A Sharpe ratio is a mean excess return divided by a standard deviation. The standard deviation measures how far returns are scattered from their average - nothing more. It says nothing about whether that scatter leans toward frequent small losses and one rare large gain, or the reverse: frequent small gains funding one rare large loss. Two return streams can share the same mean and the same standard deviation while having opposite shapes, and the Sharpe ratio, by construction, cannot see the difference.
Here are two twelve-month return streams, computed to match exactly:
- 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 month. Mean 1%, standard deviation 2% - identical to A - worst month -5.63%, nearly six times deeper than A’s.
Both score a Sharpe ratio of exactly 0.5.
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’s formula uses only the first two moments of a return distribution - mean and variance - and has no term for the third, skew. Two distributions with matching first two moments and opposite third moments score identically, even though one of them is concentrating its entire risk into a single tail event.
This is not a hypothetical curiosity. A body of research going back to Leland (1999) and Spurgin (2001) has shown the Sharpe ratio can effectively be gamed this way: sell away the upside, collect a steady premium, and the resulting left-skewed payoff can score a Sharpe ratio at least as attractive as a symmetric strategy earning the identical average return - right up until the rare loss arrives.
Short-volatility products lived this through the 2010s. Systematically selling insurance against market moves - collecting the “volatility risk premium” - produced Sharpe ratios researchers estimate around 0.5-0.8 across multiple decades, a conventionally attractive number. On 5 February 2018, a single-day volatility spike since nicknamed “Volmageddon” erased that record: the VelocityShares Daily Inverse VIX Short-Term ETN (XIV) fell 96% in one session and the product was delisted days later. The Sharpe ratio computed across the calm years never saw that day coming - a formula built from mean and standard deviation has no way to price in a loss that only shows up once.
None of this makes the Sharpe ratio useless. For return streams that are roughly symmetric, it remains a reasonable single-number summary. It means the number alone cannot distinguish a strategy that spreads its risk evenly from one that concentrates it into a single rare event - and two funds quoting an identical Sharpe ratio can be running entirely different kinds of risk.
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