## What Is Downside Risk?

Downside risk is an estimation of a security's potential loss in value if market conditions precipitate a decline in that security's price. Depending on the measure used, downside risk explains a worst-case scenario for an investment and indicates how much the investor stands to lose. Downside risk measures are considered one-sided tests since the potential for profit is not considered.

#### Understanding Risk And Time Horizon

### Key Takeaways

- Downside risk is an estimation of a security's potential loss in value if market conditions precipitate a decline in that security's price.
- Downside risk is a general term for the risk of a loss in an investment, as opposed to the symmetrical likelihood of a loss or gain.
- Some investments have an infinite amount of downside risk, while others have limited downside risk.
- Examples of downside risk calculations include semi-deviation, value-at-risk (VaR), and Roy's Safety First ratio.

## Understanding 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 bounded by zero. The investor can lose their entire investment, but not more. A short position in a stock, however, as accomplished through a short sale, entails unlimited downside risk since the price of the security could continue rising indefinitely.

Similarly, being long an option—either a call or a put—has a downside risk limited to the price of the option's premium, while a short call option position has an unlimited potential downside risk because there is theoretically no limit to how far a stock can climb. Short puts, on the other hand, have downside risk limited because the stock or market cannot fall below zero.

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 possible rewards. Downside risk is in contrast to upside potential, which is the likelihood that a security's value will increase.

## Example of Downside Risk: Semi-Deviation

With investments and portfolios, a very common downside risk measure is downside deviation, which is also known as semi-deviation. This measurement 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.

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

$\begin{aligned} &\sigma = \sqrt{ \frac{ \sum_{i=1}^{N} (x_i - \mu)^2 }{ N } } \\ &\textbf{where:} \\ &x = \text{Data point or observation} \\ &\mu = \text{Data set's average} \\ &N = \text{Number of data points} \\ \end{aligned}$

The formula for downside deviation uses this same formula, but instead of using the average, it uses some return threshold—the risk-free rate is often used.

Assume the following 10 annual returns for an investment: 10%, 6%, -12%, 1%, -8%, -3%, 8%, 7%, -9%, -7%. 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% and the downside deviation of this data set is 3.27%. This shows that about 40% of the total volatility is coming from negative returns and 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.

## Other Measures of Downside Risk

### The SFRatio

Other downside risk measurements are sometimes employed by investors and analysts as well. One of these is known as Roy's Safety-First Criterion (SFRatio), which allows portfolios to be evaluated based on the probability that their returns will fall below a minimum desired threshold. Here, the optimal portfolio will be the one that minimizes the probability that the portfolio's return will fall below a threshold level.

Investors can use the SFRatio to choose the investment that is most likely to achieve a required minimum return.

### VaR

At an enterprise level, the most common downside risk measure is probably Value-at-Risk (VaR). VaR estimates how much a company and its portfolio of investments might lose with a given probability, given typical market conditions, during a set time period such as a day, week, or year.

VaR is regularly employed by analysts and firms, as well as regulators in the financial industry, to estimate the total amount of assets needed to cover potential losses predicted at a certain probability—say something is likely to occur 5% of the time. For a given portfolio, time horizon, and established probability *p*, the *p*-VaR can be described as the maximum estimated loss during the period if we exclude worse outcomes whose probability is less than *p*.