www.robertwcolby.com
Technical Market Indicators

Dow Theory

The following is an excerpt from my 820-page research book,
Colby, Robert W.,
The Encyclopedia of Technical Market Indicators, Second Edition,
McGraw-Hill Publishing, 2003 (click here for a description).


The Dow Theory is a major corner stone of technical analysis. It is one of the oldest and best known methods used to determine the major trend of stock
prices. It was derived from the writings of Charles H. Dow from 1900 to 1902 published in the daily newspaper he founded, The Wall Street Journal. Dow's Theory was further refined by analysts and writers S. A. Nelson, William P. Hamilton, and Robert Rhea in the first few decades of the 20th century.

Seven Basic Principles of Dow's Theory

1.
Everything is discounted by the price Averages, specifically, the Dow-Jones Industrial Average and the Dow-Jones Transportation Average. Since the Averages reflect all information, experience, knowledge, opinions, and activities of all stock market investors, everything that could possibly affect the demand for or supply of stocks is discounted by the Averages.

2.
There are three trends in stock prices. 1) The Primary Tide is the major long-term trend. But no trend moves in a straight line for long, and 2) Secondary Reactions are the intermediate-term corrections that interrupt  and move in an opposite direction against the Primary Tide. 3) Ripples are the very minor day-to-day fluctuations that are of concern only to short-term traders and not at all to Dow Theorists.

3. Primary Tides going up, also known as
Bull Markets, typically unfold in three up moves in stock prices. The first move up is the result of far-sighted investors accumulating stocks at a time when business is slow but anticipated to improve. The second move up is a result of investors buying stocks in reaction to improved  fundamental business conditions and increasing corporate earnings. The third and final up move occurs when the general public finally notices that all the financial news is good. During the final up move, speculation runs rampant.

4. Primary Tides going down, also known as
Bear Markets, typically unfold in three down moves in stock prices. The first move down occurs when far-sighted investors sell based on their experienced judgment that high valuations and booming corporate earnings are unsustainable. The second move down reflects panic as a now fearful public dumps at any price the same stock they just recently bought at much higher prices. The final move down results from distress selling and the need to raise cash.

5.
The two averages must confirm each other. To signal a Primary Tide Bull Market major trend, both averages must rise above their respective highs of previous upward Secondary Reactions. To signal a Primary Tide Bear Market major trend, both the Dow-Jones Industrial Average and the Dow-Jones Transportation Average must drop below their respective lows of previous Secondary Reactions. A move to a new high or low by just one average alone is not meaningful. Also, it is not uncommon for one average to signal a change in trend before the other. The Dow Theory does not stipulate any time limit on trend confirmation by both averages.

6.
Only end-of-day, closing prices on the averages are considered. Price movements during the day are ignored.

7. The Primary Tide remains in effect until a Dow Theory reversal has been signaled by
both averages.

Further Helpful Elaboration on the Dow Theory  

The whole point of this time-honored theory is the identification of major movements of the stock market. Such major moves take quite some time to unfold, and prices change by a considerable amount. Although not specified by the Dow Theory, the Primary Tide usually lasts a year to several years. Bull Markets typically run toward the longer length, while Bear Markets are shorter in duration but more violent in the velocity of downward price movement.  

Victor Sperandeo has quantified Dow Theory definitions. (See Sperandeo, Victor,
Trader Vic--Methods of a Wall Street Master, John Wiley & Sons, New York, 1991.) He found that 75% of Primary Tide Bear Markets declined from 20.4% to 47.1% in price. Also, 75% of Bear Markets lasted between 0.8 and 2.8 years. Bull Markets lasted much longer: 67% lasted between 1.8 and 4.1 years.  

The Secondary Wave is a reaction or correction in the opposite direction to the Primary Tide. This intermediate-term Secondary Wave typically lasts from three to 13 weeks. It typically retraces one-third, one-half, or two-thirds of the preceding Primary Tide swing. Sperandeo found that 65% last from three weeks to three months, and 98% last from two weeks to eight months. Further, Sperandeo found that 61% retrace between 30% and 70% of the previous Primary Swing in price.  

The Minor Ripple typically lasts only one day to three weeks. It is ignored as insignificant noise by the Dow Theory. Sperandeo found that 98.7% last less than two weeks. 

