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the group enjoyed have now vanished, eliminating the compulsion to sell the stock for a quick pro t. This temporary softening of prices is the pullback, and those people watching the stock chart closely can take advantage of this by acquiring the stock at the prebreakout price. It is an especially attractive opportunity since the stock has, in a manner of speaking, tipped its hand about its price direction since it has nally broken out of its price range. The stock of the company Potash, shown in Figure 9.4, broke above the upper end of its price range and swiftly moved from $38 to $44. It then started slipping back to $38, and for the rst few months of 2004, the stock bobbled between a miniature price zone of $38 to $44 before doubling in value. This pullback created a great opportunity for getting into the stock at a relatively low-risk price. After the breakout, the saucer s price range of $18 to $38 was a thing of the past. The stock was now trading above $38. It took a few months to get the strength and con dence to soar over 100 percent, but during that period, a savvy trader could have acquired the stock at a price very close to the initial breakout level (without the misery of holding on to a do-nothing stock for many years beforehand). Some of the most exceptional market gains in history have been enjoyed following the decisive breakout of a stock above a long-established price range. The more de ned and longer the chart pattern, the better it is for owners of that stock. An extraordinary instance of this is shown in

For simplicity we take c to be a positive fixed constant; but a and b are variable parameters. We shall see that the system has a phase transition at a = 0, which is either of first or second order, depending on the sign of b. For definiteness, think of a and b as functions of temperature and pressure. Then the condition a = b = determines the critical temperature Tc and critical pressure Pc. Introducing as usual t = (T - TJ/~ and p = (P - PJ/PC' we shall take a and b to

(17.60)

(17.61)

Setting Bt/J/Bm = 0, we obtain five roots, as befits a quintic polynomial:

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(17.62)

4ae)

(17.63)

Noting that t/J(O) = a, we conclude that m = is a maximum if a < 0. This means that for a < 0, the only possible minima are m . Substituting (17.62) into (17.61), we obtain

Figure 9.5 with 3M (at the time of the breakout, the company was called Minnesota Mining & Manufacturing). The age of the price range was substantial, spanning from 1973 to 1986. Once the stock broke above resistance, it hardly ever looked back (except for the crash of 1987 which, interestingly, pushed the stock back to the top of its former trading range and no lower). The stock moved literally thousands of percent higher after this breakout. It is easy to see in retrospect how obvious these patterns are. It seems that, armed with this knowledge, people would know exactly what to do. But this is not the case, and it again goes back to human psychology. When a breakout occurs, a person examining the stock doesn t have the bene t of the next 20 years of price history. They can see only what has happened so far. Imagine yourself looking at 3M in 1986 just after it broke above its former resistance level. You would be confronted with a stock which (1) had done very little for more than a decade, and (2) was at a higher price than anyone had ever paid for it. You might feel foolish considering paying a premium price for a do-nothing stock. Those already owning the stock might feel compelled to increase their holdings and add to their pro ts, but for newcomers, a stock that has just made a new high price is seldom tempting because everyone else was able to get the stock before, when it was cheap.

(17.64)

Therefore m+ corresponds to a minimum, while m_ corresponds to a maximum:

(a < 0)

(17.65)

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