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