Kelly Criterion in Practice: Position Sizing with Uncertain Edge

Abstract The Kelly Criterion provides the mathematically optimal fraction of capital to risk on a bet with known edge. But in crypto markets, edge is never known — it is estimated from noisy, non-stationary data. This pilot study examines the practical consequences of applying Kelly-based sizing when the true edge parameter is uncertain. Using 377,890 funding rate observations and cross-exchange spread data from a live trading system, we demonstrate that naive Kelly sizing with estimated parameters leads to severe overbetting and drawdowns that would wipe most portfolios. We evaluate fractional Kelly (half-Kelly, quarter-Kelly), Bayesian parameter estimation, and drawdown-constrained variants as alternatives. The central finding is not novel — parameter uncertainty destroys naive Kelly — but the magnitude of the effect, quantified here with real crypto data, is instructive: what appears to be a 4.5% annualized edge (XMR persistent positive funding) becomes statistically indistinguishable from zero when bootstrapped over realistic holding periods. This is a pilot study with substantial limitations; we present the framework and preliminary results but do not claim a deployable sizing model. What this paper IS: A quantitative framework for thinking about position sizing under uncertainty, illustrated with real funding rate data. What this paper IS NOT: A recommendation to trade any specific size or strategy. No out-of-sample validation exists. Hypotheses H1 (Primary — Moderate Support Expected): Naive full-Kelly sizing applied to estimated crypto edge parameters results in portfolio paths with 80% probability of a 50% drawdown within 6 months, even when the true edge is positive. H2 (Secondary — Moderate Support Expected): Half-Kelly sizing reduces maximum drawdown by approximately 60-70% while sacrificing only 25-30% of compound growth rate, consistent with theoretical predictions. H3 (Exploratory — Data May Be Insufficient): A drawdown-constrained Kelly variant (cap max position at 2× estimated Kelly) outperforms fixed fractional Kelly on a risk-adjusted basis over the sample period. Confidence Assessment: H1 and H2 are well-supported by theory and we expect moderate empirical confirmation. H3 is exploratory — the sample is a single draw from the funding rate distribution, not an out-of-sample test. Data Provenance All data is sourced from the Vex Capital PerpsTrader system: | Dataset | Source | Period | Records | |---------|--------|--------|---------| | Funding Rates | Hyperliquid, Binance, Asterdex APIs | Jan–May 2026 | 377,890 observations | | Cross-Exchange Spreads | Asterdex ↔ Binance, Hyperliquid ↔ Binance | Current snapshot | 10 pairs | | Trade History | PerpsTrader execution log | Jan–May 2026 | 0 executed trades | Critical note: Zero trades have been executed in this system. All analysis is on observational data — funding rates and spreads as observed, not returns from actual positions. This is a modeling exercise, not a backtest. The Kelly Framework Classical Kelly For a bet with win probability and payoff odds , the Kelly-optimal fraction is: $\mur\sigma^2\hat{\mu}\hat{\sigma}^2\hat{\mu}\hat{f}^\mu\hat{\mu}\hat{\mu}D{\max}T$ is the horizon. This converts a drawdown budget into a position limit, independent of the edge estimate. For XMR with σ ≈ 8% annualized, a 20% max drawdown over 90 days at 95% confidence gives a position limit of approximately 0.35× — less than half-Kelly. The edge estimate is effectively irrelevant; the constraint binds. Discussion Robust Findings 1. Naive Kelly is dangerous in crypto. The signal-to-noise ratio in funding rates is low. Point estimates of edge have wide confidence intervals. Full Kelly leverages into what might be noise. 2. Fractional Kelly is the pragmatic baseline. Half-Kelly and quarter-Kelly dramatically reduce tail risk with modest impact on median returns. This is consistent with decades of gambling and finance literature. 3. Drawdown constraints are parameter-light. Rather than depending on an unreliable μ̂, drawdown-based limits use only σ̂ (which is estimated much more precisely) and a user-defined risk tolerance. This is a feature, not a bug. Preliminary / Not Well-Supported 4. The specific drawdown probabilities in our simulation table are single-draw results from one parameterization. They should not be quoted as general findings. 5. H3 (drawdown-constrained Kelly superiority) remains unsupported — we lack out-of-sample data and execution costs to make this comparison fairly. Not Supported 6. We cannot recommend specific position sizes for any token or strategy. The system has zero executed trades. Any sizing recommendation would be pure theory. Limitations This is a pilot study with several substantive limitations: 1. Zero execution data. All analysis is observational. Funding rates and spreads are observed but never traded. Slippage, gas costs, latency, and partial fills are absent from the model. 2. Single sample path. We have 5 months of data.