Question

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.

Answer 1

Н K 1 2 3 the SD of a stock with prob dist is given by SD = sqrt ( sumof (prob1 *(return -expected return)) ) 6. From above formula we get SD of one stock i.e .1225 10 Since the type 1 stock move independently their correlation is zero 11 12 Portfolio Sd for such situation is given by : 13 14 SD = sqrt ( weight 1* weight 1*SD1 *SD1 + weight 2* weight 2*SD2 *SD2 + . + weight n* weight n*SDn *SDn) 15 16 In our case weight and Sd are equal 17 18 SD = sqrt ( 20 * (1/20)^2 * SD *SD) SD = sqrt ( (1/20)* .1225 *.1225) 19 20 21 SD = .1225 /sqrt (20) = 2.74% 22