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.
- Inputs
- Form inputs / CSV
- Runtime
- Instant
- Privacy
- Client-side · no upload
- API key
- Not required
- Methodology
- Open →
Inputs
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. 99% smaller than deterministic Kelly because edge uncertainty σ_μ = 2.00% raises the effective 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
Effective Kelly fraction
25%
practitioner damping
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)/αSee methodology for derivation and references.
How to use
Step-by-step
- 1
Enter expected per-trade edge (decimal, e.g., 0.02 = 2%) and standard error of the edge estimate.
- 2
Enter expected per-trade variance.
- 3
Read the recommended position size as a fraction of capital. Compare against full Kelly (faster growth, less safety) and quarter-Kelly (slower growth, more safety).
- 4
Increase the edge SE assumption to see how uncertainty erodes recommended size. The sizer is more conservative than Kelly when SE is high.
- 5
Re-run as your trade log grows — tighter edge SE estimates allow larger sizes safely.
Glossary references
Terms used by this tool
Questions people ask next
FAQ
How is this different from Kelly?
Kelly maximizes long-run growth assuming you know edge and variance. The Edge-Variance sizer instead maximizes risk-adjusted return (Sharpe) under uncertainty in both edge and variance. Output is more conservative than Kelly when estimates are noisy.
What's the role of edge uncertainty?
If your edge estimate has wide error bars, the sizer reduces position size. The math is documented in the methodology page: position size scales inversely with the standard error of the edge estimate. Tight edge estimates → larger sizes. Wide ones → smaller.
How do I estimate edge SE?
From bootstrap resampling of your trade log. Run 1000 bootstrap samples, compute the mean of each, and the SD across bootstrap means is your edge SE. The tool runs this for you when you upload a trade log; you can also enter the SE manually.
What if I don't have a trade log yet?
The sizer accepts manual edge and edge-SE inputs. For paper trading or theoretical strategies, set the SE to 50%+ of the edge — i.e., assume your estimate is half noise. This produces conservative initial sizing that you can tighten as your trade log grows.
How does this compare to fixed fractional sizing?
Fixed fractional (always bet 2% of bankroll) is simple but ignores edge variation across opportunities. The Edge-Variance sizer adjusts position size per trade based on that trade's edge and SE. For strategies with stable edge across opportunities, the difference is small. For strategies with conviction tiers, the difference is large.
Related deep dive
All articles →Read further
Long-form context behind the tool output.
- Tutorial · Runnable·8 min
Conviction-Scaled Kelly Bet Sizing
Full Kelly is brutally unforgiving of over-estimation. Quarter-Kelly with a conviction-tier mapping and a per-trade cap is the defensible default.
Read - Comparison · Benchmark·10 min
Risk Parity vs Kelly: When Each Sizing Framework
Risk parity and Kelly solve different problems. Risk parity wins when correlations are stable and edge is noisy; Kelly wins when edge is concentrated.
Read
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