Coefficient of Variation (CV)
Standard deviation divided by mean — risk per unit of return. Unitless, so it compares cleanly across investments with different return scales.
When to use: Use to compare risk-efficiency across very different assets (a low-return bond fund vs a high-return equity fund). Lower CV = more return per unit of risk. Closely related to Sharpe ratio (CV uses mean directly; Sharpe uses excess return over Rf).
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| CV | Coefficient of Variation | Standard deviation divided by mean — risk per unit of return | integer |
| Returns | Periodic Returns | Sequence of periodic returns as decimals (e.g. 0.05 for 5%) | % |
Real-Life Examples
Example 1: Volatile Equity vs Stable Bond
Equity quarterly returns: 4%, −2%, 6%, 3%, 8%.
Given
Step-by-Step
CV near 1 — the standard deviation is roughly equal to the mean, indicating high relative risk. Compare against a fund with mean 1% and σ 0.5% (CV = 0.5) — even though the absolute volatility is lower, the relative volatility is much better.
Frequently Asked Questions
CV uses the mean return in the denominator; Sharpe uses excess return over the risk-free rate, with σ in the denominator. CV is purely about risk-per-unit-of-return; Sharpe adjusts for the opportunity cost of holding risk-free assets. Both are useful — CV for raw risk-efficiency, Sharpe for risk-adjusted excess return.
When mean returns are near zero or negative — CV explodes or flips sign. Use only when mean is meaningfully positive. For comparing strategies, also avoid CV when investments have very different risk-free rate exposure (use Sharpe instead).
Lower CV is generally better (less risk per unit of return). For investments, you want high mean and low σ, which makes CV small. CV doesn't convey return level on its own — pair with absolute return.