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 59 % probability that the firm will have a 24 % return and a 41 % probability that the firm will have a - 20 % return. What is the volatility​ (standard deviation) of a portfolio that consists of an equal investment​ in:

a. 36 firms of type​ S?

b. 36 firms of type​ I?

Answer 1

E(R) = p1 x R1 + p2 x R2 = 59% x 24% + 41% x (-20%) = 5.96%

Variance, V = p1 x [R1 - E(R)]² + p2 x [R2 - E(R)]² = 59% x (24% - 5.96%)² + 41% x (-20% - 5.96%)² = 0.0468318

Hence, standard deviation = SD = V^1/2 = (0.04683184)^1/2 = 0.216406654 = 21.64%

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 36 firms of type​ S = SD = 21.64%

Part (b)

I firms move independently. The stocks are uncorrelated.

Hence, the standard deviation of a portfolio that consists of an equal investment​ in 36 firms of type​ I

= SD / n^1/2 = 21.64% / (36)^1/2 = 3.61%