Consider an economy with two types of firms, S and I. S firms all move together. I firms move independently. For both types of firms, there is a 60% probability that the firms will have a 15% return and a 40% probability that the firms will have a 10% return. What is the volatility (standard deviation) of a portfolio that consists of an equal investment in 20 firms of (a) type S, and (b) type I?

My Question: Finding Standard deviation of type I stocks- not sure how solution was found (see below)

B. E(R)) = 0.15(0.6) - 0.1(0.4) = 0.05 SD(R1) = (0.15 0.05)2 x 0.6+ (0.10 0.05)2 x 0.4 = 0.1225 Type I stocks move independently. Hence the standard deviation of the portfolio is SD ((R1,1 + R1,2 + ... + R1,20)) = Jvar (26 (R1,1 + R1,2 + ... + R120)) - J() Var(Ria) +...+ (1)*x Var (Ruzo) = so(eta) 0,125 = 0.0274 2.74% 2.74% There is a benefit for diversification