What are the Sharpe and Sortino ratios?

Both answer the same question in slightly different ways: how much return did this strategy earn for the risk it took? Raw return alone cannot distinguish a strategy that earned 12% smoothly from one that earned 12% through violent swings.

Sharpe ratio

Sharpe = (average monthly return above cash / standard deviation of those excess returns) x the square root of 12

The numerator strips out what you could have earned sitting in cash. The denominator measures how much the monthly returns scattered around their own average. The square root of 12 annualizes a figure computed from monthly data.

Higher is better. As a rough guide, above 1.0 is good and above 2.0 is unusual over a long period, though these rules of thumb depend heavily on the era and the asset class.

DMS uses the arithmetic mean of monthly returns here, not the compound annual growth rate. This is the standard construction and it is what makes the figure comparable to Sharpe ratios published elsewhere. A version built on CAGR runs systematically lower, by roughly half the annualized variance, purely as an artifact of the formula rather than anything about the strategy.

Sortino ratio

Sortino keeps the same shape and changes what counts as risk. Instead of the standard deviation of all returns, it uses the deviation of only the losing months.

Sortino = (average monthly return / deviation of months below zero) x the square root of 12

The reasoning is straightforward. Standard deviation treats a surprise gain as risk, identical to a surprise loss of the same size. Nobody experiences it that way. Sortino counts only the outcomes that actually hurt.

The threshold here is zero, not the risk-free rate, and it is zero on both sides of the calculation. The minimum acceptable return is "do not lose money," and the numerator is measured against that same standard. Using one threshold in the numerator and a different one in the denominator produces a figure that is not comparable to anything, which is worth knowing if you are checking our numbers against another source.

Sortino is essentially always higher than Sharpe for the same strategy, since the denominator is built from a subset of the same months and the numerator is not reduced by the cash rate. The two are not comparable to each other in absolute terms. Compare Sharpe against Sharpe and Sortino against Sortino.

The gap between them is informative in itself. A strategy whose Sortino greatly exceeds its Sharpe has volatility concentrated on the upside, which is exactly what you want. A strategy where the two sit close together has volatility distributed evenly in both directions.

The risk-free rate

Sharpe needs a risk-free rate. DMS uses the actual return on cash over the period you have selected, taken from the cash series in the return data rather than from a fixed assumption. When cash data is unavailable it falls back to 4% per year.

This is the honest approach, and it has a consequence worth understanding: the bar moves across eras. In the early 1980s cash yielded close to 10%, so a strategy needed to earn well into double digits before its excess return was even positive. Through the 2010s cash yielded nearly nothing and almost any positive return counted as excess. A Sharpe ratio from the 1980s and one from the 2010s are not measuring against the same standard.

Sortino, using a zero threshold, is unaffected by this. That is one of its advantages when comparing across long periods with very different interest rate regimes.

When the Inflation Adjusted toggle is on, the risk-free rate is deflated along with the strategy returns, so the Sharpe comparison stays internally consistent rather than measuring a real return against a nominal benchmark.

Comparing our figures against other sites

If a ratio here differs from one you have seen elsewhere for a similar strategy, the cause is usually one of these rather than a disagreement about the underlying returns:

• Trading friction. The Include Trading Friction toggle is on by default here, which lowers returns and therefore both ratios. Not every source deducts trading costs.
• The risk-free rate. A source using zero, or a fixed assumption, will report a higher Sharpe than one using the realized cash return.
• The Sortino threshold. Some sources measure downside against the risk-free rate rather than against zero, which produces a lower figure than ours.
• Arithmetic versus geometric. A source using CAGR in the numerator reports a lower Sharpe than one using the arithmetic mean.
• The period. These are window-scoped statistics. Two sources covering different date ranges are not measuring the same thing.

Which one to use

For DMS strategies specifically, we lead with the Ulcer Performance Index rather than either of these. UPI divides excess return by drawdown pain instead of by volatility, and for strategies designed to limit drawdowns rather than to limit volatility, it captures the design goal more directly.

Sharpe and Sortino are here because they are the standard vocabulary of the field, and because a strategy that looks good on one measure and poor on another is telling you something worth investigating.

Limitations shared by both

• They assume returns behave normally. Financial returns have fatter tails than the bell curve implies. Both ratios systematically understate the likelihood of the extreme month.
• Neither knows anything about sequence. Shuffle a strategy's monthly returns into a random order and both ratios come out identical, even though the shuffled path might have depleted a retirement account and the real one did not.
• Neither penalizes a long recovery. A strategy that stays underwater for eight years can post a perfectly respectable Sharpe. This is precisely the blind spot the Ulcer Index was invented to cover.
• Both are window-scoped and respond to the toggles, like every other statistic on the site.