Thecovarianceis the most basic measure of how two assets move together. The covariance is the expected value of the product of the deviations of the two random variables around their respective means. The symbol for the covariance between X and Y is Cov(X,Y). Since the formula is often applied to the returns of assets, the formula below has been written in terms of the covariance of the return of asset "i" and the return of asset "j:"
Cov(Ri,Rj) = E{(Ri- E(Ri)] * [Rj- E(Rj)]}
Example:The economy can experience one of the following three states "S" next year: boom, normal, or slow economic growth. An expert source has calculated that P(boom) = 0.30, P(normal) = 0.50, and P(slow) = 0.20 percent. The corresponding returns for stock A and stock B are in the designated columns in the table below. The last column is the product of each return around the expected value weighted by the respective probability.
Event
P(S)
RA
RB
[RA- E(RA)] * [RB- E(RB)] * P(S)
Boom
0.3
0.20
0.30
.00336
Normal
0.5
0.12
0.10
.00020
Slow
0.2
0.05
0.00
.00224
 
 
E(RA) = 0.13
E(RB) = 0.14
0.0058