This guide explains the formula, a worked example, why full Kelly is too aggressive in practice, how fractional Kelly works, and how to apply it to trading strategies.
The Kelly formula
For a bet that wins a fixed amount or loses a fixed amount, the Kelly fraction is:
f* = W − (1 − W) ÷ R
where:
- f* is the fraction of capital to risk on each trade,
- W is the probability of winning,
- R is the ratio of the average win to the average loss.
If the result is zero or negative, the strategy has no edge and Kelly says do not trade it.
A worked example
A strategy's tested results show:
- Win rate: 55%, so W = 0.55.
- Average win: ₹1,200. Average loss: ₹1,000. So R = 1.2.
f* = 0.55 − 0.45 ÷ 1.2 = 0.55 − 0.375 = 0.175
Full Kelly says risk 17.5% of capital per trade. On a ₹10 lakh account, that is ₹1,75,000 at risk on each trade, where "at risk" means the amount lost if the trade hits its stop.
That number should feel alarming. It is mathematically optimal for long-run growth under perfect knowledge, and reckless in practice.
Why full Kelly is too aggressive
Your estimates are uncertain
Kelly assumes you know W and R exactly. In trading you only have estimates from a backtest or a short live record. If your true win rate is 52% instead of 55%, the correct Kelly fraction in the example falls from 17.5% to 12%. Betting more than the true Kelly fraction reduces long-run growth, and betting twice the true Kelly fraction drives expected growth to zero.
Drawdowns are severe
Even with perfect estimates, full Kelly produces deep drawdowns. In the theoretical model, a bettor at full Kelly has about a 50% chance of seeing their capital fall to half its peak at some point. At half Kelly, that chance falls to about 12.5%, while long-run growth falls by only about a quarter.
Trades are not independent
Kelly assumes each bet is independent. Trading results often cluster, with losses coming together in volatile periods, which makes drawdowns worse than the formula expects.
Fractional Kelly
Most practitioners use a fraction of the Kelly bet, such as half or a quarter:
| Fraction | Risk per trade in the example | Growth compared with full Kelly | Drawdowns |
|---|---|---|---|
| Full Kelly | 17.5% | 100% | Very deep |
| Half Kelly | 8.75% | About 75% | Much shallower |
| Quarter Kelly | 4.4% | About 44% | Shallow |
Even quarter Kelly here is far above the 1% to 2% risk per trade that many traders use. That gap is a reminder that Kelly is a ceiling, not a target.
Applying Kelly to trading strategies
- Use out-of-sample results for W and R, not the best backtest. See avoiding overfitting.
- Use costs-included figures for wins and losses.
- Shrink the estimate. Assume your edge is smaller than the backtest shows.
- Take a fraction, such as a quarter of the result.
- Cap it. Apply a maximum risk per trade, such as 2%, whatever the formula says.
- Check with Monte Carlo. Simulate the drawdowns at your chosen size. See Monte Carlo simulation.
- Translate to lots. Divide the rupee risk by the loss per lot at the stop, and round down.
Translating to position size
Suppose quarter Kelly with a 2% cap gives 2% risk on a ₹10 lakh account: ₹20,000. If a trade's stop would lose ₹6,000 per lot, the position is three lots (₹18,000 at risk), because four would exceed the limit. The position size calculator does this step.
Kelly for options strategies
Option strategies often have a high win rate and a large average loss, such as credit spreads. Kelly handles this through R. For example, a strategy that wins 75% of the time with an average win of ₹4,000 and an average loss of ₹12,000 has R = 1/3:
f* = 0.75 − 0.25 ÷ (1/3) = 0.75 − 0.75 = 0
Kelly says there is no edge: the high win rate exactly balances the large losses. Any costs would make it negative. This is a useful check on strategies that look attractive because they win often.
Kelly vs fixed-fraction sizing
| Kelly | Fixed fraction | |
|---|---|---|
| Basis | Your estimated edge | A risk level you choose, such as 1% |
| Adapts to edge | Yes | No |
| Sensitivity to estimates | High | Low |
| Typical use | As a ceiling or a guide | As the everyday rule |
Many traders use fixed-fraction sizing day to day and use Kelly to check that their fraction is well below the theoretical maximum.
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Frequently asked questions
What is the Kelly criterion in simple words?
A formula that suggests what share of your capital to risk on each trade, based on your win rate and how large your wins are compared with your losses.
Should I use full Kelly?
Almost never. Your estimates are uncertain and full Kelly produces deep drawdowns. Most practitioners use half or less, with a hard cap.
What if Kelly gives a negative number?
The strategy has no edge on your estimates, and Kelly says not to trade it.
Does Kelly work for intraday trading?
The maths applies to any repeated bet, but intraday strategies often have small edges and high costs, which make the Kelly fraction small or zero.
Sources
- Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal, 35(4), 917–926
- Thorp, E. O. (2006). The Kelly Criterion in Blackjack, Sports Betting and the Stock Market. In Handbook of Asset and Liability Management, Elsevier
- MacLean, L. C., Thorp, E. O. and Ziemba, W. T. (2011). The Kelly Capital Growth Investment Criterion. World Scientific