UM AND OSCILLATORS
 
 
FIGURE 6-8 Lane’s patterns. (a) Left and right crossings. (b) Hinge. (c) Bear market setup.(d) %K-slow failure.
 
 
 
MK HingeLeft crossing Right crossing{a) (6)PricesHigher bottomsWK ~~f%D /
Lower bottoms
{c) {a)
 
Relative Speed and Patterns of the Stochastic and RSI
Increasing the calculation period is a way of smoothing the values of indicator, whether itis viewing weekly instead of daily prices, using a 200-day average instead of a 10-day, orselecting a 20-day stochastic over a 5-day. The two most popular oscillators, the RSI andstochastic, can be very similar if the time periods are chosen correctly. In Figure 6-9, a Trea-sury bond chart for June 1996 delivery is used to show how the RSI and stochastic patternschange by varying the number of days in the calculation.
The 5-day raw stochastic is shown in panel 6 of Figure 6-9. Its characteristic is thatwhenever prices close on a 5-day high or low, the stochastic value is 100 or 0 and the indi-cator cannot provide any value. Smoothing the raw value offsets this problem at the cost ofintroducing a lag; this example will avoid that additional problem and use only the raw sto-chastic. Figure 6-9 (panel c) contains a 5-day RSI that tends to show similarities to the 5-daystochastic as bond prices become more actively traded toward the right part of the chart.Nevertheless, the RSI does not tend to approach peak values. Smoothing the stochastic byusing 20 days, as shown in Figure 6-9 (panel @), gives a very similar picture as the 5-periodRSI in panel c of Figure 6-9. The pattern has all the same ups and downs, although the sto-chastic continues to show more extreme values. The last two panels of Figure 6-9 (panelse and f) compare the standard 14-period RSI with a much longer 40-day stochastic withsimilar results as in Figure 6-9 (panels c and @). The patterns are very similar, but the sto-chastic moves to extremes more often.
Creating a Stochastic from the RSI
Any series or indicator value can be converted to a raw stochastic, %K, without adding lagby replacing the closing price with the indicator value. This creates a measure of where thatindicator lies in its high-low range over the period selected and may simplify the compari-son needed to generate buy and sell signals. A stochastic created from an RSI would be?
° Tushar Chande and Stanley Kroll, The New Technical Trader John Wiley & Sons, New York, 1994).OSCILLATORS 139
 
 
FIGURE 6-9 Comparison of RSI and stochastic. (Panel a) Treasury bond prices for the June1996 delivery. (Panel b) The 5-day raw stochastic often reaches maximum and minimum val-ues. (Panels ¢ and d) Comparing the 5-day RSI with the 20-day stochastic. (Panels e and f)Comparing the 14-day RSI with the 40-day stochastic.
 
Arn eer yr terilost Q96 C=107422 +07 O=107M9 H=107°22 L=10749
{a)
 
(b)
 
 
 
 
 
 
 
 
 
 
 
 
 
Source: Charts created with TradeStation® by Omega Research, Inc.\
140 MOMENTUM AND OSCILLATORS
 
