28 -28 -28 -2810 -28 -28 -28 -28 -28 -28 -28 -28 -28 -28  -28 -2825 ~28 -28 -28 -27 -28 -28 26 -26 -26 -26 -2.650-26 -26 6 26 -26 -26 -230 -22 -22 -22 2275-12 0-12 2 “14 -14  -15 “16-14 -15 0-15 “15100-15 -15  -15  -l6 -17 0-19 -7 -5 ~6 6 -6150 58 57 57 5.3 5.4 49 40 36 3.5 3.5 3.5200 2.2 2.2 2.2 Le 7 1.6 28 27 27 27 27250-25 -25 -25 -25 -25 -25 -4 -1 2.0 2.0 2.0300 3.6 3.6 34 3.4 3.2 3.1 25 24 24 24 24
b. Siemens: 1,452 Days (2/3/87 to 11/23/92)
5 15 Ls 21 16 2 14 Lg LS 12 12 12 1.210 118 17) 1200 «114 10.6 8.5 8.2 75 67 6.0 6.0 6.025 «10.1 10.1 9.4 88 7.4 68 5.0 3.7 3.5 3.0 3.0 3.050 63 63 6.1 5.6 89 67 67 8.4 88 77 77 7775 9.8 94 IA 16 2 IL 83 10.0 97 87 87 87
100 5.2 5.2 48 49 41 3.1 48 59 59 5.3 53 5.3150 5.0 49° 49 5.0 +50 42 3.0 47 78.077 7.0 70200 _ 3.6 3.6 3.6 3.2 29 22 29 18 29 28 28 28250 45 44 44 43 3.9 3.3 44 5.2 49 49 49 49300 44 44 44 42 5.4 49 4.1 27 24. 24 24 24
¢. Deutschemark: 2,570 Days (11/24/82 to 1/23/92)
5-19-19 -19 -19 -L9  -18 -18 -I18 -18 -I8 -I18 -1810-14 -f.b -10  -10  -hI ° A=7 -.6 -6 -6 —6 -6 -625 17 2.6 3.6 29 3.8 3.8 5.5 5.7 5.3 5.2 49 5.450 5.2 69 68 64 37) 128 «110 115 108 108 10.8 10.875 3.4 48 61 5.6 85 134 10.0 87 78 76 76 76
100 ~ 5.3 72 8.5 8.3 45 108 115 TA 94 75 75 7S150 5 3 O 4 16 8.1 68 77 5.3 3.6 3.6 3.6
 
 
 
 
 
  
 
 
20 27 20) 617) LL OST 9H 7H20 «80 98f Bt Bl 65 55 72 88 54 IO 91 10430 7 #2 SOCALd. Eurodollars: 2,556 Days (1/03/83 to 12/14/92)
5 12 13 14 1 lo tO ilo ito oul th th Lt
10 18 2.1 3.1 a 27 26 27 27 27 27 27 2725 3.8 3.0 67 61 8.2 TA TA 74 7A 7A 7A 7450 4.0 85 (10.5 77 Bi. 7.8 17 77 17 77 77 777S 65 10.2 8.1 92 108 10.0 99°. 99 9.9 99 99 99100 71 48 89 63 64 72 78 78 78 78 78 7.8
150 4.1 18 29 2.6 64 5.0 76 76 76 76 76 7.6200 73 5.4 38 A 29 59 65 65 65 65 65 65250 tl -8 -8 al 4s 3.8 69 5.6 5.6 5.6 5.6 5.6300 2 ol 78 8 3 67 5.6 54 54 5.4 5.4 5.4
 
 
* Exponential smoothing was used to-create a trend with buy and sell signals given when the trendline turned up or down, respectively. Stops.apply to absolute losses, all orders were executed at the close of the day, and there were no commissions or slippage charged. Although stopsimprove performance in specific cases, there does not seem to be a consistent pattern. Smaller stops are espgcially erratic, as the trends in-crease in length, often showing aiternating better and worse performance.
607 
TABLE 23-4 Comparison of 4-Year Results*Comparison of Cash Return versus Risk-Adjusted Return
 
Stop-Loss in Whole Percent
 
 
 
 
 
 
 
 
 
 
 
