The Kelly Criterion: Optimal Sizing and Why Nobody Uses Full Kelly

The formula and what it means

BINARY VERSION
   f* = p - (1 - p) / R

   p = probability of winning
   R = ratio of win size to loss size
   f* = fraction of capital to risk

Example: 40% win rate, winners are 3x losers
   f* = 0.40 - 0.60 / 3 = 0.40 - 0.20 = 0.20
   Full Kelly says risk 20% of capital per trade.

CONTINUOUS APPROXIMATION (for return series)
   f* = mean return / variance of returns

Example: strategy with 12% expected annual return and
         18% annual volatility
   f* = 0.12 / 0.0324 = 3.7  ->  3.7x leverage at full Kelly

Both results illustrate the problem. Risking 20 percent of capital per trade, or running 3.7 times leverage, is far beyond what any disciplined trader would consider. Kelly is mathematically correct about growth maximisation and practically unusable at full size.

Why nobody uses full Kelly

• Drawdowns are brutal. At full Kelly, a drawdown of 50 percent from a peak is a routine occurrence rather than a crisis. Most traders abandon a strategy well before that.
• Edge estimates are wrong. Kelly assumes you know p and R exactly. In practice both are estimated from a limited sample with substantial error, and overestimating the edge means the computed size is above optimal, where growth falls rapidly.
• Overbetting is asymmetrically punished. The growth curve is roughly flat just below optimal and falls steeply above it. Betting half of optimal costs a quarter of the growth; betting double optimal produces zero growth.
• Returns are not independent. Kelly assumes each bet is independent. Trading returns are serially correlated and cluster, which makes realised drawdowns worse than the theory suggests.
• The edge changes. A size computed from a historical edge becomes wrong when the edge decays, and Kelly does not know that it has.

Fractional Kelly in practice

The key property is that growth falls slowly as you reduce size while volatility falls linearly. Half Kelly gives up a quarter of the growth for half the volatility, which is an excellent trade for anyone who has to live through the drawdowns. Quarter Kelly is the most commonly cited practical choice for strategies with genuine but uncertain edges.

Applying it to a real strategy

1. 1

   Estimate p and R from out-of-sample results

   Use forward-tested or out-of-sample data rather than the optimised backtest, which overstates both figures.

2. 2

   Compute full Kelly and immediately discount it

   Apply a fraction of 0.1 to 0.25 for most retail strategies, reflecting the uncertainty in the estimates.

3. 3

   Convert to a per-trade risk percentage

   The result is usually far closer to the conventional 0.5 to 1 percent per trade than to the raw Kelly figure, which is a useful sanity check on standard practice.

4. 4

   Cap by drawdown tolerance, not only by Kelly

   Run a Monte Carlo simulation at the proposed size and check the distribution of maximum drawdowns. If the 95th percentile exceeds what you can sit through, reduce the size regardless of what Kelly says.

5. 5

   Re-estimate periodically

   Recompute from rolling live results rather than from the original backtest, and reduce size if the realised edge is below the estimate.

6. 6

   Account for correlation across positions

   Kelly for a single bet does not extend directly to a portfolio of correlated positions. The portfolio equivalent requires the covariance matrix and produces smaller individual sizes.

Kelly and volatility targeting

The continuous form of Kelly, mean divided by variance, has a direct relationship with volatility targeting. If you assume a constant expected return, then Kelly sizing implies scaling exposure inversely with variance, which is exactly what volatility targeting does.

This is why volatility targeting is often described as an implicit Kelly implementation: it does not require estimating the edge, only the variance, which is far easier to measure reliably. For most practical purposes, targeting a fixed portfolio volatility at a conservative level achieves what fractional Kelly aims at, with fewer fragile estimates.