Correlation of Returns
Correlation of Returns
Covariance scaled by the two standard deviations, so it always lies between −1 and +1. It measures how reliably two assets move together, independent of how volatile each one is.
When to use: Use to judge diversification. The lower the correlation between two holdings, the more their combination reduces risk; a correlation of 1 means no diversification benefit at all.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| Corr | Correlation | Sample correlation coefficient, −1 to +1 | factor |
| 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: fund 4%, 3%, 5%, 2%, 6%; benchmark 3%, 2%, 4%, 2%, 5%.
Given
Step-by-Step
A correlation of 0.97: the fund tracks its benchmark very closely. Holding both would add almost no diversification.
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
Despite very different volatilities the two move almost in lockstep (0.99). Covariance alone could not show that; correlation strips out the scale.
Frequently Asked Questions
Anything well below 1. Two assets at 0.3 correlation cut portfolio volatility noticeably; at −0.5 they hedge each other. Correlations tend to rise in crises, which is when diversification is needed most.
If either series is constant its standard deviation is zero and the ratio has no meaning. The formula reports an error in that case.