Covariance Source

Covariance can be found on page 107 of Chapter 4. It is defined as a measure of relatedness that depends on the unit of measurement. Below is an example of how to calculate covariance:

event probability return A return B
1 40% 20% 7%
2 30% -15% -5%
3 15% 10% 8%
4 10% 4% 6%
5 5% 0% -4%

(1) Notice that the sum of probabilities sum to 1. Now we can calculate the average return of stock A
A: (.4)(.2) + (.3)(-.15) + (.15)(.1) + (.10)(.04) + (.05)(0)
A: .08 + -.045 + .015 + .004 + 0
A: .054, or 5.4%
(2) And now stock B
B: (.4)(.07) + (.3)(-.05) + (.15)(.08) + (.1)(.06) + (.05)(-.04)
B: .028 + -.015 + .012 + .006 + -.002
B: .029, or 2.9%
(3) Now our covariance equation
cov = (.4)(.2 - .054)(.07 - .029) + (.3)(-.15 - .054)(-.05 - .029) + (.15)(.1 - .054)(.08 - .029) + (.1)(.04 - .054)(.06 - .029) + (.05)(0 - .054)(-.04 - .029)
cov = .007724