How mathematical modelling seduced Wall Street (NS)

How mathematical modelling seduced Wall Street

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.

Institutional Investor

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.

See Also

Kauffman, the End of a Physics Worldview, takes a more theoretical approach to the same issue. Or Good, a mathematician who explores the limitations of theories and models.

Dave Marsay


About Dave Marsay
Mathematician with an interest in 'good' reasoning.

19 Responses to How mathematical modelling seduced Wall Street (NS)

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  2. B Alldred says:

    I read your Article in this weeks NewScientist ‘Unruly Humans vs the lust for order’ and it left me feeling exasperated with you. The luxury of the educational insight you received, which highlighted the perils of believing your Maths models, has probably come quite cheap to you. Personally I teach Maths to school children upto the age of 18 years old. Some of them use Maths to develop mechanical and statistical models as a part of the courses they study. I reinforce the need for caution and check that they understand that the map is not the territory, and get them to describe the limits of their models. This perseverance with accuracy and caution has served my students well. You and your colleagues (in the financial sector) lack of perseverance has cost me some of my salary this year and is about to cost me, my family and my professions long term security because of the changes in the terms and conditions to my pension. Hindsight is a wonderful thing, when you have been made wealthy from creating the illusion of knowledge.

    The title of your article in the NewScientist also seems to be a pragmamorphism. The human mind seems (from what I perceive) to group like and unlike. This is not ‘Lust’.

    • Dave Marsay says:

      Ben, You are not the first to accuse me and my colleagues of lack of perseverance. Over the years I have dealt with quite a few in finance and economics who have persevered in highlighting risks, including one colleague who was involved in assessing the risks arising from the then proposed ‘big bang’ and who failed to give the desired answer. This is not a route to job security. I have also worked with many who seemed to have some understanding not sufficiently convinced: until the day they ‘cashed out’, when they privately agreed with us.

      My own view is that lack of perserverance is not the problem, but a lack of understanding of the causes of the confusion of map and territory, which is much wider spread than just finance. The view that financial analysts who had taken the approach to risk that you and I might approve of would have been sacked is probably reasonable. Only politicians seemed to be well placed to do something about it, but in the UK those who seemed to understand it couldn’t see what they could do about it.

      I think that part of the problem is that the electorate expects too much, too simply. It sound like you are doing your bit to educate people on the nature of real complex problems, but is that because of or despite of current education policy? My own view is that there are many areas where simplistic approaches lead to avoidable, serious, unintended problems, and that we probably need to take a broad approach across them all, to set a context in which the underlying financial problems can be tackled.

      We may also need to re-think some of our deepest habits. For example one needs to understand the limits of ‘pragmatism’. Also, when you say “The human mind seems (from what I perceive) to group like and unlike. This is not ‘Lust’.” It does seem to me that this habit of classification is deeply implicated in many of the situations that lead to problems. But I am not clear that it is either necessary or possible to try to educate people on the limits of classification. But there does seem to be something more general resembling a ‘lust for order’ that is important. Mathematics is an antidote to such lusts, but mathematicians are often seen as in the grip of them. We could be part of the solution! Dave

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  5. My attempts early in my career as an analyst, ( I am 64 yrs old) to apply some form of what I considered ‘practical altruism’, to my approach to economics and business, often caused me to be passed over, in favor of those more aggressively willing to forego ‘caution’, in their drive for personal recognition and financial success, as opposed to a more practical balanced approach to risk analysis. My belief being at the time and still is, that it is impossible to divine any truly accurate logarithmic model for “human nature” or the human equation if you like?

    I still am of this belief and today I am somewhat more popular as a result of my writings over the years, in opposition to the “blitzkrieg” that became the trickle down, unfettered free market dynamic, fully supported by the belief that you and your associates quantum physics, could somehow divine an equation that could forecast and therefore eliminate, mankind’s frailties and basically reduce risk to a simple and fully quantifiable factor!

    This grew over time (30 years), to become the ‘facts of life’ in commerce and risk analysis and I must say, that while a ‘mea culpa’ from you and your associates may appear to you as a pointless exercise, I am in agreement with Mr Allred and those others that might prefer some additional public expression, that your complex approach to economic modeling “failed’ and in essence resulted in the current Global mess we are in!

    In order to perhaps also satiate the continuing ideological debate and furor that still rages, as to which system or economic format might serve mankind better for the future? It is people of your calibre and training that need to act and become more vociferous, to help defuse the ideological divide, between those that would continue this failed modeling, as it favors their minority position of power and wealth, and those of us that desire a return to a more practical definition of liquidity and sensible valuations in all sectors.
    Together with a dissembling of one of the most heinous results of your discipline, that of the ardent speculator, who made fortunes using your logarithmic calculus, and who are still today in control of this substantial weapon against the leveling of sovereign debt risk and the future of millions of peoples pensions and asset values! Mea culpa, mea culpa, mea maxima culpa should be your cry and it should be heard in every corner of the business and political community

    • Dave Marsay says:


      I am something of a fan of Keynes, and not at all supportive of ‘quants’. I have been engaged in crisis avoidance and ‘management’, where in the late 90s some of us took the view that the financial sector had the greatest potential for a man-made disaster. We found some economists who had been pushing the same buttons to little effect, other than (like you) a negative one on their careers. We have found much the same.

