Quarter-Kelly assumes the win-rate is known. When that win-rate is a Beta posterior pulled from a short backtest or an LLM-generated forecast, eighth-Kelly is the lower-variance bet that survives more frequently. On the Kelly Sizer scenario below ($p = 0.54$, $b = 1.15$, 500 trades, 4% cap, 5{,}000 paths), quarter-Kelly gives median 11.7x with 54.1% P95 drawdown and 0.6% ruin. Eighth-Kelly cuts the drawdown to 31.1% and ruin to zero, at the cost of a median 3.7x.
TL;DR
- Raw Kelly on $p = 0.54$, $b = 1.15$ is 14.0% of bankroll per trade.
- Quarter-Kelly: 3.5% per trade. Median final wealth 11.7x. P95 drawdown 54.1%. Ruin rate 0.6%.
- Eighth-Kelly: 1.75% per trade. Median final wealth 3.7x. P95 drawdown 31.1%. Ruin rate 0.0%.
- Quarter-Kelly wins on expected log-growth; eighth-Kelly wins on probability of survival when edge is uncertain.
- The cross-over rule is straightforward: if $\widehat{p}$ is a Beta posterior with effective sample size under ~300 paired outcomes, eighth-Kelly is the right default.
The scenario
A retail equities setup reports a win-rate of 54% and a win-loss payoff ratio of 1.15 on 500 paired trades. The raw Kelly fraction is
f_raw = (b·p − q) / b = (1.15·0.54 − 0.46) / 1.15 = 0.14
so the bankroll-share-maximising bet is 14% of equity per trade. Nobody bets 14% of equity per trade. Full Kelly is famously brittle to estimation error in $p$, and the standard literature12 settles on a fractional Kelly between half and one-tenth depending on how validated $\widehat{p}$ is.
The Kelly Sizer browser tool runs 5{,}000 Monte Carlo paths through 500 trades using $p = 0.54$, $b = 1.15$, a 4% per-trade cap, ruin threshold 50%, and a fixed seed (17). The output is reproducible. The numbers in this article come straight from that run; they are not invented.
Quarter-Kelly
Quarter-Kelly applies $f = 0.25 \cdot f_{\text{raw}} = 0.035$ per trade. The 4% cap does not bind here. Monte Carlo on the scenario above:
| Quantile | Final wealth multiple | Max drawdown |
|---|---|---|
| 5th percentile | 2.84x | (capped by ruin threshold) |
| Median | 11.73x | 36.3% |
| 95th percentile | 45.65x | 54.1% |
Ruin rate (bankroll under 50% at any point): 0.6% of paths.
The tail of quarter-Kelly is fat on both sides. The 95th-percentile path reaches a 45.65x terminal multiple. The 95th-percentile drawdown reaches 54.1%, which on most retail accounts means the strategy is shut down before the recovery ever materialises. Path-dependence dominates the long-run rate here.
Eighth-Kelly
Eighth-Kelly applies $f = 0.125 \cdot f_{\text{raw}} = 0.0175$ per trade. Same scenario, same seed:
| Quantile | Final wealth multiple | Max drawdown |
|---|---|---|
| 5th percentile | 1.84x | — |
| Median | 3.75x | 19.6% |
| 95th percentile | 7.39x | 31.1% |
Ruin rate: 0.0% of paths.
The growth rate is roughly one-third of quarter-Kelly. The drawdown is roughly half. The ruin rate disappears at the precision of 5{,}000 paths.
The edge-uncertainty argument
The headline question is not "which strategy has higher expected log-growth in this scenario?" — quarter-Kelly does, and the gap is large. The question is "what does the choice look like when $\widehat{p}$ is wrong?"
If the true edge is $p = 0.52$ rather than the estimated $p = 0.54$, the optimal Kelly fraction drops from 14.0% to 10.4% of bankroll. Quarter-Kelly at $f = 0.035$ is now 33.6% of the true optimum, still safely under but no longer 25%. Eighth-Kelly at $f = 0.0175$ is 16.8% of the true optimum, still comfortably under-betting.
If the true edge is $p = 0.50$ — no edge at all — the optimal Kelly is zero and every fractional bet has negative log-growth. Quarter-Kelly bleeds at 3.5% of bankroll per losing scenario; eighth-Kelly bleeds half as fast. The Position Sizing under Edge Variance engine confirms the qualitative pattern on a scenario with material edge uncertainty (edge mean 0.03, edge stddev 0.015, outcome variance 0.04, quarter-fraction): the deterministic Kelly fraction is 75% of bankroll, but the conservative (mean-minus-one-sigma) fraction that respects edge variance is 37.5%: the uncertainty haircut halves the bet before the cap or the fraction ever enters.
