100 X volatility = -28.8 +.485 x average price

box size = -3.347 +.0147 x price

The exaa figures for the box size corresponding to specific price levels are shown in Table 11-3. Understanding that box sizes must be in practical increments, a variable box point

and-figure chart can be constructed that changes box size as the price increases according to 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 started with a 10 box?" The long-term charts show that prior to 1970, prices were relatively stable and fiuctuated in normal ranges. Finding the proper box size for the initial interval forms the basis for continuing into more volatile years. In the 1970 shidy by Thiel and Davis entitled Point and Figure Commodity Trading.. A Computer Evaluation (Dunn & Haigitt), they approach the problem of variable box size and reversal value strictly scientifically. They proceeded to test a good sanpling of commodity futures maikets, varjing both the box size and reversal value, and recorded the resulting profits or losses and the reliability of the combination (percentage of profitable trades) For exanple, the Januarj- 66 soybean contract test results are presented in Table 11-5.

The shidy included the years 1960-1969, with data supplied by Dunn andHaiitt. This coincides exactly with the time interval needed to determine the basic box size and reversal. In their shidy, Thiel and Davis draw conclusions and present alternatives for their selections, but the interests of this analj-sis are slightly different. Table 11-6 shows the final choice. The most important part of Table 11-6 is the reversal value, expressed as a percentage of the 10-year fiuctuation. This figure represents the best choice of value for rescaling as a fixed percentage of the markets average price. The proper reversal criteria for each price level can now be selected using the rate of increase shown in the first and second formulas and the base price from Table 11-6.

For convenience, all box sizes will be chosen to correspond to the standard 3-box reversal. In general, a reversal value of 60 for soybeans would be profitable if plotted on a scale of 2 x 3, 3 x 2, 6 x 1, or 1 x 6, where the first number is the box size and the second is the number of boxes for a reversal. By having the percentage reversal value, the box and reversal criteria can be varied in a logical manner as the prices rise or W. Using the Januarj-

:an contract, boxes can be assigned in such a way that the reversal value is close to 2.38°o of the annual range (taken from Table 11-6). The results are the parameters shown in Table 11-7.

rtuim & Hargitt Financial Seraces, be , West Lafayette, IN

TABLE 11-6 Optimum Box and Reversal Criteria for 1 OYears-1 960-1969 (Davis and Thiel)

TABLE 11-7 Holding the Chart to a 2.38% Reversal Value

Indexing and Logarithmic Scale

One way to fransform prices into a percentage is by indexing. The steps needed to create an 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 trjing to create a chart with boxes that varj- in price by an amount equal to a percentage, and much simpler. If boxes

represent a percentage change, they can be marked 95, 96, 97------103, 104.... and so forth, each box representing a

Po 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>o change in price, equal to a proportional 0.01 logarithmic box size. It is interesting that the results of the Davis and Thiel study determined that the optimal box size would be the equivalent of a 2.38°o price change over a 10-year period, remaikably close to the logarithmic equivalent.

Price Objectives Using Percentages

If the entire price senes has been converted to an index, and plotted on a point-and-figure chart with percentage boxes, then the calculations for horizontal and vertical price objectives are applied to the index values in the normal manner. If prices are used instead of index values or percentages, then the price objectives must also be put into a compounded growth form. For exanple, a price objective of 5 boxes, each box equal to 233%, would be compounded (in spreaddieet notation) as:

1 ,1 *¥*1 1= llM . %

Stock Dividends and Splits

For those appljing point-and-figure charts to stocks, an adjustment must be made whenever a stock dividend is issued or the stock splits, because the chart represents the price of one share. Splits and dividends result in stock multiplying factors:

These multiplication factors can be used to correct the box size of a percentage, or logarithmic pointand-figure chart by dividing all the boxes by the multiplication factor; therefore, the new box sizes represent the value of one share.

See Luis "Price projections on point andfisure charts " Teclnucal Analysis . .- & CfnTnodities (My 1 William GS Br.,, "Logantiimic P.nt SFisure n,.-«tii,?." Tecimical Analysis ..f£t..ck.- & CinTnodities (My 1995.

Variable-Scale Comparative Results

A simple way of determining the best selection of scaling is to plot the results. The choice of equal percentage increases presented no problem. A standard point-and-figure chart was drawn with incremental price ranges assigned the necessarj-box size as follows:

Once the master chart is constracted, it will never have to be changed, if prices rise above the top of the scale, additional boxes can be numbered with laiger increments. Using the standard 3-box method of charting, each January soybean futures contract was plotted in Figure 11-14 and the results are shown in Table 11-8. The profits were consistently good except for 1976. It should be noted that the number of trades increased as the average price increased ttiroughout the test period. This can be expected since the box size does not increase as quickly at higher prices as does the price-volatility relationship Because of this steadj- lag, the sensitivity of the sj-stem will increase noticeably at peak levels.

The size of the chart based on the price-volatility approximation taken from Tables 11-3 and 11-4 is much smaller than the one used for equal percentage increases. Because the box sizes increase so rapidly, the formations appear more uniform at all price levels, and the number of trades occurring during each confrad was reasonably constant. The results of this method show that its application to a long-term chart would be practical. Any one con-contained only a small number of reversals and was able to generate from one to three trades (We 11-9).

TABLE 11 -8 Results Using Equal Percentage Increases (Method 2)

FIGURE 11-14 Point-and-figure cliart for January soybeans using price-volatility scaling.