * 0.3 + (5% - 6%)^2 * 0.3 + (1% - 6%)^2 * 0.3 = 10.2%The variance of the countercyclical stock is calculated in the same way. The expected return of the countercyclical stock is (-8% + 2% + 14%) / 3 = 2%. The variance of the countercyclical stock is therefore:(-8% - 2%)^2 * 0.7 + (2% - 2%)^2 * 0.7 + (14% - 2%)^2 * 0.7 = 12.6%The variance of the portfolio is therefore:0.3 * 10.2% + 0.7 * 12.6% = 11.1%The portfolio standard deviation is therefore:sqrt(11.1%) = 4.97%

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