Beta-Adjusted Hedge Calculator

Size SPX, NDX, SPY, or QQQ puts to hedge a stock position using beta and option delta.

Calculator output is informational and not a trading recommendation. See Terms §17.

Position
Put spread alternative (tunes only the spread card below)
Position Value

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Beta (252d)

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Hedge Notional

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β × position value × hedge fraction
Cheapest Annual Cost

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% of position per year if rolled continuously
Hedge Instrument

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Candidate Put Hedges
Moneyness Strike Bid–Ask Mid Δ IV OI Contracts Cost Cost % Annual % Coverage Breakeven
Put Spread Alternative
configured above

Buy an OTM put and sell a further-OTM put as a debit spread. Sized to the same contract count as buying the long leg outright — you collect premium from the short leg, dramatically reducing cost in exchange for capping the payoff at the short strike. Tune the strikes via the "Put spread alternative" inputs in the form above; further-OTM = cheaper, narrower payoff window.

Spread Cost

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vs Outright

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premium reduction relative to the 3% OTM outright put
Max Payoff

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if hedge instrument expires at or below the short strike
Annual Cost

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% of position per year if rolled continuously
Leg Strike Mid Δ Contracts Net Debit Width Coverage Breakeven

How This Calculator Works

The math

A delta-neutral, beta-adjusted hedge sizes contracts so the option's delta dollars offset the beta-scaled dollar exposure of your stock position: 

contracts × |put_delta| × hedge_price × 100 ≈ beta × shares × stock_price

Solving for contracts gives the fractional answer; we round up to the nearest whole contract — for an insurance position you'd rather over-hedge by a fraction than under-hedge.

Hedge instrument choice

SPX / NDX are cash-settled European-style index options with ~$500K–$2M notional per contract. Most efficient for large positions. SPY / QQQ are physically-settled American ETF options with ~$50K–$60K notional per contract — better granularity for smaller positions and easier to leg in/out.

Beta is computed against SPY when hedging with SPX or SPY, and QQQ when hedging with NDX or QQQ (the ETF return series is statistically equivalent to the underlying index for hedge-sizing purposes, and is what the local price-history database tracks).

Reading the table

  • Coverage shows how much of the beta-adjusted notional the rounded-integer contract count actually hedges. 1.00 = exact; 1.5 = 50% over-hedged from rounding up.
  • Breakeven is the index drop (% from the current level) at expiration that makes the hedge gain equal the premium paid. Smaller drops past breakeven = pure profit on the hedge.
  • ATM puts have the highest delta (and cost). OTM puts are cheaper but need a bigger move to pay off — and require more contracts to deliver the same delta-dollar coverage.

When the position is too small

One SPX contract carries ~$500K+ of notional exposure; NDX is even larger. If the theoretical contract count is well below 1, ceiling-rounding will over-hedge significantly — switch the "Hedge with" dropdown to SPY or QQQ for ~10× finer granularity at the cost of higher per-dollar premium.