Figure Variable Box Size for Specific Price Levels (Method |)
 
 
Box Price Box Price Box _ Price Box Price Box PriceA 245 2A 380 4h 516 6A 652 8A 787va 262 24 397 4A 533 6A 669 84 804% 279 “2A 4l4 4h 550 6A 686 8% 821I 295 3 431 5 567 7 703 9 838th 312 34% 448 5A 584 TA 720 9% 85514 329 34 465 5A 601 74 736 9% 872lA 346 vA 482 5% 618 TA 753 oA 8892 363 4 499 6 634 8 770 40 906
i
reTABLE !1-5 Thiel and Davis’s Results, January 66 Soybeans
 
 
Box Reversal = Resutis
Size — — Boxes Profitability Profit Per Trade
0.500 - 4 2 of 12 14.874 -1.239
0.500 5 2 of 12 -14.874 4.239
0.500 6 2 of 10 15.124 1.512
1.000 4 | of2 3.00 4.500 .
4,000 . 1 lof | 7.25 7.25276 POuvT-AND-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 eachprice 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 1x 6, 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 & Hargitr Financial Services, Inc., West Lafayette, IN,
TABLE I1-6 Optimum Box and Reversal Criteria for 10 Years—1 960-1969 (Davis and Thiel)
 
 
 
Approximate 10-Year
Price Range Reversal ‘Fluctuation
1960-1969 Average Box Size Reversal. Value — (%)‘Wheat. 113-225 169.0 lng 3 boxes AAg = $225 2.66Corn 88-154 210 lag 4 boxes 6¢ = $300 4.95Soybeans 196-309 252.0 2¢ 3 boxes 6¢ = $300 2.38Soybean meal 48-102 75.0 75 pts 2 boxes {50 = $150 2.00Soybean oil , 73-123 98 25 pts | box 25 = $150 255Cattle 19-34 26.5 20 pts 2 boxes 40 = $160 1.50Pork bellies 18-55 36.5 25 pts 6 boxes 150 = $540 4.10Potatoes 1.9.8.4 5.15 5 pts 3 boxes “15 = $75 . 291Copper 29-52 40.5 50 pts Aboxes . 200 = $500 4.93Sugar 2-12 7.0 10 pts 5 boxes 54 = $560 7.14Cocoa 12-51 34.5 25 pts 7 boxes 175 = $525 5.55Silver 85-245 165.0 100 pts 2 boxes 200 = $200 1.21
 
 
TABLE 11-7 Holding the Chart to a 2.38% Reversal Value*
 
 
Soybean Highest ~ Lowest Annual Reversal BoxControct Price Price Range ~ Volue SizeJan 71 315 251% 63h TK %Jan 72 346 - 284% 61% -lA AJan 73 444 300 144 3% VkJan 74 91S 354% 560% 13% 44Jan 75 961 509 452 10% 34Jan 76 705 439% 2654 6h 2AJan 77 7824 490 292" 7 2%
 
* All values in cents.ASTUDY IN POINT-AND-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 tying 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, a price objective of 5 boxes, each box equal to 2.33%, would becompounded (in spreadsheet notation) as:
Objective = 100 * ((1 + .0233)45 ~ 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:’°
 
StockMuttplicotionActivity Foctor10% stock dividend il30% stock dividend 1.32-for-| stock split 2.03-for-2 stock split 15
 
These multiplication factors can be used to correct the box size of a percentage, or loga-rithmic point-and-figure chart by dividing all 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 (g/bu) Box size (¢/bu)240-286 2¢286-351 2A¢351-417 3¢417-480 3A¢480-544 4¢544-598 4A¢598-648 5¢648-725 SAg725-917 6¢
 
Once the master chart is constructed, it will never have to be changed. If prices riseabove the top of the scale, additional boxes can be numbered with larger increments. Usingthe standard 3-box method of charting, each January soybean futures contract was plottedin Figure 11-14 and the results are shown in Table 11-8. The profits were consistently goodexcept for 1976. It should be noted that the number of trades increased as the average priceincreased throughout the test period. This can be expected since the box size does notincrease as quickly at higher prices as does the price-volatility relationship. Because of thissteady lag, the sensitivity of the system will increase noticeably at peak levels.
The size of the chart based on the price-volatility approximation taken from Tables 11-3and 11-4 is much smaller than the one used for equal percentage increases. Because the boxsizes increase so rapidly, the formations appear more uniform at all price levels, and thenumber of trades occurring during each contract was reasonably constant. The results of thismethod show that its application to a long-term chart would be practical. Any one contractcontained only a small number of reversals and was able to generate from one to three trades(Table 11-9).
 
