Kelly Criterion

Also: Kelly bet · optimal f

The Kelly criterion sets the bet size that maximizes long-run growth of capital, given your edge and odds. It is the mathematically optimal sizing rule — and brutal if your edge is overestimated.

Given a positive edge, how much do you bet? Bet too little and you leave growth on the table; bet too much and variance eventually ruins you. The Kelly criterion solves for the fraction of capital that maximizes the expected log of wealth — i.e. long-run compounding — which for a simple bet is edge / odds.

Kelly’s danger is its dependence on inputs. Your “edge” is an estimate, and Kelly sizing is exquisitely sensitive to overestimating it: full Kelly on an inflated edge produces stomach-churning drawdowns and can be worse than not trading. This is why practitioners use fractional Kelly — a half or quarter of the full number — trading a little growth for far smoother equity.

For an autonomous agent this is critical. An agent that trusts its own backtested edge and sizes at full Kelly will blow through drawdown limits. The safe design caps sizing at fractional Kelly and clamps it inside a hard policy limit, so a mis-estimated edge can’t translate into an uncontrolled bet.

  • sizing
  • risk
  • growth

Research source: rSwarm research library →

Related concepts

Regime Detection

Regime detection classifies the market's current state — e.g. calm, trending, or stressed — often with a Hidden Markov Model over volatility and return features, so a strategy can adapt.

Value at Risk (VaR)

VaR estimates the maximum loss a position or portfolio is unlikely to exceed over a horizon at a given confidence — e.g. '95% 1-day VaR of $4k.' Useful as a limit, dangerous as a guarantee.