reversal (usually three), is meant to indicate a sig-nificant contrary move and can be used as an objective indication of a change of direction.One approach to taking profits is shown in Figure 11-10.
In Figure 11-10a, a trailing 3-box reversal value is used for the stop-loss once there isa sustained move of at least 10 boxes. To reenter the move in the same direction, the sametechnique is used (Figure 11-10), adding another 4 boxes of profits while keeping thenew risk small. In Figure 11-10c, this method lost 4 boxes of the potential profits when thereversal was short-lived.
In general, taking small profits in this way does not improve profits, because it mostoften misses the biggest moves. It may, however, reduce the risk of loss at a rate even fasterthan the reduction in profits, yielding a better reward-to-risk ratio. A new rule should becarefully tested to know its effect on different market conditions. If successful, it shouldalways be used. Selective use is more likely to limit potential profits without reducinglosses. This topic is covered thoroughly in Chapter 21 (“Testing”).
Alternate Treatment of Reversals
‘Traditional point-and-figure charting favors the continuing trend. On highly volatile days, oroutside days, it is possible for both a trend continuation and a reversal to occur. Point-and-figure rules require that the trend continuation be recorded and the reversal ignored. Figure11-11 shows a comparison of the two choices. In the example, prices are in an uptrend whena new 1-box high and a 3-box reversal both occur on day 6. In Figure 11-118, the traditionalapproach is taken, resulting in a continuous upward trend with a stop-loss at 790. Taking thereversal first as an alternate rule, Figure 11-11¢ shows the same trend with a stop-loss at 805.
 
FIGURE 11-10 Cashing in on profits.
 
 
 
x xx xx x xx Sox x _ XeReemerxo x OX xO xxo XOX xox% §-—cioseour XOX BA- x XOX .x xox X \eioseout-  & XO x--Enter xx XOX x- x XOX xx x0” New xx x x x Qesysterm xX oxox x x x stop. x x xxX OxXOX xoxox XOxSkx00 XOxSystem xBxs. x O- vee Fe 8 % -(@ () o 
268 POINNT-AND-FIGURE CHARTING
FIGURE I-11 Alternate rhethods of plotting point-and-figure reversals. (2) Sample pricesfor plotting. (b) Traditional method. (c) Alternate rule taken on day 6. 1
 
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Plotting the reversal first will usually work to the benefit of the trader; both the stop-loss and change of trend will occur sooner. Subsequent computer testing proved this to betrue, The alternate rule will not help when the reversal value is small and’ the optionalreversals, or outside days, occur frequently.
|
Base widthWs = 9
 
PRICE OBJECTIVES
Point-and-figure charting has two unique methods for calculating price objectives: bort-zontal and vertical counts. These techniques do not eliminate the use of the standard bar icharting objectives, such as support and resistance levels, which apply here as well,
xThe Horizontal Count !
The time that prices spend in a consolidation area is considered important in determiningits potential move. One technique for calculating price objectives is to measure the widthof the consolidation (the number of columns) and project the same measurement up ordown as the target of the move. The point-and-figure horizontal count method is a moreexact approach to the same idea.
The upside price objective is calculated as
Hy =P, + WR) gqooeesoe
2. Horizontal count price objectives.Cocoa March 74 (£4)
 
where Hy is the upside horizontal count price objective- — —P, is the price of the lowest box of the base .W is the width of the bottom formation (number of columns)Ris the reversal value (number of boxes times the value of one box)
 