RSTroday — RST town-day StochRSI = <2) ——— =v ew _¥ RSIpday high ~ RSLy-cay tow ‘
Larry Williams’ Oscillators
Larry Williams has been known for his development of trading methods based on oscilla-tors since his publication of the A/D Oscillator in 1972. Although they have changed overthe 14 years spanning these systems, some similarities are apparent in Williams’ three tech-niques that follow.
AID OscillatorIn 1972, Jim Waters and Larry Williams published a description of their A/D Oscillator inCommodities magazine. For their system, A/D means accumulation/distribution ratherthan the usual notation of advance/decline, a well-known interpretive index for stocks.They used a unique form of relative strength, defining buying power (BP) and selling(power (SP) as .
BP = high — open SP = close - low
where the values used were today’s open, high, low, and closing prices. The two values, BPand SP show the additional buying strength (relative to the open) and selling strength(compared with the close) in an effort to measure the implied direction of the day’s trad-ing. The combined measurement, called the daily raw figure (DRF) is calculated as
BP + SP2 x (high — low)The maximum value of 1 is reached when a market opens trading at the low and closes atthe high: BP — SP = high — low. When the opposite occurs and the market opens at the highand closes on the lows, the DRF will be 0. Each price series will develop its own patterns,which can be smoothed or traded in many ways similar to a momentum index. TheWaters/Williams A/D Oscillator solves problems of volatility and physical limits. The dailyraw figure completely adjusts to higher or lower trading ranges because the divisor itself isa multiple of the day’s range; and because each day is treated independently, the cumula-tive values of the momentum index are not part of the results. This day-to-day evaluationcauses the DRF to vary radically and requires some smoothing technique or cycle inter-pretation to make it useable. As an example, look at the January 1977 soybean contract forthe two months before delivery, November and December 1976. Table 6-1 shows the cal-culations for the DRF and for the smoothed DRF using an exponential moving average witha smoothing constant of 30% (selected arbitrarily). The daily raw figure is plotted as thesolid line on a scale of.00 to 1.00 in Figure 6-10 and is extremely erratic in its movements.The dotted line is the smoothed DRF. Once plotted, two horizontal lines can be drawn toisolate the peaks and bottoms of the DRF; the top part becomes a zone representing anoverbought condition and the bottom zone represents oversold. Bear in mind that theselines were drawn after the DRF was plotted and cannot be construed as predictive; how-ever, in the article by Waters and Williams, their example’of soybean oil had lines drawn ina similar place. Corresponding broken lines were drawn to indicate the overbought andoversold state for the smoothed DRF.
The rules for using the A/D Oscillator were noi defined in the Commodities magazinepresentation, but some simple rules could be: a
Sell when the DRF (or smoothed DRF) penetrates into the overbought zone. Close out .all accumulated long positions, if any, and go short on the open of the next trading day. =
Buy when the opposite condition occurs,
DRF =
 TABLE 6-1
AID Oscillator—January 1977 Soybeans
 
 
 
 
 
30% DRF SmoothingORF _ 30% 30%1976 ORF Smoothed  SmoothedDate Open High tow Close ~=—sdDRF_~— Signal ~— Price DRF Signal* PriceW-01 682 686 674%, = 678A 34 3411-03 679 683 655 65843 2811-04 658 676 658 671487 Sell AS105 674 678 665 6734 48 674 A611.08 673 685 671 674%, 54 AB1109 673 673 660 666 2B AlN10 667 676A 665 675 BS Sel. 54H-ll 660 6624 645 651 24 660 ASW112 652 658 6504 653 57 49WIS 652 652 627 632% Wl Buy 37 BuyH-16 6394 "655 6364 654% 90 Selt Soon 53 2 639%1-17 653671 649 668485 653 83N18 667 6744658 6664 48 58et9 670 691 669% 678% 0 621-22 680691 6754 6904 84 Sell 68 Sell11-23 689 6964 674K TSK 20 Buy > 689 34 } 6991-24 68L, 686 678% 680 43 Ss ai Sl11-26 678 6814 = 670K 7% Buys A1-29 670 675 661% 672 57 670 4611-30 668 677% . 666 674A 78 5612-01 676 68lh 673 677 56 561202 678 Blk «675. 6794 6 5712-03” 679 687 679 685% 92 Sell 68 Sell12-06 690 6984 689 6964 84 60 2B > 9012-07 700 700 690 6904 02 Buy I12.08 691 708 691 706 94 Sell 691 41209 705 712 702 703 40 705 5712-10 704 704 696 6964 03 Buy Al1213 693 695 6904 69K 33 693 38 Buy12-14 696 TOK = 694 Tol 83 Sell, 52 696(2-15 701 702 684 687 an Buy .~701 39 Buy,1216 688% 69285 OK wt Ss 68a a7 a812-17 690 690 676 677A 05 Buy 34 Buy12-20 680 6844 679% 683% 82. Sell = 680 49 > ego12-21 682 6e8 679 6874 80 682 5812-22 688 693 6864. 689% 60 3912-23 689 693, 6844 6924 7 6212-27 695 705 694 700% 76 6612-28 701 7064 697K 708K 6 69 Sell12.29 708 710 699 699% By A 52 70812:30 7034 708 698 7064 65 703% 56Basic DRF Performancet_ 30% Smoathed DRF Performance?16 signals 7 signals4 compounded signals 3 compounded signals12 profits ~ 5 profitsAverage profit 13,08¢ Average profit 210gA losses 2 lossesAverage loss 14.25¢ Average loss 6.50¢Net profit/loss 99.964 Net profit/loss 97.504
 
