## Coefficient of Variation

Coefficient of variation (CV) is a statistical tool for defining the comparative variability of a particular data set. In other words, it indicates the distribution of the data points around the mean in a given data set. It is calculated in percentage (%) terms. It is used to understand the relative dispersion of data amongst various data series. A lower CV is always better. Coefficient of Variation Calculator is an online calculator for quick calculation of CV.

Both risk and returns are considered together for evaluating a portfolio’s performance. The coefficient of variation is the percentage of risk in return. Say, for example, the CV of Portfolio A with an average return of 25% is 32%. This means that the probable risk in return is 8% (i.e., 25 * 32%). Hence, it helps in selecting among various investment alternatives.

## Formula

Standard deviation is divided by the average return for calculating CV. Mathematically presentation of the same is as follows:

**Coefficient of Variation (CV)** = (σ / x̄) * 100

Where σ = Standard Deviation

and x̄ = Average Return

## About the Calculator / Features

The Coefficient of Variation Calculator is simple and handy. One has to enter the following figures into it.

- Standard deviation
- Average return

## Calculator

## How to Calculate using Calculator

The person accessing the calculator has to input the following mentioned particulars into it:

### Average Return

Average return can be calculated on the basis of past returns on the investment or portfolio as well as expected future returns. It is the mean of returns. A total of the past years return is divided by the total number of years under calculation. This will help in arriving at an average return from past data. While the total of expected future returns multiplied by the probabilities of respective years is divided by the number of years under calculation. This will provide an average return from the future data. It is generally denoted by x̄.

### Standard Deviation

Standard deviation is the volatility in the returns. It can also be computed on the basis of past and future data. It is denoted by σ. In the case of past data, it is the square root of total of (x – x̄)2 divided by the number of periods. However, in the case of future data, it is the square root of the probability of (x – x̄)^{2}.

## Example of Coefficient of Variation

Mr. X, an investor, wish to compare three stocks: α, β, and λ, for making an investment for his portfolio. He has the following information about three stocks:

Particulars | Stock α | Stock β | Stock λ |

Average return (x̄) | 18% | 25% | 8% |

Standard deviation (σ) | 12% | 20% | 3% |

Mr. X decided to evaluate all three stocks on the basis of the coefficient of variation.

Stocks | Coefficient of Variation | Calculation |

α | 66.67% | (12 / 18) * 100 |

β | 80% | (20 / 25) * 100 |

λ | 37.5% | (3 / 8) * 100 |

### Interpretation

As stated above, a smaller coefficient of variation is good than one which is high. In the example above, β has the highest CV among the three, and that of λ is the lowest. This simply means that the stock λ is the best-performing stock instead of the fact that it has the lowest return out of all. Same way, β having the highest return of all, is the least performing among the three.

## Cautions

Coefficient of variation is a comparative tool that also has a few limitations. This is less reliable in the case of volatility. Also, it is not useful when the mean or average is close to zero. There are other indicators for similar comparisons, such as Sharpe’s Ratio.