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It is now necessary to evaluate explicitly the largest eigenvalue of V. Using (15.117), we obtain 1 2= lim -log A n-"oo n

(15.118)

y(v)

= -(2k - 1)

(15.119)

~ 00,

(15.120) 2= - 1 12~ dvy(v) = - 1 1~ dvy(v) 4'TT 0 2'TT 0 where the last step results from (15.105), which states that y(v) = y(2'TT - v). To express 2 in a more convenient form, we recall that y( v) is the positive solution

FIGURE 7.36 This is typical price action following a trendline break, as prices push up against the former supporting trendline.

(15.121)

ep = fi , > 0 1 e- 2 <t> 8 = tanh-

number formats, 89 number series, 87

(15.122)

Fig. 15.4 Region of integration in (15.127).

A straightforward calculation shows that sinh 20 cosh 20 Hence (15.121) can also be written as cosh y( v) = cosh 2<1> coth 2<1> - cos v We find the following identity helpful in the reduction of (15.120): (15.124)

= --=

(15.123)

", dt log (2 cosh z - 2 cos t) 1

FIGURE 7.38 The safest place to short a market after a trendline break is when it is up against the resistance line.

(15.125)

y(v)

'" dv/log(2cosh2<1>coth2<1> - 2cosv - 2cosv ' ) 1

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(15.126)

1'" dv 1'" dv/log [2 cosh 2<1> coth2<1> -

2(cos v + cos v')] (15.127)

The double integral in (15.127) extends over the shaded square in the vv ' plane shown in Fig. 15.4. It is obvious* that the integral remains unchanged if we let the region of integration be the rectangle shown in dotted lines, which corresponds to the range of integration

level it may simply fall away. But it is de nitely safer to wait for the possibility that it does so. It takes a lot of buying power to overcome the disappointment of a trendline break. Figure 7.39 shows a closer view of the NASDAQ s attempt to get back above its trendline. It took about four months to do so, and in the end, it failed, because the uptrend was simply no longer valid. Continued strong volume can push a stock in an uptrend, even if a former trend has been damaged. One of the most amazing stocks of 2005 and 2006 was NutriSystem (symbol NTRI), showed in Figure 7.40. Bears would have had a number of opportunities to short the stock at relatively safe levels, but in this graph, they would have lost money each time. The techniques being illustrated here are certainly no guarantee of pro t. But they do provide a measuring tool to know when you are wrong with your speculation.

+ v'

(15.128)

81 = - 82 =

v + v'

2, v'

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(15.129)

1" d8 1" d8 log (2cosh2cf> coth2cf> - 4 cos 8 cos !82) = -\ 1" d8 1"/2 d8 log (2 cosh 2cf> coth2cf> - 4 cos 8 cos 82) 7T = -\ 1" d8 d8 log (2 cos 82) 7T + -\ 1" d8 1"/2 d8 2 log (_D_ - 2 cos 8 7T cos 82

1"/2

FIGURE 7.39 This illustrates how much strength is required for a stock to make an assault on its former trendline.

7T 1

(15.1301

and where the identity (15.125) has been used once more. Since cosh- 1 x log [x + /x 2 - 1], we can write

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