Sharpe ratio

A fund's Sharpe ratio and a trading journal's Sharpe ratio are computed from different series, and the journal's is almost always the flattering one. The reason is the days with no trades.

The formula

Sharpe = (mean daily result ÷ standard deviation of daily results) × √252

Daily results are the sum of net P&L for each day, the deviation is the sample deviation, and 252 is the conventional count of trading days in a year. Under two days there is nothing to compute and the figure is left empty.

The ratio is a signal-to-noise measurement: how large is a typical day relative to how much days vary. Higher is steadier, not necessarily more profitable — a method earning half as much with a quarter of the variation scores better.

Assumption one: it is computed on money, not returns

The textbook definition uses percentage returns. A journal has no reliable running balance — deposits, withdrawals and untracked accounts all break it — so ours divides currency by currency.

The units cancel, so the ratio is still a valid number, and it has a genuine advantage: double every position size and both the mean and the deviation double, leaving Sharpe unchanged. It measures the shape of your results rather than their scale, and it cannot be distorted by a deposit.

What it costs you is comparability. A fund's Sharpe is a return-based figure, and quoting yours next to it is comparing two different constructions.

Assumption two: the risk-free rate is zero

The full definition subtracts the risk-free rate before dividing, on the reasoning that returns you could have earned in treasury bills are not compensation for risk.

Ours does not subtract it. For a short-term trading account this is defensible — you are not holding capital for a year — but it means the figure is generous by roughly the ratio of the annual short rate to your annualised volatility. When rates are near zero the difference is nothing. When they are not, a strategy with a reported Sharpe of 0.6 may have a real one closer to 0.4.

Assumption three, and the important one: flat days do not exist

This is where a journal's Sharpe departs most from a fund's, and it is almost never stated.

The series we build contains one entry per day on which a trade closed. A day you did not trade produces no entry. A fund's daily return series includes every calendar day, and days with no activity enter as zeros.

Zeros are not neutral. They pull the mean down and they pull the deviation down too, and the two effects do not cancel. The result is that a journal Sharpe answers:

How consistent are my trading days?

while a fund Sharpe answers:

How consistent is my account, calendar day by calendar day?

For someone trading every session those questions nearly converge. For someone taking three setups a month they do not converge at all, and the journal figure is the more flattering of the two — it never sees the weeks of nothing.

The annualisation is an assumption too

Multiplying by √252 assumes days are independent and that you produce roughly 252 of them a year. Neither is guaranteed:

  • Independence. A losing day that leads to an oversized revenge day is correlated with the one before it, and the √252 scaling understates the true annual variation whenever that pattern exists. See revenge trading for what that dependence looks like in a statement.
  • Count. Trade 60 days a year and annualising by √252 inflates the figure against someone who traded all 252.

What it hides

Sharpe punishes upside and downside identically. A month of unusually large winners raises the deviation and lowers your Sharpe, which is the wrong answer to a good outcome — the objection that produced the Sortino ratio, which counts only losing days in the denominator.

It also has nothing to say about sequence. Sharpe is computed from an unordered set of daily figures, so the same days rearranged into a six-week losing run produce an identical Sharpe and a completely different account. That is what maximum drawdown is for, and the two should always be read together.

More in Trading terms, defined by how they are computed

  • Net P&LThe result of a trade after commission and swap, and why the sign convention in broker exports makes double-counting so easy.
  • Profit factorGross profit divided by gross loss, the edge case that breaks it, and why a high profit factor on few trades means almost nothing.
  • ExpectancyThe expected value of one trade, the break-even win rate it implies, and why the figure needs an error bar to mean anything.
  • R-multipleExpressing results as multiples of the amount risked, why it survives account growth, and the case where R stops being comparable.
  • Win rateWhat share of trades finished positive, how break-even trades are counted, and why the figure is uninterpretable without the win-to-loss ratio.
  • Maximum drawdownThe largest peak-to-trough fall in your account, and the measurement choice that decides whether a prop account survives.
  • Trailing drawdownA loss limit that rises with your account and usually never falls back, plus the two sentences in a rulebook that decide when it can end your account.
  • Consistency ruleA cap on how much of your profit may come from a single day or trade, why it exists, and how it turns a winning account into an unpayable one.
  • Payoff ratioThe size relationship between a typical winner and a typical loser, how break-even trades drop out of both averages, and why the realised ratio rarely matches the planned one.
  • SQN (System Quality Number)Mean R divided by the standard deviation of R, multiplied by the square root of the sample, and the two reasons the score is not comparable between accounts.
  • Sortino ratioDownside deviation instead of total deviation, the two competing conventions for computing it, and which one our implementation uses.
  • Average holding timeHow long a typical trade stays open, why open positions are excluded from the average, and the reason a disposition-effect account reports a short one.