Lesson 22 of 25 · 6 min

Dealer hedging, and flow that nobody chose

A market maker with no opinion still has to sell into declines, and the amount is set by a curvature rather than a judgement.

Track 3 covered gamma as the curvature of delta and vega as sensitivity to implied volatility. This lesson is about what that curvature obliges a hedger to do, which is a different question from what it measures.

A party that has sold options and hedges the exposure holds a book with negative gamma. Negative gamma means the required hedge moves against the hedger: as the underlying falls, the hedge ratio grows, so shares must be sold to stay hedged. As it rises, shares must be bought. The adjustment always leans in the direction the market is already going.

The obligation is not discretionary in any meaningful sense. A hedged book that is left alone stops being hedged, and a party whose business is providing contracts rather than taking views cannot choose to carry the resulting exposure. So the selling happens, at whatever price is available, in whatever size the curvature dictates.

Put an illustrative size on it. Suppose a book's hedge requirement changes by $1,850,000 of stock for each one percent fall in the underlying. A 1.4 percent fall on the first session requires $2,590,000 of selling. A 4.3 percent fall on the second requires $7,955,000. Across the two sessions that is $10,545,000 of supply, none of it chosen by anybody and none of it responsive to price.

For a pledged portfolio this is a statement about the liquidation window rather than about the holding. Track 7 lesson 9 made the point that a haircut is mostly a claim about how many sessions an exit takes. Sessions during which other parties are obliged to sell the same name are worse sessions than average to be selling into, and the obligation is concentrated in exactly the falling markets in which a lender would be acting. The exit window a haircut assumes is not an empty window.

Key terms

Negative gamma: A position whose required hedge grows as the underlying falls and shrinks as it rises. Maintaining the hedge therefore amplifies the move rather than damping it.
Hedge requirement: The quantity of the underlying a hedger must hold to be neutral. It changes with price, which is what turns a static position into recurring trades.
Obliged flow: Trading a party must do to remain hedged, rather than trading it wants to do. It is insensitive to price and concentrated in large moves.

Worked example

Two sessions of hedging with no view taken

An illustrative book whose hedge requirement changes by $1,850,000 of stock per one percent move in the underlying.

Session one, a 1.4% fall: $2,590,000 sold
Session two, a 4.3% fall: $7,955,000 sold
Total across the two sessions: $10,545,000
Amount attributable to a view on value: $0
Direction of the flow relative to the move: Always with it

Ten and a half million dollars of selling produced by a hedge ratio. The same obligation runs in reverse on the way back up, which is why it is amplification rather than one-way pressure.

Check yourself

A hedged book must sell $1,850,000 of stock for each one percent the underlying falls. Sessions of −1.4 percent and −4.3 percent occur. How much selling, and what decided it?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.