 
02 05 10 AS 25 50 1.00 2.00 400 7.00 10.00 NONEDeutschemark: [,030 Days (11/22/88 to 1 1/23/92)Annualized Rate of Return (on Cash, in Percent)
5-75 -71 -73 -63 -99 -85 -71 -7.1 -7.1 -7.I -7100 TT10 -68 -50 -53 -62 -76 -70 +44 +43 43 -43 4.3 4325 28 5.5 5.4 5.4 5.4 4.2 65 74 74 7A 7A 7450 5.6 10.2 99 10.1 9.6 8.3 83 87 8.0 8.0 8.0 8.075 28 22 16 16 5.0 7.0 5.1 5.0 3.6 3.4 3.4 3.4
100 13 42 3.6 3.5 TA 5.4 87 8.6 9.3 9.1 9.1 9.1150 1.2 3a 7 7 =i 76 9.3 12 88 75 72 72200 53 9.1 89 87 8.2 64 79 9.7 7.0 $.2 46 46250 5.9 8.3 al 8.0 77 67 61 79 5.2 5.6 49 47300 2.0 1.8 LS 1.2 3a 45 64 8.1 5.4 66 5.9 55Annualized ROR (Adjusted for 25% Drawdown) :
S$ -37 -36. -36 -38 42 -40 -36 -36 -36 -36 ~3.6 3.610 -3.9 -28 -29 -32 -36 -3.5 -25 -24 +24 -24 2.4 2425 27 48 46 46 46 33 71 10.9 10.9 10.9 10.9 10.950 127 23.300 225 25.2. 27 173 160 16.8 15.5 15.5 (5.5 15575 44 3.6 2.2 2.2 78 145 75 66 44 42 4.2 42
100 2.8 87 7.0 68 18.1 95 18.1 113 19.1 18.6 18.6 18.6150 3.7 24 17 L7 -17— 121 12.0 146 10.8 8.3 8.0 8.0200 140. 22.0 19.3 19.2 7.1 13.4 13.2 IS. 91 5.9 5.3 53250 14.7 18.8 17.6 167 16.0 128 99 129 74 8.2 7.2 69300 57 45 3.4 2.8 19 8.3 98 12.8 7.0 10.3 9.2 87Eurodollars: 1,042 Days (11/22/88 to 12/14/92)
Annualized Rate of Return (on Cash, in Percent)
5 3 ‘3 3 3 3 3 3 3 3 3 3 310 a a 1.0 Ll 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.025 3 4 3 1.2 13 13 13 1.3 13 13 13 1.350 3 3 1.0 13 1.6 16 16 16 16 16 ‘16 16rh) 7 8 Ll A 1.3 1.3 13 1.3 1.3 13, 13 13100 ag 3&8 1.0 1.0 il 1.0 1.0 1.0 1.0 Lo 1.0 Lo150 0 al - 1 -.1 6 3 2 a 9 3a a ao200 al -l l I 7 Ll il Ll Ll Ll Ll Ll250 2 2 2 2 3a 1.2 1.2 1.2 1.2 1.2 12 1.2300 2 3 2 -3 4 6 6 6 6 & 6 &Annualized ROR (Adjusted for 25% Drawdown)
5 29 24 24 24 24 24 24 24 24 24 24 2410 21.9 224 257 195 25.9 _ 259 259 “259 259 259 25.9 25.925 29 46 11.3 286 329 329 329 329 329 329 32.9 32.950 78 126 238 330 ' 388 388 388 -388 388 388 38.8 38.85 185 207 274 27.1 32.6 320 320 320 320 320 32.0 32.0
100 22.1 183 259 256 285 256 256 256 256 25.6 25.6 25.6150 a 14 +13 0-13 73 14 10.9 10.9 10.9 10.9 10.9 10.9200 35 17 1.2 1.0. at 138 14.1 14.1 14.1 14.1 14.1 14.1250 44 5.9 49 44 (68 148 15.1 i510 715.1 15.1 15.1 15.13004.3 65 $60 -3.4 4.1 $2 .5.4 5.4 5A $4. - 54 54
sR* The pattern in che "NONE" column (no stops) shows that the risk-adjusted results. in general, are more consistent than unadjusted returns.RANKING OF MARKET: JR SELECTION 609
 
