Taleb vs Merton, Cont.

Nassim Nicholas Taleb is angry. Not in the YouTube clip of the same name, but rather at Nobel laureate Bob Merton, whom Taleb attacked in a paper he co-wrote with Emanuel Derman of Columbia.

In the wake of that paper appearing, Merton sent Taleb a detailed and equation-filled eight-page note, dated December 2005, taking issue with the paper. "His argument was that my argument was not compatible with portfolio theory," says Taleb, who says that Merton assumed, in his paper, the very constructs -- things like beta -- which Taleb criticized; which are as meaningful for him as astrology; and which have no place in the world of financial economics.

Merton never published that note. Rumor has it, however, that he posed Taleb's paper as a problem set for his students. And a few months later, a paper appeared under the names of Doriana Ruffino and Jonathan Treussard, defending Merton, and saying, in its abstract, that Taleb's paper "is inconsistent with modern equilibrium capital asset pricing theory" -- the same portfolio-theory concepts which Taleb rejects and which Merton had used in his own note.

Treussard was working for Merton at the time, at Integrated Finance Limited [IFL] in New York, and Taleb takes Treussard's paper to be no less than Merton writing under someone else's name: "it was written by Merton and published by one of his employees," he says.

Taleb responded to Ruffino and Treussard in a footnote in a paper co-written with Espen Haug and entitled "Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula", which rapidly became one of the most downloaded papers of the year at ssrn.com. In the footnote, Taleb and Haug accused Treussard (and, by implication, Merton) of being "scientists lecturing birds on how to fly, and taking credit for their subsequent performance - except that here it would be lecturing them the wrong way."

More recently, on Tuesday, the Economist's economics blog reignited the debate, saying unambiguously that Treussard had disproved Taleb's theories. The author of that blog entry didn't write it on the direct instructions of Merton, but she, too, worked for Merton at IFL, and considers him a mentor.

Taleb, a former options trader, smells weakness.

It is quite distressing for Merton that he can't find anybody to defend him in financial academia, other than his minions. The man invented a fantasy world in which his argument is airtight, and then he said my argument doesn't hold. But in his fantasy world, LTCM [the hedge fund which Merton co-founded and which blew up in 1998] couldn't happen.

And so, on a quiet Friday, I'm letting myself be pulled into a clash of egos between Taleb and Merton. For the record, although I'm sympathetic to Taleb's side of the debate, I have no reason to believe that Merton is waging some kind of deliberate proxy campaign against him.

The interesting thing for me about this particular academic feud, however, is that that for all its viciousness, the stakes really aren't low at all. Taleb is working towards nothing less than the outright dismantling of Black-Scholes, portfolio theory, and the enormous financial edifices which have been built upon them; if he's successful, essentially all the quants on Wall Street would be out of a job. Which I think is probably reason enough for many people to defend Merton right there: the man himself doesn't need to direct anything at all.

Comments

[Tom Armistead:]

The events of the past year provide a considerable amount of empirical evidence that Taleb's theories are a closer approximation of reality than Merton's.

The two men can battle for acedemic prestige if they want, or if that grows tedious they could go back to the drawing board and propose some alternative solutions that will create a stable financial system.

Jan 04 08:28 AM

[stefalb:]

As a long time futures and options trader I have known for a long time that the volatility part of Black-Scholes is badly flawed and discredits the entire formula. Past performance is no guaranty for future performance and a global dynamic economic system totally out of balance makes Black Swan events much more likely. Specific risks can be minimized by modern portfolio theory but systemic risks, as we have seen in 2008, can not at all or only with great difficulty minimized. Arguably the more specific risk is minimized by institutionalizing it in the system, the more systemic risk increases, the more volatility becomes unquantifiabel, and the more Taleb is right!!!

Jan 04 10:03 AM

[jaume ribe,...:]

Seen the two first comments. Agree (of course Taleb is right), yet we must recognize that, so far it is still difficult for Taleb and Mandelbrot to come up with the Holy Greal to leave with millions from WS. But, according to the specialized papers, in the last (current) Black Swan, Taleb has earned a lot of money (and for sure not applying the Merton's prehistoric theories).

Jan 04 11:04 AM

[NWA10000:]

What is Merton's theoretical defense of Long Term Capital?

