The Sortino Ratio: Measuring Only the Risk That Hurts

When reviewing crypto assets or US-listed instruments, investors often look at how much return they generated for the risk taken. A common measure is the Sharpe ratio, which compares an asset's excess return over a risk-free rate to its total volatility. Total volatility, however, includes both upward and downward price swings. For many investors, the real 'risk' they care about is the possibility of losing money—the downside volatility. This is where the Sortino ratio comes in.

The Sharpe ratio can sometimes paint a less-than-ideal picture. Imagine an asset that has had a few spectacular months where its price shot up by 50% or more. These large positive returns would increase the asset's total volatility, thereby lowering its Sharpe ratio, even though those gains are exactly what investors hope for. The Sortino ratio corrects for this by using a measure called downside deviation instead of total volatility. Downside deviation only accounts for returns that fall below a specified target rate of return.

Understanding Downside Deviation

Downside deviation, the core of the Sortino ratio, measures the dispersion of returns below a predetermined target return. This target can be anything an investor chooses, but it's often set at the risk-free rate or zero. For example, if our target return is 0% per month, downside deviation would only consider the months where the asset lost value, and it would measure how far those losses deviated from 0%. Months with positive returns, no matter how large, add no shortfall to this calculation.

Calculating the Sortino Ratio: A Worked Example

Let's consider a hypothetical digital asset over four months, with fictional monthly returns. Suppose our target return for this calculation is 0% per month. Here are the monthly returns:

• Month 1: +10%
• Month 2: -5%
• Month 3: +20%
• Month 4: -8%

First, we identify the returns below our target of 0%: -5% and -8%. These are the 'bad' returns.

Next, we calculate the downside deviation. The shortfalls below the 0% target are 5% and 8%, and the two positive months count as zero shortfall. We square each shortfall (0, 25, 0 and 64), average them over all four months (89 / 4 = 22.25), and take the square root. This gives a downside deviation of approximately 4.72%.

The average monthly return over the same period is (10 - 5 + 20 - 8) / 4 = +4.25%. The total volatility of these four returns, their standard deviation around that average, is approximately 11.37% per month, so with a 0% risk-free rate the Sharpe ratio would be 4.25% / 11.37% = approximately 0.37.

However, using the Sortino ratio, we compare the average excess return to the downside deviation. If we assume the risk-free rate is 0%, the Sortino ratio would be our average return (4.25%) divided by the downside deviation (4.72%). This gives us a Sortino ratio of approximately 0.90.

In this scenario, the Sortino ratio is higher than the Sharpe ratio. This difference highlights how the Sortino ratio can provide a more favorable view of assets that exhibit strong positive performance alongside moderate negative performance, as it disregards the impact of those positive swings on the risk measure.

Limits of the Sortino Ratio

While the Sortino ratio offers valuable insights, it's not without its limitations. Like many statistical measures, its reliability is heavily dependent on the length and quality of historical data. A short trading history, perhaps only a few months for a new digital asset like a recent token launch, might not provide enough data points to generate a statistically significant downside deviation. This can lead to misleadingly high or low Sortino ratios.

Furthermore, the choice of the target return is critical. A different target can significantly alter the calculated downside deviation and, consequently, the Sortino ratio itself. For instance, setting the target return at 1% instead of 0% would mean that any month with a return of exactly 1% or higher would not contribute to the downside deviation. An investor must carefully consider what level of return they deem acceptable before losses begin, and what constitutes 'risk' for their specific portfolio.

How does the Sortino ratio compare to the Sharpe ratio?

The Sharpe ratio uses total volatility, encompassing both positive and negative price swings, as its risk measure. The Sortino ratio, conversely, focuses exclusively on downside deviation, measuring only the volatility of returns that fall below a specified target return. This makes the Sortino ratio a more focused metric for investors primarily concerned with capital preservation and avoiding losses.

What is a good Sortino ratio?

A 'good' Sortino ratio is relative and depends on the asset class, market conditions, and the investor's chosen target return. Generally, a higher Sortino ratio indicates a better risk-adjusted return, meaning the asset generated more excess return per unit of 'bad' risk. Ratios above 1.0 are often considered favorable, but comparisons are most meaningful when evaluating assets within the same category or against their historical performance.

Can the Sortino ratio be negative?

Yes, the Sortino ratio can be negative. This occurs if the asset's average return is below the chosen target return, and the downside deviation is positive. A negative Sortino ratio suggests that the asset has, on average, underperformed the target return and has also experienced negative volatility below that target. Such a scenario indicates a poor risk-adjusted performance relative to the selected benchmark.

This information is intended to help you understand different risk measures; it is not investment advice.