position-sizing

Options Position Sizing

Translate "I have $X in capital and a max-loss tolerance of $Y per trade" into a number of contracts. Supports two methods: fixed-max-loss (recommended for most retail) and fractional Kelly (for users who have a win-rate / payoff estimate).

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Step 1: Capture Inputs

Input	Notes	Default
Total account capital	Used for the % of book check	required
Max loss tolerance per trade	$ or % of book	1–3% of book
Trade max loss (per contract)	From options-payoff	required
Trade max profit (per contract)	required for Kelly
Win probability estimate	required for Kelly
Buying-power requirement (per contract)	For broker margin sizing	varies

If trade max loss is "unbounded" (naked call, ratio spread short side) → refuse to size with this skill. Use a closing rule instead, or pick a different structure via strategy-selector.

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Step 2: Fixed-Max-Loss Sizing

N_contracts = floor( max_loss_tolerance / per_contract_max_loss )

Cap further by:

1. Buying-power: N ≤ floor(account_capital / BP_per_contract)
2. Concentration: a single underlying shouldn't be > 20–25% of book BP

Worked example: $50,000 account, willing to risk $500/trade, iron condor with $4.20 max loss → N = floor(500 / 420) = 1 contract.

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Step 3: Fractional Kelly (advanced)

Full Kelly fraction:

f* = (p · b − (1 − p)) / b

Where p = win prob, b = win/loss ratio = max_profit / max_loss.

Do not use full Kelly for options. Standard practice is 0.25 · f* ("quarter Kelly") because:

1. Your p estimate is noisy.
2. Path-dependent drawdowns are brutal at full Kelly.
3. Variance of returns is enormous — full Kelly leads to expected log-utility but huge equity swings.

contracts = floor( 0.25 · f* · account_capital / per_contract_max_loss )

Refuse to size if f* ≤ 0 (negative edge — the trade has negative expected value). State this explicitly. Don't size a losing trade.

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Step 4: Sanity Checks

1. Won't blow the account on N consecutive losses: at 3 standard deviations of consecutive losses (binomial), would the account survive? If not, halve N.
2. Margin call risk on undefined-risk legs: if buying-power requirement could grow with adverse moves (short put), assume worst case = strike × 100. Use that as your BP, not the broker's initial margin.
3. Correlated positions: if user already has 5 short-vol trades on tech names, don't size a 6th tech short-vol — concentration risk dominates per-trade math.

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Step 5: Respond to User

Method	N contracts	$ at risk	% of book	Notes
Fixed max-loss	…	…	…	Recommended
Quarter Kelly	…	…	…	Requires reliable p estimate
BP-capped	…	…	…	Broker constraint

End with: "Final size: N = min(...)" — the most restrictive of the three.

Important caveat to include: "Your stated win probability is a guess. If it's wrong by 10%, Kelly sizing scales linearly. Always start smaller than you think."