function as a low-pass filter.This is illustrated in Figure 8.5, where the moving average has been cen-tered? (lagged by 0.5 x period -1). Note that the output of the moving-average operator is essentially the trend of the original time series withthe high frequency oscillations about the trend removed.
The smoothing effect is accomplished by averaging the values of thetime series within a moving data window called the look-back span. Thiseliminates or reduces the magnitude of fluctuations with durations that areequal to or less than the duration of the look-back span. Thus, a 10-day mov-
Input: Output:Time Series Time Series
Moving-
AverageOperator
 
Time Time
FIGURE 8.5 Moving-average operator: low-pass filter.Case Study of Rule Data Mining for the S&P 500 399
ing average will reduce the amplitude of fluctuations for which peak-to-peakor trough-to-trough duration is less than 10 days, and it will completely elim-inate a fluctuation with a duration that is exactly equal to 10 days.
The benefit of smoothing comes at a cost—lag. In other words, fluctu-ations in the raw price that manifest in the smoothed version experiencesome delay. Thus, a trough in the raw price does not produce a trough inthe moving average until some later date. The amount of lag dependsupon the length of the look-back span. A longer look-back span producesmore smoothing while producing more lag.
The lag induced by a simple moving average, which gives equalweight to all elements in the window, is equal to one-half of the look-backspan minus one. Thus, the output of an 11-day simple moving average hasa lag of (11 — 1)/2 or 5 days. This means that trend reversals in the inputtime series, which are of sufficient duration to manifest in the moving av-erage, will not show up until 5 days later.
There are many types of moving averages, from the simple moving av-erage that gives equal weight to each element in the data window, to so-phisticated smoothing methods that use complex data-weightingfunctions. The benefit conferred by a complex weighting is improved filterperformance—less lag for a given degree of smoothing. The field of digitalsignal processing is concerned with, among other things, the design ofweighting functions that maximize filter performance. Digital filters thatare relevant to TA are discussed in two books by Ehlers.'!
The calculation for a simple moving average is given by the followingformula.'*
Moving Average Operator
Pr+ Pry + Pra... + Pent]MAy=—§ ————__——n
n¥ Priv]-
n
Where:P: = Price at time tMAt = Moving average at time tn= Number of days used to compute moving average400 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
The lag of a simple moving average can be reduced while maintain-ing the same degree of smoothing by using a linearly weighted movingaverage. As pointed out by Ehlers'® the lag of a linearly weighted movingaverage with a look-back span of n days is (n — 1)/3 compared with (n —1)/2 for a simple moving average. Thus, a linearly weighted moving aver-age with a span of 10 days will have a lag of 3 days whereas a simplemoving average with the same span will have a lag of 4.5 days. The lin-ear-weighting scheme applies a weight of n to the most recent datapoint, where n is the number of days in the moving average look-backspan, and then the weight is decreased by one for each prior day. Thesum of the weights becomes the divisor. This is illustrated in the follow-ing equation:
Linear Weighted Moving Average
Weightsa
(n) x Pe+ (n-1) x Pe] +... + (H-(t-n+1)) x Prn+1
 
WMAt =: n+n1+...+ (trl)ee
Sum of Weights
Where:Pr = Price at time tWMA; = Weighted moving average at time tn= Number of days used to compute moving average
The case study used a four-day linearly weighted moving average tosmooth indicators used in rules that signal when the indicator crossesabove or below a critical threshold. Smoothing mitigates the problem ofexcessive signals that an unsmoothed version of the indicator wigglingback and forth across the threshold would produce. The calculation of aCase Study of Rule Data Mining for the S&P 500 401
four-day linearly weighted moving average is illustrated in the followingequation:
Four Day Linear Weighted Moving AverageWeights
SS
ma
a ~ mn(4)x Pro + (3)x Pry + (2)x Pp-2 + (1)x Pe-310
i
Sum of Weights
 
