On a $p=0.55$, $b=1.40$ edge, raw Kelly is 22.86% of bankroll and quarter-Kelly is 5.71% — but a 3% per-trade cap binds, so the sized bet is 3%. Run through the Kelly Sizer on 3,000 Monte Carlo paths over 300 trades (seed 41), the capped-Kelly bet produces a median terminal multiple of 14.5x with a 22.8% median drawdown. A flat 2% fixed-fractional bet on the identical scenario produces a median of 6.2x with a 15.7% drawdown. Kelly wins decisively on growth; fixed fractional wins on a tighter drawdown distribution and on insensitivity to mis-estimated edge. For LLM-derived edges with noisy $p$, the choice is not aesthetic — fixed fractional is the right default below ~500 paired observations, where the win rate that feeds Kelly is itself the least trustworthy number in the system.
TL;DR
- Scenario: $p=0.55$, $b=1.40$, 300 trades, 3,000 Monte Carlo paths, 3% per-trade cap, seed 41.
- Raw Kelly: 22.86% of bankroll. Quarter-Kelly: 5.71%. The 3% cap binds, so the sized bet is 3%.
- Capped-Kelly bet (3%): median 14.5x, drawdown median 22.8%, P95 drawdown 34.7%, ruin rate 0% (50% threshold).
- Fixed-fractional 2%: median 6.2x, drawdown median 15.7%, P95 drawdown 24.4%, ruin rate 0%.
- Kelly's edge is growth (14.5x vs 6.2x) and it dominates the wealth tails. Fixed fractional's edge is a materially tighter drawdown distribution and robustness to a mis-estimated $p$.
- For LLM signals with $<500$ paired live observations: fixed fractional. Above: quarter-Kelly with a hard cap is defensible.
The scenario
A retail momentum strategy reports $p = 0.55$ win rate and $b = 1.40$ payoff ratio on a backtest. The full-Kelly fraction is $(0.55 \times 1.40 - 0.45)/1.40 = 0.2286$, so raw Kelly is 22.86% and quarter-Kelly is 5.71%. With a 3% per-trade cap, the cap binds and the actual sized bet is 3%. The Kelly Sizer on 3,000 Monte Carlo paths through 300 trades, seed 41, returns this for the capped-Kelly bet; the "Fixed 2%" column is the same engine and seed run with the cap set to a constant 2% bet:
| Metric | Capped Kelly (3%) | Fixed 2% |
|---|---|---|
| Bet fraction | 3.00% (raw 22.86%, quarter 5.71%, cap binds) | 2.00% (always) |
| Median final wealth | 14.50x | 6.22x |
| P5 final wealth | 5.31x | 3.18x |
| P95 final wealth | 39.63x | 12.18x |
| Median drawdown | 22.8% | 15.7% |
| P95 drawdown | 34.7% | 24.4% |
| Ruin rate (50% equity) | 0% | 0% |
On this favorable edge, capped Kelly wins on growth across the entire wealth distribution — its P5 (5.31x) is above the fixed-2% median (6.22x is the fixed median, and 5.31x is Kelly's downside fifth percentile). Fixed fractional's win is not in the tail wealth; it is the tighter drawdown distribution (15.7% vs 22.8% median, 24.4% vs 34.7% at P95). Neither rule registers any ruin across 3,000 paths at the 50%-of-equity threshold, because the edge is genuinely positive and the bets are small. The honest reading: when $p$ and $b$ are actually correct, Kelly is better on almost every axis except path smoothness. The case for fixed fractional rests entirely on $p$ and $b$ being wrong.
What each sizing rule assumes
Kelly
Kelly's formula maximises long-run log-growth1 when:
- $p$ is known.
- $b$ is known.
- Trades are independent.
- Maximum loss per trade equals the stake.
All four assumptions are violated to some degree in retail. The fractional Kelly variants (quarter, eighth) trade growth for robustness to the first violation2. The per-trade cap and the strategy diversification handle the others.
Fixed fractional
Fixed fractional bets a constant percentage of bankroll regardless of edge or variance3:
- Does not require estimating $p$ or $b$.
- Does not require any model.
- Is trivially auditable: "we bet 2% on every signal."
The cost is that fixed fractional cannot scale with conviction. A signal that the trader is unusually sure about gets the same bet as a marginal one.
When Kelly is the right default
For edges with hundreds of validated live outcomes, stable $p$ estimates, and tolerable drawdowns:
- Documented PBO < 0.2.
