Question

Suppose you have interest only in two stocks, A and B. You expect that returns on the stocks depend on the following three states of the economy, which are equally likely to happen:

State of economy: (Return on stock A) (Return on stock B)  

Bear: (6%) -  (-4%)

Normal: (10%) - (6%)

Bull: (8%) - (25%)

A) calculate the expected return for each stock:

B) calculate the standard deviation of return of each stock:

C) calculate the covariance between two stocks:

D) Could you obtain diversification benefits by combining these two stocks into a portfolio? why or why not? Be sure to quantify your answer.

Answer 1

1.
Expected return:
Stock A=1/3*(0.06+0.10+0.08)=0.08

Stock B=1/3*(-0.04+0.06+0.25)=0.09

2.
Standard Deviation:
Stock A=sqrt(1/3*(0.06-0.08)^2+1/3*(0.10-0.08)^2+1/3*(0.08-0.08)^2)=0.016329932

Stock B=sqrt(1/3*(-0.04-0.09)^2+1/3*(0.06-0.09)^2+1/3*(0.25-0.09)^2)=0.120277457

3.
Covariance=1/3*(0.06-0.08)*(-0.04-0.09)+1/3*(0.10-0.08)*(0.06-0.09)+1/3*(0.08-0.08)*(0.25-0.09)=0.000666667

4.
Correlation=0.000666667/(0.016329932*0.120277457)=0.339422278

Yes there is diversification benefits as correlation is less than +1