| Home | My photos | Forex | My trading | Contacts |
|
|
You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
|
Investors on Wall Street see for themselves that when a person in the long line chooses to take both portfoliosI reiterate that this approach to stock price movements is rather stark, but it does nevertheless locate the debate. People who believe there is some pattern to the market, whether exploitable or not, will believe that its movements are characterized by sequences of complexity somewhere between those of type two and type three above. A rough paraphrase of Kurt Godels famous incompleteness theorem of mathematical logic, due to the aforementioned Gregory Chaitin, provides an interesting sidelight on this issue. It states that if the market were random, we might not be able to prove it. The reason: encoded as a sequence of Os and 1s, a random market would, it seems plausible to assume, have complexity greater than that of our own were we also so encoded; it would be beyond our complexity horizon. From the definition of complexity it follows that a sequence cant generate another sequence of greater complexity than itself. Thus if a person were to predict the random markets exact gyrations, the market would have to be less complex than the person, contrary to assumption. Even if the market isnt random, there remains the possibility that its regularities are so complex as to be beyond our complexity horizons. In any case, there is no reason why the complexity of price movements as well as the complexity of investor/computer blends cannot change over time. The more inefficient the market is, the smaller the complexity of its price movements, and the more likely it is that tools from technical and fundamental analysis will prove useful. Conversely, the more efficient the market is, the greater the complexity of price movements, and the closer the approach to a completely random sequence of price changes. Outperforming the market requires that one remain on the cusp of our collective complexity horizon. It requires faster machines, better data, improved models, and the smarter use of mathematical tools, from conventional statistics to neural nets (computerized learning networks, the connections between the various nodes of which are strengthened or weakened over a period of training). If this is possible for anyone or any group to achieve, its not likely to remain so for long. Game Theory and Supernatural Investor/Psychologists But what if, contrary to fact, there were an entity possessing sufficient complexity and speed that it was able with reasonably high probability to predict the market and the behavior of individuals within it? The mere existence of such an entity leads to Newcombes paradox, a puzzle that calls into question basic principles of game theory. My particular variation of Newcombes paradox involves the World Class Options Market Maker (WCOMM), which (who?) claims to have the power to predict with some accuracy which of two alternatives a person will choose. Imagine further that WCOMM sets up a long booth on Wall Street to demonstrate its abilities. WCOMM explains that it tests people by employing two portfolios. Portfolio A contains a $1,000 treasury bill, whereas portfolio B (consisting of either calls or puts on WCOM stock) is either worth nothing or $1,000,000. For each person in line at the demonstration, WCOMM has reserved a portfolio of each type at the booth and offers each person the following choice: He or she can choose to take portfolio B alone or choose to take both portfolios A and B. However, and this is crucial, WCOMM also states that it has used its unfathomable powers to analyze the psychology, investment history, and trading style of everyone in line as well as general market conditions, and if it believes that a person will take both portfolios, it has ensured that portfolio B will be worthless. On the other hand, if WCOMM believes that a person will trust its wisdom and take only portfolio B, it has ensured that portfolio B will be worth $1,000,000. After making these announcements, WCOMM leaves in a swirl of digits and stock symbols, and the demonstration proceeds. Investors on Wall Street see for themselves that when a person in the long line chooses to take both portfolios, most of the time (say with probability 90 percent) portfolio B is worthless and the person gets only the $1,000 treasury bill in portfolio A. They also note that when a person chooses to take the contents of portfolio B alone, most of the time its worth $1,000,000. After watching the portfolios placed before the people in line ahead of me and seeing their choices and the consequences, Im finally presented with the two portfolios prepared for me by WCOMM. Despite the evidence Ive seen, I see no reason not to take both portfolios. WCOMM is