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Risk Management

Kelly Criterion

A mathematical formula used to determine the optimal theoretical size of a series of bets to maximize long-term wealth growth.

Detailed Financial & Mathematical Context

Formulated by J. L. Kelly Jr. at Bell Labs, the Kelly Criterion calculates the exact proportion of capital to risk on a trade with known edge and odds. In quantitative finance, traders use Fractional Kelly (0.25x or 0.5x) to prevent large drawdowns caused by parameter estimation error.

f^* = \frac{p \cdot b - q}{b}

Video Explainer & Key Moments

Master capital allocation and logarithmic wealth maximization using the Kelly formula and institutional Fractional Kelly rules.

0:00 - The Origins of Information Theory in Finance
Claude Shannon and J. L. Kelly Jr.
2:20 - Deriving the Full Kelly Formula
Edge divided by odds (f* = (p*b - q)/b)
4:20 - Risk of Ruin & Geometric Growth Maximization
Why betting over Kelly leads to guaranteed ruin
6:20 - Fractional Kelly (Half and Quarter Kelly)
Mitigating estimation error in real financial markets
7:50 - Multi-Asset Portfolio Kelly Allocation
Covariance matrix integration for multi-bot systems

Frequently Asked Questions

What is the Kelly Criterion in quantitative finance?

The Kelly Criterion is a formula that calculates the optimal percentage of portfolio capital to allocate to an investment or trade in order to maximize long-term compound geometric growth rate.

What is the formula for the Kelly Criterion?

The formula is f* = (p * b - q) / b, where f* is the fraction of portfolio equity to wager, p is the win probability, q is the loss probability (1 - p), and b is the payout ratio (Average Win / Average Loss).

Why do institutional quantitative funds use Fractional Kelly?

Full Kelly assumes exact knowledge of future probabilities and payoffs. Because financial market statistics are non-stationary, Full Kelly produces severe volatility and deep drawdowns. Fractional Kelly (0.25x to 0.5x) provides 75-90% of maximum growth with much smaller drawdowns.

What happens if a trader over-allocates beyond the Kelly Criterion?

Betting more than the Full Kelly fraction creates negative expected compound growth and mathematically guarantees portfolio ruin over an extended series of trades.

How do you apply the Kelly Criterion across multiple uncorrelated strategies?

In multi-strategy systems, quants use matrix Kelly allocation, which incorporates the covariance matrix of strategy returns to optimize simultaneous capital allocations without exceeding total portfolio risk limits.

Related Concepts

Position Sizing
Risk of Ruin
Expected Value
Capital Preservation

Comprehension Check

If a trading strategy has a 60% win rate (p = 0.60) and a 1:1 risk-to-reward ratio (b = 1), what is the Full Kelly fraction?

[A]10%
[B]20%(Correct Answer)
[C]40%
[D]60%
Explanation: Using the formula: f* = (0.60 * 1 - 0.40) / 1 = 0.20 (or 20% of capital).
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