What does gamma actually tell a hedger, and how is it used in practice?

Question

AcadiFi · Accepted Answer

Gamma is the rate of change of delta per unit change in spot. For a non-dividend European call, Γ = φ(d1) / (Sσ√T), where φ is the standard normal density. Gamma peaks for at-the-money options near expiry and shrinks for deep ITM or OTM positions. A long option position always has positive gamma; a short option position always has negative gamma.

Why it matters: if you delta-hedge continuously, gamma determines rebalancing P&L. A long-gamma book profits from realized volatility because each rebalance buys low and sells high. Conversely, a short-gamma book loses when markets move, because hedges chase the price.

```mermaid
flowchart LR
    A[Spot moves up] --> B[Delta rises]
    B --> C[Long gamma: sell shares high]
    C --> D[Profit on rebalance]
    A --> E[Short gamma: buy shares high]
    E --> F[Loss on rebalance]
```

Example: Harkvale Desk is long 500 ATM calls with Γ = 0.045 per share. A $2 move in the $75 underlying adds 0.045·2·500·100 = 4,500 additional delta units to rebalance. If IV implied a 16% annualized move but realized is 24%, the long-gamma P&L over a week may exceed theta bleed, producing a net gain. FRM candidates should remember gamma scales inversely with time-to-expiry for ATM options, which is why 'gamma squeezes' explode near weekly expiries.

What does gamma actually tell a hedger, and how is it used in practice?

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