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 net defined in the Commodities magazine
presentation, but some simple rules couid be:
Sell when the DRF (or smoothed DRF) penetrates into the overbought zone. Close outall accumulated long positions, if any, and go short on the open of the next trading day.Buy when the opposite condition occurs.
DRE =
 
 
 
 
 
 
TABLE 6-1 A/D Oscillator—January 1977 Soybeans30% DRF SmoothingORE _ 30% 30%1976 ORF Smoothed  SmoothedDate Open ‘High ~—s Low — Close. —sDRF_—Signal__—Price DRF Signal Price11-01 682 «686TH = 678K 4 3411-03 679 6835S BKB 28104658676 5B TIA BT Sell 4S1105 674-678 665 TK AB 674 4611-08 673, 685 STL GTA SA AB11-09 673. 673 66D 66K 2B Al11-10 667 676K 665 TS. 85 Sell 4I-11 660 662% 645 SI 24 660 AS11-12 652658 650K 653 37 # .WIS 652652 GT 32H Buy ; oy /1-16 6394 655636 654% 90 Sell = 6394 33 > 639%N17 653 67 649 668K BS 653 8311a 667 «674% 5B 66GA AB 381-19 670691 669% 678% 70 6211-22 680° 691 «675% 690% 84 Sell 8 Sell11-23 689 696% «674K 675% 20 Buy *° 689 oy 689124 68, 686 678% 680 a eat st11-26 678 «681% 670K—67I%H® 2d Buys. 211-29 670-675. 6HIK 7D ST 670 4611-30 668 «= «677K. 666 674K 7B 361201 676 681K 673677 56 561202 678 = 681K 675, 679K 7 set1203 679-687 679 685% 92 Sel r12-06 690 6984 689 696% 84 690 B > 6901207 700 «700 690 690K 02 Ny st12-0869! 70g 69706 94 Sell > 691 2(209 7050712, 702,703 40 705 371210 704 = 704.696 696K OB Ys Al1213 693695. 690K GIA 33 693 38 Buy1214 696 = 701694701 83 Sell 32 6961215 701 70268487 a Buy S701 39 By(216 668% 692685 690K A 6884 a7 68841217 690690676 G77A 0S Buy N 34 Buy12.20 680 © 684% 679% 683% 82 Sell. 680 ao 6801221 682 688679 BTA BO 682 5812-22 688 = 693, 686K. 689% 60 5912-23 689-693, BAA 69K TI 621227 695705 694 700% 76 612-28 701 706% 697K 705% 76 69 Selli229 708710699 699% HL Buy \ 32 7081230 703% 708 698 706K 8S 703% 56Basic DRF Performancet_ 30% Smoothed DRF Performance!16 signals 7 signals4 compounded signals, 3 compounded signals12 profits - 5 profitsAverage profit (3.08¢ ‘Average profit BlogA losses 2lossesAverage loss 1425¢ Average loss 6.50%Net profitioss 99.964 Net profitiloss 97.509
 
ale caken the following day on open.
+ No commissions have been deducted.
 
141
 
 
  
442 MOMENTUM AND OSCILLATORS
 
 
FIGURE 6-10 A/D Oscillator.
’
.oversousnt f
     
 
 
“SVERBOUC HT
Gna
 
 
VERSEBoni!
 
 
 
 
 
‘OVERSOLD¥
 
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 showat the method is viable and that a smoothing technique can be iPee a et ocding z iq applied to the DRF to varyWaters and Williams used a simple 10-da i5 y momentum for their example of the A/DOscillator. The choice of interval can be determined by examinii% ing the ta chart for the natural cycle of the prices. *y 8 the tops and booms ofIn reviewing the A/D Oscillator, there are modifications to be consi¢ 5 onsidered. 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 resultin,DRE. For example, the following trading occurs: *
 
 
Open High Low Close DRF ADRF EL ADRFMonday 43.00 4400 40.00 41.00 25
‘Tuesday 42.00 42.00 39.00 40.00 7
‘Wednesday 38.50 38.50 38.00 38.00 00
Thursday 42.00 42.00 39.00 40.00 ‘17
Friday 40.00 43.00 40.00 42.00 ‘83
  
 
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 momentumi. ‘The problem scems 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 ZADRFMonday 43.00 44.00 40.00 41.00 25Tuesday 42.00 42.00 39.00 40.00 AZ 7 nA7Wednesday 38.50 (40.00) 38.00 38,00 37 +04Thursday 42.00 42.00 (38.00) 40.00 25 12Friday 40.00 43.00 40.00 42.00 83 +58
 
