journal of technical analysis (jota). issue 37 (1991, spring)

SPRING 1991

ISSUE 37

A PUBLICATION OF THE MARKET TECHNICIANS ASSOCIATION

71 BROADWAY, 2ND FLOOR, C/O NYSSA l NEW YORK, NEW YORK 10006 l (212) 344-1266

MARKET TECHNICIANS ASSOCIATION JOURNAL

Issue 37 spring 1991

Editor

James J. Bohan Merrill Lynch

New York, New York

Associate Editors

John R. McGinley Technical Trends

Wilton, Connecticut

Michael J. Moody Smith Barney Harris Upham

Los Angeles, California

Manuscript Reviewers

Charles D. Kirkpatrick II Kirkpatrick & Company, Inc. Philadelphia, Pennsylvania

David Upshaw, C.F.A. Waddell and Reed Investment Management

Shawnee Mission, Kansas

Frederick Dickson TDA Capital

Westport, Connecticut

Anthony W. Tabell Delafield, Harvey, Tabell

Princeton, New Jersey

Richard Orr, Ph.D. John Gutman Investments Lexington, Massachusetts

Henry 0. Pruden, Ph.D. Golden Gate University

San Francisco, California

Frank D. Korth Kemper Financial Services

Chicago, Illinois

Printer

Tritech Services New York, New York

Publisher

Market Technicians Association 71 Broadway, 2nd Floor

New York, New York 10006

MTA JOURNAL / SPRING 1991 1

MARKETING TECHNICIANS ASSOCIATION, INC.

Member and Affiliate Information

ELIGIBILITY: REGULAR MEMBERSHIP is available to those “whose professional efforts are spent practicing financial technical analysis that is either made available to the investing public or becomes a primary input into an active portfolio management process and for whom technical analysis is the basis of their decision-making process.”

AFFILIATE category is available to individuals who are interested in keeping abreast of the field of technical analysis, but who don’t fully meet the requirements for regular membership. Privileges are noted below.

APPLICATION FEES: A one-time application fee of $10.00 should accompany all applications for regular members, but is not necessary for affiliates.

DUES: Dues for Members, and Affiliates are $150.00 per year and are payable when joining the MTA and thereafter upon receipt of annual dues notice mailed on July 1.

Benefits of MTA

Regular Members Affiliates

Invitation to Monthly MTA Educational Meetings Yes Yes

Receive Monthly MTA Newsletter Yes Yes

Receive MTA Journal Yes Yes

Use of MTA Library Yes Yes

Participate on Various Committees Yes Yes

Eligible to Chair a Committee Yes No

Eligible to Vote Yes No

Colleague of IFTA Yes Yes

Annual Subscription to the MTA Journal ONLY-$35.00 minimum two issues.

Single Issue of MTA Journal (including back issues)-$20.00 each.

2 MTA JOURNAL / SPRING 1991

STYLE SHEET FOR THE SUBMISSION OF ARTICLES

MTA Editorial Policy

The MARKETTECHNICIANSASSOCIATIONJOURNAL~~ publishedbythe Market Technicians Associ- ation, 71 Broadway, 2nd Floor, New York, NY 10006 to promote the investigation and analysis of price and volume activities of the world’s financial markets. The MTA Journal is distributed to individuals (both academic and practitioner) and libraries in the United States, Canada, Europe and several other countries. The Journal is copyrighted by the Market Technicians Association and registered with the Library of Congress. All rights are reserved.

Style For The MTA Journal

All papers submitted to the MTA Journal are requested to have the following items as pre- requisites to consideration for publication:

ences should be put at the end of the article. Sub- mission on disk is encouraged by arrangement.

4. Greek characters should be avoided in the text and in all formulae.

1. Short (one paragraph) biographical presenta- tion for inclusion at the end of the accepted article upon publication. Name and affiliation will be shown under the title.

2. All charts should be provided in camera-ready form and be properly labeled for text reference.

5. Two submission copies are necessary.

Manuscript of any style will be received and examined, but upon acceptance, they should be prepared in accordance with the above policies.

3. Paper should be submitted double-spaced if typewritten, in completed form on 8% by 11 inch paper. If both sides are used, care should be taken to use sufficiently heavy paper to avoid reverse side images. Footnotes and refer-

Mail your manuscripts to:

James Bohan Merrill Lynch, No. Tower World Financial Center New York, NY 10281-1214

MTA JOURNAL /SPRING 1991 3

MARKET TECHNICIANS ASSOCIATION

Board of Directors, 1999-91

Officers/Office Manager

President Vice-President/Long Range Vice-President/Seminar Robert Prechter, Jr., CMT Bruce Kamich Ken Tower New Classics Library MCM Inc. Delafield, Harvey, Tabell PO. Box 1618 71 Broadway, 10th Fl. 600 Alexander Road Gainesville, GA 30503 New York, NY 10006 Princeton, NJ 08543-5209 4041536-0309 212l908-4326 6091987-2300

Treasurer Secretary MTA Office Manager Philip Erlanger Steven Nison, CMT Shelley Lebeck Fidelity Management Merrill Lynch, No. Tower Market Technicians Association 82 Devonshire Street-N9A World Finl. Center, 21st Fl. 71 Broadway, 2nd Fl., cJo NYSSA Boston, MA 02109 New York, NY 10281-1321 New York, NY 10006 6171570-7248 2121449-1859 2121344-1266 FAX: 2121673-9334

Committee Chairpersons

Programs James Stewart NatWest USA 175 Water Street, 20th Fl. New York, NY 10038 2121602-1732

Newsletter Ned Davis/Tim Hayes Ned Davis Research PO. Box 1287 Nokomis, FL 34274-1287 8131484-6107

Journal James Bohan Merrill Lynch, No. Tower World Financial Center New York, NY 10281-1214 2121449-0552

Accreditation John Brooks, CMT Davis, Mendel & Regenstein 5600 Glenridge Drive, #210 Atlanta, GA 30342 40412524008

Membership* Mike Epstein Richard A. Rosenblatt & Co. 20 Broad Street, 26th Fl. New York, NY 10005 2121943-5225

Education Ralph Acampora, CMT Prudential-Bathe Sec. 1 Seaport Plaza, 23rd Fl. New York, NY 10292 2121214-2273

Library Michael Moody, CMT Smith Barney 333 South Grand Avenue, 52nd Fl. Los Angeles, CA 90071 213/486-8901

Ethics and Standards Robert Nurock, CMT Investor’s Analysis, Inc PO. Box 988 Paoli, PA 19301 215/296-2411

IFTA Liaison Philip Roth, CMT Dean Witter Reynolds 2 World Trade Center, 63rd Fl. New York, NY 10048 2121392-3516

Placement Ken Spence Salomon Brothers 7 World Trade Center, 40th Fl. New York, NY 10048 212/783-3791

Marketing Ron Daino, CMT Smith Barney 1345 Avenue of Americas, 27th Fl. New York, NY 10105 212/698-6006

Computer Applications John Carder, CMT Topline Investment Graphics PO. Box 4283 Boulder, CO 80306 303/440-0157

Futures Philip Becker Bufka and Rodgers 425 No. Martingale Road, #1350 Schaumburg, IL 60173 7081240-2240

Continuity Charles Comer, CMT CL GlobalPartners 95 Wall Street, 17th Fl. New York, NY 10005 2121428-6121

*Membership Vice Chairpersons San Francisco Hank Prnden 415/459-1319 Los Angeles Bob Kargenian 7141634-2188 At Large Phil Roth 2121392-3516


TAl3LE OF CONTENTS

Moving Averages Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Fred Dickson Fred Dickson has made a number of contributions to the Journal over the years. The current article on moving averages fulfills his CMT requirements. The moving average is an old tool which has been used primarily to identify trends. The use of moving averages to determine trading signals has produced more questionable results. By raising the issue of risk, however, Fred has shown that the moving average still serves a useful function.

Share Repurchase Announcements: 19851989 . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 G. Gernon Brown III The bull market of the 1980’s was fueled by a new source of buying power. Mergers and acquisitions as well as corporations repurchasing their own stock added to the traditional sources of liquidity for the equity market. Gernon Brown takes a look at the effect of repurchase announcements on individual stocks and arrives at some interesting conclusions which could be of practical use.

Gauging Investor Sentiment . . . . . . . . . . . . . . . . . . . . . . . . .I3

Stock Market Price Behavior: Random Walks and Nonlinear Dynamics . . . . . . . . . .28 Peter A. Mulieri Early studies using traditional linear statistical testing techniques

Ginger Kock Mutual fund cash has been claim that market price changes follow a a popular indicator among technicians. The random walk pattern. Some of the early validity of the indicator was questioned work which refuted the random walk theory, in an article appearing in the Financial however, has shown evidence that price Analysts Journal. The article was reprinted changes are not random because of the in the August 1989 MTA Journal. Ginger existence of nonlinear relationships. Peter Kock questions the methodology behind the Mulieri provides us with a discussion of how 1988 article and shows that mutual fund nonlinear dynamics can apply to stock mar- cash can still be a useful tool. ket price changes.

MTA JOURNAL I SPRING 1991 5

The Use of Price-Volume

Crossover Patterns in

Technical Analysis. . . . . . . . . . . . .35

S. Kris Kaufman and Marc Chaikin Tra- ditional technical analysis involves the sub- jective evaluation of chart patterns. There are rules but chart interpretation has been considered an art form. For many the evaluation of price and volume patterns will remain in the art sphere. More technical analysts, however, are using computers to identify patterns. Pattern recognition methods have come into vogue because of more individuals with quantitative skills and because of advances in computer technology. Kris Kaufman and Marc Chaikin have provided us with a glimpse at their approach by identifying patterns that tend to be successful, and by providing the probability of success.

Pattern Recognition Signal Filters . . . . . . . . . . . . . . . . . . . .42

David Aronson In November of 1989, Futures magazine published an article, titled “Using pattern recognition to find trading signal filters,” by David Aronson and John Stein. The article was extracted from a more comprehensive paper by David Aronson. We thought that a full exposition of the article would be worthwhile. There has been a pro- liferation of system development in recent years. The article goes a step further, however, by using artificial intelligence to filter the signals from an existing system. The result is improved profitability, a reduction in risk and a greater chance of success.