A
Line is a narrow sideways price range, extending ten calendar days or longer, the longer in time the more significant. The usual guideline to define a narrow range is approximately 5%, although William Hamilton classified a price range in excess of 11% from February to June 1929 as a Line. The Averages usually break out of a Line in the same direction as the Primary Tide. These breakouts are quite reliable. Although a Line can mark a reversal to a new direction opposite to the established Primary Tide, such reversal signals are much less reliable. 

No matter how large a move in just one Average, it would not be sufficient to indicate a change in the Primary Tide unless the other Average confirmed. Non-confirmations (divergences where one Average exceeds a preceding Secondary Wave reaction price extreme on a closing price basis but the other Average fails to confirm) function only as warnings to be alert for the possibility of an actual signal ahead.  


It is not necessary that both Averages confirm on the same day or even the same month, though some authorities believe the closer the better and become more wary as the days pass without confirmation. In the absence of joint confirmation by both Averages, there is no signal of major trend change--in fact, there is non-confirmation. 

As a final important detail, the most minimal unit of price measure for the Averages (down to a penny, that is, 0.01, with no rounding off) strictly counts, when comparing the current closing price of each Average to its previous
Secondary Wave extreme close. 

There are six phases of the full bull through bear cycle:
Skepticism, Growing Recognition, Enthusiasm, Disbelief, Shock and Fear, and Disgust. 

1.
Skepticism. In a major Bull Market, the first phase is accumulation of stocks at bargain prices by the "smart money" (the most knowledgeable and experienced investors). Meanwhile, the mass mood toward the stock market ranges from disgust to general skepticism. Stocks are depressed, and may have been for  a long time. Still, some investors know that the cycle always turns up, even while fundamental business conditions still appear grim. The smart money begins to bid for out-of-favor stocks, which are selling at temptingly low bargain prices. Transactional volume, which has been low, starts to improve on rallies reflecting the entrance into the market by these forward-looking, patient investors. 

2. Growing Recognition. The second Bull phase is known as the mark-up phase. Stock prices rise on increasing transactional volume. There is growing recognition that fundamental business conditions will improve. Stocks move up big. It is a very rewarding time to be in the market.  

3.
Enthusiasm. The third Bull phase is marked by popular enthusiasm and speculation. Sentiment indicators are near record levels. Fundamentals now appear extremely positive. There even may be widespread talk of a "new era" of rapid economic growth and never-ending prosperity. Stories of speculators making millions in the market flood the media. Everybody is optimistic and is buying, so transactional volume is extremely heavy. Late in this third phase, however, volume starts to diminish on rallies, as greedy buyers shoot their wads and become fully invested, usually on margin. Also, the smart money has reminded itself that "no tree grows to the sky" and all good things must eventually come to an end. Consequently, those knowledgeable investors, who bought early at wholesale prices, stop buying. Moreover, they begin the distribution phase, parceling out their stocks a retail prices. Smart selling intensifies as the greedy but unsophisticated mob snaps up overvalued stocks at absurdly high prices. Late in this game, tell-tale bearish technical cracks start to appear under the "obviously" bullish surface. Technical divergences  in stocks and groups are caused by irrational buying of the wrong stocks by unsophisticated players while the smart money liquidates the best stocks. Stocks may begin to churn and make little net progress. 

4. Disbelief. The first Bear Market phase is marked by clear and widespread technical deterioration, even while almost everybody is still feeling extremely bullish. But when everyone who ever is going to buy has already bought, there is only one direction for prices to go--down. When buying power is used up, there is insufficient demand to absorb the accelerating distribution of stocks by the smart money at current prices, so prices have to move lower. An ever increasing number of stocks already have stalled out and formed potentially bearish chart patterns. But even as stocks break critical chart support levels, this clear bearish technical evidence is widely ignored by the uninformed masses. After all, fundamental business conditions are still rosy, and "buy the dips" is still the advice of the brokers and the dealers and their paid spokesmen in the media. The public hopes and believes that the "conventional wisdom" of all the highly-compensated Wall Street analysts, strategists and economists is right. Besides, the public has been told that they bought for the long term, and over the long term stock prices always go up. So, stock price declines are met with general disbelief. The public would buy more, if only they were not already fully margined. But they are. So they can't.  

