Example 1 A Continuous Three Term Proportion - Voila! Maybe the Markets are Perfect After All The number of days from the 1962 bottom to the 1974 bottom is 3093. The number of days from the 1974 bottom to the 1982 bottom is 1984. The number of days from the 1982 bottom to the 1987 peak is ? 1984 = 0.64145 0.64145 x 1984 = 1273 3093 A is to B as B is to C 1273 is to 1984 as 1984 is to 3093 ( 1984 ) ² = 1273 3093 We have just taken up a lot of space to show the same relationships in several different ways. About ninety percent of you were probably bored silly and wondering why we would waste so much time and space on such an elementary proposition. Well, the reason is just as simple as the principle we just belabored: The market itself can be simple. If you get comfortable with just one thing, simple continuous proportions, you will astound yourself as to the amount of knowledge you can mine from the markets, and in the process you should be able to mine some gold. Figure 1 illustrates the above relationships on a graph covering the time period from the 1962 bottom to the 1987 peak. It illustrates that the two "time distances" between the three major bottoms, 1962-74-82, bear the same relationship to each other as the time distance between the last bottom, 1982, and the 1987 peak bear to each other to the day, covering a period of 25 years & 6350 trading days!
Example 2 Important Familial Relationships The turning points that are involved in Example 1 have "proven" that they are part of the underlying architecture of the market, because they have demonstrated the importance of their relationship to each other. Therefore, we can expect them to "strike" again: The total number of days from the 1962 bottom to the 1982 bottom is 5077 The total number of days from the 1962 bottom to the 1987 peak is 6350: 5077 = 0.7995 6350
0.7995 x 5077 = 4059
5077² = 4059 6350
This is another three term continuous proportion This time we only showed the same thing in a few different ways ...soon we'll just show it one way. Chart Example 2 illustrates that 4059 days forward from the 1982 bottom is the DJIA bottom of 09/01/98! Now we are covering a time span of over thirty six years! When will it end? Never!
Figure 2
Example 3 Chart Figure 3 is merely a composite of the first two examples. It is provided to offer a better perspective on understanding how this "family" of turning points works together.
Figure 3
Example 4 Decoding Distortions On The Plane
In the picture above, a cylindrical mirror, placed in the center of an oil painting, "decodes" the distortions in the seemingly random smears of paint, so that these smears are shown to be an easily understood and rational picture; the clearly defined subject matter easily identified. The type of transformation created with the cylindrical mirror alters distance, and therefore is not isometric, as are reflections, rotations, and translations, all of which preserve distance. Anamorphosis: Distorted projection or representation of an image on a plane, or curved surface, which, when viewed from a certain point in a certain manner, as by reflection from a curved mirror, appears regular and in proportion. Anamorphoscope: An instrument for restoring an image, or picture, distorted by anamorphosis, to its normal proportions. It usually consists of a cylindrical mirror. An excellent illustration of anamorphosis is the comparison of the relative positions and distance between two points on a flat map of the earth, and those that would appear, for the same points, on a sphere, such as the more accurate portrayal of the earth provided by a globe. Another example: Try to recall how your face appeared in a fun house mirror. Try to recall the mirror that made your nose look as though it jutted out six
inches from your face, and your eyes became tiny dots, pulled in so close to the sides of your nose that they almost merged. Your ears were flattened to the sides of your head and barely visible. Basically, the "front to back" vector of your head had been enlarged, and the "side to side" vector had been diminished. You definitely appeared out of proportion, and distorted. If the reverse had happened to your head, your ears would have been two feet apart, and your nose flattened against the front of your face. You could accomplish the same alterations by stretching a rubber Halloween mask, the type that fits over your head like a hood. By stretching it one way, and then the other you could almost reproduce what the fun house mirror had done to your face. If you took a picture of the Halloween mask, or your distorted image in the mirror, you would have a difficult time recognizing that the picture represented a human face. If you then viewed the picture’s reflection in a slightly concave/convex mirror, you would probably recognize the original face, or mask. If you consider that "time" might be 3-dimensional, relative to market movements, then it is understandable why its depiction upon a standard chart, a plane, might not be a true portrayal of the proportional/spatial relationships between various points in time, i.e. the nose, the ears, the eyes. If the cylindrical mirror shown "decoding" the oil painting in the illustration at the beginning of this section were replaced with a circle, then each point on the plane (oil painting) could be described by locating its image relative to the circle. This transformation is termed an "inversion". This basic book on Ermanometry will not probe deeply into the restoration of three dimensional forms from their image on the plane. However, inversions themselves will be used extensively to demonstrate proportional relationships. The reader may note a conceptual relationship between this concept and the ability of the same market move to exist simultaneously in different shapes. These chameleon moves (relative to shape, not color), are primarily illustrated in the MacArthur Syndrome.
