Question

# Suppose the expected returns and standard deviations of stocks A and B are E(RA) 0.15, E(RB)...

1. Suppose the expected returns and standard deviations of stocks A and B are E(RA) 0.15, E(RB) 0.25, σA 0.40, and σB 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?

E(RA) = 0.15,

E(RB) = 0.25,

σA = 0.40,

σB = 0.65

Corr(A,B) = 0.5

a). WA = 0.40

WB = 0.60

Expected return of portfolio is E(RP) = WA*E(RA) + WB*E(RB) = 0.4*15 + 0.6*25 = 21%

standard deviation of the portfolio is SDp = SQRT((WAA)2 + (WBB)2 + 2*WAA*WB*σB*Corr(A,B))

SDp = 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.

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