5.
Shock and Fear. The second Bear phase is marked by a sudden mood change, from optimism and hope to shock and fear. One day, the public wakes up and sees, much to its surprise, that "the emperor has no clothes". Actual fundamental business conditions are not panning out to be as positive as previously hoped. In fact, there may be a little problem. The smart money is long gone, and there is no one left to buy when the public wants out. Stock prices drop steeply in a vacuum. Fear quickly replaces greed. Repeated waves of panic may sweep the market. Transactional volume swells as the unsophisticated investor screams, "Get me out at any price!" Sharp professional traders are willing to bid way down in price for stocks when prices drop too far too fast. The best that can be expected, however, is a dead-cat bounce that recovers only a fraction of the steep loss.  

6.
Disgust. The third Bear phase is marked by discouraged selling and, finally, total disgust toward stocks. Fundamentals clearly have deteriorated and the outlook is bleak. Prices move lower and lower as discouraged sellers liquidate holdings at distress prices. Even the best stocks, which initially resisted the downtrend, succumb to the persistence of the Bear. In the late stages of the disgust phase, downward price movement continues but the negative rate of change eventually begins to slow. Transactional volume, which was high in the panic phase, starts to diminish on price declines as liquidation runs its course.

Eventually, after everyone who is capable of selling has sold already, the Bear Market is exhausted. The discouraged public lament is, "never again." After stocks are totally sold out, the stage is then set for the cycle to begin again. When everyone who ever is going to sell has already sold, there is only one direction for prices to go--up.     

These phases are no secret. They have been written about by Dow and his successors for more than a century. These phases repeat endlessly, over and over again. Still, the public never learns. It is all too easy, it is merely human nature, to get caught up in the mass mood of the moment, lose all perspective and run with the emotions of the crowd. If you do not learn how to recognize the technical indications, and if you are not disciplined, the easiest thing in the world to do is to allow yourself to be pulled along by the mass mood, the "group think". But that is the way to be wrong at the critical turning points, to buy at tops and sell at bottoms, and to consistently underperform the market. To make money and outperform the market, we need to do the opposite. The Dow Theory tells us how.   

Indicator Strategy Example for the Dow Theory

The venerable Dow Theory after more than a century has stood the test of time. Our tests of the Dow Theory against the actual historical data covering the past 112 years from 1899 to 2011 confirms the importance of this major contribution to technical analysis. We attempted to minimize subjectivity and judgement, and we added no other forms of analysis. We checked and rechecked our signals against available published sources. Based on trend confirming closing prices only for  the Dow-Jones Industrial Average and the Dow-Jones Transportation Average, using only the Seven Basic Principles of Dow's Theory exactly as enumerated above, we found very positive results for both long and short signals.  

At Arthur A. Merrill's suggestion (on page 84 of his
Behavior of Prices on Wall Street, Second Edition, The Analysis Press, Chappaqua, NY, 1984, 147 pages), we multiplied by 0.7339 all closing prices for the old 12-stock Dow-Jones Industrial Average series prior to December 12, 1914, in order to make it comparable with the new 20-stock Industrial Average introduced at that time. (Previous compilers of Dow Theory signals failed to make this adjustment, throwing off their tabulations of hypothetical profits.)  

Starting with $100 and reinvesting profits over 110 years from 1899 to 2009, total net profits, long and short, for this Dow Theory strategy would have been 2,401,697.59, assuming a fully-invested strategy, reinvestment of profits, and zero transactions costs, fees, dividends, and taxes. Of the closed trade signals, 78% (51 of 65) would have produced profitable trades and 22% (14 of 65) would have produced losses. Trading was inactive with only one trade every 20 months on average. Even short selling, which is included in this strategy, would have been profitable.