WMAt =
Where:Pr = Price at time tWMAt = Weighted moving average at time tn= Number of days used to compute moving average
Channel-Normalization Operator(Stochastics): CN
The channel-normalization operator (CN) removes the trend in a timeseries, thus clarifying short-term fluctuations around the trend. Channelnormalization detrends the time series by measuring its current posi-tion within a moving channel. The channel is defined by the maximumand minimum values of the time series over a specified look-back span.In this way it is similar to the channel breakout operator discussedearlier.
The channel normalized version of a time series is scaled to the range0 to 100. When the raw time series is at its maximum value within thelook-back span, CN assumes the value of 100. When the series is at theminimum value within the look-back span the CN is equal to zero. A valueof 50 indicates the series is currently midway between its maximum andminimum values.402 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
The calculation of CN is illustrated in the following equation:
Channel Normalization Operator
St- Smin-nCNt =| —————————_ | 100
Smax-n~ Smin-n
Where:CNt = n day channel normalized value on day tSt = Value of time series at time tSmin-n = Minimum value of time series, last n daysSmax—-n = Maximum value of time series, last n daysn= Channel look-back span in days
An example of the calculation is illustrated in Figure 8.6.
In terms of its filtering properties, the CN operator functions as ahigh-pass filter. In contrast to the moving average, a low-pass filter, CN ex-presses the short-period (high-frequency) oscillations in its output whilefiltering out the long-period fluctuations or trend. This is illustrated in Fig-ure 8.7. Note that the input series has a distinct upward trend, but the out-put series has no trend.
InputSeries Look-Back Span
Channel Maximum: 83
 
 
 
 
 
Channel Minimum: 60 .Time
Channel Normalized Value = (75 - 60)/(83-60) = 0.65
FIGURE 8.6 Channel normalization.Case Study of Rule Data Mining for the S&P 500 403
Input: Output:Time Series Time Series
 
 
E> cy- Operator
 
Time Time
FIGURE 8.7 Channel normalization operator: a high-pass filter.
The CN operator has been known in TA at least as far back as 1965when Heiby" used it to formulate divergence rules. He measured diver-gences by comparing the channel normalized value of the S&P 500 withthe channel normalized value of a market breadth indicator. According toHeiby, a divergence occurred when one series was in the upper quartile ofits 50-day range (CN > 74) while the other series was in the lower quartileof its range (CN <26). Sometime in the early 1970s, a virtually identical op-erator was described by George Lane,'* who dubbed it stochastic. Unfor-tunately, the name is a misnomer. In reality, stochastic is a mathematicalterm that refers to the evolution of a random variable through time. Thereis nothing random about the CN operator, which is a completely determin-istic data transformation. This text uses the term channel normalization(CN) rather than Lane’s term, because it accurately describes what the op-erator does. Most TA writings continue use the term stochastics. The casestudy utilizes the CN operator for two types of rules: (1) extremes andtransitions and (2) divergences. They are discussed in following sections.
Indicator Scripting
As discussed earlier, the time series that are used as inputs to the rulesmay either be in raw form, just as they comes from the market, or in theform of indicators—times series that have been created by applying oneor more mathematical, logical, or time-series operators to one or moreraw time series. The specification of an indicator may require the applica-tion of several operators. For example, the raw time series might first besmoothed with a moving average and then channel normalization is ap-plied to the smoothed version. When the creation of an indicator involvesmultiple steps, it is convenient to express it in terms of an indicatorscripting language (ISL). An ISL expression succinctly depicts the set oftransformations used to create the indicator from raw time series.404 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
My first exposure to an ISL was Gener, which was developed in 1983for Raden Research Group by friend and colleague Professor John Wol-berg. Today, ISLs are common. All rule back-testing platforms," such asTradeStation, Wealth-Lab, Neuro-Shell, Financial Data Calculator, and soforth have an ISL. Though each ISL has features unique to it, they sharesimilar syntaxes. The most basic ISL statement is a time-series operatorfollowed by a set of parentheses that contain the arguments of the opera-tor. The arguments are the items that must be defined for the operator todo its thing. Operators differ in terms of the number of arguments re-quired. For example, the moving-average operator requires two argu-ments: a data series to which the operator will be applied and the numberof periods in the look-back span. Thus a moving-average indicator wouldbe specified by a statement such as this:
Moving Average Indicator = MA (input series, N)
Where:MA is the moving average operatorNis the number of days in the moving average.
The general form of an indicator expression in scripting lan-guage is:
Indicator = Operator (Argument,, Argument,, . . . , Argument,)
Where:iis the number of arguments required by the operator.
Figure 8.8 shows the ISL syntax for the operators defined thus far:channel breakout, moving average, and channel normalization.
A key benefit of ISL is the ability to define complex indicators by nest-ing operators. In nesting, the output of one operator becomes an argu-ment for a second operator and so on. For example, if one wanted todefine an indicator that is the 60-day channel normalization of anothertime series that is a 10-day moving average of the Dow Jones Transporta-tion Index, the expression for the indicator in ISL would look somethinglike this:
Indicator = CN [MA(DJTA, 10), 60]Case Study of Rule Data Mining for the S&P 500 405
Channel-Breakout Operator (CBO)Number of Arguments = 2:
Indicator = CBO (Time Series, n)
 
