April 15: Kelly Criterion (For binary outcomes)
How much should you bet when you have an edge? The Kelly Criterion gives a mathematical answer: bet enough to maximize long-term growth, but not so much that a losing streak wipes you out.
The Kelly Criterion can lead to aggressive bets or investments. Many traders reduce position sizes using “fractional Kelly” (half-Kelly) to limit volatility and drawdowns.
Formula
\( f = \frac{b p - q}{b} \)
where:
- f = fraction of capital to invest
- b = odds received on the bet (e.g., if you win $1 for each $1 bet, then b = 1)
- p = probability of winning
- q = probability of losing (q = 1 - p)
Underlying Assumptions
- You can repeat the bet an infinite number of times.
- Your winning probability (p > 1/(b + 1)) is known and consistent.
- Capital can be divided and reinvested infinitely.
- The goal is to maximize the long-term logarithmic growth of wealth.
- No transaction costs or slippage.