The Dow Jones

Industrial Average

Alternative Computation

Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .52

Walter J. Mar&lo Many investors quote the Dow Jones Average and use it synony- mously as the “market.” For a variety of reasons, the average has been considered an imperfect measure of the market. Walter J. Marullo shows alternative methods for con- structing the average discussing there biases and distortions. A suggestion for change is made in the current method of computation.

Membership and

Affiliate

Information.. . . . . . . . . . . . . . . . . . . . . . . .2

Style Sheet for the

Submission

of Articles.. . . . . . . . . . . . . . . . . . . . . . . . . .3

MTA Officers and

Committee

Chairpersons.. . . . . . . . . . . . . . . . . . . . . .4

Editor’s

Commentary . . . . . . . . . . . . . . . . . . . . . . .7


Editor’s Commentary James Bohan, Editor

The appearance of the Journal improved significant- John Brooks and also by the Journal committee. ly in the past year due to the efforts of the previous Those starting the accreditation program this year Journal editor John McGinley. The double column will be required to write a paper as the third level type set allows us to print more information in a of the CMT program. With that in mind, we have smaller space and improves readability. John has decided to conduct a workshop at the seminar in San- also helped in the transition to a new editorial board ta Barbara in May, entitled “How to write a CMT and has agreed to stay active in the Journal. We will paper for the Journal.” A number of Journal staff try to make further improvements, but the current members, former and present, will be on hand to of- format will suffice for now. We are, however, open to fer suggestions. From the workshop, we hope to suggestions from the membership. Mike Moody also develop more specific guidelines on writing an arti- helped in assimilating the current Journal. Mike is cle for the Journal. If you think that you would like in Los Angeles and having geographical diversifi- to work on the Journal, please contact the Journal cation on the editorial board should help identify editor. Your expertise in a certain area of technical sources for new articles. analysis could be helpful in guiding another member

The initial problem facing the Journal editors through a CMT paper. last fall was a dearth of articles. In the last couple Contributions from graduate students have of months, however, the number of articles submit- opened up a new source of research material. Three ted has increased, thankfully. We will put out articles from students at the University of Virginia another Journal in the not too distant future. Colgate Darden School of Business Administration

At a board meeting last Fall it was decided that appear in this Journal. We have other articles under the MTA would publish two regular Journals a year consideration. Ralph Acampora is responsible for de- instead of three. The seminar edition has been elim- veloping the program at UVa. Members of the MTA inated from the regular Journal series. It was felt have been asked to provide a topic and give guidance a compilation of the papers presented at the seminar to students who may have limited exposure to tech- did not meet the requirements of the Journal. If the nical analysis but are well versed in research tech- flow of articles continues at a high level we will pub- niques and have good writing skills. No doubt the lish another edition of the Journal. Failing enough program will add to the storehouse of technical articles, we have the option of compiling the best knowledge. Ralph is also heading discussions with articles on a topic from the old Journals (15 years the University to provide a course on technical anal- worth) and presenting them together in a special ysis. A movement to seek relationships with other edition. Issue 31 Winter 19831989 was devoted to Universities is also underway. statistics. An issue with the best articles on senti- It is interesting to see the areas technicians are ment or momentum would be a welcome edition to exploring. The topics submitted for publication have our libraries. been diverse, but some trends are prominent. There

We are always trying to develop new sources is a strong interest in quantitative techniques for articles. The CMT program should generate a spawned by the increased availability of cheap com- significant number of papers in coming years. puting power. Chaos, artificial intelligence and Writing a paper instead of taking part two of the ex- pattern recognition are prominent topics. Trading amination is an option we have been urging in the systems are also in vogue. past few years. For instance, Fred Dickson’s article A good portion of the membership is primari- on moving averages in this edition of the Journal is ly interested in traditional technical techniques for fulfillment of the CMT requirements. which can provide help on the job. Therefore, we do

An article for the CMT must be approved by need more practitioner articles from the regular the accreditation committee currently chaired by membership. Astroanalysis and the stock market,

MTA JOURNAL/SPRING 1991 7

technical analysis and bonds, and the usefulness of interest rate forecasts represent some of the topics we have in the works.

The MTA Board of Directors, at its March meeting, approved the following definition of technical analysis.

Technical analysis is the study of data generated by the action of markets and by the behavior of market participants and observers.

For the definition to be included in the MTA constitution it will have to be approved by the entire membership. If included in the constitution the definition will be followed by the following statement.

Such study is usually applied to estimating probabilities for the future course of prices fir a market, investment or speculation by interpreting the data in the context of precedent.

The definition is short, but appears to include most of what is commonly accepted today as technical analysis. If need be the board can amend the definition. It is important to have a definition of technical analysis. It should help the Journal, the CMT accreditation committees and members in deciding on the appropriateness of topics for papers which will be published in fulfillment of accreditation requirements.

Those who read Steve Leuthold’s article in the Summer issue of the Journal, “E.S.C. ‘Sedge’ Coppock and VLT Momentum,” will be interested to know that The Encyclopedia of Stock Market Tech- niques, published by Investors Intelligence, has an article, “Practical Relative Strength Charting,” by Coppock, assisted by Charles Bleser.

If you have input or comments on the articles in the Journal feel free to pass them on.


Moving Averages Revisited Frederic H. Dickson

Overview Over the last ten years products such as Computrac, Technifilter and Technifilter Plus have provided the Technical Analyst with excellent tools to test various technical indicators and trading systems including moving averages of various lengths. In general, tests conducted using the analytical software show that the use of moving averages for market timing produces inconsistent or poor results when compared to a benchmark buy and hold strategy. As a result, many analysts have discarded the moving average.

Results of tests using an analytical approach borrowed from the academic world of quantitative portfolio management, the risk/return scatter diagram and a testing procedure which considers average daily performance over the test period, strongly suggest that moving averages do provide valuable information for purposes of market-timing. The ap- preach presented provides the serious technical analyst with a model which can be used for testing moving averages and other technical tools. This paper strongly suggests that any investment technique must be considered in terms of both risk and return.

Analytical Role of Moving Averages My basic equity investment philosophy revolves

around an assumption that future stock price movements are caused by changes in the market sentiment. Market sentiment is measured by the price/ earnings ratio, changes in earnings expectations for the company and changes in investor sentiment toward the company measured by the price/earnings ratio relative to the market. As a portfolio manager and market technician, my efforts have been spent trying to observe the dynamic interplay between these fundamental and expectational properties by watching prices fluctuate over time. Investors universally agree that skillful market timing improves the price performance from investing in individual stocks.

Since I regard changes in the market price/ earnings ratio as a primary variable which impacts stock prices, I rely on using various technical tools to help monitor both the price and earnings components

of the price/earnings ratio. In particular, I began to use moving averages to identify price trend reversal points at an early point in my career and out of hab- it continued to employ them even as their effectiveness was being seriously challenged by other practi- tioners and serious students of technical analysis.

About ten years ago, computerized software for testing technical analysis strategies became widely available. Programs such as Computrac, Technifilter and Technifilter Plus made possible testing a wide array of technical indicators and trading systems. These programs brought a sense of objectivity to the evaluation process in that they provided a disciplined structure for evaluating a specific tool on a consistent basis with real-life constraints. The programs eliminated the emotional element from the evaluation process by making sure that decision rules were followed precisely without fail.

In general, these programs provided simulation capability for a specific indicator based on a specific start and stop date or a single testing period. In addition, they consider execution costs and delays in buy and sell transactions after a signal. They produced detailed profitability results of the simulation as well as percentage success/failure rates and tests of significance. Applying these tests to tried and true indicators, I discovered (along with many other analysts) that tools such as the moving average by itself performed poorly and probably should be abandoned. However from practical experience, I still believed their use added value even though I did not know how to measure it and sensed that the testing procedures were missing a key aspect of performance.

Are Moving Averages Effective Tools? Shown in Chart One is a graph of the Standard

& Poors 500 Composite Index daily price history between December 31, 1985 and December 31, 1990. Also shown on the graph are two moving averages, 80 days and 200 days. Using this data set, I will present a simulated test of buy/sell rules (consistent with the methods commonly used in the analytical software packages) using these moving averages, and then compare the results to another testing process


r STANDARD AND POORS 500 INDEX

80 AND 200 DAY MOVING AVERAGES

“m

350 -

300 -

250 -

12/31/8! 12m%6 12/29/87 121’27188 12/26/89 12R4190

_ 200 DAY MOVING AVERAGE w 80 DAY MOVING AVERAGE

which evaluates the moving average signals giving equal consideration to risk as well as expected return. The classical testing programs suggest discarding these tools based on the profits generated in a simulation over the time period under consideration. The refined test results, which consider average profitability and risk reduction on an average daily performance basis within the time period under consideration, suggest a different conclusion.

Classical Testing Procedure Daily prices for the S&P 500 Composite Index

between December 31,1985 and December 31,199O were captured from the FACTSET pricing database and entered into a Lotus l-2-3 spreadsheet. Moving averages of various lengths from 20 to 240 days were calculated across the time period. In order to facilitate consistent comparison of the results using moving averages of different lengths of time, a test period beginning December lo,1986 and ending December 31,199O was selected. Simulations for each moving average would begin and end on these dates.

For evaluation purposes, it was assumed that the investor would have followed the system for the entire length of the simulation. A buy signal occurs when the closing price moves above the moving average and a sell signal occurs when the closing price moves below the moving average. Buys would be made at the closing price on the day following a buy signal as indicated by the moving average and execution costs would be assumed to be 0.5%. Sells would be made at the closing price on the day following a sell signal as indicated by the moving average and executions costs would also be assumed to be 0.5%. It is assumed that during periods when the system dictates being out of the market, the cumulative profits are held in a non-interest bearing account.

Profits are calculated for each trade including execution costs and cumulative profits are calculated over the entire simulation period. Comparison would be made between the profits earned from strategies assuming the investor made “long” purchases only, made “short” sales only and was invested either long or short over the entire simulation period. The benchmark would be profits earned from a buy and hold strategy covering the entire time period.

