# Downside Deviation

Downside deviation is a risk statistic measuring volatility. It is a variation of standard deviation that focuses only upon the “bad” volatility.

## How Is it Useful?

Downside deviation addresses a shortcoming of standard deviation, which makes no distinction between the “good” or upside deviations, and the “bad” or downside deviations. Both upside and downside deviations have an equal influence on the calculation of standard deviation. Downside deviation seeks to remedy this by ignoring all of the “good” observations and by instead focusing on the “bad” returns.

## What Is a Good Number?

Like most other risk metrics, the lower the number the better. A value of zero would be the best possible value. However, it is important to understand the number in the proper context. One would need to look at the downside deviation of a relevant benchmark or an appropriate peer group in order to get a good feel for the downside deviation.

## What Are the Limitations?

In order for a downside deviation measure to be useful, there must be enough “bad” observations for the calculation to be statistically significant. While an investor might feel that lacking “bad” events in a data stream is actually positive, the usefulness of the metric would be limited if that was the case.

## What Does the Graph Show Me?

The below graph shows a volatile series of returns used for the calculation of both standard deviation and downside deviation. Standard deviation incorporates all of the datapoints in the series. With downside deviation, the “good” months are excluded, and only the “bad” months are counted.

There are several different ways in which one can define what counts as a “bad” observation with downside deviation. One might consider any negative return to be a “bad” observation. Alternatively, one could set the breakpoint as falling short of the risk-free rate. Another variation would be to consider any return that is less than the long-term average to be “bad”.

## What Are Typical Values?

In the table below, the downside deviation was calculated with a minimum acceptable return (MAR) of 0.0%. In other words, only monthly returns less than zero would be counted in the calculation of downside deviation. Two takeaways are apparent. Equity asset classes have higher downside deviations, as returns more frequently fall short of the 0.0% MAR. Also, this happened more frequently in the 2000s than in the 1980s and 1990s, so downside deviations tend to be higher in the most recent decade.

Math Corner:

The most important variable in the equation for downside deviation is the definition for what counts as being a “bad” observation. Denoted as “c” below, only the returns less than “c” are included in the calculation for downside deviation. Frequently used values for “c” are the risk-free rate, a hard-target value like 0%, or the mean return of the return series itself.

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