Kelly Criterion in Trading: The Optimal Bet Size
The Origin of Kelly: From Bell Labs to Wall Street
In 1956, John Larry Kelly Jr. at Bell Labs published a paper on information theory that would revolutionize gambling and eventually trading. His insight: there exists a mathematically optimal fraction of your capital to bet that maximizes long-term growth. Bet more than Kelly, and you actually reduce growth while increasing risk. Bet less, and you leave returns on the table.
Edward Thorp brought Kelly to practice — first at blackjack tables, then on Wall Street. His fund returned 15.1% annually for 20 years with never a losing year. The secret wasn't better stock picks. It was position sizing via Kelly.
The Kelly Formula Explained
The basic formula: f* = (b × p − q) / b
- f* = optimal fraction of capital to risk
- b = win/loss ratio (average win ÷ average loss)
- p = probability of winning
- q = probability of losing (1 − p)
Let's work through examples at different win rates:
| Win Rate | Win/Loss Ratio | Kelly % | Half Kelly |
|---|---|---|---|
| 50% | 2.0 | 25.0% | 12.5% |
| 55% | 1.5 | 21.7% | 10.8% |
| 60% | 1.2 | 26.7% | 13.3% |
| 40% | 3.0 | 20.0% | 10.0% |
| 45% | 2.0 | 17.5% | 8.8% |
Notice something critical: when Kelly returns a negative number, it means you have no edge — don't trade that strategy at all. This is one of Kelly's most valuable features: it tells you when to walk away.
Why Full Kelly Is Dangerous in Practice
Full Kelly is mathematically optimal in a world of perfect information and infinite time horizons. Real trading doesn't have either. Here's why full Kelly terrifies experienced practitioners:
Estimation error: Kelly assumes you know exact win rate and R:R. In trading, these are estimates from historical data. A 2% overestimate of win rate can lead to 30%+ over-betting.
Fat tails: Markets have extreme events beyond normal distribution. Kelly doesn't account for the “impossible” move that happens anyway.
Drawdown tolerance: Full Kelly historically produces 50–85% drawdowns. The math says you'll recover eventually. Your psychology says you'll panic-sell at the bottom.
Non-independence of trades: Kelly assumes each bet is independent. Trading strategies often have correlated outcomes — signals that cluster during specific regimes, effectively increasing position sizing beyond what Kelly intended.
Fractional Kelly: The Practical Solution
Almost every serious practitioner uses fractional Kelly. The logic: sacrifice some growth rate for dramatically better risk characteristics.
Half Kelly (0.5f*): The most popular choice. Achieves ~75% of full Kelly growth rate. Reduces maximum drawdown by roughly 50%. Provides a natural buffer against estimation errors.
Quarter Kelly (0.25f*): Best for uncertain estimates or volatile markets like crypto. Achieves ~50% of full Kelly growth. Drawdowns stay manageable even during black swan events.
The beauty of fractional Kelly: even at quarter Kelly, you're still sizing optimally relative to your edge. You're just being more conservative about how much edge you actually have — which is always the right approach when real money is on the line.
Why Fractional Kelly Dominates in Real Trading
The mathematical argument for fractional Kelly goes deeper than simple caution. Consider the asymmetry of errors: if you overestimate your edge by 20% and use full Kelly, you over-bet substantially, destroying capital through excessive drawdowns. If you underestimate by 20%, you simply earn slightly less. Half Kelly naturally protects against the more dangerous direction.
| Fraction | Growth vs Full Kelly | Max DD Reduction | Best For |
|---|---|---|---|
| Full (1.0f*) | 100% | Baseline | Theoretical only |
| Half (0.5f*) | ~75% | ~50% | High-confidence strategies |
| Third (0.33f*) | ~60% | ~65% | Moderate-confidence strategies |
| Quarter (0.25f*) | ~50% | ~75% | Uncertain estimates, volatile markets |
Kelly with Variable Win/Loss Sizes
The basic Kelly formula assumes binary outcomes — you either win a fixed amount or lose a fixed amount. Real trading has a distribution of win and loss sizes. A trend-following strategy produces many small losses and occasional large wins. A scalping strategy shows consistent small wins and rare large losses.
For non-binary outcomes, most traders approximate Kelly by using the average win and average loss from their backtest results. This works when the distribution of trade outcomes is reasonably stable. When the distribution is highly skewed — as with trend-following strategies that produce 80% small losers and 20% large winners — the basic formula tends to oversize positions because it doesn't account for outcome variance.
The practical fix: when your strategy produces highly variable trade sizes, reduce your Kelly fraction further. If the standard deviation of trade returns exceeds 2× the mean return, use quarter Kelly or lower.
Implementing Kelly in Backtesting
To use Kelly in your backtesting workflow:
- Run initial backtest with fixed fractional sizing (1–2%)
- Extract statistics: win rate, average win, average loss from the trade log
- Calculate Kelly: f* = (b×p − q) / b using your strategy's actual numbers
- Apply fractional Kelly: choose half or quarter depending on your confidence
- Re-run backtest with Kelly-based sizing
- Compare metrics: Sharpe, max drawdown, CAGR between fixed and Kelly approaches
In StratBase.ai, you can test different position sizing methods on the same strategy to directly compare outcomes.
One critical tip: calculate Kelly from out-of-sample data, never from the same period you optimized on. Using in-sample stats inflates your edge estimate, leading to over-betting.
Kelly Criterion Limitations
Kelly has boundaries that traders should respect:
Parameter instability. Kelly requires accurate win rate and reward-to-risk estimates. These shift as market conditions change. A strategy with 55% win rate in a trending market might drop to 45% during chop — making the trending-market Kelly sizing dangerously aggressive.
Serial correlation. Kelly assumes trade independence, but many strategies exhibit winning and losing streaks. This clustering means the actual risk of ruin is higher than Kelly's independence assumption predicts.
Capital constraints. Kelly can suggest risking 20–30% per trade for high-edge setups. Even at half Kelly, that's 10–15% — impractical for strategies holding multiple positions simultaneously.
Further Reading
About the Author
Financial data analyst focused on crypto derivatives and on-chain metrics. Expert in futures market microstructure and funding rate strategies.
FAQ
What is the Kelly Criterion formula?▾
The Kelly Criterion formula is: f* = (b × p - q) / b, where f* is the fraction of capital to bet, b is the net odds (reward/risk), p is the probability of winning, and q is the probability of losing (1-p). For trading: if your strategy wins 60% of the time with a 1.5:1 reward/risk, Kelly says bet (1.5 × 0.6 - 0.4) / 1.5 = 33% of capital per trade.
Why do traders use half Kelly instead of full Kelly?▾
Full Kelly maximizes the geometric growth rate but creates extreme volatility — drawdowns of 50-80% are mathematically expected. Half Kelly achieves about 75% of full Kelly's growth rate while cutting peak drawdowns roughly in half. It also provides a buffer against estimation errors in win rate and reward/risk ratio, which are never perfectly known in real trading.
Can you use Kelly Criterion for crypto trading?▾
Yes, but with important caveats. Crypto markets have fat tails (extreme moves beyond normal distribution), so standard Kelly tends to over-bet. Use quarter-Kelly or less for crypto strategies. Also, recalculate parameters frequently since crypto market dynamics shift rapidly. Backtest your strategy across multiple market regimes before applying Kelly to live capital.
Comments (0)
Loading comments...