Coefficient of Variation: Formula, Interpretation, and a Worked Example

What the coefficient of variation measures

The coefficient of variation (CV) compares standard deviation with the mean return:

Coefficient of variation = σ / mean return

It answers a relative question: how much variability is associated with each unit of average return? When the mean return is positive, a lower CV generally indicates less variability per unit of mean return.

In Quizara's CFA Level I 2027 course, this sits in V1 Quantitative Methods → Module 5 → Other Dispersion Measures. The course note writes CV as sample standard deviation divided by sample mean, using the plain mean return rather than an excess return. Keep both inputs on the same return horizon; if you annualize, restate the mean and standard deviation on a consistent basis.

Compare two investments

Suppose two investments have returns measured over the same period.

B has the higher average return, but it also has more variability relative to that average. Under this metric, A has the lower risk per unit of mean return.

Where CV helps—and where it breaks

CV is useful when the means are positive and the investments are comparable. It becomes unstable or misleading when:

• the mean return is zero, because the denominator is zero;
• the mean return is negative, which can reverse the intuitive “lower is better” reading;
• the return distributions, horizons or measurement units differ;
• you need to subtract a risk-free rate, in which case Sharpe ratio may answer the more relevant question.

Do not write that a high CV means “higher return for the same risk.” A high CV means more standard deviation per unit of mean return in the ratio’s positive-mean setting.

Check your understanding

CV versus Sharpe ratio

Coefficient of variation

σ / mean return

Use when comparing relative variability around a positive mean.

Sharpe ratio

(return − risk-free rate) / σ

Use when excess return relative to a risk-free benchmark is the question.

Common mistakes

1. Putting the mean in the numerator instead of the denominator.
2. Comparing CVs built from different return periods.
3. Ranking a negative-mean investment with the same “lower is better” rule.
4. Confusing CV with a risk-adjusted return measure that uses a risk-free rate.

FAQ

Is a lower CV always better?

Only under the usual positive-mean, comparable-input assumptions. The denominator and the measurement context matter.

Does CV replace standard deviation?

No. Standard deviation measures absolute dispersion; CV scales dispersion by the mean.

Is CV on the CFA Level I exam?

It is part of the statistical measures used to compare dispersion relative to return. Expect a calculation and an interpretation question.

Curriculum context and further reading

The CFA Institute statistical measures reading places coefficient of variation alongside measures of dispersion. Use the official Statistical Measures of Asset Returns reading and the current curriculum for the exact learning outcome.