ECON484-Topic #2: Quants and Math in Business

Mathematical analysis has become more commonplace in both business and finance. The “quants” on Wall Street and at hedge funds have transformed investment worldwide. In the first video below, interviews with different quants both attack and defend the reliance on mathematical models. Quantitative finance is in general using complex mathematics to model economic and financial relationships. In the second video, James Mirrlees talks about the role of developing models in economics and the use of it as a tool. There is an inherent danger in relying on mathematics because of the assumptions that we make in our models, and the inability of many of these people to realize that their assumptions have real repercussions if they do not hold true. Wilmott and Derman (featured in the first video) have released a “Modelers Hippocratic Oath” which is meant to keep quants from causing harm.

Quants: The Alchemists of Wall Street

James Mirrlees – Mathematics and Real Economics

Questions to think about

  • Do you believe that economics and quantitative finance need to think more deeply about this “Hippocratic Oath” for economics and finance? Or do you believe that explanations of economic/financial models are understood to be approximations to reality?
  • The role of uncertainty in general is a fundamental problem in the “science” of finance and economics which cannot (as of today) be tamed. I want you to think about the role of assumptions in economics and how mathematics formalizes those assumptions. Do you believe that there needs to be a better way of transmitting these theories to reality, or do you believe that we should keep mathematical modeling to a minimum in economics and finance?
  • Paul Krugman argues against necessarily relying on “elegant” mathematics and focusing more on “dirtier” math in thinking about the real world. Do you think that there is overreliance on the elegant math in many cases? Or do you see solid and elegant mathematics as a necessary foundation for economic research.

11 thoughts on “ECON484-Topic #2: Quants and Math in Business”

  1. I don’t think anybody would deny the peculiar air of importance that seems to surround mathematics. This may be due to the fact that mathematics is inherently difficult. And because of its difficulty, only a small number understand it. For those that do understand (or assume they know) the esoteric language, you can see how this can create to a certain extent, an exclusive and consequently, elite club. And like any exclusive club, its members tend to think too highly of their membership. You can sense this mindset on campus when quantitative-heavy majors secretly scoff when hearing the workload complaints of those whose majors require less math.

    In this sense, it’s no surprise to see people give the benefit of the doubt to complicated models. To a particular degree, Greek letters and mathematical language seem more grounded, and therefore elegant and correct, even if the formula goes above our heads. Furthermore, it is also very convenient to hide behind complex formulas and blame the faults of reality on something metaphysical.

    On face, the “Hippocratic Oath” for economics and finance seems to be an unnecessary accompaniment. The modelers themselves must rigorously derive, prove, and ensure that their models are reasonable and dependable to begin with. That should go without saying because otherwise, they wouldn’t be employed. I am of the opinion that the fallibility of any model is thusly addressed in this fashion, even if it is on a subconscious level and not explicitly stated. Although Quants are asked to depict reality in a succinct formula, I don’t think they really lose sight of their inherent human limitations, especially after spending 12 straight hours a day at the public library. Almost all formulas in general must operate on assumptions. At the end of the day, although their models are flawed, it’s the best they’ve got. Why not continue using it if it’s been working? But it is also easy to see how models would sacrifice the drudge for prettier, more convenient notation.

    As mentioned, there is a peculiar elegance to mathematical models. Paul Wilmott* points out that representing numerous concepts and ideas into a compact and sophisticated form is beautiful, almost Shakespearian. We shouldn’t abandon the rigor that mathematical models inject into the study. Mathematics ties directly into financial and economic principles and provides a substantive foundation for which the theory depends upon. It is the theoretical framework that economists and financial whizzes must operate under before they hammer out the kinks to apply to the real world. As absurd as the idea is presented, nobody can create the Black Box* without first approaching it from a theoretical scale. In short, Ivory Tower economics needs to exist in order to provide a proper and challenging framework for economics to build upon. Otherwise, there wouldn’t be too much separating economics and sociology. But I don’t believe that to be the problem.

    The real problem may lie in how these formulas are perceived by investors who are seduced by the complex mathematics. If a particular method is seen to have proven itself, why wouldn’t firms market its methods as a tool to exploit the market? Over time (albeit, it’s never really a “long time” per se), when a model continues to prove itself, its legitimacy essentially compounds at the rate at which money comes through the door. And you can imagine how much money was coming through, given low interests rates in the past decade and the magnitude of the crash. Paul Krugman describes the scenario of associating “beaut[iful models], clad in impressive-looking mathematics, for truth”[1]. If investors mistake this legitimacy with truth, then the Hippocratic Oath would have a more reasonable basis. Almost like a health warning on cigarette packages, the oath would serve more as a message to investors: long run ingestion of the model will not only be bad for your lungs.

