Question

You have a three-stock portfolio. Stock A has an expected return of 11 percent and a standard deviation of 41 percent, Stock B has an expected return of 15 percent and a standard deviation of 59 percent, and Stock C has an expected return of 13 percent and a standard deviation of 41 percent. The correlation between Stocks A and B is .30, between Stocks A and C is .20, and between Stocks B and C is .05. Your portfolio consists of 45 percent Stock A, 27 percent Stock B, and 28 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: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.) σp2 = xA2 σA2 + xB2 σB2 + xC2 σC2+ 2xAxBσAσBCorr(RA,RB) + 2xAxCσAσCCorr(RA,RC) + 2xBxCσBσCCorr(RB,RC) Expected return % Standard deviation

Answer 1

Expected return%=	Wt Stock A*Return Stock A+Wt Stock B*Return Stock B+Wt Stock C*Return Stock C
Expected return%=	0.45*11+0.27*15+0.28*13
Expected return%=	12.64
Variance	=w2A*σ2(RA) + w2B*σ2(RB) + w2C*σ2(RC)+ 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB) + 2*(wA)*(wC)*Cor(RA, RC)*σ(RA)*σ(RC) + 2*(wC)*(wB)*Cor(RC, RB)*σ(RC)*σ(RB)
Variance	=0.45^2*0.41^2+0.27^2*0.59^2+0.28^2*0.41^2+2*(0.45*0.27*0.41*0.59*0.3+0.27*0.28*0.59*0.41*0.05+0.45*0.28*0.2*0.41*0.41)
Variance	0.100531 = 10.05%
Standard deviation=	(variance)^0.5
Standard deviation=	31.71%