Kelly Criterion

Q: What is Kelly for options?

Kelly tells you optimal fraction of bankroll to risk, maximizing long-run growth. FlashAlpha computes it via numerical integration.

Q: What is half-Kelly?

Half the optimal fraction — achieves ~75% of full Kelly growth with much less variance. Strongly recommended.

Q: Why does Kelly Criterion matter for trading?

Kelly Criterion is the mathematical answer to the question 'how big should I size this trade?' By balancing edge against odds, it maximises long-run geometric growth without betting too large on any single trade. Systematic traders use Kelly (usually scaled down to 1/4 or 1/2) to size positions across strategies with different win rates.

Q: When is Kelly Criterion good versus bad for a trader?

Good for disciplined systematic traders with measurable edges, sized at fractional Kelly. Bad when edges are over-estimated or when full-Kelly is used on volatile strategies — leads to ruin. Near-zero edge means the trade should be skipped; Kelly outputs itself as a filter.

Canonical definition, formula, interpretation, and API reference.

Definition

Optimal position sizing from information theory. Uses numerical integration over lognormal distribution for options.

Formula

f* = argmax E[log(1 + f x R)]

Solved via numerical integration over +/-6 sigma with 2000 steps.

Inputs

spotstrikeDTEsigmapremiummu

Output

kelly_fractionhalf_kellyexpected_roiprobability_of_profit

Interpretation

kelly > 0: positive edge — bet this fraction
Half-Kelly recommended in practice
kelly = 0: negative expected value — don't trade

API Reference

Endpoint

GET /v1/pricing/kelly

Tier

Growth+

Response field

sizing.kelly_fraction, half_kelly, analysis.expected_roi, recommendation

Why Kelly Criterion Matters for Trading

TL;DR

Kelly sizes a bet by edge/odds. Full Kelly maximises long-run growth but blows up on volatile trades. Most pros use quarter-Kelly for survivability.

What it measures: A position-sizing formula f* = (bp - q) / b for a binary bet, where b is odds, p is win probability, q = 1 - p.
What it signals: How much of your bankroll to risk per trade, given an estimated edge.
Why we measure it: Undersized winning strategies compound too slowly; oversized winning strategies eventually ruin. Kelly is the mathematical bridge.
Who uses it: Systematic traders, professional gamblers, quant PMs, disciplined retail.

How to read Kelly Criterion

Positive edge + disciplined fraction

Quarter- or half-Kelly sizing
Long-run geometric growth
Recoverable drawdowns
Matches sizing to edge

Good for: edge-backed systematic trading

Full Kelly or negative edge

Full-Kelly on volatile strategies = ruin
Negative edge → stop betting
Overestimated edge = oversized position
Classic retail blow-up path

Bad for: high-vol strategies, no-edge trades

Near-zero edge

Kelly says size ~ 0
Skip the trade
Don't force conviction
Disciplined 'no' is the output

Skip

Rules of thumb

Never full Kelly on real markets. Edge estimates are noisy. Cut to 1/4 or 1/2 Kelly to survive overestimation.
Kelly scales with edge, not conviction. A 'strong feeling' with no measured edge is not a Kelly input — it's ego.
Drawdowns follow Kelly size. Half-Kelly cuts max drawdown roughly in half for similar growth.
Update as edge changes. As markets regime-shift, recompute. A 2022 edge is not a 2026 edge.
Pair with stop-losses. Kelly assumes your edge is real. Hard stops protect against the times it isn't.