FIGURE860B40820
To complete this formula, the base (width of the bottom or top formation) needs to be iden-tified. Count the number of columns, W; not including the breakout column and multiply -that width by the value of a minimum reversal, R; then add that resuit to the bottom point ofthe base to get the upper price objective. The base can always be identified after the break-out has occurred. For example, Figure 11-12 shows the March 74 contact of London Cocoa
= 19
Base width W,
560 
270 POINT-AND-FIGURE CHARTING
(&4 box) forming a very long but clear base. The reversal value is £12, and the width of thebase is 19 columns (not counting the last column, which included the breakout). Added tothe lowest point of the base (£570) this gives an objective of £798, reached on the left shoul-der of the topping formation. Another alternative is the wider base, marked as W; = 25. Usingthis selection results in a price objective of £870, by adding 25 x £12 = £300 to £570, the low-est point of the base.
The downside objective is calculated in the same manner as the upside objective:
Hp =P - (WXR)
where Ap is the downside horizontal count price objectivePx is the price of the highest box of the top formationWis the width of the top formation (number of columns)Ris the reversal value
Some examples are given for downside objectives in the same cocoa diagram (Figure
11-12). A small correction top could be isolated at the £720 level and two possible topwidths, W; and Ws, could be chosen. W;, the broader top, has a width of 9 and a downsideobjective of £632. Ws has a smaller width of § and a downside objective of £680. Althoughthe lesser objective, calculated from Ws, is easy to reach, the farther one is reasonablebecause it coincides with a strong intermediate support level at about £640.
‘The very top formation was small and only produced a nearby price objective similarto the first downside example; there would be no indication that prices were ready for amajor reversal. The top also forms a clear head-and-shoulders pattern, which could beused in the same-manner as in bar charting to find an objective. The height of the top ofthe head to the point on the neckline directly below is 20 boxes; the downside price objec-tive is 20 boxes below the point where the neckline was penetrated by the breakout of theright shoulder, at 776, giving £696 as an objective.
The horizontal count can also be applied to a breakout from a triangular formation,similar to the one on the very far right in Figure 11-12 (marked “Head-and-shoulders objec-tive”). The width of the formation, W, is the widest point in the center of the triangle, andthe upward objective is also measured from the center, rather than from the bottom of thetriangle. -
The Vertical Count
‘The vertical count is a simpler and more definitive calculation than the horizontal count.As with the horizontal count, there is adequate time to identify the formations and estab-lish a price objective before it is reached. The vertical count is a measure of volatility, theamount of rebound from a top or bottom, and can be used to determine the size of aretracement after a major price move. To calculate the upside vertical count price objec-tive, locate the first reversal column after a bottom. To do this, a bottom must be estab-lished with one or more tests or a major resistance line must be broken. The vertical countprice objective is then calculated:
Vp = lowest box + (number of boxes in first reversal --X minimum number of boxes in a chart reversal)The downside vertical count price objective is just the opposite:Visoun = highest box — (number of boxes in the first reversalx minimum number of boxes in a chart reversal)
Examples illustrating the vertical count are easy to find. Consider the following cases:
 
PRICE OBJECTIVES wm
1. A cattle chart (Figure 11-13) has an obvious bottom at 36.66 and a 13-box reversalimmediately following. Using the vertical count, a retracement of three times theprimary reversal (13 boxes) is added to the low of the bottom. The price objectiveis then 41.73, 39 boxes above the low.
2. Following that upward move in cattle, there is a top of 43.42 followed by a down-ward column of 9 boxes. The price objective becomes 27 boxes below the high, or
SSFIGURE 11-13 (a) Cattle point-and-figure chart.
come {bor = 13 poe, es rena
   
  
 
 
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 272 PU.AT-AND-FIGURE CHARTING
 
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FIGURE 11-13  (Continued)~b) Corn point-and-figure chart.
 
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X39.91, a likely goal on the chart because it is also the center of the only technical ad-justment during the downtrend.
3. Corn (Figure 11-13) topped at 312% and had an 11-box reversal in the next col-umn; the price objective is 33 boxes lower at 271. Although that goal fell short ofthe lows by quite a distance, it netted about a 27¢ profit from the system sell signal.Earlier in the contract, there was an intermediate bottom at 278% with a 6-box re-versal. The price objective of 301% was in the center of the prior major resistancelevel and resulted in another good trade.
As a simple measurement tool from contract highs or lows, this technique seems tohave some reliability once the bottom or top becomes clear. It is, however, far from perfect.
A STUDY IN POINT-AND-FIGURE OPTIMIZATION
‘Throughout the point-and-figure discussion, there has been constant reference to rever-sal value or 3-box reversal, although there has been no explicit suggestion of any alterna-tive. In looking back at Table 11-1, it can be seen that the box sizes used prior to 1971were generally smaller than the 1975 box sizes. In addition, larger boxes are used forlong-term continuation charts and smaller ones for individual contracts of maximum term
 
