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 replaces the standard deviation with downside deviation.

Standard deviation, the most widely used measure of investment risk, has some limitations, such as the fact that it treats all deviations from the average — whether positive or negative — as the same. However, investors are generally more concerned with negative divergences than positive ones, i.e., downside risk is a bigger concern. Downside deviation resolves this issue by focusing only on downside risk.

Another advantage over standard deviation is that downside deviation can also be tailored to the specific objectives and risk profile of different investors who have various levels of minimum acceptable return.

The purpose of the Sortino and Sharpe Ratios is to enable investors to compare investments that have different levels of volatility, or in the case of the Sortino Ratio, downside risk. Both ratios look at excess return, that is, the amount of return in excess of the risk-free rate. The risk-free rate is often represented by short-term Treasury securities.

If two investments have the same return, say 10%, but one has a downside deviation of 9% and another 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.

If the risk-free rate is 1%, then the Sortino Ratio for the first investment is (10% - 1%)/ 9% = 1.0. The Sortino Ratio for the second investment is (10% -1%)/ 5% = 2.0.