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The Dow Theory
William 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
20
Figure 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
Pri
ce I
ndex
-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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Bootstrap Tests
What is the distribution of Hamilton’s portfolio returns in the market followed a random walk?
What is the distribution of Hamilton’s portfolio returns if he had randomly chosen “Bear”, “Bull” and “Neutral?”
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Bootstrap Results
R andomiz ing R eturns: B oots tra p Results
A ctualV alues
m ean median std t-test .95pe rcentile
rank
D ow B eta 0.326 0.305 0.311 0.091 0.060 0.446 0.501
D ow A nnual Return 10.73% 5.14% 4.98% 1.98% 2.435 8.38% 0.992 D ow S td. 10.44% 10.18% 10.14% 0.93% -2.088 8.89% 0.007
D ow S harp e Ratio .559 0.510 0.497 0.207 3.371 0.856 1.000
D ow Jensen M easure 4.04% -1.55% -1.68% 1.97% 2.364 1.79% 0.990 C owles A nnual Return 10.75% 10.80% 10.86% 2.64% 0.036 15.06% 0.519
C owles Std. 12.83% 12.77% 12.76% 1.01% -1.511 11.45% 0.027 C owles S harpe Ratio 0.456 0.460 0.453 0.214 0.303 0.812 0.634
Random izing S trategies : B ootstrap Results
A ctualV alues
m ean median std t-test .95pe rcentile
rank
D ow B eta 0.311 .306 .306 .099 .051 .467 .509D ow A nnual Return 9.95% 4.97% 4.93% 1.80% 276.60% 8.00% 1.00
D ow S td. 8.24% 9.04% 9.03% 0.36% -222.00% 8.40% 0.03
D ow S harp e Ratio 1.208 .551 .547 .204 3.225 .86 1.00D ow Jensen M easure 3.12% -1.76% -1.75% 1.97% 247.70% 1.48% .990
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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
variables
Neural 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
0.940.95
0.960.970.98
0.991
1.01
1.021.03
-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
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