Sharpe Ratio Explained: What the Number Actually Tells You

Two strategies can report the same return for the year and be nothing alike. One earned it in a straight line, the other by surviving a stretch that would have closed most accounts. The Sharpe ratio separates those two cases by dividing what a strategy earned above a benchmark by how much that surplus varied.

The formula fits in a spreadsheet cell, which is part of the trouble. It gets quoted without the three conditions that decide whether the answer means anything: which version was computed, what interval it was measured on, and how many observations stand behind it. The depth of a decline is left to our maximum drawdown page.

What the Ratio Actually Divides

The numerator is a differential return: the return of the thing measured minus the return of whatever it is compared against. The denominator is the standard deviation of that same difference.

Both halves refer to the difference, not the raw return, because the variability of a difference is not that of either part alone. The benchmark was originally a riskless rate, which is why the numerator is often called excess return; the 1994 revision generalised it to any benchmark.

Ex Ante and Ex Post Are Two Different Measures

Sharpe defined two versions in the same paper and said plainly that he did so to avoid ambiguity. Explanations aimed at traders rarely mention that there are two.

The ex ante ratio uses an expected differential return and a predicted standard deviation. It is a forecast, and the paper treats it as the version for decisions.

The ex post ratio uses the historic average and standard deviation of returns that already happened. The paper is explicit that the two carry different roles: the historic version is the one that actually gets computed, while the forward-looking one is what the theory is about.

Every ratio printed by a platform or shown on a track record is the ex post one. Treating it as a forecast is the most common misuse of the figure.

A Sharpe Ratio Without a Return Interval Is Not a Number

Sharpe headed a section Time Dependence: the ratio is not independent of the period over which returns are measured. Feed the same account in using daily returns, then weekly, then monthly, and three different ratios come out. No trade changed, only the sampling.

The usual repair is to annualise, scaling by the square root of the number of periods in a year. Sharpe described that as common practice which can provide reasonably meaningful comparisons, and attached conditions to it, including the possibility that returns are serially correlated.

That is a convention, not an identity. It holds when returns are independent from one period to the next, and an equity curve that trends or mean-reverts breaks it. A ratio quoted with no interval cannot be checked.

Why Leverage Cannot Improve It

Sharpe titled a section Scale Independence and proved the result inside it. Trading a position larger multiplies the average differential return and its standard deviation by the same factor, so the quotient is unchanged.

So the intuition that a good strategy can be made to look better by trading it larger is arithmetically wrong. Numerator and denominator move together.

What leverage changes is everything the ratio is silent about: how far the account falls, how close it comes to a stop out, and whether it survives to collect the average. That is why the figure belongs next to an account-level loss limit rather than instead of one, as our risk management page sets out.

How Long a Record Has to Be Before the Figure Means Anything

Sharpe drew the link to significance testing himself. Multiply the historic ratio by the square root of the number of returns behind it, and the product is the t-statistic of the mean differential return.

Turned around, at the conventional two-standard-error threshold and working in monthly returns, the months required come out at roughly forty-eight divided by the square of the annualised ratio.

A modest but genuine edge takes years of monthly data to demonstrate, which is why most published track records are too short to establish the number they advertise.

The bottom row cuts the other way: a very high ratio clears the threshold on little data, so that is where a short record and a lucky stretch are hardest to tell apart. Serial correlation makes every figure optimistic.

Where the Figure Comes From in a Platform Report

MetaTrader 5 exposes it in the strategy tester as a named statistic, STAT_SHARPE_RATIO, listed in the MQL5 documentation beside the recovery factor and the profit factor. It sits in the same block of results as the drawdown figures, which is the company it should be read in.

Because the platform builds it from its own internal series, a spreadsheet on monthly closing balances will rarely agree; the difference is the interval. The same holds for a backtest result, where the ratio inherits every assumption of the test, including its costs and data quality.

When the Ratio Understates the Risk

Standard deviation measures dispersion in both directions. A month far above average widens it as much as one far below, so the denominator penalises a strategy for its best periods as well as its worst.

For roughly symmetric returns that is fair. For returns that are not, it misleads in a specific and dangerous way. A strategy that collects small gains and loses heavily but rarely produces a long run of low-variance months: the denominator stays small, the ratio looks excellent, and nothing warns about the loss that has not happened yet.

The Sortino ratio replaces the denominator with downside deviation so only shortfalls count: not a better measure but a different question, and on symmetric returns it adds nothing.

Who This Page Is Not For

It is not for anyone looking for a threshold. The bands in circulation, in which one is called good and three exceptional, appear repeatedly without a traceable source, and none is offered here. Nor is it a method for choosing between strategies: the ratio discards the path, the duration of the losses and the shape of the distribution.

It does not evaluate the rules attached to an evaluation programme, where the binding constraint is usually a loss limit rather than a performance statistic; those are set out under funded account programmes. What it is for is knowing what a quoted ratio can support: which version, on what interval, over how many observations.

Frequently Asked Questions