About Thu, 21 Jan 2010
Computational and sociological analyses of financial modeling
I have been reading a number of papers that examine financial modeling in the context of the current crisis from a computational complexity and sociology of knowledge point of view:
- Looking Out, Locking In: Financial Models and the Social Dynamics of Arbitrage Disasters, by Daniel Beunza and David Stark, September 2009
- Credit Models and the Crisis, or: How I learned to stop worrying and love the CDOs by Damiano Brigo, Andrea Pallavicini and Roberto Torresetti, December 2009
- The Credit Crisis as a Problem in the Sociology of Knowledge, by Donald MacKenzie, November 2009
- Computational complexity and informational asymmetry in financial products, by Sanjeev Arora, Boaz Barak, Markus Brunnermeier and Rong Ge, October 2009.
I liked all these papers and learned a lot from each of them which is not the same as saying that I agree with all of them.
The paper that I liked most was Beunza and Stark which is really about cognitive interdependence and systemic risk. Their work is based on an ethnographic study of financial modeling carried out over a three year period at a top-ten global investment bank. Some of their conclusions are:
Using models in reverse, traders find out what their rivals are collectively thinking. As they react to this knowledge, their actions introduce a degree of interdependence ...
Quantitative tools and models thus give back with one hand the interdependence that they took away with the other. They hide individual identities, but let traders know what the consensus is. Arbitrageurs are thus not embedded in personal ties, but neither are they disentangled from each other.
Scopic markets are fundamentally different from traditional social settings in that the tool, not the network, is the central coordinating device.
Instead of ascribing crises to excessive risk-taking, misuse of the models, or irreflexive imitation, our notion of reflexive modeling offers an account of crises in which problems unfold in spite of repeated reassurances, early warnings, and an appreciation for independent thinking.
Implicit in the behavioral accounts of systemic risk is an emphasis on the individual biases and limitations of the investors. At the extreme, investors are portrayed as reckless gamblers, mindless lemmings, or foolish users of models they do not understand. By contrast, our detailed examination of the tools of arbitrage offers a theory of crisis that does not call for any such bias. The reflexive risks that we identified befall on arbitrageurs that are smart, creative, and reflexive about their own limitations.
Though the paper is written in a sociological language, what it most reminded me of was Aumann’s paper more than 30 years ago on “Agreeing to disagree” (The Annals of Statistics, 1976). What Beunza and Stark describe as reflexivity is closely related to Aumann’s celebrated theorem: “If two people have the same priors, and their posteriors for a given event A are common knowledge, then these posteriors must be equal.”
The Brigo et al paper is mathematically demanding as they take “an extensive technical path, starting with static copulas and ending up with dynamic loss models.” But it is very useful in explaining why the Gaussian copula model is still used in its base correlation formulation though its limitations have been known for several years. My complaint about the paper is that it focuses too much on the difficulties in fitting the Gaussian copula to observed market prices and too little on the difficulties of using it to estimate the impact of plausible stress events.
MacKenzie focuses on “evaluation cultures” which are broader than just models. They are “pockets of local consensus on how financial instruments should be valued.” He argues that “‘Greed’ – the egocentrically-rational pursuit of profits and bonuses – matters, but the calculations that the greedy have to make are made within evaluation cultures”. MacKanzie highlights “the peculiar status of the ABS CDO as what one might call an epistemic orphan – cognitively peripheral to both its parent cultures, corporate CDOs and ABSs.”
The Arora et al paper is probably the most mathematical of the lot. It essentially shows that an originator can put bad loans into CDOs in such a way that it is computationally infeasible for the investors to figure this out even ex post.
However, for a real-life buyer who is computationally bounded, this enumeration is infeasible. In fact, the problem of detecting such a tampering is equivalent to the so-called hidden dense subgraph problem, which computer scientists believe to be intractable ... Moreover, under seemingly reasonable assumptions, there is a way for the seller to ‘plant’ a set S of such over-represented assets in a way that the resulting pooling will be computationally indistinguishable from a random pooling.”
Furthermore, we can show that for suitable parameter choices the tampering is undetectable by the buyer even ex post. The buyer realizes at the end that the financial products had a higher default rate than expected, but would be unable to prove that this was due to the seller’s tampering.