Jan 04 11:16 AM

[morph366:]

I couldn't agree more with your comment that the stakes are much higher than may appear on the surface as simply a dispute between two theorists. Here, for what it's worth, is a contribution that I wrote recently that provides a different slant on what are deep flaws in the current orthodoxy in academic finance.

One of the most refreshing things that could emerge from the current crisis in the financial markets would be for a radical rethinking of the way that finance is taught at the most prestigious business schools. Future MBA’s should be taught something more historically and philosophically oriented on the nature of risk, rather than the same mathematics that is useful in the physical sciences but is more or less useless when applied to the world of financial economics.
There has been a lot of commentary about the reasons why so many of the experts did not see the coming crisis and many well documented examples of the irresponsible and negligent failures of those should have been managing risks for the banks and the financial services industry. What is far less commented on is the fact that the underlying financial theory of risk and the probability of financial accidents arising is not just wrongly conceived, but dangerously so. None of us, including the test pilot, would entrust our lives to a new airliner which had not been robustly stress tested under the most extreme modelling conditions for aerodynamics and metal fatigue etc. and yet financial products were sold that not only were not thoroughly tested but, in assessing the likelihood of accidents or failures, the financial engineers used the wrong modelling techniques.
There is a serious conceptual problem in modelling a financial product with techniques from the physical sciences because of the sudden and dramatic discontinuities in financial time series data. Sharp gaps and other severe dislocations show that price, and economic behavior in general, cannot be adequately represented as following a trajectory which can then be analyzed in any standard statistical theory. One of the most severe consequences of this conceptual error is the fallacy, which has been more than amply demonstrated by the current financial meltdown, that the probability of large moves in asset prices can in any sense be mapped according to any kind of normal distribution, Gaussian or otherwise.
A simple example can illustrate the inappropriateness of standard statistical theory to the world of finance. There is no meaningful sense to even estimate the probability of discovering a man who is 25 standard deviations from the average height of male human beings, and yet in a well known quote by a senior Goldman Sachs executive who, when asked why one of their funds had lost more than 30% during the onset of the financial crisis, is reported to have said

“We were seeing things that were 25-standard deviation moves, several days in a row. There have been issues in some of the other quantitative spaces. But nothing like what we saw last week.”

From this quotation alone it should be clear to orthodox risk managers educated within the traditional notions of academic finance theory, that there is something profoundly ill conceived with using probability theory based upon a normal distribution, and all the Value at Risk baggage that comes with it, in order to quantify risk in portfolio construction and risk management.

What is needed is a new foundation for the understanding of how to quantify risk and the likelihood of financial collapses and contagion. There have been some promising developments in this field by writers such as Mandelbrot, Hyman Minsky and even Nassim Taleb but the field is still in its infancy. Perhaps there is no underlying logic to financial behavior and that we have to accept that financial meltdowns are as unpredictable as massive earthquakes. But the fact that many people did see our current “falling off a cliff” coming suggests that we may be in a much better position than seismologists.

Jan 04 12:46 PM

[M-P:]

This is an interesting feud. Like most things, there is some veracity in both of their positions. When you paint it as X or Y, it makes for a better story. As with any metric, if you only look at one, you will probably not see the true picture - but, without trying to quantify something, it becomes very difficult to agree on definitions, assumptions, and meaning. If it's so "soft" that you can't put a number around it, what is it exactly - how do you know when you see it. Also, most metrics should be looked at as more of a range or confidence interval type vs. point estimates. The latter are just not that precise.

There is great article around VaR (Value at Risk) in The New York Times by Joe Nocera. Basically, VaR took on a life of it's own and was used as an incentive comp metric for risk managers and others. As you can imagine, it was gamed and risk managers "packed" risk into the tails of a distribution and could lower the VaR number with CDS' and various puts.

I'd like to see some integration of both NT's position and Merton. The tail probabilities are higher than we think and can have more of an impact - we should fully explore and quantify those. Also, Beta and portfolio theory give us some insight into volatility and diversification, but not the full picture. At the end of the day, you can't outsource judgment to a metric - it needs to be integrated with your experience, values, and objectives. The search for some sort of unified theory or an SAT like metric will probably continue, but should be seen for what it is.

Jan 04 01:04 PM

[CaptainJJack:]

Having dealt with financial modeling in a prior life, I end up coming down closer to Taleb than Merton.

ALL of the financial models I have seen require an assumption about variance.

