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February 2006 Letter and Contribution Awards

In a pleasing circle, contributions and letters to the editor kept pace with record visits to Daily Speculations in February. Daily Speculations is a benevolent forum to encourage good thinking about the market. Material is provided free by us and our readers. Because incentives work, and to augment the mutual benefits of participating in the forum, we offer awards each month for top contributions or letters to the editor. Some highlights among the many augmenting posts in February:

  1. The discussion on cycles in late February was one of the best ever on Daily Spec. Special recognition and thanks to Phil McDonnell, Bruno Ombreux, Jim Sogi, Tom Ryan and John Bollinger for their elucidating comments.
  2. Jim Sogi gets deeper and deeper, while helping us and others stay afloat. We thank him for his posts on binary modeling and rogue waves, which elicited a post from a very interesting and erudite new contributor, mathematician Michel Olagnon.
  3. Tom Ryan, known to Daily Spec readers for practical and scholarly insights on geology and trees, startled us with a thought-provoking post relating Shakespeare's playwriting to speculation. (Feb. 3)
  4. Alex Castaldo consistently enlightens readers with essays that present the results of his intense study and thought with great clarity and wit. We recommend his latest, “Fibonacci’s immortal contribution to Finance” (Feb. 12).
  5. The Letters to the Editor section drew a highly interesting comment (Feb. 21) on the racial element in the opposition in Europe to the acquisition of Arcelor by Mittal of India. The author requested anonymity.
  6. Shane James’s letter on destructive memes (Feb. 16) offered a highly entertaining inside view of medium-term currency forecasting at investment banks.

We award $500 to Jim Sogi and Michel Olagnon, and $250 to the others mentioned. Winning posts appear below. -- Victor Niederhoffer and Laurel Kenner

The Cycles Thread

Binary Modeling, by James Sogi

Given that we are at the same price as 52 days ago, the question arises what will the outcome of this range be? Following up on Dr. Zussman's recent excellent studies on up days and down days, some counting is in order. Within the range 21 days were down open to close and 29 up. Within that same range, 21 days closed above the mean and 31 below. Does this mean anything?

Modeling Binary Data by David Collett is perhaps the most clearly written explanation of statistics terms that I have read. Collett gives excellent explanations of the the formulas he uses with good examples of models and how to insert the numbers from the data into the formula. Very few other authors writing about statistics have succeeded in such understandable writing. There is the best discussion of models and hypotheses ever. The trick is to convert the models of disease, growing rose cuttings and the like into stock price data use. The truly amazing thing to me is that 2x2 contingency tables of win/loss, success/failure, or up/down data can reveal valuable information and that formulas and models exist to quantify such things as up and down days in a range. This was made popular by Bernoulli in 1713 and is known as the Bernoulli Distribution. It is based on the rules of probability.

The key is to organize the data into meaningful criteria, and formulate a mathematical model or hypothesis that will, when tested on the data, render meaningful results and add to understanding. Knowing the limitations is a necessary part of the process. No model will provide all the answers, and no model will explain the phenomena. No hypothesis or model proves anything, as that is not the purpose of statistical analysis. The goal is to determine if there is a systematic element amid the random noise, and to identify the systematic component and the extent to which it is different, if at all, from the random component. The purposes are for prediction, explanation, description or criteria for further study and refinement. The computations, as the following will show, are simple. More difficult is characterizing the data in ways a million others have not, and getting an edge on them. One must ask the right question.

We return now to Dr. Zussman's idea of up days and down days and combine that with my idea of sales in the top of the range and on the bottom. Conventional advice is that increasing down days and down volume is bearish, and that momentum will continue. This theme is what creates those big down days like the 7th, the idea that selling will continue. My hypothesis is the opposite. What if we hypothesize the more selling at the lower end, as evidenced by down days and by days closing at lower prices in the range, exhausts the supply of available sellers, the so called 'weak hands'. Also assume that there is a pool of cash and investors who are not as exhaustible as the weak hands. This model gives us the criteria to count up/down days, and closes in up part of range or lower range as evidence of exhaustion of sellers on the idea that sellers use up their energy by down closes and driving price in low part of range. Market data is particularly computable with binary analysis due to the fact that a day is either up or down, as is your P&L. Thus the count is set as a 2x2 contingency table of up days, or closes in high or low range in binary success or failure of the criteria. A test of the proportions using the Chi squared distribution and Monte Carlo simulation computes an exact p score. Here is another amazing thing: that computers can solve the equations and do massive number crunching in a blink.

         +     -
oc+     31    21
hi/lo   21    31

The R script to test this follows.

 chisq.test(m,simulate.p.value = TRUE, B = 10000)

       Pearson's Chi-squared test with simulated p-value (based on
10000 replicates)

data:  m
X-squared = 3.8462, df = NA, p-value = 0.078

The result is not significant at the 5% level.