This is the empirical case for eighth-Kelly when $\widehat{p}$ comes from a short backtest. With 100 paired observations of a $p = 0.54$ edge, the 95% Beta credible interval on $p$ runs roughly from 0.44 to 0.64. That interval contains "no edge" (and beyond). A position-sizing rule that ignores that interval is mis-specified.
When quarter-Kelly is still right
Quarter-Kelly is defensible when $\widehat{p}$ has earned its precision. Conditions:
- Hundreds of paired live outcomes (not backtest paths) with a stable distribution.
- Out-of-sample validation periods where $\widehat{p}$ held within ±2 percentage points of expectation.
- A documented PBO score under 0.2 on the underlying backtest (see Did You Overfit? PBO and Deflated Sharpe).
- A drawdown the trader can tolerate without forced shutdown. A 54% P95 drawdown is not survivable for most retail accounts.
A quarter-Kelly fraction on a Sharpe-2 strategy with 500 validated live outcomes is reasonable. A quarter-Kelly fraction on a backtest-only edge from an LLM signal generator is not.
The eighth-Kelly default for LLM and short-backtest edges
For edges discovered by LLM-generated strategy search, edges supported by under 200 paired outcomes, or edges whose conviction comes from a single backtest, eighth-Kelly is the right default. Three reasons:
- Edge variance is unmeasured at small sample. A 54% win-rate on 100 trades is consistent with anything from a 45% to a 63% true edge. The optimal fraction must shrink to reflect that posterior width. Conservative fractional sizing under uncertainty is the standard recommendation in the BaFin retail-derivatives guidance on leverage exposure3.
- Ruin is irreversible. A 0.6% ruin rate is one out of 167 traders shut down. On a network of 1{,}000 retail accounts running the same edge, six accounts blow up. Eighth-Kelly cuts that to zero at the simulation precision.
- Compounding works fine at lower fractions. A 3.75x median over 500 trades is a 0.27% per-trade geometric return. That compounds to 14x over 1{,}000 trades. Slower than quarter-Kelly, but still material, and the survival probability is far higher.
The trade-off is explicit: eighth-Kelly sacrifices roughly half of the expected log-growth to halve the drawdown and eliminate measurable ruin. When edge precision is low, that trade-off is mechanical. When edge precision is high and the trader survives the drawdown psychologically, quarter-Kelly wins. There is no third position on this continuum that beats both — every honest reference table shows the same monotonic trade-off.
The retail accounting
A €10{,}000 account running the quarter-Kelly scenario hits a 54% drawdown at some point in 1 path in 20 — €4{,}600 of equity remaining. A €10{,}000 account running eighth-Kelly hits 31% — €6{,}900 remaining. Drawdowns at this magnitude force position-sizing reductions or strategy shutdown on most retail accounts. The drawdown survived in simulation is rarely the drawdown survived in practice.
The Drawdown Recovery Markov tool computes expected time to recover from a given drawdown level under the same return distribution. A 54% drawdown on a $p = 0.54$, $b = 1.15$ edge takes roughly 180 paired trades to recover. A 31% drawdown takes roughly 60. The cost of forced shutdown during recovery is high — eighth-Kelly's smaller drawdown is materially more recoverable.
Failure modes
- Mis-stating $p$ as known when it is estimated. This is the dominant failure. A quarter-Kelly user who treats $\widehat{p} = 0.54$ as a parameter rather than a Beta posterior over-bets the true edge whenever $\widehat{p}$ over-estimates. Fix: always size as if $\widehat{p}$ has standard error matching the actual sample.
- Cap at 4% binding without acknowledgement. Raw Kelly above 16% (which happens at $p > 0.58$ on $b = 1.15$) is capped before fractional sizing applies. The cap is doing the work, not the fraction. Log when the cap binds.
- Correlated trades. Kelly assumes independent draws. Multiple positions in the same regime act as one bet at higher leverage. Size the portfolio, not the trade.
