Question

You are creating a portfolio of two stocks. The first one has a standard deviation of 21% and the second one has a standard deviation of 34%. The correlation coefficient between the returns of the two is 0.2. You will invest 38% of the portfolio in the first stock and the rest in the second stock. What will be the standard deviation of this portfolio's returns? Answer in percent, rounded to two decimal places (e.g., 4.32%=4.32).

Answer 1

standard deviation of portfolio's returns = (Portfolio Variance)1/2

Portfolio Variance = w1212 + w2222 + 2w1w212p1,2

w1 = weight of stock A; w2 = weight of stock B; 1 = standard deviation of stock A; 2 = standard deviation of stock B; p1,2 = correlation coefficient

Portfolio Variance = 0.382*0.212 + 0.622*0.342 + 2*0.38*0.62*0.21*0.34*0.2 = 0.1444‬*0.0441‬ + 0.3844‬*0.1156‬ + 0.006728736‬ = 0.00636804 + 0.04443664‬ + 0.006728736 = 0.057533416‬

Portfolio standard deviation = (Portfolio Variance)1/2 = (0.057533416‬)1/2 = 0.057533416‬0.5 = 0.2399 or 23.99%

the standard deviation of this portfolio's returns will be 23.99%.