| Home | My photos | Forex | My trading | Contacts |
|
|
You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
|
Investors who notice some exploitable stock market anomaly may either act on it, thereby diminishing its effectivenessFrom Paradox to Complexity Groucho Marx vowed that hed never join a club that would be willing to accept him as a member. Epimenides the Cretan exclaimed (almost) inconsistently, All Cretans are liars. The prosecutor booms, You must answer Yes or No. Will your next word be `No? The talk show guest laments that her brother is an only child. The author of an investment book suggests that we follow the tens of thousands of his readers who have gone against the crowd. Warped perhaps by my study of mathematical logic and its emphasis on paradoxes and self-reference, Im naturally interested in the paradoxical and self-referential aspects of the market, particularly of the Efficient Market Hypothesis. Can it be proved? Can it be disproved? These questions beg a deeper question. The Efficient Market Hypothesis is, I think, neither necessarily true nor necessarily false. The Paradoxical Efficient Market Hypothesis If a large majority of investors believe in the hypothesis, they would all assume that new information about a stock would quickly be reflected in its price. Specifically, they would affirm that since news almost immediately moves the price up or down, and since news cant be predicted, neither can changes in stock prices. Thus investors who subscribe to the Efficient Market Hypothesis would further believe that looking for trends and analyzing companies fundamentals is a waste of time. Believing this, they wont pay much attention to new developments. But if relatively few investors are looking for an edge, the market will not respond quickly to new information. In this way an overwhelming belief in the hypothesis ensures its falsity. To continue with this cerebral somersault, recall now a rule of logic: Sentences of the form H implies I are equivalent to those of the form not I implies not H. For example, the sentence heavy rain implies that the ground will be wet is logically equivalent to dry ground implies the absence of heavy rain. Using this equivalence, we can restate the claim that overwhelming belief in the Efficient Market Hypothesis leads to (or implies) its falsity. Alternatively phrased, the claim is that if the Efficient Market Hypothesis is true, then its not the case that most investors believe it to be true. That is, if its true, most investors believe it to be false (assuming almost all investors have an opinion and each either believes it or disbelieves it). Consider now the inelegantly named Sluggish Market Hypothesis, the belief that the market is quite slow in responding to new information. If the vast majority of investors believe the Sluggish Market Hypothesis, then they all would believe that looking for trends and analyzing companies is well worth their time and, by so exercising themselves, they would bring about an efficient market. Thus, if most investors believe the Sluggish Market Hypothesis is true, they will by their actions make the Efficient Market Hypothesis true. We conclude that if the Efficient Market Hypothesis is false, then its not the case that most investors believe the Sluggish Market Hypothesis to be true. That is, if the Efficient Market Hypothesis is false, then most investors believe it (the EMH) to be true. (You may want to read over the last few sentences in a quiet corner.) In summary, if the Efficient Market Hypothesis is true, most investors wont believe it, and if its false, most investors will believe it. Alternatively stated, the Efficient Market Hypothesis is true if and only if a majority believes it to be false. (Note that the same holds for the Sluggish Market Hypothesis.) These are strange hypotheses indeed! Of course, Ive made some big assumptions that may not hold. One is that if an investor believes in one of the two hypotheses, then he disbelieves in the other, and almost all believe in one or the other. Ive also assumed that its clear what large majority means, and Ive ignored the fact that it sometimes requires very few investors to move the market. (The whole argument could be relativized to the set of knowledgeable traders only.) Another gap in the argument is that any suspected deviations from the Efficient Market Hypothesis can always be attributed to mistakes in asset pricing models, and thus the hypothesis cant be conclusively rejected for this reason either. Maybe some stocks or kinds of stock are riskier than our pricing models allow for and thats why their returns are higher. Nevertheless, I think the point remains: The truth or falsity of the Efficient Market Hypothesis is not immutable but depends critically on the beliefs of investors. Furthermore, as the percentage of investors who believe in the hypothesis itself varies, the truth of the hypothesis varies inversely with it. On the whole, most investors, professionals on Wall Street, and amateurs everywhere, disbelieve in it, so for this reason I think it holds, but only approximately and only most of the time. The Prisoners Dilemma and the Market So you dont believe in the Efficient Market Hypothesis. Still, its not enough that you discover simple and effective investing rules. Others must not find out what youre doing, either by inference or by reading your boastful profile in a business magazine. The reason for secrecy, of course, is that without it, simple investing rules lead to more and more complicated ones, which eventually lead to zero excess returns and a reliance on chance. This inexorable march toward increased complexity arises from the actions of your co-investors, who, if they notice (or infer, or are told) that you are performing successfully on the basis of some simple technical trading rule, will try to do the same. To take account of their response, you must complicate your rule and likely decrease your excess returns. Your more complicated rule will, of course, also inspire others to try to follow it, leading to further complications and a further decline in excess returns. Soon enough your rule assumes a near-random complexity, your excess returns are reduced essentially to zero, and youre back to relying on chance. Of course, your behavior will be the same if you learn of someone elses successful performance. In fact, a situation arises that is clarified by the classic prisoners dilemma, a useful puzzle originally framed in terms of two people in prison. Suspected of committing a major crime, the two are apprehended in the course of committing some minor offense. Theyre then interrogated separately, and each is given the choice of confessing to the major crime and thereby implicating his partner or remaining silent. If they both remain silent, theyll each get one year in prison. If one confesses and the other doesnt, the one who confesses will be rewarded by being set free, while the other one will get a five-year term. If they both confess, they can both expect to spend three years in prison. The cooperative option (cooperative with the other prisoner, that is) is to remain silent, while the non-cooperative option is to confess. Given the payoffs and human psychology, the most likely outcome is for both to confess; the best outcome for the pair as a pair is for both to remain silent; the best outcome for each prisoner as an