Moving-Average Operator (MA) or Linear Weighted MA (LMA)Number of Arguments = 2:
Indicator = MA or LMA (Time Series, n)
 
Channel-Normalization Operator (CN)Number of Arguments = 2:Indicator = CN (Time Series, n)
FIGURE 8.8 Indicator scripting language for three TA operators.
INPUT SERIES TO RULES: RAW TIME SERIESAND INDICATORS
 
This section describes the 24 raw time series used in the case study aswell as the 39 time series that were ultimately used as rule inputs. Ten ofthe 39 inputs were in the form of raw unprocessed time series: S&P 500closing price, Dow Jones Transportations Index closing price, NASDAQComposite Index closing price, and so forth. The additional rule 29 inputswere indicators derived from one or more raw time series.
Raw Time Series
The 24 raw time series used in the case study came from two sources:Ultra Financial Systems*’ and Market Timing Reports.”! They are shownin Table 8.1.
Indicators
Twenty-nine of the 39 rule inputs were indicators derived by transform-ing one or more raw time series with various mathematical, logical, and406
CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
TABLE 8.1 Raw Time Series
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Number Raw Data Series Abbreviation Source] S&P 500 Daily Close SPX Ultra 82 S&P 500 Open SPO Ultra 8&3 DJIA High DJH Ultra 84 DJIA Low DJL Ultra 85 DJIA Close DIC Ultra 86 S&P Industrials SPIA Market Timing Reports7 Dow Jones Transports DJTA Market Timing Reports8 Dow Jones Utilities DJUA Market Timing Reports9 NYSE Financial Index NYFA Market Timing Reports10 Dow Jones 20 Bonds DJB Ultra 811 NASDAQ Composite Close OTC Ultra 812 Value Line Geometric Close = VL Ultra 8&13 NYSE Advancing Issues ADV Ultra 814 NYSE Declining Issues DEC Ultra 815 NYSE Unchanged Issues UNC Ultra 816 NYSE New 52-Week Highs NH Ultra 8&17 NYSE New 52-Week Lows NL Ultra 8&18 NYSE Total Volume TVOL Ultra 819 NYSE Upside Volume UVOL Ultra 820 NYSE Downside Volume DVOL Ultra 8&21 3-Month T-Bill Yields T3M Market Timing Reports22 10-Year T-Bond Yields TIOY Market Timing Reports23 AAA Bond Yields AAA Market Timing Reports24 BAA Bond Yields BAA Market Timing Reports
 
time-series operators. This section describes the transformations used toproduce these indicators.
The indicators are presented in four categories: (1) price and volumefunctions, (2) market-breadth indicators, (3) prices-of-debt instruments,
and (4) interest-rate-spread indicators.
Price & Volume Functions.
Fifteen (15) indicators were functions
that combine price and volume information. A number of studies haveCase Study of Rule Data Mining for the S&P 500 407
shown that trading volume contains useful information both on itsown and when used in conjunction with price.” Technical analysispractitioners have suggested a number of price and volume functions:on-balance volume, accumulation distribution volume, money flow,negative volume, and positive volume. Each of these functions is de-scribed below.
The price-volume functions were used to create two types of indica-tors: (1) cumulative sums and (2) moving averages. An indicator definedas a cumulative sum is the algebraic sum of all prior daily values of theprice-volume function. The daily value of a price-volume function can ei-ther be a positive or negative quantity. Thus, an indicator defined as thecumulative sum of the on-balance volume, at a given point in time, is equalto the sum of all prior values of the daily on-balance-volume quantity. Anindicator defined as a cumulative sum will display long-term trends simi-lar to those observed in the levels of asset prices and interest rates. Inother words, these indicators are nonstationary time series.
In contrast, a moving average of a price-volume function will be a sta-tionary time series. In other words, it will not display trends. This is ex-plained by the fact that a moving average only considers the observationswithin the look-back span. Since price and volume functions can assumeboth positive or negative values, a moving average will tend to remainwithin a relatively confined range near zero. See Figure 8.9.
Cumulative SumPrice-Volume Function
 
