span used to determine if a stock was making a newlow or a new high varied from 2.5 months in mid-March to as long as 14.5months just before mid-March. Most of the data used in this study waspost-1978.
Despite the distortions created by the variable look-back span, ruletests based on pre-1978 high-low data suggested that the indicator’s infor-mation content was robust to this distortion. For example, Fosback devel-oped and tested an indicator called the high-low logic index over theperiod 1944 to 1980. His results showed that indicator demonstrated pre-dictive power over the entire period even though the bulk of the data wasinfected with the variable look-back span distortion.” The formula forconstructing the CHLR series is shown here:**
Cumulative New Highs New Lows (CHLR)
CHLR; = CHLRz-) + HLRt
HLRr al nuhit - nuloradvt + dect + uncht
Where:
CNHL, = Cumulative New Highs New Lows on day tHLRt = New Highs New Lows on day tnuhit = NYSE new 52-week highs day tnulot = NYSE new 52-week lows day tadv; = NYSE advancing issues for day tdec; = NYSE declining issues for day t
uncht = NYSE unchanged issues for day t
Moving Averages of New Highs/New Lows Ratio (HLRI1 andHLR30). Moving averages of the daily high/low ratio were constructedfor 10- and 30-day periods (HLR10 and HLR30). In ISL they are:
HLR10=MA(HLR, 1 0)HLR30=MA(HLR, 30)
Prices-of-Debt Instruments from Interest Rates. Typically, inter-est rates and stock price levels move inversely. However, by taking the recip-Case Study of Rule Data Mining for the S&P 500 417
rocal (l/interest rate) interest rates can be transformed into price-liketime series that are, in general, positively correlated with stock prices.This reciprocal series can be multiplied by a scaling factor such as 100.Thus, a rate of 6.05 percent would be equivalent to a price of 15.38 (1/6.05x 100).
This transformation was used in the case study and was performedon four interest rate series: three-month treasury bills, 10-year treasurybonds, Moody’s AAA corporate bonds, and Moody’s BAA corporatebonds.
Interest Rate Spreads. An interest-rate spread is the differencebetween two comparable interest rates. Two types of interest-ratespreads were constructed for the case study; the duration spread andthe quality spread. The duration spread, also known as the slope of theyield curve, is the difference between yields on debt instruments havingthe same credit quality but having different durations (i.e., time to matu-rity). The duration spread used in the case study was defined as the yieldon the 10-year treasury note minus the yield on the three-month treasurybills (10-year yield minus 3-month yield). The spread was defined in thisway rather than 3-month minus 10-year so that an upward trend in thespread would presumably have bullish implications for the stock market(S&P 500).*”
A quality spread measures the difference in yield between instru-ments with similar durations but with different credit qualities (defaultrisk). The quality spread for the case study was based on two ofMoody’s® long-term corporate bond series: AAA,®® which are the high-est rated corporate debt, and BAA,“ a lower rated grade of corporatedebt. The quality spread is defined here as AAA yield -BAA yield. Whenrates on lower quality debt (higher default risk such as BAA ratedbonds) are falling faster than rates on higher quality debt such as AAArated bonds, it is interpreted as indication that investors are more will-ing to assume additional risk to earn the higher yields on lower qualitydebt. In other words, a rising trend in the quality spread is a signal thatinvestors are willing to take higher risks to earn higher returns. By thisreasoning, the quality spread should trend in the same direction asstocks.
TABLE OF 40 INPUT SERIES USED IN CASE STUDY
 
