horizontal count, there is adequate time to identif the formations and establish a price objective before it is reached. The vertical count is a measure of volatility; the amount of rebound from a top or bottom, and can be used to determine the size of a retracement after a major price move. To calculate the upside vertical count price objective, locate the first reversal column after a bottom. To do this, a bottom must be established with one or more tests or a major resistance line must be broken. The vertical count price objective is then calculated:

i;, = low» bon (nunbct rfbiifi in Risl crvfiml xminimunnniinlicrnl brai in 9 tW revenal)

kr-inl prikcoicdivceiuhilicrpilml.

Examples illustrating the vertical count are easjo find. Consider the following cases:

1. A catUe chart (Figure ll-13a)has an obvious bottom at 36.66 and a 13-box reversal immediately following. Using the vertical count, a reU-acernent of three times the primarj- reversal (13 boxes) is added to the low of the bottom. The price objective is then 41.73, 39 boxes above the low.

2. Followmg that upward move in catUe, there is a top of43.42 followed by a downward column of 9 boxes. The price objective becomes 27 boxes below the high, or

FIGURE 11 -13 (a) CatUe point-and-figure chart.

FIGURE 11 -13 (Continued) (b) Com point-and-figure chart

39.91, likely goal on the chart because it is also the center of the only technical adjustment during the downtrend.

3. Com (Figure 11 -13b) topped at 312 1 /2 and had an 11 -box reversal in the next column; the price obj ective is 33 boxes lower at 271 1/4. Although that goal fell short of the lows by quite a distance, it netted about a 27c profit from the sj-stem sell signal. Earlier in the confrad, there was an intermediate bottom at 278 3/4 with a 6-box reversal. The price objective of 301Y4 was in the center of the prior major resistance level and resulted in another good trade.

As a simple measuTHhent tool ffTncontr.ictl- hs or ttus tednuque seerns to have some relianlitr once tiie b-tfTn or top becomes clear Itis, bwever, far

A STUDY IN POINT-AND-FIGURE OPTIMIZATTON

Throughout the point-and-figure discussion, there has been constant reference to reversal value or 3-box reversal, although there has been no explicit suggestion of any alternative. In looking back at Table 11-1, it can be seen that the box sizes used prior to 1971 were generally smaller than the 1975 box sizes. In addition, laiger boxes are used for long-term continuation charts and smaller ones for individual contracts of maximum term

1 to 1 1/2 years. These differences are due to changing price levels and volatility as Wyckoff had suggested.

Prior to 1971, prices had been steadily increasing, but at a much slower rate than 1974-1976. In a single year, the price fluctuation of any one maiket was easj4o anticipate. Since 1969, prices have moved to unprecedented levels and back, with high volatility. The stock maiket, represented by a wide range of indices, has continued to gain and expand in dollar volatility throughout the early 1990s.

In 1969, sugar prices were plotted on a 5-point scale while prices ranged from 2.86C to 3.95c per pound; the possible span of point-and-figure boxes that could be filled was 22. In 1973, sugar prices went to almost 600 per pound, approximately 20 times their 1969 price. The daily limits were expanded from Y20 to 2c~more than the price had moved in 1 year. The use of a 50 point-and-figure box would result in a new reversal column on any day the maiket failed to continue its prior direction, and it no longer served the fiinction of smoothing the price movement, it took 1,200 boxes (10 feet of graph paper) to record the moves all the way up to 600.

One reason why the sugar scale changed from 50 to 200 boxes or soybeans from Ic to 100 was the practical need to fit the point-and-figure chart on a single page. Oddly enough, rescaling to fit a piece of paper of constant size has considerable merit. Look at soybeans in 1970. The range of the January 71 fiitures contract was 25 1 5/8 to 315 and required a page of graph paper with only 64 boxes and an assigned value of I per box. Table ll-2a shows what happens if the same number of boxes is used each year and if the scale is changed to accommodate the frill price range. The reversal value is forced to increase so that the size of the point-andfigure chart and formations will look the same regardless of the price level. This is called keeping the sensitivity constant. The point-and-figure method, with its increased reversal value due to laiger box size, will generate about the same number of reversals and buy and sell signals at any price level. Had prices increased without the box size increasing, the sj-stem would have had more frequent reversals, as in the sugar example, and it would be considered more sensitive to price changes. Table ll-2b

shows the comparable scaling for the SaJ 500 from 1988 jailer the "crash") through 1996. During this period, the stock index had an equal number of years with slightly higher volatility, as well as years with as much as 50°o lower volatility. During the quieter years there would have been very few frading signals

The relationship of reversal value to the average price for soybeans from 1971 through 1977, and the S&P from 1988 through 1996 gives a price-volatility relationship, shown in the last column of Table ll-2a. It is important to know to what degree prices will fluctuate as they advance and decline. This can become a valuable risk management tool.

Before continuing, certain questions must be ad;ed of this method:

Why were soybeans started with a 10 box .. why not V20or 5c?

Does this price-volatility relationship represent the best approach to rescaling?

How can it be used?

It can only be assumed that the original selection of a 10 box for soybeans was a combination of both a smoothing attempt (chosen as a multiple of the minimum move) and convenience. The convenience part is easj- to see; all the box sizes in Table 11-1 were even numbers. The first point-and-figure charts were drawn using the smallest allowable move and later refined to larger increments to identify long-term trends, and major support and resistance levels. However, it is necessarj- to find a more logical selection of starting parameters.

To answer the second question, the impact of rescaling on trading must be considered. As prices rise, boxes become larger and the minimum rid; becomes proportionately greater

TABLE 11 -2 Keeping the Size of the Chart the Same

The risk of trading one contract increases at the same rate as the volatility expressed as a percentage of average price. If the box sizes are not increased when prices rise, rid; can be kept small, but frequent losses will occur and frading will be based on extremely short-term trends.

There are few alternatives to rescaling, the two most reasonable being:

Method 1-Rechart at new price levels using larger box values to keep the size of the chart constant and the sensitivity fixed as shown in Table 11-2.

Method 2-lncrease the box value at a rate based on a fixed percentage of the current price so that a chart with a box value of 3 points at a price of 300 (Po value) would have a 6-point box at a price of 600.

B-aiwroaclieseeectivelvmcrease tiie box value andndc wlrtle re.hicms tiie seiisitivitv f the chart as pnces increase

Solving the Scaling Problem

To avoid being arbifrary in selecting a price-volatility scaling relationship, we perform a regression analj-sis on the average price and box size to get a formula for the relationship. A linear approximation was performed using the soybean values in Table 1 l-2a, based on a 3-box reversal, with the following results: