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Kelly Criterion Curve

The Kelly Criterion Curve indicator gives you the leverage/return tradeoff by displaying a bell curve with growth and leverage. This indicator shows where you are on the risk curve depending your allocation/leverage used and the optimal leverage to use in any asset.

What Does It Show?
The indicator plots the Kelly growth function:
g(f) = μ·f - 0.5·σ²·f²
Where:

g(f) = Expected growth rate at leverage f
μ = Annualized return
σ = Annualized volatility
f = Leverage multiplier

The curve peaks at the Optimal Kelly leverage (full Kelly) and then declines, showing that:

Too little leverage = underutilized capital
Too much leverage = volatility drag destroys returns

The curve is dynamically divided into zones based on your asset's return profile:

Underinvesting (Green) - Too conservative, underutilized capital
Optimal Sizing (Teal) - Sweet spot for position sizing
High Risk (Yellow) - Diminishing returns, high volatility drag
Never Logical (Red) - Risk outweighs reward
Suicidal (Black) - Negative expected returns

Position Markers

★ Kelly Optimal (Green/Red) - Maximum long-term log growth leverage
½ Kelly (Yellow) - Conservative sizing (recommended most times)

Settings for Kelly Calculation

Lookback Period - Historical data window for calculations (default: 252 = 1 year)
Annual Trading Days - For annualization (default: 252)
Use Log Returns - More accurate for compounding (recommended: ON)
Curve Smoothness (20-200) - Number of points on curve (default: 100)
Maximum Leverage Display (2-10x) - X-axis range
Show Short Positions - Display negative leverage for short strategies. Note the chart is not fully optimized for shorts.
Show Optimal Kelly Marker - Mark optimal leverage on curve
Show Half Kelly Marker - Mark conservative leverage

How to Use

Look at Optimal Kelly - This is the theoretical maximum for the period analyzed
Use Half Kelly for conservative sizing
Check which risk zone your position falls into
If your leverage is in the High Risk zone → Consider reducing
If you're in Never Logical or Suicidal → I wish you good luck because you will need a lot
If you're in Underinvesting → You may be too conservative

IMPORTANT
The indicator is based on past returns and volatility. It CANNOT predict:

Market crashes
Regime changes
Black swan events

If you use Optimal Kelly and suddenly there's a crash, you are toasted.

Full Kelly maximizes long-term growth but can experience large drawdowns
Most traders use ¼ to ½ Kelly for risk management
You should almost never use full Kelly, unless you are extremely confident

Remember leverage amplifies gains and losses

Notice how Max Growth isn't simply Ann. Return × Leverage
The formula accounts for volatility drag (the cost of using leverage)
Higher volatility = lower optimal leverage

The Kelly Criterion was developed by John L. Kelly Jr. in 1956 for information theory and later adapted for gambling (card counting for example, pioneered by Edward O. Thorp), and investing.

Optimal Leverage:
f* = μ / σ²
Expected Growth Function:
g(f) = μ·f - 0.5·σ²·f²
This is a quadratic function that forms the bell curve you see on the chart.

This indicator pairs perfectly with my other indicators:
Kelly Optimal Leverage Indicator
Jensen's Inequality + Kelly Leverage
Multi-Leverage VAR/VaG Indicator

For deeper insights on Kelly Criterion and optimal leverage:
Read my article: Unlock the Power of Monte Carlo
Read these papers:
Alpha Generation and Risk Smoothing using Managed Volatility
Leverage for the Long Run - A Systematic Approach to Managing Risk and Magnifying Returns in Stocks

Trading with leverage involves substantial risk of loss.
The Kelly Criterion provides a theoretical framework - actual trading requires additional risk management, market analysis, and psychological discipline.

Some examples of using the Kelly Criterion Curve:
Russel 2000, last 500 days Kelly curve

Here's you can see that the optimal sizing over the last 500 days would have been around 1.7x leverage and that full Kelly is 3.4x leverage.
While Russel 2000 returned 16%, full Kelly would have returned 27.8%, and more that full Kelly (3.4x leverage) would lower the returns.

Berkshire Hathaway, last 1000 days Kelly curve

BRK stock optimal Kelly (full Kelly) is 2.5x for the last 1000 trading days. To reduce volatility, one could use 1/2 Kelly which is 1.25x leverage.

Bitcoin, last 2000 trading days Kelly curve

Very interestingly, the indicator tells us not to leverage Bitcoin. Even a 2x leverage can lead to ruin given its volatility, and in fact, in 2025 many traders got liquidated while leveraging Bitcoin by 2x.

Let me know if you have questions, suggestions and comments.
- Henrique Centieiro

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HenriqueCentieiro

Hedge Fund Manager at Maverick Capital | Wealth Educator | 20+ yrs investing | Stocks, ETFs & Crypto alerts | Join Henrique Wealth Academy for trade alerts & indicators → skool.com/be-limitless/

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HenriqueCentieiro

Hedge Fund Manager at Maverick Capital | Wealth Educator | 20+ yrs investing | Stocks, ETFs & Crypto alerts | Join Henrique Wealth Academy for trade alerts & indicators → skool.com/be-limitless/

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