gone, perhaps to the financial district of London or Frankfurt or Tokyo, to make similar offers to other investors, and portfolio B is either worth $1,000,000 or not, so why not take both portfolios and possibly get $1,001,000. Alas, WCOMM read correctly the skeptical smirk on my face and after opening my portfolios, I walk away with only $1,000. My portfolio B contains call options on WCOM with a strike price of 20, when the stock itself is selling at $1.13. The paradox, due to the physicist William Newcombe (not the Newcomb of Benfords Law, but the same mocking fourletters WCOM) and made well-known by the philosopher Robert Nozick, raises other issues. As mentioned, it makes problematical which of two game-theoretic principles one should use in making decisions, principles that shouldnt conflict. The dominance principle tells us to take both portfolios since, whether portfolio B contains options worth $1,000,000 or not, the value of two portfolios is at least as great as the value of one. (If portfolio B is worthless, $1,000 is greater than $0, and if portfolio B is worth $1,000,000, $1,001,000 is greater than $1,000,000.) On the other hand, the maximization of expected value principle tells us to take only portfolio B since the expected value of doing so is greater. (Since WCOMM is right about 90 percent of the time, the expected value of taking only portfolio B is (.90 x $1,000,000) + (.10 x $0), or $900,000, whereas the expected value of taking both is (.10 x $1,001,000) + (.90 x $1,000), or $101,000.) The paradox is that both principles seem reasonable, yet they counsel different choices. This raises other general philosophical matters as well, but it reminds me of my resistance to following the WCOM fleeing crowd, most of whose B portfolios contained puts on the stock worth $1,000,000. One conclusion that seems to follow from the above is that such supernatural investor/psychologists are an impossibility. For better or worse, were on our own. Absurd Emails and the WorldCom Denouement A natural reaction to the vagaries of chance is an attempt at control, which brings me to emails regarding WorldCom that, Herzog-like, I sent to various influential people. I had grown tired of carrying on one-sided arguments with CNBCs always perky Maria Bartiromo and always apoplectic James Cramer as they delivered the relentlessly bad news about WorldCom. So in fall 2001, five or six months before its final swoon, I contacted a number of online business commentators critical of WorldComs past performance and future prospects. Having spent too much time in the immoderate atmosphere of WorldCom chatrooms, I excoriated them, though mildly, for their shortsightedness and exhorted them to look at the company differently. Finally, out of frustration with the continued decline of WCOM stock, I emailed Bernie Ebbers, then the CEO, in early stating its case and quixotically offering to help by writing copy. I said Id invested heavily in WorldCom, as did family and friends at my suggestion, that I could be a persuasive wordsmith when I believed in something, and WorldCom, I believed, was well positioned but dreadfully undervalued. UUNet, the backbone of much of the Internet, was, I fatuously informed the CEO of the company, a gem in and of itself. I knew, even as I was writing them, that sending these electronic epistles was absurd, but it gave me the temporary illusion of doing something about this recalcitrant stock other than dumping it. Investing in it had originally seemed like a no-brainer. The realization that doing so had indeed been a no-brainer was glacially slow in arriving. During the 2001-2002 academic year, I took the train once a week from Philadelphia to New York to teach a course on numbers in the news at the Columbia School of Journalism. Spending the two and a half hours of the commute out of contact with WCOMs volatile movements was torturous, and upon emerging from the subway, Id run to my office computer to check what had happened. Not exactly the behavior of a sage long-term investor; my conduct even then suggested to me a rather dim-witted addict. Recalling the two or three times I almost got out of the stock is dispiriting as well. The last time was in April 2002. Amazingly, I was even then still somewhat in thrall to the idea of averaging down, and when the price dipped below $5, I bought more WCOM shares. Around the middle of the month, however, I did firmly and definitively resolve to sell. By Friday, April 19, WCOM had risen to over $7, which would have allowed me to recoup at least a small portion of my losses, but I didnt have time to sell that morning. I had to drive to northern New Jersey to give a long-promised lecture at a college there. When it was over, I wondered whether to return home to sell my shares or simply use the colleges computer to log