Question

1. Suppose the expected returns and standard deviations of stocks A and B are E(R_A) 0.15, E(R_B) 0.25, σ_A 0.40, and σ_B 0.65, respectively.

a. Calculate the expected return and standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation between the returns on A and B is 0.5.

b. Whether the risk (standard deviation) of the portfolio will decrease or increase if the correlation between the returns on A and B decreases and becomes negative?

Answer 1

Given about two stocks,

E(R_A) = 0.15,

E(R_B) = 0.25,

σ_A = 0.40,

σ_B = 0.65

Corr(A,B) = 0.5

a). W_A = 0.40

W_B = 0.60

Expected return of portfolio is E(R_P) = W_A*E(R_A) + W_B*E(R_B) = 0.4*15 + 0.6*25 = 21%

standard deviation of the portfolio is SD_p = SQRT((W_A*σ_A)² + (WB*σ_B)² + 2*W_A*σ_A*WB*σ_B*Corr(A,B))

SD_p = SQRT((0.4*40)² + (0.6*65)² + 2*0.4*40*0.6*65*0.5) = 45.70% or 0.4570

b). As, correlation decreases and moves to negative, third term of the formula also turn negative. This will decrease the risk of the portfolio.