Sharpe, Sortino and Calmar

By Otto Research 3 min read Article 59 of 95

Return alone says nothing about the risk taken to earn it. Three ratios put the two together, and each answers a slightly different question.

Sharpe

The Sharpe ratio is the annual return above the risk-free rate, divided by the annual standard deviation of returns. It measures return per unit of variability, up or down alike. A Sharpe of 0.5 is modest, 1.0 is good for a retail strategy over a long period, and 2.0 is exceptional and usually a sign of a short record or a hidden risk. Because it counts upside variability as risk, it penalises strategies with occasional large winners, and because it is computed from returns over a period, a record of a few months produces a figure with no reliability.

Sortino

The Sortino ratio replaces the standard deviation with the downside deviation, the variability of returns below zero or below a target. It stops penalising large winners and is fairer to strategies with low win rates and big winning trades. Its values run somewhat higher than Sharpe for the same strategy, and the same warnings about short records apply.

Calmar

The Calmar ratio is the annual return divided by the maximum drawdown over the period, conventionally three years. It answers the question a trader actually asks: how much did I make for the worst I had to sit through? A Calmar above 1 means the annual return exceeded the worst drawdown. It depends on a single event, the maximum drawdown, and a lucky period inflates it.

How they are gamed

A grid or martingale record has very low variability for years, since losses are never realised, and shows a high Sharpe and Sortino right up to the blow-up. A short record in a favourable period produces high values of all three. Monthly returns give higher Sharpes than daily returns for the same strategy, and the calculation basis should be stated.

Worked example

Strategy A returns 18 per cent a year with a 9 per cent standard deviation and a 12 per cent maximum drawdown: Sharpe about 1.5, Calmar 1.5. Strategy B returns 30 per cent with a 22 per cent standard deviation and a 34 per cent maximum drawdown: Sharpe about 1.2, Calmar 0.9. B made more money; A made it more efficiently and with a drawdown most people could hold. Run at higher risk, A would have matched B's return with a smaller drawdown.

What this means when an EA is trading

Where an EA's record publishes these ratios, use them to compare candidates at a similar length of record, and prefer Calmar for the question of survivability. Discount all three heavily on records under two years. And apply the grid test first: a high Sharpe with a 95 per cent win rate is a description of held losses, not of a good strategy.

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