Kelly Criterion Optimal Growth Calculator
Maximize Long-Term Logarithmic Portfolio Growth with the Kelly Formula
Formula & Mathematical Definition
Where f* is the optimal fraction of capital, p is the probability of winning, q is the probability of losing (1 - p), and b is the win/loss payout ratio (Average Win / Average Loss).
Step-by-Step Calculation Guide
Establish the empirical win probability (p) and loss probability (q = 1 - p) from backtest sample data.
Calculate the average win payout divided by average loss amount (b = AvgWin / AvgLoss).
Apply the Kelly formula (f* = (p*b - q) / b).
Multiply raw Kelly by fractional safety factor (e.g. 0.25 for Quarter-Kelly) for sustainable equity growth.
Frequently Asked Questions
Why should traders use Fractional Kelly instead of Full Kelly?
Full Kelly maximizes logarithmic growth assuming known and stationary parameters. In real financial markets, parameters are estimates. Full Kelly suffers from severe drawdowns (up to 50-70%). Quarter-Kelly captures 75% of the growth rate with only a fraction of the volatility.
What does a negative Kelly Criterion fraction mean?
A negative Kelly fraction indicates that the trade setup has negative Expected Value (EV < 0). In this scenario, you should not take the trade, or alternatively, take the opposite side if possible.
How do you calculate the payout ratio (b) for the Kelly formula?
The payout ratio (b) is calculated by dividing your average dollar winning trade by your average dollar losing trade across a statistically significant historical sample size (100+ trades).
Can the Kelly Criterion be used with continuous variable outcomes?
Yes. The continuous Kelly formula uses the expected mean return divided by the variance of returns (f* = μ / σ²), which is widely used in quantitative portfolio rebalancing.
What is the risk of over-betting according to Kelly theory?
Betting more than the Full Kelly fraction creates negative expected compound growth and mathematically guarantees long-term portfolio bankruptcy (risk of ruin = 100%).