This IS an exponential smoothing foiniula usmg the high price for a long position and the low when a short is held. For this method the smoothing constant is called the acceleration factor (AF), and it is initially set to at the beginning of each trade. After a day in which a new exfreme occurs (a new high when long, or a new low when short), the AF is increased by . In terms of moving average dajs, the AF begins at 99 days and increases speed to a maximum of a 9-day moving average, but not in a linear fashion. The acceleration factor, AF, cannot be increased above the value .2C.

In the SAR calculation, the highest high of the current move is used when a long position is held, and the lowest low is used when a short is held. This feature keeps the SAR at its highest possible level during an upward move. An additional rule compensates for this sfrength and prevents premature reversal by not allowing the SAR to gel any closer than the price range of the most recent 2 dajs:

If long, the SAR may never be greater than the low of today or the prior day. If it is greater than this low, set the SAR to that low value. A reversal will occur on a new intraday low that penetrates the SAR.

FIGURE 17-2 Parabolic Time/Price Sjstem, Feb 96 S&P 5 , -minute chart.

Source. Chan cieaied with TmdeStaUorfbv Omega Resean*, Inc

For short positions, the SAR is initialized as the high of the recent move, AF =.C2, and the daily calculation uses the lowest low of the current price move. To allow some price fluctuation, the SAR may never be below the high of today or the prior day.

Wilders Parabolic Time/Price Sjstem was unique in varjing the smoothing constant to satisfj the notion that time worked against the frade. The idea of increasing the speed of the frend as the frade becomes more profitable is still a concept that has validity and has not been adopted in other adaptive methods. One weak point may be that AF alwajs begins at . Although this allows the frade latitude to develop without being stopped out. a maitet that is moving quickly through the buy or sell signal would be better traded with a faster frend This method also requires fairly consistent price swings to produce profits.

A sfrong point is that the initial Stop and Reversal is the market exfreme high or low rather than an arbitrarj, computer-generated point. Also, the SAR does not get closer than the previous days high or low, which prevents a reversal when the maitet is moving sfrongly in a profitable direction. For those readers interested in the fiirther development of this method, the Parabolic Time/ftice Sjstem is combined with Directional Movement (described in Chapter 23) to form the Directional Parabolic Sjstem discussed in Chapter 6.

The following Easj Language user function allows the user to specify the starting value of the smoothing constant A F m i n, the increment A F i n c, and the maximum value A F m a x. This provides for more flexible testing Optimization of these values has been reported to produce good results.

IParabolU-VRT

This version of the Parabolic system was written by

Sam Tennis, VISTA Research and Trading, Inc.,

8103 Camino Real, South Miami, FL 33143. Emeil: skt@vista.com

and reformatted by PJ Kaufman I

llnput values were formerly AFmin = AFactor, AFinc = AFactor, and = Limitl {Sample usage; Plotl (Parabolic.VRT (0.02, 0.02, 0.20)[ , "Parabolic-): Function returns SAR (stop & reverse) price objectivel

input: AFmimnumericsimple), AFinc(numencsimple), AFmax(nLmericsimplej; vars: Position(l), AF(AFmin), SAR(low[0]), Hithigh[0]), Lo(Low[D]):

if ©currentbar <- 1 then Position = I; if ©currentbar > 1 then begin

if High > Hi then HI - High;

if Low < Lo then Lo = Low;

if Position - 1 ther begin

if Low <- SARCl] then begin Position = -1; SAR - Hi; AF t 3 = AFmin; Lo = Low; Hi - High;

end; (Reverse position long to short!

end else begin

if High SAR[]] then begin Position - 1; SAR = Lo; AF - AFmin; Lo - Low; Hi = High;

end; iReverse position short to longi

end;

