TradingCalcSharpe Ratio Calculator
RISK/STATS · SHARPE RATIO · ADVANCED
Sharpe ratio with the Lo (2002) serial-correlation-aware annualization correction, plus the Probabilistic Sharpe Ratio (Bailey & Lopez de Prado). Not just the naive sqrt(q) scaling.
Comma, space, or newline separated. No thousand separators (write 43250.50, not 43,250.50).
365 = crypto convention (trades every day). Benchmark Sharpe is per-period, same frequency as your returns, used only for the Probabilistic Sharpe Ratio (PSR) below.
The formula
Lo (2002)'s correction replaces the naive sqrt(q) annualization with a factor that accounts for lag-1 serial correlation:
- eta(q) = q / sqrt(q + 2(q−1) × ρ₁)
- SR_annualized = SR_periodic × eta(q)
The Probabilistic Sharpe Ratio (Bailey & López de Prado, 2012) then answers a different question: given this sample's length, skewness, and kurtosis, how confident can you be the TRUE Sharpe exceeds a benchmark?
Worked example
Monthly Sharpe of 0.5, periods-per-year 12, lag-1 autocorrelation 0.3:
- eta(12) = 12 / sqrt(12 + 2×11×0.3) = 12 / sqrt(18.6) ≈ 2.78
- Lo-corrected annualized Sharpe = 0.5 × 2.78 ≈ 1.39
- vs. the naive figure: 0.5 × sqrt(12) ≈ 1.73 (overstated)
Where to go next
Sharpe only measures reward per unit of total volatility. For a downside-only view, or the full risk picture in one call, see the portfolio tearsheet (which includes both Sharpe figures plus Sortino, drawdown, and Calmar), or check tail risk directly with the VaR / CVaR calculator.
Use via API or MCP
This calculation is available as a deterministic API call for bots and AI agents.
Why is the naive sqrt(q) annualization wrong?
Multiplying a periodic Sharpe ratio by the square root of periods-per-year only gives the correct annualized figure when returns are independent (no serial correlation). Andrew Lo's 2002 paper "The Statistics of Sharpe Ratios" showed real strategies routinely have autocorrelated returns, and the naive scaling can overstate the true annualized Sharpe by a wide margin.
What does the Lo correction actually change?
It replaces sqrt(q) with an adjustment factor that accounts for lag-1 serial correlation: eta(q) = q / sqrt(q + 2(q-1)*rho_1). Positive autocorrelation shrinks the annualized Sharpe versus the naive figure; negative autocorrelation inflates it.
What is the Probabilistic Sharpe Ratio (PSR)?
A statistic from Bailey & Lopez de Prado (2012) that answers a different question than the Sharpe ratio itself: given this sample's length, skewness, and kurtosis, how confident can you be that the TRUE Sharpe ratio actually exceeds a benchmark? Two strategies can report the identical Sharpe ratio while having very different statistical confidence behind that number.
Why do skewness and kurtosis matter for the Sharpe ratio's reliability?
The Sharpe ratio's own sampling distribution is normal only under specific assumptions. Negative skew or fat tails (excess kurtosis) widen the estimator's true uncertainty beyond what a plain standard error would suggest: PSR's denominator directly incorporates both.
What periods-per-year should I use for crypto?
365 is the standard crypto convention, since crypto markets trade every day (unlike traditional markets' ~252 trading days). Use whatever matches your actual return frequency: 365 for daily returns, 52 for weekly, 12 for monthly.