Question

An investor forms a portfolio of two stocks, Alpha and Beta. Information regarding the two stocks is shown below: STOCK: Expected Return Standard Deviation Alpha 8.00% 30.00% Bravo 9.00% 50.00% The correlation between returns on Alpha and Bravo is 0.30. The investor will put 60% of her wealth in Alpha and the 40% of her wealth in Bravo. What is the standard deviation of the investor’s portfolio?

30.66%

27.66%

29.13%

31.17%

24.61%

Answer 1

Standard Deviation of portfolio=√(W Alpha^2 × σ Alpha^2) +(W Beta^2 × σ Beta^2)+2 × r × W Alpha × W Beta × σ Alpha × σ Beta
Where,
W Alpha=Weight of Alpha
W Beta=Weight of Beta
σ Alpha=Standard Deviation of Alpha
r = correlation coefficient
=√(0.6^2 × 30%^2) +(0.4^2 × 50%^2) + 2×0.3 × 0.6 × 0.4 × 30% × 50%
=√324+400+216
=√724
=30.66%