72 88 Iho 9.1 10.4300 7 4 2-1 5S 5. 5.1 $6 43 123 107 10.4d. Eurodollars: 2,556 Days (1/03/83 to 12/14/92)
5 42 13 14 Lo 1.0 Lo Lt Vt Ll Loh AL10 18 2 nn > A 1 > © A 2 27 272538 430 67 82 74 T4 TA TA TA 74 TA50 40 85 (05 77 B81 78 77. 770 TTT 77 777S 65 10.2 8 92 108 100 99 99 99 99 99 99
oo 71 48 89 63 64 72 78 78 78 78 78 7850 4) 18 0290 260 640 5.076 7G 7H 7H 76 762000 7.300 SA 8 4°29 59 65 65 65 65 65 65250 hE 3B 8 4d 38 69) 56 SG SH 568 56300 2 1 8-8 3 67 $6 54 54 SA 5.4 5.4
nn* Exponential smoothing was used to create a trend with buy and sell signals given when the trendline turned up of down. respactively. topsapply to abscluce 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, thera does not seem to be a consistent pattern. Smaller scops are espgcially erratic, as the trends in-‘crease in length, often showing akternating 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 Percent02 0510'S SSSI 2.00 4.00 7.00 “10.00 NONEDeutschemark: 1,030 Days (11/22/88 to 1 1123/92)
Annualized Rate of Return (on Cash, in Percent)
 
 
 
 
  
 
 
 
 
 
5 75 7.1 73 83 9.9 -7d 71 TA 7.1 ~7.1 7.110 -6.8 -5.0 5.3 62 -7.6 44 43 43 43 43 ~4325 28 5.5 34 5.4 5.4 6S 74 7A 74 TA 7450 56 102 99 101 96 83 87 80 80 80 8075 28 22 1.6 16 5.0 5.1 5.0 3.6 3.4 3.4 34
100 13 4.2 3.6 3.5 74 87 8.6 9.3 9. 9.4 9. 10 120 9 77 HL 93 112 88 75 72 72200 «530 (98) 89) BT BD 79 97 «70 «5.246 46250 5.9 8.3 8.1 8.0 77 6.1 79 5.2 5.6 49 47300 2018S 64 81 54 66 OS 55Annualized ROR (Adjusted for 25% Drawdown)
5 37 3.6 -3.6 38 42 4.0 3.6 3.6 -3.6 -3.6 3.6 3.610-39 -28 -29 -32 36 -25  -24 -24 -24 -24 -2425 27 48 46 4.6 7A 10.9 10.9 10.9 10.9 10.950 127 233 225 252 160 168 155 155 155 15575 44 3.6 22 22 75 6.6 44 42 42 42
100 28 «487 7068 181 11319 186186186.1s0 37 2.4 17 7 12.0 14.6 10.8 8.3 8.0 8.0200 140 220° 193 192 1320 151 9 5953 53250 14.7 18.8 17.6 16.7 99 12.9 74 8.2 7.2 69300 57 4S 3.4 28 a 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 23 3 3 3 3
10 9 9 1.0 hl 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.03 3 4 9 12 13 13 13 13 LB 1350 3 5 10 13 16 16 16 1.6 1.6 1.6 S16 1.675 7 B&B 1 1 13 13 13 13 13 13 13 1.3100 3 8 1.0 1.0 Ll 1.0 1.0 1.0 1.0 1.0 1.0 1.00 Om 6 9% 9 9 9 9 9 320002 l A al ee i rm250 2 2 2 2 go 12 12 12 1.2 2 12 1.2300 2 3 2 -3 A 6 6 6 6 6 6 &Annualized ROR (Adjusted for 25% Drawdown)
5 29 24 24 24 24 24 24 24 24 24 24 2410 219 224 «257 195 25.9 25.9 259 259 25.9 25.9 25.9 25.925 29 46 13 28.6 32.9 32.9 32.9 32.9 32.9 32.9 32.9 32.9
50 76 126 238 330 388 388 388 -388 388 388 38.8 38.87 185 207 274 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 7 14 13-13 73 I4 109 109 109 109 109 10.9200 3.5 7 12 1.0. ot 13.8 141 14. 14d 14 14.1 14.1250 44° «59 «64.900 44 (168 (148 ISL ESE ESA TSE ISI 15.1300 430¢« 8S SKA f2 $4 $4 54 S54 -54 54
———<——* The pattern in the NONE" column (no stops) shows that the risk-adjusted results, in generalyare more consistent than unadjusted returns.
 