Dow Theory Signals: 68 Signals in 112 Years             
# : Signal : Date : INDU : % P&L : Equity
0 : Short : 12/11/1899 : 67.43 : 0.00% : 100.00
1 : Long : 10/20/1900 : 59.54 : 11.70% : 111.70
2 : Short : 11/8/1902 : 62.90 : 5.64% : 118.00
3 : Long : 7/12/1904 : 51.37 : 18.33% : 139.64
4 : Short : 4/26/1906 : 92.44 : 79.95% : 251.27
5 : Long : 4/24/1908 : 70.01 : 24.26% : 312.24
6 : Short : 5/3/1910 : 84.72 : 21.01% : 377.85
7 : Long : 10/10/1910 : 81.91 : 3.32% : 390.38
8 : Short : 1/14/1913 : 84.96 : 3.72% : 404.92
9 : Long : 4/9/1915 : 65.02 : 23.47% : 499.95
10 : Short : 8/28/1917 : 86.12 : 32.45% : 662.19
11 : Long : 5/13/1918 : 82.16 : 4.60% : 692.64
12 : Short : 2/3/1920 : 99.96 : 21.67% : 842.71
13 : Long : 2/6/1922 : 83.70 : 16.27% : 979.78
14 : Short : 6/20/1923 : 90.81 : 8.49% : 1,063.01
15 : Long : 12/7/1923 : 93.80 : -3.29% : 1,028.01
16 : Short : 10/23/1929 : 305.85 : 226.07% : 3,352.00
17 : Long : 5/24/1933 : 84.29 : 72.44% : 5,780.22
18 : Short : 9/7/1937 : 164.39 : 95.03% : 11,273.10
19 : Long : 6/23/1938 : 127.40 : 22.50% : 13,809.71
20 : Short : 3/31/1939 : 131.84 : 3.49% : 14,290.99
21 : Long : 7/17/1939 : 142.58 : -8.15% : 13,126.81
22 : Short : 5/13/1940 : 137.63 : -3.47% : 12,671.08
23 : Long : 2/1/1943 : 125.86 : 8.55% : 13,754.70
24 : Short : 8/27/1946 : 191.04 : 51.79% : 20,877.94
25 : Long : 5/14/1948 : 188.60 : 1.28% : 21,144.60
26 : Short : 11/9/1948 : 173.94 : -7.77% : 19,501.02
27 : Long : 10/11/1949 : 186.74 : -7.36% : 18,065.97
28 : Short : 4/2/1953 : 280.03 : 49.96% : 27,091.21
29 : Long : 1/19/1954 : 288.27 : -2.94% : 26,294.04
30 : Short : 10/1/1956 : 468.70 : 62.59% : 42,751.64
31 : Long : 4/21/1958 : 450.72 : 3.84% : 44,391.65
32 : Short : 3/3/1960 : 612.05 : 35.79% : 60,281.13
33 : Long : 11/4/1960 : 596.07 : 2.61% : 61,855.01
34 : Short : 4/26/1962 : 678.68 : 13.86% : 70,427.57
35 : Long : 11/9/1962 : 616.13 : 9.22% : 76,918.47
36 : Short : 5/5/1966 : 899.77 : 46.04% : 112,328.45
37 : Long : 1/11/1967 : 822.49 : 8.59% : 121,976.19
38 : Short : 6/12/1969 : 892.58 : 8.52% : 132,370.61
39 : Long : 12/23/1970 : 823.11 : 7.78% : 142,673.09
40 : Short : 4/27/1973 : 922.19 : 12.04% : 159,847.04
41 : Long : 1/27/1975 : 692.66 : 24.89% : 199,632.43
42 : Short : 12/27/1977 : 829.70 : 19.78% : 239,128.91
43 : Long : 8/2/1978 : 863.01 : -4.01% : 229,528.59
44 : Short : 7/2/1981 : 959.19 : 11.14% : 255,108.90
45 : Long : 8/31/1982 : 901.31 : 6.03% : 270,502.83
46 : Short : 2/1/1984 : 1,212.31 : 34.51% : 363,840.72
47 : Long : 8/3/1984 : 1,202.08 : 0.84% : 366,910.97
48 : Short : 10/16/1987 : 2,246.73 : 86.90% : 685,769.57
49 : Long : 2/29/1988 : 2,071.62 : 7.79% : 739,218.41
50 : Short : 1/25/1990 : 2,561.04 : 23.62% : 913,858.67
51 : Long : 6/4/1990 : 2,935.19 : -14.61% : 780,350.32
52 : Short : 8/17/1990 : 2,644.80 : -9.89% : 703,147.17
53 : Long : 1/18/1991 : 2,646.78 : -0.07% : 702,620.76
54 : Short : 8/21/1992 : 3,254.09 : 22.95% : 863,838.78
55 : Long : 2/3/1993 : 3,373.79 : -3.68% : 832,062.92
56 : Short : 3/30/1994 : 3,626.75 : 7.50% : 894,449.33
57 : Long : 2/13/1995 : 3,954.21 : -9.03% : 813,689.32
58 : Short : 7/15/1996 : 5,349.51 : 35.29% : 1,100,811.32
59 : Long : 11/11/1996 : 6,255.60 : -16.94% : 914,357.96
60 : Short : 8/4/1998 : 8,487.31 : 35.68% : 1,240,558.77
61 : Long : 1/6/1999 : 9,544.97 : -12.46% : 1,085,964.51
62 : Short : 9/23/1999 : 10,318.59 : 8.11% : 1,173,981.96
63 : Long : 6/6/2003 : 9,062.79 : 12.17% : 1,316,858.70
64 : Short : 11/21/2007 : 12,799.04 : 41.23% : 1,859,750.38
65 : Long : 7/23/2009 : 9,069.29 : 29.14% : 2,401,697.59
See the current Dow Theory Signal in my weekly Colby Global Markets Report.