* Signals taken the following day on open.+ No commissions have been deducted.
141142 MOMENTUM AND OSCILLATORS.
 
 
FIGURE 6-10 A/D Oscillator. {
 
esessses
 
 
 
OVERSOLD +SSmovihed)
 
 
oversou |+ 4
 
 
If the DRF (or smoothed DRF) enters an overbought or oversold zone more than oncewithout the opposite zone being entered, one additional position is added at each reentry.Following these rules, the A/D Oscillator showed excellent success for both the raw andsmoothed values. Accepting the after-the-fact designation of zones, the results still showthat the method is viable and that a smoothing technique can be applied to the DRF to varythe speed of trading.
_ Waters and Williams used a simple 10-day momentum for their example of the A/DOscillator. The choice of interval can be determined by examining the tops and bottoms ofa chart for the natural cycle of the prices.
In reviewing the A/D Oscillator, there are modifications to be considered. Conceptu-ally, the value of the oscillator should be +1 when prices are rising rapidly. The mostextreme example is a locked-limit no-trading day, representative of the strongest (or weak-est) market, But for that case, the open, high, low, and closing prices are all the same andthe DRF cannot be determined (since the divisor is zero). A more basic problem concernsgap openings. A much higher opening with a stronger close would also upset the resultingDRE. For example, the following trading occurs:
 
 
Open High Low Close DRF ADRF = ADRFMonday 43.00 44.00 ' 40.00 41.00 25 .Tuesday 42.00 42.00 39.00 40.00 7 -.7 -7Wednesday 38.50 38.50 38,00 38.00 00 417 00Thursday 42.00 42.00 39.00 40.00 A7 ~33 -33Friday 40.00 43.00 40.00 42.00 83 +50 +17
 
Note that on Wednesday, the DRF indicates that the momentum has reversed, but-in factthe price is falling rapidly and gives no indication of recovering; it may actually be gainingmomentum. On Thursday the price soars up and closes in the midrange, but the DRFshows a new downward momentum. The problem seems to be related to lack of associa-tion with the prior closing price. The daily movement can take on different appearances ifthe entire range was above or below the closing price. To form this link, replace the cur-rent high or low with the prior closing price if that price was outside the current tradingrange. The following example shows the results smoothed out and leaves the trend intact.
 
 
Open High Low Close DRF ADRF = ADRFMonday 43.00 44.00 40.00 41,00 25Tuesday 42.00 42.00 39.00 40.00 AZ 7 AT ~,17Wednesday 38.50 (40.00) 38.00 38.00 37 +04 =13Thursday 42.00 42.00 (38.00) 40.00 25 =12 -25
Friday 40.00 43.00 40.00 42.00 83 +58 +33OSCILLATORS 143
 