TABLE 11-8 Results Using Equal PercentageIncreases (Method 2)
—rades Net PLTotal Profitable == (¢/bu)~ January 1966 — 2 } +22~ January 1971 - 4 3 vo ad- January 1972 3 2 +8%January 1973 2 1 +93%January 1974 20 9 +23%January 1975 12 7 +554%January 1976 16 7 175%
- Total +548%* 1¢ commissions deducted,A STUDY IN POINT-AND-FIGURE OPTIMIZATION 279eS
—FIGURE 11-14 Point-and-figure chart for January soybeans using price-volatility scaling,
 
Box Pricese té/ou,)
  
               
x 9}x0 x x0ay 816% a0 XOX O}7753 xo XOX1xO X8X 0!xO XO 12x9 x 9xo x o xx0. 7 1 Xox ox xox 2x079x Oxoaxtd3° 5X0oo° u0 00 12
bx
 
 
 
 
 
  
Xx wax
 
4.January January January January January Jaouary
9971 1972 1973 1974 1975| 1976
 780 POINT-AND-FIGURE CHARTING
 
ng
TABLE 11-9 Results Using Price-Volatility Scaling
 
 
 
 
Trades
Individual Net P/L*
Contracts Total Profitable (¢ibu)January {971 3 | -28January 1972 2 1 +hJanuary 1973 1 1 +109January 1974 2 | +32January 1975 l 0 24January 1976 3 { -234
Total -144%
Continuous
trading
1971-1976 10 5 ~70
 
* l¢ commission deducted,
The plotted results appear to be much better than the tabulated results. This can beattributed to the increased risk at higher price levels. Although the number of boxes in a los-ing reversal remained small, the value of the loss increased by a factor of 25 from the bot-tom to the top of the chart. The few profits and losses that occur at higher price levels willbe so significant in the final results that the earlier trading performance is unimportant.
Both variable box approaches offer unique possibilities for identifying trends butincrease the problems of risk management. Some of these effects can be offset by reducingthe invested margin as prices rise. Other techniques are discussed in Chapter 23.| 12
Charting Systems
 
first to be affected were the moving average, or mathematical trending methods, as
well as easy-to-program indicators, followed by systematic optimization. Morerecently, econometric analysis, cycles, and pattern recognition have been the subject ofnew computerized research. Many quote services that offer graphics can convert a barchart to a point-and-figure chart at the push of a button. Yet the techniques normally usedin classic charting, such as trendlines, channels, and special patterns, have not yet beenbombarded with automated analyses.
The systems included in this chapter are those that might be used by a traditionalchartist. They do not all require the presence of a chart to be followed, but they are clearlyinterpretations of natural price patterns. The time that it takes for a price to move from onelevel to the next is not significant in many of these charting systems; it is only the level itselfthat is important.'The only restriction is that the systems presented could all be verifiedand tested using a computer.
SWING TRADING
The foundation for the largest number of chart-based systems is the swing chart. Similar topoint-and-figure, a swing is an upward or downward movement of a minimum size, regard-less of the time it takes to achieve that move. Unlike point-and-figure, there are no boxes,and the notation does not use Xs and Os. The only difference between one swing chart andanother is the swing filter. Once prices have reversed from a high or low point by the min-imum amount specified by the swing filter, a new vertical line is drawn in a column to thetight of the current one. An example of a swing chart is given in Figure 12-1.
Rules for using the swing chart generally follow those of point-and-figure. New buyand sell signals occur at points where the new swing penetrates the level of the prior swingin the same direction. Secondary signals are given if the new signal is in the same directionas the existing trend. Stop-loss orders can be placed at trend reversal levels or ata point offixed dollar loss.
A swing method is very different from a moving average technique because it does notrequire prices to move to a new level to maintain the existing trend. In a swing philosophy,prices can move sideways or stand still within a trend. Analysts will find its attributes simi-lar to a breakout method.
The following systems are all unique, but at the same time they are clearly simple vari--ations of the swing method of charting.
A Classic Chartist’s Swing Method
Originally, all swing charts were the product of analyzing a price chart. They were observedpatterns that preceded the more modern percentage retracements that now need a pocketcalculator. A classic technique for finding the swing highs and lows uses the followingsteps’ and is shown in Figure 12.2.
T« rapid growth of computerization has had a great impact on technical trading. The
' Based on William F. Eng, “A Mechanical Trading System,” Technical Analysis of Stocks & Commodities (July 1986).Further informacion can be found in Eng, The Technical analysis of Stocks, Options & Futures (Probus, 1988).282 CHARTING SYSTEMS
 