Criticisms of Dow's Theory

Despite its impressive record, Dow's Theory has been subjected to its share of criticism. Because it merely identifies and follows major trends, it does not anticipate or forecast turning points, and it is always a bit late after the turning points. But given the difficulties of forecasting, this might actually be an advantage. The most significant criticism is that possible imprecision and subjective judgement in the interpretation of a Secondary Reaction could produce confusion as to the precise timing of Dow Theory signals. More precise specific definitions and trading rules can overcome this criticism.

The strengths of Dow's Theory far outweigh any weaknesses. Dow's Theory has proven itself over the past 112 years to be a useful, sound and profitable investment approach. Dow's Theory has made extremely important contributions to the development technical analysis. Technical students would benefit greatly from a thorough study of the Dow Theory, including the detailed historical performance of its signals. It would be time well invested. 


New Frontiers for Dow's Theory

Considering its absence of evolutionary change, it is all the more remarkable that the Dow Theory has survived the test of time over the past turbulent century of unprecedented events, which included two world wars, a world-wide economic depression, and mind boggling triumphs of science and technology unimaginable in Charles H. Dow's day. Consider too that Dow created from scratch a predictive stock market barometer over a period of just a few years, with only a small quantity of primitive data and with no computer. If Charles H. Dow and his successors, S. A. Nelson, William P. Hamilton, and Robert Rhea, were alive today, they might extend their pioneering work with the help of vastly more data and power to analyze that data than they ever could have imagined. 

Properly governed by sensible discipline to insure valid procedures and logic, the computer can handle complex data far more efficiently than our unaided mental capabilities ever could. It can quickly find patterns in reams of confusing data, patterns that the human eye could never see and the human mind could never grasp. Since it has no emotions, and it does not care if our pet hypothesis is accepted or rejected, the computer does not see signals that are not really there, and it does not ignore signals that are really there. We can not match the computer's ability to be coldly calculating. It can help us to precisely define decision rules, with which we can then actually execute precisely defined actions. We must always remember, however, that because the computer lacks judgement and common sense, we must impose on it reasonable limitations, lest it spew forth more misleading noise than we already have to deal with.  

New Dow Theory Hypotheses for Computer-Assisted Testing

Hypothesis One: We can use objective and precise analysis to identify a signal. Since distinguishing between Primary Tides, Secondary Reactions, and Minor Ripples is the biggest problem human analysts have with Dow's Theory, let us program our computer to define these movements by the criterion of maximization of profits.    

At its most basic level, excluding any qualifications or subtleties, Dow's Theory requires an advance that rises above a previous high for a buy signal and a decline that falls below a previous low for a sell signal, for both averages. This simplest possible definition is similar to what has been called a Price Channel Trading Range Breakout Rule. (This is also known by futures traders as Richard D. Donchian's n-period trading rule and one of Richard Dennis's Turtle trading rules.) It is one of the oldest and simplest trend following models: we buy when the daily closing price moves up to a new n-period high; then we sell long and sell short when the daily closing price moves down to a new n-period low. This is a precisely definable model that leaves no room for doubt or fuzzy thinking. We can work with such a model.  

