Sharpe Ratio: It Penalises Good Surprises
The Sharpe ratio divides a return above what cash pays by the standard deviation of those returns, giving a reward-per-unit-of-variability figure. Because it uses total variability, it penalises upside movement exactly as much as downside, and it assumes a distribution returns do not follow.
How it works
The Sharpe ratio is a fraction. Return minus the rate paid on cash on top, the standard deviation of those returns underneath.
Subtracting what cash pays is the part people skip. A 6% return when cash pays 5% is not the same achievement as 6% when cash pays nothing, and the ratio is built to make that difference visible.
It exists to make returns comparable. A method returning 30% with wild swings and one returning 12% steadily cannot be ranked by return alone, and the ratio is one attempt at a common scale.
Two structural problems
Standard deviation counts every deviation, in both directions. A method that occasionally returns far more than usual is penalised for it, identically to one that occasionally loses far more.
The second problem is the distribution. On this site’s shared 576-bar history, 8 of the 575 bar-to-bar moves exceeded three standard deviations.
A normal distribution across that many observations implies fewer than two. The measured shares within one, two and three deviations were 74.1%, 93.2% and 98.6% against the bell curve’s 68.3%, 95.4% and 99.7%. A ratio built on a distribution that understates its own tails understates the risk it is measuring, which is the substantive criticism of it.
And a smooth curve can be produced deliberately. Strategies that make small amounts consistently and lose large amounts rarely report excellent ratios right up until the rare event, because the denominator only sees what has already happened.
In practice
Costs come off the top line. They reduce the return without necessarily changing the variability, so a high-turnover method’s ratio falls further than its equity curve suggests.
The input is an equity curve. Price, volume and market conditions are all irrelevant to the calculation, which is both its generality and its blind spot.
Annualising uses the square root of time, which assumes periods are independent. A daily ratio multiplied by the root of 252 overstates the annual figure where returns are serially correlated.
A single gap can dominate the denominator because deviations are squared, so one event can halve a reported ratio for the period containing it.
No stop changes it directly. Stops cap individual trades; the ratio describes the distribution of period returns, and the lever that moves it is position size.
Turnover is the quiet drag. At 2% of a median bar’s range per round trip on this history, an active method spends a meaningful share of its numerator before the ratio is computed.
One more figure belongs beside it, and it comes from this site’s own corpus. Of the 31,760 trading and investing videos studied, exactly 1 has “sharpe ratio” in its title, against 258 videos for “backtest” at a median of 3,630 views. The measure that decides whether a result is worth anything is almost absent from the material teaching people to produce results.
That gap is worth naming rather than complaining about. A backtest produces a curve, which is photogenic; a ratio produces a number that usually says the curve is less impressive than it looks. Compute it anyway - it takes one line beside any equity curve you already have.
What to read alongside it
Two numbers fix most of its blind spots. The maximum drawdown says how bad the worst moment was, which the ratio never reports; the ulcer index says how long the account spent below its peak, which the ratio also never reports.
And the sample period has to be stated with the figure. A ratio computed over three years of one regime is a description of that regime. A Sharpe ratio quoted without a period, a drawdown and a trade count is not a performance claim — it is one number from a table, chosen because it was the most flattering.
What the Sharpe ratio is not
It is not a measure of downside risk. It counts both directions.
It is not distribution-free. The bell curve is assumed.
It is not comparable across periods. Length and regime both matter.
And it is not gameable-proof. A smooth curve is easy to construct.
When it fails
A nearly flat equity curve produces a small denominator. In a range a method that grinds out almost nothing with almost no variability can report a respectable ratio while earning less than cash, which is the arithmetic working exactly as specified and telling you nothing useful.
The second failure is a short sample. Fewer than a hundred periods and the figure is mostly noise.
A third is comparing across strategies with different return shapes. An options seller and a trend follower are not on the same scale here.
A fourth is ignoring the cash rate. It changes, and a ratio computed against the wrong one is wrong.
And a fifth is treating a high figure as a recommendation. It says variability was low relative to return, on the sample measured.
The original data
Of the 31,760 videos in this site’s corpus, 1 has “sharpe ratio” in the title against 258 for
“backtest” at a median of 3,630 views; the counts are in research/corpus-coverage.json. On this site’s
shared 576-bar history the 575 bar-to-bar returns have a mean of 0.0068% and a standard
deviation of 0.347%. Measured shares within one, two and three deviations were 74.1%, 93.2% and 98.6%
against the normal distribution’s 68.3%, 95.4% and 99.7%, with 8 moves beyond three deviations. The maximum
drawdown was 3.76% and the ulcer index 1.67%. The figures are in research/series-measurements.json,
produced by site/measure_series.py.
The tail count is the specific reason to distrust a high ratio. Eight three-deviation moves where the model allows fewer than two means the denominator was computed from a distribution that does not describe the data — and every reported figure inherits that error. Ask for the drawdown and the trade count whenever you are shown a Sharpe ratio; those two numbers answer the questions it cannot, and a claim that survives all three is worth considerably more than one that survives only the first.
Related
Standard deviation is the denominator and its assumptions. Ulcer index penalises only downside persistence. And drawdown is the number to demand alongside any ratio.
I use it as a screening number and never as a verdict. A method with a high ratio and a shape I would not want to hold is still a method I would not want to hold. Where it genuinely helps is stopping me from being impressed by a return that came with variability I had not looked at.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.