 
OSCILLATORS 143
‘Another construction of an oscillator can be made using the highs and lows relative tothe prior close:
Hy- Gin
H.-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,-1 2 Ly; but ifC.-1>H; or L, > G,-1, G-1 replaces either H, or Z, 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.
A word 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.
OF
 
%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 _ highy ~ closes~ range ~ highto — Lowio
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 orfandamental 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.
%R
The Ultimate Osciffator
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;, SBys, and SBzs. -
4, Total the true range R, over the same three periods, SR;, SRis, and SRo.
» Lary Williams, “The Utimate Oscillator,” Technical Analysis of Stocks & Commodities (August 1985) 
 
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 areach 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 ral‘Then, a sell order can be placed when the oscillator fails (on the right shoulder).
aa holding a short position, close out the short when a long signal occurs, or whenthe level is reached, or if the oscillator ri O88 poithe 20% eel seach tor rises above 65% (the stop-loss point)
. A buy signal occurs using the opposite techniques as the short signal (rule 1).
" If a long position is held, close out longs when a short signal occurs, or when the
70% level is reached, or if the oscillator falls below 30% (after being above 50%).
Aw
_ 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 madé by WilliamBae 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 i
(“Trend Calculations”). 6 in Chapter 4
4 William Blau, Momentum, Direction and Divergence (John Wiley & Sons, New York, 1995).
 
FIGURE 6-11 Williams’ Ultimate Oscillator.
 
 
 
 
 
i =70h ist peak Long objective6s \_ pc Se iatare shat stop-loss 7 Peak60 - .55 J. Set!*0 .4s Vv4035 Long stop-loss3 7 short objective BuyPeak
 
 
DOUBLE-SMOOTHED MOMENTUM 145
True Strength Index
Much of Blau's work combines double smoothing of momentum values (1-period pricedifferences), 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:
astcctose.rs) = 222% @SmoothedAverage(@SmoothedAverage(close ~ close[1],7)s)(close,r:s) = Ge moothedAverage (@Smoothedaverage (@abs(close — close[ 1]),7),s)
where r is the period of the first momentum smoothings is the period of the second momentum smoothingclose-close[1] is the 1-day momentum
Written in TradeStation format, where the two smoothing periods are soothI and
smooth2, this formula is:
num = @smoothedaverage(@smoothedaverage(close -close(1],smooth1),smooth2);
denom = @smoothedaverage (@smoothedaverage (@absvalue(cl ose-close(1]),smoothl),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 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 TST 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 Stochast
Because of Blau’s great interest in double smoothing, he defines the general form of adouble-smoothed stochastic as:
DS(q,ns) =100 x @SmoothedAverage (@SmoothedAverage (close ~ @Lowest(low.g),7),5)@SmoothedAverage(@SmoothedAverage (@Highest (high,g) — @Lowest(low.g),7).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,g) is the denominator of Lane's stochastic, thegreatest high-low range over the past q periods@SmoothedAverage(. . . ,7),s) is an exponential smoothing first over 7 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 TS! with a standard momentum over the same period.
[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.
KF = 100 x 1OSEiader = OSE peresclose siny
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(loserocay — CLOS€previouss 72)@avg (highway — 1oWoday, 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 =
" Tushar Chande and Stanley Kroll, The New Technical Trader John Wiley & Sons, New York, 1994).
 
ADDING VOLUMETO 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:
> volume,MV = (price, — price;-n) x
 
n
MV = (close - closefn])*@Average(volume,n)
‘Alternately, the price change of periods could have been divided by 1 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 incteases 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.
(Percentage momentum with volume)MV = (close - closefn]) / closetn] * @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.
Gene Quong and Avrum Soudack, “Volume-Weighted RSI: Money Flow,” Technical Analysis of Stocks & Com-modities (March 1989). 
 
“148MOMENTUM AND OSCILLATORS,
high + low + close3
14-day positive money flow14-day negative money flow
Money Flow = volume x
Money Ratio =
100
Money Flow Index = 100 - —————_—_1+ Money Ratio
Herrick Payoff Index
Using the change in the underlyin;
he ch: g value of the futures contract, rather than onl
change in price, the Herrick Payoff Index (HPI) combines volume and open interest to
generate an indicator that, as the basic momentum calculation, is not bounded but scaledjown to a manageable value and smoothed using a .10 smoothing factor, s (about 19 days).
The daily value is:\(2 [0%,- Of-11min(OL, OF, - 1) )|and the index is an exponential smoothing of the individual daily calculations:HPhhoaay = HPTpceious + 5X (HPheoday — HPI previous)where # is todayt- 1 is the previous day
¢f is the conversion factor (value of a basis pointV, is today’s volume Poin move)
   