The derivatives that Arora et al discuss are weird binary CDOs and my interpretation of this result is that in a rational market, these kinds of exotic derivatives would never be created or traded. Nevertheless, this is an important way of looking at how computational complexity can reinforce information asymmetry under certain conditions.
Posted at 18:10 on Thu, 21 Jan 2010 17 comments permanent link
Comments...
Naveen wrote on Thu, 21 Jan 2010 19:16
Re: Computational and sociological analyses of financial modeling
Prof, Wanted to know the following, more in a spirit of the same "sociology of knowledge" perspective 1. Motivation for such an effort. What was the basic question you were trying to answer 2. The criteria behind selection of the papers.
Thanks
Prof. Jayanth R. Varma wrote on Thu, 21 Jan 2010 20:06
Re: Re: Computational and sociological analyses of financial modeling
Motivation: I am just trying to understand what happened. Each discipline provides one perspective. For example, I have read a lot of financial history and a lot about stochastic processes. I will probably post about that as well.
Criteria: These are just the papers that I found most interesting. They are all "deep" analyses in some way - none of the superficial journalistic opinionated stuff that one reads so much these days.
Naveen wrote on Thu, 21 Jan 2010 20:34
Re: Computational and sociological analyses of financial modeling
I think I got it wrong regarding the second question . Let me reframe it
Q. Once you decided to familiarize yourself with the sociology of knowledge perspective, what was the criteria used to select specific papers. I am asking this since I find that you have completely skipped articles based on "critical theory", for instance, among other perspectives in sociology.
Prof. Jayanth R. Varma wrote on Fri, 22 Jan 2010 10:32
Re: Re: Computational and sociological analyses of financial modeling
Examples?
Naveen wrote on Mon, 25 Jan 2010 20:31
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I started with this
McGoun, E.G., 1995. The history of risk measurement. Critical Perspectives on Accounting 6, pp. 511–532
Will add the entire list I had read.
Naveen wrote on Wed, 27 Jan 2010 09:51
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KEASEY, K.; HUDSON, R. Finance Theory: A house without windows. Critical Perspectives on Accounting, v. 18, n. 8, p. 932-951, 2007.
Resistance is futile: the assimilation of behavioral finance George M. Frankfurtera and Elton G. McGoun, Journal of Economic Behavior & Organization Volume 48, Issue 4, August 2002, Pages 375-389
I would like to hear from you on the perspective these literature put forward.
Prof. Jayanth R. Varma wrote on Fri, 19 Feb 2010 19:51
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I read all these papers and then re-read them again after a gap of two weeks. Unfortunately, after two readings, I am unable to agree with anything that they say.
1. The McGoun paper is quite wrong in thinking that modern finance is based on relative frequency probabilities at all. The standard models are based on subjective probabilities (for example, PC Fishburn, "A general theory of subjective probabilities and expected utilities", The Annals of Mathematical Statistics, 1969).
2. Keasey-Hudson is largely devoted to criticizing a paper by Canner et al. After reading both papers, it appears to me that Keasey-Hudson do the same puzzle solving - changing the distribution, the decision criterion - that they accuse Keasey-Hudson of doing. I do not think highly either of the Canner et al. paper or of the Keasey-Hudson paper. They are both discussing asset allocation models that are hopelessly obsolete - recall that the Black-Litterman model was proposed as far back as 1992.
3. Frankfurter and McGoun is the strangest of all. They are unhappy when finance theory incorporates some insights from behavioural finance. In the other papers, they were unhappy with finance theory not accepting such insights.
There are many problems with modern finance theory, but unfortunately the above papers do not help us identify, understand or deal with these problems.
Naveen wrote on Sat, 20 Feb 2010 13:57
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To pick one of the papers for detailed analysis ..
You wrote “The McGoun paper is quite wrong in thinking that modern finance is based on relative frequency probabilities at all. The standard models are based on subjective probabilities (for example, PC Fishburn, "A general theory of subjective probabilities and expected utilities", The Annals of Mathematical Statistics, 1969).”
