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 43 % probability that the firm will have a 8 % return and a 57 % probability that the firm will have a negative 2 % return. What is the volatility? (standard deviation) of a portfolio that consists of an equal investment? in:

a)15 firms of type? S?

b) 15 firms of type? I?

a) SD of 15 firms of type? = 4.95%

b) SD of 15 firms of type? I = 1.2781%

Step-by-step explanation

E(R) = p1 x R1 + p2 x R2 = 43% x 8% + 57% x (-2%) = 2.3%

Variance, V = p1 x [R1 - E(R)]² + p2 x [R2 - E(R)]² = 43% x (8% - 2.3%)² + 57% x (-2% - 2.3%)² = 24.51%

Hence, standard deviation = SD = V^1/2 = (24.51)^1/2 = 4.95%

Part (a)

Since, S firms all move together, hence there will be no benefit of diversification and hence the standard deviation of a portfolio that consists of an equal investment? in 15 firms of type? S = SD = 4.95%

Part (b)

I firms move independently. The stocks are uncorrelated.

Hence, the standard deviation of a portfolio that consists of an equal investment? in 15 firms of type? I

= SD / n^1/2 = 4.95% / (15)^1/2 = 1.2781%