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What is the standard deviation of the returns on a portfolio that is invested in Stocks A, B, and C? Twenty percent of the po

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Answer #1

Answer is 5.65%

Weight of Stock A = 0.20
Weight of Stock B = 0.45
Weight of Stock C = 0.35

Boom:

Expected Return = 0.20 * 0.17 + 0.45 * 0.09 + 0.35 * 0.09
Expected Return = 0.1060

Normal:

Expected Return = 0.20 * 0.08 + 0.45 * 0.06 + 0.35 * 0.08
Expected Return = 0.0710

Recession:

Expected Return = 0.20 * (-0.240 + 0.45 * 0.02 + 0.35 * (-0.13)
Expected Return = -0.0845

Expected Return of Portfolio = 0.04 * 0.1060 + 0.81 * 0.0710 + 0.15 * (-0.0845)
Expected Return of Portfolio = 0.049075

Variance of Portfolio = 0.04 * (0.1060 - 0.049075)^2 + 0.81 * (0.0710 - 0.049075)^2 + 0.15 * (-0.0845 - 0.049075)^2
Variance of Portfolio = 0.00319533

Standard Deviation of Portfolio = (0.00319533)^(1/2)
Standard Deviation of Portfolio = 0.0565 or 5.65%

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