the biggest surprises, as far as I was concerned,so I thought it would be interesting to examine some of their charts. Figures 3 and 4 include the
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Stocks & Commodities V. 10:1 (38-42): Futures According To Trend Tendency by E. Michael Poulos
long-term random walk index (LRWI ), a trend indicator. An L RWI of highs greater than 1.0 indicates amove beyond that expected for a random walk, and therefore an uptrend, while an LRWI of lows greaterthan 1.0 indicates a downtrend.The charts show very clearly that the pound gets beyond the random walk boundary (with an index of1.0) with greater strength and for more extended periods than wheat does.If you're a trend-following futures trader, these rankings can help you answer one of your most importantquestions of which future to trade.E. Michael Poulos, (516) 423-2413, writes software and works in the research and development ofcomputer trading aids for Traders' Insight.
REFERENCESFeller, W. [ 1968]. An Introduction to Probability Theory and Its Applications , Volume 1, John Wiley &Sons.Poulos, E. Michael [1991]. "Of trends and random walks," S TOCKS & COMMODITIES, February.Stewart, Ian [1989]. Game, Set and Math, Blackwell Publishing.Weaver, W. [1982]. Lady Luck, Dover Publishing. Does not refer specifically to random walk theory butdoes indicate that the standard deviation of the number of heads in a series of coin tosses varies asthe square root of the number of tosses.
FIGURE 1: The ratio of each average channel height to the average channel height for one day wasgreater than the square root of the length. This consistency indicates that the yen trends.
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Stocks & Commodities V. 10:1 (38-42): Futures According To Trend Tendency by E. Michael Poulos
FIGURE 2: The ratios shown above for yen and the S&P 500 are similar to those given in February,even though the histories differ: January 1975 through April 1990 for yen, and June 1982 through April1990 for the S&P 500.
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Stocks & Commodities V. 10:1 (38-42): Futures According To Trend Tendency by E. Michael Poulos
FIGURE 3: The pound ranked high for tending to trend. A reading greater than 1 for either the LRWIhighs or LRWI lows indicates a trend is under way.
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Stocks & Commodities V. 10:1 (38-42): Futures According To Trend Tendency by E. Michael Poulos
FIGURE 4: Wheat ranked last for trend tendency. Readings below 1 indicate a lack of a trend
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Stocks & Commodities V. 10:1 (38-42): SIDEBAR: THE RANDOM WALK INDEX
THE RANDOM WALK INDEXThe channel height ratio to one day figures given show a consistent excess beyond the square rootcolumn. This excess indicates the presence of trends and hints how to create a trend "yardstick." If notrends were present, the ratios would be expected to all fall exactly on the square roots, and thus an"expected random walk" over n days would be the square root of n multiplied by the average daily range(same as average one-day channel height).We define the random walk index (R WI) as the ratio of an actual price move to the expected randomwalk. If the move is larger than a random walk (and therefore a trend), its index would be larger than 1.0.To keep track of where today's high is relative to previous lows and where today's low is relative toprevious highs, we need two indices:RWI of high=(H-Ln)/(Avg.mg.x n )RWI of low=(Hn-L)/(Avg.mg.x n )where "Hn" and "Ln" are the high and lows of n days ago and "avg rng" is the average daily range overthe n days preceding today. In day-to-day use, these indices are calculated over a range of lookbacklengths. Use the largest value returned for today's indicator. Thus, we let the market determine thelookback interval,rather than use a fixed arbitrary one as many current indicators do.In addition, Figure 1 gives us a very important insight, showing the distribution of lookback lengths forthe largest RWI (how many times did the largest RWI occur looking back two days, three days, four, five,six...?). Since the curve of Figure 1 bends at a fairly sharp corner, the entire curve can be approximatedby only two straight lines. This means that the markets, to a very good approximation, can be thought ofas displaying two distinct personalities. The corner of Figure 1 is showing us where the dividing linebetween short- and longterm behavior is, between seven and eight days. We therefore calculate two R WIS,one for short term (two to seven days' lookback), and one for longer-term (eight days and up). Theshort-term one is a good overbought/oversold indicator and the long-term one is a very good trendindicator.
