performance-metricstatistics

Sharpe Ratio (夏普比率)

Mean excess return per unit of total volatility. The standard summary statistic for a strategy's risk-adjusted return.

Definition

For a return series r_t with mean \bar r, standard deviation \sigma, and risk-free rate r_f:

SR = \frac{\bar r - r_f}{\sigma}

Annualized by multiplying by \sqrt{P} where P is the number of periods per year (12 for monthly, 252 for daily, 52 for weekly).

Statistical properties

  • The sample Sharpe ratio has a known sampling distribution (Lo, 2002) that is not normal in finite samples — it has a positive bias and a heavy left tail.
  • For testing SR differences between two strategies, the Stationary Bootstrap is the standard tool when returns are autocorrelated (which is common for momentum and many quant strategies).
  • For testing a single SR against zero, the Jobson-Korkie test (with the Memmel correction) is the closed-form option.

Use in this wiki

The Moskowitz, Sabbatucci, Tamoni & Uhl (2025) paper reports Sharpe ratios throughout and tests differences via stationary bootstrap. The key results cited on Time-Series Momentum and CTA Strategy are:

  • Linear TSMOM (12M, daily): SR ≈ 0.70
  • Binary TSMOM (12M, daily): SR ≈ 0.83
  • FS Nonlinear TSMOM (12M, daily): SR ≈ 0.83
  • Empirical NL TSMOM (12M, daily): SR ≈ 0.84 (statistically different from others at p < 0.03)
  • Sortino ratio: uses downside deviation instead of total volatility.
  • Calmar ratio: mean return / max drawdown.
  • Information ratio: \bar r / \sigma_{r - r_b} vs. a benchmark.

See also

References

  • Sharpe, W.F. (1966). "Mutual Fund Performance." Journal of Business, 39(1).
  • Lo, A.W. (2002). "The Statistics of Sharpe Ratios." Financial Analysts Journal, 58(4).
  • Moskowitz, T.J., Sabbatucci, R., Tamoni, A., & Uhl, B. (2025). "Nonlinear Time Series Momentum." Working paper.