问一道题：NO.PZ2020010304000015

问题如下：

Suppose that the annual profit of two firms, one an incumbent (Big Firm, X1) and the other a startup (Small Firm, X2), can be described with the following probability matrix:

If an investor owned 20% of Big Firm and 80% of Small Firm, what are the expected profits of the investor and the standard deviation of the investor’s profits?

选项：

4.18; 8.39

4.18; 70.39

2.18; 8.39

2.18; 70.39

解释：

The expected profits are E[P] = 20% * E[X1] + 80% * E[X2] = 4.18.

The variance of the portfolio is (20%)^2*Var[X1] + (80%)^2*Var[X2] + 2(20%)(80%)Cov[X1, X2]

This value is 0.04 * 1534.36 + 0.64 * 2.41 + 2 * 0.16 * 23.37 = 70.39, and so the standard deviation is USD 8.39M.