1. When CAPM and MPT are still based on relative frequency probabilities, how are you saying that standard models in Finance are based on subjective probabilities. 2. How did you interpret that the Mcgoun paper is recommending the use of subjective probability for measurement of risk. Remember the whole paper is about measurement of risk. The main point being risk is not variation or dispersion of past data . And it is exactly the way risk is measured now.. past volatility. But still the paper is not pitching for usage of subjective probability instead. 3. The bedrock of finance , atleast as taught in MBA schools, is CAPM and MPT. Given the historical debate on risk measurement as clearly shown in the paper, how do you rate these models. 4. The paper never claimed that subjective probabilities are never used. Your dismissal of the paper as wrong on this basis clearly needs a relook
Prof. Jayanth R. Varma wrote on Sun, 21 Feb 2010 11:07
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No, CAPM and MPT are based on subjective and not relative frequency probabilities. In single period models, you could think of the subjective probabilities as being the same as the historical probabilities. But in multi-period models like the inter-temporal CAPM (ICAPM), the probabilities are time varying and so the relative frequency definition fails completely.
Some models assume that all investors agree on the same subjective probabilities.
But there are plenty of models that assume that each investor uses a different set of subjective probabilities. Two examples are: Treynor and Black, "How to use security analysis to improve portfolio selection," Journal of Business, 1973 and Black and Litterman, "Global portfolio optimization", Financial Analysts Journal, Sep-Oct 1992.
Naveen wrote on Sun, 21 Feb 2010 21:43
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" CAPM and MPT are based on subjective and not relative frequency probabilities"
How is Beta calculated? subjective.. ??
"In single period models, you could think of the subjective probabilities as being the same as the historical probabilities."
Could you please elaborate on this. I am thoroughly confused here. For me historic probabilities is objective. Whether you measure it or I measure it, the probability based on historical data would be same.. How can it ever be subjective..
We should not engage in a language game.
Prof. Jayanth R. Varma wrote on Tue, 23 Feb 2010 12:29
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Consider that we are about to toss a dented coin. You think P(heads) is around 0.4, I think it is around 0.6 (I am deliberately keeping this a little vague to avoid getting into hard mathematics). At this stage, we have subjective probabilities and they disagree.
We now toss the coin 20 times and observe 9 heads. Our subjective beliefs will come a little closer to each other but are still different. If we toss the coin 10,000 times, our beliefs may become practically indistinguishable and we can call it "objective probability." Importantly, objective probability arises only as an idealized mathematical limit with infinite sample sizes. Almost all real probabilities are subjective.
Objective probability is a useful approximation if we assume long histories. But what if after every 100 tosses, the coin is changed? We may never end up agreeing even after 10,000 tosses.
It is same problem in CAPM. If we assume that probabilities are constant over time, we can talk about "objective probabilities" as a loose approximation and can use it to calculate betas. If the probabilities are time varying, then only the subjective route is available. The beta has to be computed using the variances and covariances of the subjective probability distribution.
For example, I can start with a Normal-Wishart prior, observe whatever little relevant historical data is available, compute the posterior Normal-Wishart distribution and use that to compute the beta.
A good paper on subjective probabilities from a philosophy of science perspective is Jaakko Hintikka, "Unknown Probabilities, Bayesianism, and de Finetti's Representation Theorem", Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1970 (1970), pp. 325-341. Bruno de Finetti's theorems are hugely important.
Naveen wrote on Thu, 25 Feb 2010 11:35
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Prof, With all due respects, Let me disagree once again and completely.
1. The example you gave to support your argument that subjective probabilities are used in Finance models and to calculate Beta in particular is actually supporting what McGoun ( 1995) suggests, that finance models use relative frequency to measure risk. In the biased coin example of yours, you are precisely doing that. And that is what you tried to negate.
2. In fact, lack of qualitative understanding of relationship between events, variables etc and blind usage of past data to measure different versions of risk is cited as the major reason for collapse of many a investment banks. Different versions of usage of past data is no way to say that they are subjective measurements. Subjective reasoning, not necessarily using past data would be the dimension in categorizing between subjective and objective. And subjective reasoning would involve interpretation on how things are and how things would emerge and for that one may not need Excel or SPSS.
