The Kelly Formula: What Percentage of Capital Should You Risk per Trade?
Most people choose how much to risk by intuition. The Kelly formula calculates the bet fraction that maximizes long-term wealth growth when win probability and payoff ratio are known. Its practical importance lies less in giving a perfect answer than in showing that many people bet far above that level.
The Formula Fits on One Line
Kelly requires only win probability and payoff ratio.
f = Fraction of capital risked per bet
p = Probability of winning
q = Probability of losing = 1 − p
b = Payoff ratio, amount won ÷ amount lost
Example
Win rate 55% · Payoff ratio 1.5
f = (1.5 × 0.55 − 0.45) ÷ 1.5
= (0.825 − 0.45) ÷ 1.5
= 0.375 ÷ 1.5 = 0.25 → 25%
Here 25% does not mean opening a position worth 25% of capital. It means being prepared to lose 25% of capital in that bet. Confusing the two can multiply actual exposure. See the definitions of win rate and risk and reward.
When the Result Is Zero or Negative
Kelly's first use is assessing whether there is a reason to bet, before asking how much.
f = (1.0 × 0.5 − 0.5) ÷ 1.0 = 0
→ No reason to bet.
45% win rate · 2.0 payoff ratio
f = (2.0 × 0.45 − 0.55) ÷ 2.0
= (0.9 − 0.55) ÷ 2.0 = 0.175 → 17.5%
→ Positive despite winning fewer than half the bets.
60% win rate · 0.5 payoff ratio
f = (0.5 × 0.6 − 0.4) ÷ 0.5
= (0.3 − 0.4) ÷ 0.5 = −0.2
→ Negative: betting more reduces wealth.
The third case is a common trap. A 60% win rate feels good, but winning small and losing twice as much creates a negative result. This is equivalent to negative expectancy and R-multiples. Profit factor examines the same issue through gross profits relative to gross losses.
Fees Can Reverse the Result
The preceding calculations assume zero costs. In reality, round-trip fees reduce wins and increase losses, worsening b from both sides.
Assuming no fees
b = 1.0 ÷ 1.0 = 1.0
f = (1.0 × 0.52 − 0.48) ÷ 1.0 = +0.04 → 4%
Including a 0.10% round-trip fee
Net win = 1.0% − 0.10% = 0.90%
Net loss = 1.0% + 0.10% = 1.10%
b = 0.90 ÷ 1.10 = 0.818
f = (0.818 × 0.52 − 0.48) ÷ 0.818
= (0.425 − 0.48) ÷ 0.818 = −0.067
→ The result flips from 4% to negative.
Narrower targets and stops make this reversal easier. A 0.10% fee consumes 10% of a 1% target. See round-trip trading costs for the costs of one trade and frequency and fee drag for accumulation across trades.
Using the Full Result Can Halve Your Account
Kelly maximizes long-term growth, not comfort. Using the whole fraction, or full Kelly, produces severe interim drawdowns.
Full Kelly → About a 50% chance of eventually experiencing an account decline to half its value.
Half Kelly, f/2 → About 12% for the same event.
Quarter Kelly, f/4 → Below about 2%.
How much growth is sacrificed?
Half Kelly = 75% of maximum growth.
Quarter Kelly = about 44%.
This explains half Kelly's popularity: it retains three-quarters of growth while reducing the probability of halving from 50% to about 12%. Maximum drawdown covers returns needed for recovery, and risk of ruin examines the chance of an account approaching zero.
The real lesson is what happens when you bet more than Kelly. In theory, twice Kelly reduces long-term growth to around zero; above that, the account shrinks even with a good win rate. Overbetting can reverse the sign of growth, rather than merely making results slightly worse.
A Five-Percentage-Point Win-Rate Error Can Cause Overbetting
Win rate and payoff ratio are estimates from historical records. Even mild optimism can substantially change the result.
Estimated win rate 55% → f = 25.0%
Actual win rate 50% → Appropriate f = 16.7%
→ Risking 25% is 1.5 times the appropriate amount.
Actual win rate 45% → Appropriate f = 8.3%
→ Risking 25% is 3 times the appropriate amount.
→ A 10-percentage-point error creates threefold overbetting.
With only about 30 trades, apparent 55% and 45% win rates can readily switch. Trade sample size explains when estimates become more credible, while losing-streak probability explains long streaks unrelated to skill. Half or quarter Kelly provides a buffer for estimation error, not merely an expression of fear.
Converting Risk into an Actual Order Size
Because f is the fraction you can lose, you need the stop distance to calculate order size.
Full Kelly f = 25% → Risk per trade $1,250
Quarter Kelly f = 6.25% → Risk per trade $312
Stop 3% below entry
Order size = $312 ÷ 0.03 = $10,400
Exposure relative to capital = 10,400 ÷ 5,000 ≈ 2.1×
Narrow the stop to 1.5%
Order size = $312 ÷ 0.015 = $20,800
Exposure 4.2×: the risk amount is unchanged, but exposure doubles.
A narrower stop enlarges the order for the same risk and increases fees and slippage. See position sizing for the process of setting risk first and calculating order size backward.
Assumptions and Limitations
Kelly is conditional. Without the following assumptions, obtaining a number does not make it meaningful.
If they continually change with conditions, reliable inputs are absent.
② Independent bets
If positions move together, their actual risks add up.
③ Adequate sample
At least dozens of trades, preferably more than 100.
④ Use half or less in practice
Half Kelly or quarter Kelly.
⑤ Apply a separate cap
Even if the formula returns 30%, limit per-trade risk to a few percent of capital.
Independence is especially important in crypto. Five altcoins often move with BTC, creating effectively one bet rather than five. Applying Kelly separately to each can greatly exceed appropriate aggregate risk.
The separate cap is a safeguard independent of the formula. A 25% result does not make repeatedly risking 25% of capital realistic for most people. Monte Carlo simulation can replay identical win rates and payoff ratios to visualize account fluctuations. The multiplication across successive bets follows compounding.
Recap
② f is the fraction you can lose per trade, not the order size.
③ 55% wins and 1.5 payoff → f = 25%.
④ Zero or negative f means no reason to bet.
⑤ Fees can turn +4% into −6.7%.
⑥ Full Kelly has approximately a 50% probability of halving the account.
⑦ Half Kelly retains 75% growth with a 12% halving probability.
⑧ Twice Kelly reduces growth to near zero.
⑨ A 10-percentage-point win-rate error can cause threefold overbetting.
⑩ In practice, use quarter Kelly plus a separate cap.
Kelly's result is a line not to exceed, rather than a target. If your current risk fraction exceeds it, reducing size takes priority over trying to improve the win rate.
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