There’s an interesting story in the New York Magazine by Michael Osinski–the author of the main software package used to create the CMOs and CDOs that have helped cripple the financial system.
Osinski’s story is worth a read in its own right. But what I found curious about it was that he appears unaware of a flaw that existed in those products from the outset–the presumption that the standard mathematics of risk and return could be applied to financial assets. He doesn’t even mention this topic, but statements like the following imply that his software used a standard probability distribution to calculate risk and return for a given bond:
“Working with another programmer, I wrote a new mortgage-backed system that enabled investors to choose the specific combinations of yield and risk that they wanted by slicing and dicing bonds to create new bonds. It was endlessly versatile and flexible. It was the proverbial money tree…”
Though these distributions don’t have to be “Gaussian”–the “Normal Distribution” that lies behind the ubiquitous “Bell Curve”–all these distributions “tend” towards that one, and they certainly share one feature: they have finite variances around the mean outcome.
Sorry for some of the statistical jargon so far: the basic point is that, if some process–like rolling dice at a casino–follows one of these distributions, then you can calculate both the average score (which for a roll of two dice is 7) and the odds of a particular score (say 12, the odds of which are one in 36) coming up. You can also calculate that some outcomes are so rare as to be effectively impossible–such as rolling 12 twelve times in a row (such an outcome would occur only once in every 5 million trillion attempts).
The problem is that mortgage defaults aren’t like dice rolls. Which face on one dice turns up on the top doesn’t affect what the other dice do: a 6 on one dice has absolutely no impact on the likelihood of another dice also turning up 6. But if your neighbour defaults on a housing loan, you are more likely to do so too–because her mortgagee sale will depress the likely price for your house, and her disappearance from the neighbourhood will decrease incomes there, indirectly affecting yours, and so on.
Crucially, price rises in an asset market are also correlated: a rising asset market leads to the rising expectations that Minsky’s “Financial Instability Hypothesis” describes so well, and a falling one puts the process in reverse.
In this sense, asset price movements have more in common with earthquakes than with dice rolls. The best stylised model of an earthquake was built by a physicist called Per Bak–he called it “the sandpile model“.
Consider a child building a mound of sand at a beach by smoothly pouring dry sand out of a bucket. Initially, the sand spreads wide, then it gets to the point where sideways movement requires more force than each sand grain can impart, so the mound begins to rise up. It gets steeper–approaching a pyramid shape–and as it gets steeper, the structure gets precarious. Then another grain is added, and the whole structure suddenly collapses in an avalanche. The avalanche then stops, the pyramid is much less steep, the sand pile broader. The child continues adding sand, it pyramid rebuilds, then collapses at some trigger point, and so on.
The process building the sand pile doesn’t change–it’s always more sand grains dropping out of the bucket–but at somewhat unpredictable moments, the behaviour of the aggregate sand pile changes, from building upwards to collapsing, and then rebuilding again.
The pattern replicates what we see with earthquakes: movements in the earth’s tectonic plate occur all the time, and most of the time, each movement just adds to the existing level of tension between those plates. But every now and then, one additional movement occurs, the whole mass shifts, and a major earthquake results. As Per Bak put it, “a big earthquake is a small one that doesn’t stop”.
The pattern of movements you get from such a process can look superficially like a Normal distribution–the famous Bell Curve–but it differs from it in two fundamental ways. Firstly, there are many more movements near the average; secondly, there are also many more movements way, way away from the average–so many more that, in what is known as a pure “Power Law” distribution, the standard deviation is infinite: any scale event can occur, and will occur given enough time.
What does that mean for CDOs and CMOs? Since they presumed a “Normal” distribution (or at best one drawn from the class of statistical distributions where standard deviations are finite), they categorically ruled out the possibility of “large events”–such as, for example, house prices falling 10% in a year.
There is no example of the numbers Osinski’s programs may have used, but for example if a bond had assumed that house prices move up at 5% a year with a standard deviation of 2% around that trend, then a 5% fall in house prices would only occur once every 3.5 million years. A 10% fall would only occur once every 31 trillion years–it simply couldn’t happen.
Yeah, right.
In fact, in a Power Law process, movements of that scale will occur, and far more frequently than predicted by these standard probability functions. Osinski shows no awareness of this:
It hurts when people say I caused this mess. I was and am quite proud of the work I did. My software was a delicate, intricate web of logic. They don’t understand, I tell myself. Perhaps it was too complicated. But we live in a world largely of our own device. How to adjust and control these complexities, without stifling innovation, is the problem.