What does it mean? According to the hypothesis, it cannot be rejected that the sellers are getting real exhausted. So there still may be some sellers left out there. The similar 12/29 study indicated significant low end selling going on on an intraday basis. The New Year's rally followed. In any case, a fun study with good lessons for further use.

To Be Long or Not To Be Long, That Is The Question, by Tom Ryan

Inspired by Dr. Castaldo's excellent post, I thought I would write a bit about Elizabethan theater. In 2004 and 2005 I undertook in the spirit of self improvement a renewed study of Shakespeare which culminated in a part in the Arizona Theater Company's production of Macbeth. To prepare, I re-read most of the plays, read Norwich's Shakespeare's Kings, rented and viewed 11 of the film productions, and listened to 36 hours of lecture by Dr. Peter Saccio of Dartmouth. I highly recommend the lectures on CD/tape by Saccio; not only are they highly informative and insightful but are engaging and easy to listen to as well. My favorite screen adaptations are the 1935 version of A Midsummer Night's Dream, the 1953 version of Julius Caesar, the 1965 film of Othello starring Olivier, the 1966 version of the Taming of the Shrew with Richard Burton, the 1979 version of Macbeth with Ian McClellan and Judi Dench, and all three of the 1990's films by Kenneth Branagh, in particular his Henry V.

While refraining from praise, criticism, or analysis, I would like to point out that there are some interesting structural parallels between speculating and the plots of Shakespeare's plays. Although the plays have traditionally been characterized as "Comedies", "Histories", and "Tragedies", these distinctions are quite arbitrary in many respects as the comedies can have humorous (Taming of the Shrew) and tragic (12th night) endings, the histories can end in calamity (Richard III) or victory (Henry V), and the tragedies can be resolved heroically (Malcolm regaining the throne in Macbeth) or terribly (Othello's suicide). The much better description of most of Shakespeare's plays is that they are "test of character plays"; even where the plot involves mainly farce there are usually several important underlying issues that are examined thru the actions of a few main characters. All of the plays occur in five acts, and in each play the first act introduces us to the problem which must be resolved before the end of the play. Much like Beethoven's first movements often set the stage for the remainder of the symphony, Shakespeare does likewise in all his plays. The themes involve desire and one's ability or inability to fulfill that desire whether the desire is for a lover, political power, or money. Obstacles to fulfillment are placed within the plot, sometimes these are external, but mostly they are internal as hard choices are forced upon the main characters as events unfold. How the characters respond to situations and what choices they make is what makes all of the plays interesting and relevant to us 400 years after their first production.

One of the principal techniques that causes us to come back to these plays time and time again is that Shakespeare simultaneously uses both private and public dialogue. Shakespeare explores in nearly every play the dichotomy between public and private behavior (Romeo and his secret love for Juliet, Angelo publicly punishing people for the same sins he conducts in private in Measure for Measure). This allows the audience to see into the inner workings of the characters minds while following the overall external action as it unfolds (for a notable example we have Hamlet). Technically, Shakespeare invented the individual soliloquy which really does not play a role in classical Greek theater, and often he intermingles within the same scene private conversation on one part of the stage with public dialogue on another.

The reason why this technique is so important and should be of interest to speculators is that it facilitates the main theme in all of the plays no matter what category they might be placed, which is an awakening, or self realization (anagnorisis) by one or more of the main characters during the course of the play. It is also a reason why the metaphysical references (ghosts) to heaven and hell exist in many of the plays, as the changes and self realizations are presented literally as soul defining moments. One of the distinguishing characteristics between the tragic endings and the heroic endings in the plays is often the timing when this sudden anagnorisis occurs, usually too late in the tragic cases. To emphasize the importance of the anagnorisis, Shakespeare also uses other contrasting characters who make no progress at all in their personal growth, including some of his more famous supporting characters such as Iago in Othello, Malvolio in 12th night, Shylock in the Merchant of Venice, and Falstaff in Henry IV.

The captivating feature with these plays is that the audience also undergoes a type of anagnorisis in parallel with the plot and develops a clearer picture of the true nature of the main characters as the plays unfold. More importantly, this understanding always occurs for the audience before the characters actually come to the see it in themselves. Hence this tension is what creates the buildup and drama no matter what category the play might be in. By the end of Act V some version of this self realization finally occurs on stage resolving the plot one way or another, with one of the more famous being King Lear on his death bed after havoc has claimed his kingdom, "Oh I am a very foolish fond old man".