Example 5 Spherical Markets - Three Dimensional Example
Please recall that the article in the February issue of Stocks & Commodities used three market moves between 1974 and 1978. Therefore, assuming that the viewer is already familiar with these moves, they will be used to illustrate 3-D characteristics of the markets. Consider that the 859 day line segment connecting the 74-78 lows is hinged at the 76 peak, breaking 859 into two
moves: 497 (up) and 362 (down). Consider that the change in major trend, from up to down, could be compared to a "break" in time, and that "time" changed "direction" ninety degrees. The diagrams in this example illustrate 2 perpendicular planes of a 3-D triangle.
Consider that one leg of the right triangle is 859 days and the other, is 497. The "down" move of 362 days meets the 497 day move at a right angle and creates a new plane. The hypotenuse of triangle ADC, on this plane, equals 1056 days. 1056 is the exact number of days from the "break" point at the 1976 high, to the 1980 S&P peak. The value '1056 days' is also generated by many other geometric figures using the values of line segments connecting major turning points between 1974 and 1978: Please refer to the MacArthur Syndrome – Example 6 and note the hypotenuse of a right triangle with legs of 497 & 362 is 614.86: The hypotenuse of a triangle, with legs of 859 and 614.86 is, you guessed it! 1056 Now, figure out why this is so.
Example 6 "MacArthur Syndrome" - Market Moves Reincarnate Figures 14 & 18 in the Log Spiral article in the February issue of Stocks & Commodities illustrated the "reincarnation" of the 1102 & 1147 day market moves on segments of the log spiral. On this site, the figures are 13 & 17. Reincarnation of market moves is a very powerful tool in both projection and confirmation of important market moves. At Ermanometry research we refer to this very common phenomenon, as the "The MacArthur Syndrome." General MacArthur is famous for his statement, upon leaving the Philippine Islands, "I Shall Return." He is also famous for another statement, "Old Soldiers Never Die, They Just Fade Away. " Market moves always return, never die, and although they may to "fade away" for a while, they are merely not visible on the plane. Think of an underground river that rises to the surface occasionally. Or, child playing hide and seek, "now you see me, now you don’t." Ermanometry uses various methods to decode the hiding places of these playful market moves and bring them into the sunlight. They can run, but they can’t hide!
MacArthur SYNDROME CHART EXAMPLE Please note that once again we are using the same ’74 -‘78 moves to illustrate a principle. Are you beginning to get the feeling that these moves might contain some sort of market DNA? Maybe these moves are a fractal. Perhaps,but we never use the word fractal. Marketing wizards with no respect for the amazing beauty of true fractals, and the genius of Benoit Mandelbrot, have thrown the word around indiscriminately, applying it to everything and anything with which they could stretch a connection. It has become a buzzword. We have not seen a single instance of the proper application of this proposition! If we may twist a familiar expression: Marketing swine are casting pseudo pearls before eager, unsuspecting seekers of trading truth. Any day now we expect to receive solicitations from "FRACTAL DEPOT-BUY ONE GET ONE FREE!" for "new and improved fractals", "industrial strength fractals", ad nauseum! We apologize for digressing, but we do feel very strongly about get rich schemes and buzzwords " Back to the future" (because the 1473 day move in this example will return again ) and on to the chart explanation:
Using constant dollar data, the S&P made a major high in 1968 (the constant dollar peak from the 1932 low) and declined to 1982. The number of days from the 1968 peak to the NOMINAL PRICE LOW in 1974 is 1473. Beginning at the 1974 low, the market moved up for 497 days to the 1976 peak, and down for 362 days to the 1978 low. Using 497 and 362 as legs of a right triangle, generates a hypotenuse of 614. The sum of the 3 sides, the perimeter, equals 1473. As one works with various market moves they become like old friends with distinct personalities. This fellow walked the straight and narrow from 1968 down to 1974, but the bottoming out process warped him a bit and he got mixed up with "bad company". As punishment he was reincarnated as a triangle! Even market moves have karma!