- 500+ paired live trades.
- $p$ point estimate within ±2 percentage points across rolling windows.
- Trader can survive 30-50% drawdown without forced shutdown.
Capped Kelly at the parameters above gives roughly 2.3x the median terminal wealth of fixed 2% (14.5x vs 6.2x). Over 300 trades, the compounding gap is large — but it only materialises if the realised $p$ stays close to the estimated 0.55.
When fixed fractional is the right default
For edges with limited live data, drifting estimates, or where the trader cannot tolerate the Kelly drawdown:
- Under 500 paired live observations.
- $p$ estimate has visible standard error.
- Drawdown above 30% would force strategy shutdown.
- Strategy is part of a larger portfolio where consistency matters more than per-strategy optimisation.
Fixed fractional at 1-2% per trade absorbs all four. The growth gap is real (10-20% lower terminal wealth in expectation) but the survival probability is higher.
The hybrid pattern
In practice, retail systems often run a tier-mapped hybrid:
def size_bet(confidence: float, bankroll: float) -> float:
if confidence < 0.55:
return 0 # skip
if confidence < 0.65:
return 0.01 * bankroll # fixed 1%
if confidence < 0.80:
return 0.02 * bankroll # fixed 2%
return min(quarter_kelly(confidence, payoff_ratio), 0.04 * bankroll)
This pattern uses fixed fractional for the noisy tier and Kelly only for the high-confidence tier where $p$ estimates are more reliable. The Conviction-Scaled Kelly piece walks the tier-mapping logic in detail.
What the engine's drawdown distribution tells us
On this scenario the Kelly Sizer reports a 0% ruin rate for both rules across 3,000 paths at the 50%-of-equity threshold. The edge is real and the bets are small enough that no path loses half its equity. Ruin probability is therefore not where the two rules diverge here — the divergence is in the drawdown distribution.
The capped-Kelly bet runs a 22.8% median maximum drawdown with a 34.7% P95. Fixed 2% runs 15.7% median and 24.4% P95. That 10-point gap at the tail is the load-bearing case for fixed fractional: not that it avoids ruin (neither rule does on a genuinely positive edge), but that it keeps the worst observed drawdown comfortably under the 30% line where many retail traders abandon a strategy. A 34.7% P95 drawdown is the kind of number that gets a system switched off mid-track-record, locking in the loss before the Kelly growth advantage can compound.
Push the per-trade cap above 3% and the Kelly drawdown distribution widens further while ruin starts to appear; that is the regime where the cap stops protecting and the estimation-error risk below becomes acute.
The estimation-error sensitivity
The whole case for fixed fractional rests on $p$ being wrong. Work the formula $f^* = (p \cdot b - (1-p))/b$ at $b=1.40$ across a downward mis-estimate of the win rate:
- $p=0.55$ (estimated): raw Kelly 22.86%, quarter-Kelly 5.71%.
- $p=0.52$ (true): raw Kelly 17.71%, quarter-Kelly 4.43%.
- $p=0.50$ (worse): raw Kelly 14.29%, quarter-Kelly 3.57%.
- $p=0.417$ (break-even): raw Kelly ≈ 0%.
Uncapped quarter-Kelly sized on the estimated 0.55 (5.71%) is a 1.29x over-bet relative to the true quarter-Kelly at $p=0.52$ (4.43%), and a 1.60x over-bet if the truth is 0.50. The over-bet is structural: the estimation error feeds straight into the formula and scales the bet linearly. As the realised win rate slides toward the 0.417 break-even, raw Kelly collapses toward zero while a Kelly bet sized on the stale 0.55 estimate keeps betting 5.71% — that is the regime that produces the deep drawdowns.
The 3% cap is what saves capped Kelly here: at the true $p=0.52$, true quarter-Kelly (4.43%) is above the 3% cap, so the capped 3% bet is actually conservative relative to the optimum. The cap converts Kelly into something closer to fixed fractional precisely when the edge is being over-estimated. Fixed 2% never moves at all — it does not "know" the edge and so cannot over-bet on a stale estimate.
For sizing decisions where edge estimation has visible standard error, fixed fractional is the more honest default because it does not pretend to optimise, and a hard cap on a Kelly bet is the second-best substitute when you want some conviction scaling without exposing yourself to the full estimation error.
