Delta-hedging

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Delta-hedging

In swap hedging, matching your hedge exactly to your swap obligation, and remaining market-neutral — or as market neutral as you can. (strictly you could delta hedge with a delta other than one, I suppose, but most folks mean delta-one hedging. This is what prime brokers do when they trade synthetic equity swaps. They make their money not from trading equities, but by lending money to their clients, so their clients can trade equities.

Say a client requests a synthetic equity position on Vodafone from its prime broker. To accommodate this, prime broker goes into the market and buys VOD shares at 10. Broker fills its client’s swap order at 10. Voila: prime broker is perfectly hedged, delta-one for this new swap position: if VOD goes up, the PB’s swap obligation goes up. If VOD goes down, PB’s swap obligation goes down.

The prime broker’s problem here is that it has had to fork out 10 for that VOD stock it bought as its hedge. It had to borrow that 100 from its treasury department. Its treasury department is fond of telling everyone it is “not a goddamn charity”, and charges what the desk considers a usurious interest rate to access its money. But: c’est la vie: the treasury’s not for turning, so the prime broker has to reduce its funding costs another way.

If this is the only VOD position on its books, it can do this by borrowing some treasury securities in the market, collateralising that with the VOD stock, and giving those treasuries to the treasury department in reduction of its debt. The treasury department likes treasury securities. They count as almost as good as money.

Now if the PB has two VOD offsetting positions on its books: one long and one short, its physical hedges cancel each other out, and it can (and, indeed, must) sell its VOD stock to remain market neutral, and in that case can also return money to its treasury department to reduce its funding cost.
In swap hedging, delta-hedging with a delta of one: that is, matching your hedge exactly to your swap obligation, and remaining market-neutral — or as market neutral as you can. This is what prime brokers do when they trade synthetic equity swaps. They make their money not from trading equities, but by lending money to their clients, so their clients can trade equities.

Example

Say a client requests a synthetic equity position on Vodafone from its prime broker. To accommodate this, prime broker goes into the market and buys VOD shares at 10. Broker fills its client’s swap order at 10. Voila: prime broker is perfectly hedged, delta-one for this new swap position: if VOD goes up, the PB’s swap obligation goes up. If VOD goes down, PB’s swap obligation goes down.

The prime broker’s problem here is that it has had to fork out 10 for that VOD stock it bought as its hedge. It had to borrow that 100 from its treasury department. Its treasury department is fond of telling everyone it is “not a goddamn charity”, and charges what the desk considers a usurious interest rate to access its money. But: c’est la vie: the treasury’s not for turning, so the prime broker has to reduce its funding costs another way.

If this is the only VOD position on its books, it can do this by borrowing some treasury securities in the market, collateralising that with the VOD stock, and giving those treasuries to the treasury department in reduction of its debt. The treasury department likes treasury securities. They count as almost as good as money.

Now if the PB has two VOD offsetting positions on its books: one long and one short, its physical hedges cancel each other out, and it can (and, indeed, must) sell its VOD stock to remain market neutral, and in that case can also return money to its treasury department in reduction of its finding cost.