How much of your capital should you bet on a single idea — even if you are fairly confident it is correct? Most investors answer this question by feel, by convention (5% position limit, 10% maximum), or by risk management rules set by compliance teams. The Kelly Criterion offers a mathematically rigorous answer derived from information theory: bet exactly the fraction of your capital that maximises the long-run geometric growth rate of your wealth. It is elegant, powerful, and consistently misapplied.
The intuition: why not bet more?
Suppose you have a coin that lands heads 60% of the time. You can bet any fraction of your bankroll on each flip. Why not bet everything? The first flip: 60% chance your bankroll doubles, 40% chance it goes to zero. A single loss wipes you out entirely — and since you cannot recover from zero, your geometric growth rate is ruined. Why not bet half? Better, but still too much: the variance of outcomes is high, and over many flips the geometric growth rate falls below its maximum. Kelly calculates the exact fraction that optimally balances growth and protection: in this case, f* = (0.6 − 0.4) / 1 = 20% of bankroll per flip.
Kelly in practice: fractional Kelly
Full Kelly is theoretically optimal but practically uncomfortable. It produces significant portfolio volatility and drawdowns — betting 20% on every favourable flip still produces large swings over 100 flips. Most sophisticated practitioners use fractional Kelly: betting a fixed proportion (typically 25–50%) of the full Kelly fraction. Half-Kelly, for instance, achieves approximately 75% of the maximum geometric growth rate but with dramatically lower volatility and drawdown. The trade-off: fractional Kelly forgoes some long-run growth in exchange for a smoother journey and lower probability of severe interim losses.
Kelly and portfolio theory
The Kelly Criterion has deep connections to modern portfolio theory. Maximising the expected log of wealth — what Kelly prescribes — is equivalent to choosing the portfolio on the efficient frontier that a log-utility investor would select. This investor is more risk-averse than a linear-utility investor but less risk-averse than more cautious alternatives. The Kelly portfolio tends to be concentrated: because it allocates proportionally to the information ratio (Sharpe ratio squared, in continuous time), it overweights high-conviction high-Sharpe positions significantly. This is why Kelly-inspired sizing often leads to position concentrations that feel uncomfortably large to conventional portfolio managers used to equal-weighting or risk-parity approaches.