    *http://www.youtube.com/watch?v=ed2FWNWwE3I
    [1] http://www.nytimes.com/2009/09/06/magazine/06Economic-t.html?_r=1&em=&pagewanted=all

  2. The most important thing I took from these two videos is that all of the financial models used in the world are tools and nothing more [2] [3]. In other words you need more than tools to build a house; the same goes for the construction of the financial market. If these “tools” are solely relied on then the market can likely crash and falter because it needs some support in addition to these tools. The Hippocratic Oath is the support to these tools; it is the common sense and warning label that goes with the financial and economic tools [1]. Together the two are fool proof, it is when these warnings are forgotten about and ignored that we can run into trouble in the market. Financial and economic models are only approximations of reality and should only be used as that. I think this is what happened in the 2008 crash of the market; models for collateralized debt obligations were being used blindly without knowing how they actually worked and what would cause them to not work. I agree with Emanuel Derman that it was not the models’ fault for this crash, but instead it was the improper use of them [2]. Until financial and economic models go hand-in-hand with the Hippocratic Oath they will never be flawless. These models are guidelines and should be treated that way; they should never have more emphasis on their results than their assumptions and conditions. This is a balance that needs to be kept in order and the following of the Hippocratic Oath does a good job of this.
    One reason why these models make so many assumptions and have so many conditions to be met for them to be accurate is because it is nearly impossible to model human nature. Although assumptions make sense statistically, there are many people who are irrational and may not follow the assumptions set forth by particular models. However, to model certain things, these assumptions must be made so it becomes a double edged blade. Either we have no model or we have a model that assumes things that may or may not be true; this relates back to the idea that models are approximations to reality. I think that theories should be better transmitted to reality, but I do not see how this is possible so long as people are not one hundred percent predictable. One important aspect of any financial model is that risk is balanced. If the party on one side of a derivative is experiencing more risk than the other side, the riskier side should be rewarded more as said in the first video by Paul Wilmott [2]. However, when it comes to CDO’s, risk is difficult, but very important to assess [5]. I think that this is one thing that led to the 2008 crash as well, because it is never a good thing when people are taking on more risk than what they are led on to believe. Everything in the financial market revolves around information, when this information is incorrect it can lead to catastrophe.
    The “elegant” math that gives us complicated financial and economic models is great. It gives us the ability to price derivatives and understand the market better which provides everyone with more information creating more balance. This is all good, but at the same time not everyone understands the elegant math that drives all of this. I do agree that there is an overreliance on elegant math because if you do not understand it and you use it blindly then you are breaking the Hippocratic Oath. I think that elegant math is completely necessary and helpful, but it has to be understood by those who use it. Paul Krugman agrees that we need elegant math, but he also made a point to say that he has also read and understood insightful economic papers that did not have any math in them at all [4]. I think he was trying to say that although the elegant math is a nice tool, we need to use other resources as well to understand economics and finance; as long as we have the ability to do both we will be better off than just knowing one or the other.

    [1] http://www.wilmott.com/messageview.cfm?catid=3&threadid=67869
    [2] http://www.youtube.com/watch?v=ed2FWNWwE3I
    [3] http://www.youtube.com/watch?v=-39znKX8kC8
    [4] http://krugman.blogs.nytimes.com/2009/09/11/mathematics-and-economics/
    [5] http://www.curacao-law.com/wp-content/uploads/2008/10/federal-reserve-cdo-analysis-2004.pdf

