Downside Risk: What It Is and How To Calculate It (2024)

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 profit potential is not considered.

Assessing Risk

Investments can have a finite or infinite amount of downside 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. Unlimited downside risk can exist with a short position in stock through a short sale since the price of the security could continue rising indefinitely.

Similarly, being long anoption—either a call or a put—has a downside risk limited to the price of the option's premium, while a “naked”short call option position has an unlimited potential downside risk because there is no limit to how far a stock can climb. A naked call option is considered the riskiest option strategy, since the seller of the option doesn’t own the security, and would have to purchase it in the open market to fulfill the contract.

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. Investors often compare the potential risks associated with a particular investment to possible rewards.

Measuring Downside Risk

Semi-Deviation

With investments and portfolios, a common downside risk measure is downside deviation or semi-deviation. It is a variation of standard deviation that measures the deviation of only bad volatility and 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:

$\begin{aligned} &\sigma = \sqrt{ \frac{ \sum_{i=1}^{N} (x_i - \mu)^2 }{ N } } \\ &\textbf{where:} \\ &x = \text{Data point or observation} \\ &\mu = \text{Data set's average} \\ &N = \text{Number of data points} \\ \end{aligned}$​σ=N∑i=1N​(xi​−μ)2​​where:x=Datapointorobservationμ=Dataset’saverageN=Numberofdatapoints​

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.

The SFR Ratio

The SFR Ratio, or Roy's Safety-First Criterion evaluates portfolios 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 the required minimum return.

VaR

At an enterprise level, the most common downside risk measure is 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 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, such as something 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.

The Bottom Line

Investors assume a level of risk that a securityincreases or decreases in value. Downside risk represents the worst-case scenario and may be precipitated by a market or economic event that causes a decline in the security's price in the short term.