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Knowing that support become resistance (and vice versa), and understanding how prices can cling to trendlines is powerful knowledge that you can turn into pro table opportunities. Knowing how to use trendlines well can help you minimize your risk at the same time. When prices fall beneath support and try to get back to the trendline, it s as if the prices are kissing the underbelly of the line. Keep in mind very few people know how to use trendlines (and even fewer know how to use them well), so it s not as if the markets are zealously following one agreed-upon line and marking prices along it. But the mass psychology driving millions of individuals to do what they do in the markets helps create these phenomenon and those practiced in charting can exploit them. Imagine you had watched Allegheny Technology climb from $2 to thousands of percent above that level, and you wanted to short the stock. But because the stock was so strong, you didn t know where to enter the trade. The trendline for the stock (Figure 7.35) was broken

(15.115)

*B. Kaufmann (loc. cit.) shows that the plus sign is to be chosen in both (15.110) and (15.111).

This condition is invariant under any permutation that sends {Z k} into {Z PI- }. Therefore the eigenvalues of (15.110) consist of those eigenvalues (15.106) for which an even (odd) number of - signs appear in the exponents, if the +( - I sign is chosen in (15.110). From (15.106) and (15.105), we conclude that the largest eigenvalue of V/)

+Y2n-2)

where the sign corresponds to the sign in (15.109). As n ~ 00, these two possibilities give the same result, for Yo is negligible compared to the entire exponent in the last equation. A similar conclusion can be reached for Vi). Therefore we conclude that as n ~ 00 the largest eigenvalue of V/} largest eigenvalue of Vi)

+Y2n-2)

(15.116)

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The largest eigenvalue of V is the larger one of (15.116), which by (15.105) that for Vi). Therefore the largest eigenvalue of V is

when the stock was about $22, and the stock kept climbing. Shorting the stock in the subsequent months would have been a very unpro table decision, since the stock climbed hundreds of percent more. Waiting until the price nally mustered enough strength to touch the underside of the trendline at $77.50 would have created a much safer opportunity for the short sale. The typical action after a price break usually does not take as long as that, however. Figure 7.36 shows a more common pattern of the price quickly moving down after the price break, regaining its strength, and then pushing back up to touch the underside of its former support line. The danger of shorting a stock merely because it has broken support is highlighted in Figure 7.37. After the initial break, the stock (Hilton) did indeed fall badly. But it didn t take long for it to recover and make a series of new lifetime highs. A person bearish on this stock would have been wise to wait until the price was just barely underneath the former support level before placing the short. That way, if the price does manage to cross above the line, you can close the position quickly with a relatively small loss. This kind of thinking applies not just to individual securities but to entire markets as well. The NASDAQ Composite (Figure 7.38) broke its support line and, similar to Hilton, initially fell swiftly, gathered its strength, and began moving substantially higher. The market eventually got extraordinarily close to the trendline, which would have represented a very lowrisk price level to short the market. Of course, there s no guarantee a stock or index will have enough strength to get close to its former support

(15.117)

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