The coefficient of variation (COV) is the ratio of the standard deviation of a data set to the expected mean. Investors use it to determine whether the expected return of the investment is worth the degree of volatility, or the downside risk, that it may experience over time.

Dividing the volatility, or risk, of the investment by the absolute value of its expected return determines its COV.

### Key Takeaways

- An investor can calculate the coefficient of variation to help determine whether an investment's expected return is worth the volatility it is likely to experience over time.
- A lower ratio suggests a more favorable tradeoff between risk and return.
- A higher ratio might be unacceptable to a conservative or "risk-averse" investor.

## Understanding the Coefficient of Variation (COV)

Suppose an investor is comparing the COV for three investments. The investor is risk-averse, so the goal is to determine which of the three choices offers the best risk/reward ratio.

The three potential investments being scrutinized here are a stock called XYZ, a broad market index named DEF, and bond ABC. A quick use of the COV formula shows the following:

- Stock XYZ has volatility, or standard deviation, of 15% and an expected return of 19%. That means the COV is 0.79 (15% ÷ 19%).
- The broad market index fund DEF has a standard deviation of 8% and an expected return of 19%. The coefficient of variation is 0.42 (8% ÷ 19%).
- The third investment, bond, ABC, has a volatility of 5% and an expected return of 8%. The coefficient of variation therefore is 0.63 (5% ÷ 8%).

Investors' risk aversion differs from one investor to another. However, rational investors seeking to maximize the returns for the risks they take should choose to invest in the broad market index DEF because it offers the best risk/reward ratio. That means the lowest, since the risk is in the numerator and the reward is in the denominator. This means the lowest volatility percentage per unit of return.

Choosing an investment is always a balance between risk and reward. The amount of risk you are willing to take on defines your investing style.

The same investor would reject stock XYZ, even though it has the same expected return as the index, because it is more volatile than the index.

Bond ABC carries the least risk, but the return is relatively low.

## Usefulness of COV

The flaw in COV, as in most analytical factors, lies in the fact that it is inevitably based on historical data. And, as the prospectuses say, past performance is no guarantee of future results.

Nevertheless, COV is extremely reliable when it is applied to the analysis of bonds and other highly stable investments.

It may be somewhat less reliable when it comes to stocks, but it is a fact that many stocks, such as pharmaceuticals or technology startups, are by their nature much more volatile than others, such as blue-chip stocks.

Therefore, it would make perfect sense to compare the COV of a blue-chip stock fund or an S&P 500 index fund to a pharmaceutical stock. The comparison would give the investor a sense of whether the potential for an outsized return is worth taking a risk.