Downside Deviation: Definition, Uses, Calculation Example

What Is Downside Deviation?

Downside deviation is a measure of downside risk that focuses on returns that fall below a minimum threshold or minimum acceptable return (MAR). It is used in the calculation of the Sortino ratio, a measure of risk-adjusted return. The Sortino ratio is like the Sharpe ratio, except that it replaces the standard deviation with downside deviation.

Understanding Downside Deviation

Standard deviation, the most widely used measure of investment risk, has some limitations. For example, it treats all deviations from the average—whether positive or negative—as the same. However, investors are generally only bothered by negative surprises. Downside deviation resolves this issue by focusing solely on downside risk. However, downside deviation is not the only way to look at losses. Maximum drawdown (MDD) is another way of measuring downside risk.

An additional advantage of downside deviation over standard deviation is that downside deviation can also be tailored to the specific objectives. It can change to fit the risk profiles of different investors with various levels of minimum acceptable return.

The Sortino and Sharpe ratios enable investors to compare investments with different levels of volatility, or in the case of the Sortino ratio, downside risk. Both ratios look at excess return, the amount of return above the risk-free rate. Short-term Treasury securities often represent the risk-free rate.

Suppose two investments have the same expected return, say 10%. However, one has a downside deviation of 9%, and the other has a downside deviation of 5%. Which one is the better investment? The Sortino ratio says that the second one is better, and it quantifies the difference.

Calculation of Downside Deviation

The first step of calculating the downside deviation is to choose a minimum acceptable return (MAR). Popular choices include zero and the risk-free T-bill rate for the year. We'll just use one here for simplicity.

Secondly, we subtract the MAR from each of the returns.

The third step is to separate all of the negative numbers, in this case, -3, -12, and -4. Then, we square the negative numbers to obtain 9, 144, and 16. The next step is to sum the squares, which gives us 169 in this case. After that, we divide it by the number of observations, 9 in our example, to get about 18.78. Finally, we take the square root of that number to get the downside deviation, which is about 4.33% in this case.

What Downside Deviation Can Tell You

Downside deviation gives you a better idea of how much an investment can lose than standard deviation alone. Standard deviation measures volatility on the upside and the downside, which presents a limited picture. Two investments with the same standard deviations are likely to have different downside deviations.

Downside deviation can also tell you when a "risky" investment with a high standard deviation is likely safer than it looks. Consider an investment that pays 40% half the time and still pays 20% in less successful years. Such an investment would have a much higher standard deviation than one that simply paid 5% every year. However, few people would say that getting paid 5% every year was really safer. Both of these investments would have a downside deviation of zero using 5% as the minimum acceptable return (MAR). That tells us that they are both perfectly safe investments.

Limitations of Downside Deviation

Downside deviation does not convey any information about upside potential, so it provides an incomplete picture. In the previous example, we learned that an investment with a 50% chance of getting 40% and a 50% chance of getting 20% had the same downside deviation as getting 5% for sure if we use 5% as the minimum acceptable return (MAR). However, the first investment has a much higher upside potential. In fact, it is guaranteed to outperform, the only question is by how much.