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Notional vs net: complexity is our enemy

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The credit default swap (CDS) market, where AIG played, had notional outstanding value of about $45 trillion at the end of 2007 (about $60 trillion now). Of course many of these contracts are partially canceling, so the net value of contracts in the market is much smaller than the notional value.

Unfortunately, the network diagram (network of contracts) probably looks something like this:

Imagine removing — due to insolvency, lack of counterparty confidence, lack of shareholder confidence, etc. — one of the nodes in the middle of the graph with lots of connections. What does that do to the detailed cancelations that reduce the notional value of $45 trillion to something more manageable? Suddenly, perfectly healthy nodes in the system have uncanceled liabilities or unhedged positions to deal with, and the net value of contracts skyrockets. This is why some entities are too connected to fail, as opposed to too BIG to fail. Systemic risk is all about complexity.

Here’s a simple example of a network of contracts whose notional value is much larger than its net value. Suppose A = AIG, B = Barclays and C = Citigroup have traded CDS contracts related to a particular pool mortgages. If defaults in the pool exceed some threshold, A must pay B $1 billion, but will receive $1.1 billion from C. Now suppose there is a third contract in which B pays $1 billion to C if defaults exceed the threshold. The notional value of all contracts is $3.1 billion, but the net value that changes hands is only $.1 billion. So notional value is 31 times net.

B’s position is completely neutral and A and C only have $.1 billion at risk. This may sound contrived, but it’s actually not unrealistic.

Everything is fine until, say, A has a problem. Suppose A becomes insolvent and *poof* disappears. B and C are left with a naked $1 billion bet on mortgages. Suddenly the notional value, which wasn’t previously very representative of the amount at risk, due to the cancelations, isn’t far off from the amount at risk ($3.1 vs 1 billion).

Now scale this little example up to, say, $45 trillion in notional value, thousands of bets and dozens of firms, and you’ve got systemic risk!

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Written by infoproc

September 18, 2008 at 5:22 pm

17 Responses

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  1. As I drove into work this morning, listening to a story on NPR about how much of a problem credit default swaps caused for AIG, I found myself wondering what you would think of all of this, Steve. It had been a while since I had read your blog. I’m glad you see you’re still very much interested. It’s way more than I can take in on my lunch break. πŸ˜‰

    It’s interesting to me that a significant part of the problem in the financial markets of late is related to the exact financial instruments that I studied with you a couple years ago — CDSs and CDOs, etc. What are you hearing from your quant friends these days about how things look from their perspective? Does it sound like this may be just a passing phase or do they/you think it lead to a shift in how complicated financial instruments are built and traded?

    Also, do you think now would be a good time for someone to consider beginning a career as a quant? Don’t get me wrong, that’s not my intention. I’d be curious to hear your thoughts, though.

    Brian

    September 18, 2008 at 7:52 pm

  2. A sea change is coming: more regulation, higher risk aversion, more aversion to math.

    On CNBC you can already hear non-mathematical industry types trying to blame it all on models.

    Nevertheless the long term trend is still to greater securitization and more complex derivatives — i.e., more quants! But hopefully people will be much more skeptical of models and their assumptions. Personally I think it is the more mathematically sophisticated types (or, more specifically, perhaps those who come from physics and other mathematical but data driven subjects πŸ˜‰ who are likely to be more skeptical about a particular model and how it can fail. People who don’t understand math have to take the whole thing as a black box and can’t look at individual moving parts.

    Robert Shiller is still optimistic. See this recent interview:

    http://www.econtalk.org/archives/2008/09/shiller_on_hous.html

    steve

    September 18, 2008 at 8:31 pm

  3. Steve,

    Exactly the right question. And I think the answer in simplest terms is “build an exchange”. These transactions should go through a clearinghouse with margin requirements, etc. Also major CDS writers are effectively insurance companies and the math for doing insurance conservatively — all talk of Archimedean copulas to one side — isn’t really new. But it requires honest oversight and a prudential culture.

    Brian,

    I think we were listening to the same interview — Michael Greenberger on Fresh Air?

    STS

    September 18, 2008 at 9:25 pm

  4. Actually, that was the wrong link. Here’s the interview I had in mind. A couple of times I wanted to shout “those are NOTIONAL amounts!”, but on the whole he had great insights to offer.

    STS

    September 18, 2008 at 9:28 pm

  5. STS, thanks for the link.

    I think my post was totally obvious to about half of the readership, but the point was still worth making.

