Yale School of Management The Dow Theory William Peter Hamilton’s Track Record Re-Considered Stephen J. Brown (NYU Stern School) William N. Goetzmann (Yale School of Management)

Yale School of Management Background on the Dow Theory Charles Henry Dow  Dow indices developed for timing studies William Peter Hamilton  Editorialist applied “Dow Theory” Principles  market follows trends  Industrial and transportation sectors confirm  high volume indicates move

Yale School of Management 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, vs. 100% stocks  Dow: 12% return per year  1/2 DJIA & 1/2 DJTA: 15.5% return per year Conclusion: no timing skill!

Yale School of Management 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!

Yale School of Management 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?

Yale School of Management 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

Yale School of Management The Dow Theory 1903 to 1929

Yale School of Management 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

Yale School of Management Hamilton’s Portfolio Vs. S&P

Yale School of Management 100% S&P vs. Hamilton

Yale School of Management Event Study What happened to the DJIA after a call?  Line up returns in event-time  average across call of same direction

Yale School of Management Bull vs. Bear Calls

Yale School of Management 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?”

Yale School of Management Bootstrap Results

Yale School of Management 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?

Yale School of Management Predicting Hamilton’s Signals Use information available on the editorial date (and to us now) See if we can forecast Hamilton’s signals Perform out-of-sample test to see if our recovered Dow Theory worked.

Yale School of Management 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

Yale School of Management Stepwise Regression

Yale School of Management 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

Yale School of Management Neural Net Events

Yale School of Management Neural Net Events

Yale School of Management Conclusions The Dow Theory reputation was deserved Hamilton followed a momentum strategy The spread between bull and bear calls has continued out of sample, albeit diminished