A STUDY IN POINT-ANu-FIGURE OPTIMIZATION 273
 
1 to 1% years, These differences are due to changing price levels and volatility as Wyckoffhad suggested.
Prior to 1971, prices had been steadily increasing, but at a much slower rate than1974-1976. In a single year, the price fluctuation of any one market was easy to anticipate.Since 1969, prices have moved to unprecedented levels and back, with high volatility. Thestock market, represented by a wide range of indices, has continued to gain and expand indollar volatility throughout the early 1990s.
In 1969, sugar prices were plotted on a 5-point scale while prices ranged from 2.86¢to 3.95¢ per pound; the possible span of point-and-figure boxes that could be filled was22. In 1973, sugar prices went to almost 60¢ per pound, approximately 20 times their 1969price. The daily limits were expanded from %¢ to 2¢-—more than the price had moved in 1year. The use of a 5¢ point-and-figure box would result in a new reversal column on any
_ day the market failed to continue its prior direction, and it no longer served the function
of smoothing the price movement. It took 1,200 boxes (10 feet of graph paper) to recordthe moves all the way up to 60¢.
One reason why the sugar scale changed from 5¢ to 20¢ boxes or soybeans from 1¢ to10¢ 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 in1970. The range of the January 71 futures contract was 251% to 315 and required a page ofgraph paper with only 64 boxes and an assigned value of 1¢ per box. Table 11-2a showswhat happens if the same number of boxes is used each year and if the scale is changed toaccommodate the full price range. The reversal value is forced to increase so that the size ofthe point-and-figure 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 itsincreased reversal value due to larger box size, will generate about the same number ofreversals and buy and sell signals at any price level. Had prices increased without the boxsize increasing, the system would have had more frequent reversals, as in the sugar exam-ple, and it would be considered more sensitive to price changes. Table 11-2b shows thecomparable scaling for the S&P 500 from 1988 (after the “crash”) through 1996. During thisperiod, the stock index had an equal number of years with slightly higher volatility, as wellas years with as much as 50% lower volatility. During the quieter years there would havebeen very few trading signals.
‘The relationship of reversal value to the average price for soybeans from 1971 through1977, and the S&P from 1988 through 1996 gives a price-volatility relationship, shown inthe last column of Table 11-2a. It is important to know to what degree prices will fluctuateas they advance and decline. This can become a valuable risk management tool.
Before continuing, certain questions must be asked of this method:
Why were soybeans started with a 1¢ box... why not 4¢ or 5¢?-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 1¢ box for soybeans was a com-bination of both a smoothing attempt (chosen as a multiple of the minimum move) andconvenience. The convenience part is easy to see; all the box sizes in Table 11-1 wereeven numbers. The first point-and-figure charts were drawn using the smallest allowablemove and later refined to larger increments to identify long-term trends, and major sup-port and resistance levels. However, it is necessary to find a more logical selection ofstarting parameters. ~
‘To answer the second question, the impact of rescaling on trading must be considered:As prices rise, boxes become larger and the minimum risk becomes proportionately greater. 
274 POINT-AND-FIGURE CHARTING
TABLE 11-2 Keeping the Size of the Chart the Same(0) Soybeans (January Futures Contract)
 
 
 
Reversal as
Total Percentage
Box Number Reversal ~—of Average
Year High Low ~— Average = Size__—=Reversal_—_of Boxes Value %1971 315 281 283 1.00 3 64 3.00 1.061972 346 282 314 1,00 3 64 3.00 0.961973 444 300 372 225 3 64 6.75 1811974 91s 349 632 884 3 64 26.83 4.201975 961 509 735 7.06 3 64 21.19 2.881976 70S 439 572 416 3 64 1247 2.181977 782 490 636 456 3 64 13.69 21S(b) S&P 500 Futures (Continuous Daily Prices)
1986 250 205 228 0.70 3 64 21L 0.931987 330 175 253 2.42 3 64 7.27 2.881988, 280 240 260 0.63 3 64 1.88 0.72$989 350 280 315 1.09 3 64 3.28 1.041990 365-285 325 125 3 64 3.75 1151991 410 310 360 156 3 6 4.69 130t992 440 390 41s 0.78 3 64 234 0.561993 470 425 448 0.70 3 64 24t 0.471994 480 435 458 0.70 3 64 211 0.461995 610 460 535 2.34 3 64 7.03 1311996 745 600 673 2.27 3 64 6.80 1.01
Ee ———
‘The risk of trading one contract increases at the same rate as the volatility expressed as a per-
centage of average price. If the box sizes are not increased when prices rise, risk can be kept
small, but frequent losses will occur and trading 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 thechart constant and the sensitivity fixed as shown in Table 11-2.‘Method 2—Increase the box value at a rate based on a fixed percentage of the currentprice so that a chart with a box value of 3 points at a price of 300 (1% value) wouldhave a 6-point box at a price of 600. —_—Both approaches effectively increase the box value and risk while reducing the sensitivityof the chart as prices increase. aan
Solving the Scaling Problem‘To avoid being arbitrary in selecting a price-volatility scaling relationship, we perform a
regression analysis 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 11-2a, based ona 3-box reversal, with the following results:
- 100 volatility = ~28.8 + .485 x average pricebox size = -3.347 + .0147 x price
‘The exact figures for the box size corresponding to specific price levels are shown in Table11-3. Understanding that box sizes must be in practical increments, a variable box point-
 