With a little imaginative database manipulation and much persistence, we were able to analyze the daily closing prices of both the Dow-Jones Industrial and Transportation Averages simultaneously in a single test, rather than just one at a time, like we had to do in the good old days. Specifically, we created an artificial file in Microsoft Excel, where we copied the Transportation Average's closing price (multiplied by 100 to avoid handling decimals) into the field (column) normally reserved for the Industrial Average's daily Volume, then we copied this file into a data file management software program, DownLoader for Windows, by Equis International, Salt Lake City, www.equis.com. With this prepared data and MetaStock® for Windows software, also from Equis,  running on a pentium-class computer, we are able to search up to 32,000 different period lengths applied to the entire century's daily market data (more than 25,000 days) in a single test. Our exact testing program is printed below.    

Indicator Strategy Examples for 
Price Channel Trading Range Breakout Rules Applied to Both Averages


We tested our Price Channel hypothesis twice: first, on the Dow-Jones Industrial Average alone; second, on both Industrials and Transports together, requiring joint confirmation. We found that Charles H. Dow was correct in stating that confirmation by both Averages is more significant and produces a better outcome than a breakout by one Average alone. Testing only one variable period length applied equally to both Industrials and Transports over the past 101 years, for a long-only strategy with no short selling,  hypothetical net profits were highest at a 90-day period length. Profits would have been more than double those of the passive buy-and-hold strategy. But because this strategy did not approach the traditional Dow Theory's results, we keep trying.

The Equis International MetaStock® System Testing rules, where the current Dow-Jones Transportation Average (multiplied by 100 to eliminate the fraction) is inserted into the data field normally reserved for Volume (V), are written as follows:
      
Enter long: C>Ref( HHV(C,opt1),-1) AND V>Ref( HHV(V,opt1),-1) 
Close long: C<Ref( LLV(C,opt1),-1)  AND V>Ref( LLV(V,opt1),-1)
Enter short: C<Ref( LLV(C,opt1),-1)  AND V>Ref( LLV(V,opt1),-1)
Close short: C>Ref( HHV(C,opt1),-1) AND V>Ref( HHV(V,opt1),-1)
  
OPT1 Current value: 90    

Hypothesis Two: Period lengths should be allowed to vary according to the long or short nature of the signal. The statistical tabulations published by Robert Rhea in the 1930's and Victor Sperandeo in 1991 show that Bull Markets and Bear Markets have been much different in extent and duration. Therefore, look-back period lengths for buy and sell signals should not be the same. Furthermore, the requirements for each of the four possible market actions (buy long, sell long, sell short, and cover short) need not necessarily be the same. Therefore, we will allow these parameters to vary.  

Hypothesis Three: Period lengths for each Average should be allowed to vary independently. Since the historical behaviors of the Dow-Jones Industrial and Transportation Averages obviously differ, with the two Averages even trending in opposite directions occasionally, let us allow different parameters for each Average.  

Combining the three hypotheses, we completely cover all trading possibilities. We allow two separate period lengths for each of the four possible market actions (buy long, sell long, sell short, and cover short), one period length applied to the closing prices of the Dow-Jones Industrial Average (INDU) and a separate period length applied to the closing prices of the Dow-Jones Transportation Average (TRAN).    With four possible actions (buy long, sell long, sell short, and cover short) and two price Averages to test, there are eight indicators ( 4 X 2 = 8 ) to test for each model. We can vary the number of specific period length values (more generally known as parameter sets) for each indicator. As Louis B. Mendelsohn (Designing and Testing Trading Systems: How to Avoid Costly Mistakes, Mendelsohn Enterprises, 25941 Apple Blossom Lane, Wesley Chapel, FL 33544, www.profittaker.com) has pointed out, as we allow an arithmetic increase in the number of parameter sets (period lengths), the number of models tested increases geometrically. For example, if we allow three period lengths for our eight indicators, we test three to the eighth power = 3 X 3 X 3 X 3 X 3 X 3 X 3 X 3 = 6561 models. But if we attempt to add just one more period length to our test, we jump up to 4 to the 8th power = 4 X 4 X 4 X 4 X 4 X 4 X 4 X 4 = 65,536 models. Adding just that one extra period length overwhelms our present software resources, which limits us to 32,000 models in a single test. Although our computing power is great compared to the past, it is still limited for testing complex models.   