Example 7 Combination of "MacArthur Syndrome" - Market Moves Reincarnate and Spherical Markets - Three Dimensional Example
Example 8 The ’74 -'76 -’82 moves, from a different perspective, generate the major low on April 4, 1994.
Please remember that Figure 15, page 27, in the Log Spiral article, Stocks & Commodities, illustrated how the 497 day move (’74 up to ’76) and the 859 day move (‘74 low to ’78 low) generated a continuous 3 term proportion, the third term being the 1484 day move down from the ’76 top to the ’82 low. Now we will use 497 and 1484 as the first 2 terms of another 3 term continuous proportion, which is the same as merely squaring the ratio between 859 and 497. The concept of spherical market time is noted throughout the explanations of Ermanometry’s methodologies. Spheres imply circular or eliptical parameters. We’ll start out with "circles", but first another little review of your very basic high school geometry..you do remember it don’t you? The theorem of Thales tells us that any angle inscribed in a semicircle must be a right angle. Similar right triangles are a very simple and
efficient tool for graphically portraying continuous proportions. Remember, the rectangular spiral consisted of a series of similar right triangles. Now we are going to assume that the 497 and 1484 day moves are represented as axes segments from the rectangular spiral, meeting at point X, and generate the next term in a continuous 3 term proportion, and since 497 is to 1484 as 1484 is to 4431, the third term is 4431. See below:
Next we’ll draw the lines AB and BC, and we have the large right triangle ABC, with 2 similar right triangles inside, ABX and BXC. See below:
Let’s consider A&B&C points on the circumference of a circle. See below:
Line segment AC is obviously the diameter of the circle. The diameter is the sum of AX and XC, 497 plus 4431, for a total of 4928. On the chart accompanying this example text please note that the exact number of days from the ’74 low (starting point for the 497 day move) to the major low of 04/04/94 is 4928 days.
Example 9 Generating the 1990 Gulf War Low, from the 1974– 1976 move Figure 9
Please recall the discussion of Compound Pivots in the log spiral article, Stocks & Commodities, February ,1999, and that in 1982 the two end pivots were 08/09 and 08/12. The decline from the 1976 top to the 08/12/82 low is 1487 days, 3 more than the 1484 days used in the previous example. One of the rules of Compound Pivots: Each pivot must be used for projections. The principle illustrated in this example, using the perimeter value of a right triangle, is also shown in Figure 23, (figure 22 on this site) page 34, of the log spiral article, Stocks & Commodities, February , 1999.
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The Quest for Accurate Data: Why it is Important "Data geeks" is a term often applied to our personnel here at Ermanometry Research. We've even been called data freaks. Sometimes the language gets still more colorful, and we love it! From our perspective, the strongest language is the greatest compliment, provided that it refers only to our obsession with accurate data. We consider it confirmation that we are doing our job. Our research requires us to be compulsive about accurate data. One of the foundations of our work is that market movements are not random. This applies to all freely traded markets, cash and futures, from grains and metals to financials and equities. Our thesis that all markets conform to specific dynamic patterns, both in price and time, was not a preconception for which we sought evidence. This thesis was developed from overwhelming evidence uncovered through painstaking data analysis. The book, Ermanometry-The Perfectly Patterned Stock Market, contains hundreds of pages with this evidence and the methods used to decode market moves. Ermanometry measures moves of more than 60 years using increments no larger than a single trading day. We do not count in weeks, months or years. The permissible error factor on these massive moves is less than one/thousandth of one percent. Accurate data is imperative in this analytical environment. For example, Ermanometry Research has projections for more than 16 time periods of major support or resistance for the DJIA and S&P 500 during 1999. Among the most significant are those centered on April 12 and September 1. If the indices exceed the highs of January 8, 1999, we expect them the be making historic highs about April 12. These projections result from the application of proprietary algorithms to the number of trading days between previous major turning points. We consider turning points to be those days on which the market reaches new intraday high or low extremes and then reverses. Closing prices are considered. Some of our algorithms require multipliers as large as four. Assume that a projection was based upon applying a multiplier of four to a move counted as 100 days. Assume that the true turning point actually occurred on day 99, but faulty data caused us to believe the turn occurred on day 100. Multiplying the incorrect total of 100 days by four, and then adding the resulting 400 days (accurate data would have given a total of 396) to day 100 of the previous move, would actually create an error of five days. A four-day error resulted from the multiplication, and adding the result to day 100 instead of day 99 of the previous move increases the error factor to five days. Obviously, this is unacceptable. Thus a data error of only one day could cause our high probability projection of a major trend change in the indices to be shifted from the time period centered on April 12 to one a whole week later, centered on April 19. The extent to which Ermanometry Research requires accurate data may not apply to the average trader/analyst. We believe in the KISS principle (keep it simple, stupid) and a trader should never get so involved in "details" that the big picture is obscured. A favorite expression of ours is... some people are so fervent over details they get caught in their own underwear. Nevertheless, Ermanometry has found many errors in the official records of major exchanges, regarding both the actual count of trading days and daily high/low prices, and all market participants should be aware of the potential for errors and the results of using bad data. A few bad ticks may not have much effect on moving averages and oscillators, but errors have a cumulative impact. Trendlines can be terribly skewed if the bad ticks include an important high or low. Figure 1 illustrates an erroneous daily high that still resides in data banks 10 years after it occurred. It contains a "spike" that occurred on October 31, 1988 and shown on the five-minute chart of the S&P 500 Index. If the analyst was using real time data and small increment time charts, the spike would have been obvious, and a correction made. However, on an hourly chart the spike would not necessarily be evident. The error would be almost impossible to detect on a daily bar chart.
