You have a three-stock portfolio. Stock A has an expected return of 14 percent a

Question

You have a three-stock portfolio. Stock A has an expected return of 14 percent and a standard deviation of 35 percent, Stock B has an expected return of 18 percent and a standard deviation of 53 percent, and Stock C has an expected return of 17 percent and a standard deviation of 35 percent. The correlation between Stocks A and B is .07, between Stocks A and C is .20, and between Stocks B and C is .19. Your portfolio consists of 45 percent Stock A, 25 percent Stock B, and 30 percent Stock C. Calculate the expected return and standard deviation of your portfolio. The formula for calculating the variance of a three-stock portfolio is: (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

sp2 = xA2 sA2 + xB2 sB2 + xC2 sC2+ 2xAxBsAsBCorr(RA,RB) + 2xAxCsAsCCorr(RA,RC) + 2xBxCsBsCCorr(RB,RC)

I found the expected return, but I keep getting 40.45% for my Standard deviation and that is not correct. I need help finding the standard deviation.


Standard deviation: %

Explanation / Answer

Expected return = 0.45 RA + 0.25 RB + 0.3 RC
Expected return = 0.45*14+0.25*18+0.3*17 = 15.9%

sp2 = xA2 sA2 + xB2 sB2 + xC2 sC2+ 2xAxBsAsBCorr(RA,RB) + 2xAxCsAsCCorr(RA,RC) + 2xBxCsBsCCorr(RB,RC)

sp2=0.4520.352+0.2520.532+0.320.352+2*0.45*0.25*0.35*0.53*0.07+2*0.45*0.3*0.35*0.35*0.2

+2*0.25*0.3*0.35*0.53*0.19

sp2 =0.006821

sp=0.2612 = 26.12%

Expected standard deviation = 26.12%

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