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Stocks & Commodities V. 10:1 (38-42): SIDEBAR: THE RANDOM WALK INDEX
SIDEBAR FIGURE 1
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Stocks & Commodities V. 9:7 (298-300): What Is A Trend, Anyway? by John Sweeney
What Is A Trend, Anyway?by John Sweeney
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reader reacting to the Settlement article in January on trading basics (Settlement, "Trading simply:
Minimizing losses," Stocks & COMMODITIES, January 1991) asked a key question: What is a trend? Howdo I identify it when I'm trading? (Personally, I use dual moving averages.) Most of us could think of anumber of ways of defining trends, but it fascinates me what our analytical methods tell us about our ownthinking. Typically, our thought of "trend" amounts to no more than drawing lines upward or downward.I think it should also encompass drawing them horizontally.The trend is our friend, we think, because that's when price changes occur in some unidentified, regularprogression upon which event we make money. Questioning the key elements — persistent movementover time — by looking at charts, it's evident that tradeables can move smoothly, like the Eurodollars inFigure 1 or Treasury bills (Fed managed), or abruptly, like, say, gold, which is notorious for opening $20away from where it's been for the last six weeks (Figure 2).My conclusion? Trending behavior varies by tradeable and is more apparent in "managed" prices (such asspecialist supported stocks and short-term interest rates) or markets of mammoth size where the sheernumber of participants precludes truly abrupt change — say, debt and currencies. Despite this, we lookfor (hope for?) a straight line progression of prices from one level to another, hence the urge to drawstraight lines on all charts of fluctuating prices.By drawing straight lines, are we really trying to model this variegated behavior or just expressing ourown preconceptions and, thus, limitations of thought? Prices do exhibit persistence (that is, statisticaldependence): they usually open "around" where they closed and the next price is "around" where the lastprice was. However, even if that phenomenon justifies describing that behavior with a single line, I can'tthink of a reason for it to be straight. Though straight lines can be powerful analytical tools (Figure 3),our strong preference for them is foremost our own wishful thinking.STRAIGHT LINE ELEGANCEA nifty refinement of the straight line approach was developed by John Ehlers for his cyclic analysiswork. He'd run a regression line (line A in Figure 4) through the last 20 days of data and record the R2.Then he would extend the line one day further back in time and recalculate the R2. If it stayed the sameor increased, then the added day was consistent with the previous 20-day trend and he would go backanother day to repeat the calculation. Stepping backward in this fashion (line B in Figure 4), he'deventually find a point where the R2 decreased (the gap in Figure 4), an indication that the latest addedprice was inconsistent with the most recent trend.
All these straight-line methods are explications of our intuitivesense of expressing trend as direction, even if only horizontal.The beauty of this approach is that it is indifferent to prices rising, falling or staying level. It points out to
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Stocks & Commodities V. 9:7 (298-300): What Is A Trend, Anyway? by John Sweeney
FIGURE 1: Short-term interest rates generally have good price continuity day to day, behaviorconducive to defining trend.
FIGURE 2: While short rates have few gaps and small gaps, gold can move abruptly from one pricelevel to another, behavior different from an ideal trend. (Data courtesy CompuTrac/M Dial Data)
Stocks & Commodities V. 9:7 (298-300): What Is A Trend, Anyway? by John Sweeney
FIGURE 3: Straight lines are maligned as moronic but can be powerful tools, especially in detrendedseries like the relative strength index. Here, RSI neatly calls the beginning and end of a trend in bonds.
FIGURE 4: John Ehlers's elegant trend definition steps backward through the data until the coefficientof determination decreases, indicating values inconsistent with the current trend.
Stocks & Commodities V. 9:7 (298-300): What Is A Trend, Anyway? by John Sweeney
FIGURE 5: A 6% filter of the S&P 500 wipes out all the small moves, implicitly defining a number oftrends of that size or better.
FIGURE 6: Averages are an intellectual extension of straight lines, but at least they reliably followprices without our intervention.
