When I first began to work as a quant, laymen scoffed at the notion of using math to model markets. Now, twenty-five years later, the tide has turned and contemporary laymen regard math in markets with fear and awe. In my experience, however, not only laymen but even academic economists misunderstand how trading firms make practical use of financial models, and so I want to explain here how such models models work.
Preamble: The Great Financial Crisis
In 2008, when the crisis began, pundits blamed financial engineering for the market’s meltdown. Paul Volcker, whose grandson was a financial engineer, wrote the following harsh paragraph as part of an otherwise sensible speech he gave in 2009:
“A year or so ago, my daughter had seen … some disparaging remarks I had made about financial engineering. She sent it to my grandson, who normally didn’t communicate with me very much. He sent me an email, „Grandpa, don’t blame it on us! We were just following the orders we were getting from our bosses.“ The only thing I could do was send him back an email, „I will not accept the Nuremberg excuse.“
Since then opinions about modelers and the meltdown have become more Informed. Spain and Ireland developed housing market bubbles that, unlike those in the US, were not inflated by complex financial engineering. Paul Krugman has suggested that the root cause of the crisis lay in the West’s rapid withdrawal of capital from Asia after the currency crisis of 1998, leading Asian countries thereafter to concentrate on export, saving and hoarding. Who really knows the truth about complex events? Though few are blameless, the central banks’ zero interest rate policy (reheat at the first sign of cooling, hair of the dog that bit you) has played (and continues to play) a large role in the crisis. I believe financial models were responsible too, mainly by being used, sometimes dishonestly, to tempt investors to stretch for optimistically high yields in a low-interest rate environment.
And now, onto models.
The One Law of Financial Modeling
Let me begin with physics, the inspiration for most financial models.
In physics, the aim of modeling is divination: Newton’s laws tell you where a rocket will go; the standard model predicts the existence of a Higgs boson and how to discover it.
About economics, Prof Andrew Lo of MIT has written: “We economists wish to explain 99% of all observable phenomena by three simple laws, like the physicists do, but we have to settle, instead, for 99 laws that explain only 3% …”. That is a very good line, but fortunately it isn’t true.
In finance, though it may not seem obvious, the point of a model is not prediction, but rather, trying to figure out what unfamiliar or complex securities are worth. In that regards, there is only one reliable law, The Law of Analogy:
If you want to know the value of a strange financial security, use the known prices of another familiar collection of securities that are as similar to it as possible.
The Law of Analogy is not a law of nature. It’s merely a rough reflection on the practices of human beings.
Here’s a simple yet prototypical financial model I made up that has most of the characteristics of more sophisticated models.
Suppose I want to manufacture and sell cans of exotic tropical fruit salad containing litchees, loquats, pineapples and guavas. How do I estimate the price? To begin with, I find out the current price of the ingredients. Some may need to be imported, involving shipping and duty. Canning costs money too. I can build a model of how to combine the ingredients. In more technical terms, I can figure out how to replicate the exotic fruit salad from more familiar ingredients, and thus crudely estimate the fair price. Then I can make some rule-of-thumb corrections for marketing and markup, judging what the market will bear.
This model tells me the price of cans of salad from the price of fruit. And, conversely and more riskily, it can tell me the price of guavas from the price of salad, litchees, loquats and pineapple.