  3. This “Hippocratic Oath” should become a primary characteristic of economic and finance. A key argument of the Quants video is that the models are not the focus of the blame should be, but the real blame lies within those who use the models. The number one aspect of models to remember is that they are just that, models. A model does not necessarily coincide with the real world. The Quants video suggests that the reason many of these models do not work well is because they are abused by estimators and businesses who want to achieve a specific goal. A linear model, although usually extremely unrealistic, can be helpful as long as the correct numbers are used. “The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It” by Scott Patterson points out how the same models of today can be used effectively without structural changes to them (1). He emphasizes that information gathering is a more important aspect of modeling than the model itself. Mathematical models are relatively easy to develop because of all information sharing of today and utilization of assumptions. A reasonable model, even if it contains some significant assumptions, can help develop a guideline for the financial future, if the information and numbers plugged into the equations are as accurate as possible. For example, a quant fund group known as Renaissance Technologies put together a hedge fund called Medallion back before the financial crash in 2007-2008. This hedge fund has been considered the most successful one in history, as in survived the crash essentially “unscathed.” The reason this hedge was successful was because the group of analyst that put it together was comprised of “cryptographers and people trained in speech recognition,” which basically means people trained in the art of information. This quant fund group succeeded not because of an elaborate, realistic model, but because of the ability to read into the details of the economy, extract the hidden facts, and transform them into meaningful quantitative figures for the sake of the model. So, just as the other sources suggest, the models are not to blame, but rather the quants using them. As my source illustrates, models can be extremely reliable as long as the information is correct. The many economists and quantitative finance modelers who spend their time data mining and taking short cuts are what give models a bad name. They all use the same models, so why are there a small few that find accurate results? A true understanding of the information that is collected!

    (1) http://seekingalpha.com/article/188342-model-misbehavior-the-quants-how-a-new-breed-of-math-whizzes-conquered-wall-street-and-nearly-destroyed-it-by-scott-patterson

  4. Many of the attacks laundry listed in the videos and articles above towards the use of quantitative finance in the above listed videos and articles are oddly reminiscent of Dr. Naseem Taleb’s general argument that growing complexity in the financial environment and increased reliance on assumptions in financial and economic modeling, could and will become increasingly more dangerous with the increases of funds depending on their stability. Although I feel that this view of skepticism towards quantitative approaches does obviously carry much support (and for good reason), I feel that the responsibilities stipulated in the “Modeler’s Hippocratic Oath” are essential to producing a more responsible, less risky financial market where meltdowns trickling from CEO offices to mortgage applicants would become much less likely. If modelers took into account every possible agent that could flip their models upside-down, such as whether or not the derivatives they are selling can be covered by all the underlying fixed payments all the way down to the base payments, and made the vast array of scenarios evident to the customer, both optimistic and pessimistic, I do not believe that bubbles caused by such intertwined dependencies would be as likely. I personally have no issue with mathematical/financial modeling as long as assumptions are made fully transparent to the prospective consumer. There is a little bit of responsible financial modeling I read about in the WSJ however, calling themselves ESG funds, or funds that invest combining quantitative methods as well as “Environmental, Social, and Governance practices.” Although these types of funds are few in number and yield less profit than other types, I believe that this is the more responsible direction to head towards.
    [1] http://online.wsj.com/article/SB10001424052748703778304575590573739696114.html?KEYWORDS=esg

  5. I think we can all agree that backlash against mathematics itself is unwarranted, it is logically equivalent to blaming the gun or the bullet instead of the person operating it. And it is quite obvious that every good modeler or Quant realizes that man made models to predict social events will never be perfected. However, while the ethical aspects of the oath may stick for the short-run, just as the Quant with the British accent pointed out, eventually (perhaps within months) everything will go back to business as usual, which is also fine by me. I personally don’t have any objections to over-leveraged hedge funds doing excessive speculation as long as the government isn’t there to provide incentive for future exacerbation. I think the point that Alex brought up about the hedge fund that made it through untouched used speech analysis to extract hidden information was interesting in the sense that we will always be making continuous improvements that makes our models better than the previous generation, it is the natural evolution of human development. Friedman famously noted that “inflation is everywhere and always a monetary phenomenon.” I would add that hubris is also everywhere and always a social phenomenon, we simply cannot escape its seduction with arbitrary oaths.
    On the topic of modeling uncertainty and making assumptions, I think that surely for every assumption we make we are reducing aggregate uncertainty so while theory may dictate a certain sign on a certain expression, it is doing so at the expense of heavy black swan exposure. So at the very least we should keep that in mind while we model and integrate mathematics in economics.
    Finally on the Krugman topic, I think his point is well taken that obviously the model with the closest representation of the world should not be overlooked just because the math is “dirty”, while aesthetically pleasing math ought not to be fixated upon if the math poorly models how the real world works. I would have to plead ignorance on this since I haven’t really had serious exposure to high level maths in economics.

