The Wired cover article this month is worth a read but brings me on a big rant. The article covers how people trained in theoretical physicists migrated into Wall Street over the last 30 years and created the math that lead the financial bubble bursting.

I was trained as a condensed matter theoretical physicist at the University of Illinois at Urbana-Champaign. My advisor created the company that built software similar to the ones that powered this disaster when I was there (mid 90’s). Half of my advisor’s students ended up “quants” on Wall Street.

You’re. In. My. House.

And I have only one anecdote to relate.

The bucket of water

When I first went to Illinois, the only thing I knew is I didn’t want to be in high energy or astrophysics. I didn’t know what “condensed matter” physics was because at Caltech this was called “Applied” Physics. In fact, a famous professor there coined the term “squalid state” physics when referring to this field, which is also known as solid state physics.

So I decided to audit the thermodynamics/statistical physics elective taught by a theoretical condensed matter physicist. Thermodynamics is the arithmetic of condensed matter physics and because Illinois, at the time, was ranked the #1 graduate school in the country in this field, it was a very popular course for first year students.

(This professor was, on the side, developing ultra-fast ways of computing the Black-Sholes equation which guides financial derivative pricing. With the advent of that equation, these derivatives became amenable to the techniques physicists have used to study non-equilibrium physics. Derivatives are not the calculus derivatives you shied away from in high school or college; they’re called derivative because they have no intrinsic value but are contracts that “derive” their value from something that does—for instance, an option is a simple derivative (contract) that allows you to buy a stock (real intrinsic ownership) in a company at a future date at a future price. The math to study this begins with a non-equlibrium reaction-diffusion equation. This why these firms had to hire “quants” in the first place—the average business schooler finds himself about five years of straight-A college and graduate level applied mathematics lacking.)

Because I’m weird, I decided to do the homework problems as a way to make sure I was understanding what was going on in class. The third of the four problems on the first homework set was legendary for its difficulty. It was like so:

3. A bucket of water is standing in a shop window on a bright summer’s day. You go intot he shop and find that the bucket is warmer on the side facing into the shop.. How is this possible? Why am I asking this question?

Some students spent the entire week trying to answer it, including some generating some quite involved mathematical models explaining how this can happen.

Which was sort of the point.

The answer

I wrote my answer in the margin of the problem when I received it.

“It’s that way because it is. Just like hot water freezing faster than cold, thermodynamics doesn’t explain this.”

When I showed it to my classmates, most of them thought I was naïve.

Thermodynamics is the part of condensed matter physics that studies systems at equilibrium. You take a two things, push them together and the eventually the temperatures equal out as they exchange heat. It tells you what will happen when it “eventually” happens.

It never said anything about how it gets there.

The mistake in the “hot water freezing faster” paradox is believing that “temperature” is a relevant concept here when the system isn’t even close to “eventually.” A misconception is to believe hot water has to get “cold” before it freezes when you put the water outside in subzero temperature. Thermodynamic concepts like temperature only apply when the system is in equilibrium. When it’s actually doing shit, the model breaks down and there is no usable math any physicist in the world can use until the system gets close to equilibrium. Water doesn’t need to get cold first, it can just start crystalizing as fast as you can pull energy away from it. And if the water molecules are moving around fast because they started warmer, they can move into position faster.

Similarly, when you start discussing which side of the pail is warmer, you are clearly talking about something not at equilibrium yet. So trying to come up with the wherefore using mathematics which only covers a system at rest is ignorance itself.

The professor wanted you to tie yourself in knots for hours or days so you could remember that salient point. The reason the problem is assigned is to show the graduate student the limits of physics. Not being aware of it led the scientific community to award the only Nobel Prize in the sciences based on a lie.

That if you aren’t aware of those limits you might end up so convoluted and abstracted that a six-year-old child would have a better explanation than a student who has studied it for the last four years. That you could hail as a genius someone who is an obvious fraud.

Perhaps I knew the answer so quickly because I’m closer to a six-year-old child than a physics graduate student? In any case, it was because of incidents like this, that I ended up becoming that professor’s research assistant.

How this applies to the Wall Street Disaster

The equations may be very complicated, but at its heart it’s simple. We’re talking about people dealing with money. People. With. Money. People with money are even less predictable than a quantum mechanical many-bodied system of dihydrogen monoxide could ever be. You should never forget what you’re dealing with and the limits of the models you make to describe it.

At the end of the day, a lot of smart people forgot their first lesson in graduate school: that sometimes all that learning can make them have less sense than a six-year-old.

Which makes them a lot of dumb people.

7 thoughts on “Quants

  1. It’s weird. I still don’t know who thought they could sell subprime and not expect losses.

    Having worked at a mortgage company and having been on the team which deal with investor reporting, we had the numbers right there. During the 2001 recession, default rates on our subprime product approached 20%.

    But what changed from 2001 to 2007?

    Well in 2001 that product was 5% of the business. By 2007 it was over 50%. So a 20% loss on 5% of business was containable.

    Someone thought the rules had changed, but I don’t know why they thought that.

  2. @Steve SheldonBlind use in equations, I suppose. Derivative contracts (futures) on the mortgages you mentioned are not sold as-is but are instead bundled into pools that are then sliced into tranches. In Black-Scholes the big factor is the computation of the beta (risk) which. By creatively slicing these contracts into pieces that fool the models into thinking that they’re inversely correlated (instead of tightly correlated) and then backing “best” part of these tranches with insurance contracts, the equations end up ascribing a low risk rating (as low a a U.S. Treasury Bill!) to this crap.

    In other words, by fiddling with the software long enough, someone could make it ascribe a low beta to a pool composed entirely of high beta contracts. The models had many breakdowns.

    It’s bullshit. You’re fooling the equations behind the software, but not common sense. Eventually there would be an accounting with all this imaginary wealth these hedge funds were creating.

  3. Added a correction. Apparently Numerix didn’t sell to CDOs and CDSs. Another thing to note is to read the Wired article closely—as much as you can blame the quants for creating bad models, you can blame the financial people far more for abusing the model.

    It seems a lot of people were using these equations blindly.

  4. I was very glad to see the problem of bucket posted here. I had gone through that problem in the past but couldn't come up with a convincing answer. I had also thought that very likely the system is not in thermodynamic equilibrium. But the question still remains as to why (assuming that the bucket is kept in the window for a "long" enough time with the same temperatures around) this phenomenon may be observed. Maybe thermodynamics, as we understand it, does not answer this question. All the same, there must be some explanation for it? It's certainly no miracle. I would be glad if you can shed some light on it.

    1. The system is definitely not in equilibrium so nearly any answer should work…

      For instance, “Someone came in earlier and turned around the bucket.” is perfectly valid. Almost anything could have happened because the math we (thermodynamics at least) only explains what happens in equilibrium.

      There is math that describes things in dynamic states… even dynamic equilibrium (i.e. chaos theory). But there are a lot of issues of using math like that for this problem… at that point the problem is ill-posed.

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