He couldn’t be proud of what he has done, had he known that he had used a fundamentally inappropriate model as the foundation of how risk and return were calculated. As usual, ignorance rules in this folly.
I’ll return to this topic in more detail in next month’s Debtwatch.
Everybody always reaches for power laws and self-organized criticality to explain correlations. There are simpler explanations and tools for undertsanding risk correlation.
For example, simply looking for cross-correlation at different characteristic time-scales and show the underlying structure of different industries. See here.
The larger point is that power laws are usually only an approximation, an approximation that applies only within a certain range of scales. On my view, it’s better to start with a naive view of the underlying dynamics and build up from there rather than making assumptions about scalability.
Specifically, there is no a priori reason to believe that power laws should apply rather than non-homogeneous poisson distributions when considering temporal shifts in demand or supply.
I think that it may have been posted here before, but the article on David X Li’s mathematical function is a must read for anyone interested in how we got to the present crisis.
http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all
Both Li and Osinki assume the risk to be Gaussian at some level. Li’s function then reduces this to a single number (gamma) that is based on recent trading history.
The analogy is clearly of driving very fast by looking in the rear-view mirror only. Li never pretended that his equation could predict the future, but it was used as a tool to replace gambling with “mathematical certainty”.
By the time that the truth was discovered, the equivalent of the entire planet’s income had been gambled several times over. We are all going to have to take a trip to rehab and do the equivalent of a detox.
There is just no way that giving everyone (individuals, companies or banks) large amounts of money and telling them to gamble some more is going to help.
Interesting questions – how were the risks calculated, what is the real risk of a correlated group of mortgages.
I’m interested in another aspect too, what loss of information about the underlying risks occurs when the various mortages are grouped, or the resulting bonds are grouped?
In addition to that, what loss of market variation is due to converged policy? Prior to securitisation a lender might have their own proprietary model to ascribe credit risk to a mortgage, so across multiple lenders there may a number of variants. But securitisation forces them into a single model (embeded in the software) and that model is certified by a ratings agency (paid to do so of course).
As Benoit said “the theory thinks things change slowly and can be corrected, they dont realise things (markets/assets prices)can change brutally and many bad things can happen”.
Most modern economists use a simple bell curve for risk, they forget in REALITY at the egdes of the bell curve there are large cliffs, where risks may not be highly likely but have grave effects.
I noticed today in Chris Joyes article he asks the question does anyone really know what a bubble is.
I think he might be suffering from the Alan Greenspan syndrome. I hope he gets better soon.
Reuters
“Australia may slash welfare payments, including pensions for the rich and popular childcare subsidies, to contain government borrowing in the face of huge stimulus spending and weak tax revenue, a report said on Tuesday.
The federal government’s finances are plunging into the red after six years of budget surpluses, weighed down by about $53 billion ($US36 billion) in stimulus measures and falling tax revenues as the economy slams into reverse.”
It had to come eventually. This is just the start of course. Now that the surplus has been comprehensively squandered, it falls on those with some savings or so called “wealth” to pony up the cash that will keep Govt spending alive. Soon to be followed no doubt by the inevitable tax increases.
Welcome to the Aussie version of the Govt Looters.
http://www.businessspectator.com.au/bs.nsf/Article/Australia-govt-to-slash-welfare-in-budget—report-QN38N?OpenDocument
Does anyone know the types of “off-balance sheet” derivatives the Australian banks have exposure to, and a guestimate of the risks involved?
Hi riemannzeta,
I agree that there are better explanations than a Power Law, which I see as a characterisation of the data rather than a model of how it is generated. I’m also familiar with Joe McCauley’s work that argues a lot of apparent Power Law correlations come from spurious effects caused by data binning. However as I’ll show in the next Debtwatch, a simple ranking of the log of movements versus the log of the size of those movements generates a Power Law-like result for both earthquake data and stock exchange data. A Gaussian fit is OK for 3 standard deviations, but monstrously wrong for anything outside 3SD. That’s the basic point of this little post–which I know I have to provide more detail on to elaborate, hence the larger post I’ll make in the next Debtwatch.
Hi Ernie,
As far as I’m aware the biggest exposure to derivatives in Oz is interest rate swaps. They would probably account for about 90+% of Oz banks’ exposure to derivatives.
I’m not sure of the scale, or if it is recorded anywhere.