  6. Dr. Woods here at JMU would always preach about how there are two kinds of econometricians, the good and the bad. What he meant by this is there is good econometricians that would do the best they could to predict their subjects causation no matter what, the bad econometrician would pervert their models into proving what they want it to. The relevance of Dr. Woods preaching coincides with the “Hippocratic oath” of financial and economical modeling mentioned in the “Quants: the Alchemists of Wall Street” video [1]. Although one would be foolish to believe these models are bullet proof and make no assumptions, one should be able to expect the model was crafted by a team of educated quants using everything possible to assure its accuracy. Within the video very shocking information is shared. First of all we learn that people without solid mathematical understandings are in charge of the financial engineers. The financial engineers will propose these models to their superiors, and the superiors will not be able to understand the model but assume they are correct because of how intelligent the engineers are. This should not be! The superiors should have a stronger understanding then the modelers themselves. I believe it is ridiculous to just assume something is correct because you do not understand it. Then we find out if the superiors don’t like the models outputs, they will send them back to the quants and tell them to produce more pleasing results. This is the most ridiculous thing said yet. It is just like Dr. Wood’s bad econometricians.
    There should clearly be a “modelers Hippocratic oath” but who can afford to abide by it. Companies don’t want to hear your refusing to change the models to meet their desires because of a pledge you made. You will be fired on the spot, that’s where this idea falls apart. It would be nice for everyone to abide by this rule but it’s just unrealistic. The fields of Finance and Economics can attract very greedy personal, unfortunately these people tend to be the “higher-ups” in the company such a CEO and CFO, and these greedy people will stop at nothing to yield higher profits. This means that any financial modeler not producing what they want will be replaced by someone who will. I would like to believe there is a solution to making every quant abide by the oath, but until these formulas and models can be regulated by an outside source, I do not see everyone abiding.

    [1] “YouTube – Quants: The Alchemists of Wall Street (Marije Meerman, VPRO Backlight 2010).” YouTube – Broadcast Yourself. Web. 11 Nov. 2010. .

  7. The mathematical models used on the trading floor of Wall Street are not understood to be approximations of reality. Any effort to convince oneself otherwise is illusory. In several dictionaries (perhaps the more archaic ones), the word price is nearly synonymous with value. In the fast paced world of quantitative finance prices are generally not nearly equivalent to intrinsic value, and are often the means to an end.
    Since many of the trading firms on Wall Street have been conditioned to make as much money for their clients (and themselves) as quickly as possible, long term value-investing takes a backseat to speculation, as stated in the Meerman film, “The companies themselves don’t matter, what they do doesn’t matter. Its the way their stocks move that matter” (42:01). This is a far cry from the original use of the stock market system to provide capital to firms that may become more profitable. Instead it becomes a game of hot potato with vehicle prices. The models produced in the world of the traders cannot really be taken more seriously than “best guess”, with an infinite number of factors that are excluded. I think Nassim Taleb would scoff at any “quant” who thinks they have accurately depicted reality in their complex model. Even if they have, will reality today be the same as reality tomorrow? Will they be robust against black swan events? Unlikely.

  8. I will begin here by stating that I largely agree with what everyone else has said: mathematics is a powerful tool that helps economists tremendously but, like all other tools, should be used with caution.

    I’ll focus more on the externalities of the economic profession’s reliance upon math before returning to my general impressions. The two points I’ll consider both concern informational asymmetry. The first is the problem of asymmetry that results within organizations from modelers using complex math. As the “Alchemists” video pointed out, quants’ supervisors at investment banks are usually management-types who have no standing to assess financial algorithms. Thus, they must simply accept that they are legitimate, and the quants are given disproportionate power over a firm’s decisions. (1)

    Most puzzling to me is the fact that there exist numerous alternatives. Accounting, for example, is similar to financial engineering in that it is a specialized skill, but in that industry managers are regularly drafted from the ranks of senior accountants. They are very apt at spotting out flaws in their employees’ work, and thus their teams function as conceived. Research institutes, such as NBER, are headed by the world’s most renowned economists, people perfectly capable of judging the work of those below them. In this vein, I find it ludicrous to believe that the world’s best investment banks cannot find mathematically inclined persons who also possess management skills. It’s not a stretch to say that such managers could very well have mitigated the effects of 2008’s collapse.

