I’m not going to try to explain Villani’s work beyond this. Let me just mention a few random things from what Yau said, and some even more random thoughts that I had during the talk. One of the latter was that amongst the other mathematicians Yau mentioned were Cergignani, who conjectured that the decay to global equilibrium of, I think, solutions to the Boltzmann equation is exponentially fast, Toscani, who proved with Villani that this conjecture is almost always (in a certain precise sense)correct (which was interesting as there are counterexamples due to Bobylev and Cergignani himself), and Gualdani, whose role in the story I did not write down and have forgotten. Could there be a pattern here?Okay, just kidding. It's a slow evening.
The announcer of these prizes, whose name I didn't catch, quipped weakly that Villani was a real French (as opposed to Châu who works in France), and that you could tell from his last name that Smirnov is Russian (albeit based in Switzerland).
Once again the Langlands program comes up trumps in Ngô Bảo Châu's work; Smirnov's contributions are in mathematical physics and analysis; Lindenstrauss has applied ergodic theory to classical number theory; and Villani's work is in mass transport (which, contrary to what you might imagine, has little to do with either the London Underground or imprisonment in the Andamans), an active field contributing to plasma physics.
Congratulations to all of them.
I attended the latest useR! conference this week, which lasted three days (Aug 12-14) at Dortmund. We've been using R at work for about a year or so now, and there's much to learn about this incredible statistical language and its ancillary 'packages', tools developed by academicians and practitioners in a variety of disciplines, all available free and online, supported by a vast cast of enthusiasts and gurus. So here I was, toting my little bag of goodies, and ambling from room to room to listen to some very interesting presentations across the R user spectrum.
The conference was held at the Statistics department of the Technical University of Dortmund. Only two weeks earlier, torrential rains had flooded the large auditorium of the department. Stains were still visible, but a massive cleanup before our arrival meant that everything appeared as it should - ready for four hundred visitors.
Unlike Curving Normality who blogged regularly and live from the various sessions he attended, I am doing this from back at home. I did take notes during the talks on a little pad that was given to us courtesy Google, but my handwriting these days is much worse than it used to be, and I doubt even a pharmacist would be able to make much of it. Still, here goes - summaries of three of the more interesting talks I attended.
The first talk I attended was on Loss Functions by a professor of actuarial studies, Vincent Goulet. Actuaries are interested in such things as ruin, the distribution of insurance claims, and the probabilistic properties of insurance payouts. To model these events, Goulet introduced an R package named 'actuar', in which he proposed several families of distributions, including those called censored. These, in particular, are interesting to insurance specialists. A client with a deductible is not going to make a claim if he thinks his damages cost less than the deductible to make good. In such a situation, the distribution of claims would be left-censored. Likewise, insurance payouts are usually capped by the size of the cover. Payouts, therefore, follow a right-censored distribution.
This is of relevance to us in finance as well, especially if we want to model the effects of management fees on a portfolio. Because irrespective of how well a manager performs, he always gets his management fee, the returns to a client from the manager are always that much less than the manager's overall performance. For the manager's revenue stream, on the other hand, there's an effective floor - and that can be modelled by a left-censored distribution.
An example of the multifarious uses of statistical tools came from Miriam Marusiakova, of the Charles University of Prague, who presented an R package 'forensic' to help in DNA fingerprinting. It is well-known that the DNA composition of any two human beings (other than identical twins) are distinct. Since it is unfeasible to compare DNA strands in their entirety from various possible sources, forensic scientists have isolated certain markers that can serve as witnesses for distinction. Unfortunately, these markers themselves do not provide sufficiency of difference, and so a statistical analysis is required to determine how likely it is that the DNA found at a location came from one person or many.
Naturally, this is important! Let's say that a certain amount of DNA was found at a crime scene. There is a victim V and a suspect S. There are three possibilities: a portion of the DNA is known to be of the victim; there's only one type of DNA, suspected to be that of the offender; there's several sources of DNA found. The prosecution's hypothesis is that some of the DNA came from S. The defence's hypothesis is that the remaining DNA came from persons unknown U. How to determine which of the hypotheses is the correct one?
