The Dow Theory:

*William Peter Hamilton's Track Record *

*Re-Considered*

Very Preliminary! Comments Welcome. Please do not Quote.

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William N. Goetzmann

*Yale School of Management*

Stephen J. Brown

*Leonard Stern School of Business, NYU*

March 25, 1997

Abstract: Alfred Cowles' (1934) test of the Dow
Theory apparently provided strong evidence against
the ability of the ability of Wall Street's most famous
chartist to forecast the stock market. In this paper, we
review Cowles' evidence and find that it supports the
contrary conclusion -- that the Dow Theory, as
applied by its major practitioner, William Peter
Hamilton over the period 1902 to 1929, yielded
positive risk-adjusted returns. A re-analysis of the
Hamilton editorials suggests that timing strategies
based upon the Dow Theory yield high Sharpe ratios
and positive alphas.

For a current version of this paper, please contact:

William N. Goetzmann

Yale School of Management

Box 208200, New Haven, CT 06520-8200

william.goetzmann@yale.edu

Aknowledgements: I thank my colleagues Geert Rouwenhorst and N. Prabhala for helpful comments. All errors are the sole responsibility of the author.

Alfred Cowles' (1934) test of the Dow Theory apparently provided strong evidence against the ability of Wall Street's most famous chartist to forecast the stock market. Cowles' analysis was a landmark in the development of empirical evidence about the informational efficiency of the market. He claimed that market timing based upon the Dow Theory resulted in returns that lagged the market. In this paper, we review Cowles' evidence and find that it in fact supports the contrary conclusion -- that the Dow Theory, as applied by its major practitioner, William Peter Hamilton over the period 1902 to 1929, yielded positive risk-adjusted returns. The difference in the results is due to the lack of adjustment for risk. Cowles compared the returns obtained from Hamilton's market timing strategy to a benchmark of a fully invested stock portfolio. In fact, the Hamilton portfolio, as Cowles interpreted it, was frequently out of the market. Adjustment for systematic risk appears to vindicate Hamilton as a market timer.

In order to estimate the risk-adjusted returns that may have been obtained by following the
Dow Theory over the Hamilton period, we classify the market forecasts he made over 255 editorials
published in the *Wall Street Journal* during his tenure as editor. Using the riskless rate as a
benchmark, we find that Hamilton's ratio of correct to incorrect calls was higher than would be
expected by chance. Using total return data for the Cowles index of stock market returns and the
S&P index over the 27 year period, we find that the systematic risk of a trading strategy proposed
by Cowles based upon the *Wall Street Journal* editorials was relatively low. We apply market
timing measures used to identify skill to the time-series of returns to the Hamilton strategy, and we
find significant positive evidence. An event-study analysis of the Dow Industrial Index around
Hamilton's editorials indicates a significant difference in mean returns over a 40 day period
following "Bull" vs. "Bear" market calls. The event study also shows that Hamilton's forecasts were
based upon a momentum strategy.

Our finding suggest a plain reason why the Dow Theory remains to this day a popular method for timing the market. During the first three decades of this century it appeared to work. Regardless of whether it has worked since then, this early success established a reputation which has endured for decades.

This paper is organized as follows. The next section provides historical background on the
Dow Theory and William Peter Hamilton. Section III describes the empirical test of the Dow Theory
published by Alfred Cowles in 1934, and discusses it's interpretation in light of current methods of
risk adjustment. Section V describes our re-analysis of the Hamilton editorials and section VI
concludes.

**William Peter Hamilton and the Dow Theory**

Most of what we know of the Dow Theory of stock market movements comes not from the
founding editor of *The Wall Street Journal,* Charles Henry Dow, but from his successor, William
Peter Hamilton, who assumed the editorship of the paper upon Dow's death in 1902. Over the next
27 years until his own death in late 1929, Hamilton wrote a series of editorials in *The Wall Street
Journal* and in *Barron's, * discussing and forecasting major trends in the U.S. stock. Hamilton cited
his predecessor Charles Dow's theory of stock market movements as the explicit basis for market
predictions. In his 1922 book *The Stock Market Barometer*, Hamilton further elucidates the basic
outlines of the theory. The theory pre-supposes that the market moves in persistent "Bull" and
"Bear" trends. While determination of these trends is hampered by short-term deviations, Hamilton
asserts that "charting" past fluctuations in the industrial and transportation indices allows the analyst
to identify the primary market movement.

