Kelly Criterion

Kelly Criterion

The Kelly Criterion determines the optimal fraction of capital to bet on each trade to maximize long-run wealth growth. Overbetting leads to ruin; underbetting leaves growth on the table.

Formula

f* = p - q/b

Where:

• p = probability of winning
• q = 1 - p = probability of losing
• b = win/loss ratio (e.g., if you gain $1.50 per$1 risked, b = 1.5)

Adjusted Kelly with Transaction Costs

In practice, trading has costs. Subtract the cost per trade as a fraction:

f_adj = f* - cost_per_trade

Example

p = 0.55, b = 1.5:

f* = 0.55 - 0.45/1.5 = 0.55 - 0.30 = 0.25

With cost = 0.01: f_adj = 0.24

A Kelly fraction of 0 or negative means the edge does not justify the risk.