Figure 2 CME S&P 500 Index-Nov. 88 Time and Sales-10/31/88 2:21 2:22 2:23 2:24 2:25 2:26
27879 27878 27877 27939 27871 27871
27888 27878 27876 27873 27871 27871
27888 27877 27875 27872 27872 27873
27878 27875 27872
27939
27873
27873
Please note above that the last tick at 2:23 was 279.39, 64/100 away from the previous tick...the first tick at 2:24 repeated this aberration, and then prices returned to "normal". The 279.39 ticks were almost certainly an error. NYFE NYSE Index Spot Time and Sales-10/31/88 2:21 2:22 2:23 2:24 2:25 2:26
15682 15682 15681 15679 15679 15679
15683 15682 15681 15679 15679 15679
15683 15682 15681
15682 15682
15679 15679
15679 15679
This is the time and sales data for the NYSE Composite, the best surrogate for the S&P 500. This index did not reflect a sudden rise and fall at 2:23. This is conclusive proof that the data for the S&P was faulty.
Figure 2 is a "time and sales" listing for the S&P 500 Index and the NYSEC for five minutes on 10/31/88. Figure 3 S&P 500 Index, Monday October 31, 1988 Total call volume 4,942 Total put volume 4,581 The Index: High 279.39
Total call open interest 224,261 Total put open interest 229,841 Low 277.14; Close 278.97, +0.44
Figure 3 shows the statistics printed in all of the financial papers on the next day. Please note that the erroneous tick is shown as the high for the day. This error is "forever" embedded in every historical data bank that Ermanometry has investigated. Vendors of historical data are in a difficult position. They may know of errors but if their data conflicts with the "official" data, the client will most likely assume that the official records are correct and the vendor's data is wrong. Therefore, the vendors will usually retain the faulty data rather than conflict with the official records. A bad tick in an index is usually caused by a bad tick in one of the individual stocks in the index. The NYSE will normally correct the error in the individual stock data. However, the indices are calculated by outside vendors. Therefore, unless the outside vendor picks up the correction message sent by the NYSE for the individual stock and then recalculates the index and sends out a correction message to be inserted at the proper time, the index will remain uncorrected. It is a mistake to assume that these corrections will be made. There is one recent development that may alleviate the problem of bad ticks in the DJIA. Dow Jones & Company, Inc. has recently canceled old licenses which allowed a multitude of outside data vendors to compute and distribute the various Dow Jones & Company, Inc. averages. Dow Jones & Company, Inc. will compute the averages and the Chicago Board of Trade will be the exclusive gateway for redistribution of the calculations to other vendors. At this time we do not know if the averages will be recomputed when bad ticks in individual stocks are corrected and the corrections in the averages then distributed. Even if these corrections in the averages are made, there is still the problem of inserting the corrections into individual data bases. The type of error represented in figure 1 is particularly insidious because if the analyst corrected the spike on an intraday chart he may have assumed that the bad tick had been permanently eliminated. Unfortunately, since the bad tick represented the high for the day, those data feeds that recap the daily high/low, often received from other vendors, would show the bad tick as a high. Thus the error would show on the daily chart even though the analyst had eliminated it on the intraday charts. Some errors are innocuous but Murphy's law appears to have undue influence upon when the most errors occur. A disproportionate share of errors occurs at the end of explosive or panicky moves. These are the most chaotic moments and the environment in which errors thrive. The "end" of such moves often contains the extremes for the period and price action analyzed. Therefore, the analyst must consider all extremes suspect until verified. Remember, errors at extremes affect not only timing, but trendlines, oscillators, and almost every tool in the analyst's arsenal. It is impossible to truly appreciate the large number of price corrections, insertions, deletions, etc. without having had the experience of watching the data stream printed out on the yellow paper tape from an old Western Union type ticker. Corrections will appear almost every few inches. Sometimes the entries are as simple as changing a bid or ask quote to an actual trade,
