Suppose the expected returns and standard deviations of stocks A and B are E(RA)=0.09, E(RB)=0.15, σA=0.36, and σB = 0.62, respectively.

a) Calculate the expected return and standard deviation of a portfolio that is composed of 30 percent of A and 70 percent of B when the correlation between the returns on A and B is 0.4.

b) Calculate the standard deviation of a portfolio with the same portfolio weights as in part (a) when the correlation between the returns on A and B is 0.

c) How does the correlation between the returns on A and B affect the standard deviation of the portfolio?

 

a)   Expected return of a portfolio = 13.20%

Standard deviation = 48.74%

b)  Standard deviation = 44.72%

c)     There is a direct relationship between stocks' correlation coefficient and standard deviation of a portfolio.

Step-by-step explanation

a)   Expected return of a portfolio = weight of stock A * expected return of stock A + Weight of stock B * expected return of stock B

          = 0.3 * 9% + 0.7 * 15%

           = 13.20%

Standard deviation of a portfolio is given by;

∂_p=[w²∂_A²+(1-w)²∂_B²+2*w*(1-w)*∂_A*∂_B*cor_AB]^1/2

Where;

w- Proportion invested in stock A, 0.3

(1-w)- Proportion invested in stock B, 0.7

∂_A²- Variance of stock A, 36 ² = 1,296%

∂_B²- Variance of stock B, 62 ² = 3,844%

∂_A- Standard deviation of stock A, 36%

∂_B- Standard deviation of stock B, 62%

Cor_AB- correlation coefficient between stock A and stock B, 0.4

∂_p= [(0.3)²*1,296+ (0.7)²*3,844+2*0.3*0.7*36*62* 0.4]^1/2

  = (116.64 + 1,883.56 + 374.976)^1/2

  = 2,375.176 ^½

  = 48.74%

b)     ∂_p= [(0.3)²*1,296+ (0.7)²*3,844+2*0.3*0.7*36*62* 0]^1/2

 = (116.64 + 1,883.56 + 0)^1/2

  = 2,000.2 ^½

  = 44.72%

c)     Correlation coefficient between stocks has a direct effect on the standard deviation of a portfolio. For instance, when correlation coefficient decrease, standard deviation also decrease and when correlation coefficient increase, standard deviation of a portfolio also increase.