If Position - 1 then begin

if Positicntl] = 1 then begin

SAR = SAR[I] + AF * (HighilJ SAR[1]); if Hi > Hi[l] and AF < AFrna;< tren AF - AF » AFinc; end; Iwe have been "long for at least ore bar! if SAR > Lew ther SAR = Low; if SAR > Icw[I] ther SAR = Low[l]; end Hong I else begin

if Position[l] - -1 then begin

SAR = SftR[I] + AF * (Lcw[l] - SAfi[l]); if Lo < Lo[l] ard af < AFmex then af = AF * AFinc; end; Iwe have been short* for at least one bar if SAR < High then SAR = High; if SAR < HighLl] then SAR = High[l]; end; IshcrtJ

Parabolic.VRT - SAfi;

The MasterTrading Formula

Another landmait method of creating a variable-speed spproach is Marts Master Tradmg Formula. It is also based on an exponential smoothing formula where the smoothing constant and band around the trendline are calculated daily, based on maitet volatility. Marts general technique is to combine the average true range (the maximum of

yesterdays close and todays high or low) for the past ] 5 dajs with the net change over the same time period. Each of these volatility elements is ranked from ] to 2] by defining a maximum value for each one and dividing that maximum into 20 equal zones (the 2]st being anything higher). The two rankings are then averaged to get a correlated volatility factor (C\T). Another ranking of 2] zones is created by dividing the highest C\T into 20 equal parts. The C\T then relates linearly to a range of smoothing constants from .084 to .330, representing the spproximate exponential equivalents of the moving average dajs from 5 to 23. The trendline value is then created daily using the formula

TREM5(today) = TREND(prior) + C\T(today) x [HLC(today) - TREM5(Prior)

where HLC (today) is the average of the high, low, and closing price. As with the other adaptive methods, the speed of the trend increases as volatility increases.

A band is also placed around the frendline, based on an inverse relationship to the correlated volatility faaor The band is widest when there is low volatility and the smoothing constant produces a slow trend; it is narrowest in fast highly volatile maitets. Rules for frading Marts IVfester Formula follow the basic band-trading rules. The sjstem is alwajs in the maitet, tating long positions when the upper band is broken and short positions when the lower band is crossed.

ADAPTIVE MOMENTmt CALCULATIONS

Varjing the period of calculation does not have to be limited to a trend formula. The period for any technique can also be adaptive. The following techniques spply the same concept to indicators.

1 Donald lAirt. ISe Trading F. m,ula Bo. -Vs. En .twaters, IF, 1< . 1)

Variable-Length Stochastic

Written by Frank Key, this adaptive technique uses Kaufinans efficiency ratio, ER. It changes the stochastic period within the default range of 5 to 30, using only integer values. The effect is that, when prices are trending with respect to the stochastic, the stochastic period is lengtiiened to allow the trading signal to stay with the trade. At tuming points in the maitet, the stochastic period is shortened causing the reversal signal to be more responsive.

Stochastic period

N5P = @IntPort!on(ER X (Hexpenod Hinperiod) + Hinperlod) Adaptive stochastic ASTOK - @slowK(HSP)

where ASTOK Is the adaptive stochastic value today (based on NSP days) Maxperiod is the maximunn period, suggested as 30 Minperiod is minimum period, suggested as 5 E R is Kaufmans efficiency ratio

The variable-length stochastic uses the efficiency ratio in a manner opposite to Kaufinans AMA. While the AMA increases in speed when the trend gets sfronger. Keys variable-length stochastic decreases in speed. This technique gives price more room to fluctuate during periods in which a sfrong trend is also associated with high volatility

Trend-Adjusted Oscillatir

One problem that confronts many traders who use stochastics or other oscillators is that the oscillator values tend to cluster at the bottom of the chart when the frend is down, and at the top when the trend is up. For a counterfrend frader, this results in many oversold conditions during a downtrend, which can give false buy signals. A frend-adjusted oscillator 7 can help this bias by correcting the value of the oscillator by the amount that the trend of the oscillator varies from its midpoint (usually 50°o). Therefore, if a ]0-day oscillator has been steadily declining and its 5-day moving average has a value of 40, then the current oscillator value is raised by ]0°o (the midpoint of 50 minus the