A Sharpe ratio is read as a measure of risk-adjusted return. It is a measure of return per unit ofdispersion, and dispersion is not the same thing as risk once a return stream stops being symmetric.
The ratio divides mean excess return by standard deviation. Standard deviation measures how far returns scatter from their average and nothing else - it carries no information about whether that scatter leans toward frequent small losses and one rare large gain, or the reverse. What follows constructs two return streams that match on both inputs and differ entirely in shape.
Two Streams, Identical on Both Inputs
- Strategy A: alternates +3% and -1% every month. Mean 1%, standard deviation 2%, worst month -1%.
- Strategy B: +1.60% in eleven months, -5.63% in one. Mean 1%, standard deviation 2% - identical to A - worst month -5.63%, nearly six times deeper.
Both score a Sharpe ratio of exactly 0.5. An allocator screening on that number alone has no basis for preferring either.
The Formula Has No Term for the Third Moment
Strategy A is symmetric. Strategy B is left-skewed: a small, more-likely-than-not gain most months, funded by the chance of one large loss. The Sharpe ratio uses only the first two moments of a distribution - mean and variance - and has no term for the third. Distributions matching on the first two and opposing on the third score identically, however differently their risk is arranged.
This is a structural property rather than an estimation problem, and it does not improve with a longer sample. Mixtures of two Gaussians alone generate an unlimited family of non-normal distributions sharing a single Sharpe ratio. Higher moments do not move the point estimate at all; what they move is the confidence one can have that the estimate reflects skill rather than the shape of the payoff.
The Ratio Can Be Manufactured Deliberately
Research going back to Leland (1999) and Spurgin (2001) established that this is exploitable rather than merely theoretical. Sell away the upside, collect a steady premium, and the resulting left-skewed payoff scores a Sharpe ratio at least as attractive as a symmetric strategy earning the same average return - until the rare loss arrives.
Bailey and Lopez de Prado’s Deflated Sharpe Ratio was built to address both failure modes at once: it corrects the uncertainty around the estimate using skewness and kurtosis, and it adjusts for the fact that a reported ratio is usually the winner of many trials rather than a single independent test.
Volmageddon Is the Worked Example
Short-volatility products lived this through the 2010s. Systematically selling insurance against market moves produced Sharpe ratios researchers estimate around 0.5 to 0.8 across multiple decades - a conventionally attractive number, and an accurate one for the period measured.
On 5 February 2018 a single-day volatility spike erased that record. The VelocityShares Daily Inverse VIX Short-Term ETN fell 96% in one session and was delisted days later. No Sharpe ratio computed across the preceding calm years could have anticipated it, because a statistic built from mean and standard deviation has no mechanism for pricing a loss that occurs once.
What This Means for Allocators
Ask for the third and fourth moments alongside the ratio. Skewness and kurtosis are cheap to compute from the same return series and answer the question the Sharpe ratio structurally cannot.
Treat an attractive Sharpe on a short-volatility or premium-selling strategy as a description of the sample rather than of the strategy. The number is not wrong; it is answering a narrower question than the one being asked of it.
And read the worst month next to the ratio. Two funds quoting an identical Sharpe can be running entirely different kinds of risk, and the drawdown column is where that difference first becomes visible.
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