Time
Moving AveragePrice-Volume Function
0 Time
FIGURE 8.9 Cumulative sum versus moving average of price-volume functions.408 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
Cumulative On-Balance Volume. Perhaps the first invented price &volume function was the cumulative on-balance-volume indicator,which is attributed to Joseph Granville and Woods and Vignolia.” It is acumulative sum of signed (+ or —) total market volume. The algebraicsign of the volume for any given day is determined by the sign of thechange in a market index for the current day, week, or whatever timeinterval is being used. The case study used daily market changes in theS&P 500 to determine the appropriate sign for the volume. If the priceof the index rose on a given day, that day’s entire NYSE volume was as-signed a positive value and the number of shares traded was added tothe prior cumulative sum. On days when the price declined, the NYSEvolume was assigned a negative value and added to the prior cumula-tive sum (i.e., subtracted).
The computation for the cumulative on-balance volume is shown inthe following equation:?4
Cumulative On-Balance Volume (COBV)
COBV: = COBV:-1 + (ftVi)
ft =1.0 if Pct> Pct-|
ft =-1.0 if Pet < Pct]
fr =0 if Pcp = Pcp]Where:
OBV; = (ftVt) = On-Balance Volume for day tCOBV; = Cumulative On-Balance Volume for day tVt = NYSE volume for day tPct = Closing price S&P 500 for day t
Moving Averages of On-Balance Volume. In addition to the cumula-tive on-balance volume, two moving averages of daily on-balance vol-Case Study of Rule Data Mining for the S&P 500 409
ume were considered: for 10 and 30 days (OBV10, OBV30). In ISL theywould be:
OBV10=MA(OBV, 1 0)OBV30=MA(OBV, 30)
where OBV represents the on-balance volume for a given day.
Cumulative Accumulation-Distribution Volume (CADV). Anotherprice-volume function, accumulation distribution volume, isattributed to Marc Chaiken.”* However, there are several similar func-tions including: Intra-day Intensity developed by David Bostian andVariable Accumulation Distribution developed by Larry Williams.These transformations attempt to overcome a perceived limitation inon-balance volume, which treats the entire day’s volume as positive(negative) even if the market index had a miniscule positive (negative)price change. It was felt that minor price changes should not be treatedthe same as large price changes. The proposed modifications to on-balance volume sought to ameliorate on-balance volume’s all-or-noneapproach.
Chaiken proposed that a day’s price activity could be more accu-rately characterized by quantifying the position of the closing pricewithin the high-low range. Specifically, his calculation takes the differ-ence between the closing price and the midpoint of the daily range anddivides the difference by the size of the range. The assumption is that,when the market closes above the midpoint of its daily range, bullish oraccumulation activity dominated the day’s trading activity (accumula-tion) and should predict higher prices. Conversely when the marketcloses below the midpoint of its daily range, the day is said to be domi-nated by bearish or distribution activity and should predict lowerprices. Only if the index closed at the low of the day or the high of theday is the entire day’s volume assigned a negative (distribution) or posi-tive (accumulation) value. More typically, the close is somewherewithin the day’s range resulting in some fraction of the volume being as-signed to accumulation (positive volume) or to distribution (negativevolume). The range factor, which is defined below, quantifies the posi-tion of the closing price within the day’s range. The range factor ismultiplied by the daily volume, and this figure is accumulated to pro-duce the cumulative sum. The calculation is shown in the followingequation.”°410 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
Cumulative Accumulation/Distribution Volume
CADV; = CADV;-) + (Vt x Rfp
(Pct — Plt) — (Pht — Pct)(Pht — Plt)
Range Factor (Rft) =
Where:ADV; =Vt x Rft = Accumulation/Distribution Volume for day tCADV; = Cumulative Accumulation/Distribution Volume for day tVt = NYSE volume for day tRft = Range factor for day tPct= Closing price Dow Jones Industrials for day tPlt = Low price Dow Jones Industrials for day tPht = High price Dow Jones Industrials for day t