Using this approach, the following table presents the simulation results using moving averages of various lengths. On the basis of these simulated test results, most analysts would probably conclude the use of moving averages of any periodicity for market timing “long” trades would be unproductive. From the array of averages tested, the 160 and 200 day moving averages posted the best results based on profitability. The 200 day moving average was profitable slightly more than 50% of the time (not significant using the Chi Square statistical test of significance) however, underperformed the buy and hold benchmark strategy by more than 10% over the four year test period. The 160 day moving average produced profitable signals only 25% of the time, however, even with this low batting average, it was the most profitable system tested. The results of the test seem convincing. Why use a tool that signiticant- ly underperformed the benchmark and at best was an accurate predictor only 65% of the time?

Chart One

48 Profit- % profit Description able per %Cum HOLD LONG ONLY # Trades Trades Trade Profits

20 DAY hfA 52 44.2% -.43% -22.19%

40 DAY MA 35 48.6% -.18% -6.30%

60 DAY MA 34 41.2% -.15% -4.93%

80 DAY MA 23 65.2% .52% 11.92%

100 DAY MA 21 38.0% .16% 3.43%

120 DAY MA 20 45.0% .24% 4.80%

140 DAY MA 20 40.0% .36% 7.29%

160 DAY MA 12 25.0% 1.74% 20.92%

180 DAY MA 14 42.8% 1.01% 14.20%

200 DAY MA 11 54.5% 1.77% 19.48%

220 DAY MA 15 40.0% 0.43% 6.40%

240 DAY MA 12 25.0% .75% 8.96%

BUY AND HOLD 1 lOO.% 30.98% 30.98% BENCHMARK

Test Results Using a Risk/Reward Framework Many investors look to technical analysis as a

tool to help reduce market timing and stock selection risk. The classical performance test considers in detail the profitability of a technical trading system but fails to address the risk reduction properties which are produced by the technical tool. After


recognizing that trading profits generated using even the optimum 200 day moving average failed to beat the buy and hold strategy by a wide margin, the analyst should not discard the tool without cdn-

sidering whether it is effective in reducing risk. The academic community has developed a

basic model for evaluation of risk and return, the capital asset pricing model. The basis for measuring return is the average daily % profit generated by the asset (or in this case trading system) and the basis for measuring risk is the standard deviation of daily % returns. Even technical analysts agree that increased risk must be compensated by in- cremental expected return. By measuring return using average daily % profit, any bias generated from selecting a specific start and stop date for measuring tests results is minimized. Chart 2 presents a framework which allows comparison of various returns (or technical trading systems) on the basis of risk and reward tradeoffs.

The average daily returns of the buy and hold strategy were 0.35% and the standard deviation (risk) was 1.31% per day and shown on the chart as point BH. By connecting a line starting at the 0.0 point and extending to the point marked BH, the analyst has a benchmark which allows comparison of various strategies to the buy and hold strategy.

If a tested strategy produces results which are plotted above the diagonal line, the strategy has more favorable risk/reward properties than the benchmark. If the results are plotted below the diagonal line, the strategy is inferior to the benchmark on a risk/return basis.

The simulated test results for the various moving averages are plotted on Chart 3. The risk and return statistics for the various moving averages are

Chart 2 RISK/RETURN FRAMEWORK

FOR EVALUATING MA STRATEGIES BENCHMARK IS BUY AND HOLD STRATEGY

-00.5 I 0.M) 0 50 1.00 1.50

RISK-% STD DEV OF DAILY RETURNS


FOR EVALUATING MA STRATEGIES BENCHMARK IS BUY AND HOLD STRATEGY 0.06

0.05 LONG

1

PROFITABLE

z 40 60

a -0.01 - UNPROFITABLE 3 I I

2.0

-0.03 1 I 0.00 0.50 1.00 1.50

RISK-% STD DEV OF DAILY RETURNS


FOR EVALUATING MA STRATEGIES BENCHMARK IS BUY AND HOLD STRATEGY

3 a p 003.

%

B 002

/..

0.00 v I

0.00 0.50

RISK-% STD DEV OF DAiL! RETURNS 1.50

also shown in Appendix A. The 160 and 200 day moving averages produced results which were superior to the buy and hold strategy. Thus, when risk is considered, these strategies are preferable to the buy and hold benchmark. The other moving averages produced results inferior to the buy and hold benchmark. The decision about whether to abandon the 160 and 200 day moving average is no longer so clear cut. These tools produce valuable information when both return and risk reduction is considered. In addition, it should be noted that by using average daily performance as the measurement basis the results are not biased by the selection of a specific start and stop date. The results give a consistent picture of risk and return over the entire test period.

The risk/return framework presented above as- sumes that only “long” trades would be undertaken.


Chart 4 presents the simulated results assuming that both “long” and “short” trades were executed as signalled by the moving averages. This is perhaps the most reliable guage to test the effectiveness of the various moving averages in market timing.

As seen in the Chart 4, seven of the eleven moving averages tested produced risk adjusted results in excess of the buy and hold benchmark. The 80 day moving average was the most profitable trading strategy when applied to both “long” and “short” sales. It should be noted that the improved results were the result of improved profitability as measured by the average daily percent profits, not reduced risk. In fact, the test results suggest little differential in risk regardless of which moving average was employed to generate the trading signals. From this perspective several strategies should be regarded as providing useful information to the analyst involved in market timing.

Conclusion The inferences drawn from the tests presented

above are by no means exhaustive. They are presented as a challenge to the serious student of technical analysis to stimulate reevaluation of moving averages as a working tool and to introduce a testing framework which considers both risk and return. It is easy to jump to an erroneous conclusion by looking at simple tests of significance or cumulative profits over a single simulated period for the test strategy versus the benchmark. If a system provides greater profits with no increase in risk it is clearly superior.

Appendix A Simulation Results-Moving Averages of Differing Lengths

Applied to the Standard & Poors 500 Composite December 1986-December 1990

Description

20 DAY MA

40 DAY MA 60 DAY MA 80 DAY MA

100 DAY MA

120 DAY MA 140 DAY MA

160 DAY MA 180 DAY MA 200 DAY MA

220 DAY MA 240 DAY MA

BUY AND HOLD BENCHMARK

Long + Long Long + Short

Long 96 std. Short 96 std. 46 Daily Dev. of % Daily Dev. of Return Return Return Return

- .021% BOO% .044% 1.397% - .003% .801% .046% 1.395% - .002% .807% .043% 1.398%

.013% .762% .056% 1.394%

.006% .776% .037% 1.397%

.008% .761% .035% 1.398%

.OlO% .773% .034% 1.403%

.021% .756% .044% 1.399%

.016% .752% .039% 1.400% .0200/c .747% .042% 1.400% .020% .753% .023% 1.404% .Oll% .761% .024% 1.401%

.035% 1.354% .0350/o 1.354%

Personal preference may lead an individual to choose a system which generates greater return at a higher risk or a lesser return at reduced risk.

r Frederic H. Dickson is a founder and Managing Direc- tor of TDA Capital Manngement Company, Westport, CT Fred is apast President of the MTA and has previously contributed several articles to the MTA Journal on vwioz~~ subjects. As Chairman of the Education Commit- tee, Fred was involved in thepreparation ofthe original CMT Part I examination in 1988 and currently serves on the Editorial Board of the M!l’A Journal.

L


GAUGING INVESTOR SENTIMENT Ginger Kock

Overview The mutual funds’ cash ratio attempts to give an indication of institutions’ short-term ability to invest in the stock market. Also regarded as a sentiment indicator, this ratio can gauge whether fund managers are scared or greedy by virtue of their liquidity level. In 1981, a study was released which casts doubt on using this ratio to predict changes in stock prices. In this paper, I will bring the 1981 study up to date and will determine if my conclusions confirm those reached previously. In addition, I will question the validity of the analytical approach used for part of the 1981 study and show that a more feasible approach can be taken.

Market Indicators For years stock market technicians have

sought simple and useful indicators to indicate whether the market was too high or too low, thereby signalling an impending trend reversal. Their numerous studies have examined the relationship between indicators and stock prices to assist them in strategic investment decisions. One group of such indicators monitors investor sentiment. Notable among these indicators are the mutual funds’ cash ratio, the short interest ratio, and the odd-lot ratio.

One sentiment indicator useful at market bot- toms, once extremely popular, is somewhat neg- lected today: the odd-lot ratio. It monitors small investors’ trading activity through the percentage of odd-lot sales to odd-lot purchases. According to conventional wisdom, odd-lotters are the most consistently incorrect of all market spectators, and thus they represent something one could go contrary to. Technicians believe odd-lotters’ increased selling shows pessimistic sentiment and marks a time to buy stocks. Garfield A. Drew was the most advent supporter of the Odd-Lot Theory. After exam- ining yearly data of stock transactions of less than loo-share lots, Drew concluded that “the public-although not necessarily ‘wrong’ in the end- does tend to become less correct in its actions just before the market embarks on an important change in trend.“’ Further, and more importantly, he hypo-

thesized that changes in odd-lot trading reflect changes in market sentiment among small investors.

Unfortunately, in recent years, the odd-lot ratio has lost much of its usefulness, because small investors no longer trade as much in odd-lots. With other investment alternatives available in the market, these investors are now able to turn to mutual funds, options, futures and even money market funds as vehicles in which to place their funds in anticipa- tion of market moves.

We are obligated to find other ways to measure market sentiment and coincidentally potential market demand, because when money is on the side, ifsen- timent changes in favor of the market, then these un- invested funds may return to the market. In this study I will examine one of the ways to measure this demand: institutional cash levels and what they may say about these managers’ collective mindset. As we shall see, by studying the data, it is clear that when fund managers have been convinced to hold large amounts of cash-thereby signalling bearish sentiment-it has been a good time to be fully invested, and vice versa.

1981 Study In 1981 Ranson and Shipman released a study

(see MTA Journal, August 1989) in which they tried to determine whether a relationship exists between stock prices and the cash-asset ratio of equity mutual funds. They calculated the cash-asset ratio from 1967 to 1978 by dividing funds2 liquid assets by total assets, and tested this ratio against the Standard & Poor’s 500 index for the time period.

Ranson and Shipman presumed-and logic argues-that the cash-asset ratio would be low at market troughs and high at market peaks, because fund managers theoretically would be fully invested at times prior to upswings and lightly invested at times when the market is about to decline. This theory makes sense on paper, but their study in fact showed quite the opposite: “the cash-asset ratio tends to be low at market peaks and high at market troughs,“3 as any technician will tell you.

