Delta-hedging: Difference between revisions

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-{{g}}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 [[synthetic prime broker]]s try to do when they trade [[synthetic equity swaps]]. This is because they make their money not from trading equities, but by lending to their clients, so their clients can make money trading equities.
+{{g}}
+{{capsule delta-hedging}}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 broker]]s 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.
-===Worked example===
+===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.
-Client requests a [[synthetic equity]] position on Vodafone from its [[prime broker]]. To accommodate this, [[prime broker]] goes into the market and buys Vodafone at 10. Broker fills its client’s swap order at 10.  Voila: prime broker is perfectly hedged, [[delta-one]] for the swap. If VOD goes up, PB’s swap obligation goes up. If VOD goes down, PB’s TRS 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.
-[[Prime broker]]’s problem here is that it has had to fork out 10 for that VOD stock that it holds as its hedge. And 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 will be charging the PB desk what the desk considers a usurious interest rate. But: ''c’est la vie'': the treasury’s not for turning, so the PB has to reduce its funding cost 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]].<ref>Note this process is economically identical to [[rehypothecation]] of a long custody position in [[cash prime brokerage]].</ref>
-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. Note this process is economically identical to [[rehypothecation]] of a long custody position in [[cash prime brokerage]].
+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.
-Now if the [[PB]] has two VOD positions on its books: one long and one short, the 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.