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You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
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Selling by both influential investors triggers a general sell-offConnectedness and Chaotic Price Movements The end of my involvement with WorldCom, when I as particularly concerned about what the new day would bring, I would sometimes wake up very early, grab a Diet Coke, and check how the stock was faring on the German or English exchanges. As the computer was booting up, I grew more and more apprehensive. The European response to bad overnight news sometimes prefigured Wall Streets response, and I dreaded seeing a steeply downward-sloping graph pop up on my screen. More often the European exchanges treaded water on WCOM until trading began in New York. Occasionally Id be encouraged when the stock was up there, but I soon learned that the small volume sold on overseas exchanges didnt always mean much. Whether haunted by a bad investment or not, were all connected. No investor is an island (or even a peninsula). Stated mathematically, this means that statistical independence often fails; your actions affect mine. Most accounts of the stock market acknowledge in a general way that we learn from and respond to one another, but a better understanding of the market requires that ones models reflect the complexity of investors interaction. In a sense, the market is the interaction. Stocks R Us. Before discussing some of the consequences of this complexity, let me consider three such sources for it: one micro, one macro, and the third mucro (yup, its a word). The micro example involves insider trading, which has always struck me as an odd sort of crime. Few people who arent psychopaths daydream about murder or burglary, but many investors, I suspect, fantasize about coming upon inside information and making a bundle from it. The thought of finding myself on a plane next to Bernie Ebbers and Jack Grubman (assuming they flew economy class on commercial airliners) and overhearing their conversation about an impending merger or IPO offering, for example, did cross my mind a few times. Insider trading seems the limit or culmination of what investors and traders do naturally: getting all the information possible and acting on it before others see and understand what they see and understand. Insider Trading and Subterranean Information Processing The kind of insider trading I want to consider is relevant to seemingly unexplained price movements. Its also related to good poker playing, which may explain why the training program of at least one very successful hedge fund has a substantial unit on the game. The strategies associated with poker include learning not only the relevant probabilities but also the bluffing that is a necessary part of the game. Options traders often deal with relatively few other traders, many of whom they recognize, and this gives rise to the opportunity for feints, misdirection, and the exploitation of idiosyncrasies. The example derives from the notion of common knowledge introduced in chapter 1. Recall that a bit of information is common knowledge among a group of people if they all know it, know that the others know it, know that the others know that they know it, and so on. Robert Aumann, who f i rst defined the notion, proved a theorem that can be roughly paraphrased as follows: Two individuals cannot forever agree to disagree. As their beliefs, formed in rational response to different bits of private information, gradually become common knowledge, the beliefs change and eventually coincide. When private information becomes common knowledge, it induces decisions and actions. As anyone who has overheard teenagers gossip with its web of suppositions can attest, this transition to common knowledge sometimes relies on convoluted inferences about others beliefs. Sergiu Hart, an economist at Hebrew University and one of a number of people who have built on Aumanns result, demonstrates this with an example relevant to the stock market. Superficially complicated, it nevertheless requires no particular background besides an ability to decode gossip, hearsay, and rumor and decide what others really think. Hart asks us to consider a company that must make a decision. In keeping with the WorldCom leitmotif, lets suppose it to be a small telecommunications company that must decide whether to develop a new handheld device or a cell phone with a novel feature. Assume that the company is equally likely to decide on one or the other of these products, and assume further that whatever decision it makes, the product chosen has a 50 percent chance of being successful, say being bought in huge numbers by another company. Thus there are four equally likely outcomes: Handheld+, Handheld-, Phone+, Phone- (where Handheld+ means the handheld device was chosen for development and it was a success, Handheldmeans the handheld was chosen but it turned out to be a failure, and similarly for Phone+ and Phone-). Lets say there are two influential investors, Alice and Bob. They both decide that at the current stock price, if the chances of success of this product development are better than 50 percent, they should (continue to) buy, and if theyre 50 percent or less they should (continue to) sell. Furthermore, they are each privy to a different piece of information about the company. Because of her inside contacts, Alice knows which product decision was made, Handheld or Phone, but not whether it was successful or not. Bob, because of his position with another company, stands to get the rejects from a failed phone project, so he knows whether or not the cell phone was chosen for development and failed. That is, Bob knows whether Phone- or not. Lets assume that the handheld device was chosen for development. So the true situation is either Handheld+ or Handheld-. Alice therefore knows Handheld, while Bob knows that the decision is not Phone- (else he would have received the rejects). After the first period (week, day, or hour), Alice sells since Handheld+ and Handheld- are equally likely, and one sells if the probability of success is 50 percent or less. Bob buys since he estimates that the probability for success is 2/3. With Phone- ruled out, the remaining possibilities are Handheld+, Handheld-, and Phone+, and two out of three of them are successes. After the second period, it is common knowledge that the true situation is not Phone- since otherwise Bob would have sold in the first period. This is not news to Alice, who continues to sell. Bob continues to buy. After the third period, it is common knowledge that it is not Phone (neither Phone+ nor Phone-) since otherwise Alice would have bought in the second period. Thus its either Handheld+ or Handheld-. Both Bob and Alice take the probability of success to be 50 percent, thus both sell, and there is a mini-crash of the stock price. (Selling by both influential investors triggers a general sell-off.) Note that at the beginning both Alice and Bob know that the true situation is not Phone-, but this knowledge is mutual, not common. Alice knows that Bob knows it is not Phone-, but Bob does not know that Alice knows this. From his position the true situation might be Phone+, in which case Alice would know Phone but not whether the situation is Phone+ or Phone-. The example can be varied in a number of ways: there neednt be merely three periods before a crash, but an arbitrary number; there may be a bubble (sellers suddenly switching to become buyers) instead of a crash; there may be an arbitrarily large number of investors or investor groups; there may be an issue