The study noted two different considerations to account for the cash-asset ratio’s divergence. First,


fund managers were likened to our old odd-lotters, the difference between the change in the cash posi- in that they too can’t time the market right. Second, tion associated with the S&P change and the change the raw liquid asset figures were thought to be one in total assets associated with the same S&P of the prime culprits uficting stock price movement. change.“5 By breaking out the ratio’s parts, the When managers carry low cash levels, there are no authors’ study showed that the percentage changes excess funds to put into the stock market. Since the of the raw cash position had no correlation whatever market can not rise without buying, this would limit with the S&P 500 (R-squared .087), the percentage the upside and possibly result in a market top. Both changes of the raw total assets position had an over- explanations were disregarded by the authors of the whelmingly positive correlation with the S&P 500 study. “In the first case, it is just as difficult to be (R-squared .957), and the cash-asset ratio had an consistently wrong at market turning points as it overall negative correlation (- 97) with the S&P 500. is to be consistently right. And, with respect to the The percentage changes of the cash position did not second, changes in buying power per se do not nec- explain any significant fraction of the changes in essarily imply changes in investors’ perceptions.“’ stock prices, while the percentage changes of the

A third and more viable alternative presented total assets position did. by Ranson and Shipman concerns the correlations The 1981 study concluded that “the negative between changes in the cash-asset ratio’s numerator correlation between changes in the cash-asset ratio (liquid assets) and denominator (total assets), and and changes in the S&P 500 is fully accounted for by changes in stock prices. In order to explain the cash- the almost tautologous relation between total assets asset ratio’s components, “the equation states that and the market index.“6 In other words, the assets’ the change in the cash-asset ratio that corresponds tigure is so large, it is the functional equivalent of the to a given percentage change in the S&P 500 equals market. Thus you are in essence using the market as

LIQUID ASSET RATIO VS S&P 500 Exhibit 1

S&P 500 LIQUID ASSET RATIO

r 6%

0 llllllll”llllll~llllillllllllllllllillllllllillllllllilillllllllllllllillllllliilllllllllll~l’llll”l’lllllllll II 1” “’ “I ‘1”

82 83 84 85 86 87" 88 ‘I 89 90

~ 0% ,I,,,:, ,,, .,

79 80 81

YEAR

- LIQ ASSET + S&P 500

Source: Investment Company Institute

14 MTA JOURNAL/SPRING 1991

an indicator to track the market, a tautology. Prom this, Ranson and Shipman deduced that the liquid asset ratio could not be proven as a reliable indicator of market movement.

However, there are two important additional influences on cash levels other than sentiment: (1) the existence of more attractive high yield investments available during the time period; (2) the need for high cash reserves to meet net redemptions during bear markets. The cash (liquid assets) position of mutual funds includes its cash, receivables, government securities and other short-term debt instruments, less its current liabilities. In the 1960- 1978 time frame, interest rates progressively rose from the 2-4% level in 1960-1964 to the 59% level in 1966-1970 and finally to the 9-12% level in 1973-1974, before backing down to the 4-6% level in 1976-1977. After the study period in 1978, interest rates ranged from 5% in 1986 to 17% in 1981. With short-term instruments providing investment returns of this caliber, fund managers would have been correct in holding more cash than normal to

obtain the higher yields, instead of investing these funds in equities. In addition, huge net redemptions of equity funds during bear markets (such as in 1962, 1966, 1970, and 1974) required fund managers to have cash on hand to meet these commitments. As a result, the cash position could have been distorted.

1990 Study I have brought Ranson and Shipman’s 1981

study up to date through the 1979-1990 time period to determine whether their results still hold. Using monthly data, I constructed Exhibit I which shows the liquid asset ratio tracked against the S&P 500. As one can see, the cash-asset ratio appears inverted to the market index; a pattern consistent to that found in the 1967-1978 time period. A regression analysis of the data shows that the percentage changes of the raw cash asset position (Exhibit 2) have effectively no correlation with the S&P 500, but the percentage changes of the raw total assets position (E&bit 3) have an extremely high positive correlation with the S&P 500, and the cash-asset ratio

% CHANGE IN CASH VS % CHANGE S&P 500 JANUARY 1979 - AUGUST 1990

Exhibit 2

I

-20% ! I I I I I I

-25% -20% -15% -10% -5% 0% 5% 10% 15% S&P 500

-1


% CHANGE ASSETS VS % CHANGE S&P 500 JANUARY 1979 - AUGUST 1990

Exhibit 3

ASSETS 2 0 %

-30% I I I

-25% -20% -15% -10% -5% 0% 5% 10% 15% S&P 500

has a high negative correlation with the S&P 500. correlated with the market index. Therefore, the Clearly, the percentage changes of the cash position ratio in this time period continues to be suspect, be- (R-squared .164) still do not significantly explain cause the numerator explains nothing of the S&P the changes in the S&P 500, while the percentage 500, yet its denominator does. changes of the total assets position (R-squared .913) Although the commercial paper method showed continue to do so. From this data, my analysis recon- alternative investments did not seem to entice fund firms the conclusions derived by Ranson and Ship- managers, one can hypothesize that these invest- man in 1981. ments may have a greater effect when they are at

In pursuing whether sensitivity existed in the extremes. Logically, when rates are astronomical (at data, I invoked three methods to alter the data for 20-25%), it would be foolish for fund managers not the time horizon. First, I adjusted the raw cash and to capture these yields for brief periods, as they total asset figures by three-month lead and lag times would find it difficult to accomplish the same returns to see if fund managers anticipated or reacted to in the equity market. These periods would not ef- market information. Second, I adjusted the raw cash feet the overall correlation figures in any meaningful and total asset figures for net cash flows, i.e. cash way. In the 1979-1990 time frame, interest rates rose flows in minus cash flows out. Third, I adjusted the from the 9-11% level in 1979 to peak at the 15-17% raw liquid asset ratio figures for commercial paper level in 1980-1981; before dropping to the 9-12% level rates to see how attractive alternative investments in 1983-1984, falling further to the 5-8% level in were to fund managers. Under all three scenarios, 1986-1987, and settling in at the 6-9% level in 1988- the percentage changes of the cash position still had 1989. At the end of the period in 1990, interest rates no correlation with the S&P 500, while the percent- were hovering around the 8% range. (See A Final age changes of the assets position were again highly Thought.)


RAW CASH FIGURES VS RAW S&P 500 JANUARY 1979 - AUGUST 1990

Exhibit 4

Cash (billions) 35

0

0 100 200 S&P 500

-1

300 400

RAW ASSET FIGURES VS RAW S&P 500 JANUARY 1979 - AUGUST 1990

Exhibit 5

Assets (billions) 300

0

0 100 200 S&P 500

300 400


An Argument Over Approach While I have validated the results of the 1981

study, I question whether its authors in fact used the correct method to test the data. As mentioned earlier, Ranson and Shipman focused on the percentage changes of the cash and total assets positions in their analysis, thereby suggesting that a causal relationship exists between a change in each position and a change in the S&P 500. It is my opinion that the authors chose the wrong statistical test on which to base their analysis for this part of the study. The analysis above clearly shows that percentage changes of the cash position have no eftrect on or correlation with the market.

I believe Ranson and Shipman should have used the raw figures themselves-not the percentage changes-of the cash and total asset positions and their correlations with the S&P 500. My tests show that technicians are correct to be more concerned with fund managers’ cash levels, not changes in their cash levels, in using this indicator to assess market sentiment and predict market direction.

With further regression analyses of the data, I determined that the raw cash position (R-squared .957) now significantly explains the S&P 500, and the raw total asset position (R-squared .987) continues to, naturally. Additionally, I altered the data with the three methods used above, finding that correlations of adjusted data did not significantly improve the correlations of unadjusted data.

My results can be seen in Exhibits 4 and 5. Ex- hibit 4 shows a scatter diagram of the raw cash figures plotted against the raw S&P 500 figures. The points are clearly clustered, demonstrating the two variables have a much better fit than before and that the raw cash figures do in fact correlate with the S&P 500 (compare with Exhibit 2). Exhibit 5 shows a scatter diagram of the raw total asset figures plotted against the S&P500. Again, the points show a cluster formation with an even tighter tit than in Exhibit 3. The raw total asset figures clearly explain movements in the S&P 500 to a significant degree, for the obvious reasons discussed above.

Conclusions When Ranson and Shipman released their

study in 1981, they stipulated that “information con- cerning the deployment of (mutual funds’) assets is of little value in forecasting stock price changes.“’ It created quite a stir among stock market technicians, as many had given great emphasis to the mutual funds’ cash ratio.

By updating the 1981 study to the present, several conclusions remain: the denominator of the liquid asset ratio (total assets) is so large it drags the en-

tire ratio into correlation, no matter what the cash figures might be. Despite this distortion, I believe the liquid asset ratio continues to be a valid coincident indicator. Observations of the data show that fund managers have been consistently wrong in their market timing. Knowledge of this behavior pattern can be useful to analysts. Perhaps the fund managers of today are the odd-lotters of the past; in any case, one would surely be well advised to go contrary to them.

A Final Thought While I have identified a more valid method of

studying this data, at best I can only show it is a coincident indicator because no improvement was gained by advancing the data. Analysts have found that monitoring extremes in this ratio have produced profitable future investment results. This involves not correlation analysis, but threshold analysis (i.e., above one benchmark is bullish and below another bearish etc.). Perhaps a future study will consider this aspect in greater detail.

FOOTNOTES

1. Garfield A. Drew, “A Clarification of the Odd Lot Theory,” Financial Analysts Journal, Vol. 23 (September-October 1967), p. 107. 2. R. David Ranson and William G. Shipmen, “Institutional Buying Power and the Stock Market,” Financial Analysts Journal, Vol. 37 (September-October 1981), pp. 62-68. 3. Ibid, p. 63. 4. Ibid, p. 63. 5. Ibid, pp. 64-65. 6. Ibid, p. 65. 7. Ibid, p. 62.

