Question

An investor has decided to form a portfolio by putting 25% of his money into McDonald’s stock and 75% into Cisco Systems stock. The investor assumes that the expected returns will be 8% and 15%, respectively, and that the standard deviations will be 12% and 22%, respectively.

a. Find the expected return on the portfolio.

b. Compute the standard deviation of the returns on the portfolio assuming that

(i) the two stocks’ returns are perfectly positively correlated

(ii) the coefficient of correlation is .5

(iii) the two stocks’ returns are uncorrelated

Calculate Part B and explain why part 1, 2 and 3 differ in values.

Answer 1

a. Expected return on the portfolio = 0.25(0.08) + 0.75(0.15) = 0.1325

b. Standard deviation, = { w₁²₁² + w₂² ₂² + w₁w₂ Cov(k₁,k₂) }  

where w_i is the proportion of i^th asset , _i² is the variance return of the i^th asset and Cov(k_i,k_j) is the covariance of the returns of the i^th and j^th asset.

i) = { 0.25² * 0.12² + 0.75² * 0.22² + 0.25*0.75*1*0.12*0.22 } = 0.1819

ii) = { 0.25² * 0.12² + 0.75² * 0.22² + 0.25*0.75*0.5*0.12*0.22 } = 0.1749

iii) = { 0.25² * 0.12² + 0.75² * 0.22² } = 0.1677