The Sortino ratio addresses a shortcoming of using standard deviation as a measure of risk in a return-versus-risk trade-off ratio. Standard deviation punishes a manager equally for “good” risk and “bad” risk. Downside deviation adjusts for this by only counting the “bad” risk and ignoring “good” observations in a return series. The Sortino ratio replaces standard deviation with downside deviation, so it is the added return per unit of “bad” risk rather than overall risk.

Like most ratios, the higher the Sortino ratio the better. One would hope to see substantial excess return above and beyond the risk-free rate, accompanied by little downside deviation. A scenario such as this would produce a large Sortino ratio. It is important to keep in mind the asset class under consideration when analyzing Sortino ratios.

Since the Sortino ratio uses downside deviation as its measure of risk, any limitations of downside deviation carry over to the Sortino ratio. With downside deviation there must be enough “bad” observations in order for the calculation to be statistically significant.

The below two graphs illustrate the two halves of the Sortino ratio. The numerator is identical to the numerator in the Sharpe ratio. It is the rolling excess return above and beyond the risk-free rate, as displayed in the upper graph. The lower graph illustrates how the Sortino ratio uses downside deviations, or the “bad” occurrences in a data stream as its measure of volatility risk.

One would expect to see Sortino ratios change significantly for most asset classes between the two decades of the 1980s and 1990s and the “lost decade” of the 2000s. Indeed, that is the case. The numerator of the Sortino ratio was reduced in the 2000s as many asset classes struggled to outperform the risk-free cash rate. The denominator was increased, as markets exhibited more downside deviations short of the 0.0% minimum acceptable return (MAR).

Math Corner:

The below calculation for the Sortino ratio is not complicated, as it is simply a variation of the Sharpe ratio. It is up to the user to define what the breakpoint is for minimum acceptable return (MAR) in the calculation of downside risk. Frequently used values for MAR are the risk-free rate or a hard-target value like 0%.

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