You have a three-stock portfolio. Stock A has an expected return of 16 percent a

Question

You have a three-stock portfolio. Stock A has an expected return of 16 percent and a standard deviation of 37 percent, Stock B has an expected return of 20 percent and a standard deviation of 55 percent, and Stock C has an expected return of 14 percent and a standard deviation of 37 percent. The correlation between Stocks A and B is .09, between Stocks A and C is .20, and between Stocks B and C is .21. Your portfolio consists of 35 percent Stock A, 15 percent Stock B, and 50 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:

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

The expected return:
The standard deviation:

Explanation / Answer

Expected return = 0.35 RA + 0.15 RB + 0.5 RC
Expected return = 0.35*16+0.15*20+0.5*14 = 15.6%

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

sp2=0.3520.372+0.1520.552+0.520.372+2*0.35*0.15*0.37*0.55*0.09+2*0.35*0.5*0.37*0.37*0.2+2*0.15*0.5*

0.37*0.55*0.21

sp2 =0.07572

Sp=0.2752 = 27.52%

Expected standard deviation = 27.52%

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