What Kelly Actually Is
John L. Kelly Jr., a researcher at Bell Labs, published "A New Interpretation of Information Rate" in 1956. The paper was ostensibly about information theory applied to gambling on horse races, but its result generalized immediately: given a favorable bet with known edge, there exists a single bet fraction that maximizes the expected long-run growth rate of the bettor's bankroll.
For a simple binary bet (win probability p, lose probability q = 1 − p, net odds b), the Kelly fraction is:
f* = (bp − q) / b
For a trading strategy with per-trade expected return μ and variance σ², the continuous-time analog is:
f* = μ / σ²
Either form expresses the same idea: bet more when your edge is larger; bet less when your outcome is more variable.
Why Full Kelly Breaks in Practice
The theoretical appeal of full Kelly is that it maximizes geometric growth. The practical problem is that full Kelly produces drawdowns that are punishing even in expectation, and catastrophic if the edge has been overestimated.
At full Kelly, the typical time-to-recover from a 50% drawdown is several years even for systems with strong edge. This is not a bug — it is a mathematical property of the optimum. The expected long-run growth is maximized, but the path to that growth includes periods of severe drawdown that would cause most human traders to override the system.
Worse: Kelly sizing is extremely sensitive to the edge estimate. If the true edge is half of the estimated edge, full-Kelly sizing on the estimate produces negative expected growth. In practice, edge estimates based on historical data carry substantial error bars. A strategy whose backtest shows Sharpe 1.5 may have a true Sharpe of 0.8 after deflation for overfitting, transaction costs, and regime change. Full Kelly on the inflated estimate is effectively double-Kelly on the true distribution — and double-Kelly has negative expected growth.
Fractional Kelly: The Practitioner's Choice
The standard response is fractional Kelly: size at some fraction k < 1 of the full Kelly amount, typically 0.5 (half-Kelly) or 0.25 (quarter-Kelly).
The math of fractional Kelly is encouraging. At half-Kelly, expected growth is three-quarters of full Kelly — you give up 25% of growth in exchange for roughly 50% reduction in volatility of returns. At quarter-Kelly, expected growth is 7/16 (about 44%) of full Kelly with a much smaller drawdown profile.
Edward Thorp, who pioneered the practical application of Kelly to blackjack and then to statistical arbitrage at Princeton Newport Partners, has written extensively that he operated at roughly half-Kelly in his fund. His 2007 paper on the Kelly criterion remains the clearest practitioner's treatment.
Applying Kelly to Futures Trading
Futures-specific features complicate direct application:
- Fixed contract size. You cannot size 37.8% of a position in ES. You trade 1 contract, 2 contracts, etc. For small accounts, micro contracts (MES, MNQ) give finer granularity but still discretize.
- Margin, not capital, is the denominator. Kelly's bet fraction is a fraction of wealth. For futures, what corresponds to "wealth" is debatable — full margin requirement, exchange-minimum margin, cash balance, or something else.
- Correlated trades. If a strategy takes multiple concurrent positions in correlated instruments, per-instrument Kelly sizing leads to aggregate over-exposure. Kelly must be applied to the portfolio return distribution, not trade-by-trade.
The practical adaptation most professional systematic traders use: estimate Kelly at the portfolio level, discount heavily (half or quarter) for parameter uncertainty, and cap total portfolio heat at a fraction well below the theoretical limit.
Conclusion
Kelly is the right mathematical framework for thinking about position sizing — not because full Kelly is the right answer, but because Kelly clarifies what the question is. Sizing is about maximizing long-run growth subject to surviving the short-run drawdowns implied by the sizing choice. Full Kelly maximizes growth at the cost of drawdown. Fractional Kelly sacrifices a little growth for much-better drawdown behavior and much-better robustness to edge-estimation error.
The right fraction is not universally determined; it depends on confidence in the edge estimate, tolerance for drawdown, and the strategy's correlation structure. A reasonable default for a retail futures strategy with an honestly-estimated edge: quarter-Kelly. For a system whose edge has been verified across multiple out-of-sample periods: half-Kelly. Full Kelly: almost never.
Disclaimer: FalcoAlgo is a software product of Falco Systems LLC and is not a registered investment adviser. This article is for educational purposes only and does not constitute investment, trading, tax, or legal advice. Futures trading involves substantial risk of loss. Hypothetical performance results have inherent limitations and are not indicative of future results.
