Emanuel Derman says it is essential for the aspiring super-quant to overlay theoretical knowledge with pragmatic common sense.
For the past few months, I’ve been teaching financial engineering at Columbia University, where I’ve been struck again by the difference between what can be taught in school and what can be learned on the job. Most of my quant generation arrived on Wall Street ignorant of financial theory; we began to learn its principles under the duress of having to quickly do something practical for someone on a desk. Nowadays, there’s an entire industry devoted to quant training. But in many ways, quantisation still requires apprenticeship, and so, for a recent conference talk, I tried to think about some of the things you discover when you finally put your training into practice.
There are very few laws
Unhappily, there are few unalterable laws of quantitative finance. No Maxwell’s equations, no Navier-Stokes. The only universally applicable law is that of approximate similarity, which states that the best estimate of the unknown market value of a security is the price of another security that’s closely similar to it. You need to find (or invent) a model to establish the similarity between two securities by demonstrating the equivalence of their future payouts under a wide range of circumstances. Most of the mathematical complexity in finance involves finding a decent description of the range of future scenarios.
Although all you have is the limited power of this simple law, you must take your model of similarity seriously. Temporarily, like a fiction reader, you must suspend disbelief in your model. Then, when it’s complete, remind yourself that economics and valuation involve the behaviour of people, and think hard about what could go wrong.
Don’t get too carried away by mathematics
Mathematics is crucial to financial modelling, but it’s not central. It shouldn’t obscure the fact that finance and economics aim to be practical. If economics is about anything, it’s about the real world. For this reason, I often find myself questioning whether undergraduates should learn quantitative finance. Sensible modelling requires so much experience, taste and compromise that perhaps it should be postponed until students are more mature. Better as an undergraduate to learn solid concrete skills that are of unquestionable value rather a host of financial models that may be transient and incorrect.
The models you learned are the beginning, not the end
When I hired people to help value securities, I used to receive resumes from a headhunter who would market her candidates by rattling off mantras such as ÔKnows HJM, knows BK, knows VAR, knows extreme value theory. What more could you want?’ What I wanted was not someone with an encyclopaedic knowledge, nor even the capacity to think fast on their feet, though both are good qualities. I wanted someone who understood that the famous models they had learned are not sacrosanct, that models were not the end point but the starting point. I wanted people who weren’t afraid of tinkering with the models they inherited, who were willing to invent their own. In most cases, despite the vast sophistication of published models, people on trading desks use simpler home-grown versions that make approximations to run rapidly and are modified to take account of the real world idiosyncrasies that weren’t part of the standard models’ assumptions. Models aren’t holy. You have to overlay known models with heuristics. You have to mess with them every day.
Data has no voice
Data alone doesn’t tell you anything; you need to think and theorise. Fischer Black once wrote: ÒI find theory to be far more powerful than data when we’re trying to estimate expected return… When I read an empirical paper I usually seek out the theory section and ignore the tables.Ó Almost 150 years earlier, according to the physics Nobel prize-winner Steven Weinberg, Charles Darwin described a similar viewpoint in a letter to a friend: ÒAbout 30 years ago there was much talk that geologists ought only to observe and not theorise, and I well remember someone saying that at this rate a man might as well go into a gravel pit and count the pebbles and describe all the colours. How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!Ó So, be prepared to have a view, to make a theory. Data comes from the external world and must confirm or repudiate theories; theories come from you.
Abandon all hope…
Genuinely enthusiastic students sometimes ask what will happen when you find the ultimate model. On Wall Street, no-one knows what the correct model is, but they go ahead and price and trade anyhow. It’s a bit like the trial in Alice in Wonderland Ð ÔSentence first Ð verdict afterwards’. Black-Scholes is 30 years old and people are still debating its exactitude. Steve Figlewski recently wrote a somewhat tongue-in-cheek paper on whether a model with no principles at all was any worse than Black-Scholes. But practitioners don’t use Black-Scholes merely for its presumed exactitude; they use it because it provides a rational framework for thinking perturbatively. In a real job, you won’t have a 20-year time series to back-test your model. And even if you did, 20 years ago there was no volatility smile in equities, five years ago there was no smile in gold. So the model of 20 years ago and the model of today cannot be the same. A year ago I chaired a round-table session on smile models. In the past, I had often polled practitioners on which model they thought was the right one for the equity smile, but I could never get a consensus. So, at that round table, I simply asked both traders and quants their opinion of the best hedge ratio Ð greater than, equal to or less than the Black-Scholes value. There was still no agreement. Fifteen years after the appearance of the volatility smile, it’s humbling to remember that we still don’t have a canonical model. As a result, we all have to be existentialists in matters of financial valuation, making our own decisions about what’s meaningful. There is no model-God, and he won’t give you the data to calibrate his ultimate model.
Models are powerful sales tools
One imagines that models are all about arbitrage, and that the right one can find you bargains and make you money. Sometimes that’s true, but models are equally valuable in dealing with clients and customers. Models are a helpful way of looking at the world. If you can get everyone to look at the world your way, then you can sell them things based on your views. This isn’t dishonest. It’s a reflection of the fact that the locus of financial value is vague and confusing, and any order you can plausibly impose on prices is immensely helpful to investors. Unless you can replicate perfectly and hold to expiry, a large part of value is in the mind.
Software is honourable
Academics often overemphasise models, but much of the success of a model depends on software engineering. It’s not hard to create a conceptually more advanced model. But how do you use it? You need live market data, historical time series, databases, input screens and calibration.As a result, for every financial engineer who works on a model you may need three or four more software engineers to make it usable. In modern markets, there is a very fuzzy line between model and software.
In academic life, one likes to believe that content is all that counts. But even in universities, though truly stunning truths may become known no matter how uneloquently they are stated, form matters. Many finance professors like to recount with a strange mix of regret and pride how they need to publish in approved journals and in an approved style to get tenure. When models are used to establish the similarity of securities, to compare rather than predict, then persuasiveness is important. ÒIn the end,Ó according to Fischer Black, Òa theory is accepted not because it is confirmed by conventional empirical tests, but because researchers persuade one another that the theory is correct and relevant.Ó So, when you build a model, you have to explain it, in words. And until you can, you won’t completely understand it.
Between Feynman and Freud
What people most need to learn when they come to the practice of quantitative finance is how to overlay their theoretical knowledge with pragmatic common sense. Aristotle, in his Nichomachean Ethics, wrote that one should adopt a degree of precision appropriate to the subject. Though he was thinking of ethics, the same is true of quantitative finance. Until some unlikely future revolution, finding this middle ground is a practitioner’s major challenge. One must learn how to be neither too concrete nor too abstract, to choose some part of the spectrum between behavioural and quantitative, between science and psychology, between Feynman and Freud.
Risk Magazine – Trends
July 2003 / Volume16 / No7