    I think a central exchange and stronger regulation would solve the systemic issues caused by complexity. A prudent regulator would have imposed this a few years ago! (People were keeping track of trades on slips of paper for a long time! I think I referenced some articles about this on the blog.)

    But it still wouldn’t prevent a speculative bubble like the one we had…

    Back to Brian’s original question: is it a good time to head into finance? certainly not. I think the fact that 50% of the Harvard graduating class headed into finance last year is a good signal for a market top πŸ˜‰

    steve

    September 18, 2008 at 10:30 pm

  6. Oh no! It’s that Greenberger guy again…

    Let’s hope he’s read up on the subject since his last interview. Maybe Terri will understand more this time than before…

    http://infoproc.blogspot.com/2008/04/credit-crisis-for-pedestrians.html

    steve

    September 18, 2008 at 10:36 pm

  7. I guess I stepped in it with the Greenberger link πŸ˜‰ Sure, he’s a lawyer and a regulator, not a quant. But he’s talking to a pretty broad audience and expressing an understandable Cassandra complex: he feels he recommended regulatory changes that would have made a difference and was ignored out of complacency (at best) or conflicts of interest.

    STS

    September 19, 2008 at 12:07 am

  8. This was very illuminating to me, Steve. Thanks!

    It seems to me that another job of regulators for the future is to constantly look for the weak links in such networks,i.e., ones whose failure can cause a lot of damage. It should be a very challenging mathematical problem to find good upper bounds on magnitude of potential losses, involving powerful ideas in graph theory, statistical physics and the like. I am surprised it was not done already…

    MFA

    Anonymous

    September 19, 2008 at 12:35 am

  9. No worries — he was better this time!

    I (may have) actually learned something! Greenberger claims that by statute (due to some deregulation passed by Congress — maybe even by McCain’s advisor Phil Gramm!) regulators were not allowed to intervene in CDS markets.

    Apparently MotherJones is all over this story:
    http://www.motherjones.com/news/feature/2008/07/foreclosure-phil.html

    I may have to blog about it if I have some time…

    steve

    September 19, 2008 at 12:38 am

  10. http://bits.blogs.nytimes.com/2008/09/18/how-wall-streets-quants-lied-to-their-computers/

    “In fact, most Wall Street computer models radically underestimated the risk of the complex mortgage securities, they said. That is partly because the level of financial distress is β€œthe equivalent of the 100-year flood,” in the words of Leslie Rahl, the president of Capital Market Risk Advisors, a consulting firm.

    But she and others say there is more to it: The people who ran the financial firms chose to program their risk-management systems with overly optimistic assumptions and to feed them oversimplified data. This kept them from sounding the alarm early enough. “

    But look physicists get off free: quants are “mathematicians, computer scientists and economists.” Wait, I’m one of those now….

    Dave Bacon

    September 19, 2008 at 12:45 am

  11. I think Greenberger was referring to the Commodity Futures Modernization Act (CFMA) of 2000. Specifically Section 103 on pages 35-36 of this version.

    STS

    September 19, 2008 at 12:52 am

  12. Of course section 407 is nice too.

    STS

    September 19, 2008 at 1:00 am

  13. MFA – I think the math is pretty straightforward *if* you have access to the whole network of contracts. Unfortunately we don’t! The Fed would give a lot for a map like the one above — it would make cleaning up the mess much easier.

    What I don’t understand is why someone who buys a CDS as insurance thinks their counterparty will actually be there if/when the sh*t really hits the fan!

    steve

    September 19, 2008 at 1:28 am

  14. Steve,

    “What I don’t understand is why someone who buys a CDS as insurance thinks their counterparty will actually be there if/when the sh*t really hits the fan!”

    You’re unsure of this because the interesting mathematical question is precisely the correlation among defaults. There’s some kind of a phase transition (not sure how rigorously I mean to apply that term) as the intensity of defaults increases. In finance, they talk vaguely of “contagion” — but it’s really sort of a percolation phenomenon on that network you put up.

    Of course, being aware of this, I share your puzzlement at the behavior of CDS traders. It’s particularly sad that AIG — a veteran insurance firm — didn’t manage the risks better. Maybe it was a case of assuming that models that worked for products with greater natural diversification (from geographic range or demographic diversity) would apply without this characteristic “phase transition” being incorporated.