Stocks & Commodities V. 9:7 (298-300): What Is A Trend, Anyway? by John Sweeney
us that, quantitatively, trend can be persistent horizontal price levels (that is, lack of price movement) aswell as moving up and down. Since this view of price action is more comprehensive than the intuitive"up or down," I prefer it. It subsumes the two-state model that prices are either moving or not moving andsuggests a quantitative approach to defining "movement," abnormal departures away from the regressionline or sharp changes in the slope and/or shortening of the period of the regression line.Refinements, such as having a threshold level of change in the R2, using the slope of the regression lineto define breakout, or even checking beyond the point of declining R2 for prices that would return theregression's coefficient to its previous values, are easy to imagine. It also ingeniously solves the timeissue: how long must a trend persist to be a trend? Ehlers's approach has its limitations, but it's robust andrewards elaboration.OTHER STRAIGHT-LINERSIn the vein of time, I also classify the various wave approaches (Elliott, Dow) as variants of the straightline approach because they subsume price movement into lines between peaks and valleys. I've alwaysthought the best encapsulation of these approaches was Art Merrill's Filtered Waves , Basic Theory,which takes the straightforward approach that defining the percentage retracement would define thewaves — the trends — for you (Figure 5). Longtime STOCKS & COMMODITIES readers may be familiarwith these retracement charts from Art's monthly column, which usually uses them for comparisonagainst various indicators. Software for generating them is included in RTR's Technifilter Plus orMetaStock Pro 2.5.A 5% filter, for instance, would "filter out" all movements of less than 5% from the previous high or low.Here, it's easy to see that one's "scale" — and, effectively, one's time horizon (given normal movements)— can be set by the size of movement one seeks. I personally look for a 6% wave in the Standard &Poor's, so I'm unlikely to see a minor wave (a "minor" trend) of 1% or 2%. I'm also trading in a differentrealm than those following the Dow theory (10% to 25%).BEYOND STRAIGHT LINESAll these straight-line methods are explications of our intuitive sense of expressing trend as direction,even if only horizontal. Once secure with line-drawing, averages are a refinement, since they reliablyfollow prices (Figure 6) without our intervention or judgment. In trends, they aren't quite straight but areclose enough to make the connection for most people.True refinements are French curves and fitted curves such as Bezier and regressions to exponentialcurves (à la Tom Kimball of Florida, of newsletter fame). Here, regression could also be used, perhapssearching through an entire family of potential curves for consistent fit over a given period of time.Again, price action is reduced to a simple line, but it's meant to be more indicative of the market's action.To wrap up, we usually identify trend after it's started by the slope of the lines we draw on our charts,whether straight or curved. However, if trend is persistence in price movement over time, trading rangeactivity is a trend of sorts. We'll need a sharper definition if we just want price activity that's goingsomewhere. Our inability to isolate what we want is our own limitation: a predilection for simple lines.John Sweeney is STOCKS & COMMODITIES' Technical Editor.
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Stocks & Commodities V. 8:10 (377-381): Early Trend Identification by John F. Ehlers
Early Trend Identificationby John F. Ehlers
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mpressive profits can be accumulated just by staying with a position during a trend. We would all be
millionaires if only we could identify the trend early in its onset. While the trends are obvious inretrospect, it's another matter altogether to identify the trend in the heat of battle. Not only that, there maynot be a trend at all at the time we expect one.If we make a reasonable mathematical model of the market we can examine it parametrically. Theconclusions we draw from this model can help us establish our entry points and strategies for trading thetrends. We will view the market as a random walk problem to create our model.Random walk for the marketIn the same way that water can only flow downstream, time cannot be reversed in trading. In addition,prices can only be higher or lower in the same way that the river can only bend to the right or left. Theseelements constrain the random walk problem to a special form that mathematicians call "drunkard'swalk." In the simplest form of this walk, the "drunk" steps only into a square diagonally to the right orinto a square diagonally to the left as he steps forward. He must make a new decision with each step. Tomake the decision random, he flips a coin to determine the direction he will take. Repeated many times,the overlay of paths that he follows will look like a smoke plume. The question of the drunkard'sdestination can be answered through a well-known partial differential equation called the DiffusionEquation. The density of the smoke particles in the plume is analogous to the probability of thedrunkard's location. A multiple-exposure photograph of the drunkard's walk repeated over and overwould show its randomness. This photograph would show the composite paths to have a uniform density,