onto my Schwab account to do so. I decided to go home, but there was so much traffic on the cursed New Jersey turnpike that afternoon that I didnt arrive until 4:05, after the market had closed. I had to wait until Monday. Investors are often nervous about holding volatile stocks over the weekend, and I was no exception. My anxiety was well-founded. Later that evening there was news about impending cuts in WorldComs bond ratings and another announcement from the SEC regarding its comprehensive investigation of the company. The stock lost more than a third of its value by Monday, when I did finally sell the stock at a huge loss. A few months later the stock completely collapsed to $.09 upon revelations of massive accounting fraud. Why had I violated the most basic of investing fundamentals: Dont succumb to hype and vaporous enthusiasm; even if you do, dont put too many eggs in one basket (especially with the uncritical sunny-side up); even if you do this, dont forget to insure against sudden drops (say with puts, not calls); and even if you do this too, dont buy on margin. After selling my shares, I felt as if I were gradually and groggily coming out of a self-induced trance. Id long known about one of the earliest stock hysterias on record, the seventeenth century tulip bulb craze in Holland. After its collapse, people also spoke of waking up and realizing that they were stuck with nearly worthless bulbs and truly worthless options to buy more of them. I smiled ruefully at my previous smug dismissal of people like the tulip bulb investors. I was as vulnerable to transient delirium as the dimmest bulb-buying bulbs. Ive followed the ongoing drama of the WorldCom storythe fraud investigations, various prosecutions, new managers, promised reforms, and court settlements-and, oddly perhaps, the publicity surrounding the scandals and their aftermath has distanced me from my experience and lessened its intensity. My losses have become less a small personal story and more (a part of) a big news story, less a result of my mistakes and more a consequence of the companys behavior. This shifting of responsibility is neither welcome nor warranted. For reasons of fact and of temperament, I continue to think of myself as having been temporarily infatuated rather than deeply victimized. Remnants of my fixation persist, and I still sometimes wonder what might have happened if WorldComs deal with Sprint hadnt been foiled, if Ebbers hadnt borrowed $400 million (or more), if Enron hadnt imploded, if this or that or the other event hadnt occurred before I sold my shares. My recklessness might then have been seen as daring. Post hoc stories always seem right, whatever the pre-existing probabilities. One fact remains incontrovertible: Narratives and numbers coexist uneasily on Wall Street. Markets, like people, are largely rational beasts occasionally provoked and disturbed by their underlying animal spirits. The mathematics discussed in this book is often helpful in understanding (albeit not beating) the market, but Id like to end with a psychological caveat. The basis for the application of the mathematical tools discussed herein is the sometimes shifty and always shifting attitudes of investors. Since these psychological states are to a large extent imponderable, anything that depends on them is less exact than it appears. The situation reminds me a bit of the apocryphal story of the way cows were weighed in the Old West. First the cowboys would find a long, thick plank and place the middle of it on a large, high rock. Then theyd attach the cow to one end of the plank with ropes and tie a large boulder to the other end. Theyd carefully measure the distance from the cow to the rock and from the boulder to the rock. If the plank didnt balance, theyd try another big boulder and measure again. Theyd keep this up until a boulder exactly balanced the cattle. After solving the resulting equation that expresses the cows weight in terms of the distances and the weight of the boulder, there would be only one thing left for them to do: They would have to guess the weight of the boulder. Once again the mathematics may be exact, but the judgments, guesses, and estimates supporting its applications are anything but. More apropos of the self-referential nature of the market would be a version in which the cowboys had to guess the weight of the cow whose weight varied depending on their collective guesses, hopes, and fears. Bringing us full circle to Keyness beauty contest, albeit in a rather forced, more bovine mode, I conclude that despite rancid beasts like WorldCom, Im still rather fond of the pageant that is the market. I just wish I had a better (and secret) method for weighing the cows. |
|
|||||||||||||
Previous Issues
|
| ©2007 Olesia | Home • My photos • Forex • News • My trading • Contacts |