    STS

    September 19, 2008 at 3:36 am

  15. Dave Bacon: “The people who ran the financial firms chose to program their risk-management systems with overly optimistic assumptions and to feed them oversimplified data.”

    Sure. Because then you can optimize your PERSONAL profits:

    “Your company makes assumptions about how bad the risk will be, and based on those assumptions, you determine that this trade is profitable for your employer. You then personally take a nice chunk of those profits in your next bonus as a reward for having been smart enough to get your company into this lucrative transaction. And because this upfront booking of expected profits from these transactions is so lucrative, not only do you get an enhanced bonus — but so do the other members of your group, your supervisor, their supervisor, and the president and other senior officers of the firm….

    “Now, it quickly becomes clear to any reasonable person that if you can double the profits your firm recognizes on a transaction by keying in four small assumptions changes on a computer model, each of which sounds individually reasonable, and the end result of those changes is to double the bonus you get paid this year – then the key to making some serious personal money is making the right assumptions! Something that is equally plain to your peers at competitive firms.”

    Jun

    September 19, 2008 at 6:54 pm

  16. Steve,

    I’ve enjoyed reading your blog the last couple days. As to my question about whether now is a good time to head into finance, what you said about 50% of the Harvard graduating class heading into finance last year being a good signal for a market top makes a lot of sense. I guess PhD physicists who decide to leave academia will find other things to do… πŸ˜‰

    STS,

    I appreciated your comment about a phase transition or a sort of a percolation phenomenon. Oh, and I was actually listening to Morning Edition yesterday morning.

    Brian

    September 19, 2008 at 7:38 pm

  17. This little loop with major players invalidates any Black-Scholes or Binomial pricing system they may have used for CDSs/CDOs. All such pricing formulas implicitly assume independence between transactional events for the underlying Gaussian statistics to be valid. A loop like this blows that out of the water.

    It’s literally like assuming you can calculate the temperature of a room temperature solid from a Boltzmann distribution when in fact you’re dealing with a superconductor or superfluid operating under Bose-Einstein, at best, and non-ergodic quantum mechanics at worst. BS is based on condensed matter physics where price maps to temperature and you presume to have enough atoms (transactions) for the system to be in equilibrium. Dubiously at best!

    No wonder bubbles were formed. A small error in pricing models (and I’m not talking about small errors above) feeds into a feedback loop with small delay and likely plenty of gain (greed)! Instability by any measure.

    Let’s be clear though. It’s not the model that has the problem but the abuse of the model by ignoring the basic assumptions that must be met to allow the model to be valid. No different than trying to Newtonian physics in cases when Relatistic or Quantum Mechanics are the correct models – you know when to switch when the assumptions are violated for the simpler model.

    A related issue is that this clearly shows the “zero sum” aspect of derivative insurance – there is not statistical pooling/portfolio effect to actually reduce expected risk but rather simply transferring the risk, in toto.

    The presumption of derivatives being “insurance” is that the other party can better “handle” the risk is centrally dependent, again, on statistical independence of risk. “Derivative as insurance” is nothing more than presuming pooling risk dilution on a pool you don’t even control, unlike explicitly pooled insurance!! Making the risk pool an externality when the outside world is too small to support an externality!

    How independent can the risk be for another player in the same, small market performing essentially the same market function? About zero chance! And if you are really eating your own manure… yeah, insurance alright!

    The thing is that with globalization, there really are no economic events that are independent anymore! So any risk assessment based on Gaussian distributions are suspect! Which is pretty much all modern quant finance.

    It’s possible to use alternate distributions that are better suited to this co-dependent reality. But most academic financial research has been “in the street under the street light because the light is better” rather than back in the “dark alley” where everyone knows the real answer is. In other words: “We used Gaussian distributions because there were easiest to use”. Which is OK – most engineering is done with linear models where chosen because they are simple. The difference is that much of an engineer’s training is related to 1) knowing when you aren’t linear and can’t assume your model is valid, and 2) learning ways of keeping systems linear as long as possible. No such self-discipline is apparently taught as Harvard or Yale business schools.

    On top of that, the math that would be required is not what most folks learn about or can handle, making it frighteningly exotic even for quants.

    All I can say is this stuff is and should be obvious to anyone playing with this stuff “for real” and the people involved in these businesses are either greedy and delusional, or educated but unknowledgeable.

    Cassandra

    September 20, 2008 at 8:50 am


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