individual is to confess and have ones partner remain silent. The charm of the dilemma has nothing to do with any interest one might have in prisoners rights. (In fact, it has about as much relevance to criminal justice as the four-color-map theorem has to geography.) Rather, it provides the logical skeleton for many situations we face in everyday life. Whether were negotiators in business, spouses in a marriage, or nations in a dispute, our choices can often be phrased in terms of the prisoners dilemma. If both (all) parties pursue their own interests exclusively and do not cooperate, the outcome is worse for both (all) of them; yet in any given situation, any given party is better off not cooperating. Adam Smiths invisible hand ensuring that individual pursuits bring about group well-being is, at least in these situations (and some others), quite arthritic. The dilemma has the following multi-person market version: Investors who notice some exploitable stock market anomaly may either act on it, thereby diminishing its effectiveness (the non-cooperative option) or ignore it, thereby saving themselves the trouble of keeping up with developments (the cooperative option). If some ignore it and others act on it, the latter will receive the biggest payoffs, the former the smallest. As in the standard prisoners dilemma, the logical response for any player is to take the non-cooperative option and act on any anomaly likely to give one an edge. This response leads to the arms race of ever more complex technical trading strategies. People search for special knowledge, the result eventually becomes common knowledge, and the dynamic between the two generates the market. This searching for an edge brings us to the social value of stock analysts and investment professionals. Although the recipients of an abundance of bad publicity in recent years, they provide a most important service: By their actions, they help turn special knowledge into common knowledge and in the process help make the market relatively efficient. Absent a draconian rewiring of human psychology and an accompanying draconian rewiring of our economic system, this accomplishment is an impressive and vital one. If it means being noncooperative with other investors, then so be it. Cooperation is, of course, generally desirable, but cooperative decisionmaking among investors seems to smack of totalitarianism. Pushing the Complexity Horizon The complexity of trading rules admits of degrees. Most of the rules to which people subscribe are simple, involving support levels, P/E ratios, or hemlines and Super Bowls, for example. Others, however, are quite convoluted and conditional. Because of the variety of possible rules, I want to take an oblique and abstract approach here. The hope is that this approach will yield insights that a more pedestrian approach misses. Its key ingredient is the formal definition of (a type of) complexity. An intuitive understanding of this notion tells us that someone who remembers his eight-digit password by means of an elaborate, long-winded saga of friends addresses, childrens ages, and special anniversaries is doing something silly. Mnemonic rules make sense only when theyre shorter than what is to be remembered. Lets back up a bit and consider how we might describe the following sequences to an acquaintance who couldnt see them. We may imagine the l s to represent upticks in the The first sequence is the simplest, an alternation of Os and 1s. The second sequence has some regularity to it, a single 0 alternating sometimes with a 1, sometimes with two 1s, while the third sequence doesnt seem to manifest any pattern at all. Observe that the precise meaning of . . . in the first sequence is clear; it is less so in the second sequence, and not at all clear in the third. Despite this, lets assume that these sequences are each a trillion bits long (a bit is a 0 or a 1) and continue on in the same way. Motivated by examples like this, the American computer scientist Gregory Chaitin and the Russian mathematician A. N. Kolmogorov defined the complexity of a sequence of Os and 1 s to be the length of the shortest computer program that will generate (that is, print out) the sequence in question. A program that prints out the first sequence above can consist simply of the following recipe: print a 0, then a 1, and repeat a half trillion times. Such a program is quite short, especially compared to the long sequence it generates. The complexity of this first trillion-bit sequence may be only a few hundred bits, depending to some extent on the computer language used to write the program. A program that generates the second sequence would be a translation of the following: Print a 0 followed by either a single 1 or two 1s, the pattern of the intervening l s being one, two, one, one, one, two, one, one, and so on. Any program that prints out this trillion-bit sequence would have to be quite long so as to fully specify the and so on pattern of the intervening 1s. Nevertheless, because of the regular alternation of Os and either one or two 1s, the shortest such program will be considerably shorter than the trillion-bit sequence it generates. Thus the complexity of this second sequence might be only, say, a quarter trillion bits. With the third sequence (the commonest type) the situation is different. This sequence, let us assume, remains so disorderly throughout its trillion-bit length that no program we might use to generate it would be any shorter than the sequence itself. It never repeats, never exhibits a pattern. All any program can do in this case is dumbly list the bits in the sequence: print 1, then 0, then 0, then 0, then 1, then 0, then 1, . There is no way the ... can be compressed or the program shortened. Such a program will be as long as the sequence its supposed to print out, and thus the third sequence has a complexity of approximately a trillion. A sequence like the third one, which requires a program as long as itself to be generated, is said to be random. Random sequences manifest no regularity or order, and the programs that print them out can do nothing more than direct that they be copied: print 1 0 0 0 1 0 1 1 0 1 1 ... . These programs cannot be abbreviated; the complexity of the sequences they generate is equal to the length of these sequences. By contrast, ordered, regular sequences like the first can be generated by very short programs and have complexity much less than their length. Returning to stocks, different market theorists will have different ideas about the likely pattern of Os and 1s (downs and upticks) that can be expected. Strict random walk theorists are likely to believe that sequences like the third characterize price movements and that the markets movements are therefore beyond the complexity horizon of human forecasters (more complex than we, or our brains, are, were we expressed as sequences of Os and 1s). Technical and fundamental analysts might be more inclined to believe that sequences like the second characterize the market and that there are pockets of order amidst the noise. Its hard to imagine anyone believing that price movements follow sequences as regular as the first except, possibly, those who send away only $99.95 for a complete set of tapes that explain this revolutionary system. |
|
|||||||||||||
Previous Issues
|
| ©2007 Olesia | Home • My photos • Forex • News • My trading • Contacts |