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  • Clever Mathematicians vs. Financial Risk

    Posted by Jonathan on February 28th, 2009 (All posts by )

    See here (via here).

    This is a timeless issue. The specific risk model under discussion isn’t the central issue. It never is. The central issue is that financial-risk models whose effectiveness depends on the accuracy of their assumptions about the distribution of securities-price movements eventually blow up. This is why “portfolio insurance” failed in (helped to precipitate) the 1987 crash, why Long Term Capital Management blew up, why Fannie Mae’s risk estimates vastly understated the real risk and why countless other “value at risk” schemes cause more problems than they mitigate. In simple terms, these schemes assume that in the event of portfolio losses you will be able to sell off your portfolio incrementally without incurring further large losses. In practice, the very fact that your portfolio is experiencing an extreme decline in value means there are no buyers except at lower prices and that further losses are probably inevitable: if the life boats are all on one side of your supposedly unsinkable ship you may still capsize if the passengers move there en masse. This is human nature and can’t be hedged away by invoking clever math, though clever people keep making this mistake (and will keep making it, because human nature doesn’t change).

    In the long run the only reliable way to limit the risk in your market portfolio is to structure it so that you don’t lose money if the impossible happens. But this is expensive (insurance usually is), and it’s always tempting to lower your costs, and raise your short-run returns, by assuming you don’t have to worry about 100-year floods. The problem is that 100-year floods occur in financial markets every five or 10 years.

    BTW, this is also why the notion of “stress testing” banks is fatally flawed. You cannot assess the risk of loss in a financial portfolio by asking what happens under conditions of moderate, i.e., likely, financial stress. If there is a systematic fatal weakness, however improbable, in your financial system the markets will eventually find it and the system will blow up.


    14 Responses to “Clever Mathematicians vs. Financial Risk”

    1. seanf Says:

      Mathematical modelling works only as well as the model. Li had a great idea but it was flawed by 2 fatal assumptions implicit in classical economic theory.

      — That markets are efficient and always price risk correctly. They aren’t and don’t, so substituting a derivative market assessment of risk will not always work. Li understood this but the traders who followed him did not.

      — That people behave rationally when it comes to financial decisions, the rational actor hypothesis. This assumption was assumed to be true (with some reservations) as recently as the 1990s, but has now been conclusively shown to be false. Behaviorial economics and empirical research demolished it.

      I hear what Shannon is saying when he criticizes economics for being a pseudo-science, because of the lack of predictability and falsifiablity. Valid. At the same time it’s considerably easier to model, say, quantum electrodynamics or even complex fluid flow, than it is to model human behavior. Nature follows laws. Humans do so imperfectly at best. The pursuit of certainty in economics, like the pursuit of utopias in politics, has always led to failure.

      Perhaps one way of thinking about it is that in physics, the model is reality – or at least comes very close to it. But in economics, models are a very imperfect imitation and blind trust in them has always led to disaster.

      This is why, for example, law and economics has foundered of late. Yes, with if we assume no transaction costs and perfect information then there is no need for government regulation of much economic activity. Absolutely. The problem is that in the real world there are always transaction costs and imperfect information. If we ignore these, given the “crooked timber” of human nature, Enron and Bear/Lehman/the whole CDO mess is inevitable at some point.

      That’s the case for regulation and that is why, despite being sympathetic to some parts of the libertarian agenda, I’ve never been able to buy libertarian economic thought. Ideology is all very well until the rubber hits the road.

    2. david foster Says:

      Seanf…problem is, the regulators too are human and are made out of equally “crooked timber.” Too often, government is viewed as an idealized parent: actually, it is made up of people (whether Congressmen or GS-11s) who are themselves economic actors, pursuing their own desires for money, status, power, adulation, and/or security.

