Risk Management
Kelly Criterion: Size Your Positions for Maximum Long-Run Growth
Most retail traders pick position sizes arbitrarily — $500 per trade, or "whatever feels right." That approach ignores the single most important input: the quality of your edge. Kelly Criterion does the opposite. It takes your edge — your win rate and your average win-to-loss ratio — and returns the exact fraction of capital that maximizes long-run compounded growth.
This is not a trading strategy. It is a mathematical framework for answering one question: given that I have a verified edge, how much should I bet on each occurrence?
Why Arbitrary Position Sizing Destroys Edge
Consider two traders with identical systems — 55% win rate, 1.5:1 average win-to-loss ratio. Trader A risks a flat $500 per trade regardless of account size. Trader B risks a fixed 3% of current capital per trade.
Both traders expect a positive outcome over 100 trades. But the path — the drawdowns, the compounding, and critically the probability of ruin before reaching 100 trades — differs entirely based on sizing alone. A positive expected value does not protect you from sequence risk. Running three losses in a row at 20% of capital per trade can force you out of the market before your edge has a chance to play out.
The Kelly Formula
The Kelly fraction — the optimal percentage of capital to risk per trade — is:
Where:
- = fraction of capital to risk per trade (0.20 = 20%)
- = win rate — the probability of a winning trade
- = win/loss ratio — average winning trade divided by average losing trade
A negative means you have no mathematical edge. Do not trade the system.
Kelly maximizes the expected logarithm of wealth, which is equivalent to maximizing long-run compounded growth rate:
This is why Kelly sizing produces faster long-run growth than any fixed-fraction system — it is mathematically optimal given accurate inputs.
A Concrete Example System
The numbers below come from a backtested momentum day-trading system — 200 trades across six months of data, not cherry-picked:
Win rate above 50%, R above 1.0, profit factor above 2.0. This system has edge. Kelly will return a positive fraction.
Computing the Kelly Fraction
For this system: W = 0.58, R = 1.75.
*f = W − (1 − W) / R**
Step by step:
f* = 0.58 − (1 − 0.58) / 1.75
f* = 0.58 − 0.42 / 1.75
f* = 0.58 − 0.24
*f = 0.34 — Kelly says risk 34% of capital per trade**
W, R = 0.58, 1.75 — win rate and R ratio from backtest
kelly = W - (1 - W) / R — apply Kelly formula
print(f"Full Kelly: {kelly:.1%}") — Full Kelly: 34.0%
print(f"Half Kelly: {kelly * 0.5:.1%}") — Half Kelly: 17.0%
print(f"Quarter Kelly: {kelly * 0.25:.1%}") — Quarter Kelly: 8.5%
On a $50,000 account, full Kelly says risk $17,000 per trade.
That is not a typo. Kelly is mathematically optimal — but only if your edge estimate is perfectly accurate and you have infinite psychological tolerance for drawdowns.
In practice, 34% per trade will produce 60–80% drawdowns on a normal run of bad luck. Read the next section before applying any Kelly output to a live account.
Use the live calculator to compute your own Kelly fraction:
Should You Even Use Kelly?
Kelly assumes your edge estimate is accurate and stable. Before applying any output to live capital, answer these questions:
Full Kelly vs. Fractional Kelly vs. Fixed Sizing
No professional systematic trader runs full Kelly on live capital. The comparison below shows why:
| Full Kelly — 34% | Half Kelly — 17% | Quarter Kelly — 8.5% | Fixed 2% | |
|---|---|---|---|---|
| Capital at risk | 34% per trade | 17% per trade | 8.5% per trade | 2% per trade |
| Expected max drawdown | 60–80% on bad runs | 25–40% | 10–18% | 6–10% |
| Recovery from 5 losses | Extremely slow | Manageable | Fast | Fast |
| Psychological survivability | Very low | Moderate | High | Very high |
| Growth rate | Theoretically maximum | ~75% of full Kelly growth | ~50% of full Kelly growth | Conservative but consistent |
| When to use | Never in live trading | Experienced traders, verified live edge | Recommended starting point for most traders | New systems, uncertain edge, learning phase |
Half-Kelly retains roughly 75% of the optimal growth rate while cutting maximum expected drawdown roughly in half. That tradeoff is why most quant funds operate somewhere between quarter-Kelly and half-Kelly.
What the Equity Curve Actually Looks Like
The chart below simulates half-Kelly sizing (17% per trade) across 20 recorded sessions using our example system — 58% win rate, 1.75 R ratio, starting from $50,000:
Half-Kelly Equity Curve — Simulated 20 Sessions
Starting at $50,000. After 20 sessions at half-Kelly the simulated account reaches ~$101,700 — a 103% gain. The same system at 2% fixed returns roughly 22% over the same period. The volatility — including the sharp dips in session 5 and session 12 — is the cost of that compounding.
From Kelly Fraction to Actual Share Count
Kelly gives you a fraction of capital to risk — not a dollar amount to buy. Convert it using your stop distance:
For our example system at quarter-Kelly (multiplier = 0.25) on a $50,000 account:
Use the position size calculator to apply this to your own entry and stop:
Frequently Asked Questions
What if my win rate estimate is wrong?
This is the largest practical risk with Kelly. An estimate that is 5 percentage points too high can inflate your Kelly fraction by 30–40% and push sizing into genuinely dangerous territory.
Consider the sensitivity: if your true win rate is 52% but you model 58%, your Kelly fraction goes from ~14% to ~34% — more than double. Running that oversized position on a weaker-than-modeled edge produces drawdowns far larger than your model predicts.
The fix: always apply a conservative haircut to your win rate estimate. If backtesting shows 58%, model at 54%. The cost of undersizing is slower growth. The cost of oversizing is potential ruin.
What is fractional Kelly and which fraction should I use?
Fractional Kelly means running a fixed proportion of the full Kelly output — typically half, quarter, or tenth.
- Half Kelly (0.5×): Retains approximately 75% of the optimal growth rate at roughly half the drawdown. Most institutional systematic traders operate in this range.
- Quarter Kelly (0.25×): Retains approximately 50% of optimal growth at roughly 25% of the drawdown. Recommended as the starting point for most retail systematic traders.
- Tenth Kelly (0.1×): Conservative. Produces results similar to a well-calibrated fixed-percentage system.
Start at quarter-Kelly for any new live system. Graduate to half-Kelly only after 6+ months of live performance confirms the edge holds out of sample.
Why does Kelly require recalculation on every trade?
Kelly gives you a fraction of current capital — not a fixed dollar amount. As your account grows, position sizes grow. As your account shrinks during a drawdown, position sizes shrink automatically. This is the mechanism that prevents ruin.
If you fix your dollar size based on an initial Kelly calculation and do not update it, you are not running Kelly — you are running a fixed-dollar system with a Kelly-informed initial number. For true Kelly compounding, recalculate before every trade using your current account value.
Can Kelly be applied to options or futures?
Yes, with modifications. The R ratio must reflect the actual payout structure of the instrument:
- Defined-risk options spreads: Use max profit as the win and max loss as the loss. Kelly works cleanly.
- Naked options: Theoretical max loss can be uncapped — Kelly produces undefined or absurdly large fractions. Never apply Kelly to undefined-risk positions.
- Futures: Kelly works well. Use dollar risk (ticks × tick value × contracts) as your loss unit.
For options, always use defined-risk structures (vertical spreads, iron condors, calendars) if you intend to size with Kelly. The math requires a bounded loss.