Sharpe, Sortino, Omega and Calmar

These four ratios weigh what a strategy earned against how rough the ride was, so a steady climb scores higher than a wild one that ends in the same place.

Von Lohengramm T7 - BTCUSD and Exponential Order Flow Pressure - SOXX are both strategies that held up well in their markets. The BTC one has a Sharpe of 1.80; the chip-stock one has 1.14. That isn't a statement about which one made more money. It says that for every unit of up-and-down movement its account went through, the BTC strategy earned more. Return tells you where the account ended up; these ratios tell you what the trip there was like.

Imagine two accounts that both double over five years. One climbs fairly steadily. The other crashes 60% twice along the way. Almost everyone would rather have held the first, and the ratios agree: they divide "what it earned" by "what it put you through". Higher is better for all four.

"Middle half" covers the middle 50% of all published strategies over their full history. It's a sense of scale, not a promise.

Sharpe

Sharpe looks at the account's change on every bar. Von Lohengramm T7 trades on 5-day bars; over 863 of them since 2015 its account rose on average 1.25% per bar, and those bar-to-bar changes typically swung about 5.9% around that average. Gain divided by swing is 0.21 per bar. Scaled up to a year of 73 bars, that's a Sharpe of 1.80.

A strategy with the same average gain but twice the swings would score half as much.

Sharpe = average bar return ÷ standard deviation of bar returns × √(bars per year). The standard deviation is the population version (divides by n), and the risk-free rate is 0. Bars spent Flat count as zero returns in both the average and the standard deviation. Bars per year come from the strategy's own bars: 73 for 5-calendar-day bars (crypto, crypto indexes, gold, the S&P 500), so √73 ≈ 8.54; and about 52 for funds like SOXX, whose bars are 5 trading days, so √52 ≈ 7.2. Example: 1.251% ÷ 5.94% × 8.54 ≈ 1.80.

A Sharpe from a fund factsheet or another website is usually worked out on daily returns, often with a risk-free rate subtracted. It isn't directly comparable. Compare Sharpe with Sharpe inside this app.

Sortino

Sharpe treats a big jump up as "risk", just like a big drop. Nobody minds a jump up, so Sortino only counts the downs. Von Lohengramm T7's losing bars, measured this way, come to about 2.95%, half its full swing of 5.9%, because many of its big moves were upward. With the same 1.25% average gain, that gives a Sortino of 3.62, twice its Sharpe.

When Sortino is much higher than Sharpe, the strategy's bumpiness is mostly upside. When the two are close, it goes down about as violently as it goes up.

Sortino = average bar return ÷ downside deviation × √(bars per year), with bars per year as for Sharpe. Downside deviation = √(sum of the squared returns of losing bars ÷ number of all bars). Winning and flat bars count as zero but still count in the number of bars.

Omega

Omega simply adds up every gain and every loss. Von Lohengramm T7's 303 rising bars add up to about +1,979%, its 226 falling bars to about −900% (and 334 bars it sat in cash and didn't move at all). 1,979 ÷ 900 gives an Omega of 2.20: the ups outweighed the downs a little more than two to one.

Above 1, gains outweigh losses; below 1, losses win.

Omega = sum of positive bar returns ÷ sum of the sizes of negative bar returns, with a threshold of 0. With no losing bars at all, the app shows ∞. Read that as "no losses recorded", not as a score to rank by.

Calmar

Calmar puts two numbers you already know side by side: yearly growth (CAGR) and the worst fall (Max DD). Von Lohengramm T7: 120.0% ÷ 42.9% gives 2.80. For the SOXX strategy: 29.8% ÷ 33.7% gives 0.88, less than a year of average growth for every unit of its worst fall.

Calmar is the most personal of the four, because the worst fall is what makes people quit. It's also the most fragile: a single bad stretch decides it, and a strategy that once fell 80% keeps a low Calmar however good the rest was.

Calmar = CAGR ÷ Equity max DD, both over the window shown.

Using them well

• Compare within a market. Crypto strategies swing more than gold or stock strategies and are judged against wilder markets. A Sharpe of 1.1 on chip stocks may be as impressive as 1.5 on BTC.
• Use them to break ties. Two strategies with similar CAGR and Max DD? Sort the folder by Sharpe or Sortino to see which got there more smoothly.
• Mind the window. Over one or two years, a handful of bars dominate these ratios. Over the full history they're more stable.

When you see "–"

On portfolios

Portfolios get all four ratios, worked out on their combined account line. The bars are the merged dates of all the strategies on the board, and bars per year is worked out from how densely those dates fall, so a board that mixes crypto with stock funds doesn't simply use 73. That's how a portfolio's ratios can end up higher than those of most strategies inside it: Four Pillars Index [GPS] shows a Sharpe of 1.84 and a Calmar of 3.35, because when its parts don't fall at the same time, the whole is smoother than any one of them.

Related

• Metrics at a glance
• Return and CAGR
• Drawdown
• How the backtests are built