Kelly Criterion
Optimal fraction of capital to risk per bet to maximise long-term geometric growth.
Definition
Developed by John Kelly at Bell Labs in 1956, the Kelly Criterion gives the bet size that maximises the expected logarithm of wealth — equivalent to the long-term compounded growth rate. For continuous returns it reduces to mean / variance. Full-Kelly maximises growth but is brutally volatile: most professional managers use a fractional Kelly (half-Kelly or quarter-Kelly) to control drawdowns while keeping most of the growth advantage.
Formula
Binary outcome:
f* = (p * b - q) / b
where p = win prob, q = 1-p, b = win/loss ratio
Continuous returns:
f* = (mu - Rf) / sigma^2
where mu = expected return, sigma^2 = varianceWorked example
A strategy has expected return 15%, risk-free 4%, annualised volatility 20%. Full Kelly = (0.15 - 0.04) / 0.20^2 = 2.75 — meaning 2.75x leverage. In practice you would never trade full Kelly; half-Kelly (1.375x) or quarter-Kelly (0.69x, i.e. 69% of capital) are common to absorb estimation error in mu.
How ARIA Analyst uses it
ARIA uses half-Kelly by default in the Position Sizing Agent and lets users dial down to quarter-Kelly when running Auto-Invest in live mode.
Related terms
Sharpe Ratio
Risk-adjusted return measured as excess return per unit of total volatility.
Volatility (σ)
Standard deviation of returns — the most common dispersion-based risk measure.
Maximum Drawdown
The largest peak-to-trough decline of equity over a given window.
Walk-Forward Analysis
A backtesting procedure that retrains the model on a rolling window and tests on the next out-of-sample period.
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