The third book I recently read that has some math or physics content is Wall Street Journal reporter Scott Patterson’s The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It. It’s a very lively and entertaining telling of a story which features quite a few mathematicians who have gone on to make (and then sometimes lose) absurd amounts of money using mathematical models to try and exploit market inefficiencies. Jim Simons and his large group of mathematicians and other Ph.D.s at Renaissance play a significant role, and among other mathematicians who make an appearance is Neil Chriss, co-author of Representation Theory and Complex Geometry, one of the most well-known books on geometric representation theory (now available as a “Birkhauser Classic”).
Patterson’s story emphasizes heavily the relationship to gambling. He writes extensively about Ed Thorp, who developed the theory of card-counting, did well with this at casinos, then moved on to the hedge fund business. Just about everyone profiled in Patterson’s book is described as having read and been inspired by Thorp’s 1962 book on card-counting (Beat the Dealer). Many of them are serious poker players, and the book opens by describing the scene at the one of the recent Wall Street Poker Night Tournaments. These are yearly events (Chriss and Simons are among the organizers) that bring together quants and professional poker players to play high-stakes poker, with proceeds donated to Math for America.
The subtitle of the book puts the blame for the financial crisis on this kind of activity, but there’s not much evidence given to justify this. Most of the book is about various hedge funds, and the stories of failure are pretty much the same old story of Long Term Capital Management’s failure back in 1998. Finding some sort of market inefficiency and exploiting it tends to work for a while, but sooner or later either others start doing the same thing or patterns change, sometimes very quickly. If one has gotten greedy and started using too high levels of leverage, one can get in trouble fast. The best-run hedge funds (for instance, Renaissance) managed to stay out of trouble, others didn’t. How much of a public problem all this is remains unclear. To a large extent the failures just lead to some rich people (and universities like Harvard) becoming less rich, while some hedge-fund owners and employees see their income go down but get to keep the fees earned while they were taking too much risk. It’s very clear why a lot of mathematicians and physicists go into this.
None of this though seems to have had a determining part in the disastrous financial crisis of recent years and its ongoing effects. The book has little to say about a more significant failure that involved a different group of quants, those responsible for the bad mathematical models used to justify the mortage securitization business. From what I can tell, there the story is that if there’s a lot of money to be made creating a financial instrument carrying large risks obscured by complexity, it’s not hard to find people willing to help you sell it by creating bad mathematical models of its behavior.
The story of The Quants is a remarkable one, whether or not the people described have some responsibility for the current state of the financial industry and the dangers still embedded in it. While reading the book I couldn’t help thinking that it would be a good idea if the best of them would play a little less poker and take on another pro bono task, that of coming up with a good understanding of the current pathologies of the financial system, and models useful in the task of figuring out how to change it to something more socially desirable.
…when you have good understanding of the current pathologies of the financial system, the natural thing is to try to make money from it for your fund.
Do you expect people from Renaissance to go public with their models – or to complain to the regulators that certain trading schemes shouldn’t be allowed?
very well said. this pretty much sums up the defect of our current system.
@milkshake
What do you mean by “the natural thing” ? Altruism is also a “natural thing”. “Socially desirable” would be to expose those pathologies to work towards a system that does *not* only work for a few and leaves the major part of roughly 7bn. people in its wake.
I’m waiting for the paperback to come out in England – but what i’m interested in is the implication/accusation that quantitative analysts were responsible for the crash.
I recall a recent television program on the crisis that used NASA’s imperial/metric mistake as a framing analogy before cheekily adding that some of the people who had designed these faulty financial products were themselves rocket scientists. You wonder if there are moves to scapegoat the quants or whether it’s just an interesting angle.
Also, you allude to the social value of this kind of work. In the UK the most common destination for science graduates (in applicable fields) is banking. The discrepancy between employment opportunities and starting salaries in the financial sector to any other is (or was) mind boggling. I’ve never really seen this issue raised in the mainstream media. Perhaps it’s less apparent in the U.S. but it’s surely indicative of a wider social problem.
@above: Indeed I’ve seen many people graduating in math, material science, neuroscience, biology and so on getting into banking. I’m simply amazed at how banking in the UK is such a large industry that absorbs a considerable proportion of all science graduates.
“Representation Theory and Complex Geometry” is based on lectures that V Ginzburg gave as a visitor at the U of Chicago before he eventually became a professor there. N Chriss was a graduate student who took lecture notes that formed the basis of the book.
LTCM blew up because they started getting into products (e.g. merger “arbitrage” and gilt swap spreads) that they did not have a mathematical model for worth the name. In the end it turned out that the LTCM math PhDs – despite having larger genitalia (financially speaking, of course) – were less good at the seat-of-the-pants trading done by the other market players.
