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Metrics / Sharpe

Sharpe Ratio

4 min read · Metric

Excess return per unit of volatility, annualised. The most-quoted and most-misread number on a result card.

What it is

The Sharpe ratio measures how much return you earned per unit of volatility accepted, after netting out the risk-free rate. A Sharpe of 1.0 means one unit of excess return for every unit of return standard deviation — a rough sanity floor for systematic strategies.

Sharpe is a sample statistic, which is the source of most of its problems. Different sampling frequencies produce different Sharpes for the same equity curve; small samples produce wildly noisy Sharpes; non-normal returns make the number harder to interpret than it looks. See the Sharpe vs PSR vs DSR concept article for the deflated versions that fix these problems.

Formula

# Daily returns, annualised
sharpe = (mean(r_daily) - r_f_daily) / std(r_daily) * sqrt(252)

# Monthly returns, annualised
sharpe = (mean(r_monthly) - r_f_monthly) / std(r_monthly) * sqrt(12)

# r_f is the risk-free rate over the same period

The sqrt(N) term annualises — it converts whatever the native sampling frequency is into the common annual unit. Without it, daily Sharpe and monthly Sharpe can't be compared.

Typical ranges

  • SPY long-run: 0.4–0.6.
  • Decent systematic strategy: 0.7–1.2 net of costs.
  • Strong: 1.5–2.0 sustained over multi-year samples.
  • Above 2.5 on short samples: almost certainly noise or selection bias. The same parameters won't hold up over longer windows.
  • Above 4.0: a Renaissance-tier claim. Treat with extreme skepticism — usually look-ahead bias, capacity-limited HFT, or fitted to a brief regime.

Common mistakes

  • Not annualising. Daily Sharpe of 0.07 sounds awful but annualises to 1.1 (×sqrt(252)). Always state whether the number is annualised.
  • Comparing across frequencies. A strategy with great daily Sharpe and weak monthly Sharpe is harvesting short-horizon noise — the daily number flatters via mechanical aggregation.
  • Ignoring skew and kurtosis. Two strategies with identical Sharpe but very different return distributions are very different bets. A negative-skew strategy with a 1.5 Sharpe blows up occasionally; a positive-skew 1.5 Sharpe is more comfortable.

What the platform flags

Quantis always shows Sharpe alongside PSR (probability the true Sharpe is > 0 given sample noise) and DSR (PSR adjusted for the candidate variants tested). On a small sample, a Sharpe of 1.5 with PSR 70% is much weaker evidence than the headline implies. The deflated versions are the trust pills, not the headline itself.

Further reading