Another construction of an oscillator can be made using the highs and lows relative tothe prior close:
Ai~Gi-1
O,= W-L,
The two days are linked together and the ratio of the high price relative to the prior closeis measured against the total range for the day. For the normal case, H, 2 C,_, 2 L,, but ifC,.. >H, or L, > C;~1, C,-, replaces either H, or L, to extend the range. The value of O, willbe either 1 or 0 for these extreme cases, As with the A/D Oscillator, the values derived fromthis method may also be smoothed.
Oscillators are not the only tools for measuring momentum or for determining over-bought or oversold conditions, Because it is very different from either a charting techniqueor a moving average, it is valuable either on its own or as a confirmation of anothermethod.
Aword of caution: Trading against the trend can be exciting and profitable, but at con-siderably greater risk than a trend-following system. The problem with selling an over-bought condition is that there is no way to hold losses to a minimum. Once a shortPosition is entered, the momentum or the oscillator value could sustain its strength andmove against the position.
%R Method
After the publication of Williams’ How I Made One Million Dollars... Last Year... Trad-ing Commodities (Conceptual Management, 1973), the %R oscillator became well known.It is a simple way of calculating where today’s closing price fits into the recent tradingrange. Using the last 10 days, define
_ buying power _ highio ~ closeyoaay -~ range —>highip — lowyo
Williams’ 10-day %R is actually a 10-day stochastic, using the high price rather than thelow price in the numerator; therefore, it is the complement (100 minus the 10-day sto-chastic) of the original stochastic calculation, With a chart that has 0 at the top_and 100 atthe bottom, a value below 95% will give a buy signal, and one over 10% will give a sell sig-nal. Williams viewed this as a timing device to add positions within a major technical orfundamental trend, Trades were not to be entered if they contradicted the major marketdirection. Readers should refer to the earlier section in this chapter, “Stochastics,” for moreinformation.
The Ultimate Oscillator
In the Ultimate Oscillator, Williams seems to combine his original idea of the A/D Oscilla-tor with a great deal of Wilder’s RSI." He adds the unique feature of three concurrent time_Periods to offset the negative qualities of the short time period of the %R, without slowing“the system too much. The Ultimate Oscillator works as follows:
1. Calculate today’s buying pressure B, by subtracting the true low from the closingprice. The true low is today’s low or yesterday's close, whichever is lower.
2. Calculate today’s true range R, by taking either the greater of today’s high and low,today’s high and yesterday’s close, or yesterday’s close and today’s low.
3. Total the buying pressure B, separately over the three intervals of 7, 14, and 28 days,designated as SB, SB,4, and SBy.. -
4, Total the true range R, over the same three periods, SR;, SRig, and SR».
°° Larry Williams, “The Ultimate Oscillator,” Technical Analysis of Stocks & Commodities (August 1985).144 MOMENTUM AND OSCILLATORS
 
5. Divide the sum of the buying pressures by the corresponding true range, that is,SB-/SR; and scale by multiplying the 7-day value by 4 and the 14-day value by 2. Allthree calculations are now in the same scale.
Notice that the nearest seven values for the buying pressure and the true range areeach used seven times; that is, they are multiplied by both the scaling factors of 4 and 2,and used once more in the 28-day calculation. Williams has created a step-weightedmomentum, assigning values of 7, 3, and 1 to the first 7 days, second 7 days, and last 14days, respectively. The last 14 days account for only 10% of the total.
The rules for using this oscillator (see Figure 6-11) are:
1, A sell signal occurs when the oscillator moves above the 50% line (an upward di-vergence), and the oscillator peaks and then fails to break the peak on the next rally,Then, a sell order can be placed when the oscillator fails (on the right shoulder).
2. If holding a short position, close out the short when a long signal occurs, or whenthe 30% level is reached, or if the oscillator rises above 65% (the stop-loss point)after being below 50%.
3. Abuy signal occurs using the opposite techniques as the short signal (rule 1).
4. If a long position is held, close out longs when a short signal occurs, or when the70% level is reached, or if the oscillator falls below 30% (after being above 50%).
Williams’ Ultimate Oscillator has combined many important features, includingweighting time periods, setting objectives, stop-loss points, and chart interpretation. Thereare two obvious weaknesses in this approach.
1. The chart rules add a great deal of.subjectiveness to the method. Waiting for a fail-ure of a second peak is another way of looking for a broadening top—a slower risefollowed by a rounding pattern, Waiting for a pattern may add reliability if inter-preted properly, but it defeats the effect of the oscillator being a leading indicator.
2. The stop-loss rules apply only after the oscillator has crossed 50%, If it moves thewrong way immediately, there is no risk control.
DOUBLE-SMOOTHED MOMENTUM . -
The most recent contributions to the study of momentum have been made by WilliamBlau.” In addition to creating new momentum indicators, he has added substantial valueto the old ones. Also refer to his work on double smoothing of momentum in Chapter 4(“Trend Calculations”).
1 william Blau, Momentum, Direction and Divergence (John Wiley & Sons, New York, 1995).
 