      My own view is that any reasonable analogy with quantum physics is helpful (e.g. complimentarity and the uncertainty principle). The problem has been that we have had daft analogies with physics. I have updated my blog to include a link to Derman, who says more about daft analogies wih physics and provides a mea culpa, which you might appreciate.

      On a technical point, you talk about ‘caution’ in the face of the otherwise unrecognized risk. Some people have mistaken what I have advocated for a ‘cautious’ approach. In fact what one needs to do is open one’s eyes, in which case one will see opportunities as well as risks. This isn’t about being cautious, but about doing things differently. For example, instead of churning out people who would make good quants, we should be educating people along the line that Derman suggests, but not throw out the mathematical baby with the quant bathwater.


  6. Thank you for your reply. Keynesian principles aside ( I too am a supporter of his sense of order in economic theory) The major enemy of altruistic principles and thought must be recognized as the accepted dark side of the human equation. That being generally, greed and power?

    I take it from Dermans musings on this issue, that he also in hindsight, would as a matter of a more rigid form, for new students of mathematics/physics, emphasize the more “cautionary” models of Keynes and thereby hopefully reduce the danger, of a future repetition of the folly of the most recent past? Which clearly paid unabated homage to that very dark side of the human equation?

    “We need free markets but we need them principled” ………. Derman…….?

    Now begins the debate as to what exactly are defined as those acceptable”principles”? Ideological idealism? With perhaps religious underpinnings, rather than mathematical modeling? In other words a continuance of the age old debate, even from the times of Plato and Aristotle? Just as flawed a debate in other words as has ever confronted mankind, but perhaps more familiar and therefore more predictable, than any other form of ‘new’ modeling?

    Thank you again for your reply and I hope that the intelligencia, teaching our next generations, are more willing to apply this cautionary reprimand from Derman, as to “not throwing the math baby out with the quant bath water ” but to also realize the social implications of ignoring the practical realities of history and the need for an humanely equitable association to any economic progress!

    • Dave Marsay says:


      We seem to have similar views. In a democracy the principles need to be understood and accepted, which may mean re-discovered and re-invigorated. For some, the argument may need to be utilitarian, but I think one could take a more cultured approach, if it would be appreciated.

      A small step would be to recognize that things could go wrong, to have academics educating us all on the potentialities, and to have a firm institution(s) to monitor, warn and inform policy and (as a last resort) intervention. But perhaps more urgent is the question of whether a recovery will be automatic once the finance system is fixed.


      • Kudos David,

        I am afraid, regardless of ‘positive’ actions at any level, it will perhaps be a generational period, before we as a civilization will again feel confident, as to the stability of any of our future economic modeling, within the capitalist model. Overly restrictive regulation may become the necessity in the short term. (Somewhat akin to the barn door closing after the escape of the horse?) The dysfunctional gap meantime, between our ideological decision making processes and the practical reality of sound economic modeling, is substantial and will remain so I fear, until the dreamed of ideal society is somehow achieved?

        That still remains the little “big” question, of philosophies and functions, and how to marry them somehow, into a harmonious normalcy, or perhaps a utopia?…….:-) This speaks to the educational conundrum as well? I think you nor I will live to see it achieved? Thank you for your kind attention. I thoroughly enjoyed the banter,


  7. David,

    Notes from another blog debate some time ago……. Speaking of utopian dreams?…..:-)

    • Dave Marsay says:

      Thanks. I certainly doubt the proposition that economies will automatically take off once we have secured banks and sovereign debt. I think that we need some sort of vision that is going to inspire people and address the sort of issues that you raise, at least giving some grounds for hope.

      In the UK, green technology looked like it might be it for a while. Now we seem to be wanting to go back to the status quo. How’s that going to work?

      • David, Since you finished with a question I feel duty bound to respond.

        The issues facing the combined leadership of the G8, or the older economies, are certainly sufficient to frighten any politician. Being an optimist, I believe they are in transit toward those clearly evident solutions, such as defining new standards for liquidity and asset valuations, capital reserves etc. The fearful, are those that recognize the variances in the social and cultural equations, in the various member nations. That response to change is much harder to forecast or control. But I do believe in Europe particularly the effort will be successful. Options are limited otherwise?
        I am confident also in my own analysis, that the Asian and the BRIC nations will strongly support the Euro and thus my optimism. I have a personal stake in this outcome as well.