The case study used data for Dow Jones Industrials for the calcula-tion of the accumulation-distribution function rather than the S&P 500 be-cause daily high and low prices were not available for it. I assumed thatthe closing position of the Dow Industrials within its range would be simi-lar to the closing position of the S&P 500 within its range.
Moving Averages of Accumulation Distribution Volume. Movingaverages of daily accumulation/distribution values were constructed for10- and 30-day periods. In ISL they are:
ADV10=MA(ADV, 1 0)ADV30=MA(ADV, 30)
Cumulative Money Flow (CMF). Cumulative money flow (CMF) issimilar to CADV with the exception that the product of volume andrange factor is further multiplied by the price level in dollars of the S&P500 Index. This is intended to measure the monetary value of the vol-ume. The price level used is an average of the daily high, low, and clos-ing prices. The computation is shown in the following equation:”’Case Study of Rule Data Mining for the S&P 500 411Cumulative Money Flow
CMF; = CMFy-) + (Vt x Apt x Rfp
(Pct - Pit) - (Pht - Pcp)(Pht - Plt)
Range Factor (Rf}) =
Where:MF = (Vt x Apt x Rft) = Money Flow for day tCMFt = Cumulative Money Flow for day tApt = Average price S&P 500 for day t: (Hi + Lo + Close)/3Vz = NYSE volume for day tRft = Range Factor for day tPct = Closing price Dow Jones Industrials for day tPlt = Low price Dow Jones Industrials for day tPht = High price Dow Jones Industrials for day t
Moving Averages of Money Flow. Moving averages of money flowwere constructed for 10- and 30-day periods. In ISL they are:
MF10=MA(MF, 10)MF30=MA(MF, 30)
Cumulative Negative Volume Index (CNV). Cumulative negativevolume is an accumulation of price changes on days of lower trading vol-ume. In other words, it is a continuous algebraic sum of daily percentagechanges in a stock market index on days when volume is less than theprior day. When volume is equal to or greater than a prior day, the CNV re-mains unchanged.
The inventor of CNV is unclear. Several sources attribute it to Nor-man Fosback* but several sources, including Fosback, attribute theidea to Paul Dysart.”® However, it seems clear that it was Fosback whodeveloped objective signal rules for CNV and evaluated their predictivepower.”
The notion of negative volume is based on the conjecture that “trad-ing by unsophisticated investors occurs predominately on days of exu-berantly rising volume, whereas informed buying and selling (i.e.,412 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
smart-money activity) usually occurs during quieter periods of declin-ing volume. Therefore, the direction that the market assumes on days ofnegative volume purportedly reflects accumulation (buying) or distribu-tion (selling) of stock by those who are in the know.”®!
The computation of the index is as shown in the following equation:
Cumulative Negative Volume Index (CNV)
CNVt aa CNVt-1 + ft
ft = [(Pct/Pct-1)-1] x 100 if Vt< Vielft =0 if Ve> or = Ve
Where:
NVt = ft = Negative Volume Index for day tCNV = Cumulative Negative Volume Index for day tVt = NYSE volume for day tPct= Closing price S&P 500 for day t
Moving Averages of Negative Volume Index. Moving averages of thedaily value of negative volume index (i.e., index’s percentage change onlower volume days) were constructed for 10- and 30-day periods. In ISL:
NV10=MA(NV, 10)NV30=MA(NV,30)
Cumulative Positive Volume Index (CPV). Cumulative positive vol-ume (CPV) is the opposite of CNV. It is an algebraic accumulation of mar-ket index changes for days when volume is greater than the prior day.Positive volume index is variously attributed to Fosback’” and to Dysart.The calculation is presented in the equation that follows. It seems as ifDysart proposed the positive volume index and suggested ways of inter-Case Study of Rule Data Mining for the S&P 500 413
preting it in a subjective manner, whereas Fosback defined objective rulesand formally tested them:
Cumulative Positive Volume Index (CPV)
CPV; = CPVt-1 + ft
fr =[(Pct/Pcp-1)-1] x 100 if Ve> Ve-1ft =0 if Vp<or= Ve]
Where:
PV; = ft = Positive Volume Index for day tCPV; = Cumulative Positive Volume Index for day tV_= NYSE volume for day tPct = Closing price S&P 500 for day t
Moving Averages of Positive Volume. Moving averages of daily val-ues of the positive volume index were constructed for 10- and 30-day peri-ods (PV10 and PV30). In ISL:
PV10=MA(PY, 1 0)PV30=MA(PV, 30)