BIBLIOGRAPHY Books

Edwards, Robert D. and John Magea Technical Analysis ofStack Trends Boston: John Magee Inc., 1966. Fogler, H. Russell. Analyzing the Stack Market: Statistical Euia’ence and Methodology. Columbus: Grid Inc, 1978. Hardy, C. Colbum. The Investor’s Guide to Technical Analysis New York: McGraw Hill Inc., 1978. Lorie, James H., Peter Dodd and Mary Hamilton Kimpton. The Stack Market: Theories and Evidence Homewood: Richard D. Irwin Inc, 1985. Articles

Drew, Garfield A. “A Clarification of the Odd Lot Theory.” Financial Analysts Journal Vol. 23 (September-October 1967): pp. 107-108. Gup, Benton E. “A Note on Stock Market Indicators and Stock Prices.” Journal ofFinancial and Quantitative Analysis Vol. VIII (September 1973): pp. 673-682. Kewley, Thomas J. and Richard A. Stevenson. “The Odd-Lot Theory as Revealed by Purchases and Sale Statistics for Individual Stocks.” Finon- cial Analysts JournalVol. 23 (September-October 1967): pp. 103-106. Ranson, R. David and William G. Shipman. “Institutional Buying Power and the Stock Market!’ Financial Analysts Journal Vol. 37 (September- October 1981): pp. 6268.

Slat&, John. “New Market Guide?’ Barron’s(February 6,1967): p. 5.

Ginger Kock is a second-year student at the Darden Gradu- ateSchaolofBusinessAdministrationin Charlottesville, VA. Ginger will graduate in May 1991 after which she plans to

ment. Ginger wrote this article for her Supervised Business Study with the cooperation ofJohn R. McGinleyof Wiltan, CT


Share Repurchase Announcements: 19854989 G. Gernon Brown III

Introduction and Methodology Between 1984 and 1990 the supply of common stock decreased about $100 billion, largely due to companies repurchasing their own shares. Amidst ar- guments about the wisdom of repurchases-about whether buybacks come at the expense of future growth (suggesting that companies should preserve equity), about whether buybacks offer a cheap way to boost per-share earnings, even about the psycho- logical value of announcing a share repurchase that will not in fact be completed-several interesting and practical questions arise: What is the effect of share repurchase announcements (and of actual share repurchases) on the stock price of individual companies? Does the stock of these companies, on average, outperform the S&P 500 in the year following the share repurchase announcement? More specifically, of the companies announcing repurchases, why do those shares that produce excess returns do so? Is such performance linked to the amount to be repurchased, to the actual reduction in outstanding shares, to the earnings trend, even to the time of year the repurchase is announced?

To answer these questions, I limited my study to share repurchases announced between January 1985 and February 1989, the latter bound enforced so that I could examine a full year of performance following the announcement. In addition, each company and each share repurchase announcement used in the study met certain criteria. First, the market capitalization of each company exceeded $1 billion at the time of the share repurchase announcement. To impose this criterion, I screened the 12,000 companies in the Lotus One Source database, finding 555 companies of greater than a billion dollars in market value. An alphabetical list of these companies served later as a reference source.

Just as important, share repurchase announcements included in the study appeared as discrete items in the Wall Street Journal and were, as often as possible, “clean” common stock buyback annotmce- ments unencumbered by additional news or restric- tions. Buyback announcements omitted, for example,

ranged from those addressing only odd-lot share- holders to those involving only one shareholder or family to share repurchase announcements accom- panied by news that the company would be selling off businesses-that is, those buybacks publicly announced to be only part of what is often termed a “massive restructuring plan.”

To find “clean” buyback announcements, I used the CD-based UMVINFORM database of newspaper abstracts, restricting my search to items appearing in the Wall Street Journal. Listed below is the total number of items retrieved each year for 1985-1989:

1985: 236 items 1986: 264 items 1987: 321 items 1988: 224 items 1989: 235 items

By noting the company mentioned in each item and using the market capitalization list, I determined whether the company’s market value exceeded $1 billion. If the company met the market value test, I then read the abstract of the item to determine the exact nature of the repurchase. A further criterion required that the company still exist in the same form. (Hence, I discarded Time, Inc, now Time-Warner, and Smithkline- Beckman, now Smithkline-Beecham.) Finally, I eliminated share repurchase announcements followed less than one year later by another repurchase announcement.

The above search resulted in 78 share repurchase announcements involving 66 companies. As I hoped would be the case, the 66 companies represented a diversity of industries.

The sample of share buyback announcements, stretching from March 1985 to February 1989, proved to be diversified over time as well. The specific nature of this diversity manifests itself when we overlay onto a time line each of the 78 twelve-month periods following the share repurchase announcements.

MTA JOURNAL/SPRING 1991 19

Monthly Intensity of Sample

Month Total

3185 1 4185 3 5185 4 6185 6 7185 7 8185 8 9185 8

10185 9 11185 11 12185 13

1186 15 2186 17 3186 16 4186 15 5186 15 6186 14 7186 15 8186 18 9186 18

10186 18 1 l/86 18 12186 17

II87 15 2187 13 3187 15 4187 14 5187 13 6187 13 7187 11 8187 8

Month Total

9187 10 10187 10 11187 14 12187 18

II88 18 2188 21 3t88 20 4188 22 5188 24 6188 27 7188 27 8188 27 9188 28

10188 28 11188 24 12188 24

l/89 24 2189 26 3189 26 4189 24 5189 22 6/89 18 7189 18 8189 17 9189 14

10189 13 11189 11 12189 6

1190 6 2190 1

Of the 936 (78 x 12) “sample months,” no more than 3% fall in any one of the 60 calendar months from March 1985 to February 1990; the average number of sample months per calendar month is 15.6. Fur- ther diversity in the 78 buybacks included company stock betas ranging from .60 to 1.70; split and unsplit shares; and both rising and falling earnings trends both before and after the buyback announcement.

To compute excess returns, I first accessed through Lotus One Source the Compustat database of daily closing prices for the five-year period between March 1985 and February 1990. By subtract- ing each day’s S&P 500 return from an individual stock’s return, I derived that stock’s daily excess return-that is, the daily return above that of the S&P 500. A negative excess return implied a return lower than the S&P 500’s. To diversify away the possible effects of seasonality and the individual cir- cumstances of each company, I then “stacked” the 78 buyback periods upon one another, from Day -l-the day before the buyback announcement appeared in the Wall Street Journal (on Day 0) and the

probable day the share repurchase announcement was released on the wire services-to Day 250 one year later.

For an index I used the S&P 500 to obtain a broadly based standard against which to compare each stock’s return. Despite the larger average size of the 30 companies that constitute the Dow Jones Industrial Average, the DJIA seemed too narrow an index and, because it is price-weighted, less true a measure of market performance. Moreover, by re- gressing the S&P 500’s daily return to that of the DJIA over the entire five-year period of the study, I derived a greater than 99% correlation between the two indexes. (As one would expect, however, during shorter periods of time one index often outperformed the other.)

General Results After computing daily excess returns for each of

the 78 buybacks, I then averaged the excess returns for each day from Day - 1 to Day 250. E&bit1 graphs these excess returns on a noncumulative basis. While these returns appear essentially random for much of the one-year period-there are, for example, both many positive and many negative excess returns, as well as positive and negative spikes-salient aspects of these returns do reveal themselves. Most notewor- thy (but not surprising) are the huge excess returns at the time of the announcement on Day - 1 and Day O-1.36% and .65% respectively. Day -1’s 1.36% excess return, the largest one-day excess return in the one-year period, confirms that news of a forthcoming repurchase becomes public the day before an item appears in the Wall Street Journal. Note also the greater number of positive excess returns than negative- namely, 150 positive versus 102 negative-and the many clusters, or streaks, of positive returns, especially in the first few months. Finally, at the very end of the one-year period, note the preponderance of strongly positive excess returns.

By then cumulating these average excess returns, beginning at Day -1, we can observe that on average, for the 78 buybacks in this study, there was indeed an excess return in the year following the share repurchase announcement. Exhibit 2 depicts graphically these cumulative excess returns, while the figures below note the cumulative excess return at points during the one-year period.

Cumulative Average Excess Returns Days - 1 + 0 (“announcement day”) 2.02% Day 5 (one week) . . . . . . . . . . . . . . . . 1.96% Day 20 (one month) . . . . . . . . . . . . . . 1.71% Day 62 (three months). . . . . . . . . . . . 3.90% Day 125 (six months) . . . . . . . . . . . . 5.15% Day 250 (one year). . . . . . . . . . . . . . . 6.80%

20 MTA JOURNAL /SPRING 1991

Exhibit 1

NON-CUMULATIVE AVERAGE EXCESS RETURNS (vs. s & P 500)

1.40% ,

1.30%

1.20%

1.10%

1 .OO%

0.90%

0.80%

0.70%

0.60%

0.50% I

0.40%

0.30%

0.20%

0.10%

0.00%

-0.10%

II’ll I ‘” -0.20%

-0.30%

-0.40%

-0.50%

-0.60%

-1 20 41 62 83 104 125 146 167 188 209 2x)

7.00%

6.00%

3.00%

2.00%

1 .cm%

0.00%

Day Relative to Announcement

Exhibit 2

CUMULATIVE AVERAGE EXCESS RETURNS (vs. S&P 500)

-1 20 41 62 83 104 125 146 167 188 209 230

Day Relative to Announcement


The graph of the cumulative average excess returns makes clear the pattern during the year following the repurchase announcement: First, the immediate excess returns of the announcement day period abate somewhat in the weeks following the announcement, with the minimum cumulative excess return occurring on Day 12 (1.24%). A strongly rising trend describes the ensuing months, with a peak just past the six-month point. After falling slightly, the amount of cumulative excess return rises just before the nine-month point and then again, strongly, before the one-year point. The maximum cumulative average excess return, in fact, occurs on Day 249 (6.94).

Percentage to Be Repurchased While the stock performance of companies an-

nouncing share repurchases exceeded that of the S&P 500-on average-for the year following the buyback announcement, the performance of individual companies’ stock varied widely. To understand better the reasons for this variability, I ranked and grouped the 78 buybacks in the study according to different criteria that I believed might affect performance. In having done so, however, I readily ac- knowledge the dangers that lie in drawing conclusions from an even smaller sample of companies.

