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178 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 markei, from standard statistical techniques to more complex rules. Each unique method will measure some special characteristic of price movement To take advantage of this it is necessary to trade using a system that targets this type of price pattem. For example if you use a correlation coeffl ient, to rank the trend over 20 days then a linear regression is prob2b\y the best choice of a trendfollowing system, using a peilod no greater than 20 days. It may be interesting to list a number of trendranking approaches, then keep track of their values in a table over various time periods." For example, the five measurements below 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 , 2 x , and 4 x w days 3. Slope of an day regression ronverted to 1day S change 4. VHIder 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 represent significant trends. For the correlation coefficient, anything below .25 is most likely to be a sidewajs maitet; similarly, Wilders ADX would need to be above .20 to indicate a trend. If the results are erratic, it may be necessary to smooth the last 3 days of each value, in the case of item 5, higher volatility is often associated with greater profits and greater risk for a trendfollowing sjstem; therefore, a careful look at how ranking affects performance is warranted. Commodity Selection Index (CSl) Among Wilders trading tools is the Commodity Selection Index (CSl)," a calculation for determining which products are most likely to make the greatest move for each dollar invested. In this case, the movement measured is directional and, therefore, may apply more to trending models The CSl combines directional movement, volatility, margin requirements, 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 movement, the greater of either: 1. Plus DM (+DM), todays high minus yesterdays high, or 2. Minus DM (DM), todajs low minus yesterdays low The directional movement is either up or down, whichever is larger. It is the largest part of todays range which is outside yesterdays range. When an inside day occurs, the directional movement is zero (Figure 238). DM is expressed relative to the daily range (high minus low), defined as todays true range (TRl), the laiger of the following: 1. Todays high minus todays low 2. Todays high minus yesterdays close 3. Yesterdays close minus todays low FIGURE 238 Defining die DM.
The true range is always positive. f called the Direc tional bdic.*TTo< s brectional mdic.*T is calnilated usiue either tiie plus +DM14 = + DM14 DMH =  TR14 TR14 Once the first DM 14 is calculated, an average off technique is used to find each successrve DM14 as follows: prior +DM14 Todays +DM14 = prior+DM14 + todays +DMH The same procedure is followed for the true range: These results can also be produced using a smoothing constant of .93 as follows: Todays +DM14 = 93 X (prior +DM14) + todays +DM 1 Todays DM 14 = .93 X ( prior DM 14) + todays DM 1 TodaysTRI.4 =.93 x (prior TR14) . todays TRI At this point, the Direaional Indicator can be used as a trading indicator, and is the subjea of the nest seaion; however, Wilders interest was to use this in a more complete concept. Once the +DMI4, DMI4, and the TR14 are calculated, +D11* and DI 14 follow, and the true directional movement is the difference between +DII I and DI I I. When an upward trend is sustained, the+DII4 becomes laiger, theDI 14 becomes smaller, andthe true directional movement becomes greater. This is then normalized to allow it to be expressed as a value between 0 and 100. DI sum dDIHplusDlJ4 wliere multiplying by 100 converts ttie percemage lo a whole number Tht DX is iheti snHiothcd out using a l4day average {or 0 07 smooihing con.stam). and is called the Aierage Direclional Moivnient Imicx (ADX) AllX(todav) = AllX{prror) + O"" v llX(t(Klai)  ADX(prior)l One last adjustment is made to the exfreme variance of the ADX by taking the 14day difference ofADXs. This final rating is called the Average Directional Movement Index Rating (ADXR),
ADX(today) + ADX(14 days ago) The ADX and ADXR are shown plotted together in Figure 239 The ADX is seen to oscillate about the ADXR. Measuring the amplitude of the ADX from the zero line, a higher anlitude means higher directional movement and a sUonger frend, whether up or down. The peaks are alwajs the extremes in the same direction as the frend. If the major frend was down, the peaks would be extremely low points and the vallejs would be relatively high points. The greater the distance between the peaks and vallejs, the greater are the reactions to the frend. All this leads to the Commodity Selection Index (CSl), which is calculated as: CSl = ADXR X ATR14 x X. 1 M iso + c X lOU where ADXR = average directional movement index rating ATR14 = 14day average true range V= conversion factor; value of a Ic move (in dollars) M = maigin (in dollars) = commissions (in dollars) Note that for a particular commodity, the values in brackets do not change. By calculating them once and that value K, the CSl can be expressed as: CSI = ADXRxATR14xK A portfolio allocation can be chosen by calculating the CSl daily (or weekly) for each commodity. Simply select those products to trade that have the highest CSl or allocate multiple contracts in proportion to their CSl value. Optimizing Directional Movement The +DII4 and DII.4 are indicators that can be used in a simple trading strategj Hochheimer, known for other shidies of moving averages, crossovers, and channels, has defined the rules of a Directional Movement Sjstem in two wajs. The first set of rules are: FIGURE239 Appearance of the ADX and ADXR. I. a. if the +DI crosses above the DI, enter a buy stop on the next day using todays high price. This order remains as long as it is not executed and +DI remains higher than DI. b. If the DI crosses below the +DI, enter a sell stop on the next day using todays low price. 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 an immediate maiket entrj following the crossing of the directional indicators:
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