Coefficient of Variation (CV): Definition and How to Use It

What is the coefficient of variation?

The coefficient of variation (CV) is a standardized measure of dispersion that expresses the standard deviation relative to the mean. It shows the extent of variability in a data set in proportion to its average value and is useful for comparing variability across data sets with different units or widely different means.

CV can be reported as a decimal or as a percentage. In finance, it helps compare how much risk (volatility) is taken for a given expected return.

Formula and calculation

Population form:
CV = σ / μ
where σ is the standard deviation and μ is the mean.

Sample form (often shown as a percentage):
CV = (s / x̄) × 100
where s is the sample standard deviation and x̄ is the sample mean.

Tip: multiply by 100 to present CV as a percentage. Ensure standard deviation and mean are in the same units (e.g., both as percentages).

Steps to compute:
1. Compute the mean (μ or x̄).
2. Compute the standard deviation (σ or s).
3. Divide the standard deviation by the mean (and multiply by 100 if you want a percent).

Interpretation

• A higher CV means greater relative variability (more dispersion around the mean).
• A lower CV indicates less relative variability and generally a more favorable risk-to-reward tradeoff (for investments).
• There is no universal “good” CV; interpretation depends on the context and what you compare.

Caveat: If the mean is close to zero (or zero/negative), the CV becomes unstable or misleading.

CV vs. standard deviation

• Standard deviation measures absolute dispersion around the mean in the original units.
• CV is a relative measure (standard deviation divided by mean), allowing comparison across different scales or units.
  Use CV when comparing variability between series with different units or widely different means.

Advantages and disadvantages

Advantages
* Enables comparison across different units or scales.
* Useful for assessing relative risk versus return in investments.

Disadvantages
* Unreliable when the mean is near zero or negative.
* Can exaggerate variability if the mean is very small.

Uses and applications

CV is used across many fields: finance, economics (e.g., income dispersion), chemistry, engineering, neuroscience, and quality control. In finance, it helps investors compare assets by their volatility relative to expected returns.

Excel tip

1. Use STDEV.P or STDEV.S to calculate standard deviation.
2. Use AVERAGE to compute the mean.
3. Divide the SD result by the mean cell (×100 for percentage).

Example formula (sample CV as percent):
=(STDEV.S(range) / AVERAGE(range)) * 100

Example (ETF comparison)

Given 15-year historical annual figures:
* SPY — mean: 5.47%, SD: 14.68% → CV = 14.68 / 5.47 ≈ 2.68
* QQQ — mean: 6.88%, SD: 21.31% → CV = 21.31 / 6.88 ≈ 3.10
* IWM — mean: 7.16%, SD: 19.46% → CV = 19.46 / 7.16 ≈ 2.72

Interpretation: SPY and IWM have lower CVs than QQQ, indicating a better historical risk-return tradeoff (lower volatility per unit of return) than QQQ over this period.

Key takeaways

• CV = standard deviation ÷ mean; multiply by 100 for a percentage.
• CV allows relative comparison of variability across datasets with different scales.
• Lower CV typically indicates a more attractive risk-to-reward profile, but context matters.
• Avoid relying on CV when the mean is zero or near zero.