Sharpe ratio
Quantitative Finance glossary · Quantitative Finance
Definition
Sharpe = dfracmathbbE[R_p] - r_fσ(R_p) — excess return per unit of total risk. Annualised by multiplying by √(252) from daily, √(12) from monthly (assuming iid returns). Sample Sharpe is itself a noisy estimator with standard error ≈ √((1 + 1/2S^2)/T) — for typical T and S, the 95% CI is embarrassingly wide. Penalises symmetric vol; option-selling strategies game it by trading negative skew for raised Sharpe (Sharpe is unfair to negatively-skewed returns — see Sortino).
Sharpe ratio in plain English
The Sharpe ratio answers a fair question: was an investment's return actually worth the stomach-churning it caused? You take the return ABOVE what a totally safe option (like a government bond) would've paid, then divide by how much the returns bounced around — so it's reward per unit of nerves, and bigger is better. But two catches keep experts humble: measured over a realistic number of months, the ratio is a noisy estimate, so its true value could be much higher or lower than what you compute. And it treats all bounciness as equally bad — so a sneaky strategy that usually earns a little but occasionally blows up (like selling insurance) can post a flattering Sharpe right up until the rare disaster, which is why people also look at the Sortino ratio.
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