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You Can't Become Rich In Your Pocket Until You Become Rich In Your Mind | ||||
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Elliott enthusiasts. The waves and cycles in stock pricesTrends, Crowds,and Waves As a predictor of stock prices, psychology goes only so far. Many investors subscribe to technical analysis, an approach generally intent on discerning the short-term direction of the market via charts and patterns and then devising rules for pursuing it. Adherents of technical analysis, which is not all that technical and would more accurately be termed trend analysis, believe that the trend is their friend, that momentum investing makes sense, that crowds should be followed. Whatever the validity of these beliefs and of technical analysis in general (and Ill get to this shortly), I must admit to an a priori distaste for the herdish behavior it often seems to counsel: Figure out where the pack is going and follow it. It was this distaste, perhaps, that prevented me from selling WCOM and that caused me to sputter continually to myself that the company was the victim of bad public relations, investor misunderstanding, media bashing, anger at the CEO, a poisonous business climate, unfortunate timing, or panic selling. In short, I thought the crowd was wrong and hated the idea that it must be obeyed. As I slowly learned, however, disdaining the crowd is sometimes simply hubris. Technical Analysis: Following the Followers My own prejudices aside, the justification for technical analysis is murky at best. To the extent there is one, it most likely derives from psychology, perhaps in part from the Keynesian idea of conventionally anticipating the conventional response, or perhaps from some as yet unarticulated systemic interactions. Unarticulated is the key word here: The quasi-mathematical jargon of technical analysis seldom hangs together as a coherent theory. Ill begin my discussion of it with one of its less plausible manifestations, the so-called Elliott wave theory. Ralph Nelson Elliott famously believed that the market moved in waves that enabled investors to predict the behavior of stocks. Outlining his theory in 1939, Elliott wrote that stock prices move in cycles based upon the Fibonacci numbers (1, 2, 3, 5, 8, 13, 21, 34, 59, 93, ... , each successive number in the sequence being the sum of the two previous ones). Most commonly the market rises in five distinct waves and declines in three distinct waves for obscure psychological or systemic reasons. Elliott believed as well that these patterns exist at many levels and that any given wave or cycle is part of a larger one and contains within it smaller waves and cycles. (To give Elliott his due, this idea of small waves within larger ones having the same structure does seem to presage mathematician Benoit Mandelbrots more sophisticated notion of a fractal, to which Ill return later.) Using Fibonacci-inspired rules, the investor buys on rising waves and sells on falling ones. The problem arises when these investors try to identify where on a wave they find themselves. They must also decide whether the larger or smaller cycle of which the wave is inevitably a part may temporarily be overriding the signal to buy or sell. To save the day, complications are introduced into the theory, so many, in fact, that the theory soon becomes incapable of being falsified. Such complications and unfalsifiability are reminiscent of the theory of biorhythmns and many other pseudosciences. (Biorhythm theory is the idea that various aspects of ones life follow rigid periodic cycles that begin at birth and are often connected to the numbers 23 and 28, the periods of some alleged male and female principles, respectively.) It also brings to mind the ancient Ptolemaic system of describing the planets movements, in which more and more corrections and ad hoc exceptions had to be created to make the system jibe with observation. Like most other such schemes, Elliott wave theory founders on the simple question: Why should anyone expect it to work? For some, of course, what the theory has going for it is the mathematical mysticism associated with the Fibonacci numbers, any two adjacent ones of which are alleged to stand in an aesthetically appealing relation. Natural examples of Fibonacci series include whorls on pine cones and pineapples; the number of leaves, petals, and stems on plants; the numbers of left and right spirals in a sunflower; the number of rabbits in succeeding generations; and, insist Elliott enthusiasts, the waves and cycles in stock prices. Its always pleasant to align the nitty-gritty activities of the market with the ethereal purity of mathematics. The Euro and the Golden Ratio Before moving on to less barren financial theories, I invite you to consider a brand new instance of financial numerology. An email from a British correspondent apprised me of an interesting connection between the euro-pound and pound-euro exchange rates on March 19, 2002. To appreciate it, one needs to know the definition of the golden ratio from classical Greek mathematics. (Those for whom the confluence of Greek, mathematics, and finance is a bit much may want to skip to the next section.) If a point on a straight line divides the line so that the ratio of the longer part to the shorter is equal to the ratio of the whole to the longer part, the point is said to divide the line in a golden ratio. Rectangles whose length and width stand in a golden ratio are also said to be golden, and many claim that rectangles of this shape, for example, the facade of the Parthenon, are particularly pleasing to the eye. Note that a 3-by-5 card is almost a golden rectangle since 5/3 (or 1.666 ... ) is approximately equal to (5 + 3)/5 (or 1.6). The value of the golden ratio, symbolized by the Greek letter phi, is 1.618 ... (the number is irrational and so its decimal representation never repeats). It is not difficult to prove that phi has the striking property that it is exactly equal to 1 plus its reciprocal (the reciprocal of a number is simply 1 divided by the number). Thus 1.618 ... is equal to 1 + 1/1.618 This odd fact returns us to the euro and the pound. An announcer on the BBC on the day in question, March 19, 2002, observed that the exchange rate for 1 pound sterling was 1 euro and 61.8 cents (1.618 euros) and that, lo and behold, this meant that the reciprocal exchange rate