Kelly Criterion
By Menno van Ravels - 13 years in crypto, 3 bear markets survived, zero paid promotions
AI Quick Summary: Kelly Criterion Summary
Term
Kelly Criterion
Category
Strategy
Definition
The Kelly criterion is a mathematical formula that determines the optimal percentage of your portfolio to risk on a single bet or trade, maximizing long-term growth rate while avoiding ruin.
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The Kelly criterion is a mathematical formula that determines the optimal percentage of your portfolio to risk on a single bet or trade, maximizing long-term growth rate while avoiding ruin. It balances edge size against probability of winning.
The Kelly criterion, developed by John L. Kelly Jr. at Bell Labs in 1956, calculates the fraction of capital to wager on an opportunity where you have an edge. The formula is: f* = (bp - q) / b, where b is the odds received, p is the probability of winning, and q is the probability of losing (1 - p).
In crypto investing, the Kelly criterion helps determine position sizes. If you believe a trade has a 60% chance of returning 2x your risk and a 40% chance of losing the risked amount, Kelly suggests risking (2 × 0.6 - 0.4) / 2 = 40% of your capital. In practice, most professional traders use "half-Kelly" or "quarter-Kelly" to reduce variance.
According to a study by Thorp (2006), full Kelly betting maximizes the geometric growth rate of wealth but comes with extreme volatility — a full Kelly bettor faces a 50% drawdown about once every 20 bets. Half-Kelly reduces the growth rate by only 25% but cuts the variance in half, making it far more tolerable psychologically.
For crypto portfolios, the challenge is accurately estimating edge and win probability. Most retail investors overestimate both. A conservative approach is to use quarter-Kelly sizing and never allocate more than 5-10% to any single position, treating the Kelly output as an upper bound rather than a target.
The Kelly criterion also implies that when you have no edge (expected value is zero or negative), the optimal bet size is zero — a powerful reminder to sit out low-conviction trades.
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Frequently Asked Questions
What is the Kelly criterion formula for crypto trading?
f* = (bp - q) / b, where f* is the fraction of capital to risk, b is the win/loss ratio, p is win probability, and q is loss probability. For a trade with 55% win rate and 1.5:1 reward-to-risk, Kelly suggests risking (1.5 × 0.55 - 0.45) / 1.5 = 25% of capital. Most traders use half or quarter Kelly.
Why do traders use half Kelly instead of full Kelly?
Full Kelly maximizes long-term growth but creates extreme drawdowns — often 50%+ swings. Half Kelly sacrifices only 25% of the growth rate while cutting variance by 50%. It also provides a buffer against estimation errors in win probability and reward ratios, which are notoriously hard to estimate in crypto.
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Related Terms
Position Sizing
Position sizing determines how much capital to allocate to each trade or investment. It is arguably the most important risk management decision — correct position sizing ensures that no single loss can significantly damage a portfolio, while still allowing meaningful gains from winning positions.
Risk/Reward Ratio
The risk/reward ratio compares the potential loss on a trade (from entry to stop-loss) against the potential gain (from entry to take-profit), expressed as a ratio like 1:2 or 1:3. At a 1:2 ratio, a trader only needs to win 33% of trades to break even — a principle emphasized by risk management experts like Van Tharp and Mark Douglas.
Risk Capital
Risk capital is money explicitly set aside for high-risk, high-reward investments — capital you can afford to lose entirely without affecting your financial security or life quality. Given crypto's historical -80% to -95% drawdowns, all crypto investing should be done with risk capital only, after building an emergency fund.
Drawdown
A drawdown is the decline from a portfolio's peak value to any subsequent trough, expressed as a percentage. It measures how much an investment is 'underwater' from its high-water mark — Bitcoin is at all-time highs only about 5% of trading days, spending 95% of the time in some degree of drawdown.
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