Calculator
Position Sizing under Edge Variance
Bayesian-Kelly bet sizing when your edge is itself uncertain. Compare deterministic Kelly, Bayesian-adjusted, and conservative lower-bound versions.
Runs in your browser. Nothing you enter is uploaded, and no account or API key is needed.
Inputs
Your best estimate of the mean return per bet.
Standard error of μ: how far the true edge could plausibly sit from your estimate.
Variance, not std-dev: 0.040 is a 20.0% per-bet std-dev.
Fraction of full Kelly you actually bet; 25% is quarter-Kelly.
How this differs from raw Kelly
Raw Kelly assumes you know μ exactly. In practice μ is estimated. Bayesian Kelly (Browne & Whitt 1996) penalizes that uncertainty by adding it to the denominator — bet less when you're less sure.
Bayesian-adjusted bet size
24.8%
of bankroll. 1.0% smaller than deterministic Kelly (25.0%), because edge uncertainty σ_μ = 2.0% adds σ_μ² to the variance in the denominator.
Sizing comparison
Deterministic
25.00%
μ assumed exact
Bayesian
24.75%
penalizes σ_μ
Conservative (μ − σ)
12.50%
lower-CI version
Tail risk of recommended bet
CVaR (5%)
9.22%
expected loss in worst 5% of outcomes
Bayesian Kelly before damping
99.0%
full Kelly; you bet 25% of it
Formulas
f_det = μ / σ²_outcome
f_bayes = μ / (σ²_outcome + σ²_μ) ← penalty for edge uncertainty
f_cons = (μ − σ_μ) / σ²_outcome ← lower-bound estimate
CVaR_5% = -f·μ + f·√σ²_outcome · φ(z)/α (f = damped Bayesian size)How to use it
- Enter your expected edge per bet μ and its uncertainty σ_μ (the standard error of that estimate), both in percent.
- Enter the per-bet outcome variance σ² (a variance: 0.04 is a 20% per-bet standard deviation) and the Kelly multiplier you actually bet.
- Read the Bayesian-adjusted bet size as a share of bankroll and how much smaller it is than deterministic Kelly.
- Compare the deterministic, Bayesian and conservative (μ − σ_μ) sizes, each after your Kelly multiplier.
- Check the 5% CVaR of the recommended bet: the expected loss in the worst 5% of outcomes under a normal approximation.
The method, step by step
Size positions with Kelly by estimating your edge and its variance, then betting a fraction of full Kelly rather than the raw optimum, because the edge estimate is itself uncertain. Full Kelly assumes you know the true edge; you do not, so a half or quarter Kelly fraction protects against the overbetting that estimation error causes. Confirm the chosen fraction with a drawdown simulation before trading it.
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Estimate the edge and its uncertainty
Kelly needs an expected edge, but the honest version also needs how confident you are in that edge. Estimate both from out-of-sample data, not the in-sample fit that produced the strategy. A small sample or a wide spread of results means high uncertainty, which should pull your bet size down. Treating the edge as a point estimate when it is really a distribution is the root cause of Kelly overbetting.
Use the lower end of a confidence interval for the edge, not the central estimate. Sizing on the optimistic case is how good strategies get overbet into ruin.
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Compute the full Kelly fraction
Full Kelly is the bet size that maximizes the expected logarithm of wealth. For a simple bet it is the edge divided by the odds; for a continuous strategy it is roughly the expected excess return divided by the variance of returns. This number is the theoretical ceiling. It is correct only if your edge estimate is exact, which is why it is a starting point for discounting rather than a sizing decision in itself.
Full Kelly is famously aggressive: it routinely implies drawdowns of fifty percent or more even when the edge is real. Treat it as a maximum you will scale down from.
Kelly Criterion Calculator -
Apply a fractional Kelly discount
Bet a fraction of full Kelly, commonly one half or one quarter. The reason is mathematical, not timid: because growth is concave near the Kelly optimum, halving the bet sacrifices only a small slice of expected growth while roughly halving the volatility of wealth. Under estimation uncertainty, fractional Kelly also corrects for the systematic overbetting that comes from sizing on an edge you measured with error.
The more uncertain your edge, the smaller the fraction. A well-measured edge from thousands of trades justifies a larger fraction than a fresh strategy with fifty trades.
