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The Kelly Criterion

Trading Intelligence

8 min read

Apply the Kelly formula and its fractional variants to find the theoretically optimal bet size that maximizes geometric growth rate.

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Nash Equilibrium and No Arbitrage

8 min

Variance & Standard Deviation

9 min

Skewness & Kurtosis

9 min

Monte Carlo Simulations

10 min

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Maximize long-term growth while minimizing blow-up risk — using math, not emotion.


Introduction

Risk sizing is the silent killer of most trading accounts.

  • Too big = blow up on variance
  • Too small = no meaningful growth
  • Random = rollercoaster equity curve with no confidence

The Kelly Criterion gives you a mathematically optimal position size — balancing growth and drawdown risk.

It’s how professional gamblers, quant traders, and algorithmic funds scale with edge.


What Is the Kelly Criterion?

The Kelly Formula is designed to calculate the optimal fraction of capital to risk per trade, based on:

  • Your win probability
  • Your win/loss ratio (risk/reward)

The basic formula:

Kelly % = (Win Rate × R:R) – Loss Rate

Where:

  • Win Rate = probability of a win
  • R:R = average win / average loss
  • Loss Rate = 1 – Win Rate

Example Calculation

You have:

  • Win rate = 55% (0.55)
  • R:R = 2:1 (you make 2R when you win, lose 1R when you lose)
  • Loss rate = 45% (0.45)

Plug it in:

Kelly % = (0.55 × 2) – 0.45 = 1.1 – 0.45 = 0.65

You should risk 65% of capital per trade.

Way too aggressive, right?

Exactly. That’s why pros never use full Kelly.


Why Full Kelly Is Too Aggressive for Trading

Kelly was designed for:

  • Fixed-odds games like blackjack or horse racing
  • Environments with zero variance in edge or rules

But trading has:

  • Wild variance
  • Emotional volatility
  • Execution slippage
  • Strategy degradation over time

So traders often use:

  • ½ Kelly (more conservative, balances growth and survivability)
  • ⅓ Kelly or less (even safer for high-variance systems)

How Kelly Helps Traders (Even If You Don’t Use It Literally)

1. It forces you to quantify your edge

No EV → no Kelly position sizing → This motivates serious journaling and system tracking


2. It adjusts based on performance

Better EV → more risk Worse EV → scale down automatically

Smart traders size dynamically based on real data, not confidence or emotion.


3. It keeps your equity curve in balance

Even at ½ Kelly:

  • Growth compounds well
  • Risk of ruin drops dramatically
  • You avoid overleveraging during a drawdown

When Kelly Breaks Down

Don’t use Kelly sizing if:

  • Your system has fewer than 100+ trades tested
  • You haven’t measured variance or drawdown
  • Your emotions override execution
  • You’re trading in markets with extreme tail risk (e.g., crypto during news)

In these cases, static sizing (fixed % risk per trade) is safer until your data matures.


How to Apply This in Real Trading

  1. Calculate:
  • Win rate
  • Avg win / avg loss
  • EV over at least 100 trades
  1. Use Kelly formula (or a calculator) to get:
  • Full Kelly %
  • Then divide by 2 or 3
  1. Compare to your current risk %:
  • Are you under-sizing and missing opportunity?
  • Or over-sizing and skating on variance?
  1. Backtest both fixed % and Kelly-based compounding → See what your system supports

Final Thought

Kelly is not magic. It’s a mathematical framework to stop you from being emotional about risk.

It tells you:

  • How much edge you actually have
  • How aggressively you can grow
  • And when to scale up or down

Don’t risk based on confidence. Risk based on math.