Definition
The Kelly criterion is the position-sizing rule, derived by John Kelly in 1956, that maximizes the long-run growth rate of wealth by sizing each bet or investment as a specific fraction of current wealth determined by the bet's edge and its odds.
Why it matters
The Kelly criterion is the operational form of long-run growth maximization under multiplicative dynamics, and is mathematically equivalent to expected-log-utility maximization. It is the practical strategy that emerges from taking the time-average orientation seriously in a sequence of compounding decisions. Naming the criterion explicitly is what connects the ergodicity-economics framework to applied investment and betting practice.
How it works
For a single bet with a known probability of winning at known odds, the Kelly fraction — the share of current wealth to wager — is the share that exactly maximizes the expected log of the next period's wealth. For example, if a coin is biased to land heads 60% of the time and the payoff is even money on each flip, the Kelly fraction is 20% — bet one-fifth of current wealth on heads each time. Larger fractions and smaller fractions both produce lower long-run growth, though for different reasons: smaller fractions leave growth on the table by underbetting the edge; larger fractions incur more compounding asymmetry than the additional expected return can compensate for. The same logic generalizes from betting to investing: the Kelly-optimal allocation to a risky asset is the allocation that maximizes the long-run growth rate of wealth, with positions above the Kelly fraction — over-betting, excessive leverage — systematically underperforming over long horizons.
In practice
For an individual making sequential wealth-affecting decisions under uncertainty — investment sizing, leverage, premium spending, position concentration — Kelly's logic identifies the structural constraint that bet size has a long-run-growth-maximizing level above and below which long-run growth declines. The practical move for most non-professional investors is not to compute the Kelly fraction directly but to recognize that the criterion sets a structural ceiling on bet size that is independent of preferences. Strategies that exceed the Kelly fraction systematically underperform their less-aggressive counterparts over long horizons, a phenomenon distinct from the risk-aversion logic of expected-utility theory.
In the Longevity Standard Framework
Kelly criterion is the established formulation in ergodicity economics of the position-sizing rule that maximizes the long-run growth rate of wealth, and is the applied result that connects the abstract ergodicity-economics framework to specific investment and betting decisions. The Longevity Standard framework does not directly use Kelly sizing — its scope is lifetime-income arrangements rather than active position-sizing decisions — but the underlying logic that long-run growth maximization differs structurally from ensemble-average expected-value maximization is the same logic on which the framework's individual-path orientation rests.
Related terms
- Log utility
- Expected utility theory
- Time-average return
- Multiplicative dynamics
- Ergodicity
- Wealth trajectory
- Ruin probability
- Path dependency