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Stocks & Commodities V. 8:10 (377-381): Early Trend Identification by John F. Ehlers
widening from the initial position. The uniform density would make the sum of the paths look like smokeplume.Further, random walk does not necessarily mean chaos. A minor variation of the drunkard's walk problemis to allow the random coin-flip decision to control the change of direction rather than the directionitself— that is, the random variable becomes momentum instead of direction. The partial differentialequation describing this condition is known as the Telegrapher's Equation. The equation describeselectric waves along telegraph wires, among other subjects. You can picture the result as the drunkreeling back and forth. He overcorrects around a general direction trying to reach an objective. Thisformulation of the problem, expressed in terms of physics, accurately portrays the river and explains whythe river meanders. In a multiple-exposure photograph the paths are still randomly distributed.Nevertheless, the cycles are apparent in the shorter case of a single path. By analogy, the market hasshort-term cycles when the appropriate conditions prevail.If enough traders ask themselves whether the market will go up today, the random variable is direction.Thus, conditions are established for the solution of the Diffusion Equation. On the other hand, if enoughtraders ask themselves whether the trend will continue, the random variable now becomes momentum.You could then expect the conditions to be established for the solution of the Telegrapher's Equation. Themarket is ripe for short-term cycle activity.Identifying trends with reverse logicAs formed by the random walk, our market model is either cyclic or trending. A moving average is aboutthe only means we have to measure the trend directly. Moving averages are not very helpful because theyare always lagging functions. However, we can measure the cycles and know when the market is cyclic.By reverse logic, if the market is not short-term cyclic, it must be trending. We can identify whether themarket is cyclic in a period as short as a half cycle. Cycle analysis, therefore, can be used to spot a trendearly in its formulation.The early identification of a trend then depends on a valid measurement of short-term cyclic activity.There are two ways to do so, either by cycle elimination or by spectrum analysis. Of the two, cycleelimination is by far the easier.Let's approach the question of cycle elimination using synthesis and then reverse the procedure toestablish what we must do to perform the analysis. We can synthesize a theoretical price curve by addinga pure sinewave to a straight trendline. We then examine these two components independently. Theaverage over the period of a theoretical sinewave is always zero, regardless of where we started theaverage. If we used a moving average with a length the period of the sinewave, then the sinewave iscompletely removed and we are left with only the straight line trend.The identification of the trend is that easy. We eliminate the cyclic component when we use the averageover the cycle length. We could adjust the average as the cycle length varies and plot the resultsday-by-day. I call the result an "instantaneous trendline." A fixed-length moving average can sufficeduring periods when the cycle length is not changing. We expect the price to alternate across ourinstantaneous trendline because the price has the cyclic component. We expect to see the crossing occurapproximately every half cycle. If the price fails to cross the instantaneous trendline, we get a clear signalthat the price has moved into a trend mode—that is, the movement in the direction of the trend swampsthe cyclic movement so the expected crossing does not occur. When this happens, the price parallels our
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FIGURE 1. We can identify a trend in the first five days of its move on March 2, 1990. At this pointwe have a 10-day cycle, and the price has not crossed the instantaneous trendline within thelast five days.
FIGURE 2. This spectrum shows an excellent 12-day cycle in February 22, 1990, just after weentered our short position.Copyright (c) Technical Analysis Inc.
FIGURE 3. Here, the spectrum is taken on February 27, 1990. Note the subtle change. Thevery long cycle is starting to appear.
FIGURE 4. Figures 4, 5 and 6 show the progression of the spectrum for the next three tradingdays.
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FIGURE 5. The progression of the spectrum continues.
FIGURE 6. March 2, 1990, was the day previously declared that the trend was to be established.