The first criterion applied to the 78 share repurchases was the percentage of stock to be repurchased. The actual percentage used for each buyback was either that given in the Wall Street Journal item (whose accuracy I checked) or a figure derived from other information provided such as the number of shares to be repurchased or their current market value. When a range was given for the number of shares to be repurchased, I used the midpoint of the range. Two additional aspects of share repurchase announcements are important to note here. First, announcements are often phrased in terms of repurchasing not a definite amount but “as many as” a certain number of shares or “as much as” a certain dollar amount. Second, the period during which the repurchase is to take place varies from a few months to a few years. For the repurchase announcements used in this study, the typical wording suggested that the company would ‘during the next year” or “from time to time” repurchase shares “on the open market or in private transactions.” Such equivoca- tion, in both cases, I accepted as being a matter less of substance than of form.

Exhibit 3 lists the 78 buybacks and the percentage of common stock the company announced would be repurchased. Note that one company in the study, Dow Jones & Co., did not know at the time of its announcement the percentage of stock to be repur-

chased. Note as well that for the buybacks in this study the average percentage of stock to be repurchased is 7.1%, the median 6.0%.

To explore whether stock performance related to the percentage of stock to be repurchased, I grouped the buybacks into five quintiles determined by the percentage of shares to be repurchased. The table below gives the average figures for each quintile:

Percentage to Be Repurchased Excess Returns

Range Average Days -l+O Day 250

Ql LO-3.4% 2.2% .67% 8.70%

Q2 3.6-5.0% 4.2% 1.01% 4.58%

Q3 5.0-7.0% 5.8% 2.75% 3.87%

Q4 7.0-9.3% 8.2% 3.24% 6.60%

Q5 9.4-37.0% 15.0% 2.64% 8.87%

Using the average figures for each quintile, one ob- serves a modest correlation between the percentage of shares to be repurchased and the excess return during the announcement day period of Days - 1 and O-although no such correlation exists with the one- year performance. An examination of the individual stocks’ excess returns in each of the five quintiles reveals well-above-average announcement day excess returns-greater than 4%, say-in quintiles 3,4, and 5 and an absence of such large excess returns in quintiles 1 and 2. As one might expect, then, the average excess return for the announcement day period in quintiles 3,4, and 5 is above the average of 2.02% for the entire group of 78 buybacks. Interestingly, the number of negative excess returns for Days - 1 and O-the frequency of underperformance during the announcement day period, that is-is exactly the same for quintiles 1-4 and only slightly less for quintile 5.

It is important to emphasize that the modest correlation suggested above between the percentage of stock to be repurchased and announcement day performance holds only when average figures for each quintile are used. No such correlation exists when individual percentages are regressed against individual excess returns.

Actual Reduction in Outstanding Shares Awaiting an answer as a natural extension of

the investigation above was the question of whether the actual amount of stock a company repurchased in the year following a buyback announcement correlated with its performance for that year. Also, did the stock of companies that had actually repurchased the announced percentage one year after the announcement outperform other stocks in the study? Unfortunately, because the number of shares actual-


Exhibit 3 SHARE REPURCHASE ANNOUNCEMENTS Household Intl. HI2 871103 6.0%

(In Order of Percent to be Repurchased) Salomon, Inc. SB 880609 6.1%

Dow Chemical DOW2 870612 1.0% Cap. Cities/ABC CCB 880523 6.2% Abbott Labs ABT2 881212 1.3% Raytheon RTN 861023 6.5% Dow Chemical DOW1 850322 1.3% Westinghouse Elec. WX 860731 6.5% Intl. Bus. Mach. IBM1 860528 1.6% Unisys UIS 871215 6.7%

Kellogg K 880328 1.6% Automatic Data Proc. AUD 881107 7.0%

Minn. Mining & Mar&. MMMl 860620 1.7% Syntex SYN 890126 7.0%

General Mills GIS 860919 2.0% Schlumberger SLBl 871210 7.2% Coastal Corp. CGP 871020 2.2% Ralston Purina RAL 881212 7.4% Digital Equip. Corp DECP 880119 2.3% Rockwell Intl ROK 860318 7.4% Pacific Telesis PAC 881212 2.4% Apple Computer AAPL 860722 7.6% Merck MRKl 850807 2.5% Union Carbide UK 871023 7.6%

Quaker Oats OAT 880202 2.5% United Tech UTX 860204 8.1%

Archer-Daniels-Midland ADM 851111 2.9% DuPont DD 890126 8.3% Intl. Bus. Mach. IBM2 880928 3.0% K-Mart KM 871125 8.7%

American Home Prod. AHPl 860701 3.3% Sun Co. SUN 850308 8.8%

American Home Prod. AI-B’2 870828 3.4% Teledyne TDY 881031 8.8%

Johnson & Johnson JNJ 880614 3.6% Dana Corp. DCN 851119 9.0% First Union FTU 880420 3.7% Halliburton HAL 851122 9.2% Genuine Parts GPC 850401 3.7% American Cyanamid ACY 850531 9.3%

Digital Equip. Corp. DECl 861107 3.9% Schering-Plough SGP 860129 9.3% Merck MRK2 870729 3.9% May Dept. Stores MA 880902 9.4% MCA MCA 860806 4.0% Golden West Fin. GDW 871204 9.6%

Schlumberger SLB2 890127 4.0% Federal Express FDX 880607 10.0% Wells Fargo WFC 871119 4.1% Ford Motor F2 871113 10.1%

Minn. Mining & Manuf. MMM2 881116 4.4% Times Mirror TMC 850701 10.4%

Amer. Express AXP 860429 4.5% Ford Motor Fl 851115 10.5% Union Pacific UNP 850531 4.5% Penney, J.C. JCP 880831 11.0% Merrill Lynch MERl 870224 4.7% Tandy TAN 890130 11.0%

General Public Util. GPU 880205 4.8% CIGNA CI 890223 12.0%

Snap-On Tools SNA 880830 4.8% Dayton-Hudson DH 871022 15.4% Abbott Labs ABTl 851216 5.0% Allied Signal ALD 850930 16.0% Kerr-McGee KMG 850509 5.0% Hilton Hotels HLT 871020 16.0%

Merrill Lynch MER2 881206 5.0% Georgia Pacific GP 880330 19.0%

Nynex NYN 870918 5.0% General Motors GM 870304 20.0% Seagram VO 870909 5.0% Household Intl HI1 860115 22.0%

Dow Chemical DOW3 880803 5.3% Polaroid PRD 890131 37.0%

MCI Telecomm. MCIC 861203 5.3% State St. Boston Corp. STBK 8805 13 5.4% * (Not included: Dow Jones & Co.; DJ, 860724; GEICO GEC 880303 6.0% % unknown to company at time of announcement)

ly repurchased during a given one-year buyback no change or an increase in outstanding shares. period is difficult to obtain (the annual report, for Moreover, the average one-year excess return for the example, includes only the number repurchased dur- 17 buybacks with either no change or an increase ing the fiscal year), I was forced to use as a proxy in outstanding shares was 11.02%-significantly the actual change in outstanding shares. higher than the 7.71% average one-year excess re-

An examination of these data provides clear return for the 19 buybacks with greater than a 5% sults-namely, that for the buybacks in this study reduction in outstanding shares. there exists no correlation between the actual reduc- In addition, for only 19 buybacks did the action in common shares and one-year performance tual reduction in common shares equal or exceed relative to that of the S&P 500. This conclusion holds 90% of the announced buyback percentage (which true even when one omits the buybacks with either for these 19 ranged from 1% to 22%, with an average


of 6.3). The average one-year excess return for this group-6.75-proved virtually identical to the average excess return for the entire group of 78 buybacks. Interestingly, only a small correlation was found between the announced buyback percentage and the actual reduction in common shares. Even when buybacks with no change or an increase in outstanding shares are omitted, this correlation is best described as modest.

Earnings Trends Accepting the natural bias toward rising ear-

nings but wanting to examine the relationship between earnings trends and performance following a buyback announcement, I divided the study’s 78 buybacks into four groups: those with rising earnings both prior to and during the buyback period; those with falling earnings prior and rising during; those with rising earnings prior and falling during; and those with falling earnings both prior to and during the buyback period. To obtain earnings trends, from the O’NeiZ Database volumes I noted the quarterly earnings percentage changes and the slope of each company’s earnings line. Virtually flat earnings I classified as falling, and earnings at the end of the one-year buyback period weighed more heavily in determining the trend during that buyback period than those at the beginning.

Listed in the table below are the number of buybacks in each of the four earnings trends groups:

Earnings Trends

(A) Rising before, rising during: 43 (B) Falling before, rising during: 15 (C) Rising before, falling during: 10 (D) Falling before, falling during: 10

By combining the appropriate groups, one then arrives at the following figures:

Total, rising before: 53 Total, falling before: 25

Total, rising during: 58 Total, falling during: 20

The relatively few buybacks in groups B, C, and D and the admittedly crude categorization suggest that one must be cautious in drawing conclusions. Fur- thermore, within each group-as is the case throughout most of this study-there exists huge variability in performance. Finally, it is important to remember that I did not consider earnings relative to expectations but only the absolute trend of earnings.

The table below lists-by earnings trend group- the average figures for the announced percentage of stock to be repurchased and the excess returns:

Earnings Trend Group Performance

Earnings Percent Cumulative Excess Returns Trend to be Group Repurch. Days -l+O Day 250

t-4) 5.7% 1.82% 9.14%

03) 11.6% 1.25% 9.09%

(C) 6.5% 1.93% -6.53% CD) 7.3% 4.07% 6.62%

In the main, the results are what one would expect. Those buyback announcements preceded by falling earnings (groups B and D) were characterized by a larger percentage of shares to be repurchased- 9.84% on average-than those preceded by rising earnings (groups A and C), which averaged a 5.82% announced buyback. Also as expected was the superior performance of the 58 buybacks in groups A and B with rising earnings following the buyback announcement: These buybacks averaged a 9.13% one- year excess return. Interestingly, the 20 buybacks with falling earnings following the buyback announcement (groups C and D combined) achieved, on average, exactly the market return and did not underperform the market.

Seasonality To determine whether performance differed ac-

cording to the time of year a buyback was announced, I grouped the 78 buybacks by quarter (based on the date of the Wall Street Journal item announcing the planned buyback). The table below summarizes the results:

Average Cumulative Excess Returns by Quarter

QtG X Days -l+O Day 5 Day 20 Day 62 Day 125 Day 250 1 20 3.13% 3.54% 2.16% 2.42% 2.20% 1.24% 2 14 1.14% .57% -.280/c 3.20% 4.62% 2.31% 3 18 1.98% 1.58% 1.44% 2.24% 2.27% 5.56% 4 26 1.66% 1.77% 2.15% 6.57% 9.70% 14.35%

Note that the 34 buybacks in the first and second quarters-on average-performed significantly less well than the average for all 78 buybacks (although they still outperformed the S&P 500), and that the 26 fourth-quarter buybacks achieved more than double the 6.80% average excess return for all 78 buybacks.

A closer look at the data reveals the following about the first- and fourth-quarter extremes: that the average beta for the buybacks in these two quarters is exactly the same; that both quarters comprise a variety of earnings trends; that the percentage of stock to be repurchased is actually higher on average for first-quarter buybacks; that the excess returns for the individual buybacks in each quarter vary widely; that the probability of outperforming the S&P 500 is only 52% for first-quarter buybacks but


77% for fourth-quarter buybacks; and that the 26 fourth-quarter buybacks include 11 from the months following the crash (9 of which achieved significant one-year excess returns). Omitting the 1987 fourth- quarter buybacks reduces the average excess return for this group to 9.&!?still much higher than that of the other three quarters.

The Crash The extraordinary performance of the 1987

fourth-quarter buybacks raises the question of how these immediately post-crash buybacks affected the study’s overall results. By omitting these 11 buybacks from the study’s original 78, the average cumulative excess returns are as follows:

Average Cumulative Excess Returns (Fourth Quarter 1987 Buybacks Omitted)

Days -l+O Day 5 Day 20 Day 62 Day 125 Day 250 2.35% 2.10% 1.57% 2.89% 3.34% 4.48%

(all) 2.02% 1.96% 1.71% 3.90% 5.15% 6.80%

As is clear, while the announcement-day period and one-week returns are slightly higher with the fourth- quarter 1987 buybacks omitted, the more important one-year excess return is about one-third lower.

Another interesting question is how the buybacks whose one-year performance period was interrupted by the October 1987 crash fared versus those whose performance periods either entirely preceded the crash or began more than a few months after the crash. To answer this question, I arranged the 78 buybacks chronologically and then divided them into four groups. Listed below for each group are, first, the time period encompassed (measured from the announcement of the first buyback in a group to the end of the last’s one-year performance period); second, the S&P 500’s performance during the period; and third, the cumulative average excess returns. Note that the time periods necessarily overlap.

(1) PRE-CRASH (March ‘85September ‘87) S&P 500 up 78%

(2) CRASH-INTERRUPTED (October ‘86- September ‘88)

S&P 500 up 16% (3) IMMEDIATELY POST-CRASH (October ‘87-

December ‘88) S&P 500 up 12%

(4) POST-CRASH (January ‘88-February ‘90) S&P 500 up 34%

Cumulative Average Excess Returns Days -l+O Day 5 Day 20 Day 62 Day 125 Day 250

(1) 2.62% 2.52% 55% 1.21% 2.44% 6.43%

(2) 1.60% .99% .95% 2.08% 3.62% 6.16%

(3) -.04% 1.10% 2.51% 10.03% 16.16% 20.90%

(4) 2.36% 2.11% 2.70% 4.68% 4.07% 2.18%

As shown, groups 1 and 2 achieved one-year excess returns just slightly below the average of 6.80% for the entire study, while groups 3 and 4 significantly outperformed and underperformed, respectively, the average one-year excess return for the study. Especially telling is the strong performance of the group 3 stocks. While some concern accompanies any conclusions about the performance of groups 2 and 3 due to the small sample size-10 and 11 buybacks-two relevant points must be noted: 1) Both group 2 and group 3 include a diversity of industries, and 2) These industries during the relevant time period did not outperform the market, implying that the outstanding performance of group 3 resulted from the strength of individual stocks and not from the industries as a whole. In fact, according to the O’Neil Database volumes, many of the group 3 stocks were at that time one of the top three performers in industries with flat or falling relative strength lines.

Implications for Investment Strategy The value of any conclusions to be drawn from

this study-for the pragmatic among us, at least- lies in their real-world potential for application. Most fundamentally, for example, do the conclusions imply strategies that employ information an investor can reasonably be expected to know or find at the time of the buyback announcement? Also, can an investor capture most or all of any excess returns? And to what extent do transaction costs diminish or eliminate excess returns?

The latter two questions above have great rele- Vance for traders, for whom the best advice seems to be this: 1) Buy the stock of companies announcing large repurchases-say, 10% or greater of the common shares; 2) Buy immediately after the repurchase announcement becomes public (on Day -1); 3) Sell after five trading days. (On average, ignoring transaction costs, a 3.89% excess return should result.)

For investors, the study’s general results suggest greater rewards but demand more caution. Despite an average one-year excess return of 6.80%, the buybacks in the study evinced huge variability in excess returns. The standard deviation of 20.43% for these one-year excess returns implies only a 63% probability of any positive excess return at all-and this ignores transaction costs.

Fortunately, two investment strategies present themselves that are more specific, less risky, and more rewarding than simply buying large-cap companies announcing a buyback: 1) Buy the stock of large-cap companies announcing share repurchases during the fourth quarter of the year-in Oc- tober, November, or December; or 2) Buy companies


announcing repurchases with rising earnings prior mentioned 33% for the study as a whole); 2) the now to the buyback announcement and for which com- greater percentage of best-performing buybacks with panies the confident forecaster expects rising earn- rising earnings prior to the buyback announcement ings in the ensuing year. (83% versus 68% for the entire study); and 3) the con-

To help corroborate these strategies, I first tinued evidence of extraordinary performance by the listed all 78 buybacks in order of their one-year per- third month. At least 10 different industries consti- formance and then examined the extremes. Exhibit tute this group of 17 buybacks, although pharma- 4 lists the top 25% of buybacks in terms of one-year ceuticals now boasts four representatives. excess return. Thirteen of the 20 best-performing At the other extreme, 26 buybacks underper- buybacks (65%) were fourth-quarter buybacks (as formed the S&P 500. The underperformance mani- compared with 33% of all 78 buybacks). Note that fested itself within one month of the announced the extraordinary performance was in evidence by buyback and the average one-year performance was the third month and that these 20 buybacks repre- more than 15% below that of the S&P 500. Of fur- sented at least 13 different industries, with only ther note is that the percentage of fourth-quarter pharmaceuticals having as many as three repre- buybacks in this group is somewhat lower than that sentatives. As for the earnings groupings, while the for the study as a whole (27% versus 33%). As for percentage of best-performing buybacks with rising earnings, it was not surprising to find a higher earnings prior to the buyback announcement ap- percentage of buybacks with falling earnings dur- proximated that for the entire study, the percentage ing the one-year period following the buyback with rising earnings during the buyback period was announcement. Interestingly, this group of under- 85% as compared to 74% for the study as a whole. performers contained about the same percentage as (One must be cautious, of course, about basing in- the entire study of buybacks with rising earnings vestment strategy on information that cannot be prior to the buyback announcement. The range of known at the time of the investment-namely, future industries among the under-performers proved earnings.) narrower, with capital-intensive oil and oil service,

To account for what some may argue was the aerospace, and computers having the most uniqueness of the 1987 fourth-quarter, I omitted representatives. these 11 buybacks and then examined the top 25% of the remaining 67 buybacks. Of particular note are F’urther Study 1) the now reduced but still higher-than-average per- Several areas of study offer promise. In no par- centage of fourth-quarter buybacks among the best- titular order they are as follows: A) A comparison performing buybacks (41% versus the previously of the excess return for companies with a history of

Exhibit 4 TOP 26% IN ONE-YEAR EXCESS RETURN

QTR. MONTH EARN. l COMPANY SYMBOL DA!l’R + TO BE REP. DAY&l+0 DAY 5 DAY20 DAY62 DAY125 DAY250

1 1 (A) S&lumber SLRP 890127 4.0% 0.59% 3.71% 2.28% 10.54% 8.01% 19.18%

4 11 (A) K-Mart KM 871125 8.7% -0.90% 1.26% 6.85% 14.53% 11.60% 19.40%

4 12 (A) Pacitic T FAG 881212 2.4% -0.77% - 1.23% -3.33% 4.86% 10.75% 20.31%

4 12 (A) Abbott La ABTl 851216 5.0% 3.60% -1.06% 3.17% 0.88% 21.09% 20.52%

2 5 (A) State St. STBK 880613 5.4% 2.20% -2.24% 4.74% 14.10% 15.61% 21.00%

4 12 (A) Abbott La Awl-2 881212 1.3% 0.01% -1.35% - 1.93% 3.91% 11.04% 21.18%

1 2 (A) Quaker On OAT 880202 2.5% 2.65% 2.41% 2.23% 9.75% 3.59% 22.88%

4 11 (A) Digital E DECl 861107 3.9% -0.75% -3.53% -0.02% 23.98% 37.06% 23.42%

3 7 (A) Dow Jones DJ 869724 TJnknown to co -0.65% 3.00% 1.22% 9.63% 21.86% 23.44%

4 12 0) Golden We GDW 871204 9.6% 8.65% 15.82% 8.44% 26.37% 10.26% 25.54%

4 10 (B) DaytmHu DH 871022 15.4% -3.91% 3.94% -2.25% 7.17% 26.34% 27.33%

4 11 (A) Ford Mote F2 871113 10.1% 3.44% 5.12% 5.45% 12.38% 24.61% 30.70%

4 10 (B) Hilton Ho IiET 871020 16.0% -5.83% -3.74% 7.04% 6.72% 22.11% 32.13%

4 11 (A) Household HI2 871103 6.0% 5.27% 2.71% -1.01% 5.58% 25.99% 32.72%

1 3 CC) Dow Chemi DOW1 850322 1.3% 0.04% 1.17% -0.30% 13.71% 19.87% 36.24%

4 11 @3) Ford Mota Fl 851115 10.5% 8.70% 9.82% 10.04% 26.45% 33.38% 42.26%

3 8 (A) Merck MRKl 850807 2.5% 1.21% 3.36% 3.98% 5.14% 11.19% 43.38%

4 11 (B) Wells Far WFC 871119 4.1% -0.03% -0.78% -1.66% 15.72% 23.35% 43.99%

4 12 (III) MCI T&c MCIC 861203 5.3% 7.69% 12.61% -0.03% -26.47% - 10.84% 51.87%

3 7 (A) Apple Corn AAPL 860722 7.6% 8.10% -0.37% 7.51% 5.79% 27.90% 72.50% - - -- - -

AVERAGE 6.4% 1.97% 2.53% 2.62% 9.54% 17.74% 31.50%

*Earnings: (A) = Rising before, rising during l (R) = Falling before, rising during l (C) = Rising before, falling during l 0) = Falling before, falling during

26 M’IA JOURNAL/SPRING 1991

buybacks with those announcing a rare buyback; B) A study of excess returns based on the actual number of shares a company repurchases; 0 A more rigorous study of the effect of industry performance on individual buyback performance; D) A comparison of excess returns for the months preceding the buyback announcement and the returns for the year following the announcement; E) A study of the effect of earnings surprises among buyback companies and a more rigorous study of earnings trends before and after repurchase announcements; F) The inclusion in the study of two sets of excess returns, one using the S&P 500, the other the DJIA; and G) Specific sell disciplines for whatever investment strategies result from the preceding work.