Miriam explained that external information needs to feed into the statistics. For instance, certain genetic factors are present to a greater or smaller degree in various populations. Not incorporating these factors into the statistics leads to overstating the case against the defendant. The classical probability law, named the Hardy-Weinberg law, is inapplicable in this case.
Another twist is that the offender and/or the victim, and the defendant are related! Usually, there is an assumption that the offender and the victim are independent. Miriam's package enables the analysis of all the above possibilities.
As a concrete example, she showed the widely different conclusions that could be drawn from the O.J. Simpson murder trial of the early 1990s in California. If the various factors and match probabilities were not estimated correctly, it was as easy to prove that the DNA found at the crime site was Simpson's as it was not. Lesson - estimate accurately and account for all possible variations.
The effervescent Janet Rosenbaum of Harvard University produced one of the most entertaining examples of research I've ever come across. She dealt with the notorious abstinence (virginity) pledge in the USA, and examined whether the sexual behaviour of teenagers who took the pledge was any different from those who didn't. (See here for some of her work, and this news report at the Washington Post.) I can do no better than quote from her very thorough abstract at the conference:
Objective: The US government spends over $200 million annually on abstinence-promotion programs, including virginity pledges, and measures abstinence program effectiveness as the proportion of participants who take a virginity pledge. Past research used non-robust regression methods. This paper examines whether adolescents who take virginity pledges are less sexually active than matched non-pledgers.
Previous researchers had compared the sexual behaviour of pledging teenagers against the general population of teenagers, and concluded that, indeed, the former were less likely to have had sex, and had a lower incidence of sexually-transmitted disease. For the US conservatives, this was brilliant news, meaning they could cut federal funding for contraception and women's sexual health, and provide instead abstinence coaching and use the numbers of pledgers as a metric of success.
But, of course, the comparison is not fair. The correct thing to do would be to match pledging teens with non-pledging teens who have similar backgrounds and ideologies. After all, the people who take the pledge are not average US teens. Many of them are from evangelical families, deeply religious, often born-again. When this matching is done, the results are quite clear:
Five years post-pledge, 84% of pledgers denied having ever pledged. Pledgers and matched non-pledgers did not differ in premarital sex, STDs, anal, and oral sex. Pledgers had 0.1 fewer past year partners, but the same number of lifetime sexual partners and age of first sex. Pledgers were 10 percentage-points less likely than matched non-pledgers to use condoms in the last year, and also less likely to use birth control in the past year and at last sex.
The behaviour of pledging and non-pledging teens is statistically identical! Worse, one to five years after having taken the pledge, 84% of those teens denied having pledged. Egregiously, many who had sex before taking the pledge declared themselves virgins shortly thereafter. To add insult to injury, pledgers were often more ignorant of contraception when they did succumb and have sex, and were thus less likely to protect themselves from disease or pregnancy before marriage.
Rosenbaum concluded that federal funds would be better spent in teaching effective birth and STD control than on abstinence measures.
Other interesting presentations:
- Tomoaki Nakatani, ccgarch: An R package for modelling multivariate GARCH with conditional correlations.
- Rory Winston, Real-Time Market Data Interfaces in R. (How to connect to Reuters from R)
- Susana Barbosa, ArDec: Autoregressive-based time series decomposition in R.
- Ray Brownrigg, Tricks and Traps for Young Players.
- Wei-Han Liu, A Closer Examination of Extreme Value Theory Modelling in Value-at-Risk Estimation.
- R. Ferstl, J. Hayden, Hedging Interest-Rate Risk with the Dynamic Nelson-Siegel Model.
There are several benefits to attending a conference. One overhears some interesting gossip. One supposedly learns a thing or two about one's field. One may, if one is overwhelmed by the awesome weather, sleep through a particularly boring presentation with no qualms. And one may also have the opportunity to inveigh against those who have the temerity to not attend the conference after their paper has been accepted.
