Dow Theory Lives!

January 01, 1999

The authors realized a classic study of that first major try at technical analysis, the Dow Theory, was flawed. They retested, using a narrowly limited variation of Dow Theory on a computer-based neural network, and found positive alphas and Sharpe ratios. A test on subsequent market data found better-than-chance predictive ability. The result is difficult to square with random-walk theories: Could there yet be some basis for price-chart analysis after all?

 

It all started when one of their graduate students observed that the classic 1934 Cowles study did not consider risk-adjusted rate of return. Alfred Cowles had studied the recommendations of that early and most famous chartist of all, William Peter Hamilton, who as editor of The Wall Street Journal from 1902 to 1929 had elucidated what became known as the Dow Theory of market timing and had made numerous market calls based on it in his Journal editorials. It had appeared to work during the quarter century Hamilton wrote, and to this day the many variants of Dow Theory remain popular tools for timing the market. It is taught to undergraduate investment students as an exemplar of market-timing practice. Yet Cowles found Hamilton lagged a fully invested stock portfolio, a devastating blow to market-timing as a concept.

But in fact, Hamilton was frequently out of the market, periods when he presumably earned the riskless rate of return while waiting for a signal to get back in. In Cowles' defense, Sharpe ratios and Jensen measures would not be developed until the 1960s. Cowles concluded that Hamilton's Dow Theory would have returned 12% per annum where a straight buy-and-hold strategy using the Dow averages would have yielded 15.5%. But even a simple recalculation adjusting for risk indicated Hamilton came out 290 basis points better, when risk-adjusted.

Applying a presumptive 5% riskless rate when Hamilton was out of the market was one thing - Cowles did that. Retesting in the light of modern portfolio theory was another, and it made all the difference. Brown and Goetzmann counted up Hamilton's correct calls and incorrect calls and found the ratio of correct calls was higher than could be expected by chance. On a total-return basis, they found the trading strategy as interpreted and applied by Cowles had relatively low systematic risk, meaning less volatility. They found positive alphas. They found Hamilton's calls appeared to be based at least in part on a momentum strategy, a commonplace approach in today's markets.

SO, HOW TO RETEST?

But then came the question, How can this technique, which seemed to work for the first part of this century, be tested for its ability to work in the rest of this century? After all, Hamilton died in 1929, and was not available for consultation. This was something of a problem for Cowles, too, who wrote in 1934, but it was a bigger one for Brown and Goetzmann's more ambitious effort.

All that we know of Hamilton's Dow Theory is what he wrote in his editorials and articles in The Wall Street Journal and Barron's, and in a 1922 book, The Stock Market Barometer. Hamilton cited his predecessor, Charles H. Dow, cofounder of the Journal and of Dow Jones & Company, Inc. (which owns this publication), as the origin of the theory, but Dow was dead too. The articles were collected and elaborated on in 1932 by Robert Rhea in The Dow Theory, which set forth several principles and a dozen "axioms" that became the definition of this theory, presumably for Cowles and clearly for many other apostles of this approach in the decades since.

Briefly, the theory contended that markets were given to cycles of excessive optimism and pessimism in the short and medium terms, revolving around a primary underlying trend, and that these swings could be traded on by observing the wavelike movements of the Dow Jones Industrial Average and what is now the Dow Jones Transportation Average and acting when their movements confirmed each other in identifying the next direction of the market. Such movements would commonly follow "lines," more or less extended periods when the market went essentially sideways.

The problem was turning all this into unambiguous rules that gave buy or sell signals you could identify, measure and count. The further problem was, how to approximate the calls Hamilton would have made if he had been writing his editorials up to the present day? Cowles' approach, besides neglecting risk-adjusted return, only counted Hamilton predictions of important reversals in the market, which meant a succession of successful calls predicting, say, a continuation of a bull market would not get counted at all, however profitable they might have been to an investor.

EUREKA

The professors went back to Hamilton's editorials and coded all 255, identifying 184 of them as unambiguous bull or bear calls. The results were pretty unambiguous themselves. As set forth in the accompanying table, by one appropriate test Hamilton's score lay more than three standard deviations out -about as certain as things get in statistical analysis.

Next, Brown and Goetzmann tested an approximated trading strategy during Hamilton's editorial writing period. This test alternated between short-term commercial paper and being long or short stocks, depending on Hamilton's market call. They used Cowles'own market index, a precursor to the S&P500, for which they had monthly data for the period and which was considered the best series available for the time. They tracked Hamilton for the entire 27-year period.

The Dow Theory, as applied by Hamilton, generally beat the market on an absolute basis - even without risk adjustment -from 1902 until 1926, a long time. Hamilton's calls took the compliant investor out of stocks for the worst of the famous Panic of 1907, and out of the market during the bear runs of 1917 and 1920. And all with noticeably less volatility. Only during the final, climactic runup from 1926 to the ultimate peak and subsequent crash in 1929 did the market outperform on an absolute basis. Throw in the final historic blowoff, and the absolute returns were close to even by this measure - but the Dow Theory's substantially lower beta once again gave it a significantly better risk-adjusted return, by one measure some 400 basis points per year.

