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39 H,L, The two days are linked together and the ratio of the high price relative to the prior close is measured against the total range for the day. For the normal case. ,  : L,, but if C,t>H,otl,>C, t,C,. replaces either H, or I, to extend the range. The value of O, will be either 1 or 0 for these extreme cases. As with the Oscdlator. the values derived from this method may also be smoothed. Oscdlators are not the only tools for measuring momentum or for determining overbought or oversold conditions Because it is very different from either a charting technique or a moving average, it is valuable either on its own or as a confirmation of another method. A word of caution; Trading against the trend can be exciting and profitable but at considerably greater risk than a trendfoliowing system. The problem with selling an overbought condition is that there Is no way to hold losses to a minimum. Once a short position is entered, the momentum or the oscillator value could sustain lis strength and move against the position. %R Method After the publication of Williams oš/Afcu/Ofi«Afl/AonZ)o ars. . .Last Year... Trading CommodUies (Conceptual Management, 1973), the %R oscillator became well known It is a simple way of calculating where todays closing price fits into the recent tradirig range. Using the last 10 days, defme buying power high.o dosed range higb,olow,o Wliams 10day %R Is actually a 10day stochastic using the hi price rather than the low price in the numerator therefore, it is the complement (100 minus the 10 1 stochastic) of the original stochastic calculation. With a chan lhat has 0 at the top and 100 at the bottom, a value below 95% will e a buy signal, and one over 10% will e a sell signal. Williams viewed this as a timing device to add positions within a major technical or fundamental trend. Trades were not to be entered if they contradicted the major market direction. Readers should refer to the earlier secfran in this chapter, "Srochastics,* for more jobrmation The Ultimate Oscillator In the Ultimate OsciUator. Williams seems to combine his original idea of the A/D Oscillator with a great deal of Wilder s RSI." He adds the unique feature of three concurrent time periods to ošet the negative qualities of the short time period of the %R, without slowirig the system too much. The Ultimate Oscillator works as follows: 1. Calculate todays buying pressure B, by subtracting the true low from the closing price. The true low is todays low or yesterdays close, whichever is lower. 2. Calculate today s true range R, by taking either the greater of todays high and low, todays high and yesterdays close, or yesterdays close and today s low 3. Total the bu}ng pressure Bj separately over the three intervals of 7,14, and28days, desnated as SS,, SB, and SBa. 4. Total the true range R, over the same three periods, SR,. SR,, and 5  "Lany WUiiaim, The Ultimate OsciUaitH; IbdmicalAnalysis ttfStocks & Commodities (August 1985). 5. Divide the sum of the bujing pressures by the correaponding true range, that is, SB71SR7 and scale by multiplying the 7day value by 4 and the 14day value by 2. All three calculations are now in the same scale. Notice that the nearest seven values for the buying pressure and the true range are each used seven times; that is, they are multiplied by both the scaling factors of 4 and 2, and used once more in the 28day calculation. Williarns has
created a stepweighted momentum, assigning values of 7, 3, and 1 to the first 7 days, second 7 days: and last 14 dajs. reapectively. The last 14 dajs account for only 10°o of the total. The rules for using this oscillator (see Figure 611) are 1. A sell signal occurs when the oscillator moves above the 50°o line (an upward divergence), and the oscillator peaks and then fails to break the peak on the next rally. Then, a sell order can be placed when the oscillatcr fails (on the right shoulder). 2. If holding a short position, close out the short when a long signal occurs, or when the 30°o level is reached, or if the oscillator rises above (the stoploss point) after being below 50° o. 3. A buy signal occurs using the opposite techniques as the short signal (.rule I). 4. if a long position is held, close out longs when a short signal occurs, or when the 70°o level is reached, or if the oscillator falls below 30°o (after being above 50°o). Williams Ultimate Oscillator has combined many important features, including weighting time periods, setting objectives, stoploss points, and chart interpretation. There are two obvious weaknesses in this approach. 1. The chart rules add a great deal of subjectiveness to the method. Waiting for a failure of a second peak is another way of looking for a broadening topa slower rise followed by a rounding pattem. Waiting for a pattern may add reliability if interpreted properly, but it defeats the effect of the oscillator being a leading indicator 2. The stoploss rules apply only a there is no rid; control. er the oscillatiT has crossed 50°o. If it moves the wrong way immediately, DOUBLESMOOTHED MOMENTUM The most recent conhibutions to the study of momentum have been made by Williarn Blau." In addition to creating new momentum indicators, he has added substantial value to the old ones. Also refer to his work on double smoothing of momentum in Chapter 4 ("Trend Calculations"). WiUian, Elan, M. jnentum Direction and Divereence (J. .Lii Wiley & Sons, New Y. 1995. FIGURE611 Williams Ultimate Oscillator. True Shength Index Much of Blaus work combines double smoothing of momentum values (1period price differences), which has surprisingly litde calculation lag. By using the momentum, he has based the calculations on values more sensitive than price, then slowed them down by smoothing. He refers to this as using momentum as a proxj for price. One of Blaus most popular indicators is the True Shength index (TSI), which combines these features:
100 X @SmoothedAverage(@SmoothedArerage(close  close[l].r)5) SI(c oscrs)  @sn,ooihedAvcrage(@SmoothedAverage(@abs(dose  dosel),r).s) where r is the period of the first momentum smoothing s is the period of the second momentum smoothing c!oseclosel] is the 1day momentum Written in adeSuaion format, when: the two smoothing periods are smoolbl and smootb2, this formula is:  @snioothedaverage(®snioothedaverage(closeclose[l],snioothl),smooth?); denom  estiioothedaverage(esmoothe(laverage{eabsvalue(close closeCl]). smoothl).smooth?); TSl = 100*num / denom; The numerator is the scaled value of the doublesmoothed momentum, and the denominator is the double smoothing of the absolute value of momentum. The 1day momentum is first smoothed over the period r, and then ovei the period s. The relationship between the standard momentum (the difference in prices over r dajs) and the TSI can be seen in Figure 612. The momentum indicator, formed by using an MACD indicator with moving average values of 1 and 20, has the tjpical erratic pattem of prices, and a slit lead ahead of the peaks, formed by the pending crossing of the prices and moving average. The TSI is much smoother with peaks and vallejs aligning with those of the prices Buy and sell signals are created by smoothing the TSI signal line and bujing when the TSI crosses above the signal line. DoubleSmoothed Stochastics Because of Blaus great interest in double smoothing, he defines the general form of a doublesmoothed stochastic as: DS{q,r,s) = 100 X @SmoothedAverage(@SmoothcdAveragc(dosc  @Lowest(low,g).r)) @SmooihedAverage(@SmoothedAverage(@HighestOtigh,)  @Lowestaow,g),f,s) where close  @Lowest(low,q) is the numerator of Lanes raw stochastic, the lowest low over the past q periods @Higbest(bigb,q) @Lou)est(low,q) is the denominator of Lanes stochastic, the greatest highlow range over the past q periods @SnmotbedAvera8e(... ,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 trendline value was smoothed and added to the trend value to get what was originally considered a doublesmoothed trendline. Instead, the difference between the current price and the cor FIGLrRE612 Comparing the TSI with a standard momentum over the same period.
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