Assume that the standard deviation of the U. S. market portfolio is 18.2%, the standard deviation of the world portfolio is 17.1%, and the correlation between the U. S. and nonU. S. market portfolios is .47. Suppose you invest 25% of your money in the U. S. stock market and the other 75% in the nonU. S. portfolio. What is the standard deviation of your portfolio?

15.5%

Explanation:

The computation of the standard deviation of your portfolio is shown below:

Standard deviation of portfolio = weight of US Market portfolio ^2 × Standard deviation of US Market portfolio ^2 +  weight of Non US Market portfolio^ 2 × Standard deviation of Non US Market portfolio^2 + 2 ×  weight of US Market portfolio × weight of Non US Market portfolio × Standard deviation of US Market portfolio × Standard deviation of Non US Market portfolio × correlation

= [0.25^2 × 18.2^2 + 0.75^2 × 17.1^ 2 + 2 × 0.25 × 0.75 × 18.2 × 17.1 × 0.47]

= (0.0625 ×  331.24  + 0.5625  × 292.41  + 54.852525

= 20.7025  + 164.480625  + 54.852525

= 240.03565

Now take the square root of 240.03565 i.e 15.5%

We simply applied the above formula