Dollar Gamma Exposure: Converting Curvature into Portfolio P/L

For educational purposes only; not investment advice.

Direct answer

Dollar Gamma exposure converts model Gamma into a monetary risk measure for a stated underlying-price scenario. It answers a more useful question than raw Gamma alone: approximately how much second-order P/L would this position gain or lose if its underlying moved by a specified percentage?

The name has no universal formula. Some systems report the Gamma contribution to P/L, some report the change in Dollar Delta, and some omit the 0.5 Taylor-series factor. A risk report must show its formula, price-move unit, multiplier, position sign, and currency before values can be compared.

Two measures that must not be confused

Let Γ be option Gamma per share for a $1 underlying move, S the underlying price, q signed contract quantity, M contract multiplier, and m the scenario return in decimal form.

The local second-order option P/L for price change ΔS=mS is

Gamma P/L ≈ 0.5 × Γ × (mS)² × q × M.

This guide calls the result at m=0.01 1% Gamma P/L. It scales with the square of the assumed move. Long options have positive Gamma and short options negative Gamma, subject to the signed quantity convention.

A different measure estimates how much share-equivalent Delta changes:

Change in Delta shares ≈ Γ × (mS) × q × M.

Multiplying that by S gives a change in Dollar Delta. This is not the same as Gamma P/L. A dashboard labeled “Dollar Gamma,” “Gamma Cash,” or “GEX” may use either family of measures, so reconstruct its units rather than relying on its label.

One percent versus five percent

Suppose a stock is $100, one option has Gamma 0.04, the position is long 10 contracts, and the multiplier is 100. For a 1% move, ΔS=$1:

1% Gamma P/L ≈ 0.5×0.04×1²×10×100 = $20.

The corresponding local change in Delta is 0.04×1×10×100=40 share equivalents. These numbers describe different quantities and should not be substituted for each other.

For a 5% move, holding Gamma artificially constant:

Gamma P/L ≈ 0.5×0.04×5²×10×100 = $500.

The five-percent estimate is 25 times the one-percent estimate, not five times, because the curvature term is squared. But Gamma will usually change across a $5 move, so $500 is a local approximation, not a full revaluation. A repricing model that updates Delta, Gamma, volatility, skew, time, and rates is more appropriate for large moves.

Portfolio checklist

Confirm whether each feed’s Gamma is per share, per contract, per point, or already position-scaled.
Apply long/short signs, quantities, multipliers, adjusted deliverables, currencies, and FX conversion once and only once.
Calculate percentage scenarios with each underlying’s own spot price; identical raw Gamma on $20 and $500 stocks is not identical risk.
Sum legs on the same underlying first, then state the joint-move and correlation assumptions used across underlyings.
Report both upward and downward full revaluations because Gamma, skew, and volatility need not behave symmetrically.
Pair Gamma with Delta, Theta, Vega, financing, dividends, and transaction costs; positive Gamma does not guarantee positive total P/L.
Update near at-the-money strikes and expiration frequently, especially for 0DTE positions where Gamma can move quickly.
Stress gaps and illiquidity in which continuous Delta hedging is impossible.
Separate known account positions from dealer-GEX estimates inferred from open interest and assumed customer direction.

Common misconceptions

“Dollar Gamma has one standard definition.” Vendors use materially different formulas and scaling.
“A five-percent move is five times a one-percent Gamma result.” Under constant Gamma, the P/L curvature term is 25 times as large.
“Positive Gamma guarantees profit.” Theta, Vega, Delta, and execution can outweigh its contribution.
“Initial Gamma is valid through a large jump.” Gamma itself changes with spot, time, and volatility.
“Dollar Gamma can simply be added across stocks.” The sum represents only a stated joint percentage-move scenario.
“Public dealer GEX reveals dealer positions.” Open interest alone does not identify who is long or short.