Position Sizing with the Kelly Criterion (and Why You Should Bet Half)

The problem position sizing actually solves

Most traders obsess over entries and exits and treat position size as an afterthought. That is backwards. Once you have a positive edge, the single biggest lever on your long-run result is how much you risk per trade. Risk too little and you barely compound. Risk too much and you blow up before the edge has time to play out.

The reason is the gap between arithmetic and geometric growth. Your average return per trade (arithmetic mean) is not what your account follows. Your account compounds multiplicatively, so it follows the geometric mean, and the geometric mean is always lower than the arithmetic mean by an amount that grows with volatility. Bet bigger and your arithmetic expectation rises, but variance rises faster, so past a certain point your geometric growth actually falls.

The brutal version of this is ruin. A 50% loss requires a 100% gain to recover. An 80% loss requires a 400% gain. Drawdowns hurt asymmetrically because they shrink the base you compound from. The whole point of a sizing rule is to keep you on the part of the curve where you compound fast without wandering into the zone where a normal, expected losing streak does permanent damage. The Kelly criterion is the formula that finds the exact top of that curve.

The Kelly formula

Kelly was derived in 1956 by John Kelly Jr. at Bell Labs. In its classic betting form it answers: what fraction of your bankroll maximizes long-run geometric growth?

For trading it is cleaner to use the win-rate / reward-to-risk form. If W is your win rate and R is your reward-to-risk ratio (average win in R ÷ average loss in R), the same equation becomes:

Worked example. Take a system with a 55% win rate and an average 1.5R payoff (winners average 1.5 times the size of losers):

Twenty-five percent per trade. If that number makes you uncomfortable, good. It should. Full Kelly is the mathematically optimal size for pure growth, and it is also far more aggressive than any sane trader would run. The next section explains why.

Why full Kelly is too aggressive

Kelly maximizes the expected long-run growth rate. It does not minimize volatility, cap drawdowns, or care about how it feels to live through. Three things make full Kelly impractical for real trading.

• Drawdowns are savage

  A useful rule of thumb for full Kelly: the probability of your equity dropping to a fraction x of its peak at some point is roughly x. So a 50% drawdown happens with probability around 50%, and a 67% drawdown with probability around 33%. At full Kelly, a 50%+ drawdown is not a tail risk, it is the base case.

• Volatility scales faster than growth

  Near the Kelly peak the growth curve is flat: betting 70% of Kelly and 100% of Kelly produce almost the same growth. But variance keeps climbing the whole way up. You pay a large amount of volatility for a tiny amount of extra growth.

• Your edge is estimated, not known

  Kelly assumes you know p and R exactly. You never do. They come from a backtest or a few hundred live trades, both noisy. If your true edge is half what you measured, full Kelly on the measured number is double Kelly on the real edge, which produces negative long-run growth. Overbetting is far more punishing than underbetting.

That last point is the killer. The growth-vs-size curve is asymmetric: if you bet exactly 2× Kelly, your expected growth rate drops all the way back to zero. Bet more than twice Kelly and you lose money in the long run despite having a genuine edge. Estimation error pushes you toward overbetting precisely where it hurts most.

Fractional Kelly: bet half (or a quarter)

The fix is simple: bet a constant fraction of full Kelly. Half Kelly and quarter Kelly are the standard choices. Because growth is flat near the peak and variance falls quickly as you move below it, fractional Kelly buys a huge reduction in risk for a small reduction in growth.

Half Kelly keeps roughly three-quarters of the growth rate while cutting volatility in half: the worst-case drawdown for half Kelly is roughly the square of full Kelly's, so a 50% full-Kelly drawdown becomes about a 25% half-Kelly drawdown. That is the trade nearly every professional makes: give up a little compounding to make the path survivable. Even 6.25% per trade is more than most disciplined traders will actually run, which tells you how conservative real sizing is relative to the math.

Kelly meets reality: edges that drift

The formula assumes a stationary, known, independent edge. Live markets violate all three assumptions, and each violation pushes your safe fraction lower.

• →Your win rate is estimated. 200 trades at a true 55% win rate produce a 95% confidence interval roughly ±7%. Plug the unlucky end (48%) into Kelly and the optimal fraction can swing dramatically. Always size from the conservative end of your estimate.
• →Edges are non-stationary. A strategy that printed 55% last year may be 51% now as the market regime shifts and other participants arb the inefficiency away. Kelly computed on stale stats overbets a decaying edge.
• →Correlated bets share risk. Kelly is derived for one bet at a time. Run five correlated longs and they behave like one larger bet. Effective Kelly across correlated positions is far smaller than the sum of the individual Kelly fractions, because their losses cluster.

The practical conclusion: every source of uncertainty is a reason to bet less than the headline number. Fractional Kelly is a volatility preference, but it is mainly a margin of safety against the fact that your inputs are wrong by an unknown amount.

Practical rules that approximate Kelly safely

Most successful traders never compute Kelly explicitly on each trade. Instead they use heuristics that land in the same conservative neighborhood as fractional Kelly, while holding up well against bad inputs.

• Fixed-fractional risk

  Risk a constant small fraction of equity per trade, typically 0.5% to 2%. This is fractional Kelly in disguise: for most retail edges, half to quarter Kelly works out to roughly 1% to 3% per trade, so a flat 1% is a sane default that automatically scales position size up as you win and down as you lose.

• Volatility targeting

  Size each position so its expected dollar volatility is constant, e.g. shrink size when ATR expands and grow it when ATR contracts. This keeps risk steady across instruments and regimes, which is exactly what Kelly wants when payoffs vary.

• Cap per-trade R

  Set a hard ceiling on max risk per trade (say 2R) and per day (say 4R) regardless of how attractive the setup looks. This caps the damage from estimation error and correlated entries, which is where naive Kelly does the most harm.

The common thread is that all three keep your effective fraction small, constant in risk terms, and bounded against worst cases. That is what fractional Kelly delivers, achieved with rules simple enough to follow under pressure.

Worked example: sizing a position on a $50k account

Put it together on a concrete trade. You run the 55% win-rate, 1.5R system from earlier. Full Kelly said 25%; you have decided to run half Kelly, so your target risk per trade is 12.5%. But you also cap per-trade risk at 2% of equity, and that cap binds: 2% is far below 12.5%, so 2% is what you actually use. That gap is the whole point, the math says you could bet much more, and discipline says you should not.

If you take this exact trade and your stop is hit, you lose $1,000, or 2% of the account, exactly as planned. If it reaches target you make roughly 2.46R after fees, about $2,460. Notice that the binding constraint was the 2% cap, not the Kelly fraction. That is normal and healthy: Kelly tells you the ceiling, your risk rules keep you well underneath it, and fees quietly lower the edge you fed into the math in the first place. Size from the conservative end, recompute as your live stats update, and never let the optimal-growth number talk you into a position you cannot sit through a losing streak with.

Summary

Frequently asked questions