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The Dow TheoryWilliam Peter Hamilton’s Track

Record Re-Considered

Stephen J. Brown (NYU Stern School)

William N. Goetzmann (Yale School of Management)

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Background on the Dow Theory

Charles Henry Dow Dow indices developed for timing studies

William Peter Hamilton Editorialist applied “Dow Theory” 1902-1929

Principles market follows trends Industrial and transportation sectors confirm high volume indicates move

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Testing the Theory

Alfred Cowles III “Can Stock Market Forecasters Forecast?” E’trica 1934 Coded editorials “Bull” “Bear” or “Neutral” “Bull” = all stocks “Bear” = short stocks “Neut” = t-bills

Dow Portfolio, 1902 - 1929 vs. 100% stocks Dow: 12% return per year 1/2 DJIA & 1/2 DJTA: 15.5% return per year

Conclusion: no timing skill!

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Testing the Theory II

Bull & bear forecasts Sorted the 90 times Hamilton changed his forecast Half proved profitable, half did not

Conclusion: no timing skill!

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Problems in Cowles Analysis

100% stocks a correct benchmark? “Hamilton was long of stocks 55%, short of

stocks 16% and out of the market 29% out of the 26 years under review.”

He made 255 forecasts, not 90 Are two successive bear calls informative?

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Revisiting Hamilton’s Calls

Re-coding 46% bull calls 16% bear calls 38% neutral calls

Created contingency table call vs. capital appreciation return of DJIA until

next editorial

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The Dow Theory 1903 to 1929

BullMarket

BearMarket

BullForecast 74 56

BearForecast 18 36

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Trading Strategy Considered

Back-test of Hamilton portfolio Assume investment in S&P with dividends &

commercial paper as riskless asset. S&P index created by Cowles as capital

weighted measure of stock investment. Monthly re-balancing

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Hamilton’s Portfolio Vs. S&P

Year1903 1905 1907 1909 1911 1913 1915 1917 1919 1921 1923 1925 1927 1929

0

5

10

15

20Figure 1: Dow Theory vs. 100% Stocks

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100% S&P vs. Hamilton

100% S&P Hamilton

Strategy Return 10.75% 10.73%

Strategy STD. 12.83% 10.44%

Jensen's 0.00% 4.04%

Sharpe Ratio 45.61 % 55.89%

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Event Study

What happened to the DJIA after a call? Line up returns in event-time average across call of same direction

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Bull vs. Bear Calls

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

1.06

Pric

e In

dex

-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Days Around Editorial

buys neutrals sells

DJIA Around Editorials

Sells

Neutral

Buys

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Recovering The Dow Theory

Hamilton’s calls contain the essence of the Dow Theory.

Can we create a model of the theory?Does it correspond to the writings about it?

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Predicting Hamilton’s Signals

Use information available on the editorial date (and to us now)

See if we can forecast Hamilton’s signalsPerform out-of-sample test to see if our

recovered Dow Theory worked.

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Methodology

Step-wise regression A linear model of Hamilton “bear” signal Use AIC-like criterion to add and prune

variablesNeural network

A non-linear model of Hamilton’s signals Uses a broad range of variable transformations No “coefficients” reported

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Stepwise Regression

Intercept -1.7 60Day Ind:30Day Ind -93.8

Ind 60 Day Ret -14.2 30Day Ind:30Day Tran 64.4

Tran 60 Day Ret -9.7 60Day Tran:30Day Tran -235.8

Ind 30 Day Ret -3.7 60Day Ind:30Day Tran 100.7

Tran 30 Day Ret 6.1 60Day Tran:30Day Ind 110.3

Ind same sign Tran 0.1 60Day Tran:30Day Ind:30Day Tran

-931.3

60 Day Ind: SameSign

12.2 60Day Ind:30Day Ind:30Day Tran

345.7

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Neural Network Approach

Feature Vector Analysis A. Kumar and V.E. McGee “FEVA: Feature

vector analysis: explicitly looking for structure and forecastability in time series data,” Economics and Financial Computing, Winter, 1996

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Neural Net Events 1902-1929

0.94

0.96

0.98

1

1.02

1.04

1.06

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

BUYSELLNEUTRAL

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Neural Net Events 1930-1996

0.940.950.960.970.980.99

11.011.021.03

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

BUYSELLNEUTRAL

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Conclusions

The Dow Theory reputation was deservedHamilton followed a momentum strategyThe spread between bull and bear calls has

continued out of sample, albeit diminished