You do not have to predict the direction, but you do have to make statements about HOW MUCH, in terms of standard deviation or overall distribution, things could change if you wish to use any of the stochastic differential equation models.

Taleb's point is simply that while the various ideas, such as assuming the distribution of stock prices follow a log-normal pattern, work a lot of time, there are often big discontinuities that nobody EVER would have predicted (e.g. a black swan when based on all observable evidence at the time, there are only white swans)

And, these "once in a hundred year" events have a habit of happening a lot more often than the models predict.

For me, it is like the comfort you get when you lock three car doors.

Jan 04 01:42 PM

[GerryB43:]

The entire Capital Asset Pricing structure rests upon the assumption of continuity of causal factors. Introducing a new factor is the essence of a discontinuous event. Without a mechanism to account for changes in the factor set in a model (an error term?) any model becomes dangerous to use in constructing or managing portfolios of securities.

Even the SEC's study of the effects of mark to market accounting acknowledges the existence of anomalous effects from using the "mixed-attribute model" of valuation. Clearly, the existing models were not ready for this form of new information. We have a long way to go before a new structure for analysis can achieve widespread and confident use.

Jan 04 03:29 PM

[waynei:]

My math ability is childish and my market analysis dismal as proved in 2000 and 2008. Taleb's theory, as he explains it, can be seen in nature, in economies, in family genology in well.... everything. The scary part is Taleb has stated the housing collaspe, which predicated this financial disaster was not a black swan event, that EVERYONE knew there was a housing bobble. The black swan event is still out there, be it bird flu, nuclear war, multiple government instability, asteroid, drug cartels, pourous borders etc.....
My black swan is liver cancer.

Jan 04 05:05 PM

[kotika98:]

I had read that paper of Taleb and Derman sometime after it came out in 2005. There is not much there except raving against "dynamic replication", which they claim to be a theoretical construct. They themselves dont do anything new, just rederive the good old Black-Scholes-Merton formula by "actuarial expectation". That is not new, such derivations of the option pricing formula were around already in 1965 or so (i forget the names of the people who came with it, you can look up in the BS paper). The problem with their, and older derivations, is really how to explain that the expected rate of growth of the stock is equal to the risk-free rate. This is not an idle academic question, and can only be decided by the dynamic replication argument.

The second thing concerns the association of Merton with LTCM as a proof that the formula does not work. This is clearly hogwash - LTCM did not go down because of miscalculation of options prices but because of 20x leverage.

Finally, as a practical matter, dynamical replication and the options valuation formula was invented by Kassouf and Thorpe sometime around 1967. Their hedge fund, Princeton-Newport Partners, was one of the most successful of all time. They did dynamic hedging of convertibles. And here comes the juice - most of the time, a convertible trader is long the bonds, and therefore long gamma. This means that large, black-swan-type moves actually benefit a trader who is long gamma. Taleb and Derman had worked all their life for market makers, who are short gamma most of the time, therefore for them the imperfections of dynamical hedging can be fatal. So they are not so wrong about dynamical hedging, as a practical matter, but their paper is trash and does not add anything new to the table.

Jan 04 06:17 PM

[Gtarras:]

I have become very dissapointed with Taleb, whose first book was brilliant, imo.. But...

I have formed an opinion that Mr. Taleb is not a "builder". Remember the movie "Seven samuri"? At the end, the worrier says: "People who work the land are the ones that matter"? Or something like that.

Well, Mr Taleb offers only over-dramatic criticism of the framework build by giants much bigger than he is and ever will be (likes like Metron come to mind)...

Mr Taleb should stop barking at elephants. Or propose something that will let us "work the land" when the storm is over, instead of pursuing this overzealous self-promotion campaign...

Jan 04 08:20 PM

[Gtarras:]

To Tom Armistead:

I am curious what theories of Taleb you are referring to?

Using my previous metaphor from "Seven samuri" in earlier post, I would say that Mr Taleb's "fat tail" events theories might help to prepare us for a storm, but do not help us "work the land" at all...

Unfortunately, I changed my opinion of Taleb, and, using his own words, consider him "an intellectual charlatan"....

Jan 04 08:27 PM

[Augustus:]

Many of the comments I've read on the implementation of the financial models include references to "test pilots" and flight tests. When I read these I'm reminded that ALL pilots set up their planes on final approach in very nearly the same way. They are instructed to do that and it works thousands of times a day at airports around the world. When bad weather is observable, they make some adjustments in procedures or delay the landing - another form of adjustment.

