21 March 2013

Quants: The Alchemists of Wall Street

Yesterday I found myself watching one of the most awesome Wall Street movies according to Business Insider: “Quants: The Alchemists Of Wall Street” (2010). While not a professional quant by myself but just someone from Eastern Europe who has “math as a second language” (as they, while exaggerating somewhat, refer to the Eastern Europeans in the film) and has only got a flavor of the art of financial modeling when developing a few “black boxes”*, I should admit that there were several points of recognition for me. Therefore I’d like to share my thoughts and reflections below.

The movie

If you like, you can watch the movie first by yourself, embedded below via YouTube (takes about 48 minutes). As put in the Business Insider: “It’s a rare look inside the minds of mathematical geniuses who have invented financial models that have both destroyed and made Wall Street.”


I think the film might be entitled as “Confessions of the Wall Street Wizards” as well.

Without joking, a few smart guys – including Paul Wilmott who is often being described as the smartest quant in the world, Mike Osinski, a former Wall Street computer programmer whose fancy software helped to bring the banks to near collapse, and Emanuel Derman, a former managing director and head of the Quantitative Strategies Group at Goldman Sachs & Co – appear to feel sorry indeed about the misuses of their skills.

But the current title is to the point as well:

“Alchemist” refers to someone whose goal is to transmute common metals into gold. That’s precisely what quants have been doing by transforming subprime credits into AAA-rated securities.

And, just for the case if you are not familiar with the terminology: a “Quant” means “Quantitative Analyst”, means people in the investment industry, risk management and derivatives pricing who are performing quantitative analysis. More broadly, the term covers any individual involved in almost any application of mathematics in finance.

Thoughts and reflections**

“[As a quant] You become so isolated from the real world.”

You become isolated because the first part of your (young) life you are spending in a classroom and trying to follow a lecture that lost its meaning for you during the first 20 minutes, and a great deal of the second part of your life you are spending sitting in a box office and pondering over some equations that still do not look quite.

You are being considered as a “geek”, and most of the time you are together with the other “geeks” like you, discussing certain modeling problems that do not make sense for the other people.

If you happen to be a person who loves numbers, loves complex Excel formulas and macros, loves finding relations in the data, it’s not that bad after all. Indeed, you may even have lots of fun with this seemingly boring stuff, no matter what those who don’t understand the beauty of math would think.

Furthermore, it’s even a much greater feeling to see your models implemented on a broad scale, perhaps making a difference in the way world of finance works. And the pay is good, too. So you personally at least create an impression of being much better off than the vast majority of the other people.

It’s the “golden cage”. It’s just that you become isolated from the rest of the world without realizing it by yourself: almost all the time your mind is occupied with solving some theoretical issues that may or not have a connection to reality. In other words, there is neither time nor room for much else in your mind.

This kind of focus and ability to live in your own imaginary (ideal) world can be extremely helpful in some professions (for the authors of science fiction etc) and sometimes, but are highly dangerous when it comes to money and financial modeling, and it’s possible to make more money by manipulating the models without no one really in control of the “model risk” before it’s too late.

Your focus on the very specific theoretical and mathematical problems may easily make you “a tool” for someone else acting on false motivations – without you being able to even foresee, let alone control the undesired and unintended consequences.

“… Human society doesn’t work like that.”

I like the concept of reflexivity when it comes to observing human society and applying the methods of physics in social sciences, which although not called that way, was also one of the key points made in the movie. Human society is not objectively given. We cannot observe and model it as independent observers; what we do and say has an impact to human affairs, sometimes even very significant.

There is no absolute truth to be modeled in the world of finance; the models themselves are creating new markets, and extensive use of them may change the existing ones to the point of unknown. Thus, the very conditions in which the models are being applied keep changing all the time, among others as a result of the use of these very same models. Models are based on the past data and this way behind the reality (in addition to the issue of too short time series). History may repeat itself in general terms, but every time it does it differently in details.

Black–Scholes options pricing model, no matter the unrealistic assumptions, created the market for options because it created an illusion of correct and precise pricing of these derivatives.

Complex statistical risk models which rely on the very theoretical assumptions about distributions and correlations, justified attaching triple A ratings to the securitization products; the later in turn were a good enough argument for pension funds and others to buy pieces of millions of sub-prime credits “pooled” into one MBS or CDO paper. That made the sub-prime lending roaring and we know the (temporary) end of this story…

The option to use internal models in Basel II regulatory framework has enabled banks to claim that their core capital adequacy ratios are 12% or 15% or more whereas they may actually have been leveraged 25-30 times or more. We are in the position to see how this is playing out…

“How do you model complex relationships between thousands of people – You don’t.”

Above I mentioned the word “correlations”. This term seemed to be confusing for the woman interviewing Mr. Paul Wilmott in the movie, and my impression was that even after the explanation she didn’t get it. There is a reason why: making assumptions on correlations is perhaps one of the trickiest things in financial models.

Very simply, correlation is a statistical measure which expresses how things relate to each other: how strong is the relationship between two variables (if any), and whether they move in the same or in the opposite directions. In the world of finance it may show how two securities move in relation to each other, or it may indicate the statistical relationship between the probabilities of two borrowers defaulting together, and a few other things depending on specific context and problem being solved.

So how do you measure the complex relationships between borrower A and borrower B, borrower B and borrower C, borrower A and borrower C, if there are thousands of borrowers that all somehow relate to each other and we have millions of combinations to look into? The answer is: you don’t. You make a simplification and assume, that every borrower relates to another borrower in exactly the same way. In other words: you assume one single correlation coefficient.