608
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.
. Correlation coefficient, but no less than .25
. Sum of the net $ movement over n, 2 x n, and 4x n days. Slope of an n-day regression converted to 1-day $ change. Wilder’s ADX, but no less than .20
. 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 is
warranted.
VR WN
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 trending 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 true
range (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
13 Based on an idea suggested in Chande and Kroll, The New Technical Trader (John Wiley & Sons, 1994),143, Welles Wilder, “Selection and Direction” in Technical Analysis in Commodities, Perry J Kaufman (ed.)-(JohnWiley & Sons, New York, 1980).Hi'
 
 
 
610 RISK CONTROL,
—S— eeeFIGURE 23-8 Defining theDM.
pew— Zero DMDM
Rising Outside Insidemarket day dayee
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=+ Tg or -DM14 =— TRI4
Once the first DM14 is calculated, an average off technique is used to find each successiveDM14 as follows:4 Prior +DM14
14 + today’s +DM14
Today’s +DM14 = prior +DM1
The same procedure is followed for the true range:
priorTR14© TRI4 — PS
‘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 -DMt
‘Today's TR14 = .93 x (prior TR14) + today’s TRI
At this point, the Directional Indicator can be used as a trading 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 —D!14 follow,and the true directional movement is the difference between +DI14 and —D114. When anupward trend is sustained, the +DI14 becomes larger, the —DI14 becomes smaller, and thetrue directional movement becomes greater. This is then normalized to allow it to beexpressed as a value between 0 and 100. Y
+D114 minus -D114 DI difference
DX= pnd plus ~DN4 %100= Tr Sum — * 100where 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(prion]
Today’s TR14 = priot + today’s TR14
 
Lee
RANKING OF MARKETS JR SELECTION 6tl
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),
AlADxR = ADX (today) + Abxcs days ago)
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:
CSI = ADXR x ATRI14 x ¥,—1_M 150+C
where ADXR = average directional movement index ratingATR14 = 14-day average true rangeV= 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 X, 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.
|x 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:
2 For a general discussion of this topic, see Chapter 21.6 Frank L. Hocbheimer and Richard J. Vaughn, Computerized Trading Techniques 1982 (Merrill Lynch Com-modities, New York, 1982).
 
FIGURE 23-9 Appearance of the ADX and ADXR.
 
“ADXR 4
 
    
 
Amplitude
  
 
612 RISK CONTROL
4. 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 self 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. Ifthe +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 x
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 profitossshown 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 father 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 all 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 from© 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. .
 
 
wows beent
 
 
 
RANKING OF MARKETS FOR SELECTION 613
 
_——$_
TABLE 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 $4,117 $17,152 1238Corn 2120 26,456 -7.072 613.2120 26,456 -7.072 613Cotton 1821 37.495 21,740 (256 2419 -29,765 18,340 1462Copper 1820 219,639 = 10,230 633.12 14 88,561 13,390 1549.Deutschemark 8 13 140,538 6335-27714 14 101,476 423Gold 1510 827,980 10,740 S04. 16 12 664,390» 13.810 t041Cattle 2219 -7,850 11,710 474. «2020 - 14,860 27,920 808Soybeans 1620 254495 39,639 © 895. 1920-177,584 = -29,759 1420Silver 1611 1,034,825 82,870 788-2217 «351,360 136.585 1161TBills 37 37840 12,005 286 8 5.235 -17,545 369TBonds 87 185,371 11,326 4369 BB 118,256 -7294 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:
m= 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.
Results 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 Jarger when the ER is low. Based on a broadsampling of markets, this is a very useful patzern 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 that|
 
614 RISK CONTROL
 
—_——FIGURE 23-10 Efficiency ratio and trend performance. A clear pattern can be seen when along-term efficiency ratio (market noise) is plotted against the trend performance of a broadsampling of markets using a [6-day exponential smoothing.
(65-Day Eff Ratio and 16-Day Trend)
 
 
 
 
 
 
 