FIGURE 6-11 Williams’ Ultimate Oscillator,
 
Long objectiveshort stop-loss
First peak
            
   
Sell on faifure Peak
Sell
 
   
Long stop-loss.
short objective Buy
  
PeakDOUBLE-SMOOTHED MOMENTUM 145
 
True Strength Index
Much of Blau’s work combines double smoothing of momentum values (1-period pzicedifferences), which has surprisingly little calculation lag. By using the momentum, he hasbased the calculations on values more sensitive than price, then slowed them down bysmoothing. He refers to this as using momentum as a proxy for price. One of Blau’s mostpopular indicators is the True Strength Index (TSI), which combines these features:
100 x @SmoothedAverage(@SmoothedAverage(close ~ close[1],7)s)@SmoothedAverage(@SmoothedAverage(@abs(close — close[1]),r),s)
 
TSI(close,r,s) =
where r is the period of the first momentum smoothingsis the period of the second momentum smoothingclose-close[1] is the 1-day momentum
Written in TradeStation format, where the two smoothing periods are smooth1 andsmooth2, this formula is:num = @smoothedaverage(@smoothedaverage(close-close[1],smooth1),smooth2);denom = @smoothedaverage(@smoothedaverage (@absvalue(close- closet),smooth!) ,smooth2);TSI. = 100*num / denom;
The numerator is the scaled value of the double-smoothed momentum, and the denomi-nator is the double smoothing of the absolute value of momentum. The 1-day momentumis first smoothed over the period 7, and then over the period s. The relationship betweenthe standard momentum (the difference i in prices over r days) and the TSI can be seen inFigure 6-12. The momentum indicator, formed by using an MACD indicator with movingaverage values of 1 and 20, has the typical erratic pattern of prices, and a slight lead aheadof the peaks, formed by the pending crossing of the prices and moving average. The TSI ismuch smoother with peaks and valleys aligning with those of the prices. Buy and sell sig-nals are created by smoothing the TSI signal line and buying when the TSI crosses abovethe signal line.
Double-Smoothed Stochastics
Because of Blau’s great interest in double smoothing, he defines the general form of adouble-smoothed stochastic as:
DS(q,7,5) =
100 x @SmoothedAverage (@SmoothedAverage(close — @Lowest(low,g),r),$)@SmoothedAverage(@SmoorhedAverage(@Highest(high,q) — @Lowest(low,g),r),s)
where close — @Lowest(low,q) is the numerator of Lane’s raw stochastic, the lowest lowover the past q periods@Highest(bigh,q) - @Lowest(low,q) is the denominator of Lane’s stochastic, thegreatest high-low range over the past g periods@SmoothedAverage(. . . ,r),s) is an exponential smoothing first over r periods,then over s periods, of the numerator
Forecast Oscillator -
In Chapter 4 (“Trend Calculations”), the difference between the price and the trendlinevalue was smoothed and added to the trend value to get what was originally considered adouble-smoothed trendline. Instead, the difference between the current price and the cor-146 MOMENTUM AND OSCILLATORS,
 
 
FIGURE 6-12 Comparing the TSI with a standard momentum over the same period.
 