 
Table 8.2 lists all of the data series used as rule inputs in the case study.418 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
TABLE 8.2 Input Series Used in the Case Study
Number Description Abbreviation Form
1 S&P 500 Close SPX Raw
2 S&P 500 Open SPO Raw
3 S&P Industrials Close SPIA Raw
4 Dow Jones Transportation Index DJTA Raw
5 Dow Jones Utility Index DJUA Raw
6 NYSE Financial Index NYFA Raw
7 NASDAQ Composite OTC Raw
8 Value Line Geometric Close VL Raw
9 Cumulative On-Balance Volume COBV Indicator10 On-Balance Volume 10-Day MA OBV10 Indicator1 On-Balance Volume 30-Day MA OBV30 Indicator12 Cumulative Accum. Distr. Volume CADV Indicator13 Accum. Distr. Volume 10-Day MA ADV10 Indicator14 Accum. Distr. Volume 30-Day MA ADV30 Indicator15 Cumulative Money Flow CMF Indicator16 Money Flow 10-Day MA MF10 Indicator17 Money Flow 30-Day MA MF30 Indicator18 Cumulative Negative Volume Index CNV Indicator19 Negative Volume Index 10-Day MA NV10 Indicator20 Negative Volume Index 30-Day MA NV30 Indicator21 Cumulative Positive Volume Index CPV Indicator22 Positive Volume Index 10-Day MA PV1O Indicator23 Positive Volume Index 30-Day MA PV30 Indicator24 Cum. Advance Decline Ratio CADR Indicator25 Advance Decline Ratio 10-Day MA ADR10 Indicator26 Advance Decline Ratio 30-Day MA ADR30 Indicator27 Cum. Up Down Volume Ratio CUDR Indicator28 Up Down Volume Ratio 10-Day MA UDRI10O Indicator29 Up Down Volume Ratio 30-Day MA UDR30 Indicator30 Cum. New Highs/New Lows Ratio CHLR Indicator31 New Highs/New Lows Ratio 10-Day MA HLR1O Indicator32 New Highs/New Lows Ratio 30-Day MA HLR30 Indicator33 NYSE Volume TVOL Raw34 Dow Jones 20 Bond Index DJB Raw35 Price 3-Month T-Bill PT3M Indicator36 Price 10-Year Treasury Bond PTIOY Indicator37 Price AAA Corporate Bonds PAAA Indicator38 Price BAA Corporate Bonds PBAA Indicator39 Duration Spread (10 Year -3 Month) DURSPD Indicator
 
