Sortino Ratio

The Sortino Ratio, like the Sharpe Ratio, is also risk-adjusted, in that it attempts to take into account an investment's risk. The question that this approach has raised, of course, is this: what is the best way to quantify an investment's risk?

As we saw with the Sharpe ratio, it does so using the standard deviation. The normal standard deviation, however, is non-directional, in that it includes any deviation from the mean, either positive or negative. It looks at both equally, making no distinction between profits (upside deviation) or losses (downside deviation). Consequently, the Sharpe ratio for an investment that had 0.0% return one month and -10.0% the next will be the same for one that had a gain of 5.0% in the first month and a loss of 5.0% in the second month.

While for some this is an appropriate way of distributing the variance in returns, to others it has had a disturbing consequence - that investments with excessive profits are effectively punished for being successful. This happens because, as the upside deviation increases because of those excessive profits, so the standard deviation as a whole increases. As the standard deviation is the denominator in the Sharpe Ratio, with all other things being equal, this will have negative impact on the ratio. And as the Sharpe Ratio decreases, so the performance of the investment (per unit of risk) is also seen to decrease.

One solution to this dilemma has been proposed by Frank Sortino. Named after him, the Sortino Ratio discards the consequences of upside deviation when quantifying an investment's risk. Instead, it looks only at downside deviation (or semi-variance). It does this by asking the investor to set a Minimum Acceptable Rate of Return (MAR), which is a return that he/she would be comfortable with. Any return below this is deemed to be downside deviation and is included for the purpose of calculating the Sortino Ratio.

S = (R - MAR) / DD

The Downside Deviation itself, however, is a little more complicated. To calculate it, we have set the MAR at 5% per annum (which is the same as the risk-free rate of return from the Sharpe Ratio).

First, we identify those returns which are less than the MAR of 5.0% per annum or 0.42% per month. Using the same date we did to calculate the Sharpe Ratio, those returns are isolated in the third column of the calculation box.

Second, we then square those returns, which is shown in the fourth column.

Third, we then calculate the sum of the squared returns, which is 0.39%.

Fourth, we then need to divide that sum by the total number of months, which is 15. The result is 0.000263.

Last, we need to find the square root of that number (then multiply it by 100 to get a percentage). The answer is 1.63%, which is the monthly Downside Deviation (the annual Deviation is found by multiplying it by the square root of 12).

Monthly Sortino:

(4.4 - 0.42) / 1.63 = 2.44

Annual Sortino:

2.44 x square root 12 = 8.45

As you can see, this is significantly higher than the Sharpe Ratio, which was 2.51, and this is the result we would want to see. Essentially, what the Sortino Ratio does is peel away at the exterior of the Sharpe Ratio to see if, in this case, it is as good as it seems.

If there is an excess of downside deviation it will show up in the Sortino Ratio. We ensure this by using the same value for the risk-free rate as we do for the MAR. Therefore, the only variable is in the denominator. An excess of downside deviation will lead to a larger denominator, which means a lower Ratio.