Financial Modeling
Sterling Ratio & Burke Ratio: Multi-Drawdown Risk-Adjusted Portfolio Return
Evaluate CTA and hedge-fund drawdown resilience across multiple historical drawdown episodes using both the classical +10%-buffered Sterling Ratio and quadratic-penalty Burke Ratio.
Why single-trough Calmar is fragile and how Sterling and Burke penalize repeated drawdowns
Because the Calmar Ratio divides annualized return solely by the single worst historical drawdown, two funds with identical -12% worst troughs score identically even if Fund A suffered one brief dip in 5 years while Fund B endured four -11% drawdowns. Worse, extending the track record can never shrink historical Max Drawdown.
Deane Sterling Jones’s Sterling Ratio averages the N largest distinct drawdown magnitudes Avg_DD and adds a 10% (0.10) tail cushion in the denominator: (CAGR - R_f) / (Avg_DD + 0.10) (alongside the modern unbuffered variant (CAGR - R_f) / Avg_DD). Gibbons Burke (1994) replaced linear averaging with the root-sum-of-squares of drawdowns—(CAGR - R_f) / SQRT(SUM(DD_i^2))—so severe drawdowns carry quadratic weight.
| Multi-Drawdown Metric | Formula (CAGR=21%, Rf=4%, DDs=[6%, 8%]) | Result |
|---|---|---|
| Annual Excess Return | CAGR - R_f | 0.1700 (17.00%) |
| Average Drawdown Magnitude | AVERAGE(ABS(DD_1..DD_k)) | 0.0700 (7.00%) |
| Classical Sterling Ratio (+10%) | (CAGR - R_f) / (Avg_DD + 0.10) | 1.0000 |
| Burke Ratio (Quadratic RSS) | (CAGR - R_f) / SQRT(SUM(DD_i^2)) | 1.7000 (RSS = 10.00%) |
Classical (+10% Buffered) & Unbuffered Sterling Ratio Formula
Take ABS of drawdown inputs so negative (-0.06) and positive (0.06) conventions yield identical ratios.
=ROUND((E2 - E3) / (AVERAGE(C2:C3) + 0.1), 4)Burke Ratio (Quadratic Drawdown Root-Sum-of-Squares) Formula
Divide annualized excess return E2 - E3 by SQRT(SUMPRODUCT(C2:C3 ^ 2)) to penalize deep outlier drawdowns quadratically.
=IF(SUMPRODUCT(C2:C3 ^ 2) = 0, "NO_DRAWDOWN", ROUND((E2 - E3) / SQRT(SUMPRODUCT(C2:C3 ^ 2)), 4))Try the example
Use the original values or change them to test your understanding.