        Any move however, toward a reestablishment of the old order, that being a U.S/anglo saxon led capitalist model, relying upon the trickle down concept of economic growth, will be met with serious resistance by the emerging economies. They view this and maybe correctly, as too wild for a healthy and steady advancement of their own short and long term growth plans. The Chinese in particular will vehemently resist any return to that order. Knowing that the Chinese economy, just in terms of commodities demand, will grow to be at least 7 times the size of the U.S economy within 3-5 years should be sufficient evidence to humble the American political establishment, into the realization that they must seek a new economic format to adjust to this reality. The lies being told to the American people as to economic reality, for me are a scandal!

        How will this all play out on the US domestic scene? Frighteningly it conjours up for me a continuance of this ideological nightmare of partisan rancor and lack of direction, for any positive economic change! With this will come a debt and de leveraging environment, which will ultimately humble the people of the nation, weaken the currency and I am afraid nurture increasing civil commotion.

        I have opined before that I see jingoism as the biggest danger facing the US economy, with the potential for a marginalizing of the U.S. if this continues. The reversal of belief in geographical free trade, is a serious mistake and is driven by severe ultra nationalistic forces, that care not for practical economics?
        I am, as a Canadian with Irish roots and American cousins, clearly interested in these current U.S. challenges. I hope that this early drive by U.S. politicians to turn their back economically on their neighbors, in some crazed jingoistic, John Wayne last stand posture of defiance, will be short lived and we can join in a new economic American market bonding, north to South. All this being said I am reminded that;

        “an optimist believes we live in the best of all possible worlds, and the pessimist is afraid the optimist may be right”

        regards James

  8. I forgot Dave……….. Mr Derman seems to be grappling with the rediscovery of that age old truth expressed even by Einstein………:-)

    ” As far as the laws of mathematics refer to reality, they are NOT certain, and as far as they ARE certain, they do not refer to reality.”

    I have always remembered this as my favorite example of professional humility…..:-)

    • Dave Marsay says:

      James, It certainly is unfortunate that financiers and economists didn’t appreciate Einstein’s advice from mathematics 101. My expectation is that China will prevent Europe and America collapsing, provided that it can. The alternative would be dire for them. If nothing else, it is useful for their elites to have us to point to when the populace is discontent. (A bit like we used to point at the Soviet Union.)

      America always seems in thrall to some strange beliefs, and hence very fragile. But like many peoples, they often seem to do better in a crisis than we might think. Let’s hope so.

  9. Dave, I echo your sentiments of hope………

    What seemingly always deters the american people from immediate response to their challenges, is the ideological efforts to emphasize wedge issues, as a distraction from the realities. In this current example we see the extreme right side of the equation guilty of this abuse of practical reality or more simply the hiding of truth.

    Thanks again for the banter, James

  10. Scott Ufford says:

    Dave, your concept of mathematical modelling embraces my perhaps simplistic view that, at every step of the way of the last 30-40 years, certain ne’er-do-wells of corporate America (including elements of the federal govt) have “massaged” the costs (legally allocable fines & penalties under a sliding scale scheme that calculates the miniscule percentage of actual damages to be “repaid” to the public–oops, usually paid directly back into the govt’s coffers), as if a standard operating procedure (SOP) to attain the benefits known as outrageous levels of gains from those gray zone activities tacitly acknowledged & encouraged as “acceptable capitalism”.

    Their local economic models expanded to mirror all behaviors supportive of USA’s world military & economic empire models.

    But, once they grasped the glorious prospects of their attempts at gaming the entire system, their giddy corruptive delight expanded into corporate & militaristic behavior so far beyond the boundaries of any sane mathematical modelling that they completely ignored, or shed all rational comprehension of, how they might be draining th blood of and destroying the very living organism known as “economy” or “society” in which they did their parasitic plundering…

    Thank you for your incisive thoughts, Dave, & for sharing your book.

    • Dave Marsay says:


      Thanks for your comment. It is a vital question as to which of our many problems are due to malice, and which to incompetance. I have worked with people who have succesfully covered their brilliant gamesmanship with a veil of incompetance and buffoonery. But I am fairly convinced that the relevant part of the British financial and economic establishments were simply the victim of group-think, wishfull thinking, poor education, hubris, too much alcohol or similar.

      Happy New Year, Dave.

  11. Dave: I prefer the term “Thacherism” to explain the collapse into group think dynamics in Britain. A certain amount of Scotch and soda no doubt played a significant role as well. In the U.S. it was of course, more(Ayn) Randian or Reaganism with copious amounts of martinis.

    I do agree however that it was probably more due to incompetence than intentional malice. The game looked easy when only a few were playing, but as the lemming principle kicked in, it soon went out of control. “The rush for the open gate” Best wishes for the new year and I hope we can get the “Gini” back into the bottle….:-)

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