Fortunately, we are not forced to limit ourselves to very coarse testing with only three broad parameters. As an alternative, we can break our testing into two halves, longs only and shorts only, testing each separately. This cuts the number of indicators in each test in half, from 8 to 4. With only four indicators, we can test thirteen period lengths in one pass, since thirteen to the fourth power = 13 X 13 X 13 X 13 = 28,561 models. After we develop the long and short models separately, we can combine both models into one long and short model. Then we can do some final fine tuning of that combined model, indicator by indicator. Because we break apart our testing into pieces, however, we may well miss the best combination of parameter sets and our findings may be sub-optimal.     

After many iterations, here is what our search uncovered:   

Enter Long (Buy) when INDU rises to a new 9 trading day high and TRAN rises to a new 39 trading day high.  

Close Long (Sell)
when INDU falls to a new 22 trading day low and TRAN falls to a new 166 trading day low. 

Enter Short (Sell Short) when INDU falls to a new 22 trading day low and TRAN falls to a new 166 trading day low. 

Close Short (Cover) when INDU rises to a new 36 trading day high and TRAN rises to a new 32 trading day high.  

The results are enlightening. The asymmetry of these rules means that we do not always have a position. Note that we buy on a very sensitive, short-term price confirmation, only a new nine-day high for the INDU confirmed by a 39-day new high for TRAN. Thus, it is relatively easy to get a buy signal. In contrast, note that it is relatively hard to get sell and sell short signals: we have wait for the INDU to fall to a new 22-day low confirmed by the TRAN falling to a new 166-day low. Thus, this non-thinking model has correctly recognized the long-term bullish bias of a stock market that spends more time going up than down and has bigger rallies than declines.   

Looking at the entire period from the beginning of January 2, 1900 to February 16, 2001, the above decision rules do a consistent job of precisely defining the buy and sell signals. There is absolutely no doubt as to what the signals are and when and at what price level the signals occur. If we could have executed this strategy over the past 101 years, we would have beaten the buy-and-hold strategy by a staggering 5637.10%. Total net profit would have been $1,233,454.40. This more complex trend-following rule was more active at one trade every 290.83 days on average. Of the 127 total number of trades, 69 or 54.84% were winning trades (69 of 127 total number of trades). [See our book for full trade signal details.] 


The Equis International MetaStock® System Testing rules, where the current Dow-Jones Transportation Average (multiplied by 100 to eliminate the fraction) is inserted into the data field normally reserved for Volume (V), are written as follows:       

Enter long:  C>Ref( HHV(C,opt1) ,-1)   AND V>Ref( HHV(V,opt5) ,-1) 
Close long: C<Ref( LLV(C,opt2) ,-1)    AND V<Ref( LLV(V,opt6) ,-1)
Enter short: C<Ref( LLV(C,opt3) ,-1)    AND V<Ref( LLV(V,opt7) ,-1)
Close short: C>Ref( HHV(C,opt4) ,-1)   AND V>Ref( HHV(V,opt8) ,-1)
   
OPT1 Current value: 9 
OPT2 Current value: 22 
OPT3 Current value: 22 
OPT4 Current value: 36 
OPT5 Current value: 39 
OPT6 Current value: 166 
OPT7 Current value: 166 
OPT8 Current value: 32  

Indicator Strategy Example with
Just One Exponential Moving Average Crossover Applied to Both Averages  

Hypothesis Four:
While Price Channel is good at defining breakouts from horizontal trading ranges, often the market moves in a steeply sloping direction, either up or down. In these cases, at least, the use of sloping lines may be more productive for signal generation. An Exponential Moving Average crossover (see Exponential Moving Average) could be one example of a sloping line that could be applied to both the Dow-Jones Industrial and Transportation Averages to define a tend and a trend change signal.  

The exponential moving average crossover rule would have been a profitable indicator over all time frames and, particularly, over the shorter ones. All lengths in the range of 100-days or less would have outperformed the passive buy-and-hold strategy. For traders with very low transactions costs, exponential moving average lengths around three days would have been best. Based on the daily closing prices for the Dow-Jones Industrial and Transportation Averages for 101 years from 1900 to 2001, we found that the following parameters would have produced a significantly positive result on a purely mechanical trend-following signal basis with no subjectivity, no sophisticated technical analysis, and no judgement:   

Enter Long (Buy) at the current daily price close of the Dow-Jones Industrial Average when this daily closing price crosses above yesterday's 3-day exponential moving average of the daily closes and when the close of the Dow-Jones Transportation Average also crosses above yesterday's 3-day exponential moving average of its daily closes.  