    3. Jonathan Says:

      David is right but it’s even worse than that. Not only do regulators have mixed and often counterproductive incentives in their regulatory activities, but people who understand markets are unlikely to become regulators because they can make much more money by working in the financial industry. So the regulators with rare exceptions are not the sharpest knives in the drawer, or if they are smart they may be anti-market ideologues. In either case their understanding of the world of finance tends to be both limited and lags current reality. And of course they tend to respond to political rather than market incentives, so it is unlikely that they can be effective in limiting market excesses and their political hubris tends to exacerbate problems (Fannie Mae).

      Markets are emergent phenomena of group behavior. People make markets and people make mistakes. It will always be thus. IMO the better direction to move in is decentralization of authority so that market mistakes and regulatory mistakes get corrected before they get out of hand. The current debacle is the kind of thing that happens when pols and regulators distort markets (in this case by pushing banks to lend to high-risk borrowers, and then by subsidizing Fannie Mae to accumulate and mis-estimate risk). It presents a strong case against the kind of heavy-handed financial regulation that is now being proposed as a remedy.

    4. Brett_McS Says:

      There was an excellent documentary some years ago about Merlon & Black, two mathematicians who invented the (Merlon & Black) formula for pricing futures contracts (I’ve forgotten the details). It worked brilliantly in their trials, and so rather than just publish it and go on with their academic lives they set up a company to exploit the formula. They made billions … and then lost it all during the Asian crash. The formula kept telling them to stay in, whereas all the other traders were getting out as fast as they could. So, yes, things change. The formula is still used in the futures market – it’s brilliant and simple – but not applied in such a slavish way.

      I’ve never been able to find that documentary.

    5. seanf Says:

      jonathan and david, agreed, regulation is no panacea. but just because regulators, like referees, can be gamed doesn’t mean we shouldn’t have them at all.

      No less a deregulator than Alan Greenspan has admitted that he’d made a “mistake” all along – even he now admits self-regulation doesn’t work.

      For self-regulation to work, market participants have to sacrifice individual short-term gains for collective long-term good. That appears to be asking a little too much from humanity.

    6. Jonathan Says:

      I think you are too fixated on the issue of regulation. Extreme ups and down are characteristic of markets, not aberrant. Trying to regulate away the extremes tends merely to suppress them for a while, until there is a blowup that is much worse than what would have happened if the markets had been left alone.

    7. Brett_McS Says:

      If the regulators are actually capable of successfully regulating the market they would instead be making millions for themselves on that same market. Government regulation of the market is putting the dumb kids in charge of the smart ones. The top of the class goes to Wall Street, the bottom of the class goes into the SEC.

    8. renminbi Says:

      Whenever there is apectacular market failure the gov’t is never far away. Steve Sailer has the most plausible explanation as to how the Clinton administration began pushing banks to make bad loans. The graph in the link provided says everything.

      By the way ,has anyone here ever worked for a gov’t agency? I at least knew my two jobs were chickenshit,but never saw a hint of awareness on the part of my colleagues. Expecting anything competent from the gov’t is is to expect what cannot (except for a short time) be.

    9. renminbi Says:

      Don’t want to mislead- Bush 2 continued what Clinton started. All of the Western Democracies are presided over by Bozos.

    10. C. Smith Says:

      Common sense? OK, I’ll shut up.

    11. Anonymous Says:

      “Extreme ups and down are characteristic of markets, not aberrant”

      Agreed, no one is saying that they are not. The aim of regulation is to ensure that actors play by the rules – whether the market goes up or down is usually of no concern, that is left to the market. What is of concern is preventing market failure.

      An example of failure is what happened with the CDO market, when huge speculative investments were made on the basis of bad information (in this case, the rating agencies not doing their job, and misrepresenting actual risk). The result was a systemic breakdown of trust between actors and a consequent lack of credit. Markets run on trust. Destroy trust, the market fails to perform.

      “Government regulation of the market is putting the dumb kids in charge of the smart ones.”

      No, that’s a fundamental misunderstanding of regulation and specifically the SEC. The goal of a good regulator is not to be “in charge.” It is to enforce agreed upon rules for the common good – rules that all actors want others to play by, but rules that not necessarily everyone would want to follow for themselves. A policeman doesn’t need to have the intellect of a Supreme Court justice.