An acute irony, given the current reputation Dow theorists enjoy among financial economists, is that Hamilton's book succinctly articulates and defends the concept we now term informational efficiency of the stock market. According to Hamilton, "The market movement reflects all the real knowledge available..." This assertion is interpreted by a later prominent Dow theorist, Robert Rhea, in 1932, to mean that:

**The Averages Discount Everything: -- **The fluctuations of the daily
closing prices of the Dow-Jones rail and industrial averages afford a
composite index of all the hopes, disappointments, and knowledge of
everyone who knows anything of financial matters, and for that
reason the effects of coming events (excluding acts of God) are
always properly anticipated in their movement. The average quickly
appraise such calamities as fires and earthquakes. ^{(1)}

How, then, could the theory be consistent with the notion that past market trends are predictive of
future price movements? According to Hamilton, "...the pragmatic basis for the theory, a working
hypothesis, if nothing more, lies in human nature itself. Prosperity will drive men to excess, and
repentance for the consequence of those excesses will produce a corresponding depression." In other
words, the bull and bear market cycles envisioned by the Dow Theory are due to "the irrational
exuberance" of individual investors, which itself appears not to be rationally incorporated into prices.
While the basic outlines of the Dow Theory may be gleaned from Hamilton's book and
editorials, Robert Rhea's reduction of the Dow Theory as "theorems" is a useful guide. First, market
movements may be decomposed into primary, secondary and tertiary trends, the most important of
which are Bull and Bear markets, both of which are characterized by fundamental economic activity
as well as market price changes. Bull markets have three stages: "first...[is]...revival of confidence
in the future of business...second is the response of stock prices to the known improvement in
corporation earnings, and the third is the period when speculation is rampant and inflation apparent."
For primary bear markets, "the first represents the abandonment of the hopes on which the stocks
were purchased at inflated prices; the seconds reflects selling due to decreased business and earnings,
and the third is caused by distress selling of sound securities, regardless of their value."^{(2)}

The Dow Theory is translated into a guide to market timing by Hamilton by identifying the primary trend through a few key signs. First, trends must be confirmed by both the industrials and the transportations. In other words, market movements are unreliable unless evidenced across two different market sectors. Second, extended movements sideways, called "lines," presage the emergence of a definite trend. In other words, a big move following a period of quiescence is taken as the beginning of a primary trend in that direction.

These "theorems" are vague enough to admit a variety of statistical interpretations,
Hamilton's fellowship in the Royal Statistical Association notwithstanding. Fortunately, we have
a specific record of forecasts he made over his lifetime, which were compiled and published by
Robert Rhea in 1932, and published by *Barron's*. While not cited in his references, this source is
likely the one used by Alfred Cowles III in his analysis of the Dow Theory.

**Alfred Cowles' Analysis of the Dow Theory**

Alfred Cowles' article "Can Stock Market Forecasters Forecast?" was published in
*Econometrica* in 1934, and is widely regarded as a landmark paper in the development of the
efficient market theory. In the paper, Cowles tests the Dow Theory by coding each of Hamilton's
editorials in the *Wall Street Journal* or *Baron's* as "bullish", "bearish" or "neutral." Cowles then
assumes that on a bullish signal, an investo places 100% of his wealth in stocks (50% in the stocks
comprising the Dow Industrial Index and 50% in those comprising the Dow Transportation Index).
A bearish signal is taken as a recommendation to short the market and a neutral signal was taken
as a recommendation to invest in t-bills. Cowles adjusts the Dow index for splits and dividends and
estimated transactions costs, in order to calculate total returns to the Dow timing strategy. For
periods Hamilton is out of the market, Cowles assumes he earns a riskless rate of 5%. He then
compares this strategy to the alternative of investing 100% in the stock market over the same period.
He concludes that the Dow Theory would have yielded 12% per annum, while an all-stock portfolio
would have yielded 15.5% per annum. He regards this as *prima facia* evidence that the Dow Theory
does not work.

Despite Cowles' careful work at calculating total returns for the two strategies, he neglects to adjust for differences in relative risk. These differences in fact appear to have been substantial. According to Cowles, "Hamilton was long of stocks 55 per cent, short 16 per cent, and out of the market 29 per cent, out of the 26 years under review." These numbers suggest that the systematic risk of the strategy was a far cry from 100%. Indeed, using the crude approximation for the average beta of .55-.16 = .39, it seems that the Dow strategy earned a risk-adjusted return of .12 - [.05+.39(.155-.05)] = .029. In other words, Cowles' interpretation of Hamilton's strategy would seems to earn 290 basis points per year on a risk-adjusted basis!

Cowles also performs a non-parametric analysis of the Hamilton recommendations, reporting
the frequency of correct bull and bear market calls. Out of the 255 forecasts, he takes only the
*changes* in recommendations as data. Thus he analyzes 29 bullish forecasts, 23 bearish forecasts and
38 neutral forecasts. He concludes from this that half of the changes in position were profitable, and
half were unprofitable. The inescapable conclusion of this analysis is that an investor might just as
well have flipped a coin. Or would he? Note that Cowles neglected to consider the efficacy of
repeated bull forecasts in a rising market and repeated bear forecasts in a falling market. Any
sequence of positive calls that were confirmed by a rising market would be reduced to a single
datum. Given that the Dow Theory is essentially a momentum strategy, this possibility is not
remote. Consider an extreme example. Suppose that Hamilton had made 100 forecasts : 49 bull
forecasts in a row that proved correct, and then an incorrect bull forecast, then 49 correct bear
forecasts in a row, then an incorrect bear forecast. Cowles would have scored this as two correct
forecasts and two incorrect forecasts, however an investor following that advice might have done
quite well. The very fact that Cowles analyzes only 90 changes in position out of 255 forecasts in
a momentum-based strategy suggests that some significant percentage of the remaining 165 forecasts
may have been correct!

Of course, we cannot blame Cowles for not knowing in 1934 how to calculate Jensen's alpha.
Nor should we have expected him to fully appreciate the subtleties of conditioning in non-parametric
tests. Never-the-less, a close look at the Cowles evidence suggests that the Dow Theory, as
practiced by William Peter Hamilton merits re-consideration.

**Analysis of the Hamilton Editorials**

In order to evaluate Hamilton as a market timer, we code the 255 Hamilton editorials as
bullish, bearish, neutral or indeterminant. We then collect total return information on the U.S. stock
market information over that period, and perform parametric and non-parametric tests of trading
strategies analogous to those evaluated by Cowles. Finally we examine the price dynamics of the
Dow Industrials around editorial publication dates.

*Hamilton's Editorials*

Unfortunately, the recommendations in the editorials are not always clear. Cowles' solution
is to have five subjects score the editorials and then take the majority opinion on each. We use only
one subject to score the editorials and find eleven indeterminant cases out of the 255 which we
eliminate from the study. We calculate that the portfolio is in stocks 46% of the time, in bills 38%
of the time and short 16% of the time. These percentages are based upon the number of months
in each asset. When we count the number of bull, bear or neutral calls, the ratios are much closer
to Cowles': long 54%, neutral 24% and short 22%. Our scoring therefore appears slightly different
from the Cowles analysis, which has the portfolio long more frequently. As we show in the
following analysis, it is unlikely that the minor differences in interpretation of the editorials are the
basis for the divergence in our results.

*Non-Parametric Tests*

To address the basic question of Hamilton's timing skill, we examine how often the Dow
beats or lags the riskless rate over the interval following an editorial, conditional upon a bull of bear
call. The interval following the editorial is defined by the day following the editorial to the day of
the next Hamilton editorial. Our analysis of the frequency of successful calls differs substantially
from Cowles. Table 1 shows a contingency table indicating the relationship between market calls
and subsequent performance. The proportion of successful "up" calls is greater than failed "up" calls
and the proportion of successful "down" calls is much higher than failed "down" calls. In fact,
Hamilton appears to have been extremely successful in his bear market calls -- he was right twice
as often as he was wrong. In total, Hamilton was right 110 times and wrong 74 times, by our count.
The neutral scores are not included in this analysis, since they are interpreted as stock returns
equaling bill returns. A natural test of the Dow Theory would be a Henriksson-Merton test, however
that test is only appropriate for a bivariate investment choice.^{(3)} As an alternative, we perform a
related non-parametric test, Fisher's exact test, which indicates that the positive association
between Hamilton's calls and subsequent results. Fisher's test is statistically significant at the 1%
level. One issue of potential importance is the implicit "I told you so" option that Hamilton had.
Since we define the interval from editorial to editorial, Hamilton could simply have waited until the
market confirmed his previous call, and then written an editorial claiming success. To address this
issue, an explicit trading test in necessary.

*Testing a Trading Strategy*

Following Cowles, we simulate a trading strategy which moves from long stocks to short stocks to t-bills, depending upon the Hamilton editorial. While Cowles apparently used a 50/50 portfolio mixture of the Dow industrials and the Dow railroads, we use the Cowles market index: a value-weighted index of U.S. stocks, including income return. This is widely considered to be the highest-quality monthly return series available, and mimics a passive strategy of holding stocks. As the alternative investment, we use the short-term rate of 5% used by Cowles in his analysis. We further assume that the portfolio could only be re-balanced monthly, which allows us to use the monthly Cowles indices. Accordingly, we take the first recommendation that appeared in a month, and then assume that this is used as a guide to rebalancing at the end of the month. In those months for which we have more than one recommendation, this means that we ignored the later call. As a consequence, we do not pick up intra-month returns to the Dow strategy.

Figure 1 shows the relative performance of the Hamilton portfolio compared to a portfolio invested entirely in the market over the 27 years. Notice that, for most of the period, the stock market drifts sideways, until a major bull market begins in 1924. The Dow Theory actually beats a full market investment until 1926, at which point the fully invested portfolio advances beyond the timing portfolio. Hamilton's major success occurs 1907, when he avoids the worst of the panic of that year. He also does well in 1917 and 1920, when the Dow portfolio is out of the market during both bear runs. In general, the figure indicates that the Dow portfolio was less volatile than the fully invested strategy.

The first column of Table 2 reports the results of the simulated investment strategy over the 27 year period. The annual arithmetic return to the Dow portfolio is 9.95% (9.83% geometric), slightly below the annual average return obtained by holding the Cowles all-stock portfolio, which yields an annual arithmetic average of 10.90% (10.54% geometric). On a risk-adjusted basis, however, the Dow portfolio has a higher Sharpe ratio (1.2 compared to 5.25) and a positive Jensen measure of 3.12% -- 300 basis points per year. This high Jensen measure is due to a beta of .31 with respect to the Cowles index.

The rest of Table 2 reports the results of significance tests generated by bootstrapping the
Dow strategy. The bootstrap is performed by randomly generating stock return series' by drawing
monthly returns with replacement from the sample period. Thus, we construct a null hypothesis that
Hamilton has no forecasting ability, that the market follows a random walk, and that mean and
variance for the market are constant. We report the mean, median, standard deviation, t-test, 95%
(or 5% for standard deviations). The final column shows the rank represented by the actual value.
The Dow portfolio yields an unusually high annual return compared to the null. The expected return
from such a strategy appears to be around 5%. The actual return of 9.95% ranks above the 99th
percentile of the bootstrap distribution. While the standard deviation of the strategy is also low, it
appears that the full-investment strategy also resulted in an unusually low standard deviation.^{(4)} This
appears to provide evidence against the random walk assumption of the bootstrap. The Sharpe
measure of the Dow portfolio exceeds all of the bootstrapped values, and the Jensen measure of the
Dow portfolio exceeds the 99% level. Neither the mean return nor the Sharpe ratio for the all-stock
portfolio are unusual, although the low standard deviation puts the Sharpe ratio at the 63% level.
Note that the standard deviation of the Dow Jensen measure is 1.97%. This means we cannot reject
the joint hypothesis null that the that Jensen measure is zero and returns follow a random walk.

*Editorials as Events*

Another measure of Hamilton's skill at market timing is to treat each editorial as an event, and examine whether bull market calls are followed by positive market moves and bear market calls are followed by negative market moves. We use event-study methods and daily Dow Industrial Average data to examine the index dynamics around Hamilton's. Figure 2 shows the price path for bull, bear and neutral calls. The paths represent the cumulated sum of the equal-weighted average appreciation return of the Dow Industrial Index over the forty trading days preceding and following the publication of the editorial. Bull calls are followed by a 1.5% price increase over the next forty days on average, while bear calls are followed by 1.74% price decrease over the next forty days. The difference between these two, as measured by a two-tailed t-test allowing for unequal variance is significant at the 95% level (.034 prob.value). The neutral calls have a .21% return over the next 40 days.

The figure also indicates the basis for Hamilton's calls. Bear calls follow steep recent
declines in the Dow, while bull calls follow recent positive trends. This is consistent with a theory
of market trends. The result is clearly a momentum strategy, in which steep recent declines or
advances are taken as signals of future trends in that direction.

**Conclusion**

A review of the evidence against William Peter Hamilton's timing abilities suggests just the opposite -- his application of the Dow Theory appears to have yielded positive risk-adjusted returns over a 27 year period at the beginning of the century. The basis of this track-record seems to have been his ability to forecast bull and bear market moves. Whether this means the Dow Theory is correct, or whether it simply means that Hamilton was one lucky forecaster among many market analysts is another question. Given all of the financial periodicals published at the beginning of the century, it may not be surprising that one turned out to have been correct in calling market moves.