Close Long (Sell) at the current daily price close of the Dow-Jones Industrial Average when this daily closing price crosses below yesterday's 3-day exponential moving average of the daily closes and when the close of the Dow-Jones Transportation Average also crosses below yesterday's 3-day exponential moving average of its daily closes.  

Enter Short (Sell Short) at the current daily price close of the Dow-Jones Industrial Average when this  daily closing price crosses below yesterday's 3-day exponential moving average of the daily closes and when the close of the Dow-Jones Transportation Average also crosses below yesterday's 3-day exponential moving average of its daily closes.  

Close Short (Cover) at the current daily price close of the Dow-Jones Industrial Average when this  daily closing price crosses above yesterday's 3-day exponential moving average of the daily closes and when the close of the Dow-Jones Transportation Average also crosses above yesterday's 3-day exponential moving average of its daily closes.  

Starting with $100 and reinvesting profits, total net profits for this exponential moving average crossover strategy wound have been more than $505 million, assuming a fully-invested strategy, reinvestment of profits, no transactions costs and no taxes. This would have been more than two million percent better than a passive buy-and-hold strategy. Short selling wound have been profitable and was included in the strategy. Typical of other trend-following strategies, however, short selling would have been unprofitable in the unusually large bull market from 1980 to 2000. Note that this strategy is right on average only 40.36% of its signals, but the size of the average winning trade is 1.83 times the size of the average losing trade. This exponential moving average crossover strategy is very active at one trade every 6.35 days.   

The Equis International MetaStock® System Testing rules, where the current Dow-Jones Transportation Average (multiplied by 100 to eliminate the fraction) is inserted into the data field normally reserved for Volume (V), are written as follows:    

Enter long: C>Ref(Mov(C,opt1,E),-1) AND V>Ref(Mov(V,opt1,E),-1) 
Close long: C<Ref(Mov(C,opt1,E),-1) AND V<Ref(Mov(V,opt1,E),-1) 
Enter short: C<Ref(Mov(C,opt1,E),-1) AND V<Ref(Mov(V,opt1,E),-1) 
Close short: C>Ref(Mov(C,opt1,E),-1) AND V>Ref(Mov(V,opt1,E),-1) 

OPT1 Current value: 3   

An Evolutionary Future for the Dow Theory?

Our purpose here is not to offer any particular fix or remake of the Dow Theory. We merely hope to stimulate thinking as to how the theory might be allowed to evolve. You might use ideas herein to launch your own research. You might find your own unique guidelines in harmony with your own particular objectives and limitations. You might develop your own individual variations and interpretations, all based on the actual historical evidence. There are a very large number of indicators in our book that could be used to supplement basic Dow Theory concepts.

Think of how a theory evolves.  An observer ponders the data, forms a hypothesis, then tests the hypothesis. The hypothesis may be adjusted many times to better fit the data. The hypothesis also may change as new data becomes available. The hypothesis is allowed to evolve so that it describes observed phenomena better and better. 

Merely pondering of the data without testing it could lead to erroneous hypotheses, misconceptions, false conclusions and general confusion. Things that seem like they ought to be true often are not when you rigorously test the hypothesis against the actual data. Testing helps us clarify our thinking. Without testing, we can miss subtleties in the data and evolutionary changes in the nature of underlying phenomena over time. In the absence of testing, delusions may persist. Obsolete beliefs may lead to flawed decisions. 

Over the years, Dow's Theory has been subjected to misunderstanding due to imprecise definitions and the absence of continuous evolutionary testing. Change is constant, and no theory should be taken as etched in stone.   

Our testing must be objective, precise, and unbiased. We must maintain strict logical control over what and how we are testing at all times. Our testing must make sense. This is where experienced judgement will never be obsolete.

There is a compelling logic to defining and continuously redefining through back testing a set of decision rules that would have performed best in the past. In fact, there is no acceptable alternative. You can theorize all you want, but without historical back testing you could be on shaky ground and not know it. An objective approach based on simulated performance against actual historical data simply offers the best hard factual backing available. 


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