  
              
Caran ee1293196 C=72015 14.60 O=732.00 H=734.75 L=719.75
to PF Roe ahag vo " ‘We " wf
IMACD-PUK .8.30
‘True Strength Index -4.16
 
Source: Chart created with TradeStation® by Omega Research, Inc. ~
responding forecast (trendline) price can be calculated as a percentage and treated as amomentum indicator %F This oscillator is not bounded; however, by giving the value asa percentage, there will be more consistency over very long test periods.
Closeroday — CLOS€ previous
%F = 100 x. close roday
For practical purposes, a 3-period smoothing of %F gives more consistency. When%F = 0, then the trendline and prices are moving parallel to one another; when %F > 0, themarket is accelerating away from the trendline; and when %F < 0, prices are slowing downand the two series are converging. Traders interested in this technique should also read thesection on acceleration.
An Oscillator to Distinguish between Trending and Sideways Markets
The lack of predictability of trending markets is the greatest problem for the analyst. Thework found under the topics “Directional Movement” and “Ranking” in Chapter 23 (“RiskControl”) this book discusses that issue. Based on the idea that the trend component isstronger when price is farther from fair value, and the noise (sideways movement) isgreater when price is near value, an oscillator can be created to show the strength of thetrend component based on this concept,
@avg(close,aiay — ClOS€ previous» 7)@avg (highway —loWay, 2)As the trend increases, the average change in closing prices becomes larger relative to the
high-low range for the day. In an unusual period, when the market gaps open, it would bepossible for the closes to become larger than the daily range. In a sideways market both the
Strength Oscillator =
"2 Tushar Chande and Stanley Kroll, The New Technical Trader (John Wiley & Sons, New York, 1994).ADDING VOLUME TO MOMENTUM 147
 
change in the closes and daily range will get smaller, but the net price change over theperiod n should be close to zero. This oscillator can be smoothed by taking the change inprice over 2 or 3 days, rather than the most recent day, as well as the high-low range overthe same number of days.
ADDING VOLUME TO MOMENTUM
A momentum indicator can also incorporate volume by multiplying the price change overn periods by the total volume over that same period. The use of a cumulative period willhelp to stabilize the volume, which is often erratic. Although the sum of the volume overthe period can be used, the average will appear more familiar and can be plotted against avolume chart, In standard and programming notation, that gives the momentum times thevolume MV as:
t
> volume,
MV = (price, — price;..) x 7
MV = (close - close(n])*@Average{volume,n)
Alternately, the price change of n periods could have been divided by 7 to give a per-unitvalue. This section will include those techniques that combine price change and volume;for methods that do not use price, see Chapter 10 (“Volume, Open Interest, and Breadth”).
Scaling by a Percentage or Volatility
The same conversions can be applied to momentum with and without volume. Using a per-centage, rather than price, will add some robustness over long test periods. Because volatil-ity often increases when prices rise faster than the percentage would show, momentum canbe scaled according to a shorter measure of true range. If the true range is averaged over 20to 65 days, approximately one month to one quarter, then the 1-day change in price willbecome a relative momentum value. By using a much longer period for averaging the truerange, you can create a stable profile of the volatility changes in the underlying market.
(@ercentage momentum with volume)
SMV = (close - close(n]) / close[n] * @Average(volume,n)
(Momentum with volume scaled by true range)
TRMV = (close - close[n]) / @Average(@TrueRange,p)) * @Average(volume,n)
where @TrueRange is always calculated for the most recent period, and -@Average(@TrueRange,p)) is the average of the 1-day true range for the past p days.
Volume-Weighted RSI
In the same way that the RSI adds the positive days and divides by the sum of the negativedays, it is possible to weight each day by its volume to add another factor, called moneyflow," to the calculation. A positive or upward day is when the average of today’s high,low, and close (high + low + close/3) is greater than the previous average. Each average isthen multiplied by the volume, giving the daily money flow, and a ratio of the past 14 daysis used to create a money ratio and finally a money flow index, both steps similar toWilder’s RSI.
3 Gene Quong and Avrum Soudack