TL;DR. Kelly Fraction is the position-size multiplier that maximizes long-run geometric return. It's mathematically optimal but emotionally brutal — drawdowns at full Kelly are roughly the size of average gains. Half-Kelly captures about 75% of Kelly's growth at half the drawdown variance and is the size most professional traders actually use.
What you'll be able to do
- Read the Kelly multiplier on the Sizing panel and translate it into a position size.
- Explain why sizing above Kelly decreases geometric return even though arithmetic return keeps rising.
- Choose between full Kelly, half-Kelly, and the practical alternatives based on your specific risk tolerance.
The intuition: arithmetic vs. geometric
A coin-flip game pays 2:1 on heads, 1 on tails. Every flip, you bet some fraction of your bankroll. What fraction maximizes your long-run wealth?
Naive answer: bet everything. Every flip has positive expected return, so a bigger bet means more expected return.
Reality: bet everything once and tails ends the game. Even bet 90% — a single tails leaves you with 10% of your starting bankroll, and the math is brutal from there.
The right answer is the Kelly Fraction: bet (bp − q) / b of your bankroll where p is win probability, q = 1 − p is loss probability, and b is the payoff multiple. For the coin-flip game with 2:1 payoffs and 50% win probability, Kelly is 25% of bankroll per flip.
Why? Because optimizing arithmetic return is the wrong objective. What you actually care about is geometric return — the compound growth rate of your bankroll over many flips. Kelly is the fraction that maximizes geometric return. Bet less than Kelly and you grow slower. Bet more than Kelly and you also grow slower, because the variance penalty exceeds the additional upside.
That last part is counterintuitive enough to be worth restating. Sizing above Kelly is worse than sizing at Kelly for long-run geometric growth. Not "more risky" — worse on the metric you care about.
Kelly for trading
The coin-flip case has a closed form. Real trading doesn't — per-trade returns aren't binary, they're drawn from a continuous distribution. The general Kelly formulation for trading is:
f* = arg max E[ log(1 + f × R) ]
Where f is the fraction-of-bankroll multiplier and R is per-trade return. The platform computes this numerically by sweeping f across a range of multipliers (0.25× to 3× of current size by default) and finding the one that maximizes the geometric return of the bootstrap-resampled equity curves.
The result is reported on the Sizing panel as the Kelly Multiplier — a number like 1.4× or 0.8× that you multiply your current position size by to reach the geometric-optimal size.
What the platform actually computes
The Robustness Lambda's stationary block bootstrap produces ten thousand alternate equity curves. For each candidate multiplier, the platform applies the multiplier to per-trade PnL (with appropriate slippage scaling — see Sqrt-law Market Impact) and computes the geometric return of the resulting paths.
The multiplier with the highest geometric return is the Kelly Fraction. The platform also reports the half-Kelly multiplier (literally Kelly ÷ 2) because that's the practical recommendation for most users.
Why full Kelly is too aggressive
The math says full Kelly maximizes geometric return. The practice says full Kelly is too aggressive for almost any human to actually trade.
The reason is that drawdowns at full Kelly are roughly the size of the strategy's average gain. If your strategy averages 20% annual return at 1× sizing, full Kelly sizing produces a strategy that can sit 20% below peak for months at a time as part of normal variance. Most traders can't sit through that, even when they intellectually understand it's optimal.
Specifically, at full Kelly:
- The expected drawdown is large enough that you'll be drawn-down most of the time you're trading.
- The probability of a drawdown exceeding the expected annual return in any given year is around 50%.
- The asymmetry of compounding means a 30% drawdown at full Kelly requires the strategy to substantially exceed its expected return just to break even.
These properties are mathematically optimal for someone with a literally infinite horizon and no psychological constraints. For real traders, they produce an experience that's correlated with quitting.
Why half-Kelly is the right answer for most
Half-Kelly cuts the size in half. It produces:
- About 75% of full Kelly's expected geometric return.