PANEL A: CONTINGENCY TABLE TEST
 
Market Up
Market Down
Row Sum
Call Up
74
56
130
Call Down
18
36
54
Column Sum
92
92
 
Fisher's Exact Test Statistic: 8.74
PANEL B: HENRIKSON-MERTON (HM) NONPARAMETRIC TEST
Number when m is less than rf
N1
92
Number when m is greater than rf
N2
92
Number of observations
N
184
Number right when m is less than rf
n1
36
Number wrong when m is greater than rf
n2
18
Number of bear calls
n
54
Expected number right when m is less than rf
E(n1)
27
Standard deviation of n1  
2.53
t-test for HM test  
3.56

But that was then, and this is now. The question still remained, How do you test whether Dow Theory a la Hamilton continued to be valid after he had passed on to the Great Boardroom in the Sky, and after Cowles had written his supposed refutation of Hamilton's work?

BRING ON THE COMPUTERS

Hamilton's editorials gave the professors a rare opportunity to recover the rules actually used by this apparently successful Dow theorist. Remember, the theory depends entirely on drawing conclusions from the behavior of the stock market itself, and from no other source. That means every factor Hamilton claimed he and his mentor, Charles Dow, used to make their predictions were recorded in the stock tables from that period, 1902 to 1929. There should be no outside factors blindsiding late 20th century researchers. It ought to be possible to compare the editorials to the stock data of the time, and infer which patterns in the market inspired which calls. But that's a lot of data. What to do?

Enter something probably unimaginable in Hamilton's or Cowles' day: Artificial Intelligence. At Yale with Professor Goetzmann was a graduate student named Alok Kumar, who had an interest in analyzing the stock market for trading calls and an expertise in computer technology, in particular in the technology of neural networks. There has been considerable interest in applying neural networks to identifying and acting on trading patterns in the marketplace.

The concept is to use an algorithm designed to identify repeating patterns in a body of data. It helps if you start out with some idea of the kinds of patterns you are looking for, and in this case the researchers did. They had Hamilton's own editorials for a guide, and the entire history of price-chart analysis to work from.

TABLE II: SUMMARY OF SIMULATED TRADING STRATEGY BASED ON HAMILTON'S EDITORIALS
 
Actual Values
Median
Mean
Deviation
t-test
Percentile Values
Panel A: Randomizing Returns: Bootstrap Results
Hamilton beta
0.311
0.311
0.305
0.091
0.060
0.446
Hamilton annual return
9.95%
4.98%
5.14%
1.98%
2.435
8.38%
Hamilton standard deviation
8.24%
10.14%
10.18%
0.93%
-2.088
8.89%
Hamilton Sharpe ratio
1.208
0.497
0.510
0.207
3.371
0.856
Hamilton Jensen measure
3.12%
-1.68%
-1.55%
1.97%
2.364
1.79%
S&P annual return
10.90%
10.86%
10.80%
2.64%
0.036%
15.06%
S&P standard deviation
11.24%
12.76%
12.77%
1.01%
-1.511
11.45%
S&P Sharpe ratio
0.525
0.453
0.460
0.214
0.303
0.812
Panel B: Randomizing Strategies: Bootstrap Results
Hamilton beta
0.311
0.306
0.306
0.099
0.051
0.467
Hamilton annual return
9.95%
4.93%
4.97%
1.80%
2.766
8.00%
Hamilton standard deviation
8.24%
9.03%
9.04%
0.36%
-2.220
8.4%
Hamilton Sharpe ratio
1.208
0.547
0.551
0.204
3.225
0.860
Hamilton Jensen measure
3.12%
-1.75%
-1.76%
1.97%
2.477
1.48%

Finding patterns would not be the question. A neural network will derive patterns out of completely random data that are determined purely by chance matches or mismatches or recurrences in the numbers fed into the computer. It will "train" itself to look for the "better" (however that is defined) patterns and to apply them to new data. Rules can be developed from these results that fit the existing data perfectly but in fact could be completely meaningless. The question then would be whether the patterns the computer generated would prove to have predictive ability when applied to the new data, that is, whether they would prove "meaningful".

The years 1902 to 1929 gave their neural network quite a bit of data to digest. If you regard each trading day without an editorial market call from Hamilton as implicitly repeating the previous published market call, you can sort that quarter-century-plus into 3,599 buy calls, 1,143 sell calls, and 2,912 neutral calls. The researchers sharply limited their computer's range for applying Dow Theory. For example, most advocates of this theory and its many variants place great store in studying patterns of trading volume and how they relate to price changes. The computer was not programmed to register volume at all, let alone incorporate it into its calculations. Their neural network plugged away at this data set, and duly generated a number of patterns it rated as more predictive than others. The 12 most prominent "buy" patterns and 12 most prominent "sell" patterns are reproduced on page 37.

The professors had an ideal set of what is known as "out-of-sample" data - from 15 September 1930 to 1 December 1997 there were 17,457 trading days to let their newly "trained" computer loose upon. It duly generated 10,004 "buy" days, 6,131 "sell" days, and 1,322 neutral calls - which appears to be a reasonable distribution, considering the market has, speaking roughly and very generally, seesawed upward from its decisive bottom in 1932.

THE DIFFERENCE A DAY MAKES

But how to approximate returns? And timing? Do you assume that you're Hamilton and can buy in the morning you publish your call at the open and get prices that are on average very near the previous day's close? Or do you assume that you can't or at least don't react that quickly, and the best you can do is get that day's closing prices? The professors tried both, dubbing the morning-trade version the "Next Day Hamilton Strategy" and the afternoon-close version the "Second Day Hamilton Strategy." The surprisingly disparate results are summarized in the accompanying table:

TABLE IV: SUMMARY STATISTICS FOR OUT-OF-SAMPLE PERFORMANCE
Panel A: Whole Period
  Arithmetic Geometric Annual Standard
  Mean Mean Deviation
DJIA 7.07 5.48 18.30
HamNext 9.97 9.87 11.90
Hamilton2nd 5.91 5.52 12.10
Panel B: Subperiods
DJIA Cap App HamNext Ham2ND
1930-39 1.477 11.10 2.43
1940-49 3.213 6.04 5.66
1950-1959 9.641 9.91 5.27
1960-69 7.712 9.68 6.53
1970-79 0.409 6.74 4.30
1980-89 12.626 11.29 7.01
1990-97 15.442 16.24 10.72

The Next Day Strategy yields results persistently higher than the Second Day Strategy over a period of two thirds of a century, suggesting much of the predictive effect occurred almost immediately after the signal. The Second Day Strategy yields results that beat the DJIA some decades, lag it in other decades, but for the overall period work out to almost exactly the same return as the DJIA - with a substantially smaller standard deviation and therefore substantially less risk. This led Brown and Goetzmann to conclude that the Dow Theory, even in the limited form in which they were applying it, should not be dismissed as generating a lot of essentially random calls, which was a conclusion the original Cowles study in 1934 seemed to suggest.

Their analysis suggests that Hamilton was banking on the persistence of trends once established - momentum, if you will - yet was also on the lookout for reversals of those trends. Their automated imitation of Hamilton seemed to have at least some predictive power. It did better during the early decades, up until the 1960s, roughly speaking, but was still somewhat effective in the significantly different market (among other things more heavily dominated by institutional trading) that has evolved since. In recent years it has proved more effective in dodging the worst of bear markets than in exploiting the best of bull markets. Aquick-and-dirty test of the algorithm during the mini-crash in the summer of 1998 found it performing quite well indeed.

STILL THEORY, NOT PRACTICE

However, this was not a serious test of whether you can make any real money off Alok Kumar's computer. The professors did not allow for transaction costs (the historical record makes it difficult to get a good line on what they really were for market participants before the 1950s), and the model results in quite a bit of jumping in and out of the market. Also, they only crudely compensated for leaving out dividend income by leaving out the riskless return as well during periods when the computer called for being in cash. And they did not adopt Hamilton's more aggressive policy of selling short; bear calls just put the hypothetical portfolio into cash. The professors were not attempting to build a trading system; they were only addressing the question of whether price movements were in any way predictive of future price movements. Trying to build such a trading system would take a lot of time and effort, even though trading costs can be reduced to a fraction of what they once were by judicious use of index futures contracts and options. It would be a distraction for them; they are academic investigators of the markets, not market players.

The conclusion they drew was an academic one. The Cowles study was a watershed event, not only casting doubt on market timing as a strategy but ultimately leading to the development of the random walk hypothesis and of efficient market theory. But they showed the reality of Hamilton's performance was contrary to the conclusion Cowles made about it, and that that performance could be approximately replicated in the marketplace for decades afterward. To them, it means not only that Hamilton's work and the variants of Dow Theory that grew from it need to be reexamined more seriously, but also that the

empirical foundation of efficient market theory may not be as sound as its adherents believe. They are cautious about it: "Yes, it does have implications for the efficient market hypothesis," said Professor Brown, who once was a portfolio manager for AT&T's pension funds himself, "but it's only suggestive at this point." On the other hand, he added, "I don't know of anybody on Wall Street who really believes in that theory completely." And clearly, he and Professor Goetzmann, who once was a student of his, do not believe it either.

Find your next ETF

Reset All