Question

• Stock 1 has a expected return of 14% and a standard deviation of 12%.
• Stock 2 has a expected return of 11% and a standard deviation of 11%.
• Correlation between the two stocks is 0.5.
• Create a minimum variance portfolio with long positions in both stocks.
• What is the return on this portfolio?

Answer 1

Given that,

Stock 1 has a expected return of Ra = 14% and a standard deviation of Sa = 12%.

Stock 2 has a expected return of Rb = 11% and a standard deviation of Sb = 11%.

Correlation C(a,b) = 0.5

For minimum variance portfolio, weight of stock 1 is

Wa = (Sb^2 - Sa*Sb*C(a,b))/(Sa^2 + Sb^2 - 2*Sa*Sb*C(a,b))

=> Weight of stock 1 Wa = (0.11^2 - 0.12*0.11*0.5)/(0.12^2 + 0.11^2 - 2*0.11*0.12*0.5) = 0.4135 or 41.35%

=> Weight of stock 2 = 1 - Wa = 1-0.4135 = 0.5865 or 58.65%

Return on this portfolio is Wa*Ra + Wb*Rb = 0.4135*14 + 0.5865*11 = 12.24%