Never Go Broke: The Kelly Formula Explained
By:Kai Zeng
Which strategy leads to the highest ending bankroll? The answer is B with the 20% allocation.
This optimal betting size wasn't discovered through trial and error but through the Kelly criterion, a mathematical formula developed by John Kelly at Bell Labs in 1956. The formula determines exactly how much to invest when probability favors you, balancing aggressive betting with protection against ruin.
The Kelly formula is expressed as:
Where:
In our scenario: p = 0.60, q = 0.40, b = 1
Plugging these values into the formula: f* = (0.60 × 1 - 0.40) ÷ 1 = 0.2 or 20%
This approach applies perfectly to options strategies, where both probability and odds are known before trade entry. Let's examine iron condors as an example.
With a $100,000 portfolio trading only iron condors with these parameters:
The Kelly formula gives us: f* = (0.85 × 0.2 - 0.15) ÷ 0.2 = 0.1 or 10%
The theoretical optimal capital allocation is 10%. Monte Carlo simulations show this portfolio should generate approximately 25% profit after 100 trades with zero chance of ruin.
However, profitability varies based on success rate and odds. If we maintain the 85% success rate but increase the odds to 0.25, the optimal Kelly percentage rises to 25%. Conversely, if odds decrease to 0.15, Kelly produces a negative number—signaling the portfolio will eventually lose money.
Most professionals don't use the full Kelly percentage but instead use a fraction of it—typically between 25-75% of the calculated value. This conservative approach accommodates real-world uncertainties and personal risk tolerance. Over or under-allocating relative to the optimal Kelly threshold significantly impacts both performance and risk profile.
Kai Zeng, director of the research team and head of Chinese content at tastylive, has 20 years of experience in markets and derivatives trading. He cohosts several live shows, including From Theory to Practice and Building Blocks. @kai_zeng1
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Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.