Sortino Ratio: A Numerical Comparison with Sharpe

Sharpe treats a very profitable month as variation too. Traders generally fear downward moves more than upward ones. The Sortino ratio addresses that asymmetry.

When Sharpe penalizes favorable variation

The Sharpe ratio divides excess average return by standard deviation, which measures distance from the mean without distinguishing direction. A +15% month can therefore increase measured volatility and lower the ratio.

A +15% month does not pose the same account problem as −15%. Sortino reflects that asymmetry by retaining only below-target variation in its denominator.

The target or minimum acceptable return, MAR, marks the threshold below which a return counts as a shortfall. The guide uses 0% for simple interpretation; a risk-free reference is another possible choice.

Calculating downside deviation: Twelve months

Consider these hypothetical monthly returns.

For standard deviation, square each month's distance from the 3.75% mean, average the squares and take the square root. The guide reports 5.03%, using all twelve months.

Downside deviation includes only shortfalls below the 0% target in the squared sum. Other months contribute zero.

Compare the two ratios.

The same record produces ratios more than threefold apart. Large gains of +12% and +10% increase Sharpe's denominator, while the smaller losses keep downside deviation low.

Annualizing

Under the usual square-root scaling assumptions, multiply a monthly ratio by √12, about 3.46. The original guide gives √252 for a daily series using a 252-session year; the period count must match the actual data convention.

Sortino 8.2 looks impressive, but only four of twelve months lose money, keeping the denominator small. Short samples can inflate Sortino more readily than Sharpe. With no below-target observations, the denominator is zero and the ratio is undefined.

Equal averages, different rankings

Consider two strategies averaging +2.0% monthly.

Sharpe ranks A nearly three times as highly, but Sortino reverses the ranking. B's +15% month increases standard deviation and contributes nothing to downside deviation.

Both measures describe something useful and omit something important. B depends on one month out of ten. Remove it and the mean falls to +0.56%. A high Sortino does not establish stability; it says that this sample contains relatively little downside. Examine concentration with profit factor and expectancy and R multiples.

The denominator trap: Which period count?

Dividing the squared shortfall sum of 30 by all twelve months or by only four losing months creates materially different results.

The commonly used definition is ①: nonlosing periods contribute zero shortfall to the average. Method ② instead measures a conditional root-mean-square loss among losing periods.

The practical rule is not to compare ratios calculated with different conventions. As with consistent fees when comparing backtests, the scale must match. Check the target return, daily or monthly frequency, and denominator convention before comparing published values.

What Sortino cannot answer

Downside deviation captures loss size, but not its sequence. Four −3% months have the same contribution whether scattered or consecutive, while the account path and psychological burden differ.

Maximum drawdown captures this ordering effect. A high Sortino can coexist with −40% MDD. Whether that path is tolerable depends partly on position sizing. Sortino summarizes a return distribution without deciding whether you can operate through its path.

Calculate using returns net of fees and slippage. Gross-return ratios overstate realizable performance, especially for frequent trading.

Interpreting the number

No universal passing score exists because asset class, frequency and sample composition change the range. The guide offers these rough references.

Below 1: Thin return relative to downside; costs may consume the margin.
1–2: An ordinary reference range, subject to sample size and composition.
Above 2: Apparently attractive, but check the number of losing periods and whether removing the largest gain changes the conclusion.

If Sortino is extremely high relative to Sharpe, upward variation dominates observed downside. This can reflect a sample concentrated in a strong bull market. Including falling periods may sharply reduce it. Changes in volatility regimes also change the relationship.

Calculating from your records

1. Following this guide's closed-trade approach, form monthly or weekly net return observations after fees.
2. Choose a target; 0% is straightforward.
3. Calculate average return across all periods, using excess return when the target is nonzero.
4. Square and sum each below-target shortfall.
5. Divide by all periods and take the square root.
6. Divide step 3 by step 5.
7. Remove the highest-return period and recalculate. A halving indicates dependence on that period.

Step 7 is especially useful. With short samples, read Sortino, MDD and trade count together. Whether the account survives clustered losses also relates to risk of ruin.

Three key points

① With a zero target, Sortino = average return ÷ downside deviation. Its denominator omits favorable variation.
② Dividing by all periods versus losing periods can nearly double the result. Match conventions.
③ It captures loss size but not consecutive ordering. Read MDD alongside it.

Caution

The monthly returns, ratios and periods are hypothetical illustrations, not actual strategy performance. Historical metrics do not guarantee future returns and change with the sample. Investment decisions and responsibility remain yours.