 
FIGURE 12-1 Standard bar chart with corresponding swing chart, (a) Bar chart,(b) Swing chart, 1
iwf Wh f \Ay h nih vesly
(a) (b)
 
1. Begin at a bar (or new day) where the highs and lows are both higher than the highsand lows of the previous bar (an upswing), or both lower than the highs and lowsof the previous bar (a downswing).
2. If an upswing, connect the highs of the two periods.
3. If the next period continues to have higher highs and lows, connect the highs.
4, Continue until a bar occurs that has a lower low without making a higher high. Thisindicates a possible swing change based on the pattern of the next bar.
5. If the next bar has a lower high and lower low, the highest high of the swing is con-nected to the new lowest low and a swing change has occurred.
 
FIGURE 12-2 Constructing a classic swing chart. _Higher high
    
, Swing line
\
  
First lower low
Second low lowSwing Reversal occurs when two crczve\
days of lower lows without higher highs occur.
   
 
Source: William Eng,“A Mechanical Trading System,” Technical Analysis of Stocks & Commodities, 4, no. 7 (July1986). © 1986 Technical Analysis, Inc. Used with permission.SWING TRADING ~ 283
 
6, If the swing reversal fails, the upswing continues when a new higher high andhigher low occurs.
This particular method is called a “2-day” (2-period) technique, because it requirestwo periods to identify a swing change. The greatest benefit of this swing method is that itfinds fast changes in market direction, however, it is recommended for its ability to iden-tify stop-loss points and control risk rather than for its entry timing.
The Livermore System
Known as the greatest trader on Wall Street, Jesse Livermore was associated with everymajor move in both stocks and commodities during the 30-year period from 1910 to 1940,Livermore began his career as a board boy, marking prices on the high slate boards that sur-rounded the New York Stock Exchange floor. During this time, he began to notice the dis-tinct patterns, or habits, in the price movement that appeared in the columns of numbers.”
As Livermore developed his trading skills and eventually took his position as a profes-sional trader, he maintained the habit of writing prices in columns headed Secondary Rally,Natural Rally, Up Trend, Down Trend, Natural Reaction, and Secondary Reaction. This mayhave been the basis for what is now considered a swing chart.
Livermore’s approach to swing trading required two filters, a larger swing filter and apenetration filter one-half the size of the swing filter. Penetrations were significant 'at pricelevels he called “pivot points.” A pivot point is defined in retrospect as the top and bottomof each new swing and are marked with letters in Figure 12-3.>
As mentioned earlier, the swing chart differs primarily from the point-and-figure chartby having no box size. By measuring the change in trend as a reversal of the minimumswing filter size from the last high or low swing, the pivot points are always posted at theexact price at which they occurred. In point-and-figure charting, using a 10-point box, aprice rally that fails 5 points above the previous box will not be posted; a point-and-figurereversal is measured from the last posted box; therefore, the size of the price reversalneeded to indicate a directional change may vary up to the size of one box.
Livermore's trading technique is a unique interpretation of the swing chart. Positionsare taken only in the direction of the major trend. This trend is defined by confirminghigher highs and higher lows (uptrend), or lower lows and lower highs (downtrend),where the penetration filter is not broken in the reverse direction. That is, an uptrend isstill intact as long as prices do not decline below the previous pivot point by as much asthe penetration filter size (seen in Figure 12-2). Once the trend is identified, positions areadded each time a new penetration occurs, confirming the trend direction. A stop-loss isplaced at the point of penetration beyond the prior pivot point. Unfortunately, the pene-tration filter is not the same as a pivot point, and Livermore never revealed how it was cal-culated, It seems, however, to be a minor percentage (for example, 20%) of the currentswing size.
Failed Reversal _
In the Livermore system, the first penetration of the stop-loss calls for liquidation of thecurrent position. A second penetration is necessary to confirm the new trend. If the secondpenetration fails (at point XK in Figure 12-4), it is considered a secondary reaction withinthe old trend. The downtrend may be reentered at a distance of the swing filter below K,guaranteeing that point X is defined, and again on the next swing, following pivot point M,
2 Edwin Lefevre, Reminiscences of a Stock Operator (Books of Wall Street, Burlington, VT, 1980). First publishedby George H. Doran in 1923. -3 Jesse Thompson, “The Livermore System," Technical Analysis of Stocks & Commodities (May 1983).284 CHARTING SYSTEMS
 