40 Quality Spread (BAA-AAA) QUALSPD Indicator
 Case Study of Rule Data Mining for the S&P 500 419
THE RULES
 
The rules tested in the case study can be grouped into three categories,each representing a different theme of technical analysis: (1) trends, (2)extremes and transitions, and (3) divergence. The following sections de-scribe the rules in each category.
Trend Rules
The first category of rules is based on trends. A foundational principle ofTA is that prices and yields move in trends that can be identified in a suffi-ciently timely manner to generate profits. Practitioners have developed avariety of objective indicators to define the direction of the current trendand signal trend reversals. Among the most widely used are moving aver-ages, moving-average bands, channel breakout, and Alexander filters alsoknown as zigzag filters. These are described in Kaufman"! and there is noneed to cover them all here.
The trend rules in the case study used the channel breakout operatoror CBO to define trends in the input time series. Thus, the CBO operatortransformed the input time series into a binary valued time series consist-ing of +1 and —-1. When the trend of the input series was in an uptrend, asdetermined by the CBO, the rule’s output was +1. Conversely, when theanalyzed series was determined to be in a downtrend, the output was -1.
The identification of trend reversals in the input series by CBO is sub-ject to lag. All trend indicators necessarily incur lag—a delay between thetime the input series experiences a trend reversal and the time the opera-tor is able to detect it. Lag can be reduced by making the indicator moresensitive. For example, in the case of CBO, lag can be reduced by decreas-ing the number of periods in the look-back span. However, this fix createsa different problem—an increased number of false signals. In other words,there is a tradeoff between a trend-following indicator’s lag and its accu-racy. Therefore, all trend indicators attempt to strike a reasonable balancebetween signal accuracy and signal timeliness. Finding the optimum is achallenge in the design of any signaling system, be it a household smokedetector or a TA trend rule. In the end, optimal is whatever maximizes theindicator’s performance, such as average return, risk-adjusted rate of re-turn, and so forth. Since the behavior of financial market time serieschanges over time, the optimal look-back span for the CBO operator wouldchange as well. Adaptive versions of CBO were not used in the case study.
Of the 40 input series depicted in Table 8.2, 39 were used as inputs forthe trend rules. The open price of the S&P 500, input series 2 in Table 8.2,was excluded on grounds of being redundant of the S&P 500 close.420 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
Each trend rule was defined by two parameters or arguments: theCBO look-back span and a time series chosen from the set of 39 candi-dates shown in Table 8.2. A set of 11 values were tested as look-backspans. They were 3, 5, 8, 12, 18, 27, 41, 61, 91, 137, and 205 days. The val-ues were chosen to be separated by a multiplier of approximately 1.5. Forexample, the look-back span of 205 days is approximately 1.5 times 137days. This resulted in a total of 858 trend rules, 429 (89 x 11) based on atraditional TA interpretation, and an additional 429 inverse-trend rules.
A traditional version of a trend rule produced an output value of +1(long position in the S&P 500) when the input time series was determinedto be in an upward trend by CBO operator, and an output value of —1(short position in the S&P 500) when the time series was in downtrend ac-cording to CBO operator. Inverse trend rules simply produced the oppo-site signals (e.g., short S&P 500 when the analyzed series was determinedto be in an uptrend).
In Chapter 9, where test results are reported, the following shorthandnaming convention will be used for the traditional and inverse trend rules.A naming convention was necessitated by the large number of rules. Thesyntax of the naming convention is as follows (note this syntax is differentfrom the syntax used for indicator scripting):
Rule (TT or TD — Input Series Number — Look-back SpanWhere TT stands for a traditional trend ruleand
TI stands for an inverse trend rule
For example, the rule named TT-15-137, is a traditional trend rule ap-plied to input series 15 (Cumulative Money Flow) using a look-backspan of 137 says. A rule named TI-40-41 is an inverse trend rule appliedto input series 40 (the quality spread BAA— AAA) using a look-back spanof 41 days.
Extreme Values and Transitions
The second category of rules considered in the case study is “ExtremeValues and Transitions” or £ rules. This category is based on the notionthat a time series conveys information when it assumes an extreme highor low value or as it makes the transition between extremes. High andlow extremes can be defined in terms of fixed value thresholds if the timeseries has a relatively stable mean and fluctuation range (i.e., is station-ary). All input series used for E rules were made stationary by applyingthe CN operator.Case Study of Rule Data Mining for the S&P 500 421
Thirty-nine of the 40 input series were used for the E-type rules. Theopen price of the S&P 500 was excluded on grounds of redundancy. Theinput series used for E rules were first smoothed with a four-day linearlyweighted moving average (LMA) before applying the CN operator. Thesmoothing was done to reduce the number of signals that would have re-sulted from an unsmoothed version of the input series wiggling above andbelow the signal threshold. Though smoothing may have been inappropri-ate for series that were already smoothed, for example the 30-day movingaverage of negative volume, all series were treated with the LMA ongrounds of consistency.
In ISL, the expression for the input time series used for E rules isgiven by the expression:
=CN (LMA (Input Series, 4), N-days)Where:
CN is the channel normalization operatorLMA is a linearly weighted moving-average operator
This sequence of transformations is illustrated in Figure 8.10.
InputTime Series
 
uy
4-day LMA Smoother
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Vv
Smoothed aNTime Series
a
CN OperatorSmoothedChannel-Normalized E> .Series -
FIGURE 8.10) Smoothed channel normalized series.422 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
E-rule signals were generated when the channel normalized smoothedseries crossed a threshold. Given that there are two thresholds, an upper andlower, and given that there are two directions in which a crossing can occur(up or down) there are four possible threshold-crossing events:
1. Lower threshold is crossed in the downward direction.Lower threshold is crossed in the upward direction.Upper threshold is crossed in the upward direction.
ae N
Upper threshold is crossed in the downward direction.
These events are illustrated in Figure 8.11.
Each E rule was defined in terms of two threshold-crossing events:one specifying the long entry/short exit and the other specifying the shortentry/long exit. This scheme yields 12 possible E-rule types. They arelisted in Table 8.3. Because they cover all possibilities, there would be nopoint in including inverse versions. Note that type 7 is an inversion ofType 1, Type 8 is an inversion of Type 2, and so on.
The 12 E-rule types are illustrated in Figures 8.12 to 8.23.
Channel-NormalizedSmoothedSeries
Events
 
FIGURE 8.11 > Threshold crossing events.Case Study of Rule Data Mining for the S&P 500 423
TABLE 8.3 The 12 E-Rule Types Defined in Terms of Threshold Crossing Events
 