I would say the risks of loss are large given the large unexpected (by the banks) moves in interest rates over the last 18 months. (rates up heavily first, then down hard).
I think the fact that most of the borrowers in Oz are on variable rates does reduce the risk somewhat. But given that we do not know the scale we can’t tell whether the risk is reduced from a potential loss of 1 year’s profit or 1 week’s.
The other factor that may have increased risk is that since early last year the swaps dealers were finding it hard to get anyone to trade with them. This illiquidity may have made it hard to hedge losing or risky trades. Thus increasing overall risk.
Sorry my explanation is all over the place. I am not aware of recorded data on interest rate swaps.
I like to think of prices in financial markets as like playing dice in a casino where the rules change every now and again. The normal distribution only gives good predictions in the short run or if a rule change didn’t affect your odds too much.
When the rules do change is when you will see a 6 sigma event. The casino will say you should keep playing, but wise players will cash in their chips and look for another game.
The overall level of the banks’ Off-Balance Sheet derivative exposure is maintained the RBA. Go to
http://www.rba.gov.au/Statistics/Bulletin/index.html
and click on “Banks – Consolidated Group Off-balance Sheet Business – B4″.
The overall level is currently at $13.6 trillion (December Quarter). I have sent this link to Steve, who indicated he will do a debtwatch on this sometime in the future.
I think the debate about the proper form of the probability distribution–Gaussian? power law? Poisson? lognormal?–misses a larger point. Even if you could perfectly fit the correct distribution to the historical data, your risk model would eventually fail, because the economy is an adaptive, nonstationary system, not a sand pile or any other physical system governed by static physical laws. Analogies and mathematical techniques from physics and engineering are, I think, destined to fall short in describing economic systems because they omit a critical feature of the dynamics of these systems: the governing dynamics change over time. Indeed, the act of creating a model and using it to make investment decisions changes the system, and the more that model is used, the more the system changes. Osinski’s error was not simply that he got the distribution wrong; the whole idea of making any kind of static model using stationary probability distributions and employing that model mechanically to make investment decisions is flawed.
What’s the alternative? I’m still trying to figure that out, because the same problems apply in modeling the ecological and coupled human-environmental systems I work on.
Completely agree JamesB! However the main point in this post was to say that a Gaussian should be a no-no from first principles in areas like finance.
My alternative is to try to develop a causal model rather than a statistical one, and to set my causal process at the level where the system’s dynamics are qualitatively closed so that a model can be built. So I don’t try to model the actual input-output dynamics of production, for example, because the commodities in existence, and the input-output relations between them, change in an evolutionary way; but I do try to model broad productive sectors because, whatever else happens, we’re going to have commodities that are broadly intended for investment purposes, and others that are broadly intended for final consumption.
@Steve Keen
I probably came off too dismissive. I have seen it argued elsewhere (like here) that SOC can be a useful model of stock prices. And surely it is better as a risk model than a crude gaussian approximation.
For me, the more interesting question is what local dynamics give rise to successively larger and larger scale correlations? I don’t honestly know enough about the BTW model to know where it comes up with its predictions. But I do know that even a small change in the network of linkages that gives rise to those correlations can shift the dynamics from a power law to a poissionian distribution.
I think there must be a synchronization of supply and demand activities that is gives rise to these correlations. There are some interesting models of sync (like the Kuramoto model). And tracking the correlations as they arise might ultimately be a better method for mitigating risk then merely forecasting the size of potential disasters.
Anyway, interesting post. I just found your blog through a friend and will follow along as you continue this series of posts.
http://www.brookesnews.com/093003ausrecession.html
The economy tanks as politicians look the wrong way
Gerard Jackson
“Rudd, like Obama, is following in the destructive footsteps of Gordon Brown. Australia, the UK and the US are being led by economic and historical illiterates, men who are criminally ignorant of how free economies functions and the forces that destabilise them. Unfortunately our media commentators are every bit as bad.”
Further to the posts by Bullturnedbear and Jim about interest rate swaps, it appears that it’s not just banks that have large exposures to them. There was an interesting snippet in a Business Spectator article yesterday about the impending $1 per share call on holders of the worthless BrisConnection installments:
“… And just to make matters more complex, BrisConnections tried to protect itself against interest rate rises with a series of interest rate swaps that are now $476 million in the red – more than the [nominal $390 million the] call will raise …”
The full article is at http://www.businessspectator.com.au/bs.nsf/Article/BrisConnections-on-a-knife-edge-$pd20090330-QLQDJ
It’s funny reading about complex software to calculate risks and prices of assets. Despite intimate familiarity with software and programming of all kinds, I still cannot get my head around how it came to be that second-hand products (and especially ones that cost almost nothing to produce) unwanted by their current owners can have any kind of meaningful price at all. This is not some ideological protest, but a genuine lack of comprehension.
