Question

Q9. The expected returns and standard deviations for stocks A and B are rA=14% and rB=19%, respectively, and A=23% and B=34%, respectively. The correlation of the returns on the two stocks is AB=0.3. (a) What is the expected return, rP, and standard deviation, P, of a portfolio with weights of wA=0.60 and wB=0.40 in stocks A and B, respectively? (b) Suppose now ?? = 3%, and ?? = 7%, the portfolio had zero risk, that is suppose ?? = 0 and the correlation coefficient was −1, i.e., ??? = −1. What is the portfolio weights that correspond to that scenario?

Answer 1

(9a) Stock A: Return = rA = 14% and Standard Deviation = ?A = 23%, Stock B: Return = rB = 19% and ?B = 34%

wA = 0.6 and wB = 0.4

Expected Return of Portfolio = rP = rA x wA + rB x wB = 0.6 x 14 + 0.4 x 19 = 16%

Standard Deviation of Portfolio = ?P = [{?A x wA}^(2) + {?B x wB}^(2) + {2 x wA x wB x ?A x ?B x ???}]^(1/2) = [{0.6 x 23}^(2) + {0.4 x 34}^(2) + {2 x 0.6 x 0.4 x 23 x 34 x 0.3}]^(1/2) = 22.0909 % ~ 22.091 %

(9b) ?A = 3 % and ?B = 7 %, ??? = −1, and ?P = 0

Therefore, [{?A x wA}^(2) + {?B x wB}^(2) + {2 x wA x wB x ?A x ?B x ???}]^(1/2) = 0

[wA?A - wB?B]^(2) = 0

wA?A = wB?B

wA/wB = ?B/?A = 7/3

Therefore, wA = 0.7 and wB = 0.3 as wA + wB = 1