Covariance of Returns
Covariance of Returns
How two return series move together: the average product of their deviations from their means, using the sample divisor n − 1. Positive when the two tend to rise and fall together, negative when they offset.
When to use: Use as the raw ingredient of portfolio variance and beta. Covariance is in squared-return units, so for a readable strength-of-relationship figure use correlation.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Cov | Covariance | Sample covariance of the two return series | variance |
| AssetReturns | Asset A Returns | Periodic returns of the first asset | % |
| BenchmarkReturns | Asset B Returns | Periodic returns of the second asset over the same periods | % |
Real-Life Examples
Example 1: Fund Versus Benchmark
Five periods of returns: fund 4%, 3%, 5%, 2%, 6%; benchmark 3%, 2%, 4%, 2%, 5%.
Given
Step-by-Step
Positive: the fund and its benchmark move together. Divided by the benchmark variance (0.00017) this gives a beta of about 1.18.
Example 2: Volatile Asset Versus Steady One
Asset A: 10%, −5%, 8%, 2%, 12%; asset B: 6%, 1%, 5%, 3%, 7%.
Given
Step-by-Step
A larger covariance, driven mostly by asset A's wider swings. Whether the two are more closely related than the first pair needs correlation, which strips out the scale.
Frequently Asked Questions
The series are a sample of the assets' behaviour, not the whole population, and dividing by n − 1 corrects the downward bias of estimating the means from the same data. It matches the sample standard deviation used elsewhere on SnapFi.