Question

You are creating a portfolio of two stocks. The first one has a standard deviation of 20% and the second one has a standard deviation of 37%. The correlation coefficient between the returns of the two is 0.1. You will invest 43% 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

Answer:

23.56

Explanation:

Standard deviation of  the first stock (σ1) = 20%

Standard deviation of  the second stock (σ2) = 37%

The correlation coefficient between the returns (ρ) = 0.1.

Proportion invested in the first stock (W1) = 43%

Proportion invested in the second stock (W2) = 57%

The standard deviation of a two-stock portfolio's returns is given by

$\sigma_{portfolio} = \sqrt{w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\rho\sigma_1\sigma_2} \\\sigma_{portfolio} = \sqrt{0.43^2*0.2^2+0.57^2*0.37^2+2*0.43*0.57*0.1*0.2*0.37}\\\sigma_{portfolio} =0.2356=23.56\%$

The standard deviation of this portfolio's returns IS 23.56%