 
A STUDY IN POINT-Arw0-FIGURE OPTIMIZATION 275
and-figure chart can be constructed that changes box size as the price increases accordingto the table. These box sizes are shown with their corresponding price levels in Table 11-4.
Scaling by Constant Rate
The second choice of scaling requires answering the question: “Why were soybeans startedwith a 1¢ box?” The long-term charts show that prior to 1970, prices were relatively stableand fluctuated in normal ranges. Finding the proper box size for the initial interval formsthe basis for continuing into more volatile years. In the 1970 study by Thiel and Davis enti-tled Point and Figure Commodity Trading: A Computer Evaluation (Dunn & Hargitt), theyapproach the problem of variable box size and reversal value strictly scientifically. Theyproceeded to test a good sampling of commodity futures markets, varying both the boxsize and reversal value, and recorded the resulting profits or losses and the reliability of thecombination (percentage of profitable trades). For example, the January 66 soybean con-tract test results are presented in Table 11-5.
TABLE 11-3 Point-and-Figure Price-Volatility Relationship (Method |)
 
Average price 250 300 350 400 450 500 550 600Percentage volatility 92 "7 140 165 189 214 240 262Box size 328 1.06 1.80 254 3.20 4.01 475 5AdAverage price 650 700 750, 800 850 900 950 1000Percentage volatility 286 34 335 359 383 408 432 456Box size 6.22 6.96 7.70 8.43 917 9.9) 10.65 1138
TABLE 11-4 Point-and-Figure Variable Box Size for Specific Price Levels (Method 1!)
 
 
Box Price Box Price Box Price Box Price Box Price% 245 2% 380 4A 516 6A 652. Bh 787‘ 262 24 397 44 533 64 669 BK 804% 279 “Dh 4l4 4h 550 on 686~ BA 8211 295 3 431 5 567 7 703 9 838i% 312 3K 448 SA 584 TA 720 9% 855vA 329 34 465 5A 601 TA 736 oh 872% 346 3% 482 5% 618 TH 753 wh 8892 363 4 499 6 634 8 770 10 906
_—_
———
TABLE 11-5 Thiel and Davis's Results, January 66 Soybeans
 
 
 
Box Reversal - ResuksSize — Boxes Profitability Profit Per Trade0500 4 2of 12 14.874 -1.2390.300 5 2of 12 148740.500 6 2of 10 =15.124 15121.000 4 1 of2 3.00 1.500 -4000.” I lof | 728 7.25
i 
276 POueTFAND-FIGURE CHARTING
 
The study included the years 1960-1969, with data supplied by Dunn and Hargitt.?This coincides exactly with the time interval needed to determine the basic box size andreversal. In their study, Thiel and Davis draw conclusions and present alternatives for theirselections, but the interests of this analysis are slightly different. Table 11-6 shows the finalchoice. The most important part of Table 11-6 is the reversal value, expressed as a per-centage of the 10-year fluctuation. This figure represents the best choice of value for rescal-ing asa fixed percentage of the market's average price. The proper reversal criteria for cachprice level can now be selected using the rate of increase shown in the first and second for-mulas and the base price from Table 11-6.
For convenience, all box sizes will be chosen to correspond to the standard 3-box rever-sal. In general, a reversal value of 6¢ for soybeans would be profitable if plotted on a scale of2x3, 3x2, 6x1, or 1X6, where the first number is the box size and the second is the num-ber of boxes for a reversal. By having the percentage reversal value, the box and reversal cri-teria can be varied in a logical manner as the prices rise or fall. Using the January soybeancontract, boxes can be assigned in such a way that the reversal value is close to 2.38% of theannual range (taken from Table 11-6). The results are the parameters shown in Table 11-7.
. * Dunn & Hargitt Financial Services, Inc., West Lafayette, IN.
eeeTABLE 11-6 Optimum Box and Reversal Criteria for 10 Years—1960-1969 (Davis and Thiel)
 