    Second, I’d like to speak more generally on the impact of math on the public’s perception of economics.(3) As a number of journalists point out, there’s a huge information asymmetry between economists and the public at large – even those interested in the subject find that reading economics papers comprises a few paragraphs of concise introduction and conclusion separated by dozens of pages of math. (4) People are instead clearly drawn (5) to economists who use math to make their argument simpler – I share little in common with Dr. Krugman’s views, for example, but find his blog posts presenting time-trend data about the drop-off in aggregate demand or the impact of QE2 brutally clear and concise at making his points. (6)

    At the same time, though, I found Mr. Krugman’s denunciation of complicated mathematical models like the RBC framework to indirectly demonstrate why mathematics is so valuable. (7) He doesn’t criticize the mathematics behind the model, but rather its assumptions – that markets are rational and that unemployment is simply the result of an economy readjusting, for example. The validity of these assumptions is well beyond the scope of this post (numerous Nobel laureates disagree completely with him) but the fact remains that economic models allow for these assumptions to be stated clearly. That has tremendous value on its own – (when was the last time a New Yorker essay opened with all of the author’s biases and perceptions?) – and to me demonstrates exactly why mathematics should, and — with some adjustments to the aforementioned problems of information asymmetry — likely will continue to be the preferred mode of economic analysis.

    (1)http://www.wikio.co.uk/video/quants-alchemists-wall-street-marije-backlight-2966957
    (2)http://www.nber.org/info.html
    (3)http://blogs.hbr.org/fox/2010/03/wresting-the-economic-debate-a.html
    (4)http://blogs.reuters.com/felix-salmon/2010/04/01/economics-without-mathematics/
    (5)http://oxfordthought.com/2010/10/22/top-10-economists-on-twitter/
    (6)http://krugman.blogs.nytimes.com/2010/11/01/qe-in-the-gd/
    (7)http://www.nytimes.com/2009/09/06/magazine/06Economic-t.html?_r=1&em=&pagewanted=all

  9. @Ben Zhang
    I took particular note of your notion that economic models represent not perfection, but rather improvements on previous constructions, when watching the “Alchemists” video in particular with regards to the statement about how CDO models simply assume out of thin air that 60% of their assets will mature in a particular manner. This seemed like an excellent topic for future economic research — a model with a model, if you will — that likely will be addressed with a thorough study. Through such a small improvement, the entire financial model will represent reality more accurately, thus perfectly exemplifying the nature of progress in the discipline.

  10. From this youtube video, I realized that cause of financial crash of 2008~2009 was not fault on quant engineer. The major problem was someone who use it for wrong way. They just underestimate how risky of CDO, CDS and MBS. They just seek for high profit even they knew that it is really risky asset which called moral hazard. Those assets were really complex to derive because those assets all connected each other. That is why if one bank got bankrupt then 20~30 banks got in trouble. In my opinion, if investment bank want to use quant asset, they should estimate risky of asset and hedge those assets.

    Mathematical theory and economic theory have a lot of assumptions which have some uncertainty. If I want better theory then I have to make better assumption but those assumption depends on how economist think about theory. So theory can be change many different ways. Those theories were not proved yet but those theories are derived in mathmatical way so we can use theory to estimate future.

    http://en.wikipedia.org/wiki/Financial_crisis

  11. I agree with Mirrless in the second video when he describes math as a tool for “clarity, precision, and correctness”. Krugman goes on to note the importance of math as a tool for preciseness. There, I just agreed with Paul Krugman. But, I digress. The Mathematicians or pseudo-mathematicians that are employed by firms probably understand the shortcomings of their models. We build these models for a reason. These abstractions of reality allow us to examine phenomenon in a more simple framework that will hopefully provide us some insight as to how our modeled variables will behave in reality. But, the first video did make a good point: I believe it was the Columbia Qfin professor who mentioned that these people are ultimately employees, and that the people who use these models might have no idea what they mean, much less how they were constructed.

    Yet, I think a more interesting issue is one examined in the first video. Many of the nation’s brightest people (or people who think that they are nation’s brightest people) are aspiring to be investment bankers or quantitative analysts at large banking institutions. How many people in econ 484 are aspiring to research cancer treatments or work for the government or a non-profit organization? We have these really powerful winner-take-all effects that incentivize people to take on jobs that aren’t necessarily as productive as other jobs. I would argue that the skills of a quantitative analyst are not as valuable to all of society as are the skills of a doctor or an engineer.

    I think maybe one thing that drives these winner-take-all effects is uncertainty. Our government has a habit of spending money it doesn’t have on things like fighting wars, incarcerating people it doesn’t like (drug users), and funding/subsidizing things that make absolutely no sense. I posit that people have less incentive to work for the public good when one is unsure what the future of that public really is.

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