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.
Using The Law
That’s essentially how financial models work. When quants want to value a new, complex and illiquid security, they build a model to (approximately) replicate it out of liquid securities whose current prices they know.
If you want to reliably estimate the future unknown value of a strange new security (fruit salad, say, or an equity option or a subprime mortgage CDO) you must find a portfolio of more common liquid securities (the ingredients) that, together, are similar to the salad, under all future circumstances, because you don’t know what the future may bring. That is where risk lies. If the salad and the fruit (i.e. the unfamiliar security and the common ones) are similar under all future circumstances, no matter how the future turns out, then their current values should be equal.
To implement the model you need two things: (1) a specification of what you mean by all future circumstances (for the prices and availability of fruit, say) and (2) a model or recipe for making the salad.
Most of the mathematical complexity in finance involves describing the range of future prices of each ingredient. Given your assumptions about the range of future prices, you can use your recipe or model to estimate the price of the salad.
What Can (And Will) Go Wrong
Fruit, stock and mortgage prices can do strange things. Trying to specify all future circumstances for goods is much more difficult than trying to specify the future path of planets, and always reminds me of the1967 movie Bedazzled, starring Peter Cook and Dudley Moore. In this retelling of the legend of Faust, Dudley Moore plays a short-order cook at a Wimpy’s chain restaurant in London who sells his soul to the devil in exchange for seven chances to specify the future circumstances under which he can achieve his romantic aims with the Wimpy’s waitress he lusts after. Each time Mephistopheles asks him to specify the romantic scenarios under which he believes he will succeed in seduction, he cannot be specific or imaginative enough. He says he wants to be alone with the waitress in a beautiful wealthy place where they are both madly in love with each other.
He gets what he requested—with a snap of the Mephistopheles’ fingers, he and his beloved are transported to a country estate where he is a guest of the owner, the husband of his beloved, whose high moral standards, despite her passion, will not allow her to break her marital vows. And so it continues. In the final episode, he wishes for them to be alone together, in love with each other and undisturbed. He gets his wish: Mephistopheles makes them both nuns in a Trappist convent where everyone has taken a vow of silence.
This difficulty of being sufficiently precise is the same difficulty we have when specifying future scenarios in financial models. The future prices of fruit will be affected by unforeseen early frosts, banana republic revolutions, shipping strikes and outbreaks of new fungi. Stocks will be affected by fear, greed and contagion. Like the devil, markets eventually outwit our imagined scenarios.
Finance vs. Physics
All financial models are relative, unavoidably based on comparisons and analogies. In times of crisis, when people panic, comparisons become odious and models fail. Financial models work well only in limited regimes, when the world doesn’t change too much from the way it currently is.
Physics theories, in contrast, are more absolute. Newton tells you pretty accurately how planets move, no matter whether you panic or not.
What’s so deceptive is that though the semantics of physics (divination of the future) is very different from that of finance (comparative replication of the unfamiliar by the familiar), their mathematical syntax is closely similar. As a result, foolish or ignorant people expect the accuracy of physics from the language of finance.
There’s nothing intrinsically evil or stupid about financial modeling. But to do it well, you must have the maturity and experience to understand its limitations. And you must always be ready to look over your shoulder when you hear footsteps.