What Is the Half-Kelly Criterion?

The Position Sizing Problem

Even with a genuine edge, improper position sizing destroys portfolios. Bet too large and a string of losses wipes you out. Bet too small and your edge barely compounds. The Kelly criterion and its half-size variant solve this mathematically.

The Kelly Criterion

Developed by John Kelly at Bell Labs in 1956, the Kelly criterion calculates the optimal fraction of capital to risk on a bet with known edge:

f* = (b × p - q) / b

Where:

• f* = fraction of capital to risk
• b = ratio of win size to loss size (reward/risk)
• p = probability of winning
• q = probability of losing (1 - p)

Example

A trade with 60% win rate and 2:1 reward-to-risk ratio:

f* = (2 × 0.60 - 0.40) / 2 = (1.20 - 0.40) / 2 = 0.40

Full Kelly says to risk 40% of capital. This maximizes long-term growth but creates enormous volatility — you'll regularly see 30-50% drawdowns.

Why Full Kelly Is Dangerous

Full Kelly is optimal only if you know your exact edge. In reality:

• Win rates are estimated, not known: Your model thinks it's 60% but the true rate might be 52%
• Fat tails exist: Losses can exceed your expected loss size
• Serial correlation: Losses often cluster (market regimes), violating Kelly's independence assumption
• Behavioral tolerance: A 40% drawdown causes most people (and even algorithms) to deviate from strategy

Overestimating your edge by even 10% while using full Kelly can lead to ruin.

Enter Half-Kelly

Half-Kelly simply uses f*/2 — half the position size Kelly recommends. The tradeoffs:

Metric	Full Kelly	Half-Kelly
Long-term growth rate	100% (maximum)	~75% of full Kelly
Maximum drawdown	Severe (40-60% common)	~50% of full Kelly's drawdown
Volatility	Very high	Moderate
Sensitivity to estimation error	Catastrophic if edge overestimated	Robust — survives significant errors
Recovery time from drawdown	Can be very long	Much shorter
Practical survivability	Low for uncertain edges	High — designed for real-world uncertainty

The insight: you sacrifice only 25% of long-term growth but cut drawdown risk roughly in half. This is why nearly every professional risk manager recommends fractional Kelly (typically 1/4 to 1/2).

How Fin45 Applies Half-Kelly

For each trade, the Fin45 agent calculates position size using:

1. Estimate win probability from signal conviction score and historical accuracy of similar signals
2. Estimate reward/risk ratio from expected move (must be ≥ 5%) divided by stop-loss distance (7%)
3. Calculate full Kelly fraction
4. Halve it for Half-Kelly position size
5. Apply hard cap: Maximum 20% of portfolio in any single position regardless of Kelly output
6. Apply sector and correlation caps: 40% max sector, 30% max correlated exposure

Worked Example

Signal conviction: 0.82 (maps to estimated 65% win probability)
Expected move: +12% (reward) vs. 7% stop (risk) → b = 12/7 = 1.71

Full Kelly: f* = (1.71 × 0.65 - 0.35) / 1.71 = (1.11 - 0.35) / 1.71 = 0.445
Half-Kelly: f*/2 = 0.222 → 22.2% of portfolio
After hard cap: min(22.2%, 20%) = 20% position

Why This Matters for AI Trading

An AI agent's conviction scores are estimates, not certainties. Using Half-Kelly means:

• If the model overestimates its edge, Half-Kelly prevents catastrophic loss
• Position sizes naturally scale with conviction — higher confidence = larger position
• The hard cap (20%) provides an additional safety layer on top of Half-Kelly
• Combined with -7% hard stops, maximum loss on any trade is ~1.4% of portfolio

Position Sizing in Practice

Most traders fail not because their trade ideas are bad, but because their position sizing is wrong. Half-Kelly provides a mathematically rigorous framework that:

• Scales bet size proportionally to estimated edge
• Protects against overestimation errors
• Produces survivable drawdowns
• Still captures meaningful compounding over time

Learn more about Fin45's complete risk management framework on the Methodology page.