 
FIGURE 12-3 Trend change.
 
Second penetrationconfirms major uptrend
       
Penetration gives
downtrend signal Penetration of stop-loss
begins uptrend
Second penetrationconfirms majordowntrend
 
when prices reach the penetration level below pivot point L. It is easier to reenter an oldtrend than to establish a position in a new one.
Percentage Swings
The minimum swing value, which is the only determinate of the swing high and lowpoints, can be more robust if it is a percentage of price rather than a fixed number of pointsor fixed dollar-value. Many markets have doubled in value over the past 10 years—in stocksthe price of a technology issue could have increased 20 times and then split. A fixed valuefor finding the swing highs and lows'will be far apart at low price levels and too frequentat higher prices, unless that minimum is calculated as a percentage, p. XN
 
FIGURE 12-4 Failed reversal.
 
      
Penetration of stop-loss__ ends downtrend
“Secondary reaction” iffailure to confirm uptrend _
     
. . Sell at swing fitter -Confirms major if uptrend fails
downtrend
Sell again when downtrendis confirmedSWING TRADING . 285
 
Minimum swing value MSV, = p x price,
The most basic systematic approach to trading a swing method is simply to buy whenprices move up from the recent lows by the minimum swing value (MSV), and sell whenprices fall by the MSV from the recent high. The risk of each trade is always equal to the cur-rent value of MSV.
Finding the Swing High and Low Points
The following Easy Language program, KSWING, plots the swing high and low based on apercentage minimum swing value. For percentage swings, the interest rate yield should beused rather than price.
{KSWING: Finds most recent swing highs and lows,Plots values on a TradeStation chart. Copyright 1994-95, P.J. Kaufman, All rightsreserved.
Inputs for KSWING:swing = price swing in %}
input: swing(2.5);
vars: peswing(0), last(0), curhigh(0), curlow(0), swhigh(0), swlow(0),highbar(0), lowbar(0), chighbar(0), clowbar(0), lowp(0), highp(0),xclose(0), xhigh(0), xlow(0), divide(4);
peswing = swing / 100.;
{"divide” positions the high or low market on the plot }divide = 4;
factor = 1;
{INITIALIZE MOST RECENT HIGH AND LOW}if currentbar = 1 then begin -
curhigh = close; {current high)curlow = close; {current low}end;
{SEARCH FOR A NEW HIGH -- favor reversals}
if tast<>1 then begin - -{REVERSE FROM HIGH IF MINIMUM % SWING}
if Jow < curhigh - curhigh*pcswing then begin
Jast = 1; {last high fixed}swhigh = curhigh; {new verified high}highbar = chighbar;
curlow = low; {initialize new lows}lowp = low; {swing low for plot}
clowbar = currentbar;plotl{currentbar-highbarJ(high(currentbar-highbar} + highp*pcswing/divide,
"swinghigh");endelse begin—~4f high > curhigh then begincurhigh = high; {new current high}chighbar = currentbar;end;end;end;
{SEARCH FOR A NEW LOW - favor reversal}
if jast <> -1 then begin ~
{REVERSAL FROM LOW IF MINIMUM % SWING)
if high > curlow + curlow*pcswing then deginlast = <1;286 CHARTING SYSTEMS——_
swlOw = curlow;lowbar = clowbar;curhigh = high; {initialize current high}highp = high; {swing high for plot}chighbar = currentbar;plot2{currentbar-lowbar}(low[currentbar-lowbar] - lowp*pcswing/divide,“swinglow");endelse beginif low < curlow then begincurlow = Tow;clowbar = currentbar;end;end;end;
Wilder’s Swing Index
An automated way of determining swings is presented with trading rules in Wilder’s SwingIndex System.‘ Wilder has determined that the five most important positive patterns in anuptrend are:
1, Today’s close is higher than the prior close.
2, Today’s close is higher than today’s open.
3. Today’s high is greater than the prior close.
4. Today's low is greater than the prior close.
5. The prior close was above the prior open.
In a downtrend, these patterns are reversed.The Swing Index (SI) combines these five factors, then scales the resulting value to fall
between 100 and +100 as follows:
5p (Gr Gi) + 5(Gi— O) +.25(Gr- Ory) Ks1=50( R \z
‘where Kis the largest of |H, ~ C,_,| and |L, ~ C,_,| .M is the value of a limit moveR is calculated from the following two steps:
1. Determine which is the largest of
a |, - Gilb. \C.1 7 1ca A,-L,
2, Calculate R accordifig to the corresponding formula;a R= |H,- Gy] ~ S|Le- Gaal + 25/G-1- 0-1b. R= |L,-C_,| — 5|H,- C4] + 25|C,.. — O,..4|c R=(H,-L) + 25|C,.,- 0,.,|
Although the usefulness of the SI cannot be determined without proper testing, theformulas combine factors that have-a great deal of interest. The SI calculation uses three
+}, Welles Wilder, Jr., New Concepts in Technical Trading Systems (Trend Research, Greensboro, NC, 1978).SWING TRADING 287
 
