Guide · Risk

Kelly, fractional Kelly, and the gap between them

Kelly answers a precise question: what fraction of capital maximises the long-run growth rate of a repeated bet. It answers it optimally, and the answer is usually too aggressive to trade.

The formula

For a bet that wins with probability p and pays b to 1:

f* = p − (1 − p) ÷ b where f* is the fraction of capital to risk, p is the win probability, b is the reward-to-risk ratio

A setup that wins 45% of the time at 2R:

f* = 0.45 − 0.55 ÷ 2 = 0.45 − 0.275 = 0.175 → 17.5% of capital

Risking 17.5% of the account on one trade is not a plan, it is a countdown. That number is correct and unusable, and understanding why is the whole point of the guide.

Why full Kelly is unusable

  • Your inputs are estimates. Kelly assumes you know p and b exactly. You know them from a finite sample, and overestimating the edge overshoots the optimum badly — the growth curve falls off much faster above full Kelly than below it.
  • The drawdowns are brutal. At full Kelly, drawdowns of 50% or more are routine, not tail events. Mathematically survivable, behaviourally not.
  • Trades are not independent or sequential. Kelly assumes one bet resolves before the next. Real positions overlap and correlate, which stacks risk the formula never accounted for.
  • Edges decay. The p you measured last year is not the p in force today.

Fractional Kelly

Because the growth curve is flat near its peak but steep past it, taking a fraction of Kelly gives up little expected growth and removes most of the variance.

SizingFraction of f*Trade-off
Full Kelly100%Maximum theoretical growth, ruinous variance, extremely sensitive to estimation error
Half Kelly50%Roughly three quarters of the growth with dramatically lower drawdown — the common practitioner choice
Quarter Kelly25%Modest growth, mild drawdowns, very tolerant of a wrong edge estimate
Fixed 1% riskusually well under 25%Ignores the edge estimate entirely; robust, simple, and what most retail traders should start with

The practical reading: if your Kelly fraction says 17.5% and your rule says 1%, the rule is not being timid — it is pricing in the fact that you do not really know p.

When Kelly is genuinely useful

Not usually as a sizing rule. It is most useful as a ceiling and as a diagnostic. If your fixed risk per trade is above quarter Kelly for your measured edge, you are oversized for the edge you can actually demonstrate. And if Kelly comes out negative, the formula is telling you the setup has no edge and should not be traded at all — which is the most valuable output it produces.

The free risk toolkit computes the Kelly fraction alongside expectancy, break-even win rate, and a Monte Carlo risk-of-ruin simulation, so you can see all four move together when you change the inputs.

Educational content, not financial advice. No live profit-and-loss figures are claimed anywhere on this site; backtest and walk-forward results are always labelled as such. Full terms: /terms.html

Tools referenced in this guide

FAQ

Quick answers

What is Kelly?

The bet fraction that maximises long-run growth: f* = p − (1 − p) ÷ b, using win probability p and reward-to-risk b.

What does it give for trading?

45% win rate at 2R gives 17.5% of capital per trade — correct arithmetic, unusable in practice.

Why fractional Kelly?

The growth curve is flat below the peak and steep above it. Half Kelly keeps most of the growth and sheds most of the variance.

What if you overbet?

Growth collapses fast past the optimum. Since edges are estimated from small samples, overbetting is the likely error.

Negative Kelly?

The setup has negative expectancy. Correct size is zero — the most useful answer the formula gives.

Should beginners use it?

Mostly no. A fixed ~1% risk is more robust because it does not depend on knowing your edge precisely.