The Financial Crisis - It's the quants wot donnit!

  Pricing of options used to be a guessing game - say educated guessing plus some fingerspitzengefühl. Then along came two economists named Fischer Black and Myron Scholes in 1973 with an economic model employing the insight that the option is implicitly priced if the stock is traded.

Robert Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model and coined the term Black–Scholes options pricing model. 

Merton and Scholes received the 1997 Nobel Prize in Economics for their work. (Black died in 1995 and was thus ineligible for the prize).

Thanks to Black-Scholes, derivatives trading got a huge boost and quants poured into the industry. (A quantitative analyst is a person who works in finance using numerical or quantitative techniques. In the investment industry, people who perform quantitative analysis are frequently called quants.) Although the original quants were concerned with risk management and derivatives pricing, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance.

Well the quants are now being grilled (some would want to draw and quarter them) along with their models. In the USA a congressional panel is looking into the role that pricing and default-probability models have played in the financial crash. One publication - Wired - has even described one particular and very popular default-probability model as "the formula that killed Wall Street". Someone else has published a book called: The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It.  The Economist recently published an article with the telling header: Number-crunchers crunched.  A recent documentary on Dutch television (mostly in English - worth looking up) also came down on the model-makers. (The documentary - Quants: De alchemisten van Wall Street - can be viewed here: http://player.omroep.nl/?aflID=10567577 ).

There are all kinds of financial models that function as they are expected to - such as those for interest rates and foreign exchange. But, the models used in debt markets failed abjectly to take account low-probability but high impact events - such as the sudden fall in house prices in the United States. And when they were used in assessing the risks in the packaging of mortgages into collateralized debt obligations (CDOs) the models really went off on a tangent. CDOs are so complex that they require special designed models. But, each CDO has a specific mix of assets and the model assumptions about future defaults and mortgage rates did not fit that mix. Nor did they factor in the tendency of assets to move together in a crisis.

The CDO market, which stood at $275 billion in 2000 grew to $4.7 trillion by 2006. Complementary to the CDO market was that of credit default swaps (CDS) - a market which grew in the same period from $920 billion to $62 trillion.  CDS prices were used to calculate the correlations within CDOs - like Black and Scholes did above with option pricing. CDSs had been in existence less than a decade - a period that saw only rising house prices. There was no historical data of falling prices to balance the correlation assumptions used. And once the mortgage boom ended and home values started plummeting, correlations soared. CDOs were invariably sold on the premise that correlation was a constant rather than a variable. Those that securitized mortgages knew that the models were highly sensitive to house price appreciation. A house price decline on a national US scale would blow up the models.

Armed with a simple formula Wall Street quants had created a huge number of brand-new triple-A securities. Rating agencies (like Moody's or Standard and Poor's, for example) happily relied on the models and were eager to accommodate the issuers who paid them - even though the expected rate of return on triple-A rated tranches was oddly high for such apparently safe securities. Every player was pinning his hopes on house prices continuing to rise. "A lifetime of wealth was only one model away," according to one US regulator later fulminating in the financial ruins. The vice of greed drove this whole episode.

Despite warnings from several experts (including many quants) that the models were notoriously unstable and that they were not suitable for use in risk management or valuation, banks dismissed them because the managers empowered to apply the brakes didn't understand the arguments being made. They were too dumb - not numerate enough. And these were the people making the big asset-allocation decisions. Besides, the gravy train was moving too fast - they were making too much money to stop.

Model-makers - quants - may be down, but they're not out. The way forward is not to reject quantitative finance but to be honest about its limitations, according Emanuel Derman - one of the two best known names in quantitative financial analysis. Derman, a former quant at Goldman Sachs and now a professor at Columbia University and Paul Wilmott, a mathematician turned financial educator, have drawn up a financial Modeler's Hippocratic Oath (modeled on the Communist Manifesto - yes, really! See: http://www.wilmott.com/blogs/paul/index.cfm/2009/1/8/Financial-Modelers-Manifesto ). The oath reads:

  • I will remember that I didn't make the world and that it doesn't satisfy my equations.
  • Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.
  • I will never sacrifice reality for elegance without explaining why I have done so. Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.
  • I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.

The problem is often not complex finance but the people who practice it - according to Wilmott. Because of their love of puzzles, quants lean towards technically brilliant rather than sensible solutions and tend to over-engineer. Wilmott: "You may need a plumber but you get a professor of fluid dynamics."