MSc Physics, MSc Mathematics P. Lohmeier

APRIL 7^th, 2009 By now we are dealing with the "biggest financial crisis" in history (don't ask me how to quantify that), preoccupying news programes and weblogs -yes, this one was specifically established to keep track of the crisis- and affecting virtually everyone on the planet.

The media are supporting us with a steady flow of new information (Consumer Confidence Index, Economic Indicators Index, Financial Times Index and even more vacuous indices with meaningless titles), bad news (Toyota's sales plummet by 50%) and dark forebodings (Citigroup: -5%, AIG: -7% -do I hear more?) by the press, economists⁽¹⁾ and bankers who would like to distract from their failures, rendering it quite difficult for the common taxpayer to filter the assailing masses of information.

Thus, this weblog written by a Consultant for Risk Management is intended to analyize current events associated with the economic crisis and even (if necessary) to explain the mathematical backgrounds to understand what is going on. Objectivity is surely very important, but again, this is a weblog and not a dry scientific report, so expect an abundance of personal opinion.

Given the sheer amount of media coverage, anyone who has been following the news half-heartedly can be expected to extemporize a twenty minute presentation about the crisis. Still, there might be some people who get intimidated by and feel lost in the seemingly impenetrable fog of the financial glossary, including words like CDS, CDO, Mortage Backed Security, Key Interest Rate etc.

Rest assured that it does not matter whether you understand what is conveyed by all these shiny words. Sad to say, but this crisis is primarily a consequence of plain vanilla stupidity, maybe flanked by greed and ignorance.

So lets get started with a brief overview of the events that triggered the crisis.

The role of complex financial instruments

Among all the financial instruments that have been conceived since the times of Joseph and the Pharao (Genesis 41,41 et seq.), whose dream of seven years of famine to come made the egyptians to build up stocks (which is an option on rising grain prices in modern manner-of-speaking), there has been none more successful than risk trading.

Every medium-sized company that wants to hedge against changing exchange rates by buying options, every small home loan bank that wants to safeguard the risks of credit defaults knows about the blessings of complex financial instruments like options and derivatives.

One cannot even seriously object to making financial instruments themselfs the object of trade with the intention to generate profit, for that is exactly how the financial industry works. (By pointing this out, we want to make clear that complex financial instruments are not obscure devices for setting up sophisticated Ponzi-schemes and deceiving small investors, something that has been subliminally implied by some media coverage. As with any instrument conceived by mankind, these instruments can either be used reasonably to secure transactions or be misused to make a fast buck. Labelling complex financial instruments immoral in the face of the crisis will do no good - going down that road will lead us straight back to barter economy.) We might even allow risky speculative trades for what is life else but a sequence of decisions based upon assumptions despite the lack of complete knowledge of things to come?

Nevertheless, this should be done with a maximum of common sense and savvy which might very well be the reason why Mathematicians and Physicists have been continously replacing business administration majors in hedge funds and banks.

The background of the economic crisis

Let us scrutinize the backgrounds of the current crisis with regards to whether we should have been able to see it coming and take appropriate measures beforehand.

The crisis of the global economy is a mere consequence of a so called credit crunch which is in itself just an implication of a bursting real estate bubble. The growing and eventual bursting of this bubble can basically be traced back to one simple momentum: both banks and (private as well as institutionalized) borrowers based their decision-making on the assumption, that real estate prices would constantly rise. We will see in a minute how one thing leads to another. Let it be stressed out that at this point anyone with at least a bit of common sense and reasoning should have been alert to upcoming trouble. Apart from the fact that the very same assumptions on real estate prices led to the Lost Decade in Japan's economy (there was a time when the Emperor's palace in Tokyo was said to be as valuable as California which was obviously not bound to raise too many eyebrows back then), there is only one known entity in the universe that increases steadily with time -and that is time itself (we do not want to get into things like wormholes and Einstein-Rosen bridges here and now - all astrophysicists are welcome to bear with us, though). Dear reader, have you ever in your life encountered a dimension that increases monotonously over time -the decline of qualitiy of television programes aside? You didn't? Well...

Remark: We do not want to say that assuming increasing real estate prices will always be foolish and merely wishful thinking. Surely one can ask whether real estate prices aren't going to soar up in the long run because of climate change and rising sea levels. But one will have to put these considerations into context as the answer to this particular questions has to be "Yes, but firstly does this almost certainly not hold true for beach houses in Malibu (since they will vanish in the sea) and secondly will rising sea levels confront us with more severe problems than, let's say, securitized mortgages of home-owners in Idaho."

Back to the bubble. Mortgage banks were lending money to soon-to-be homeowners, assuming that the value of their houses will steadily increase. Indeed, if that assumption was correct, credits could be liquidated with virtually no effort or risk for both lender and borrower. Adding to this the Fed's decade-long policy of low interest rates and it's anything but a miracle that an increasing number of folks bought or built houses on credits with little (or even no) equitiy capital. Off took the real estate rocket. Some smart people even built multi-stage rockets: First you build a house with a credit by Bank A. Since the value of your property will (presumably) increase steadily, you apply -and be granted- a mortgage on that house by Bank B that is in turn invested into your next real estate project and so on.