As you can perceive, I had the opportunity to participate in each of these delicious activities. [As mentioned earlier in the week, I was in Aix-en-Provence, attending the Forecasting Financial Markets 2008 conference.] Chief among them was the gossip. Academics are like old people in this regard. They trade titillation and amusement and raised eyebrows. Unfortunately, I missed out on all these. At my table during lunch, there were, instead, hagiographies of the worthies of the world of financial econometrics. "What a fellow," said one professor admiringly of Mark Taylor.
Mark Taylor, of course, is well-known in our field. He read for a Politics, Philosophy and Economics degree as an undergraduate at Oxford (you can't study any of these in isolation, it appears) and worked in the financial industry for a bit. He then got himself a PhD from Birkbeck College and obtained a faculty position at University College, Oxford. Here, because his doctorate was not Oxon. or Cantab., he was addressed by his colleagues as Mister. The snobbery extended to virtually all his dealings with them, despite his steady progress to the heights of achievement in his field. Eventually, he left them and joined the University of Warwick, where he remains to this day.
Of course, he missed the perks of the high table and the elaborate system designed to support an academic at Oxford for conferences and things. Warwick, in comparison, is a bit of a backwater. But in the interim, he managed - while raising a family, publishing solid research and editing several journals - to obtain an MA in English Literature. And, tiring of paying expert repairers of antique clocks (the family hobby) through the nose, he apprenticed himself to one of the master clockwrights, and learned the trade.
Where the devil does he find the time?
Anyway. The FFM conference is bedevilled by one serious problem - that of presenters not showing up to present their papers after acceptance. For one thing, this completely screws up the scheduling. For another, many of them don't bother to pay the conference fee either, which results in the financial difficulties for the organisers. And finally it is incredibly frustrating for attendees who were looking forward to learning something new on a topic of interest.
I'm not sure what the deal is in the other disciplines, but this lack of attendance appears to be a serious canker among financial conferences.
The main reason for this sad lack of professionalism appears to be that it suffices for a paper to be accepted at a conference to appear on an academic's resume. We mulled over several solutions to this problem. One possibility is not to publish the accepted list of papers until the authors pay up. Another is not to do so unless they present (but why would they present unless they were told their paper was accepted?)
The FFM used to be held in London for years, and provided at one time a good mix of presentations from professionals in the finance industry and academics. These days, though, it is skewed more and more towards the ivory tower. People such as I turn up hoping to learn some new techniques in financial modelling, but some of the academic work is so removed from the day-to-day grind that it would take a person with considerably higher IQ than me to make it applicable to our grotty world of money-making.
I presented a piece of work done jointly with the head of my group. From a statistical standpoint, it was probably not completely rigorous, and I had hoped to obtain some feedback on how to strengthen the work (which I did get). For anyone who is interested, the work dealt with the extraction of currency positioning information by the use of peer-group benchmarks. For currency managers, this is interesting, because it's known that when positions get stretched (i.e., say, there's considerable selling of the US dollar and lots of buying of the Japanese yen), the positions tend to unwind rapidly, and there's usually short-term turmoil in the markets. This happens fairly regularly - so can one forecast it? A peer-group benchmark is an index that tracks the daily aggregated performance of a bunch of currency managers, and there are several published by various sources. If we, by means of our simple approach, can determine that our competitors in other banks are positioned in one particular way, and we have an indication thereby that those positions are stretched, we could take the opposite position, for example, and make a profit when the market snaps back.
Somewhat surprisingly, the simplicity of the approach won us some favourable comment, and the one or two enthusiastic questioners were inclined to suggest more rigorous statistical methods to make our results robust. They also mooted a possible collaboration, and this is something we'll have to take seriously, although I did point out that our market priorities change so often that it was unclear how much time or effort we could spend on further developing the work.
Aix is a lovely little town, and the local council provides some amount of funding for the conference. But the FFM has been held here for four years in a row now, and the organisers are thinking of alternative venues.
