# Gamma determines hedge feedback

**DL-03 · Dealer Logic · Core**

**Lesson question:** Why does the sign of Gamma reverse the rebalancing direction?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.

**Prerequisites:** DL-01

Gamma measures how option Delta changes with spot. A desk maintaining local neutrality changes its hedge in the opposite direction to that option-Delta change. This identity is the mechanical foundation of Gamma-flow explanations, not a promise about market dominance.

## Understand the mechanism

Write option Delta as D and hedge as H. Neutrality gives H=−D. A small move gives dD≈Gamma×dS and therefore dH≈−Gamma×dS.

Positive Gamma implies selling into rises and buying declines. Negative Gamma implies buying rises and selling declines. The potential damping or amplification depends on flow size, execution and competing liquidity.

## Walk through the process

Verify whose Gamma the data describe and how position signs were allocated. Check whether units are shares per dollar, dollars per point squared or another convention.

Then compare the conditional hedge quantity with relevant liquidity. A large-looking number in the wrong unit does not establish influence.

## Evidence boundary

The arithmetic is original conditional teaching material, not a measurement of current dealer positions. The cited Cboe research is historical product-specific evidence, not a live inventory feed. Model outputs should remain distinguishable from observed market facts.

## A worked example

A hypothetical book has +40 share-equivalents of Gamma per dollar. A +2 spot move adds about 80 Delta, so a neutralizing hedge sells 80 shares. At Gamma −40, the same rise instead implies buying 80.

For a −2 move both signs reverse. The graph fixes positive Gamma and varies the spot shock. It illustrates the equation rather than forecasting future dealer trades.

## Calculation popup: Calculate the hypothetical hedge

```text
dH ≈ −Gamma_book × dS
```

Fictional inputs, explicit units and fixed other factors.

1. Gamma=−40 shares/USD.

2. dS=+2 USD.

3. −(−40)×2=+80.

**Result:** Buy 80 shares.

## Graph: Gamma determines hedge feedback—worked comparison

**Horizontal:** Spot change (USD)  
**Vertical:** Hedge change (shares)

Fictional data from the written example. The chart organizes the comparison; its shape is not a forecast.

Complete numerical data are embedded in `scripts/dealer-logic/DL-03.js` and displayed as an accessible table in the HTML lesson.

## What would invalidate the reading?

Inferring negative dealer Gamma from a trending chart and then using that Gamma to explain the trend is circular reasoning.

## Check your understanding

### For Gamma −40 shares/dollar and dS=+2, what is dH?

**Answer:** Buy 80 shares.

**Why:** −(−40)×2=+80.

### What is the critical failure to avoid?

**Answer:** Inferring negative dealer Gamma from a trending chart and then using that Gamma to explain the trend is circular reasoning.

**Why:** Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome. **Critical risk check.**

## Takeaway

Return to the question: Why does the sign of Gamma reverse the rebalancing direction? State the observed facts, the assumptions and the failure condition separately.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [OIC Greeks](https://www.optionseducation.org/advancedconcepts/understanding-options-greeks)

- [Cboe 0DTE positioning study, May 2025](https://www.cboe.com/insights/posts/0-dt-es-decoded-positioning-trends-and-market-impact)