      With respect to the SEC, uring the last 8 years, there was a regulatory problem of the kind Jonathan and David described above. The politicians in charge of the SEC thought there shouldn’t be any regulatory enforcement; prosecutions fell, new markets such as CDOs were not regulated and offenders got a tap on the wrist, if that. That problem, known as regulatory “capture,” is unfortunately endemic to government regulation because regulators are always subject to political control.

      “The top of the class goes to Wall Street, the bottom of the class goes into the SEC.”

      This is demonstrably not true, not even during the last 8 years. The SEC has some staffing problems – it has more lawyers than it should and fewer economists and accountants. But it has historically attracted bright candidates because large amounts of money are at stake and SEC experience is very monetizable in the private sector. This I know personally.

      It’s easy to think in binary terms – yes/no, black/white, free enterprise good / regulation bad. It’s also wrong. Too much regulation strangles an economy. But too little kills it just as surely. Free markets aren’t things you find growing wild in Brazil. They’re human creations, and need tending – and discipline.

      Markets work best when it’s easy for everyone to play and transaction costs are low (implying minimal regulation) but also very hard to cheat (implying significant levels of regulation). That’s an inherent tension that doesn’t have an easy answer.

    12. Mitch Says:

      This just nails it, if you read the underlying explanations. Short version: the investment banks’ analysis found correlations, and they wrote models that assumed the correlations were immutable. Oops. If the future invariably resembled the past, we would all still be chipping flints.

      Wired had an article about this, and it’s well worth reading. It is cold comfort to know that the events that cost me half my retirement savings may also have cost the author of the disaster a Nobel prize, but under the circumstances, I’ll take what I can get. Damned little else on offer.

      I’m working something up for later posting, but to save you the trouble of reading it, here is what it will conclude: there is still no reliable method of calculating a liquidity premium. The investment models that just blew up assumed there is no such thing, and that there was an arbitrage profit to be made in betting that way. Once again, oops.

    13. Brett_McS Says:

      People who talk about “market failure” want to compare what actually happens in the market with “the goal of a good regulator”. To compare the reality of the one with the original intent of the other. They have either never heard of, or else don’t understand, what is called in Britain The Politics of Economics or (rather less clearly) Public Choice, in America. The performance of the market at any given time is the benchmark. If it is performing “poorly” (in someone’s opinion) the question is, can the government step in and make it perform better? And here we enter the realm known as “government failure” – as described by von Mises, Hayek, Milton, Buchanan, etc etc. “No”, in short.

      In actual fact “the smart kids” created all those complicated derivatives exactly to get around the attempts at regulation by “the dumb kids”.

    14. OnceATrader Says:

      Anyone a trader here? I mean a trader that is asked for a price on an instrument without the aid of a ‘model’, computer, black box or anything non-human.
      Believe it or not but thats how markets used to work. Yes their were crashes, but the ‘price-makers’ dominated, for they were willing to assume risk and manage it….incrementally.
      No bell curve woulda coulda shoulda build-up of position size and risk.
      Price discovery was far from perfect but always marginal, and that seemed to ensure that whilst a permanent state of imperfect price existed, it was never too far away from the equilibrium point (unless of course it was being distorted by a non-commercial entity) in the market.
      Taleb had a name for us………..Fat Tony.
      Price discovery is trial and error.
      Its also like viewing art, each human has a slightly different view of what they are seeing and what the average viewer is seeing.
      There was/is no modeling needed to explain why Mona Lisa is ‘Mona Lisa’.
      Let the markets frown and grin, be volatile and settled.
      Above all, let them be markets.
      All the regulators need do is blow the whistle and certify the players.
      My 20 cents: Jonathan has is spot on. Obama is continuing bad practice and the Keynesians continue to suck the oxygen out of the supply-side market model.
      Lets just prey that he senses the error sooner rather than later and we go back to the reality of what works.
      Effective Communication not only save us from wars & divorces, it also discovers price.
      “So what do you think it is worth?” I ask you?