Luxembourg, anyone?
The conference was held between May 30 and June 1 at La Baume Les Aix, a privately owned establishment run as a spiritual and cultural centre by the Jesuits. The expansive buildings include accommodation, a dining room, various conference halls, sheep and goats, extensive lands, and co-ed toilets.
The conference has been running annually for fourteen years now, and has usually had an even mix of academics and market participants. This year, though, there were almost no attendees from the financial sector. I found, therefore, that much of the presentation was at too high a level for me to understand. When people toss around terms such as ergodic, I tend to gape a bit, my mathematical upbringing notwithstanding. Still, it was a good experience, especially as I met several interesting theoreticians, made a good contact or two, and came away with useful ideas for work.
There was, sadly, a clear lack of organisation. Several unethical people had submitted articles but didn't show up to present them (or even inform the organisers) , much to the chagrin of interested attendees. The projectors garbled graphs and distorted presentations owing to mismatches with the new Vista laptops that were being used. On the first day, lunch was delayed, and on the second, the conference dinner was held at what turned out to be a bit of a tourist trap.
Below is a summary of the presentations I attended.
- Forecasting Under Asymmetric Loss Functions, V. Arekelian and E. Tzavalis. The idea is that symmetric loss functions, such as those usually used in portfolio theory (e.g. quadratic utility, meaning an investor is as averse to a given loss as to the same amount in profit), should be replaced by utilities that are more appropriate to the investor. Didn't get a lot of out this, except for a reference to something we might find useful, namely VaR under asymmetric loss functions.
- Forecasting Stock Price Volatility, A. Rahou et al. This was a classic case of pointless drivel. The presenter showed that he could forecast the direction and level of the next day's opening stock price, if he presented a neural network with thirteen inputs: opening price at the five previous days, moving averages at 1 week, 2 weeks, 1 month, 2 months, the first difference of prices, the RSI trading signal, the stochastic trading signal, and 'turning points'. His testing, if I understood it correctly, was a strange mixture of in- and out-of-sample, conducted in somewhat ad-hoc fashion; the paper is representative of the sort of overfitted and badly reasoned trading systems proposed by sell-side quants; the presence of the neural network ensures that nobody can truly understand why and how the system works.
- Volatility Forecasting and Value-at-Risk Estimation in the Emerging Markets: Case of a Single-Asset Portfolio in South Africa, L. Bonga-Bonga. Basic thesis is that emerging markets suffer not only from internal shocks, but also from external influences, which therefore mandate the use of asymmetric GARCH models to fit and forecast portfolio volatility. I'm not sure that there's anything new in this; I remember reading similar results during my Cass days.
- Estimating Risk-Neutral Density Functions from EUR/HUF Currency Options and Forecasting Ability, C. Csávás. The presenter, an economist with the Hungarian Central Bank, was the first of the overhead transmitters that I listened to. As far as I can tell, he used the implied volatility surface to back out the risk neutral density functions from which he attempted to forecast one-step ahead volatility. He proceeded to show that there is not much forecastability. Who would have thunk it?
- Utility-based Pricing of Weather Derivatives, H. Hamisultane. This was one enthusiastic woman with a cheerful demeanour and mannerisms. She explained at rapid clip what weather derivatives were, described how to estimate a constant risk aversion coefficient using liquid option prices, and then use Lucas' consumption based asset pricing models for the pricing. She admitted happily that they probably don't work too well in practice, and when someone asked how to hedge these products, she candidly said that she had no idea. There was an interesting post-presentation discussion, which I contributed to. A delegate, Marianna Brunetti, suggested that since the underlying (the weather) for the derivative cannot be priced, the Wang transform might be used to obtain a risk-neutral measure for it; to which I rejoined that a paper by Pelsser showed that the Wang transform was not correctly applicable in financial risk modelling. This was pretty much the beginning and the end of meaningful contribution by yours truly to any discussion during the conference.
