# Downside Risk

## What is 'Downside Risk'

Downside risk is an estimation of a security's potential to suffer a decline in value if the market conditions change, or the amount of loss that could be sustained as a result of the decline. Depending on the measure used, downside risk explains a worst case scenario for an investment or indicates how much the investor stands to lose.

## BREAKING DOWN 'Downside Risk'

Some investments have a finite amount of downside risk, while others have infinite risk. The purchase of a stock, for example, has a finite amount of downside risk; the investor can lose his entire investment. A short position of a stock, however, as accomplished through a short sale entails unlimited downside risk, since the price of the security could continue rising indefinitely.

Investors, traders and analysts use a variety of technical and fundamental metrics to estimate the likelihood that an investment's value will decline, including historical performance and standard deviation calculations. In general, many investments that have a greater potential for downside risk also have an increased potential for positive rewards. Investors often compare the potential risks associated with a particular investment to its possible rewards. Downside risk is in contrast to upside potential, which is the likelihood that a security's value will increase.

## A Common Downside Risk Measure and Example

With investments and portfolios, a very common downside risk measure is downside deviation, which is also known as semi-deviation. This measure is a variation of standard deviation in that it measures the deviation of only bad volatility. It measures how large the deviation in losses is. Since upside deviation is also used in the calculation of standard deviation, investment managers may be penalized for having large swings in profits. Downside deviation addresses this problem by only focusing on negative returns.

For example, assume the following 10 annual returns for an investment: 10%, 6%, -12%, 1%, -8%, -3%, 8%, 7%, -9%, -7%.

Standard deviation, which measures the dispersion of data from its average, is calculated as:

Standard deviation = Square root of ((x - u)2 / n)

Where:

x = data point

u = dataset average

n = number of data points

The formula for downside deviation uses this same formula, but instead of using the average, it uses some return threshold. Often the risk-free rate is used or a hard target return. In the above example, any returns that were less than 0% were used in the downside deviation calculation.

The standard deviation for this data set is 7.69%. The downside deviation of this data set is 3.27%. Breaking out the bad volatility from the good volatility shows investors a better picture. This shows that about 40% of the total volatility is coming from negative returns. This implies that 60% of the volatility is coming from positive returns. Broken out this way, it is clear that most of the volatility of this investment is "good" volatility.