Burke Ratio: Return Over Squared Drawdowns

Key Takeaways

• The burke ratio divides excess return by the square root of the sum of every squared drawdown.
• Squaring drawdowns penalizes a few deep losses far more than many shallow ones.
• A modified version divides the squared sum by the number of observations to compare across sample sizes.
• It makes no assumption about the shape of the return distribution, unlike volatility-based ratios.

What It Is

The burke ratio is a drawdown-based performance measure introduced by Gibbons Burke. Like the Sharpe ratio, the numerator is excess return, the portfolio return minus the risk-free rate. The difference is the denominator.

Instead of standard deviation, the burke ratio uses the square root of the sum of squared drawdowns, where a drawdown is each peak-to-trough decline in the equity curve. By squaring each drawdown before adding them, the measure gives outsized weight to the deepest losses. Two small dips count for little, but one large crash dominates the score.

The burke ratio is most common in managed futures and systematic trading reports, where capital preservation through bad stretches is the priority.

The Intuition

A trader can survive many small setbacks. What ends careers is the single catastrophic drawdown. The burke ratio is built around that reality.

Squaring is the trick. If one strategy has drawdowns of 5 percent and 5 percent, and another has a single 10 percent drawdown, both lose the same total, but the second has a larger squared sum. The math says a concentrated big loss is worse than the same loss spread thinly, which matches how investors actually feel about risk.

How the Burke Ratio Works

The standard formula is:

Burke Ratio = (Rp - Rf) / sqrt(sum of Dt^2)

Where Rp is the portfolio return, Rf is the risk-free rate, and Dt is each individual drawdown in the series.

The modified burke ratio scales the denominator by the number of return observations, which lets you compare track records of different lengths:

Modified Burke Ratio = (Rp - Rf) / sqrt((sum of Dt^2) / n)

A higher burke ratio is better. Because the denominator grows quickly when drawdowns deepen, the ratio falls sharply for strategies that take large hits, even if their average return looks attractive.

Worked Example

A strategy returns 15 percent over a period while the risk-free rate is 3 percent, so excess return is 12 percent. Across the period it experienced three drawdowns: 8 percent, 5 percent, and 12 percent.

Square each drawdown and sum them:

sum of Dt^2 = 0.08^2 + 0.05^2 + 0.12^2 = 0.0064 + 0.0025 + 0.0144 = 0.0233

Take the square root:

sqrt(0.0233) = 0.1526

Now the burke ratio:

Burke Ratio = 0.12 / 0.1526 = 0.79

If that 12 percent drawdown had instead been 20 percent, the squared sum jumps to 0.0489, its square root to 0.221, and the ratio falls to 0.54. A single deeper loss cut the score by roughly a third, which is the squaring penalty in action.

Common Mistakes

1. Mixing the standard and modified versions. The modified ratio divides by the number of observations and produces a different number. Comparing one fund's standard ratio to another's modified ratio is meaningless.
2. Counting drawdowns inconsistently. Some implementations use only the largest drawdowns, others use every recovery cycle. The denominator changes with the rule, so define it before comparing.
3. Assuming it replaces volatility measures. The burke ratio ignores upside variability entirely. A strategy with violent but profitable swings can score well even if its path feels wild.
4. Using a tiny sample. With only one or two drawdowns the squared sum is unstable and the ratio swings on a single event. It needs a meaningful history.
5. Reading it as an absolute grade. There is no universal "good" burke ratio. It is a relative tool for ranking similar strategies over the same window, not a pass-fail threshold.

Frequently Asked Questions

What is the burke ratio in simple terms? The burke ratio compares a strategy's excess return to the combined size of all its drawdowns, with deeper losses weighted more heavily. A higher number means better return for the drawdown pain taken.

How does the burke ratio affect investment decisions? It helps rank strategies when avoiding deep losses matters more than smoothing every wiggle. Because it punishes large drawdowns disproportionately, it favors managers who keep their worst losing stretches contained.

What is a real-world example of the burke ratio? A strategy with 12 percent excess return and drawdowns of 8, 5, and 12 percent scores about 0.79. If the worst drawdown widens to 20 percent, the score drops to roughly 0.54, even though average return is unchanged.

How can investors use the burke ratio effectively? Confirm whether the figure is the standard or modified version, and check how drawdowns were counted. Then compare only strategies of similar style measured over the same period.

How is the burke ratio different from the sterling ratio? The sterling ratio divides return by the average annual maximum drawdown, treating each year's worst loss equally. The burke ratio sums squared drawdowns across the whole series, so it punishes a single deep crash much harder.

Sources

1. PerformanceAnalytics. "BurkeRatio." RDocumentation. https://www.rdocumentation.org/packages/PerformanceAnalytics/versions/2.0.4/topics/BurkeRatio
2. PerformanceAnalytics. "Burke ratio of the return distribution." https://timelyportfolio.github.io/PerformanceAnalytics/reference/BurkeRatio.html
3. Turing Finance. "Measures of Risk-adjusted Return." http://www.turingfinance.com/computational-investing-with-python-week-one/
4. JFE Package. "BurkeRatio." R-project CRAN. https://search.r-project.org/CRAN/refmans/JFE/html/BurkeRatio.html

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.