- Investigating the Corporate Spread: a Non-Parametric Approach, C. Peroni. She considers a multi-factor non-parametric (indeed, a nonlinear) model for the term-structure of corporate debt, in which she incorporates inflation as a driver. An attendee pointed out that expected inflation can be hedged; it's the unexpected inflation that should really drive the model. I pointed out that we use the term-spread of the yield curve as a proxy for inflation, which she also incorporated in the model, and asked why then have the inflation term. She said that that could probably explain why she found the term-spread insignificant at various points, perhaps implying that the inflation term was picking up the relevant effect.
- Back-testing Value-at-Risk Based on Tail Losses, W. K. Wong. The main contention in this paper is that the use of VaR is erroneous as it does not incorporate information from the loss tail, and that the expected shortfall (ES) is a better measure. Wong used a saddle-point approximation to the tail losses; with Monte-Carlo simulation, he finds that the technique is accurate even for small samples.
- The Role of Private Information in Return Volatility and Bid-Ask Spreads in the FX Market, F. J. McGroarty. Only caught the tail of the presentation. McGroarty used the EBS as representative of FX trading volumes and the bid-ask spread, but as Pierre pointed out, the average chunk of an EBS trade is about 5 million dollars, which hasn't changed over time, so the finding that the bid-ask spread is not volatile is unsurprising. There are OTC trades of much larger sizes, which incur larger transaction costs, which were not captured by McGroarty.
- Bootstrapping the Volatility of Real Exchange Rates, L. Copeland and S. Heravi. Another massive overhead-transmission. Copeland talked about STAR models (smooth transition autoregressive) and their estimation, application and so on, and I faded rapidly.
- Time Reversal Invariance in Finance, G. Zumbach. Gilles' contention in this paper is that if a financial model is assumed to be an accurate representation of reality, it should be able to imply such facts about the data as invariance (or the lack of it) under time reversal. He shows that several families of stochastic volatility fail to demonstrate these properties; multi-scale ARCH models do better.
- The Distribution and Non-Arbitrage Price of the CPPI Portfolio, A. Cipollini. The only mathematical (stochastic calculus) paper presented at the conference, as opposed to the myriad statistical and econometric items. Cipollini discussed the pricing of a constant-proportion portfolio insurance structure, and showed how under both a bullish and bearish market, an investor could hold on to the gains made hitherto. Can't say I understood much of it, especially because I arrived late, but was hoping to study the actual paper, which - it now appears - I won't be able to do, as it is not in the conference CD-ROM. Drat.
- Changes in the Statistical Features of G10 Currencies and Their Implications for International Investors, P. Lequeux and M. Menon. As Pierre returned to London the day before the presentation, I gave it. By subtle advertising and word-of-mouth (mainly my own), I had created a buzz about this, so it was rather well attended. Unfortunately, as it was the first paper after lunch on the last day, most of the attendees were half asleep, and after my whirlwind tour-de-force, everybody was clubbed into a sensation of having walked into a fog. Seriously, though, the gist of this descriptive paper is as follows: over the past 10 years, there have been two gross trends in the USD (an appreciation initially by about 32% against the G10 currencies followed by a depreciation of about 39%), after which it has been more or less range-bound; most currency managers follow variants of momentum-based strategies, which performed well during the trending periods and have done badly in the recent (range-bound) past; the statistical tests we tried (ADF, variance-ratio, Taylor price-trend tests) failed to detect the trending regimes (why?); currency volatilities are at historic lows, but correlation between them is at all-time high, so explicit risk replaced by severe contamination (diversification) risks; we suggest that the diversification of central bank reserves has contributed to this and provide graphical demonstration of the fact. Received two interesting suggestions for further investigation: try a Granger-causality test to determine if lack of currency diversification prompted the selling of the USD by the central banks, or vice-versa; Chiara recommended the use of tests by Robinson to see if there was local non-stationarity in our time-series, which might have made the detection of trends difficult.
And so, back to London.
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