RANKING OF MARKETS FOR SELECTION
Choosing the right market to trade at the right time would clearly improve performance.To accomplish this, there are a number of ways to measure the trendiness of a market,from standard statistical techniques to more complex rules. Each unique method will mea-sure some special characteristic of price movement. To take advantage of this, it is neces-sary to trade using a system that targets this type of price pattern. For example, if you usea correlation coefficient, 7’, to rank the trend over 20 days, then a linear regression is prob-ably the best choice of a trend-following system, using a period no greater than 20 days.
It may be interesting to list a number of trend-ranking approaches, then keep track oftheir values in a table over various time periods.'* For example, the five measurementsbelow can be calculated for periods of 5, 10, 20, and 40 days.
1. Correlation coefficient, but no less than .25
2. Sum of the net $ movement over n, 2 x n, and 4 x n days3. Slope of an n-day regression converted to 1-day $ change4, Wilder’s ADX, but no less than .20
5. Average absolute value of price changes
Each measurement will need to have threshold values that determine when they representsignificant trends. For the correlation coefficient, anything below .25 is most likely to be asideways market; similarly, Wilder’s ADX would need to be above .20 to indicate a trend. Ifthe results are erratic, it may be necessary to smooth the last 3 days of each value. In thecase of item 5, higher volatility is often associated with greater profits and greater risk fora trend-following system; therefore, a careful look at how ranking affects performance iswarranted,
Commodity Selection Index (CSI)
Among Wilder’s trading tools is ‘the Commodity Selection Index (CS1),“ a calculation fordetermining which products are most likely to make the greatest move for each dollarinvested. In this case, the movement measured is directional and, therefore, may apply moreto trending models. The CSI combines directional movement, volatility, margin require-ments, and commission costs into an index that allows for comparison and selection.
Directional Movement
The tending quality of the market, as defined by Wilder, begins with directional move-ment, the greater of either:
1. Plus DM (+DM), today’s high minus yesterday’s high, or
2. Minus-DM (—-DM), today’s low minus yesterday’s low.The directional movement is either up or down, whichever is larger. It is the largest part oftoday’s range which is outside yesterday’s range. When an inside day occurs, the direc-tional movement is zero (Figure 23-8).
DM is expressed relative to the daily range (high minus low), defined as today’ 's truerange (TR1), the larger of the following:
1. Today’s high minus today’s low -
2. Today’s high minus yesterday’s close3. Yesterday’s close minus today's low
2 Based on an idea suggested in Chande and Kroll, The New Technical Trader (John Wiley & Sons, 1994).
44 J, Welles Wilder, “Selection and Direction” in Technical Analysis in Commodities, Perry'J: Kaufman (ed.)-(JohnWiley & Sons, New York, 1980).610 RISK CONTROLTT
FIGURE 23-8 Defining the-DM.
ce -
 
Rising Outside insidemarket day day
 
The true range is always positive.
The relationship of the directional movement to the true range is called the Direc-tional Indicator. Today's directional indicator is calculated using either the plus DM or theminus DM, whichever is greater.
DM14 DM14.-DM14=- .TR TRI4 |Once the first DM14 is calculated, an average off technique is used to find each successiveDM14 as follows:
 
+DM14=+
 
prior +DM14
Today’s +DM14 = prior +DM14 ~ 1g
+ today’s +DM14
The same procedure is followed for the true range:
priorTR1414
These results can also be produced using a smoothing constant of .93 as follows:Today’s +DM14 = .93 x ( prior +DM14) + today’s +DM1 ‘Today’s -DM14 = .93 x ( prior -DM14) + today’s -DM1
Today’s TR14 = .93 x ( prior TR14) + today’s TR1
Today’s TR14 = prior TR14 — + today’s TR14
At this point, the Directional Indicator can be used as atrading indicator, and is thesubject of the-next section; however, Wilder’s interest was to use this in a more completeconcept. Once the +DM14, -DM14, and the TR14 are calculated, +DI14 and —DI14 follow,and the true directional movement is the difference between +DI14 and —DI14, Wfien anupward trend is sustained, the +DI14 becomes larger, the -D114 becomes smaller, and thetrue directional movement becomes greater. This is then normalized to allow it to beexpressed as a value berween 0 and 100.
+DI14 minus —D114 DI difference= = x 101+D114 plus ~-D114 x 100 DI sum x 100
where multiplying by 100 converts the percentage to a whole number. The DX is thensmoothed out using a 14-day average (or .133 smoothing constant), and is called the AverageDirectional Movement Index (ADX)
ADX(today) = ADX(prior) + .133 x [DX(today) -— ADX(prior)]RANKING OF MARKETS -R SELECTION 611
 