I agree with Peter that the quants who did the real damage were not these (relative) small-time gamblers, but those whose models gave AAA ratings to horse-excrement sub-prime mortgage bonds. These were sold in the trillions to pension funds, insurance companies and sovereigns like Iceland, and the fallout from their crash will be felt for decades to come.
like string theory, is not the problem that the mathematical models are incapable of prediction, but only capable of wealth transfer?
George,
I don’t think the situation is at all like string theory. Mathematical models in finance make very definite (although statistical) predictions. The problem with many of the bad models wasn’t that they didn’t predict anything, but that they made specific predictions about levels of risk that were just wrong.
String theory isn’t a very effective means of wealth transfer, typically transferring rather puny postdoc salaries to a bunch of people, more substantial senior faculty salaries to a few. On the financial industry scale though, all these numbers would be rounding errors…
I have a few quant friends, and the story I heard was a little different. Contrary to media reports, most of the models were *not* wrong. Including some of the highly publicized ones. Many of these were optimized for rather short timeframe corrections.
Instead they were really very accurate, which is a large part of the problem and caused a bit of a selffulfilling prophecy. The models had a number of fallbacks to prevent catastrophic loss. They also had well defined regimes of applicability where the model was supposed to be valid.
What happened was within the span of about a week, the market entered a phase where one by one, the fallbacks of the models triggered (not necessarily a big deal at first glance), and then the regimes of applicability were passed.
At that point, you had firms that had been basing a large percentage of their forecasting and risk assessment on these things, all of a sudden lose complete predictive power. This caused a panic, which triggered more rapid selling and more models to trigger selloffs (too much redundancy on systems that are too similar).
Economically, the panic occurs not necessarily on fundamentals, but b/c the computer all of a sudden returns negative infinity within a timespan that is much too quick for rational human activity and assessment. In short, what should have been a much more gradual correction, instead turns into a near world destroyer.
But I think the point is, its not the computers or the programmers fault really. The CEO’s just didn’t listen to the fine print, nor did they appreciate just how herdish wall street really is. Moreover the best models arguably saved their companies millions of dollars by getting the firms to remove their money or rethink their risk exposure before the real selloff’s took place.
Haelfix,
Thanks, although this “the model was fine, people using it just needed to read the fine print which said there was a significant probability it might blow up in their face” argument sounds a lot like someone covering their ass ex post facto.
From what I can tell, there were a wide range of models in use, some of which did what they were supposed to (Renaissance’s Medallion fund doesn’t seem to have done too badly). Others seem to have been just absurdly bad, including those used to create many AAA-rated mortgage backed securities.
LTCM collapsed primarily because they were massively overleveraged and because they had way too much faith invested within a piece of solvable stochastic analysis that is emperically wrong since markets are not perfectly Gaussian. It is also ironic that Merton and Scholes were harsh critics of the Kelly propertional betting criterion, which is essentially a compromise between optimization of gains, relative to a given edge, while minimising risk. Ed Thorp on the other hand used the Kelly criterion as a guide when he played blackjack so that he would not overbet and wipe out his edge. If you have $2000 in liquidity or capital at the blackjack table for example, you can’t bet more than $20 a time or else volatility or negative fluctuations can wipe you out and ruin the player edge from card counting–its true for a modest blackjack bankroll and its true for a massive hedge fund portfolio. Thorp’s hands-on experience in blackjack seemed to have made him very risk adverse when he subsequently ran his successful hedge fund. Simons and his crew did’nt actually build the Medallion fund at the heart of Renaissance: this masterpiece was constructed by the brilliant Elwyn Berlekamp and Berkeley number theorist, the late James B. Ax–hence “Axcom Trading”–both of whom I guess vastly underestimated its power when they sold everything off to Simons. Interestingly, Kelly, Thorpe and Berlekamp are all very closely associated with Claude Shannon of Bell labs, the father of information theory.
Haelfix, the quants who constructed debt instruments like mortgage-backed securities have to take some blame for the current mess but only some since they were still quite a way down the “food chain”. But regardless of how good the models might have been, in reality there was simply no way to check the quality of hundreds of thousands of mortgages in these pools or whether the reality behind that triple-A mortgage rating on a six-bedroom luxury villa was that it had been sold to a Walmart’s shelf packer. The people who pushed these insane subprimes also have to take a lot of blame as is everyone in the mortgage-backed securities chain. I guess sheer greed just got in the way.