I find the parallels with speculating almost too numerous to mention, what with the daily themes generally presented at the open, the numerous obstacles that accost us at each turn during the course of the day or week and then the final moment of truth at the close. The key note here being that in speculating, there is also both a public and private dialogue going on between the speculators, the news, and the market price, and the process of price discovery is not unlike the process of self realization presented in the plays. As speculators and traders we are always on a journey of self realization as to whether we are correct or false in our positions, whether we are deluding ourselves with false beliefs or if our compass is properly aligned, and whether we can be remain humble in our few victories and resilient from our many mistakes. All the traders are indeed on a big stage yet trading is a very personal business, and we feel the same arrows of fortune as people in Elizabethan times felt.

Fibonacci's immortal contribution to Finance, by Alex Castaldo

Leonardo of Pisa, known as Fibonacci (1170-1204) wrote Liber Abaci in 1202. It was intended as a practical mathematics book, with business examples such as the division of profits among venture partners or conversions from one currency to another (with no central govt, there existed 28 different currencies in Italy alone). According to friend-of-chair William Goetzmann, Fibonacci developed the concept of Present Value of a stream of payments 700 years before Irving Fisher.

Italian traveling merchants of the Middle Ages would invest their capital in locally produced goods, then travel to another city where they would sell the goods at a profit, spend some of the proceeds on personal expenses and reinvest the remaining capital in other goods. Then on to another city.

Goetzmann quotes Fibonacci:

"A man proceeded to Lucca on business and doubled his money, and he spent there 12 denari. He then left and went to Florence; he there doubled his money and spent 12 denarii. Then he returned to Pisa, again doubled his money, spent 12, and it is assumed that he had nothing left. It is sought: how much he had at the beginning"

In modern terms Fibonacci is asking what is the present value of (12,12,12) at a discount rate of 50%. Fibonacci multiplies the periodic cash flow of 12 by the sum of individual discount factors (1/2 + 1/4 + 1/8) to come up with the answer 10.5 denari.

In this first example the numbers are artificially chosen to make the calculation easy; in more than 20 other examples that follow, Fibonacci generalizes to allow for different cash flows at different stages, different rates of return at each stop, or an extra cash flow at the end. Routine stuff for today's MBA, but pretty impressive for 800 years ago.

This, Goetzmann tells us, was Fibonacci's most important contribution: the development of Present Value, at least in a simple form. Later, in 1558, J. Trenchant would take the next step and analyze annuities, perpetuities, etc. Fibonacci made other contributions, such as convincing business people to use Arabic numerals and abandon Roman numerals, but 'retracement levels' was not one of them.

Rogue Waves, by Michel Olagnon

For a Biography of Michael Olagnon

Last spring, I had some discussions with Bruno Ombreux on statistics, processes and rogue waves. At that time, he pointed me to your site and to the discussion that you had on rogue waves.

Rogue waves can be characterized as being "higher and/or more severe than expected". Such a definition questions above all what our normal expectations are. Recently, a number of researchers, especially in the MAXWAVE project, have taken laypersons' (and at the same time, naval architects') expectations as the reference, and found that there were many more rogue waves than those expectations would suggest. They thus went on investigating theories to explain those freak waves, the "ones from nowhere".

A few other groups, including my own, have analyzed those expectations as well as some theoretical results of the mathematicians, and the results are:

  1. Most expectations are wrong, without the need to call for advanced theories. There are no more high waves than the simple theories predict. Seafarers, and probably traders as well, just wrongly put some sort of implicit bounds on extremes that might occur at a given time when they are observing the ocean surface (or the markets). According to conventional theories, there are no bounds whatsoever on what may happen, and in fact observers should rather expect to be surprised.
  2. Though there are no more freak waves as a whole than simple models predict, it is still possible and even likely that their occurrences are not purely random, and it is of utmost importance to understand where and when is going to be the next wrong place at the next wrong time, and why.
  3. Theories such as Non-Linear Schroedinger (NLS) are consistent, they may even be perfectly correct models at the time and location of a rogue wave, but their extent of validity is limited in time and space to a small neighborhood. They thus should not be used to derive statistics.
  4. A freak wave does not suck energy from its neighbors. It looks as if, but the energy gets concentrated at the time and location of the wave by pure chance and determinism from the initial conditions, there is no active transfer originating in the wave.
  5. NLS is governed by Benjamin-Feir Instability. An analog of that instability index can be computed for markets. Instability is driven by spectral width (how similar the wave-lengths of the various wave trains are) and by wave steepness (how short the waves are with respect to their heights). I have found some plots showing Benjamin-Feir Instability for the Nasdaq100 on to 2006/01/27, at one-minute rate and for the Nasdaq composite over the last 20 years or so.