For one thing, it’s over simplification of reality. Secondly, no matter how precisely you may have measured that one single correlation coefficient based on the past data, it’s not stable but changing in time. For example, in times of credit contraction the correlation of defaults is much stronger than in boom years.

Ironically, the outputs of a model such as capital to be set aside for covering the unexpected losses of a portfolio of credit exposures, is very sensitive to that far less than objectively given correlation coefficient.

In other cases, you don’t assume anything at all about a specific correlation coefficient. Instead, you base your estimates on 10,000 or 100,000 or 1,000,000 randomly generated numbers. Of course, these random numbers are generated based on certain other not much more realistic assumptions about the distributions etc.

“Go back to the drawing board!”

That’s perhaps one of the most disturbing orders for a dedicated quant trying to provide right answers. Unfortunately it is being given far too frequently, much more often than there are correctable mistakes in a model. So if your carefully calculated results are not what the management expects them to be (no matter how true you believe they are), you are being sent back to the drawing board with an instruction to come up with more suitable (pre-defined) figures no matter your personal opinions. Furthermore: you are supposed to defend these new numbers if needed – no matter what nonsense you think they are. Because you are the expert, right?

A professional quant can almost always make some modifications into the models or argue for different assumptions that are needed for delivering the necessary results. Is it a fair thing to do? That’s another debate to have in some other time and in some other place, and perhaps between some other people...

“Ok, you are making lots of money, but are you doing something useful?”

…the smartest quant said his friends had started to ask him when the entire financial industry nearly collapsed and much of the blame went to the models.

As to justify themselves, the guys in the film replied:

“It’s not models that caused the financial collapse; it’s more the question of initiatives, over exploitation and misuse of the models.”

Is it a valid argument? Valid or invalid may be a matter of judgment. I personally agree – up to a point.

Just a side note for the sake of clarity: by “misuse” I mean manipulating with models, model assumptions and/or –inputs; by “over exploitation” I keep in mind attempts to model what cannot be modeled, and/or implementation of the models in the conditions for which they are not designed.

Models cannot cause any harm unless they are being implemented, and they cannot cause any collapse unless they are being misused on a massive scale. There are plenty of incentives behind a systemic misuse or over exploitation. Every participant in the game has its own personal incentive. Needless to say: the keyword is money.

Another quote from the movie:
“Making a lot of money is like taking a drug. You feel good, you had rapture […] When somebody hands you a million dollar check or five million dollar check, you want more, yes you want more… because I’m a genius.”
(I have to quote because I’m lacking the experience of making this much money and I don’t know the effects of drugs, except having heard that they make one feeling good, even if it’s nothing but a dangerous illusion that creates addiction.)

Every “little beast” aims for making more money, but smart guys know how to do it legally. Models can be a great “help” in here (and obviously are often being used in this purpose, once one has got know how to do it) – if you don’t know it, you probably are missing an important part about the inner workings of the world of finance.

For the starters, you can use models to create a false sense of confidence about the fair value of nonsense financial instruments such as a CDO-Squared which “pools” millions of pieces of sub-prime crap. This way, you can create a market for those hmm… investment products. New products, expanded market, more sales etc. translates to higher revenues. Wouldn’t you consider that?

By implementing advanced models and creating a false sense of confidence when it comes to controlling risks, you could also significantly reduce the regulatory capital requirement for running your bank. That option has been cut back somewhat with Basel III framework (financial regulators also need to justify their existence, right?), but it’s still there. Wouldn’t you do that as well?

Obviously you’d choose to improve the return on equity of your bank if your pay as a manager depended on it… That’s just the human nature. Nothing to blame about specifically… every “little beast” would do that if he or she only could…

Obviously too, a quant cannot make millions with such tricks alone, especially considering that most often he or she is a “geek” who is hardly able to sell anything at all by him/herself. A quant needs an overhead, and the institution that is employing that quant needs his or her particular skills.

So the quant goes back to the drawing board when he or she is being sent to, and manipulates with the models and assumptions as requested. And so the institution is paying well to that quant – just not that he or she would go to another employer with all his or her skills and knowledge.

In other words, we have a perfect match that is useful (profitable) for both sides but creating a potentially disastrous combination of money-driven incentives and skills.

This leads to the last quote that I’d like to point out:

“Financial models are here to stay. If you say otherwise, you probably don’t know human nature.”

It sounds like a threat but is very logical to conclude…

However, don’t flush it down all together.

Quants are doing a good and valuable job when it comes to collecting and understanding the past data. In certain extent, the relationships discovered in the past can be extrapolated to the future; just don’t manipulate the models and don’t use them in the conditions for which they are not specifically and explicitly designed.

Borrowers and risk exposures can be ranked from the safest to the riskiest and the decisions can be based on that ranking; yet the absolute risk levels cannot be adequately forecasted…

By definition, models are simplifications of reality and provide additional information in the decision-making process, but that’s just additional information.

Last but not least

A change for better can start only from plain and simple honesty, also in the world of complex financial models. All money that you possibly get – especially considering how easily money can be “printed” – may not be worth a life spent for nonsense or even worse, for creating (financial) weapons of mass destruction.

Today it's a depressing story and it's a sad story at a time. So I better hit the "publish" button and go jogging for now.

*A financial model is often referred to as “black box” – not because it literally is a box that is black or because no one knows anything about its internal workings, but partly because not many people actually bother with taking a closer look into the mathematical formulas that transform input data (such as interest rates, exchange rates etc.) into output (depending on model, the output may be the price of a financial instrument, a risk rating, the value of a business and so one), and partly because models tend to be documented using language and symbols that are not understandable unless one has PhD in math, is an educated “financial engineer” or the like.
** Quotes are based on my memory and thus not word by word precise. Interpretations are those of my own. 

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