or vice versa, and other times entire strings of trades are deleted. Very often these deleted trades actually took place, but they are "busted" (deleted) because the trades shouldn't have been executed. Busted trades are most frequent in the futures pits. When trading is frenzied it is possible that a pit broker might not hear or see every bid/ask in the pit and the market will trade "through" a price that a broker is legitimately, diligently bidding or offering. Assume that the market is trending down from 105 in very active trading. Conditions may or may not warrant a "fast market" designation which would invoke a different set of parameters governing pit rules. Fast market conditions will not be covered in this article because it would be an unnecessary complication: Broker A is diligently bidding for 10 contracts at 101. Across the pit, Broker B bids 100 for two contracts. Broker C, standing next to Broker B, receives an order to sell four contracts "at the market." Broker C sells 2 contracts to Broker B at 100. Broker B then drops his bid to 99, and Broker C sells him two more at 99. News hits the market, there are no more offers, and bids rise to 103. The next trade is 104. Broker A never got a chance to buy any contracts at 101. Conditions were such that Broker C neither saw nor heard Broker A's bid at 101. It was an honest error. Broker A's client, seeing the prints at 100 and 99 rightfully assumed that his order to buy at 101 had been filled. The pit committee would most likely bust the trades at 100 and 99, and a deletion message would be sent. Broker C's sales at 100 and 99, would be given to Broker A who had been bidding 101. Thus the selling client would get a better price, and Broker A's buyer would have been filled on four of the 10 contracts he wanted to buy. Murphy's law not only makes sure that the most errors occur at the end of runs, but also that deletions or insertions will hover around the "even" prices, such as 100 or 150. This means that the point and figure chartist may have filled a box that should not be filled, or not filled one that should have been filled. Erroneous data can cause charts to read like comic strips, and cause oscillators and moving averages to generate false buy or sell signals, particularly in shortterm trading. The analyst can take measures to protect the integrity of his data. The obvious answer is to be constantly vigilant. The best measures are to understand the differences between various data feeds and charting software. If short-term in and out trading is done, it is helpful for the analyst/trader to have a data source that automatically transmits all error messages and deletes, inserts, and corrects the data used. There are many real-time data feeds available. Unfortunately they are not all equal in their performance concerning corrections, and speed. Another important factor is whether or not the analyst/trader can access the vendor's data base with his own computer, i.e. two way communication, or is merely a passive recipient of the data. As a passive recipient it is necessary for the analyst/trader to manually make any corrections that he may find. The kind that he would know of would probably be limited to daily high/low prices or obvious spikes. Manual corrections are time consuming and aggravating, and the trader/analyst would still be unaware of the vast majority of corrections. There are some data vendors that make corrections in the client's data even though the data is stored on the client's computer. However, the type of corrections made are usually not as comprehensive as those available to the client who has constant direct communication with the data base of a vendor that corrects every erroneous print.
The intent of this article is to make you, the reader, aware of data aberrations but not to make you paranoid about them. Bad ticks are not going to "make or break" your trading. Trading discipline and money management are more important, and they should not be neglected while you get distracted or "caught in your own underwear" in the attempt to clean up every single tick.
William T. Erman is the founder and president of Ermanometry Research, an organization devoted to advising institutional investors, hedge funds and commodity pool operators. He graduated from Harvard University in 1951, and has spent the last thirty years researching the markets. He is the author of ERMANOMETRY-The Perfectly Patterned Stock Market which details the proprietary analytic and strategic methods developed over a quarter century of study. This book offers the first opportunity for individual traders to profit from this work. Mr. Erman can be reached at ERMANOMETRY RESEARCH, P.O. Box 50785, Nashville, TN 37205. (615) 383-0210. You can visit his Web site at http://ww.ermanometry.com or e-mail
[email protected]