A huge part of the mess is also due to the “American Dream” mentality: the average American (and European) consumer living way beyond their means on credit, fuelling a lifestyle and standard or living they had’nt actually earned but which they thought they were entitled to almost as a birthright. Asset bubbles, especially real estate ones, are always due to too much credit so also blame Alan Greenspan for adjusting interest rates and flooding the system with easy money/credit and creating the credit superbubble in the first place; of course, one reason for doing that was the fear that markets would collapse following the meltdown of the aforementioned LTCM. Also when LTCM got bailed out others realized they could also take massive risks and also get bailed out if it all went wrong–a win-win situation for them and the start of the “too big to fail” mentality. Also, Clinton’s financial advisers in the late 90s, who helped dismantle the Glass-Steagall banking act of 1933 to “free things up”.
The US is now in such a crushing black hole of debt it has forever past the “horizon” of ever returning to a vibrant free-market economy–all is can do now is default on its debt or inflate/hyperinflate it away, with dire consequences. And then there is Greece and the Euro and of course China…OK I won’t rant on:) But this giant Ponzi scheme of moving money, printing money, credit, selling debt, buying debt, stimulus packages, massive bailouts and TARP is now the ultimate bubble and it simply can’t be sustained–the worst is probably still to come.
Agreed.
Not agreed. Let us take the case of merger arbitrage – one of the things that killed LTCM. Company A decides to buy company B, exchanging x shares of B for a share of A. That means that if the share price of company A is pA, then the share price of company B should be pA/x, right? If it is not then there should be a free lunch: if it is lower then buying B and shorting A will give you money for nothing and if it is higher then buying A and shorting B will give you money for nothing. This is merger arbitrage, and it is not rocket science. The problem is this: what if they change their minds about the ratio before the deal goes through? Mathematical models will not help you here (eavesdropping on board meetings would, but that is illegal). The other major thing that killed LTCM was gilt swap spreads. The 5-10 year interest rate for interbank loans in sterling was historically much too high relative to the 5-10 year interest rate for UK government debt (gilts) and did not reflect the relative credit quality. LTCM, along with everyone else, knew that this difference had to come down (this difference was determined by markets, and more specifically by the fact that many investors were only allowed to buy government debt, forcing gilt prices up and therefore yields down). LTCM were right – eventually the spread did reduce, but not quickly enough, and in the meantime their convergence trade helped to bankrupt them. Unless they could have known what every player in that market was doing, and going to do, they could not only guess when the convergence was likely to occur. Mathematical models, again, would not have helped.
I think part of the problem was that the input parameters to the models representing assumptions about risk were provided to the modellers by the business and finance people.
I think it must be satisfying to some people to speculate that quant finance models — whether for algorithmic trading or mortgage securitization — have the power to cause the kind of economic upheaval experienced over the last two years. In fact, they don’t have that power. They were a secondary factor in it.
The manifest proximate cause of the contraction was too much bad debt, especially mortgage debt. Models didn’t generate this debt. The bad debt was assumed because the prices for it, known as interest rates, were too low. Interest rates were too low because the Fed decreed them to be so (negative, in real terms) for an extended period after the dotcom implosion (itself a previous iteration of the same scenario). It would be valid to impugn the macroeconomic models consulted by the Fed in making their decisions, but these models are really just an impotent formal rationalization for the back-of-the-envelope Keynesian/Monetarist guesstimates that actually drive monetary policy.
Securitization was simply a new mechanism by which the excess green paper printed by the Fed (i.e. created out of thin-air when the Fed bought securities in “open market operations”) was goosed into the larger economy. The new mechanism made the process easier, but it didn’t create all the bogus liquidity. The Fed did. It is true that models used by the ratings agencies to declare a lot of this garbage debt perfectly safe are also nonsense, premised on naive assumptions of macroeconomic stability. That certainly didn’t help things. But everyone knew these models were nonsnse to begin with. That’s what you get from quants (or anyone else) working for the ratings agencies, which are more creatures of government than of Wall Street due to their special status as an oligopoly mandated by federal regulation.
There is a fundamental misunderstanding here. The reason the bond market blew up (and have since recovered) was mainly because of a massive “depricing” (spread widening) during the crisis across the board, way over and above fundamentals (which MBS quants concentrate on).