The contribution of this paper is not simply to show that Hamilton was a successful market
timer. Alfred Cowles' analysis of the Hamilton record is a watershed study which led to the random
walk hypothesis, and thus was a key element in the development of the efficient market theory.
Ever since Cowles' article, "chartists" in general, and Dow theorists in particular have been regarded
by financial economists with skepticism. Our replication of the Cowles analysis yields results
contrary to Cowles conclusions. At the very least, it suggests that more detailed analysis of the
Hamilton version of the Dow Theory is warranted. In broader terms it also suggests that the
empirical foundations of the efficient market theory may not be as firm as long believed.

**References**

Cowles, Alfred, 1934, "Can Stock Market Forecasters Forecast?" *Econometrica*, pp.309-324.

Hamilton, William Peter, 1922, *The Stock Market Barometer: A Study of its Forecast Value
Based on Charles H. Dow's Theory of the Price Movement*, Barrons, New York.

Henricksson, Roy D. and Robert C., 1981, "On Market Timing and Investment Performance. II.
Statistical Procedures for Evaluating Forecasting Skills," *Journal of Business*, 54:4, pp.513-533.

McCullagh, P. and J.A. Nelder, 1983, *Generalized Linear Models*, Chapman and Hall, Ltd.,
Cambridge, England.

Rhea, Robert, 1932, *The Dow Theory*, Barron's, New York.

Table 1: Non-Parametric Test of Hamilton's Market Calls

This table reports the frequency of successful versus unsuccessful bull and bear
market calls by William Peter Hamilton in his column in *The Wall Street Journal* and
in *Barron's* over the period December, 1903 through November, 1929. Identification
of "Call up" and "Call Down" is based upon a reading of the editorial to determine
Hamilton's assessment of whether the "primary movement" of the market was up or
down. "Neutral" calls, and calls for which the direction could not be assessed from
the editorial are omitted. "Market Up" and "Market Down" refer to whether or not
the rate of capital appreciation of the Dow Industrial index exceeded the riskless rate
of 5% per annum. Fisher's Exact Test is a test about the log-odds ratio
log[(upup*downdown)/(downup*downdown]. Under the null, the variance of log
odds ratio is 1/upup + 1/downdown + 1/downup + 1/updown.^{(5)}

Market Up | Market Down | Column Sum | |

Call Up | 74 | 56 | 130 |

Call Down | 18 | 36 | 54 |

Row Sum | 92 | 92 |

Fisher's Exact Test Statistic: 8.74

Table 2: Summary of Simulated Trading Strategy Based on Hamilton's Editorials

Statistics for the trading strategy are reported in Column 1. The strategy follows
Cowles (1934) and assumes a short position in the stock market is taken at the end
of the month in which a down call is made, while a long position in the market is
taken at the end of the month in which an up call is made. Neutral calls are taken as
a signal to invest in riskless securities.

Bootstrap results are based upon 500 outcomes under a null in which market returns
are i.i.d. Pseudo-histories of total monthly returns for the 27 year period are
generated by random draws with replacement from the actual distribution of monthly
returns.

Bootstrap Results | |||||||

Actual Values | mean | median | std | t-test | .95 percentile | rank | |

Dow Beta | 0.311 | 0.305 | 0.311 | 0.091 | 0.060 | 0.446 | 0.501 |

Dow Annual Return | 9.95% | 5.14% | 4.98% | 1.98% | 2.435 | 8.38% | 0.992 |

Dow Std. | 8.24% | 10.18% | 10.14% | 0.93% | -2.088 | 8.89% | 0.007 |

Dow Sharpe Ratio | 1.208 | 0.510 | 0.497 | 0.207 | 3.371 | 0.856 | 1.000 |

Dow Jensen Measure | 3.12% | -1.55% | -1.68% | 1.97% | 2.364 | 1.79% | 0.990 |

Cowles Annual Return | 10.90% | 10.80% | 10.86% | 2.64% | 0.036 | 15.06% | 0.519 |

Cowles Std. | 11.24% | 12.77% | 12.76% | 1.01% | -1.511 | 11.45% | 0.027 |

Cowles Sharpe Ratio | 0.525 | 0.460 | 0.453 | 0.214 | 0.303 | 0.812 | 0.634 |

**
**

**Notes**

1. Rhea (1932) p. 12

2. Ibid. P.13.

3. The Henriksson-Merton test assumes that the investor has the choice only to invest or not invest in the market. The timer is thus credited only with success at calling when the market underperforms a benchmark. Thus, remaining in the market is effectively a passive decision, while getting out of it is an active one. As a consequence, the H-M is a function only of the ratio of successful to unsuccessful "down" calls. The Cowles strategy attributes an active portfolio choice to both positive and negative market forecasts.

4. This is consistent with the hypothesis that the market over this period displayed mean-reversion.

5. See McCullagh, P. and J.A. Nelder, 1983, p.98 for details.