Thursday, October 23, 2008

Netting Demystified

(Derivative Dribble) Unlike most terms used in the derivatives world, netting is a good one. It has an intuitive, albeit hokey, feel (unlike other rather sterile terms such as “synthetic collateralized debt obligation”). After all, economics is about human decisions and actions, and as such, it can stand to be a bit hokey. So what is netting? The concept stems from a very simple observation: if I owe you $5 and you owe me $10, you should just give me $5. We could have several debts between the two of us, (e.g., I owe you $2 from Wednesday, $3 from Thursday), but assume we add those up into one debt, resulting in one transactional leg (line connecting us) each. In this case, netting would save us a bit of trouble since we only exchange money once, instead of twice.

That Is So Obvious And Trivial That It Can’t Be Right

The observation above is indeed an example of the same principle (netting) that is applied to swaps. Our example however, only has 2 parties. The time saved from engaging in 1 transaction instead of 2 is minimal, especially when it’s a transaction for such a small amount of money. This is a result of the fact that when there are only 2 parties, let’s say you and me, there are only 2 legs to the transaction: the money coming out of me and the money coming out of you. The netting example above reduces that to 1 leg (you pay me). That’s called bilateral netting. Again, when there are only 2 parties, the application of netting is simple. But the number of legs increases dramatically as we increase the number of parties (for my fellow graph theorists, the number of legs is twice the number of edges in a complete graph with N nodes, where N is the number of parties). For example, consider the obligations of 3 friends: A, B and C. A owes B $2; A owes C $3; B owes A $4; B owes C $5; C owes A $2; and finally C owes B $6.

We apply bilateral netting to each of the pairs. That leaves us with the following: A owes C $1; B owes A $2; and C owes B $1. We could just execute 3 transactions and call it a day. But we’re smarter than that. We notice that C is basically passing the 1$ from A onto B. That is, his inflow is the same as his outflow, so he serves no purpose in our transaction. So, we cut him out of the picture:

Note that the last step we just took, cutting C out, was not bilateral netting. It was a different kind of netting. It required a different observation, but the principle is the same: only engage in necessary transactions. Finally, we apply bilateral netting to the transaction between A and B. So, in the end, that complex sea of relationships boiled down to B paying A $1.

Balsamic Reduction

Rather then execute a disastrously complicated web of transactions, swap dealers, and ordinary banks, use clearing houses to do exactly what we just did above, but on a gigantic scale. Obviously, this is done by an algorithm, and not by hand. Banks, and swap dealers, prefer to strip down the number of transactions so that they only part with their cash when absolutely necessary. There are all kinds of things that can go wrong while your money spins around the globe, and banks and swap dealers would prefer, quite reasonably, to minimize those risks.

An Engine Of Misunderstanding

As you can see from the transactions above, the total amount of outstanding debts is completely meaningless. That complex web of relationships between A, B, and C, reduced to 1 transaction worth $1. Yet, the media would have certainly reported a cataclysmic 2 + 3 + 4 + 5 + 2 + 6 = $12 in total debts.

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