Market Breadth Indicators. Market breadth refers to the spread ordifference between the number of stocks advancing and the number de-clining on a given day, week, or other defined time interval. Breadth hasbeen measured in a variety of ways, and they are reviewed in a scholarlystudy by Harlow.” For purposes of the case study, breadth is defined asthe daily advance-decline ratio; that is, it is the difference between a day'sadvancing and declining issues divided by the total number of issuestraded. The data is based on all issues traded on the NYSE rather than analternative version that is restricted to NYSE common stocks. The seriesrestricted to common stocks, which some have claimed is superior be-cause it excludes closed-end stock and bond funds and preferred stocks,was not available in computer-readable form for the time period required.414 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
The case study’s breadth indicators are of two forms: cumulativesums of daily figures and moving averages of daily figures. For reasonspreviously explained, the breadth indicators that are cumulative sums dis-play long-term trends, whereas moving-average breadth indicators tend tohave reasonably stable mean values and fluctuation ranges.
Cumulative Advance-Decline Ratio (CADR). The cumulative ad-vance decline ratio or CADR is a cumulative sum of the daily advance-decline ratio:
CADR; = CADRp| + ADRt
ADRt = adv, - dectadvt+ decy + uncht
Where:
CADR; = Cumulative Advance/Decline Ratio for daytADR; = Advance/Decline Ratio for day tadv, = NYSE advancing issues for day t
dec, = NYSE declining issues for day tunch; = NYSE unchanged issues for day t
Moving Averages of Advance-Decline Ratio. Moving averages ofdaily advance-decline ratio (ADR) were constructed for 10- and 30-day pe-riods (ADR10 and ADR30). In ISL they are:
ADR10=MA(ADR, 10)ADR30=MA(ADR, 30)
Cumulative Net Volume Ratio (CNVR). Another measure of marketbreadth is the net volume ratio. It is based on the difference between dailyupside and downside volume. Upside (downside) volume is the total num-ber of shares traded in stocks that closed up (down) for the day. The inno-vation of calculating and analyzing upside and downside volumeseparately is attributed to Lyman M. Lowry in 1938.*4 The daily net volumeratio, a quantity that can assume either positive or negative values, is thedifference between upside and downside volume divided by total tradingvolume. The case study used statistics released daily by the New YorkCase Study of Rule Data Mining for the S&P 500 415
Stock Exchange. The cumulative net volume ratio (CNVR) is the cumula-tive sum of daily ratios:
Cumulative Net Volume Ratio (CNVR)
CNVRt = CNVRz-1 + NVRt
NVRt upvolt— dnvolt
upvol, + dnvol, + unchvolt
Where:
CNVRt = Cumulative Net Volume Ratio for day tNVRt = Net Volume Ratio for day tupvolt = NYSE advancing volume for day tdnvol,t = NYSE declining volume for day tunchvoly = NYSE unchanged volume for day t
Moving Averages of Net Volume Ratio. Moving averages of the dailynet volume ratio were constructed for 10- and 30-day periods (NVR10 andNVR30). In ISL:
NVR10=MA(NVR, 10)NVR30=MA(NVR, 30)
Cumulative New Highs-Lows Ratio (CHLR). A third measure ofbreadth, the cumulative new highs and new lows ratio (CHLR), takes alonger-term view. In contrast to CADR and CNVR, which are based ondaily price changes and daily volumes, CHLR is based on a stock’s currentprice relative to its maximum and minimum price over the preceding year.Specifically, CHLR is the cumulative sum of the daily new highs-new lowsratio (HLR), a quantity that can assume positive or negative values. Thehigh-low ratio is defined as the difference between the number of stocksmaking new 52-week highs on the day and the number of stocks makingnew 52-week lows on the same day divided by the total number of issuestraded that day. This figure is accumulated algebraically to obtain CHLR.There is nothing particularly significant about using a look-back inter-val of 52 weeks. It is simply the mostly widely available statistic for newhigh and new low data. Prior to 1978, the number of issues making highsand lows was not based on a consistent 52-week look-back span. Fromthe middle of March in any given year, the data were based only on the416 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
current calendar year. Prior to the middle of March, the figures werebased on the current and prior years. Thus, over the course of a givenyear, the look-back