Kelly Criterion Calculator -
Use a Bayesian-adjusted size when the edge is shaky
When the edge estimate is genuinely uncertain, a Bayesian approach formalizes the discount: it places a prior on the edge, updates it with your data, and sizes on the resulting posterior rather than a single point. With little data the posterior pulls heavily toward the prior, automatically shrinking the bet. As evidence accumulates, the size grows toward the data-driven Kelly. This is the principled version of fractional Kelly when you can quantify the uncertainty.
Compare the deterministic Kelly, the Bayesian-adjusted Kelly, and a conservative lower-bound version. The gap between them is a direct readout of how much your uncertainty is costing in size.
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Stress the drawdown before committing the fraction
Even a correct Kelly fraction produces deep drawdowns, and the relevant question is whether you can survive them psychologically and financially. Simulate the path of wealth under your chosen fraction, given the strategy's return distribution including skew and kurtosis, and read the time and depth of the typical and tail drawdowns. If the recovery time or the depth would force you to abandon the strategy, cut the fraction until it would not.
Size to the drawdown you can sit through, not the one you can describe in a spreadsheet. The constraint that matters is the one that makes you capitulate at the bottom.
Drawdown-Recovery Markov Simulator
Sources: A New Interpretation of Information Rate (J. L. Kelly Jr., Bell System Technical Journal (1956)) ; The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market (Edward O. Thorp (2007))
Mistakes that undo the result
Sizing on the in-sample edge
The in-sample edge is inflated by the same selection that produced the strategy. Feeding it into Kelly overbets from the start, before any live uncertainty is even considered.
Treating full Kelly as the target rather than the ceiling
Full Kelly assumes a perfectly known edge. With real estimation error it overbets, and the resulting drawdowns are far deeper than the strategy's edge can justify, often leading to capitulation at the worst time.
Ignoring correlation across simultaneous positions
Kelly sizing each position independently overbets the portfolio when positions are correlated. Several correlated bets at individual-Kelly size behave like one oversized bet during a stress event.
Questions people ask
How is this different from Kelly?
Deterministic Kelly sizes a bet at μ / σ², assuming the edge μ is known exactly. The Bayesian version adds the uncertainty of the edge to the denominator, μ / (σ² + σ_μ²), and the conservative version sizes on μ − σ_μ. All three are then scaled by your Kelly multiplier.
What's the role of edge uncertainty?
It shrinks the bet. In the Bayesian size σ_μ² is added to the outcome variance, so the haircut is small when σ_μ is small relative to the per-bet volatility and large when your edge estimate is as noisy as the bets themselves. The conservative size falls to zero once σ_μ reaches μ.
How do I estimate edge SE?
From your trade log: the standard error of the mean return per trade is the sample standard deviation divided by √n, or the spread of bootstrap means if returns are far from normal. The tool does not take a trade log; you enter the standard error directly.
What if I don't have a trade log yet?
Enter a prior. For paper or untested strategies, set σ_μ to half the edge or more, which pulls the conservative size down sharply, and tighten it as live results accumulate.
How does this compare to fixed fractional sizing?
Fixed fractional bets the same share of bankroll every time, whatever the edge. This tool sizes one bet profile from its edge, edge uncertainty and variance; to size trades with different conviction, run each profile through it separately.
The same numbers as a table
- Reference Edge-variance Kelly reference grid
Computed by this tool's engine across common inputs, to cite or download as CSV.
Related tools
- Calculators Kelly Criterion Calculator
Size positions with full, half, quarter, or eighth Kelly and stress-test the choice with a drawdown Monte Carlo simulator. Client-side. Private by default.
- Calculators Drawdown-Recovery Markov Simulator
Time to recover from an N% drawdown given monthly Sharpe + skew + kurtosis. Cornish-Fisher Monte Carlo, percentile distribution of recovery months.
- Calculators Deflated Sharpe Ratio Calculator
Bailey & López de Prado deflated Sharpe — corrects observed Sharpe for selection bias across K trials. Reports deflated Sharpe, PSR (probability of skill), and the multiple-testing haircut.
Articles
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On the canonical 50-bar tape the engine returns mean OOS Sharpe 0.653, efficiency 0.600 — but the four windows hide a regime flip the half-life rule fixes.
Use it from code
The same calculation as a JavaScript module you can import. It runs where you import it, with no request, key or rate limit.
import { compute } from "https://aifinhub.io/engines/position-sizing-edge-variance.js";