Kelly Criterion & Fractional Kelly
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Definition
The bet size that maximizes the expected long-run geometric growth rate of capital. For a simple win/loss bet: f* = p - q/b (p = win prob, q = 1-p, b = win/loss payoff ratio). For continuous returns: f* ~= mu/sigma^2 (excess mean over variance). Fractional Kelly bets a fixed fraction (e.g. half) of f*.
How to read it
Full Kelly is growth-optimal only if your estimates of edge and odds are EXACTLY right, which they never are. Kelly is aggressive: it maximizes growth but tolerates gut-wrenching drawdowns (full Kelly can expect to lose half its capital at some point with probability ~50%). Because real edges are estimated with error and fat tails, practitioners bet a FRACTION of Kelly - typically 1/4 to 1/2 - trading a small, second-order loss of growth for a large, first-order reduction in variance and drawdown. Over-betting past f* is catastrophic: growth falls AND risk rises simultaneously.
How practitioners use it
Used as context among multiple indicators — never as a standalone signal to act.
Less common professional uses
Estimation error makes the OPTIMAL fraction less than 1: if edge is uncertain, the growth-maximizing choice shrinks toward a Bayesian posterior mean, and fractional Kelly is a robust approximation to that shrinkage - it is not merely 'being cautious', it is closer to the true optimum once parameter uncertainty is priced in. The classic f* = mu/sigma^2 is derived under Gaussian returns; under FAT TAILS the same fraction over-levers because variance understates tail risk. Kelly with a fat-tailed (e.g. Student-t or jump) return model yields a materially smaller f*, and ignoring this is a common blow-up path. Kelly is horizon-invariant only for i.i.d. returns; with autocorrelation or regime switching the growth-optimal fraction becomes state-dependent, and a single static f* over-bets in high-vol regimes. Simultaneous bets require the VECTOR Kelly solution f* = Sigma^-1 (mu - r): correlations shrink the per-position size because clustered bets behave like one larger bet - sizing each leg at its standalone Kelly over-levers the portfolio.
Sources & provenance
Kelly (1956), 'A New Interpretation of Information Rate', Bell System Technical Journal; Thorp (2006), 'The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market'; MacLean, Thorp & Ziemba (2011), 'The Kelly Capital Growth Investment Criterion'
This page is educational content published by Pachira Aquatica Global LLC. It is not investment advice and not a recommendation.