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Stocks & Commodities V. 8:10 (377-381): Early Trend Identification by John F. Ehlers
instantaneous trendline without crossing it. The instantaneous trendline is a lagging function like anormal moving average. Using the instantaneous trendline method, a trend is identified when the pricedoes not cross or even appear likely to cross the trendline within a half cycle.Figure 1 is an example of where we identify a trend in the first five days of its move on March 2, 1990(900302, the cursor location). At this point we have a 10-day cycle, and the price has not crossed theinstantaneous trendline within the last five days. The price shows no tendency of trying to cross theinstantaneous trendline. Early identification allows us to capture about a 30-point profit, the majority ofthe move.We can use this technique to simply trade the trends. However, the profits are even better if we use thetrend identification to shift from a cyclic trading strategy to a trend trading strategy. Suppose in ourexample we had been trading on the basis of cycles. Trading every five days (each half cycle), we wouldhave gone long on 900131, a short-term low. From there we would go short on 900207 (short-term high),long on 900214 (a little early for a short-term low), and short on 900221. Our last short entry would be atabout 431, substantially above the 415 price where we first identified the downtrend. We would alreadyhave been in a short position on the basis of cycle trading and therefore would exploit the full extent ofthe trend movement. Shifting between cycle trading strategy and trend trading strategy therefore enhancesoverall profitability.Verifying trend identificationA spectrum display shows amplitude on the Y axis vs. cycle length on the X axis. This display allowsyou to see the relative strength of several cycles, a benefit beyond merely picking out the dominant cycle.The spectrum display also allows you to identify the quality, or resolution of the cycle measurement.Ideally, a cycle measurement is a single spike on the display. This ideal picture tells you that there is onlyone well-defined spectrum component — the dominant cycle. But what if the spectrum display is a broadbell-shaped curve? In this case, the energy is spread over a range of possible dominant cycles, with nocycle length being clearly dominant. The spectrum display indicates that the lack of resolution is reasonenough not to trade the market on the basis of cycles. For trend identification we are most interested inthe capability of the spectrum display to show the formation of two or more cycles.
Figures 4, 5 and 6 show the progression of the spectrum for thenext three trading days. Figure 6 is the spectrum for 900302, theday we previously declared the trend to be established.J.M. Hurst, in The Profit Magic of Stock Transaction Timing, advances the principle of proportionality.Simplified, the principle states that longer cycles have larger amplitudes. This principle is obvious to themost casual chart reader.We can use this principle to identify trends with the spectrum display of short-term cycles. From ourexample for gold, Figure 2 shows an excellent 12-day cycle on 900222, just after we entered our shortposition. Figure 3 shows the spectrum taken on 900227. The very long cycle, longer than 50 days, isstarting to appear. Figures 4,5 and 6 show the progression of the spectrum for the next three trading days.Figure 6 is the spectrum for 900302, the day we previously declared the trend to be established. Figure 7shows the spectrum three trading days later on 900307. Figure 7 shows that the short-term cycle has been
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FIGURE 7. Three trading days later on March 7, 1990, the spectrum shows the short-termcycle to be swamped by the trend, interpreted as a long cycle outside the calculationrange.
FIGURE 8. The spectrum for April 18, 1990, still shows substantial long cycle energy,however.
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FIGURE 9. The absence of long cycle energy for April 25, 1990, confirms the trend hasended.
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Stocks & Commodities V. 8:10 (377-381): Early Trend Identification by John F. Ehlers
swamped by the trend, which is interpreted as a long cycle outside the calculation range. Used this way,the spectrum confirms that the trend has been established.The spectrum can also confirm that the trend movement has ended. The price first crosses theinstantaneous trendline from the bottom on 900418. (We could have exited then at about 385 for a totalprofit of $4,600 on a single contract.) Figure 8 is the spectrum for 900418, and shows long cycle energy.Figure 9 is the spectrum for 900425, five trading days later. Absence of long cycle energy confirms thetrend has ended.
I'm trying to automate the entire trading strategy. One of the earlydreams for computers, you may recall, was to create robots toserve mankind.Helpful cycles and trading strategyOur example is not an uncommon event. This approach can be used to repeatedly alter your tradingstrategy as the market shifts from the cycle mode to the trend mode. All you need to do is estimate ormeasure the current short-term cycle and then take a simple average over the period of the cycle lengthand plot it as a point on your bar chart. Repeat this daily. Connecting the averages with a line creates your"instantaneous trendline." Then watch the price action relative to this trendline to identify the onset of thetrend when the price has not crossed within the last half cycle.I'm trying to automate the entire trading strategy. One of the early dreams for computers, you may recall,was to create robots to serve mankind. By recognizing when we are in a trend mode (Diffusion Equation)or cycle mode (Telegrapher's Equation), our computers should know when to apply the proper tradingstrategy. I guess that would make our computer a "know-bot"!John Ehlers, Box 1801, Goleta, CA 93116, (805) 969-6478, is an electrical engineer working inelectronic research and development and has been a private trader since 1978. He is a pioneer inintroducing maximum entropy spectrum analysis to technical trading through his MESA computerprogram.
