Intro

The table below shows the expected rates of return for three stocks and their weights in some portfolio:

		Stock A	Stock B	Stock C
	Portfolio weights	0.3	0.2	0.5
State	Probability		Expected returns
Recession	0.1	0.01	0.01	-0.05
Normal	0.5	0.04	0.05	0.02
Boom	0.4	0.09	0.07	0.1

Part 1

What is the expected portfolio return?

Correct

The portfolio return in each state is the weighted average of the individual expected returns: E(r_{P, recession}) = w_A E(r_{A, recession}) + w_B E(r_B, recession) + w_C E(r_C, recession) = 0.3 * 0.01 + 0.2 * 0.01 + 0.5 * -0.05 = -0.02

E(r_{P, normal}) = w_A E(r_{A, normal}) + w_B E(r_B, normal) + w_C E(r_C, normal) = 0.3 * 0.04 + 0.2 * 0.05 + 0.5 * 0.02 = 0.032

E(r_{P, boom}) = w_A E(r_{A, boom}) + w_B E(r_B, boom) + w_C E(r_C, boom) = 0.3 * 0.09 + 0.2 * 0.07 + 0.5 * 0.1 = 0.091

The expected portfolio return is the weighted average of the portfolio returns during a recession and a boom: E(r_P) = p_recession E(r_{P, recession}) + p_normal E(r_{P, normal}) + p_boom E(r_{P, boom}) = 0.1 * -0.02 + 0.5 * 0.032 + 0.4 * 0.091 = 0.0504

Attempt 3/10 for 10 pts.

I help need to solve for part 2

Part 2

What is the standard deviation of the portfolio returns?