# Charles Davì

## Netting Demystified

In Systemic Counterparty Confusion on October 24, 2008 at 1:24 am

#### Netting Is For Everyone, Not Just Fancy Swap Traders

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 per person, 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 = \$22 in total debts.

2. So I guess the obvious practical question is: just how magnified is the media’s ~\$81 trillion figure? After netting, how big is the derivatives (narrowly, CDS) market?

3. By the way, can I just add this blog is brilliant. You are a gifted explainer and a gift to the world!

4. PS: meant to add a zero to that number of trillions in the derivative market size figure

5. Hi Theo,

Glad you like the blog. As for the size of the derivatives market after netting, it’s probably still very large. That said, the ForEx market is much, much bigger, yet no one loses sleep over that (except in Iceland). I would poke around the web. Try the websites for the Bank of International Settlements and ISDA.

6. […] (12 days later) only \$5.2 billion in actual payments? There’s a very simple explanation:netting, and the fact that they just don’t understand it. As discussed here, the CDS market is a swap […]

7. Excellent blog. Ok, now that you have calmed everyone down on this, what do you think about leveraged super senior, cdo-squared, and synthetic cdo tranches out there, and how it relates to these minor problems in individual name cds? The worry isnt in the individual names, as you correctly point out in these very clear explanations. The worry is that these tranches are being eaten away, and who knows if/when these losses will get realized. There are a lot of positions which havent been marked down and wont have to be until there are realized losses. Those realized losses werent on the radar screen earlier but now, thanks to fnma, fhlmc, leh, wamu, iceland banks, the list is starting to get long, which means that losses are going to have to get crystallized. This fear is probably the main contributor to the explosion in CDS levels these days as this becomes apparent.Any guesses on where the data on this is? Probably in the financial transparency vortex. Anyways, keep up the good work….

8. […] Netting Demystified Derivative Dribble The \$55 trillion in collateralized debt obligations? Netting helps explain why that \$55 trillion figure may not be nearly as scary as it sounds (tags: economics finance bonds derivatives crisis mathematics) […]

9. […] that on the first payment date, LIBOR = 4%.  It follows that A owes B \$2 and B owes A \$1. So, after netting, A pays B […]

10. The netting described above is a logical net position if you add up all the trades between two or three parties. The actual trades still exist in their gross form, but for risk management purposes can be regarded as ‘net’ because they offset each other should you need to measure their effect on your bank account. The recent PR by DTCC explains that the net *payments* as a result of the Lehman credit event were around \$6bn, which is a real physical cash move resulting from the hundreds of billions of trades that existed. At another level, when a party like Lehman goes bust, much of the legal framework they traded within (such as ISDA) allows for close out netting, i.e. netting together all the money you owe Lehman, with the money Lehman owe you, to arrive at single net number you would claim from their liquidators. And to make things even more complicated, a company called TriOptima will actually enable you to *really* net down trades (like the triangle above) to end up with an actual reduced number of outstanding trades, helping everyone keep a lid on the size of databases to store the millions of trades in the market.

Bill.

11. […] and \$62 trillion. These figures refer to the notional amount of the contracts, and because of netting, these figures do not provide a meaningful picture of the amount of money that will actually change […]

12. […] our concept of exposure is to have any real economic significance, it must take into account the concept of netting. So, we define the exposure of to the risk-event defined above as the product of (i) the net […]

13. Cool reminders to graphs theory 🙂 here and some other places ot GT.. nice pieces to read I refered it on my blog.. for winter eve’s reading..
Regards

14. Dear Blogger,

I recently got a job in The City and am trying to get my head round a few things. This site is a welcome break from what I read day to day.

Excuse my lack of understanding (this is why I am here).

I understand now how the above works to the benefit of those involved.

But trades a wider level, that occur every day, do these add any value to the real economy? Large sums of money are paid out in wages, rents, utility payments… where does this ‘money’ come from? Also is the following true:

The financial system is zero sum? meaning each contract has one winner and one loser?

Also, as you elude to on here and other pages of this site, people shouldn’t point the finger at derivatives etc. for causing this financial mess; and that a lot of people pointing fingers do not understand them (me included though I am trying to read up), is it not true that of derivatives are indeed quite complex?

I welcome your comments and patience due to my lack of understanding.

B.

15. “Complex web of relationships reduced to 1 transaction worth \$1. Yet, the media have reported a cataclysmic \$22.”

Are you claiming that the contra-party risk of the system is just 1\$? This might work with some clearing house of inter-day transactions, but certainly not with OTC markets. If B fails to do its paints the system is short of \$9, and A will miss \$5 and B will miss §4. So to say the debt is §22 is more valuable information than to say that it is \$1.

• Pat,

OTC Dealers net payment and collateral obligations, they engage in trade compression, and ISDA auctions net payments and physical settlement requests, so a gross notional figure is not “useful information.”