400 1am. —ED i
Fz 800 t-te 228a ax Trend profits :p 200 eee ee eee eee ee ~~ with less noise - -& owerBOT ye9 pS - {2 6 Sov cea
sp ° FS
-100 #* |
0.08 O1 O12 0.14 O76 0.18 02 022 0.2465-Day Efficiency Ratio
 
When the efficiency ratio is high, then a trend system is a better strategy.When the efficiency ratio is low, then a countertrend system is best.
In the second case, a countertrend approach does not mean that you must set a short posi-tion when the market is moving up. It can also mean taking profits on a long position whenthere is a countertrend sell signal, or building a iong position when a countertrend buy sig-nal occurs on a price drop. While the efficiency ratio is not specifically a directional indi-cator, it does seem to classify markets as trending or nontrending.
PROBABILITY OF SUCCESS AND RUIN ©
‘The relative size of trading profits and losses; the frequency of the losses, and the sequencein which they occur comprise the equity profile of traders and systems. This profile can beused to determine the capitalization necessary to maintain wading during the losing peri-ods and allow the system to return to its full potential. In investment terminology andprobability theory, the level at which you no longer have enough money to continue trad-ing is called the point of ruin, and the chance of getting there is the risk of ruin. The prob-ability of the risk of ruin is normally expressed as -
-akr={2-4 .1+Awhere 0¢XS'l, 0 indicates no risk, and 1 certain ruinA=P~(1~P),P is the proportion of winning trades, also considered the trader's
advantagec= the beginning units of trading capital
PROBABILITY OF SUCCESS AND RUIN 6sA system of trading that has 60% profitable trades and trading capital in $10,000 units
will have a risk of ruin calculated as follows:
A= 0.60 - (1 ~ .060) = 0.20
e-(3 oy 2 (280). (2)
“\a+0.20 1.20) \3
‘When c = 1 ($10,000), R = 0.33, and when c = 2 ($20,000), R = 0.11. Therefore, the greaterthe trader’s advantage or the greater the capital, the smaller the risk of ruin (Figure 23-11).
When using profit goals, the chance of ruin should decrease as the goal becomessmaller. The relationship can be expressed as:
 
[1 +a)/(1 -A)]o- 1
= Taeaasayrrad O<RS1
where all terms are the same as above, and G is the goal in units of trading capital.
Wins Not Equal to Losses
‘The basic equations just presented are generally applied to gambling situations, where thesize of profits and losses are the same. This requires that the percentage of winning eventsexceed the losing events to avoid ruin, Futures trading, however, often results in more los-ing trades than profitable ones and must, therefore, return much /arger profits than losses.Such a structure is common to all conservation of capital, or trend-following, systems. Thissituation can be applied to the more complex form” where
C= the total capital available for trading (in units)Cp = the cutoff point, where level of ruin is reached (Ck < C7)Cy = Cr— Cp, capital available to be risked‘E = the expected mean return per trade, the probability-weighted sum of values that atrade might take
E=> Pp)
17 Fred Gehm, Quantitative Trading & Money Management (Revised Edition (Irwin, 1995).
FIGURE 23-11 Risk of ruin based on capital.
Risk
 
Capitalaan 
616 RISK CONTROL
where PL, is the possible profit or loss value, and p, is the probability of PL, occurringO<p<d. _
£; is the expected squared mean return per trade, the probability-weighted sum of allthe squared values of a trade,
> @tip)
 
-,where PL, and p, are defined above.D=G/VExP=0.5+E/(2VE)and the risk of ruin isa (eyP
Introducing an objective and a desired level of capital Z, the risk of ruin R becomes
oe [a—-PyPP - 1Rol a= PPPwhereG=VVE ~
As in the first situation, using equal profits and losses, the risk increases as the objective L
increases.
Ralph Vince, in Portfolio Management Formulas (Wiley, New York, 1990) derived sim-ilar results from P Griffin's work, The Theory of Blackjack (Gamblers Press, Las Vegas,1981), which claims to provide a “fair approximation” of risk. Vince’s approach has beenmodified for convenience and given in a way that allows spreadsheet formulas:
Risk of Ruin = ((1 — P/P)(MaxRisk/A) .where the following terms are defined in the order needed for calculation:
AvgWin is the average