A two- asset portfolio is made up of 80 per cent of Share A, for which the variance is 50%, and 20 per cent of Share B, with variance 60%. The covariance between the two shares is 25%. What is the standard deviation of the two- asset portfolio?
A) 87.54%
B) 65.12%
C) 73.23%
D) 91.63%

Question

Quizplus · Accepted Answer

The standard deviation of a two-asset portfolio can be calculated using the formula for the variance of a portfolio, which is: $$ \sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\text{Cov}(A,B) $$where:- $ \sigma_p^2 $ is the variance of the portfolio,- $ w_A $ and $ w_B $ are the weights of assets A and B in the portfolio, respectively,- $ \sigma_A^2 $ and $ \sigma_B^2 $ are the variances of assets A and B, respectively,- $ \text{Cov}(A,B) $ is the covariance between assets A and B.Given:- $ w_A = 0.8 $, $ w_B = 0.2 $,- $ \sigma_A^2 = 50\% = 0.5 $, $ \sigma_B^2 = 60\% = 0.6 $,- $ \text{Cov}(A,B) = 25\% = 0.25 $.Plugging these values into the formula gives:$$ \sigma_p^2 = (0.8)^2(0.5) + (0.2)^2(0.6) + 2(0.8)(0.2)(0.25) $$$$ \sigma_p^2 = 0.32 + 0.024 + 0.08 $$$$ \sigma_p^2 = 0.424 $$The standard deviation of the portfolio, $ \sigma_p $, is the square root of the variance:$$ \sigma_p = \sqrt{0.424} \approx 0.6512 \text{ or } 65.12\% $$Therefore, the correct answer is 65.12%.

A Two- Asset Portfolio Is Made Up of 80 Per