Noon Barbari
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Statistiques

Sortino ratio

Sharpe variant that penalizes only downside volatility, not total volatility.

The Sortino ratio, proposed by Frank Sortino in the 1980s, is a refinement of Sharpe that divides excess return by the downside deviation only — the standard deviation of returns below a target (usually zero or the risk-free rate).

Sortino rewards strategies with positive skew: a system that rarely loses but occasionally jumps higher gets a much better Sortino than Sharpe. It is more honest about the asymmetry between gains and losses that real traders care about.

Downside deviation is annualized the same way as ordinary volatility: multiply by √N (e.g. √252 for daily data). Note that with very few downside observations the estimate is noisy — Sortino is most informative on long return histories.

Formule

Sortino = (E[R_a] − R_f) / σ_down(R_a)
σ_down = sqrt(mean(min(R_a − R_target, 0)^2))

Exemple

Returns 18%, risk-free 2%, downside deviation 7%. Sortino = (18 − 2) / 7 ≈ 2.29. Strategy is genuinely positively skewed.

Comment Noon Barbari utilise Sortino ratio

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