E-Rule Types Long Entry/Short Exit Short Entry/Long Exit1 Event 1 Event 22 Event | Event 33 Event 1 Event 44 Event 2 Event 35 Event 2 Event 46 Event 3 Event 47 Event 2 Event 18 Event 3 Event 19 Event 4 Event 1
10 Event 3 Event 2
11 Event 4 Event 2
12 Event 4 Event 3
 
100
Time50
    
Threshold
 424 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
100
  
Threshold
   
Time
   
Lower
Threshold 1
       
 
FIGURE 8.13 Extreme value and transition rule: Type 2.
100
Time50
Lower
Threshold
   
FIGURE 8.14 Extreme value and transition rule: Type 3.Case Study of Rule Data Mining for the S&P 500 425
100
  
Threshold
   
Time
Threshold
  
Output
 
FIGURE 8.15 Extreme value and transition rule: Type 4.
100
Time50
  
Lower
Threshold
   
FIGURE 8.16 Extreme value and transition rule: Type 5.426 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
 
FIGURE 8.17 Extreme value and transition rule: Type 6.
 
FIGURE 8.18 Extreme value and transition rule: Type 7.Case Study of Rule Data Mining for the S&P 500 427
100
Time
    
Lower
phreshold
   
FIGURE 8.19 Extreme value and transition rule: Type 8.
100
  
Threshold
   
Time50
  
Lower
Threshold
  
Output
 
FIGURE 8.20 Extreme value and transition rule: Type 9.428 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
100
                  
Threshold
Time
Lower
Threshold
 
Output
FIGURE 8.21 Extreme value and transition rule: Type 10.
100
Time50
Lower
Threshold
 
FIGURE 8.22 Extreme value and transition rule: Type 11.Case Study of Rule Data Mining for the S&P 500 429
Output
 
FIGURE 8.23 Extreme value and transition rule: Type 12.
Parameter Sets and Total Number of E Rules. An E rule is definedby four parameters: type (1 through 12), input series, displacement of thethresholds form 50, and look-back span for the channel normalization. Be-cause both the upper and lower thresholds are displaced equally from themidvalue of 50, it is possible to specify them with a single number, theirdisplacement from 50. For example, a threshold-displacement 10 placesthe upper threshold at 60 (50 + 10) and the lower threshold at 40 (50 — 10).Two different values for the threshold displacement parameter weretested: 10 and 20. The displacement value of 20 gave the upper threshold as70 and the lower threshold as 30. Three different values were consideredfor the channel normalization look-back span: 15, 30, and 60. All parametervalues were chosen without optimization on the basis of intuition.
Given 12 possible rule types, 39 possible candidate input series, 2 pos-sible threshold displacements, and 3 possible channel normalization look-back spans, there were 2,808 E-type rules (12 x 39 x 2 x 3).
Naming Convention for Extreme Value and Transition Rules. InChapter 9, the following naming convention will be used to report resultsfor E rules:
(E)-(type)-(Input Series)-(Threshold Displacement)-(Channel Nor-malization Look-Back Span)430 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
For example, E-4-30-20-60 would be: E rule, type 4, input series 30(cumulative new highs/new lows ratio), a threshold displacement of 20(upper = 70, lower = 30), and a channel normalization look-back span of60 days.
Divergence Rules
Divergence analysis is a foundational concept of TA that concerns the re-lationship between a pair of time series. It is premised on the notion that,under normal circumstances, certain pairs of market time series tend tomove up and down together, and when they fail to do so it conveys infor-mation. A divergence is said to occur when one member of the pair de-parts from their shared trend. Typically, a divergence manifests itself asfollows: both series have been trending in the same direction, but thenone series reverses its prior trend while its companion continues its priortrend. This event, according to divergence analysis, is a potential signalthat the prior shared trend has weakened and may be about to reverse.This is illustrated in Figure 8.24. Hussman contends that divergence sig-nals are most informative when numerous time series are analyzed and asignificant number begin to diverge.”
The Dow theory is based on divergence analysis. It asserts thatwhen an index of industrial stocks and an index of transportation
Time Series2
 