One last adjustment is made to the extreme variance of the ADX by taking the 14-daydifference of ADXs. This final rating is called the Average Directional Movement Index Rat-ing (ADXR),
_ ADX(today) + ADX(14 days ago)- 2
The ADX and ADXR are shown plotted together in Figure 23-9. The ADX is seen tooscillate about the ADXR. Measuring the amplitude of the ADX from the zero line, a higheramplitude means higher directional movement and a stronger trend, whether up or down.The peaks are always the extremes in the same direction as the trend. If the major trendwas down, the peaks would be extremely low points and the valleys would be relativelyhigh points. The greater the distance between the peaks and valleys, the greater are thereactions to the trend.
All this leads to the Commodity Selection Index (CSI), which is calculated as:
ADXR
v 1CSI = ADXR x ATR1. —x ——4x % “5040
where ADXR = average directional movement index ratingATR14 = 14-day average true range
V= conversion factor; value of a 1¢ move (in dollars)
M = margin (in dollars)
C = commissions (in dollars)Note that for a particular commodity, .the values in.brackets do not change. By calculatingthem once and calling that value K, the CSI can be expressed as:
CSI = ADXR x ATR14 x K
A portfolio allocation can be chosen by calculating the CSI daily (or weekly) for eachcommodity. Simply select those products to trade that have the highest CSI or allocate mul-tiple contracts in proportion to their CSI value.
| 100
Optimizing Directional Movement'®
The +DI14 and —-DI14- are indicators that can be used in a simple trading strategy.Hochheimer, known for other studies of moving averages, crossovers, and channels, hasdefined the rules of a Directional Movement System in two ways.* The first set of rules are:
5 For a general discussion of this topic, see Chapter 21.\6 Frank L. Hochheimer and Richard J. Vaughn, Computerized Trading Techniques 1982 (Merrill Lynch Com-modities, New York, 1982).
 
FIGURE 23-9 Appearance of the ADX and ADXR.
Ampiitude
 612 RISK CONTROLOE1. a. If the +DI crosses above the —DI, enter a buy stop on the next day using today’shigh price. This order remains as long as it is not executed and +DI remainshigher than ~DI. ‘b. Ifthe —DI crosses below the +DI, enter a se// stop on the next day using today’s lowprice. Maintain this order until it is executed and while —-DI remains below +DI,Hochheimer calls the first case “directional movement with delay.” The second case is animmediate market entry following the crossing of the directional indicators:
2. a. If the +DI crosses above the —DI, buy on the open of the next day.b. If the -DI crosses below the +DI, sell on the open of the next day.
In both cases the system is always in the market.Before seeing the actual results, it is possible to generalize the expected performance.
1. Case 2 must have more trades than case 1 as a result of always taking a positionwhen a crossing occurs.
2. Because there is no commitment to the trade (i.e., no channel), there could be fre-quent whipsaws in case 2.
3. Because case 1 uses the high and low of the prior day, its entry prices will always beequal to or worse than case 2.
4. If the Directional Indicator gives a highly reliable signal, it would be better to enterimmediately, as in case 2.
Parameters Defined
The purpose of the optimization was to see if changes in the time intervals causedimprovements in results. Hochheimer chose the following parameters to test: :
1. The +DM was calculated from 7 to 20 days.
2. The ~DM varied from 5 above to 5 below the +DM value.
3. Two true ranges (TR) were calculated, the first using the weight of the +DM, theother using the weight of the -DM.
The test data covered all information available from 1970 to 1981.
Results ‘
Selected results are shown in Table 23-5. The patterns of the two cases are as expected.Case 2 has more trades, with a higher percentage of losses and higher risk. The profit/lossshown in case 1 is generally higher than case 2, indicating that, even under ideal condi-tions, the RSI generates many false signals using these rules.
It can-also be seen that those markets with a small amount of available data, T-bills,T-bonds, currencies, and gold, had the shorter intervals selected for calculazion. By observ-ing the tendency for the products with more data to use longer intervals, a standard set ofdays should have been chosen rather than allowing an apparent overfitting of the data.
The philosophy of these tests, however, should be questioned, Although the indepen-dent varying of the number of days in the +DM, —DM, and TR accounts for al] combina-tions, it seems illogical. The Directional Movement Indicator is intended to be ameasurement of relative strength over a fixed time period; it produces a percentage from0 to 100. In this study, the TR (the denominator) may have a time interval smaller than oneof the +DM or -DM, generating a value greater than 100.
The independent varying of the up and down segments of the indicator also allowed along-term directional bias to appear. This can be seen in the optimum selection of thosecommodities with the shortest amount of data: the financials markets and the currencies,In case 2, almost all of the products with 11 years of data produced interval selections thatwere nearly identical, in the area of either 14 or 20 days. °RANKING OF MARKETS FOR SELECTION 613
 
