How mathematical modelling seduced Wall Street (NS)
October 21, 2011 19 Comments
New Scientist, 22 Oct. 2011.
See also page 10 A better way to price the future takes hold.
In the print version this is ‘Unruly humans vs the lust for order’, and it ends by criticising ‘models in the physical sciences’. Whitehead, co-author of Principia Mathematica, has shown in forensic detail, in his Process and Reality, the limitations of conventional models. Keynes had also covered much the same ground in his Treatise on Probability. More recently, Good joined the dots while Prigogine developed a mathematical model showing the severe limitations of the conventional approach. Yet the online version seems to criticise ‘mathematical modelling’.
I think the actual problem of Wall Street is its pragmatism. In the short-run we earn bonuses, in the long-run we are retired. So it is pragmatic to make money while the opportunity is there. The problem is in ‘valuing the future’ (pg 10). In markets where we can always move on, we don’t. Why should we, unless we have a stake in it? But Whitehead and Keynes also note a kind of ‘lust for order’, or at least an assumption that whatever order there happens to be will endure. But whether it was short-termism or a misguided attitude to order, mathematical modelling appear innocent.
How to understand the limits of financial models is for a more financially aware audience, but raises new issues.
“… there has been a frantic attempt to prevent loss, to restore the status quo ante at all cost”
The status quo ante was very risky: we should not be seeking to return to it. (Keynes showed why.)
“Quants were the theorists”
Oh dear. If the quants had been mathematicians they would have realised that economics was an empirical subject, and appreciated the uncertainties that Keynes highlighted.
“… traders were the experimentalists, and we collaborated to develop and explore our models.”
Oh dear. In an empirical subject, how can one separate ‘theory’ and ‘experiment’ like this? And what can one deduce from traders’ experiments?
“If you are someone who cannot distinguish between God’s creations and man’s idols, you may mistake models for deep laws. Many economists are such people.”
So blame such economists, not mathematicians (or physicists).
“We have seen corporations treated with the kindness owed to individuals, in the hope, perhaps, that their well-being would trickle down to individuals, and individuals treated with the kindness owed to objects.”
Perceptive. Derman’s prescription includes:
“Avoid axiomatization. Axioms and theorems are suitable for mathematics, but finance is concerned with the real world. Every financial axiom is pretty much wrong; the most-relevant questions in creating a model are, how wrong and in what way? “
If one doesn’t axiomatize one cannot do mathematics. One is left to apply formulae and methods with no real understanding. Keynes’ attempts to axiomatize probability and economics was critical in revealing the flaws in conventional thinking. The mistake is to turn axioms into dogma.
“The dangerous part of Black-Scholes is the further assumption that the sole risk of a stock is the risk of diffusion, which isn’t true. But the more realistically you can define risk, the better the model will become. “
How does one define risk, if not with axioms? I tend to go along with Keynes, in supposing that one cannot define risk, but can give an axiomatization that falls short of the precision definition.
“When someone shows you an economic or financial model that involves mathematics, you should understand that, despite the confident appearance of the equations, what lies beneath is a substrate of great simplification and — only sometimes — great imagination, perhaps even intuition.”
Having axioms shows exactly what ‘lies beneath’. Being able to produce an axiomatization is a good test of one’s understanding. Thus financial modellers typically define away risk: the mathematics makes this clear: what else would?
“Beware of idolatry. The greatest conceptual danger is idolatry: believing that someone can write down a theory that encapsulates human behavior and thereby free you of the obligation to think for yourself. A model may be entrancing, but no matter how hard you try, you will not be able to breathe life into it. To confuse a model with a theory is to believe that humans obey mathematical rules, and to invite future disaster.”
This gives us a clue to some of the confusion. Mathematical models and rules (such as Keynes’) can reflect imprecision and uncertainty. The problem is that the customers for economic models wanted precision and certainty, and were content with models that were mathematical in the sense that they were based on formulae using mathematical operators with no concern for their validity.
Derman reminds us of some earlier (2009) advice:
“• I will remember that I didn’t make the world and that it doesn’t satisfy my equations.
• Though I will use the models that I or others create to boldly estimate value, I will always look over my shoulder and never forget that the model is not the world.
• I will not be overly impressed by mathematics. I will never sacrifice reality for elegance without explaining to end users why I have done so.
• I will not give the people who use my models false comfort about their accuracy. I will make the assumptions and oversights explicit to all who use them.
• I understand that my work may have enormous effects on society and the economy, many beyond my apprehension.”
These seems reasonable. However most modellers have been paid by people who appear to have no concern for the longer term effects, and the apparent desire to return to the status quo ante suggests that they still don’t. It is no good giving advice to modellers (mathematical or otherwise) unless there are fundamental changes to financial institutions, changes that are incompatible with conventional capitalism, “a way of life in which all the standards of the past are supposedly subservient to the goal of efficient, timely production”.
“We need free markets, but we need them to be principled.”
Agreed. Can’t mathematics help?
The Physics of an economic crisis is along much the same lines.