Time Series1
Time
FIGURE 8.24 Divergence analysis.Case Study of Rule Data Mining for the S&P 500 431
stocks are trending in the same direction, the trend they share ishealthy and likely to persist. However, if one series begins to diverge, itis taken as preliminary evidence that the trend is weakening and mayreverse. Another application of divergence analysis considers the priceof an instrument as one time series and its rate of change or momentumas the second series. Price/momentum divergence analysis is discussedby Pring.”
A divergence leads to one of two outcomes: either the series, forwhich the trend had remained undisturbed, will experience a reversal tojoin its diverging companion or the diverging series will end its errantways and rejoin its companion. A completed signal of reversal is not pre-sumed until both series have convincingly reversed and are again movingin the same direction. Thus, the fundamental idea behind divergenceanalysis is coherence, that is, the state of affairs when two waveformsare in phase with each other (see Figure 8.25). When two series are co-herent, their common trend is considered strong and expected to con-tinue. However, when their trends become incoherent, or out of phase,the future of the once shared trend is in question. Therefore, candidatesfor divergence analysis are pairs of time series that are generally coher-ent, but when they do diverge, one particular member of the pair tends tohave leading information about the other. In other words, there is arather stable lead-lag relationship.
CoherentUptrendsTrend ShouldPersist
             
  
Coherent
DowntrendsTrend ShouldPersist
    
Time
FIGURE 8.25 Trend coherence and divergence.432 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
Subjective Divergence Analysis. Subjective divergence analysistypically involves comparing the peaks and troughs of the two timeseries under consideration. A negative or bearish divergence is said tooccur if one series continues to register peaks at successively higherlevels while the other series begins forming peaks at lower levels.The failure by the second series to form peaks at successively higherlevels is also termed a bearish nonconfirmation. This is illustrated inFigure 8.26.
A positive or bullish divergence is said to occur when one series con-tinues to register successively lower troughs in an established downtrendwhile the second series begins to form troughs at higher levels. This isalso termed a bullish nonconfirmation. See Figure 8.27.
The problem with subjective divergence analysis, or any subjectivemethod for that matter, is that it the procedure is neither repeatable nortestable. One issue requiring the analyst’s subjective judgment is the tim-ing of peaks and troughs. Because the two time series may not peak andtrough at precisely the same time, it may be unclear which peaks andtroughs should be compared. Another issue is related to duration: Howlong must the divergence be in existence before deciding that one has oc-curred? Still a third unresolved issue is how much upward (downward)
     
Series 1
  
t
Confirmed Peaks
| ¥
    
Series 2
Time
FIGURE 8.26 Negative divergence (peaks compared).Case Study of Rule Data Mining for the S&P 500 433.
              
Series 2
a
DivergingTroughs
Confirmed Troughs Series 1
Time
FIGURE 8.27 Positive (bullish) divergence: troughs compared.
movement in a series is required to establish that a new trough (peak)has formed.
An Objective Measure of Divergence. These problems can be ad-dressed with objective divergence analysis. A method that objectifiespeak and trough comparisons is discussed by Kaufman* and he pro-vides computer code. Kaufman also discusses a second method thatuses linear regression to estimate the slopes in the two time seriesbeing compared. A divergence is defined as the differences in theirslopes. Both methods look interesting but no performance statistics areoffered.
The divergence rules considered in this case study were inspired bythe objective divergence method discussed by Heiby“ in his book, StockMarket Profits through Dynamic Synthesis. The two series being exam-ined by Heiby were first detrended with channel normalization. He de-fined a divergence to be in effect if one series had a channel-normalizedvalue of 75 or greater while the other series had a value of 25 or less.Thus, divergence was quantified in terms of the difference in channel-normalized values.
This suggested an initial formulation for a divergence indicator that isdefined in the equation that follows. Note that one series is always theS&P 500, the target market of the case study. The companion series, for434 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
example the Dow Jones Transports, is the series with which the S&P 500is compared. The case study compared the S&P 500 to all the time seriesin Table 8.2, except the S&P 500 open price, which was excluded ongrounds of redundancy with the S&P 500 close.
Divergence Indicator(Initial Formulation)
= CN (Companion Series, n) — CN (S&P 500, n)
Where:CN = Channel normalization operatorn= Look-back span of the channel normalization
Because the channel normalized value of each series can vary be-tween 0 and 100, this divergence indicator has a potential range of —100 to+100. For example, if the companion series is at the bottom of its channelrange (CN = 0) and the S&P 500 is at the top of its range (CN = 100), the di-vergence indicator would have a value of —100. It should be noted that thisquantification of divergence is merely one approach among several possi-bilities that may prove superior.
Limitations of the Proposed Divergence Indicator. The proposeddivergence indicator measures the degree to which two times series havesimilar positions within their respective channels. In general, this will givea reasonable quantification of the degree to which the series are in phasewith one another. For example, when the indicator registers a value ofzero, it indicates that there is no divergence; both series have the samechannel normalized values and can be presumed to be trending together.However, there can be cases for which a value of zero does not indicatethat the two series are in phase. For example, if two time series are nega-tively correlated, that is to say, they tend to move inversely with respect toeach other within their channels, the divergence indicator will assume avalue of zero as the series-normalized values cross paths. In this instance,a value of zero would be an erroneous indication that the two series aretrending together. This is illustrated in Figure 8.28 and is clearly a limita-tion of the proposed divergence indicator.
This problem could have been avoided with a more complex formu-lation of divergence indicator based on cointegration, a concept devel-oped in the field of econometrics. Cointegration was proposed in 1987by Engle and Granger.” This more sophisticated and potentially moreCase Study of Rule Data Mining for the S&P 500 435
Channel-Normalized Value Companion Series
     