aTABLE 23-5 Comparative Performance of Directional Movement Systems
 
 
 
Case | Case 2
Equity No. of Equity No. of
Days PIL Drop Trades Days PIL Drop Trades
Cocoa 2217 $43,083 $~13,019 723 2318 $-4)17  $-17,152 1238Corn 2120 26,456 -7,072 613 2120 26,456 7,072 613Cotton 1821 37.495 21,740 1256 24:19 29.765 — 18,340 (462Copper 18 20 219,639 ~10,230 633 1214 88,561 -13,390 1549Deutschemark 813 140,538 6,335 277 1414 101,476 -7,290 423Gold 15 10 827,980 10,740 504 1612 664,390 13.810 104]Catte 2219 -7.850 -11,710 474 2020 = -14.860 ~27,920 808Soybeans 16 20 254,495 ~39,639 895, 19 20 177,584 29,759 1420Silver f6tl 1,034,825 ~82,870 788 2217 = 351,360 = ~136.585 16T-Bills 37 37,840 —12,005 286 i 8 5.235 17,545 369T-Bonds 87 185,371 —11,326 436 98 118,256 7,294 739
 
Kaufman’s System Selection Indicator
A market's personality is in its price patterns. Some markets, such as the stock index, arevery volatile with gradual sustained upward moves and fast, sharp drops. In contrast,Eurodollars are very steady, often trading high volume at the same price. Qualifying mar-kets by noise allows you to decide which trading strategy is most likely to be successful.Lower noise favors trending systems and high noise makes countertrend techniques moreappropriate.
The concept of noise has been discussed in numerous sections throughout this book,and it is again of great value when choosing which system to apply to a market, and iden-tifying when a market is best treated as trending. In essence, noise is market movementthat has no direction or one in which the amount of direction is overwhelmed by volatileerratic up and down movement. It is an undercurrent of unpredictable movement causedby a broad range of participants acting for their own individual objectives. -
The calculation for noise can be found with examples in Chapter 17 (‘Adaptive Tech-niques”), As a simple reminder, it is defined as the efficiency ratio, ER:
_ Net price changeSum of price changes as positive values
Time Frame
There always appears to be more noise over short time periods. That is because noiseremains at about the same level, but price trends are not clear until they have perseveredfor at least a few days, and often for weeks. For a trend comparison we should avoid veryshort-term trends; therefore, a 16-day exponential smoothing will be used in the followingcomparison. To be certain that the efficiency ratio is stable, it will be calculated over a65-day period. .
Resuits of Efficiency Ratio Selection
Figure 23-10 shows that, when returns are compared using the efficiency ratio, profits areclearly greater when the ER is high; tosses are larger when the ER is low. Based on a broadsampling of markets, this is a very useful pattern for classifying markets. The greatest prof-its are in the upper right part of the diagram where there is less noise; the greatest lossesare in the lower left corner where there is the most noise. We can conclude that614 RISK CONTROL
 
FIGURE 23-10 Efficiency ratio and trend performance. A clear pattern can be seen whenalong-term efficiency ratio (market noise) is plotted against the trend performance of a broadsampling of markets using a [6-day exponential sm