Steve Keen,
That’s an interesting approach–getting around the adaptive nature of the system by focusing on scales at which adaptivity isn’t important. I’d guess that would only work for certain types of question, though. If you want to do what Osinski was doing–assessing the risk of losing x amount of money on some investment–you probably would have to account for adaptivity, wouldn’t you?
Jamesb
How about a multi-agent system where agents demonstrated behaviour close to that of humans, and where behaviours were modified according to empirical behavioural studies of people?
I agree with JamesB about adaptivity.
Human beings respond to incentives. If you treat human beings as if they are just mindless probabilistic events, whose risks you can diversify away by dealing with large numbers of them at a time, they will outsmart you. They will put down inflated incomes on their mortgage applications. They will claim to be owner-occupiers when they are just speculators who will rent out the property to Section 8 tenants when they get into a cash flow bind. They will bribe appraisers to report a higher than actual value.
Another common pattern in life is that the things we are most interested in build to a climax of the greatest risk and reward, where predictability is at a minimum. The events that we find most fascinating are those that are hardest to predict. We know exactly when the sun will set on December 21, 2009. That is a hugely important fact, but it’s not a very interesting one to us because it has already been taken into account. We’re more interested in things like who will win the World Series or be elected President or whether the stock market will go up or down … because those are so hard to predict.
Let’s look at a sports example of risk vs. reward. Say you are an Olympic boxer, one of 32 contenders in your weight class. You have a particular power punch that you are fond of which requires you to drop your defenses for a fraction of a second as you wind up to deliver it. In the first round, against a boxer from Bhutan, you throw it seven times with no bad results for you. In the second round, against the Ghanian fighter, you use it five times with no ill effects. In the third round against the Slovenian fighter you throw it six times and suffer one glancing blow. In the semifinal round against the Korean boxer, you throw it seven times and suffer two glancing blows.
Okay, so, in the first four matches, you’ve thrown it 25 times and suffered three glancing blows. Only a 12% problem rate, and those problems aren’t that bad: just glancing blows. You run a 1000 Monte Carlo simulations, and using that punch pays off in 973 of them. You like those odds!
Now you are in the final against the Cuban, who is the World Champion and defending Olympic gold medalist. You immediately rear back to throw your power punch … and wake up in the infirmary with your silver medal on the bedside table.
What happened?
Non-randomness. The whole Olympics were set up to pit the two best boxers in the final round. The Cuban, who might be the professional champion of the world if he were allowed out of Castro’s paradise, is just plain better than anybody you fought before. In hindsight, you can see a trend in the data but you simply couldn’t predict from it how hard you’d get hit.
A lot of things in real life work out roughly along the same lines as in organized tournaments, building to a climax. First, Hitler conquers Czechoslovakia, then Poland, then Denmark and Norway. So, feeling lucky, he invades France. Then in 1941, with all that positive data on the high rewards and low risks involved in starting wars available to him, he invades the Soviet Union and declares war on the United States. Notice a pattern?
In retrospect, things tend to evolve toward maximum unpredictability.
Steve Sailer said,
“In retrospect, things tend to evolve toward maximum unpredictability.”
Well said. You are decribing Entropy; the tendency of a system to revert to a state of maximum randomness.
Steve Sailor,
Nassim Taleb has a simple (but brutal) example in the “Black Swan”. The turkey has been well-fed by the farmer every day of its existence and trusted him, until one day at Thanksgiving…
Frank:
Your suggestion gets close to an idea I suggested in an earlier thread, and that is – basically – drawing more on disciplines like History, Social Anthropology, Behavioral Science, Biology, Sociology, International Relations, and Political Science – as well as Demographics and Market Research techniques – to construct economic models.
There are a number of academic disciplines that have done a lot of work theorising, analysing, and researching societies, institutions, cultures, and people. In some cases, they are literally down the corridor from the economics departments at many of our major universities. Yet the insights and orthodoxies in those other disciplines all too often have no baring on what happens in the economics department (with a few notable exceptions, including – of course – Steve Keen).