Erroneous Indications of In-Phase Behavior
FIGURE 8.28 Erroneous indications of in-phase behavior.
accurate way of measuring divergences uses regression analysis to de-termine if a linear relationship exists between two time series. Becausethis method can easily accommodate the case in which the pair of seriesare strongly negatively correlated (180 degrees out of phase), it solvesthe problem discussed earlier that can occur with a divergence indicatorbased on channel normalization. An additional advantage of cointegra-tion analysis is that it first applies a statistical test** to determine if thetwo series have related trends (i.e., that they are cointegrated). If thetest shows that they are cointegrated, a stationary divergence indicator”naturally falls out of the analysis. In cointegration terminology, this indi-cator is referred to as the error-correction model. It measures the degreeto which one series has diverged from the typical linear relationship be-tween the two series.
In most applications of cointegration, the error-correction model isused to predict the behavior of the spread between the cointegrated timeseries. In these applications, the divergence is predicted to revert back tothe normal state of a shared trend when the error-correction model be-comes extremely positive or negative. In other words, when the error,which is a departure from the normal linear relationship between the two436 CASE STUDY: SIGNAL RULES FOR THE S&P 500 INDEX
series, becomes extreme, it is predicted to correct back to its normalvalue of zero.
A typical application of this analysis is pairs trading. For example, ifit has been determined that Ford and GM stocks are cointegrated time se-ries and Ford has gotten high relative to GM, a short position would betaken in Ford against a long position in GM. Thus, no matter how the di-vergence is corrected (Ford falls, GM rises, or some combination) thepairs trade will generate a profit.
Fosback™ made an innovative use of cointegration analysis to develop astock market predictor. His innovation was to use the measurement derivedfrom the error correction model as an indicator to predict the movement of athird variable, the S&P 500, rather than predict the behavior of the spread be-tween the cointegrated variables. The indicator, called the Fosback Index,exploits the fact that interest rates and mutual fund cash levels are cointe-grated time series. Fosback’s work is particularly noteworthy because it pre-ceded the Engle and Granger publication on cointegration by over a decade.The Fosback Index signals when the mutual fund cash level diverges signifi-cantly from a level predicted by its linear relationship with short-term inter-est rates. The premise is that when mutual fund managers are excessivelypessimistic about stock market prospects, they hold cash reserves that aresubstantially higher than the that predicted by interest rates. Excessive opti-mism is the opposite situation. Fosback found that both excessive pes-simism and excessive optimism, measured in this fashion, correlated withfuture returns on the stock market. In effect, the Fosback Index removes theinfluence of short-term interest rates from mutual fund cash levels, thus pro-viding a purer measure of fund manager sentiment than that provided by theraw cash level, which is contaminated by interest rates.
In the interests of simplicity, the cointegration technique was not usedfor the divergence indicators in the case study. It was assumed that if acompanion series was not related to the S&P 500, it would be revealed bythe poor financial performance of the divergence rule. However, I°' be-lieve that the cointegration methodology warrants further investigation indevelopment of indicators.
Need for Double Channel Normalization. A second problem withthe initially proposed version of the divergence indicator was more seri-ous and had to be remedied. The divergence rules in the case study in