Kelly Criterion tells you how to size individual positions. But prediction markets have correlation. Positions move together. Understanding correlation prevents overexposure. Prevents ruin.
What is correlation in prediction markets
Correlation means positions move together. When one position wins, another likely wins too. Or loses. In prediction markets, correlation comes from shared outcomes.
Mutually exclusive
Only one can win. Perfect negative correlation.
Example: "Biden wins 2024" vs "Trump wins 2024". If Biden wins, Trump loses. Perfect hedge.
Positively correlated
Both likely win together. Or lose together.
Example: "Biden wins" and "Democrats win Senate". If Biden wins, Democrats likely win Senate too.
Why correlation matters
Kelly assumes independent bets. Prediction markets aren't independent. Correlation concentrates risk. You think you're diversified. You're not.
Example: overexposure
You calculate Kelly for three positions. Each suggests 20% of capital. You take all three. Total: 60% of capital.
But all three are correlated. "Biden wins". "Democrats win Senate". "Democrats win House". If Democrats lose, you lose all three. Not 20% risk. 60% risk.
Kelly didn't account for correlation. You're overexposed.
How to identify correlation
Ask one question. If Position A wins, what happens to Position B?
Mutually exclusive
If A wins, B loses. Perfect negative correlation.
Examples: "Biden wins" vs "Trump wins". "Bitcoin above $100k" vs "Bitcoin below $100k". "Shutdown happens" vs "Shutdown doesn't happen".
Positively correlated
If A wins, B likely wins. High positive correlation.
Examples: "Biden wins" and "Democrats win Senate". "Recession in 2024" and "Unemployment above 5%". "Fed cuts rates" and "Inflation below 3%".
Independent
If A wins, B is unaffected. No correlation.
Examples: "Biden wins" and "Bitcoin above $100k". "Fed cuts rates" and "Shutdown happens". Unrelated events.
Adjusting position sizes for correlation
Kelly gives you individual position sizes. Correlation means you need to reduce them. Here's how.
Mutually exclusive positions
These hedge each other. You can size both at full Kelly. But recognize you're hedging, not diversifying.
Example: "Biden wins" at 20% Kelly. "Trump wins" at 15% Kelly. Total exposure: 35%. But if one wins, the other loses. Net exposure is the difference: 5%.
Positively correlated positions
These concentrate risk. Reduce sizes. Treat correlated positions as one position.
Example: Three positions, each 20% Kelly. All correlated. Don't take 60%. Take 20% total. Split across the three. Or pick the best one.
Independent positions
These diversify risk. You can size each at full Kelly. But still cap total exposure.
Example: Three independent positions, each 20% Kelly. Total: 60%. This is fine if they're truly independent. But cap at 50% total to be safe.
Practical framework
- Calculate Kelly for each position individually
- Group positions by correlation (mutually exclusive, positively correlated, independent)
- For mutually exclusive: size both at Kelly, but recognize you're hedging
- For positively correlated: treat as one position, size at Kelly of the best one, or split Kelly across all
- For independent: size each at Kelly, but cap total portfolio exposure at 50%
- Always ask: if all correlated positions lose, what's my total loss?
Manage correlation across your portfolio
Understanding correlation prevents overexposure and helps you size positions correctly. Get early access to tools that identify correlated positions and help you manage portfolio risk across Kalshi and Polymarket.
Conclusion
Kelly Criterion tells you how to size individual positions. But prediction markets have correlation. Positions move together. Understanding correlation prevents overexposure. Prevents ruin.
Identify correlation by asking: if Position A wins, what happens to Position B? Mutually exclusive positions hedge. Positively correlated positions concentrate risk. Independent positions diversify.
Adjust position sizes accordingly. For correlated positions, treat as one position. Size at Kelly of the best one. Or split Kelly across all. Always ask: if all correlated positions lose, what's my total loss?