Consider an economy with two types of firms, S and I. S firms all move together. I firm's 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

The volatility (standard deviation) of (a) type S is 12.24% and the volatility (standard deviation) of (b) type I is 2.7%

Explanation:

In order to calculate the volatility (standard deviation) of a portfolio that consists of an equal investment in 20 firms of (a) type S, and (b) type I, we have to calculate first the expected return as follows:

expected return=(60%×15%)+(40%×−10%)

                          =0.09-0.04=0.05=5%

Therefore, the volatility (standard deviation) of (a) type S=√(0.60(15%-5%)∧2+0.40(-10%-5%)∧2)

 =12.24%

As I stock moves independently, therefore the volatility (standard deviation) of (b) type I=

SD(I Stock)= 12.24%

                      √20

                  =2.7%