price relationships, the net price direction (close-to-close), the strength of today’s trading(open-to-close), and the memory of yesterday’s strength (prior open-to-close). It thenemploys the additional factor of volatility as a percentage of the maximum possible move(K/M), The rest of the formula simply scales the results to within the required —100 to +100range. In the first step of the calculation of R, the concept of the true range reappears.
The daily values are added together to form an Accumulated Swing Index (ASI), whichsubstitutes for the price chart, allowing ready identification of the significant highs andlows, as well as clear application of Wilder's trading rules.
Terms used in the trading rules are as follows:
HSP High swing point—Any day on which the ASI is higher than both the previousand the following day.
LSP Low swing point—Any day on which the ASI is lower than both the previous andthe following day.
SAR Stop-and-reverse points (three types)—Index SAR points are generated by theASI calculation, SAR points apply to a specific price, and Trailing Index SAR,which lags 60 ASI points behind the best ASI value during a trade.
The Swing Index System rules are:
1. Initial entry:
a. Enter a new long position when the ASI crosses above the previous HSP.b, Enter a new short position when the ASI crosses below the previous LSP
2. Setting the SAR point: ~
a, On entering a new long trade, the SAR is the most recent LSP; the SAR is reset tothe first LSP following each new HSP A trailing SAR is determined as the lowestdaily low occurfing between the highest HSP and the close of the day on whichthe ASI dropped 60 points or more.
b, On entering a new short trade, the SAR is the most recent HSP, the SAR is resetto the first HSP following each new LSP. The trailing SAR is determined as thehighest daily high occurring between the lowest LSP and the close of the day onwhich the ASI rose by 60 points or more.
Keltner’s Minor Trend Rule
One of the classic trading systems is the Minor Trend Rule published by Keltner in his bookHow to Make Money in Commodities (The Keltner Statistical Service). It is still followedclosely by a great part of the agricultural community and should be understood for its sim-plicity and potential impact on markets. Sophisticated analysts must always remember thata large part of trading activity is the result of straightforward decisions that do not use hightechnology.
Keltner defines an upward trend by the failure to make new lows (comparing today’slow with the prior day) and a downtrend by the absence of new highs. This notion is con-sistent with chart interpretation of trendlines by measuring upward moves along the bot-tom and downward moves along the tops. The Minor Trend Rule is a plan for using thedaily trend as a trading guide. The rule states that the minor trend turns up when the dailytrend sells above its most recent high; the minor trend stays up until the daily trend sellsbelow its most recent low, when it is considered to have turned down, To trade using theMinor Trend Rule, buy when the minor trend rurns up and sell when the minor trend turnsdown; always reverse the position.
The Minor Trend Rule is a simple, short-term