other than buying or selling under deliberation, perhaps a decision whether to employ one stock-picking approach rather than another. In all these cases the stocks price can move in response to no external news. Nevertheless, the subterranean information processing leading to common knowledge among the investors eventually leads to precipitous and unexpected movement in the stocks price. Analysts will express surprise at the crash (or bubble) because nothing happened. The example is also relevant to what I suspect is a relatively common kind of insider trading, in which partial insiders are privy to bits of insider information but not to the whole story. Trading Strategies, Whim, and Ant Behavior A more macro-level interaction among investors occurs between technical traders and value traders. Also contributing over time to booms and busts, this interaction comes through clearly in computer models of the following commonsense dynamic. Lets suppose that value traders perceive individual stocks or the market as a whole to be strongly undervalued. They start buying and, by doing so, raise prices. As prices increase, a trend develops and technical traders, as is their wont, follow it, increasing prices even further. Soon enough, the market is seen as overvalued by value traders, who begin to sell and thereby slow and then reverse the trend. The trendfollowing technical traders eventually follow suit, and the cycle begins over again. There are, of course, other sources of variation (one being the number of people who are technical traders and value traders at any given time), and the oscillations are irregular. The bottom line of much of this modeling is that contrarian value traders have a stabilizing effect on the market, whereas technical traders increase volatility. So does computergenerated program trading, which tends to produce buying or selling in lockstep. There are other sorts of interaction among different classes of investors leading to cycles of varying duration, all of which have differential impacts on the others on which they are superimposed. In addition to these more or less rational interactions among investors I must also note influences inspired by nothing more than whim, where behavior turns on a mucro. I recall many times, for example, reluctantly beginning work on a project when a niggling detail about some utterly irrelevant matter came to mind. It may have concerned the etymology of a word, or the colleague whose paper bag ripped open at a departmental meeting revealing an embarrassing magazine inside, or why caller ID misidentified a friends telephone number. These in turn brought to mind the next in a train of associations and musings, which ultimately led me to an entirely different project. My impulsively deciding, while browsing in Borders, to make my first margin call on WCOM is another instance. When this captiousness extends to influential analysts, the effect is more pronounced. In November 2002 the New York Times reported on such a case involving Jack Grubman, telecommunications analyst and anxious father. In an email to a friend Grubman allegedly stated that his boss, Sanford Weill, the chairman of Citigroup, helped get Grubmans children into an exclusive nursery school after he raised his rating of AT&T in 1999. Gretchen Morgenson, the articles author, further reported that Weill had his own personal reasons for wanting this upgrade. Whether these particular charges are true or not is immaterial. Its very hard to believe, however, that this sort of influence is rare. Such episodes strongly suggest to me that there will never be a precise science of finance or economics. Buying and selling must surely partake of a similar iffiness, at least sometimes. Butterfly Economics, by the British economic theorist Paul Ormerod, faults these disciplines for not sufficiently taking into account the commonsense fact that people, whether knowledgeable or not, influence each other. People do not, as chapter 2 demonstrated, have a set of fixed preferences on which they coolly and rationally base their economic decisions. The assumption that investors are sensitive only to price and a few ratios simplifies the mathematical models, but it is not always true to our experience of fads, fashions, and peoples everyday monkey-see, monkey-do behavior. Ormerod tells of an experiment involving not monkeys but ants that provides a useful metaphor. Two identical piles of food are set up at equal distances from a large nest of ants. Each pile is automatically replenished and the ants have no reason to prefer one to the other. Entomologists tell us that once an ant has found food, it usually returns to the same source. Upon returning to the nest, however, it physically stimulates other ants, who might be frequenting the other pile, to follow it to the first pile. So where do the ants go? It might be speculated that either they would split into two roughly even groups or perhaps a large majority would arbitrarily settle on one or the other pile. Their actual behavior is counterintuitive. The number of ants going to each pile fluctuates wildly and doesnt ever settle down. A graph of these fluctuations looks suspiciously like a graph of the stock market. And in a way, the ants are like stock traders (or people deciding whether or not to make a margin call). Upon leaving the nest, each ant must make a decision: Go to the pile visited last time, be influenced by another to switch piles, or switch piles of its own volition. This slight openness to the influence of other ants is enough to insure the complicated and volatile f l uctuations in the number of ants visiting the two sites. An astonishingly simple formal model of such influence is provided by Stephen Wolfram in his book A New Kind of Science. Imagine a colossally high brick wall wherein each brick rests on parts of two bricks below it and, except for the top row, has parts of two bricks above it. Imagine further that the top row has some red bricks and some green ones. The coloring of the bricks in the top row determines the coloring of the bricks in the second row as follows. Pick a brick in the second row and check the colors of the two bricks above it in the first row. If exactly one of these bricks is green, then the brick in the second row is colored green. If both or neither are green, then the brick is colored red. Do this for every brick in the second row. The coloring of the bricks in the second row determines the coloring of the bricks in the third row in the same way, and in general, the coloring of the bricks in any row determines the coloring of the bricks in the row below it in the same way. Thats it. Now if we interpret a row of bricks as a collection of investors at any given instant, green ones for buyers and red ones for sellers, then the change from moment to moment of investor sentiment is reflected in the changing color composition of the succeeding rows of bricks. If we let P be the difference between the number of green bricks and the number of red bricks, then P is a rough analogue of a stocks price. Graphing it, we see that it oscillates up and down in a way that looks random. The model can be made more realistic, but it is significant that even this bare-bones version, like the ant behavior, evinces a kind of internally generated random noise. This suggests that part of the oscillation of stock prices is also internally generated and is not a response to anything besides investors reactions to each other. The theme of Wolframs book, borne out here, is that complex behavior can result from very simple rules of interaction. |
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