Question

Stock X has an expected return of 36%, a variance of .08 and a beta of .70. Stock Y has an expected return of 48%, a variance of .18 and a beta of 1.2. Stocks X and Y have a correlation coefficient of .40. For a portfolio consisting of $120,000 invested in stock X and $40,000 invested in stock Y, calculate the return on the portfolio (in %), the standard deviation of the portfolio (in %) and the beta of the portfolio (carry the work to 2 decimals).

Answer 1

Total amount invested in the portfolio = 120,000+40,000 = 160,000

Weight of stock X (Wx) = amount invested in the stock/total portfolio amount = 120,000/160,000 = 0.75 (or 75%)

Weight of stock Y (Wy) = 1 - weight of stock X = 1-0.75 = 0.25 (or 25%)

Portfolio return = (Wx*Rx) + (Wy*Ry) where

Rx (return of stock X) = 36%; Ry (return of stock Y) = 48%

Portfolio return = (0.75*36%) + (0.25*48%) = 39.00%

Portfolio beta = (Wx*Bx) + (Wy*By) where

Bx (beta of stock X) = 0.7; By (beta of stock Y) = 1.2

Portfolio beta = (0.75*0.7) + ().25*1.2) = 0.825 (or 0.83)

Portfolio variance = (Wx*SDx)^2 + (Wy*SDy)^2 + (2*Wx*Wy*Correlation coefficient*SDx*SDy) where

SDx = variance of X^0.5 = 0.08^2 = 0.2828

SDy = variance of Y^0.5 = 0.18^0.5 = 0.4243

Portfolio variance = (0.75*0.2828)^2 + (0.25*0.4243)^2 + (2*0.75*0.25*0.40*0.2828*0.4243) = 0.07425

Portfolio standard deviation = portfolio variance^0.5 = 0.07425^0.5 = 27.25% (or 0.27249)