The mortgage banks on the other hand wanted to get back the money as soon as possible. Therefore, mortgages and credits are being pooled and cut into tranches according to their risk of default⁽²⁾ and sold to investors as Collateralized Debt Obligations (short: CDOs). Thus, the bank will receive back most of the money instantaneously and pass on the risk to the buyer who, in turn will be compensated by higher interest rates on the underlying credits and mortgages.⁽³⁾

And now it's on the buyers of these CDOs to ignite multi-stage rockets. As this model was quite successful in gaining huge profits in a short period of time, the logical consequence was the iterated application, that is the buying of multiple CDOs, cutting them in tranches and rearranging them into -this is not a joke!- a CDO Squared.

The credit orgy ended just like all orgies eventually do -in a huge hangover. On the one hand, from 2007 on key-interest rates in the US began to rise, making it more and more difficult for the man on the street to pay back his credits (with his little or no equity capital). Granted, one defaulting credit does not trigger an economic crisis. Unfortunately, mortage banks had been given away money rampantly to far too many people in the subprime segment, assuming that real estate prices could one go up which would imply that in case of a credit default the house can be foreclosed with minimal losses or even a small gain. On the other hand, real estate prices stalled. Of course they would. The real estate market is just another ordinary market, governed by the law of supply and demand -how can it be possible to have a steadily increasing demand for houses no matter what the prices are? (Read this article on the bursting real estate bubble.)^[I]

It began to dawn on the first buyers of these CDOs (among them banks and professional investors) that their assets might in fact be worthless if a) too many borrowers default on their credits due to rising interest rates and b) underlying real estate prices -that have been estimated years ahead and relied on in buying decisions- can in fact not be realized.

So was there no way to see all this mishap coming? Of course there was. Investors and banks should simply have had a close look at the CDOs one is about to buy. Sure, the effort of doing that normally exceeds the capabilities of a normal bank, especially if it is engaged in large quantities of these quite complex papers. That's where the credit rating agencies come in. Questions like "Whats this paper's credit structure", "Can the borrowers afford to pay back their debts even if interest rates rise?", "What about the underlying assets? Is the assumed development in real estate pricing justified?" were passed on to external experts.⁽⁴⁾ Speaking of rating, we head on with...

...some brief mathematical considerations.

Apparently, the entire credit system is standing on feet of clay. Apart from basing business decisions on phoney assumptions of ever-rising real estate prices, the credit rating agencies rated these CDOs utilizing mathematical models that are based on the assumptions of an underlying normal distribution and uncorrelated credit recipients -if they did that at all.⁽⁵⁾

From the perspective of financial mathematics we note that it has been common knowledge since the times of Benoit Mandelbrot how counterproductive valueing financial instruments on the basis of a bell curve is.^[II] However, enhancing mathematical models used in risk management has been done only tentatively since the 1990s.

Furthermore, assuming borrowers are uncorrelated to one another was the critical point that made the credit system collaps. To show that this is not only intuitively evident, let us consider the following scenario. Presume there is a bank in Detroit that has been lending money to people who want to own a house. Obviously, the bank should know very well that many people in Detroit are working for one of the big car makers there. If there really was no correlation among debtors, one single credit default would not get the bank into serious trouble since there are many others who can compensate for the loss. The problem is: If one employee ceases to pay back his debts the bank has to ask as to why he stopped paying. Maybe the local car makers are facing difficult times and are laying off workers. In that case, the one credit default will be an indicator for more credit defaults to be expected. In fact, it could be a warning that default of a substantial part of the credits is immanent which would indeed get the bank into trouble.

One would certainly not be so foolhardy and grant loans on assumption of uncorrelated credit takers. The same principle should be applied to the financial system on a global scale. As Karl Marx pointed out, capital is as shy as a fawn and can easily dodge from bank to bank -especially in a globalized world. Thus, all banks are interconnected to one another and one bank's credit defaults can and will affect the next. The collaps of Lehman Brothers in September 2008 strikingly reassured us of this and we all saw the dire consequences for the global banking system.

First conclusions

Well, all the ladies and gentlemen working for banks, hedge funds, rating agencies or the IMF, the ECB and who ever is involved must have been aware of this to a certain extent. All these considerations and mathematical models are not rocket science (if they were, perhaps we would have been able to implement models with significant prognostic powers -and this blog would never have come into existence in the first place).

The author of this blog might be taunted with what he himself accuses the so-called financial experts: Neither did they see the obvious deficiencies of our financial system nor did they see trouble coming. Well, I have been working in the financial industry for no longer than a year and up to this point it was particle physics and differential geometry that demanded my attention.

So these are -in all necessary brevity- the reasons that got us into this mess. On all the bailout programs that have been set going recently we will have to come back in the next issue.

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