At the same time, in many businesses on one floor you have a room full of economists who model the economy based on the assumptions that people are “rational,” while on the very next floor you have a room full of sales people and the marketing department, who literally prey on the fact that people are far from rational in order to sell the products that keep the economists in a job. It’s quite absurd when you think about it.
And every few years, our Governments do a lot of the leg-work in assembling models for us. Conducting a census that collects a range of data about our society, and elections which measure political attitudes.
I maintain that it’s people who should be the basis of any economic model. The ages of people. Number of people in a household. Their income. Their gender. The industries they work in. Their political attitudes. Their ethnic backgrounds. Their religious beliefs. Whether they have any disabilities or diseases. Their level of education. Their profession. Their wealth and the resources available to them. Their cultural preferences. Their sexual preferences. Their involvement in the black market. And – perhaps the most important one – which generation they’re from.
The models, at their basis, should look at how these shift over time. They should be actively looking at things like immigration statistics, births, deaths, marriages, etc. As new factors emerge over time – for example, technological literacy – these should also be added.
What you would come up with, as a result of this, is a very dynamic – and far more realistic – basis for a model.
Then add in institutions. Rather than a simple ‘private / public’ dichotomy, let’s look at a range of institutions. Micro-businesses. Small business. Multinationals. Government departments and institutions. Not-for-profits. Clubs. Associations. Co-operatives. Unions. Political and protest organisations. Who participates in these – as consumers, as owners, in executive roles, as employees? How does this participation change over time? What impact does this have on their behavior?
And, in a country like Australia, the reality is that the big four banks and our supermarket duopoly need to be modeled as disctinct institutions if you want to understand the economy here.
I want other people’s feedback, but certainly if you constructed a model that could measure the factors I’ve discussed here, it would be far more accurate than some of the ponzi models that have been used in finance.
Reading through what I’ve just written, a slight clarification is in order. By “people should be the basis of any economic model,” I would also add that the natural environment should be a second basis for any economic theory or model; particularly a risk model.
Michael Osinski finished his article with the observation of prof Gesiak that “the U.S. government would, like Poland’s, make the currency worthless.” I totally agree with this opinion as I remember very well what happened (including the price of vodka). Unfortunately only a few people not from Central/Eastern Europe even know what he is talking about.
Now about the main topic of the article. The problem with the model used for securitization is that it applies to certain small-scale environments. I am not an economist so I will not make uneducated comments whether Gaussian distribution can or cannot be applied for risks of defaulting. However even is the normal distribution is perfectly accurate in predicting the rate of loan defaults when other external circumstances (like unemployment rate) are stable this model cannot be applied outside the range of parameters it was designed to work with. I understand that securitization worked by distributing and diluting risks associated with failures of certain elements of the system – provided that these failures were independent from each other. The model may be invalid because events may become dependant (what Steve mentioned above). Too many people going bankrupt in the neighbourhood cause prices of houses to tumble. Also – the application of the model changed the reality in which the model was supposed to work. Analysing the stability of the environment where everyone is taking a loan would require creating another model working in the macro scale. This process of massive leveraging (creating a bubble) would change the level of risk. The model used for securitization was probably viable and quite useful for the microscale and when external parameters were constant but not for the macroscale.
As a computer programmer I have witnessed a process of collapse of a complex artificially created virtual environment like a messaging system. The rules applied to message processing seemed to be obvious. Certain elements were supposed to retry failed operations. What was not anticipated (by some engineers) was the positive feedback caused by the retrial mechanism which made the system unstable in certain circumstances. This analogy can be applied to the economy – the bubble and later the collapse are driven by a positive feedback. In fact agent-based simulations try to mimic the behaviour of the real system using multiple simple entities interacting with each other according to simple pre-defined rules. The economical reality is highly non-linear, may probably be described by sets of differential equations of higher order. The economical reality is also non-stationary – what was true a few years ago may be not true now. Also – any model will be a simplification. In fact in the end we are dealing with the people who make individual decisions. It is well known that certain even very simple sets of non-linear differential equations lead to chaotic trajectories. These environments are very sensitive to external stimuli (a “butterfly effect”). 20 years elapsed since I studied these topics but I still remember one thing – modelling even a very simple physical system can be difficult. That’s why I wouldn’t blame Michal Osinski for the collapse of anything. I should probably read a bit more in order to understand these models Steve Keen is talking about. Maybe one day – I may have a chance to understand more and contribute to the discussion.