How do I construct a gamma-neutral portfolio?

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AcadiFi · Accepted Answer

Gamma neutrality requires another option, since the underlying has zero gamma. The recipe: offset your portfolio's gamma using a liquid option, then rebalance Delta back to zero using the underlying.

Mateusz Varga at Helvetia Option Partners runs a book with net gamma of -1,840 per point. He neutralizes by buying 290 contracts of the at-the-money 60-day SPX call, which has gamma of 0.063 per contract times 100 multiplier = 6.3 per contract; 290 * 6.3 = 1,827. Close enough; residual -13 is hedged with futures via Delta.

Key formula: n_hedge = -Gamma_portfolio / Gamma_hedge_instrument. After adding the option, Delta changes, so compute new Delta and trade underlying: n_underlying = -Delta_new.

Complications:
- Gamma neutrality holds only at current spot; as underlying moves, gamma of both positions shifts
- The hedging option adds vega exposure — now you're short vega if you sold the hedge
- Path dependence: rebalancing a gamma hedge itself generates transaction costs

Professional desks often target gamma neutrality within a spot range rather than at a single point. They use multiple strikes to flatten the gamma profile across a band of underlying prices. This is called 'gamma laddering' and minimizes re-hedging frequency when spot wanders.

How do I construct a gamma-neutral portfolio?

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