3. My experience, risk as is treated in finance and taught in classrooms is too one-dimensional. In fact, in classrooms it is scary. Once it is defined ( or asserted??) that risk is volatility of past data or covariance with some market index, the student gets little time to reflect. The Professor would not even be apologetic to the fact he has no other means, better way to objectively do it. A reply I got once when I asked this question is that anything else would be just subjective, subjective with a clear condescension
4. In all MBA classrooms and MBA exams, for a given data there is only one beta value. Even in the case of Bayesian approach, the case is same. In fact as I understand Bayesian approach is also objective and not at all subjective
Prof. Jayanth R. Varma wrote on Thu, 25 Feb 2010 13:58
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1. Where is the relative frequency just before the biased coin is tossed the first time?
2. Unless we happened to be experts in the physics of coin tossing, the only basis for the 0.4 and 0.6 prior probabilities just before the first toss would be qualitative and subjective judgments about the dented coin.
3. Please do not equate your classroom experience with the true state of any subject. My classroom experience of calculus was that it as a form of voodoo nonsense. When I read Archimedes, I realized that the problem was with the classroom and not with calculus.
4. Sorry, not in my classroom. And not in the classroom where I learned CAPM nearly 30 years ago.
Naveen wrote on Fri, 26 Feb 2010 12:34
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1. The initial guesses made by those two individuals are mere guesses and not intelligent choices made through subjective reasoning. Even if such guesses are not made initially, it does not make difference to the conclusions after making repeated experiments. The point is once a phenomenon under test allows repeated homogenous experiments, nobody needs to employ any subjective reasoning. Subjective Reasoning has zero value in such circumstances. No Knowledge is required.
Reasoning is employed when the phenomenon examined is complex. Complex would mean high number of variables or factors and dynamic nature. In short simple situations like the coin toss example is a case of closed systems. Complexity is a feature of open systems. Taking analogy from a simple closed system to defend arguments for complex systems would have its serious problems
In short , Subjective probability should not be relegated down to mere guesses employed by people and which has no value as your experiment itself shows. Assume they started with .1 and 0.9. Does it make any difference to the players as well the conclusions after repeated experiments
In fact The example of biased coin actually is a good one to use relative frequency to assess probability of falling head or tail for the following reasons
1. bias remains constant throughout its life. 2. All Conditions remains homogenous 3. Experiments are repeateable
No arguments there. But models based on past data are a big problem when we extend that to domains where human choices and behaviour is involved, which is what financial decisions are about.
2. Subjectivity in Beta Measurement
On the contrary I feel vindicated regarding beta calculation after referring this article by Prof. Aswath Damodaran. http://pages.stern.nyu.edu/~adamodar/pdfiles/papers/beta.pdf
While he clearly points out the fact that beta can be different for different time periods considered, stock indices considered and time intervals considered.. for a given set of data , there is no subjectivity involved
Prof. Jayanth R. Varma wrote on Sat, 27 Feb 2010 10:05
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I think we are talking past each other and there is little point in continuing the conversation further.
I believe (following deFinnetti) that ALL probabilities are subjective probabilities. You obviously think that some probabilities are objective.
Let us agree to disagree.
wrote on Sat, 27 Feb 2010 18:50
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Prof. I dont mind continuing with this conversation .. But I respect your choice
But One errata.. The debate was never about objective and subjective probabilities . It was about usage of historical relative frequency probabilities as RISK in major Finance models.
Further, I would like to hear from you about prof. Aswath's article.
No more comments from me on this topic
Ted K wrote on Sun, 21 Feb 2010 03:27
Re: Computational and sociological analyses of financial modeling
Professor Varma, I read this article in "The Economist" magazine recently and thought it was interesting. http://www.economist.com/specialreports/displaystory.cfm?story_id=15474075 I think for someone as deeply knowledgeable on Finance as you it must be like reading a children's story. Nonetheless I thought it was fascinating and I was curious what your thoughts on it were. Specifically the question of whether mathematical models have been positive or negative for U.S.A., India and world markets. Thank you
