82 / 97
Sharpe Ratio
Working definition
The ratio of a return series' mean excess return to its standard deviation — how much return was earned per unit of volatility borne, expressed as a single scalar.
The Sharpe ratio divides the mean of a return series in excess of the risk-free rate by the standard deviation of that same series. It is the most widely quoted number in quantitative finance because it does something genuinely useful: it makes two strategies with different volatilities comparable on one axis, and it refuses to reward return that was bought with proportionate risk.
Everything else about it is conditional. The statistic is annualised by multiplying by the square root of the number of periods in a year, and that scaling assumes returns are independent and identically distributed. They are not. Positive autocorrelation — from illiquid marks, smoothed valuations, or a holding period longer than the sampling interval — suppresses measured volatility and lifts the ratio without a single trade changing. Effective sample size is the correction that says how much evidence the record actually holds.
Standard deviation is also a symmetric measure applied to distributions that are usually not symmetric. A strategy that collects small premiums and occasionally pays a large one — short volatility in any of its disguises — reports a high ratio precisely because the loss has not happened yet. Skewness and excess kurtosis are invisible to the denominator, which is why they enter the deflated Sharpe ratio as explicit corrections.
And the observed value carries no information about how it was selected. Under the null hypothesis of no skill, the expected maximum across many trials is above zero, so a ratio reported without its trial count is an incomplete statistic — the problem data snooping names and the kill ledger exists to make answerable.
Why it matters
A Sharpe ratio is a summary, and every summary is a decision about what to leave out. Reading one entitles you to four questions before it means anything: over what sample, at what sampling interval, after how many trials, and net of what execution cost. A number quoted without those four describes a spreadsheet, not a market.
Commonly confused with
Neighbouring concepts that get used interchangeably, and the distinction that actually separates them.
- Deflated Sharpe ratio
The deflated version corrects the raw one for the things it silently omits — the number of trials it was selected from, and the skewness and excess kurtosis its symmetric denominator cannot see. A raw ratio and a deflated ratio computed on the same record are answering different questions.
- Volatility
Volatility is the denominator, not the risk. Standard deviation treats an upside excursion and a downside one identically, which is why a strategy that collects small premiums and occasionally pays a large one scores well right up until it pays.
- Return
A high return with proportionate risk and a modest return with little risk can produce the same ratio, which is the statistic working as intended. The failure mode is reading it backwards — a high ratio is not evidence of high return, and a strategy cannot be sized by it alone.
- Information coefficient
The information coefficient measures the correlation between a forecast and what happened. The Sharpe ratio measures the realised return per unit of volatility of a strategy that was actually run. One grades predictions, the other grades outcomes.
How to measure it in your own data
A definition you cannot test is a definition you have to take on trust. This is the shortest honest route from the concept to a number you computed yourself.
- Records you need
A return series with its sampling interval stated, the risk-free rate over the same period, and — the field almost never supplied — the number of configurations that were tried before this one was reported.
- What you compute
Mean excess return divided by the standard deviation of the same series. Annualising means multiplying by the square root of the periods in a year, which assumes returns are independent and identically distributed; check the autocorrelation before you accept that scaling, and compute the effective sample size rather than the nominal one.
- What the answer tells you
Four questions decide whether the number means anything: over what sample, at what sampling interval, after how many trials, and net of what execution cost. Positive autocorrelation from illiquid marks or smoothed valuations suppresses the denominator and lifts the ratio with no trade changing. And under a null of no skill the expected maximum across many trials sits above zero, so a ratio quoted without its trial count is an incomplete statistic rather than a good one.
Work it out yourself
Free calculators that take this concept as an input. Each shows its working, so the number it gives you can be checked rather than taken on trust.
Questions and answers
What counts as a good Sharpe ratio?
The question cannot be answered from the number alone, which is the honest and unsatisfying reply. A ratio computed on daily data over twenty years after one trial and a ratio computed on monthly data over three years after four hundred trials are not comparable quantities, even when they print the same value. Ask for the sample, the interval, the trial count and the cost assumptions before ranking anything by it.
Why does my Sharpe ratio fall when I use a shorter sampling interval?
Usually because the annualisation assumption was doing work it should not have been. Scaling by the square root of the number of periods assumes returns are independent; if they are positively autocorrelated — from a holding period longer than the sampling interval, or from marks that smooth rather than reprice — the coarser interval understated the volatility and flattered the ratio.
Can a high Sharpe ratio hide a large risk?
Yes, and the mechanism is structural rather than accidental. Standard deviation is symmetric while most return distributions are not, so a strategy whose losses are rare and large reports an excellent ratio during the period before the loss arrives. Skewness and excess kurtosis are invisible to the denominator; that is exactly why the deflated version puts them back in.
Why does the number of trials matter to a single reported ratio?
Because selecting the best result from many attempts is itself a procedure with a distribution. Under the null hypothesis of no skill, the expected maximum across many trials is above zero — so the best of four hundred configurations will look good whether or not anything real is there. A ratio reported without the trial count omits the piece of information needed to judge it.
Related terms
Derived from the links this entry makes and the entries that link back to it.
Where the term is used
Instrument pages whose published copy uses this term. Each page states what it measures and what it does not establish.
In the research
Sharpe Ratio comes up in one research note on this site.