- About 50% of full Kelly's drawdown variance.
- A dramatically lower probability of psychologically-driven exits.
The math: geometric return is a parabolic function of position size around Kelly. Half-Kelly sits halfway down that parabola, which costs about a quarter of the maximum but reduces the variance penalty quadratically. The trade is almost always worth it.
Most professional traders settle on something between half-Kelly and Kelly — typically around 60-70% of full Kelly. The platform reports half-Kelly explicitly as a UI marker because it's the empirically defensible recommendation, but the broader truth is that fractional Kelly (any fraction less than 1) is what's actually deployed.
In AlgoLift
Kelly is the headline number on the Sizing panel:
- The Kelly multiplier KPI — a single number like 1.42× that you can apply directly to your current size.
- The Half-Kelly multiplier KPI — half of Kelly, color-coded cyan to distinguish from the emerald Kelly.
- Vertical markers on the sizing frontier chart — both Kelly and half-Kelly are shown as reference lines so you can see where they sit relative to current size and the P(ruin) curve.
Kelly + Half-Kelly markers on the Sizing frontier
Reading the Kelly multiplier
| Kelly mult | Reading | Action |
|---|---|---|
| Above 2× | Significant headroom — you're undersized. | Consider scaling up, but only past Half-Kelly if your psychology can handle the variance. |
| 1.2–2× | Modest headroom. | Half-Kelly puts you at 0.6–1× — usually a good fit. |
| 0.8–1.2× | Near optimal at current size. | Stay put. Marginal upside from rebalancing is small. |
| Below 0.8× | You're overleveraged. | Scale down to Half-Kelly or below. Geometric return is suffering from variance. |
The "overleveraged" case is the surprising one and the one users most often dismiss. If your Kelly multiplier is 0.5×, your current sizing is twice the geometric-optimal. That's not "Kelly says you can take more risk" — it's "you're already past optimal and losing growth to variance."
Worked example
Two strategies, two Kelly profiles
What this shows. Strategy A has room to grow. Kelly says scale up to 1.6×, Half-Kelly says 0.8× — most users would land at half-Kelly for the variance reduction. Strategy B is the surprise: the strategy is already deployed at 2× and its Kelly is 0.7×, meaning the current sizing is nearly 3× past geometric-optimal. The geom return at current 2× is much lower than what the strategy would earn at half-Kelly. Sizing down improves long-run growth, which is the most counterintuitive Kelly result and exactly the one this strategy needs to internalize.
Common misunderstandings
- "Kelly assumes I know my edge perfectly." True — and it's why the platform reports Kelly from the bootstrap-resampled distribution rather than the original backtest. The resampling provides confidence intervals around the strategy's edge estimate, and Kelly is computed against the distribution rather than the point estimate. Still, edge estimation error is the largest source of Kelly mismeasurement in practice.
- "My Kelly is 5× — I should size up massively." Almost certainly wrong. A Kelly that high usually indicates an issue with the edge estimate (insufficient sample, in-sample overfitting, or large bid-ask hidden cost). Cross-check with Path Stability, Edge Concentration, and DSR before acting.
When Kelly is most useful
- Sizing-up decisions. When the question is "should I trade more contracts?" Kelly is the right primary input.
- Comparing strategies for capital allocation. Two strategies with similar Sharpes can have very different Kelly multipliers, and the higher-Kelly one is the better growth allocation per unit of risk.
When it matters less
- Single-allocation trading. If you're trading one contract of a futures strategy because that's the unit you can afford, the Kelly multiplier is informational only.
- Strategies with negative edge. Kelly mechanics assume positive expected value. For strategies with negative or marginally-positive expectancy, Kelly produces nonsense and the right answer is "don't trade this."
Kelly Fraction is the geometric-growth-optimal position size. Full Kelly is correct but psychologically brutal; Half-Kelly captures most of the growth at half the variance and is the practical recommendation. Sizing above Kelly hurts long-run wealth — it's not "aggressive," it's wrong.