Kelly criterion is a mathematical formula that calculates the optimal fraction of capital to risk on each trade to maximize long-term portfolio growth. Developed by John Kelly at Bell Labs in 1956, it’s used by legendary traders and investors including Ed Thorp and Warren Buffett. However, full Kelly sizing is aggressive—most traders use a fraction of the Kelly amount for safer position sizing.
- Kelly % = Win Rate - (Loss Rate / Payoff Ratio)
- Full Kelly maximizes growth but with high volatility—use half or quarter Kelly
- Negative Kelly means negative expectancy—don’t trade that strategy
How Kelly Criterion Works
The Kelly formula tells you what percentage of your capital to risk based on your edge. It balances two competing goals: bet enough to grow capital, but not so much that a losing streak wipes you out.
Kelly % = W - [(1 - W) / R]
Where:
- W = Win rate (probability of winning)
- R = Payoff ratio (average win / average loss)
Quick Reference
| Win Rate | Payoff Ratio | Full Kelly | Half Kelly |
|---|---|---|---|
| 40% | 2.0 | 10% | 5% |
| 50% | 1.5 | 17% | 8.5% |
| 55% | 1.2 | 18% | 9% |
| 60% | 1.0 | 20% | 10% |
| 60% | 1.5 | 33% | 16.5% |
Example Calculation
Your Trading Statistics:
- Win Rate: 55%
- Average Win: $450
- Average Loss: $300
- Payoff Ratio: $450 / $300 = 1.5
Kelly Calculation:
Kelly % = 0.55 - (0.45 / 1.5)
Kelly % = 0.55 - 0.30
Kelly % = 0.25 = 25%
Full Kelly suggests risking 25% of your account per trade.
But wait—that’s extremely aggressive. A four-trade losing streak would wipe out 68% of your account. This is why traders use fractional Kelly.
Kelly criterion calculates optimal position size to maximize long-term growth. The formula is Win Rate minus Loss Rate divided by Payoff Ratio. Full Kelly is too aggressive—most traders use half or quarter Kelly for safer sizing while still capturing their edge.
Why Full Kelly Is Dangerous
Full Kelly assumes:
- You know your exact win rate (you don’t—you have an estimate)
- You know your exact payoff ratio (same problem)
- You have infinite time horizon (you don’t)
- You can handle massive volatility (most can’t)
The Math of Over-Betting:
| Sizing Method | Growth Rate | Max Drawdown | Risk of Ruin |
|---|---|---|---|
| Full Kelly | Maximum | Very High | Significant |
| Half Kelly | 75% of max | Moderate | Low |
| Quarter Kelly | 56% of max | Low | Very Low |
Half Kelly achieves 75% of the growth rate with dramatically less volatility and risk of ruin. Quarter Kelly achieves 56% with very low risk.
Fractional Kelly in Practice
Most successful traders use:
| Approach | Position Size | Best For |
|---|---|---|
| Quarter Kelly | 25% of Kelly | Conservative traders |
| Half Kelly | 50% of Kelly | Most traders |
| Full Kelly | 100% of Kelly | High conviction only |
Example with Half Kelly: If Kelly = 25%, use 12.5% per trade.
Example with Quarter Kelly: If Kelly = 25%, use 6.25% per trade.
Even 6.25% per trade is aggressive by most standards. Many traders cap at 1-2% regardless of what Kelly suggests.
Kelly Criterion for Negative Expectancy
What if Kelly gives a negative number?
Example:
- Win Rate: 40%
- Payoff Ratio: 1.2
Kelly = 0.40 - (0.60 / 1.2) = 0.40 - 0.50 = -0.10 = -10%
Negative Kelly means: Don’t trade this strategy. You have negative expectancy. No position size can make a losing strategy profitable.
Practical Application
- Calculate your edge – Track at least 50-100 trades to get reliable win rate and payoff ratio
- Apply Kelly formula – Calculate the full Kelly percentage
- Use fractional Kelly – Most traders use half or quarter Kelly
- Cap maximum size – Even if Kelly says 15%, consider capping at 2-5%
- Recalculate periodically – Your edge changes; update your sizing accordingly
Common Mistakes
-
Using full Kelly – Overconfidence in edge estimates leads to over-betting. The downside is catastrophic.
-
Small sample size – Kelly from 20 trades is unreliable. You need 50+ trades minimum, preferably 100+.
-
Ignoring correlation – Multiple positions using Kelly individually can result in far more than Kelly risk in total.
-
Static calculation – Your edge varies by market condition. Recalculate Kelly as your statistics change.
How JournalPlus Tracks Kelly Criterion
JournalPlus calculates your Kelly percentage based on actual trading statistics. You can see recommended position sizes at full, half, and quarter Kelly—helping you size positions optimally based on your real edge, not guesswork.