Compliance angle
For published trading content under MiFID II / BaFin frameworks, the methodology disclosure must include the sizing rule and its assumptions4. A "quarter-Kelly with confidence band" disclosure carries more substantiation burden than a "fixed 2%" disclosure because the Kelly rule's optimality claim must be defensible against the realised edge variance.
For published research that includes specific position-sizing recommendations, fixed fractional is the lower-disclosure-burden default. Kelly disclosure requires the assumption stack to be made explicit — which is a useful exercise but adds documentation overhead.
Failure modes
- Treating Kelly's optimality as universal. It is optimal under specific assumptions that retail rarely satisfies.
- Picking fixed fractional without computing the growth gap. The gap is real and visible in any backtest.
- Mixing the two within one strategy without policy. Either pick one and document it, or build a tier-mapped hybrid and document that.
- Skipping the per-trade cap. Both rules need a cap. Without one, a high-confidence Kelly call can size to 10%+ of bankroll on a single trade.
FAQ
Which is more popular in retail?
Fixed fractional, by a wide margin. Most retail traders implement Kelly badly (using point estimates as if known) and then revert to fixed fractional after their first big drawdown. Starting with fixed fractional skips the lesson.
How do I choose the fixed fraction?
For most retail momentum or mean-reversion edges, 1-2% per trade is the defensible range. Higher than 3% requires either documented edge with hundreds of live outcomes or willingness to accept materially higher drawdowns. The Kelly Sizer Monte Carlo is the right tool for setting the number — pick the fraction that gives a drawdown distribution the trader can survive.
Can I switch from fixed fractional to Kelly once I have enough data?
Yes — and that is the right progression. Start with fixed fractional, log every trade and outcome, after 500+ paired observations re-estimate $p$ with confidence bands, then switch to quarter-Kelly if the confidence band is tight enough.
Connects to
- Kelly with Uncertain Edge: Quarter vs Eighth: Kelly variants under uncertainty.
- Conviction-Scaled Kelly Bet Sizing: the tier-mapped hybrid pattern.
- Risk Parity vs Kelly: When Each Wins: portfolio-level alternative.
- Edge-Variance Sizing for LLM Signals: sizing under explicit edge uncertainty.
- Kelly Sizer: run both rules on your edge.
- Kelly Sizer methodology: full input/output specification.
References
Footnotes
-
Kelly, J. L. (1956). "A New Interpretation of Information Rate." Bell System Technical Journal 35(4). archive.org ↩
-
MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (2011). The Kelly Capital Growth Investment Criterion. World Scientific. worldscientific.com ↩
-
Vince, R. (1990). Portfolio Management Formulas: Mathematical Trading Methods for the Futures, Options, and Stock Markets. Wiley. (Original fixed-fractional treatment.) ↩
-
ESMA (2023). "Guidelines on certain aspects of the MiFID II suitability requirements." esma.europa.eu ↩
Verified engine output
Show the recompute-verified inputs and outputs
| win_rate | 0.55 |
|---|---|
| win_loss_ratio | 1.4 |
| max_cap_pct | 0.03 |
| trades | 300 |
| sims | 3000 |
| ruin_threshold_pct | 0.5 |
| seed | 41 |
| raw kelly | 0.22857142857142862 |
|---|---|
| fractional kelly | 0.057142857142857155 |
| capped bet | 0.03 |
| bucket | strong |
| sims | 3000 |
| trades | 300 |
| final p5 | 5.305470708303095 |
| final median | 14.503360009461396 |
| final p95 | 39.63452957935475 |
| drawdown median | 0.2283430912444055 |
| drawdown p95 | 0.34746831464524514 |
| ruin rate | 0 |
Computed live at build time.
| win_rate | 0.55 |
|---|---|
| win_loss_ratio | 1.4 |
| max_cap_pct | 0.02 |
| trades | 300 |
| sims | 3000 |
| ruin_threshold_pct | 0.5 |
| seed | 41 |
| raw kelly | 0.22857142857142862 |
|---|---|
| fractional kelly | 0.057142857142857155 |
| capped bet | 0.02 |
| bucket | strong |
| sims | 3000 |
| trades | 300 |
| final p5 | 3.1797894811964422 |
| final median | 6.220575112625126 |
| final p95 | 12.178527645834654 |
| drawdown median | 0.15682236952088735 |
| drawdown p95 | 0.24416339568281992 |
| ruin rate | 0 |
Computed live at build time.