For Gamma −40 shares/dollar and dS=+2, what is dH?
Reveal the worked answer
Buy 80 shares.
−(−40)×2=+80.
Dealer Logic · DL-03 · Core
Gamma determines hedge feedback
Why does the sign of Gamma reverse the rebalancing direction?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Why dealers hedge
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.
Open the calculation without leaving this lesson
Gamma determines hedge feedback—worked comparison
Vertical: Hedge change (shares)
Horizontal: Spot change (USD)
1. Fictional example
Read the graph as a data table
| Spot change (USD) | Fictional example |
|---|---|
| -2 | 80 |
| -1 | 40 |
| 0 | 0 |
| 1 | -40 |
| 2 | -80 |
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
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
What is the critical failure to avoid?
Reveal the worked answer
Inferring negative dealer Gamma from a trending chart and then using that Gamma to explain the trend is circular reasoning.
Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome.
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.
Sources, assumptions and downloadable script
External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.
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