for 1 euro was 61.8 pence (.618 pounds). This constituted, the announcer went on, a kind of symmetry. The announcer probably didnt realize how profound this symmetry was. In addition to the aptness of golden in this financial context, there is the following well-known relation between the golden ratio and the Fibonacci numbers. The ratio of any Fibonacci number to its predecessor is close to the golden ratio of 1.618... , and the bigger the numbers involved, the closer the two ratios become. Consider again, the Fibonacci num Theres no telling how an Elliott wave theorist dabbling in currencies at the time of the above exchange rate coincidence would have reacted to this beautiful harmony between money and mathematics. An unscrupulous, but numerate hoaxer might have even cooked up some flapdoodle sufficiently plausible to make money from such a cosmic connection. The story could conceivably form the basis of a movie like Pi, since there are countless odd facts about phi that could be used to give various investing schemes a superficial plausibility. (The protagonist of Pi was a numerologically obsessed mathematician who thought hed found the secret to just about everything in the decimal expansion of pi. He was pursued by religious zealots, greedy financiers, and others. The only sane character, his mentor, had a stroke, and the syncopated black-and-white cinematography was anxiety-inducing. Appealing as it was, the movie was mathematically nonsensical.) Unfortunately for investors and mathematicians alike, the lesson again is that more than beautiful harmonies are needed to make money on Wall Street. And Phi cant match the cachet of Pi as a movie title either. Moving Averages, Big Picture People, myself included, sometimes ridicule technical analysis and the charts associated with it in one breath and then in the next reveal how much in (perhaps unconscious) thrall to these ideas they really are. They bring to mind the old joke about the man who complains to his doctor that his wife has for several years believed shes a chicken. He would have sought help sooner, he says, but we needed the eggs. Without reading too much into this story except that we do sometimes seem to need the notions of technical analysis, let me finally proceed to examine some of these notions. Investors naturally want to get a broad picture of the movement of the market and of particular stocks, and for this the simple technical notion of a moving average is helpful. When a quantity varies over time (such as the stock price of a company, the noontime temperature in Milwaukee, or the cost of cabbage in Kiev), one can, each day, average its values over, say, the previous 200 days. The averages in this sequence vary and hence the sequence is called a moving average, but the value of such a moving average is that it doesnt move nearly as much as the stock price itself; it might be termed the phlegmatic average. For illustration, consider the three-day moving average of a company whose stock is very volatile, its closing prices on successive days being: 8, 9, 10, 5, 6, 9. On the day the stock closed at 10, its three-day moving average was (8 + 9 + 10)/3 or 9. On the next day, when the stock closed at 5, its threeday moving average was (9 + 10 + 5)/3 or 8. When the stock closed at 6, its three-day moving average was (10 + 5 + 6)/3 or 7. And the next day, when it closed at 9, its three-day moving average was (5 + 6 + 9)/3 or 6.67. If the stock oscillates in a very regular way and you are careful about the length of time you pick, the moving average may barely move at all. Consider an extreme case, the twenty-day moving average of a company whose closing stock prices oscillate with metronomic regularity. On successive days they are: 51, 52, 53, 54, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 46, 47, 48, 49, 50, 51, 52, 53, and so on, moving up and down around a price of 50. The twenty-day moving average on the day marked in bold is 50 (obtained by averaging the 20 numbers up to and including it). Likewise, the twenty-day moving average on the next day, when the stock is at 51, is also 50. Its the same for the next day. In fact, if the stock price oscillates in this regular way and repeats itself every twenty days, the twenty-day moving average is always 50. There are variations in the definition of moving averages (some weight recent days more heavily, others take account of the varying volatility of the stock), but they are all designed to smooth out the day-to-day fluctuations in a stocks price in order to give the investor a look at broader trends. Software and online sites allow easy comparison of the stocks daily movements with the slower-moving averages. Technical analysts use the moving average to generate buy-sell rules. The most common such rule directs you to buy a stock when it exceeds its X-day moving average. Context determines the value of X, which is usually 10, 50, or 200 days. Conversely, the rule directs you to sell when the stock falls below its X-day moving average. With the regularly oscillating stock above, the rule would not lead to any gains or losses. It would call for you to buy the stock when it moves from 50, its moving average, to 51, and for you to sell it when it moves from 50 to 49. In the previous example of the three-day moving average, the rule would require that you buy the stock at the end of the third day and sell it at the end of the fourth, leading in this particular case to a loss. The rule can work well when a stock fluctuates about a long-term upward- or downward-sloping course. The rationale for it is that trends should be followed, and that when a stock moves above its X-day moving average, this movement signals that a bullish trend has begun. Conversely, when a stock moves below its X-day moving average, the movement signals a bearish trend. I reiterate that mere upward (downward) movement of the stock is not enough to signal a buy (sell) order; a stock must move above (below) its moving average. Alas, had I followed any sort of moving average rule, I would have been out of WCOM, which moved more or less steadily downhill for almost three years, long before I lost most of my investment in it. In fact, I never would have bought it in the first place. The security guard mentioned in chapter 1 did, in effect, use such a rule to justify the sale of the stocks in his pension plan. |
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