ReferencesHurst, J.M. [1970]. The Profit Magic of Stock Transaction Timing , Prentice-Hall.Ehlers, John [1990]. "1989 cycles," Technical Analysis of Stocks & Commodities , June.
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Stocks & Commodities V. 5:2 (64-66): Trend of the trend by Gregory L. Morris
Trend of the trendby Gregory L. Morris
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ost indicators of trend are taken for granted even though many times they are used successfully by
stock and commodity traders. It has been my experience that blindly following canned indicators can leadyou into a false sense of security, especially if you begin using the indicator when it is correctly callingthe market. If you begin using a trend-following indicator during its inevitable whipsaw period, you willlose faith and look for another indicator. Therefore, if you develop an indicator using some basic logicand reason which is related to known market action, you can have a little more faith in a particularindicator. There is also the argument of using a basket of indicators and/or using them in a tree structuredapproach. No doubt that is a safer approach, but it is not the purpose of this article.It is accepted that the successful trader must identify and follow the trend of the market to be a consistentwinner. There are, of course, many indicators available to help identify the termination of a trend andprepare you to reverse your positions. Adding even more confusion to the arena, you have to determinewhich type of trend is being identified: short, medium, or long. Again, this is not the purpose here.I would like to share with you a simple trend-following technique that seems to work very well. It worksbecause you must adapt it to the market you want to analyze. In other words, the parameters are going tobe different for each market, whether it be stocks, commodities, mutual funds, or whatever. A completeexplanation of the system will be discussed while being applied to the Dow Jones Industrial Average. Iknow what you're thinking--no one can trade the DJIA, so why use it? That's the very reason I have usedit. I did not want it to look like I had culled hundreds of charts to find one that best supported thistechnique.First of all, you must determine your trading objectives: short, medium, or long-term. Short-term (a fewdays to a few weeks) would rely on daily data for the trend information. Long-term (greater than sixmonths) would use almost exclusively weekly data. Medium-term would use a combination of both.Then, of course, there are combinations of daily and weekly that you can use to put conditional restraintsinto your trading system. The technique of using longer-term indicators to determine which side of ashorter-term indicator to make your trade is usually a profitable trading strategy. However, for thepurposes of this article, I will stick to the short- to medium-term.Determining the dominant short-term cycle is necessary to obtain the smoothing parameters for thisindicator. There are many good books available on cycles. One that I have found to be the most useful isThe Profit Magic of Stock Transaction Timing , by J.M. Hurst (Copyright 1970). Despite the horrendoustitle, the book is exceptionally logical in its explanation of market cycles and how to identify them.One method of determining cycles is to detrend the data. This is a simple concept involving the price dataand a moving average. The moving average length is based upon the trend you want to follow. Forshort-term, a moving average of 25-35 days works quite well. Basically, you subtract the moving averagefrom the price and plot the results. This is as if you had grasped the moving average line at both ends andpulled it tight so it looked like a straight line with the price data remaining in its same relative position tothe moving average.
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Stocks & Commodities V. 5:2 (64-66): Trend of the trend by Gregory L. Morris
Most indicators of trend are taken for granted even though manytimes they are used successfullyOf course you can always just count the days between lows from any daily chart or use sophisticatedmaximum entropy or Fourier analysis. Detrending just makes those lows stand out a little better.Before I go any further, a look at moving averages might be a good idea. A moving average smooths asequence of numbers such that the result is a reduction in magnitude of the short-term fluctuations, whileleaving the longer-term fluctuations little changed. Obviously, the time span of the moving average usedwill alter its characteristics.J.M. Hurst explains these alterations with three general rules:1. A moving average of any given time span exactly reduces the magnitude of the fluctuations of durationequal to that time span to zero.2. The same moving average also greatly reduces (but does not eliminate) the magnitude of allfluctuations of duration less than the time span of the moving average.3. All fluctuations of greater than the time span of the average "come through," or are also present in theresulting moving average line. Those with durations just a little greater than the span of the averageare greatly reduced in magnitude, but the effect lessens as periodicity duration increases. Very longduration