Structuring 101: Suppose you have a 1000 subprime mortgages, each at 10% interest and $100,000 original balance. Your model tells you that at worst 30% of these loans will eventually default. Now you create two $50 millon bonds A and D backed by these loans. You structure the bonds so that A will pay the buyer 500 of all 1000 cashflows (principal and interest) that come in every month, and bond D gets the remaining of the cashflows each month. If your model is right, as far as A is concerned defaults do not matter, you have a low risk bond, since it would take more than 50% of the loans defaulting for this bond to lose a penny. This is how you shift collateral default risk from bond A to bond D. Yes the collateral is garbage but statistically only half or less of it, and that is key. Based on this risk profile bond A gets an AAA rating and since it is paying a nice 10% interest, it trades at a premium. Bond D, on the other hand, holds all the collateral risk and it gets (say) a D rating. D trades at a very low price (high yield) and is bought by “savvy” investors who (1) want the very high yield and/or (2) are betting on their belief that your model is too pessimistic (i.e., they believe they have a better default model).
Now the housing market tanks and many of the 1000 loans start defaulting at a high pace, looking like you will indeed get 30% or maybe even 50% defaults. Note that unless defaults reach 51%, bond A will receive the same cashflows. What happened next was that bonds like D got crushed, as they should, but the market dumped all MBS bonds, and bonds like A (and all bonds for that matter) got also crushed in the process, because of supply and demand. Nobody wanted to hold any of these things. Since then, the market, specially for bonds A-like, has greatly recovered. A lot of hedge funds loaded up on A-like bonds when they got spectacularly cheap, priced way below their fundamental value.
MBS bond prices come from 4 factors: cashflow structure, modeled losses, modeled prepayments, and a fourth factor which is a “technical spread” (or how much investors are willing to (not) pay for the perceived un-modeled risk, liquidity, demand/supply of the bond). MBS “quants” concentrate on modeling the first 3, the fourth one was historically contained and this time it blew out (dragging down bonds like A) because of unprecedented market panic and hysteria (spiraling as institutions were forced to mark(price) to market their bond portfolios). Yes, default models are based on history, and it is true that modelers now understand that the fourth component can blow out and bonds may trade like stock, regardless of the fair value of the underlying cashflows, making modeled prices at that point irrelevant. Your car that gets you to work every day may not be worth a dime after all, if nobody wants to buy it. Can one say that A bonds should be rated F because they are backed by sub-prime loans and lost so much market value at the bottom of the crisis? Well, the hedge funds may certainly hope so, because they would be buying AAA cashflows being sold for dirt all day long. What programs like TARP (initially) and banks tried to do was to warehouse these bonds and hold them to maturity (realizing their cashflows) or until the market returns from trading bonds like they were GM stock…
Here a presentation from Professor Philip Jorion (aka MR Value-at-Risk) that gives an interesting discussion about what caused the financial crisis. There is one example that may be particularly interesting where you can see that a tranche of a CDO security was giving credit rating AAA when a more appropriate assumption about the default correlation for the underlying loans would give BBB.
http://efmaefm.org/0EFMSYMPOSIUM/Nantes%202009/efm_sympo2009.shtml
Click on Keynote PPT slides to download the presentation
The LTCM predictive models did not account for the collapse of the ruble. It is not likely that exogenous variables can be incorporated into any useful model.
Nassim Taleb discusses the limitations of statistical theory in his “Black Swan.”
The recent books about the crash have disclosed that senior management were clueless about the methods used by the quants and therefore did not comprehend the extent of the risks.
The influence of the ruble on the real estate market in the US is a subject that has just begun to be explored.
Now that water has been found on the Moon, maybe real estate markets will stage a spectacular rebound. Watch out for a huge surge in the price of subprime mortgages.
In case you did not notice, Scott Patterson was on the Daily Show on March 4th.
… coming up with a good understanding of the current pathologies of the financial system, …
The fundamental question might well be this: If the agents participating in the system use models to guide their actions, and worse yet, if they use models as a selling tool—eg, to provide bogus justifications for rating bonds as triple-A, while the underlying assumptions are being invalidated by the actual behavior of market participants—can models ever be expected to be reliable guides to the actual behavior of the financial system?
I seriously doubt it……
Hi Peter –
Thanks for book review since I probably would have missed it. What I found interesting (page 115) is that Renaissance employs a number of people who originally worked on speech recognition and are clearly well versed in Shannon information. Achim Kempf was published a series of papers utilizing some of the same technology but in a completely different context – quantum gravity.
“Information-theoretic natural ultraviolet cut-off for spacetime”
http://arxiv.org/abs/0908.3061
A perimeter seminar can be found here and Susskind can be heard asking questions.
http://pirsa.org/09090005/
I’m curious whether you find the approach promising.
Geoff,
Yes, that’s an interesting insight into the kind of thing Renaissance is interested in.
Personally I don’t find the kind of approach to quantum gravity you mention very promising, for various reasons. One is that I don’t see that throwing out geometry in favor of information theory really buys you anything, but mainly I’m skeptical that “quantum gravities” that don’t have anything to say about unification will ever be testable or useful for anything.