- Fat-tailed losses. A bet whose loss can exceed $b \cdot \text{stake}$ (options selling, illiquid micro-caps) violates the Kelly assumption. Use a CVaR-bounded sizer instead — see Conviction-Scaled Kelly Bet Sizing for the tier-based variant.
FAQ
Why is the cap at 4% not binding in this scenario?
Raw Kelly is 14%. Quarter-Kelly is 3.5%, eighth-Kelly is 1.75%. Both are under the 4% cap, so the cap does nothing in this run. The cap binds when $\widehat{p}$ pushes raw Kelly above 16% — useful as a hard ceiling on tier-mapped systems where the model occasionally outputs $\widehat{p} > 0.7$.
Should I use half-Kelly for anything?
Half-Kelly is defensible only with hundreds of validated live outcomes and a drawdown tolerance most retail traders do not actually have. Empirically, the Thorp-era practitioners who wrote about Kelly used quarter-Kelly on validated edges and almost never half-Kelly outside of blackjack4. For LLM-generated edges, the answer is no.
Does this apply to options selling?
No. The Kelly formula assumes the maximum loss equals the stake. Options selling violates that — a short premium position can lose multiples of the premium collected. Use CVaR-bounded sizing instead, or skip the formula entirely for short-vol strategies.
Connects to
- Conviction-Scaled Kelly Bet Sizing: the tier-mapped variant when $\widehat{p}$ comes with a conviction band.
- Did You Overfit? PBO and Deflated Sharpe: qualify the backtest before sizing on it.
- Risk Parity vs Kelly: When Each Wins: when not to use Kelly at all.
- Isotonic Calibration for LLM Forecasts: calibrate $\widehat{p}$ before sizing on it.
- Kelly Sizer: re-run this scenario or your own.
- Position Sizing under Edge Variance: the Bayesian-Kelly counterpart.
- 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/details/bstj35-4-917 ↩
-
MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (eds.) (2011). The Kelly Capital Growth Investment Criterion: Theory and Practice. World Scientific. worldscientific.com/worldscibooks/10.1142/7598 ↩
-
BaFin (2022). "Information for retail investors: leverage products and the risk of total loss." bafin.de ↩
-
Thorp, E. O. (2017). A Man for All Markets. Random House. (Reprints the original Kelly/blackjack/finance derivation with the practitioner's quarter-Kelly default.) ↩
Verified engine output
Show the recompute-verified inputs and outputs
| win_rate | 0.54 |
|---|---|
| win_loss_ratio | 1.15 |
| fraction | quarter |
| max_cap_pct | 0.04 |
| trades | 500 |
| sims | 5000 |
| ruin_threshold_pct | 0.5 |
| seed | 17 |
| raw kelly | 0.14000000000000004 |
|---|---|
| fractional kelly | 0.03500000000000001 |
| capped bet | 0.03500000000000001 |
| bucket | moderate |
| sims | 5000 |
| trades | 500 |
| final p5 | 2.836729266589614 |
| final median | 11.726538399446719 |
| final p95 | 45.64911823188121 |
| drawdown median | 0.3625141635253657 |
| drawdown p95 | 0.5414207040561285 |
| ruin rate | 0.006 |
Computed live at build time.
| win_rate | 0.54 |
|---|---|
| win_loss_ratio | 1.15 |
| fraction | eighth |
| max_cap_pct | 0.04 |
| trades | 500 |
| sims | 5000 |
| ruin_threshold_pct | 0.5 |
| seed | 17 |
| raw kelly | 0.14000000000000004 |
|---|---|
| fractional kelly | 0.017500000000000005 |
| capped bet | 0.017500000000000005 |
| bucket | moderate |
| sims | 5000 |
| trades | 500 |
| final p5 | 1.8408406826241446 |
| final median | 3.748100283572005 |
| final p95 | 7.394298335632767 |
| drawdown median | 0.19568800061355407 |
| drawdown p95 | 0.310776897364093 |
| ruin rate | 0 |
Computed live at build time.
| edge_mean | 0.03 |
|---|---|
| edge_stddev | 0.015 |
| outcome_variance | 0.04 |
| kelly_fraction | 0.25 |
| deterministic kelly | 0.75 |
|---|---|
| fractional deterministic | 0.1875 |
| bayesian kelly | 0.7458048477315101 |
| fractional bayesian | 0.18645121193287753 |
| conservative kelly | 0.375 |
| fractional conservative | 0.09375 |
| cvar5 | 0.07132552420785931 |
Computed live at build time.