Question

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?

Answer 1

15.5%

Step-by-step 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