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30 • The spaa of a moving average is the length of time over which data is simuned to obtain the moving average. Fcffexample, a 30-week moving average consists of l/30th of the sum of the weekly closing prices of a stock for the last 30 consecutive weeks. The span of this average is therefore 30 weeks. • A moving average lags" the data it smootiis by one-half of its span. This means that if the average is to represent a time-synchronized, smooth version of the data, the last computed point of the average must be plotted one-half span behind the last available data point. Thus, the last available point of a 30-week moving average is plotted between the 15th and 16tfa weeks behind the last closing price of the stock. • A moving average reduces precisely to zero the presence and magnitude of any cyclic component with duration exactly equal to the span of the average. • AH shorter duration components are drastically reduced, but may show some sign of their presence. • All longer duration components are definitely present. The longer the duration, the more completely the full magnitude of the component comes through, Now assume we have a stock in which a dominant component has been identified with an average duration of 20 weeks. A moving average with a span of one-half of this, or ten weeks, is constructed. The lag of this average is one-half of its span or five weeks. Thus, when this average "tops out" and turns down, the 2(>-week trading cycle has signalled a turnover at this pomt, but the price of the stock itself has been going down for five weeks already! Remembering that it is the 20-week component that caused both the ten-week average and the stock price to top out, it is seen that the total downward move due to this component is just one-half complete at this time. All of this occurs because the ten-week average wiU kill all price fluctuations of exactly ten weeks in duration and drastically reduce all shorter ones. Since the 20-week motion will come through at nearly full strength, the ten-week average will only change direction when the 2D-week cycle causes it to do so. Then the five-week lag is precisely the time required for the 20-week cycle to drive prices half as far as the 20-week cycle is going to cany them. Similariy, when the ten-week moving average bottoms out, the stock has already been rising for five weeks-and is half as far up as the 20-week cycle is going to drive it. This quality of a half-span movmg average can only work, of courae, if the price-motion model is a correct representation of stock price fluctuations. That it does work-time after time-is very powerful evidence indeed for the validity of the model. Lets list in order what must be done to make use of this timing aid: • Use a quick and rou envelope analysis to estabhsh the average duration of a dominant cyclic component on which you wish to trade. • Construct a movmg average of the closii prices of the stock which has a span equal to half the average duration of the trading cycle. If this comes out to be a fraction, round it off to the nearest whole number. • Plot the moving average on the same chart used for the stock, taking care to lag the average one-half its span behind the stock data. • When the average reverses its direction to the downside note the price of the stock and
how much it has already moved down. You may expect the downtrend to continue until the stock has; moved down this much more. • Reverse this process for moving average reversak to Uie upside to estabUsh how much further up the stock will go. The accuracy of this process can be further improved by the use of two moving averages. Proceed as before but compute and plot not only the half-span average, but the moving average whose span is equal to the average duration of the trading cycle as welL For the example used above, the trading cycle duration is 20 weeks. The half-span moving average is a ten-week one. The full-span moving average is a 20-week one. Now lets see why this is of aid. The half-span average tops out when the stock price has dropped 50% of the 20-week fluctuation amount. This means that the stock price is right in the middle of the channel enclosing the 20-week cycle at this particular time. On the other hand, the 20-week moving average is always in the middle of the 20-week channel (theoretically). Remember, tlw 20-week average reduces the 20-week cycle to zero. Thus the 20-week average represents the sum of all components of duration longer than 20 weeks, which is exactly the import of the center line of the 20-week channel! The 20-week average also drastically reduces the size of all shorter duration components, allowing only small percentages of these to "leak" through-and these are easily recognizable and graphically smoothed. Now when your ten-week average tops out, you can extrapolate both the ten- and 20-week averages through theur lag periods up to current time. This is quite simply accomplished for the 20-week average especially, since it is so "smooth." Note the price level at which the stock, the ten-week moving average extrapolation, and the 20-week moving average extrapolation meet. Subtract this from the previous peak of the current move down. This is your estimate of how much further down the stock will go. A tolerance of ±10% should be allowed for the total move estimate. As with all of the techniques discussed in this book, you should never rely on this estimate alone. But combined with the others, this method provides powerful confirmation of the validity of action signals. Lets see how it works by example. Figure VI-1 is a partial replot of the data on Alloys Unlunited used as an example in Chapter One. This stock displays a dominant component in this time period that ranges from 17 to 22 weeks in duration. For the sake of computational shnplicity we will assign it (as our trading cycle) an average duration of 20 weeks. We need therefore a ten-week (half-span) and a 20-week (full-span) moving average. The plot is presented just as a decision point is reached-the ten-week moving average has just bottomed out. We note and smooth a renmant of a 12-week component from the 20-week moving average. The result is shown in the plot as a dashed hne. We extrapolate both the ten- and 20-week averages to current time. These meet the stock price at 41. The stock has already moved up from 32, a total of 9 points. We exi>ect it to continue another 9 pomts from 41-to 50. The total move predicted is 18 points. The tolerance is ±10% of this amount, or approximately 2 points. We therefore predict that this 20-week cycle will carry prices to between 48 and 52! If we had purchased the stock on this type of criteria, coupled with any or all of the forms of graphical analysis we now know about, the resultant conclusion is that we should hold the
49 48 47 46 45 FIGURE -1 42 41 40 30 38 37 36 SMOOTHED. FULL-SPAN AVERAGE / -J EXTRAPOLATED INTERSECTION- FULL-SRiW . Using The Half-Span Average To Predict
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