Standard Deviation = [(wP * P)2 + (A * A)2 + {2 * wP * wA * P * A * Corr(A,P)}]1/2
Standard Deviation of portfolio with Stock A = [(0.8 * 0.26)2 + (0.2 * 0.22)2 + (2 * 0.8 * 0.2 * 0.26 * 0.22 * 0.2)]1/2
= [0.043264 + 0.001936 + 0.0036608]1/2 = [0.0488608]1/2 = 0.2210, or 22.10%
Standard Deviation of portfolio with Stock B = [(0.8 * 0.26)2 + (0.2 * 0.20)2 + (2 * 0.8 * 0.2 * 0.26 * 0.20 * 0.5)]1/2
= [0.043264 + 0.0016 + 0.00832]1/2 = [0.053184]1/2 = 0.2306, or 23.06%
Stock A should be selected as Portfolio's standard deviation is less when A is added to the portfolio.
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