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 trend-foliowing 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 o¹/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,o-low,o

Wliams 10-day %R Is actually a 10-day 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 o¹et 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 7-day value by 4 and the 14-day 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 28-day calculation. Williarns has

created a step-weighted 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 6-11) 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 stop-loss 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, stop-loss 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 top-a 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 stop-loss rules apply only a there is no rid; control.

er the oscillatiT has crossed 50°o. If it moves the wrong way immediately,

DOUBLE-SMOOTHED 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.

FIGURE6-11 Williams Ultimate Oscillator.

True Shength Index

Much of Blaus work combines double smoothing of momentum values (1-period 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!ose-closel] is the 1-day momentum

Written in adeSuaion format, when: the two smoothing periods are smoolbl and smootb2, this formula is:

- @snioothedaverage(®snioothedaverage(close-close[l],snioothl),smooth?); denom - estiioothedaverage(esmoothe(laverage{eabsvalue(close closeCl]).

smoothl).smooth?); TSl = 100*num / denom;

The numerator is the scaled value of the double-smoothed momentum, and the denominator is the double smoothing of the absolute value of momentum. The 1-day 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 6-12. 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.

Double-Smoothed Stochastics

Because of Blaus great interest in double smoothing, he defines the general form of a double-smoothed 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 high-low 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 double-smoothed trendline. Instead, the difference between the current price and the cor

FIGLrRE6-12 Comparing the TSI with a standard momentum over the same period.