HP = fx V,x (M,~M,-1) x[p+ (oe,[= My.
(MU, ~M,...) is the difference in the mean prices 82+ 1ow2| | (vertical bars) are for absolute value|O1, - Of, | is the absolute value of the change in open interestmin(OI,, Ol, 1) is the smaller of today and the previous open interest
s is a smoothing constant (default 10) \
The expression that divides the change in mean prices by the absolute value of the same
change is used to create a +1 or —1 value. This c lex formula can also be written in pro-. complip! P
HP = @BigPointValue * volume * ((hi1 gh-low)/2 - (high{1}-lowf1])/2) *a + CCohigh-1ow) /2 - (high{i}-lowl1})/2) / @Abs(Chigh-1ow)/2 - —igh{1]-lowl1])/2))* 2 * (@Abs(opint - opint£1]) /@Lowest(opint,2)))
HPI = @SmoothedAverage(HP ,19)
Most analysts who use the Herrick Payoff Index divide ethe value to a more useable level. The final series, Shen seen along wih paves aayappear volatile and require an interpretation using trendlines. This is due to fhe fictuaetions in volume and open interest, which are smoothed over 20 days, rather than longer.The HPI may be helpful, despite the volatility, because it is a combination of factors mot
included in most other indices. It will havea w patterns that a icompensate for market noise. pear co lead price change
From the original CompuTrac manual, which is now the Bridge Telerate division.
 
 
VELOCITY AND ACCELERATION 149
 
Comments on the Use of Volume
Volume is an important piece of information, but it can be difficult to interpret. It fluctu-ates in a much larger range than price, and may be one-third higher or lower from day today, Although it indicates market interest and potential volatility, there are many days forwhich a high or low volume does not have a consistent reaction.
Tn general, adding volume to an indicator will result in a more volatile, erratic series.‘Therefore, the first steps in using volume would be
1. Create a long-term, smoothed volume series.
2, Compare current volume for extremes to identify only those exceptional days thatshould be followed by high volatility.
3, Low volume should not be determined by a single day, but by either a few unusu-ally low days together or by a volume decay over a modest time period.
VELOCITY AND ACCELERATION
‘A method conceptually similar to momentum is derived from the concepts in physics ofvelocity and acceleration, both elements in the science of motion. Velocity, as defined inmechanics, is the rate of change of position with respect to time (also called speed). Thereare two types of velocity, average and instantaneous. The average velocity is simply calcu-lated as the mean velocity over a fixed distance and for a fixed time interval. In workingwith commodity prices, the time interval used will be days and the distance is measured inpoints; so that if silver moved 40 points in 6 days, its average velocity is
   
2Z points per day
, the average velocity is expressed
where D is the total elapsed distance over the time interval 7 For a geometric interpreta-tion of momentum, D (the change in price) can be related to T (the length of the momen-tum span) to get exactly the same results for average velocity as for slope (see Figure 6-13).
‘The instantaneous velocity v, which is the velocity calculated at a specific point in time,will be different. To determine the instantaneous velocity, a mathematical technique calleddifferentiation is used. It effectively looks at smalier and smaller time intervals and conse-quently smaller distances on the price curve until the slope calculation is reduced to a sin-gle point. The results of the process of differentiation is called the derivative and isexpressed -
maim 42-22eee At dt‘This shows that the velocity taken at any point is the result of the time interval (4) becom:ing progressively smaller without reaching zero. The rules for differentiation can be foundin any advanced mathematics book. Only the results will be presented. ‘The velocity v, rep-resents the speed or momentum of the price at the point in time #. Lf gets larger for ff.1. then the velocity is increasing; if » gets smaller, the velocity is decreasing. Becausethe velocity also denotes direction, it can be both positive and negative in value and appearsimilar to a momentum indicator. Systems applied to momentum may equally be appliedto velocity. Of course, some of the basic equations have constant velocity and cannot betised for 2 velocity trading plan, because the values never change. The straight line, simple 
“150 iLMOMENTUM AND OSCILLATORS VELOCITY AND ACCELERATION 150
 
 
FIGURE 6-13 (a) Average velocity. (6) Instantaneous velocity. ‘TABLE 6-2 Equations for Velocity and Acceleration
 
 
     
     
 
weet Basic Equation Velocity at x." Acceleration at xStraight line y=a+ bx,Curvilinear yea at bx + OF + 2%,Logarithmic (base a) y= loge x (log, e)ix, or w= M(x.In a) LQ In a)Logarithmic (natural log) Kain x, xtExponential ye" =ae*D Gt Meg tt Xen23 Moving average ya ttt Beet a=0
i
| Weighted moving average yoo A ha EP aetcast a=0
: Exponential smoothing Y= Yet Kod) yee a=0
 
Tyreasewony mc nein rete dates quan np eer 2 as parc he i member
Using the acceleration