However, the real analogy to the Black Swan is to the invisible wind shear or micro downburst that can cause a plane to crash when perfectly on the landing path. It strikes without warning and has been invisible without a known cause. Even planes arriving a few minutes earlier or later experience none of the effects. Pilots have regularly made landing errors and the wind shear is often similarly deadly. A few survivors were often considered to have made some error in the landing setup or approach that they were covering up when giving their reports of the windshear excuse.

Now we do know that windshear and micro downbursts do occur. We recognize that they can and do happen. However, there is little that can be done to avoid them. If you want to take a vacation to a destination of any distance then you will put your family on that plane and accept the risk at the landing site.

The work of Taleb is simply trying to get people to recognize that there are microbursts and wind shear. But, the question remains for the investor and the person flying, what do you do about it? Once you decide to fly you must accept the risk if you want to get to the destination. Taleb offers no alternative to the approach procedures used by pilots and risk measures used by financiers world wide.

Jan 04 09:12 PM

[stefalb:]

In a dynamic system totally out of balance the likelihood of black swan events increases exponentially. Since economics is just not an exact science and the future is inherently unpredictable then there might be just no rational way to quantify future volatility. Therefor the search for an exact formula might be intellectual charlatanism. Dynamic systems out of balance are increasingly governed by chaos(theory). Maybe that's where we will get some answers.


On Jan 04 08:27 PM Gtarras wrote:

> To Tom Armistead:
>
> I am curious what theories of Taleb you are referring to?
>
> Using my previous metaphor from "Seven samuri" in earlier post, I
> would say that Mr Taleb's "fat tail" events theories might help to
> prepare us for a storm, but do not help us "work the land" at all...
>
>
> Unfortunately, I changed my opinion of Taleb, and, using his own
> words, consider him "an intellectual charlatan"....

Jan 05 04:23 AM

[AnandG:]

I think one of the central point for Taleb is the fact that business, which is conducted in real world, must not, rely too much on theory even including those of so called (and disputed) noble winners; particularly ones that originate from such pseudo-science as economics. And I think I fully agree with him. Unfortunately most business managers have absolutely no "Business Experience"; only "Management Experience" and some good academic qualification which off-course teaches only theory.

Having seen socialism run havoc in my own country India, I believe he is justified in being irritated because of the magnitude of problem this is causing. I think for quite some time I am a bit surprised to note that most western Banks and other big companies have very similar working styles as did the organizations in failed socialist states. In both cases the management had no stake of its own and were simply following "what was taught" to be right justified by some accepted standards. That the standard itself is so deeply flawed is never a bother to them because they may not even understand it. This weak structure on which stands so many of our big comapanies and banks needs to collapse. It is no good for us to prop this up for the moment for a subsequent and much worse problem later on.

That Taleb is angry is therefore good and well be.

Jan 06 08:28 PM

[Tom Armistead:]

To Gtarras,

Theories of Taleb that I can relate to involve his criticism of various economic or financial risk models which rely on the assumption that outcomes are normally or lognormally distributed.

His theories that reality may be better described by fractals, (at least that's how I read it) are interesting and almost poetic but do little to prescribe a replacement for the RBC (risk based capital) system that has proved itself unstable.

For my own purposes as an investor and speculator, and one who uses options, I regard share prices as log-normally distributed until one or more new causal drivers enter the picture, at which point the tails feature an endless doubling or halving of the previous value, leading to extraordinary volitility and results "25 standard deviations" away from the mean.

Jan 11 04:13 PM

[HughA:]

Tom - I am a papered scientist, trained to reduce the most complicated problem into small, measureable bits - reductionism. The problem is, no one has figured out how to put all the bits back together to reconstruct the whole.

I think this is the difference between Merton and Taleb. Merton reduces the financial world to beta - ignorant of the Black Swans. When Taleb speaks of heuristics, he is pleading that we move away from models and start thinking for ourselves - we may not get it right, but we'd be better off than believing in the self-acclaimed gurus of financial economics.

Through health issues and personal experience, I've learned that you don't have to know why things work, the simple fact that they do work is good enough. In the end, reductionism (rationality) will be replaced by chaos and heuristics with Prigogine and Taleb leading the way.

Jan 14 04:18 AM