 
Approximate 10-Year
Price Range Reversal Fluctuation
1960-1969 Average Box Size Reversal Value (%)Wheat 113-225 169.0 4g Zboxes 4K = $225 2.66Corn 88-154 (21.0 tA¢ 4 boxes &¢ = $300 4.95Soybeans 196-309 252.0 2¢ 3 boxes 6¢ = $300 2.38Soybean meal 48-102 75.0 75 prs 2 boxes 150 = $150 2.00Soybean oit . 73123 98 25 pts 1 box 25 = $150 255Cattle 19-34 265 20 prs 2 boxes 40 = $160 1.50Pork bellies 18-55 36.5 25 pts 6boxes 150 = $540 410Potatoes 19-84 5.15 5 pts 3 boxes I8=$75 | 291‘Copper 29-52 40.5 50 pts Aboxes . 200= $500 4.93Sugar 212 7.0 10 prs 5 boxes 54 = $560 7.14‘Cocoa 12-51 315 25 pts 7 boxes 175 = $525 5.55Silver 85-245 165.0 100 pts Zboxes 200 = $200 121“OE
TABLE 11-7 Holding the Chart to a 2.38% Reversal Value*
 
 
Soybean Highest ~ Lowest Annual Reversal BoxContract, Price Price Range ~ Value SizeJan 71 315 251% 6K VA 4%
Jan 72 346 - 284% 6K 1% 4
Jan 73 444 300 144 34 1%jan 74 as 354% 560% 13% 44jan 75 961 509 452 10% 3hJan 76 705 439% 265% oh 2hJan 77 7824 490 2926 7. rh
F-ck  eeend* All values in cents.
 
 
A STUDY IN POINTAND-FIGURE OPTIMIZATION 277
Indexing and Logarithmic Scale
One way to transform prices into a percentage is by indexing. The steps needed to createan index can be found in Chapter 2 (“Basic Concepts”). The results of plotting a point-and-figure chart on an index will be very close to trying to create a chart with boxes that vary inprice by an amount equal to a percentage, and much simpler. If boxes represent a per-centage change, they can be marked 95, 96, 97,..., 103, 104, . .. and so forth, each boxrepresenting a 1% change in price. Because orders are placed as prices, not percentages,you will need to know the corresponding price whenever you buy and sell
A logarithmic scale represents ‘a constant 2.33% change in price, equal to a propor-tional 0.01 logarithmic box size.? It is interesting that the results of the Davis and Thielstudy determined that the optimal box size would be the equivalent of a 2.38% pricechange over a 10-year period, remarkably close to the logarithmic equivalent.
Price Objectives Using Percentages
If the entire price series has been converted to an index, and plotted on a point-and-figurechart with percentage boxes, then the calculations for horizontal and vertical price objec-tives are applied to the index values in the normal manner. If prices are used instead ofindex values or percentages, then the price objectives must also be put into a compoundedgrowth form. For example, 2 price objective of 5 boxes, each box equal to 2.33%, would becompounded (in spreadsheet notation) as:
Objective = 100 * (1 + .0233)*5 ~ 1) = 12.20%instead of simply 5 x .0233 = .1165, or 11.65%.
Stock Dividends and Splits
For those applying point-and-figure charts to stocks, an adjustment must be made when-ever a stock dividend is issued or the stock splits, because the chart represents the price ofone share. Splits and dividends result in stock multiplying factors:
 
StockMultiplicationActivity Factor10% stock dividend Nl30% stock dividend 13
2-for-1 stock split .3-for-2 stock split 1s
These multiplication factors can be used to correct the box size of a percentage, or loga-rithmic point-and-figure chart by dividing ail the boxes by the multiplication factor; there-fore, the new box sizes represent the value of one share.
° See Luis Ballesca Loyo, “Price projections on point and figure charts,” Technical Analysis of Stocks & Com-modities (July 1989). -
© William G.S. Brown, “Logarithmic Point & Figure Charting,” Technical Analysis of Stocks & Commodities (July1995). 
278 POINT-AND-FIGURE CHARTING
 
Variable-Scale Comparative Results
‘A simple way of determining the best selection of scaling is to plot the results. The choiceof equal percentage increases presented no problem. A standard point-and-figure chartwas drawn with incremental price ranges assigned the necessary box size as follows:
 
Price range (¢/bu) Box size (¢/bu)
240-286 2¢286-351 2