As far as I can tell, the results are very similar to what we see with ocean waves: "unexpected waves" are correlated with excursions of B-F instability from normal, but there is no clear causal relationship. I would compare B-F instability levels to avalanche warnings in the mountains, as avalanches and warnings are correlated, but an avalanche does not mean a warning was issued nor a warning that an avalanche will indeed occur. In addition, many warnings come too late.

A Letter on Industrial Logic, from a reader

Dear Mr. Niederhoffer & Ms. Kenner,

Since reading your book, I have continued to keep an eye on your website. Counting has certainly helped me figure some trades out and walk away from others.

The reason for writing today is to point out something to you which if it weren't true, could have been written by Ayn Rand as part of her fictional writings.

The way the European governments have sought to defend Arcelor from a hostile takeover by Mittal Steel (which I believe is very compelling), is shocking. Short of actually going out and shooting Mr. Mittal, these so called gentlemen of Europe have sought to muddy his character, his business acumen, his brilliance as a corporate visionary, his son's very obvious role as protegé, charmer and heir apparent. They have used words such as monkey man / monkey money to show their innate racism and snobbery at a man who is very much not an establishment thinker.

My favorite though is industrial logic. Finance Minister Thierry Breton says the deal defies any industrial logic (repeated today by President Chirac) - this comes from the man who presided over Thomson SA from 1997 to 2002. In which period Thomson touched a high of 80 and then collapsed to 7 again. Sure, there was the old TMT bubble going on at the same, but really, is this the man you want running the finances of one of the largest countries of the world? Are these guys thick or what? They can't show the precise savings they will create, because the management (ie Socialist Managers) at Arcelor won't let them in to do the due diligence !

At the same time, all of these men are happy for Arcelor to buy Dofasco in Canada. Note Dofasco was initially a hostile deal as well before enough enough Euros were promised.

In Europe, they have discovered a new word that I believe is just a euphemism for the old socialist interest groups: "Stakeholders". It is under the umbrella of "stakeholders" that Luxembourg is trying to defend Arcelor by pushing a poison pill law through. There are 6000 employees at the steel mill in Luxemborg I believe (could be wrong). In a country of 450,000 people and a coalition government, I guess a group of people who are 1.5% of the population are enough to cause a major protectionist tantrum. I concede however, that Luxemborg is still a shareholder unlike France so are entitled to whine and moan.

Although not a rags to riches story, Mr. Mittal has over the years exhibited enough business acumen that he should be revered in the same manner as some of his more well established luminaries on the "richest men in the world" list. I would say even more so, as he's done it in an old world /commoditized industry that everyone thought was finished and even now even now every one says is finished because of the cursed Chinese threat. Is there anything you can't blame the Chinese for in the Old or New World?

Finally, I would suggest to you that these guys with their protectionist, racist, deeply ingrained philosophies are probably worth a place in Atlas Shrugged as the socialist defenders of industry.

A Letter on Destructive Memes, from Shane James

Dear Dr. Niederhoffer,

Let us look at one segment of the meme factory and focus on one area of their prodigious production; Investment banks and medium term currency forecasting (let's use EUR USD spot). Having just left the banking side for the Hedge Fund after some years I feel I can say the following with confidence:

At any discrete (time zero) moment the EUR USD has a value and there are various banks with various medium term views about the direction of the EUR USD. These views would be espoused in, generally, the institutions monthly publication.

As the market moves away from this level (up or down) the initial reaction from the forecasters (communicated through the shorter term weekly 'research' pieces) will be to justify why the medium term view is still correct.

Should the market now accelerate further away from the initial status quo then the denial will spread to monthly type publications featuring a variety of non testable and non tradable concepts to further underpin the view.

In the meantime any firm whose view was wrong at time zero will start to adjust their view in the direction of the price action. Not, mind you, because the 'fundamentals' have changed but more to be in line with the peer group. This process continues until most forecasters support the meme.

It would be nice at this point to say, and now the market stops and reverses back in the other direction. In practice the market will continue in the direction of the meme for a time before some brave souls countenance a trend change.

This contrarian call will be the signal for an acceleration in the move -- making the meme's sponsors rejoice as their obviously long held views come to fruition!

Soon after, qualitatively, we have the conditions for the turn. And then our counting begins......

Key points:

  1. The results from following the meme sponsors' views mirror those of the returns to be achieved using a moving-average-type momentum approach.
  2. Bank research fits all the Delphi-like principles put forth in the Chair's books (Ed Spec. and Prac Spec.) Indeed, and perhaps in a different time, certain banks' research was a short term signal to go against -- immediately -- their views once published. I wonder, Dr., if you remember a certain US bank's research on the AUD USD rate in the early 1990s.

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