G. Gernon Brown III, a recent graduate of the Univer- sity of Virginia’s MBA program, is an Investment Sales Associate with Kidder, Peabody in Baltimore


Stock Market Price Behavior: Random Walks and Nonlinear Dynamics Peter A. Mulieri

Introduction A substantial amount of time and money has been spent to predict the movement of stock market prices, but despite these efforts, accurate forecasts have eluded the time series analyst. Technical analysts and chartists believe past prices contain information, which may be nonlinear, that can predict prices with accuracy sufficient to out-perform a buy and hold strategy. Others believe that past prices are independent of future prices, or that the statistical behavior of stock market prices emulates a random walk. The possibility that nonlinear structure exists is important, because it has been shown that nonlinear deterministic equations can generate chaotic time series that are indistinguishable from a random walk series using traditional linear statistical testing techniques.

Farmer and Sidorowich (1988a) have shown that the accuracy of forecasts could be significantly improved by using nonlinear modeling techniques. Their work in chaotic dynamics and nonlinear modeling demonstrates that if the source of random behavior comes from a system characterized by low dimensional nonlinear relationships (relatively few terms required to explain the system), nonlinear forecasts will be much better than those of linear models. Hence, finding evidence of low dimensional activity in a stock price time series is an essential step in improving the accuracy of forecasts. Preliminary results of a Scheinkman and LeBaron (1988) study of an aggregate stock return series using a Grassberger-Procaccia (1983) algorithm to estimate correlation dimension (a measure of the randomness of a system in the nonlinear sense), have shown indications of nonlinear dependence in the data.

Application of correlation dimension analysis techniques to four individual stock price series, and a composite of the four, is the focus of this paper. A brief overview of the random walk hypothesis is presented, followed by a discussion of the relationship between nonlinear dynamics and stock market price fluctuations, definitions, data description, and empirical results. Finally, conclusions that can be

inferred from the results and some thoughts on promising paths of research are presented.

Random Walk Hypothesis For many years, researchers in the academ-

ic and business communities have attempted to determine the nature of stock market price behavior. Pursuit of an answer to this question has evoked a considerable amount of controversy that still exists today. One school of thought believes past prices contain trends or patterns that can predict future prices, while another, the proponents of the random walk hypothesis, believe the future movement of prices are unpredictable. Statistically, the random walk hypothesis states that succes- sive price changes, for any time interval, are independent and identically distributed (IID) random variables.

Empirical tests of the random walk hypothesis, employing a multitude of statistical tests, have not come up with any conclusive evidence that supports or refutes the theory. These tests fall into two categories: 1) those that test for independence of price changes, and 2) others that test for con- formity to some probability distribution. Price change independence is the most important aspect of the random walk hypothesis, and consequently has been the topic of most debate.

A vast majority of the empirical studies employing traditional statistical techniques to date support the random walk hypothesis. However, among the researchers who argue against the random walk hypothesis, the concept of nonlinear dependencies in the data is a common theme. Levy (1967, p.69) mentions that there are serious weaknesses in the statistical tests for time series, since “they are not capable of detecting nonlinear patterns which the chartists claim exist.” Cootner (1964, p.191) discusses a test based on the range of the random walk, where the “power of the range test lies in its sensitivity to nonlinear dependence.” Alexander (19641 developed a test that claims to be capable of detecting nonlinear dependence in a stock price series.


Nonlinear Dynamics Recently, an abundance of research has been

conducted in nonlinear deterministic dynamics (the mathematical behavior of nonlinear equations or models) in the natural sciences and economics. Fluc- tuations occurring in nature and economic systems, once thought to be purely random, have been explained by nonlinear deterministic models. Extend- ing this notion to the random walk hypothesis, one can postulate that the possibility exists that a stock return time series, which appears to be random, might contain an underlying nonlinear deterministic explanation.

Brock and Sayers (19871, and Scheinkman and LeBaron (1988) consider a simple example of a nonlinear equation that illustrates how a time series can be generated from a purely deterministic process and be indistinguishable from a random series. This example takes the form of a difference equation,

where

and

:$I zAT)for OlxlyZ fix) = 2(1 - x) if M<x<l, t is time.

may be an exponential separation of the trajectories which is characteristic of a nonlinear deterministic system.

Scheinkman and LeBaron (1988) have calculated correlation dimension estimates for aggregate weekly U.S. stock return data and a selected individual stock using the Grassberger-F’rocaccia (1983) algorithm. They find strong evidence of nonlinearities in the aggregate data but find no evidence in the individual stock return series. Brock’s (1988) analysis of the same aggregate data set supported their evidence, while the results for another individual stock series provided no indication of an underlying nonlinear structure. Scheinkman and LeBaron (1988) describe the failure to detect nonlinearities in the individual stocks as a result of inherent idiosyncracies and the presence of noise.

Let us assume that the null hypothesis of the presence of nonlinearities in stock return data is, in fact, true. One then might ask, what is the process by which these nonlinear deterministic fluctuations are created? A number of possible explanations have

It has been shown that the time series generated by this difference equation form a chaotic time series. Bunow and Weiss (1985) have analyzed this series and their results indicate that the autocorrelations (a measure of the linear dependencies in the data) are essentially the same as that of a sequence of pseudorandom numbers (random numbers that are not purely random but close enough for practical purposes). Consequently, an analysis of a time series employing standard statistical techniques that rely on autocorrelation and functions could overlook an underlying nonlinear deterministic explanation. It can be argued that this example is too simplistic to model the true dynamics of a typical time series, however, higher order models are even more likely to generate deterministic chaotic trajectories that look like pseudorandom numbers.

The inadequacies of standard statistical techniques in uncovering nonlinearities in time series fluctuations create a need for alternative testing methods. Among the alternatives are two methods commonly used by researchers: the estimation of correlation dimension, and the largest Lyapunov expo- nent (not examined in this paper). In general, if the correlation dimension estimate of a time series is low relative to a truly random time series, then there is an indication that nonlinear deterministic relationships may exist in the data. Lyapunov exponents provide a measure of the rate at which average near- by trajectories separate (Farmer and Sidorowich, 1988b). If any of the exponents are positive, there

been proposed. Shiller (1984) postulates that the variability in stock returns is due to social-psycho- logical factors, where there are two types of investors, the “smart money” investor and the “ordinary” investor. The “smart money” investor would react quickly to any new information and properly assess the expected returns on stock. An “ordinary” investor can be expected to overreact to new information such as dividend/earnings announcements or major events, causing the price of the stock to be under or over valued. The “smart money” investor will properly assess the actions of the “ordinary” investor creating a feedback process similar to the dynamics of a difference equation model. This dichotomy of investor types could induce a nonlinear deterministic pattern in a stock return series that is not detectable by linear forecasting methods or standard statistical tests. Additional explanations (Brock, 1988) might include: the Monday effect (lower returns from the Friday close to the Monday open than over the rest of the week), the monthly effect (similar to the Mon- day effect), and systematic movements in the tradeoff between risk and return.

Correlation Dimension For the purposes of this paper, a description of

the concept of correlation dimension will suffice. Ac- cording to Ramsey, Sayers, and Rothman, 1988, p.3) correlation dimension is “a measure of the relative rate of scaling of the density of points within a given space. . . If the time series is a realization of a random variable, the correlation dimension estimate should increase proportionately with the dimension


ANALYSIS PROCEDURE TESTSFOR COMSINED rrsT RESULTS CONCLUSIONS

NONLINEAR DEPENDENCE ._-._ _ .__._._ - .___ - .-.-.-.__. ~

-hr ‘f-f

EMsEDoINoDlM WJmw I

DWERGENCE 7

[-==++E]

DATA COLLECTION _ To-

CORRELATION

’ INCREASE

IN DATA SET

Figure 1

of the space within which the points are contained.” ~~ mension by Grassberger and Procaccia (1983) and However, if the estimate of correlation dimension does not increase proportionately, then this is an indication that an underlying deterministic structure exists in the time series.

To understand this concept more clearly, consider a series of pseudorandom numbers generated by a digital computer. Researchers have found that for most computer generated random number gen- erators the correlation dimension estimates tend to be around 20 (in reality, if the numbers were truly random the estimate should be infinite, but random numbers generated by a computer are created by a deterministic algorithm). If we apply the correlation estimation technique to a series of stock returns and find the dimensionality estimate to be greater than or equal to 20, this would support the random walk hypothesis. Conversely, if the estimate is significantly lower, then there exists evidence of an underlying nonlinear deterministic structure.

The mathematical definition of correlation di-

Takens (19831, has been extended by Scheinkman and LeBaron (1988) by incorporating the concept of embedding dimension (see the references for the mathematical derivation). Embedding dimension is introduced as a method for testing empirical data. In the case of a stock price change series, if we con- struct a set consisting of every combination of three price changes, the embedding dimension is three. In general, the “true” correlation dimension of a time series is the point at which the correlation dimension estimates do not increase proportionately with increases in the embedding dimension.

Description of the Data Inspired by the strong evidence of nonlinear-

ities in stock return data found by Scheinkman and LeBaron (1988) using correlation dimension analysis, I decided to apply these techniques to some selected individual stock price series. A limited number of empirical analyses of individual stock issues


ORIGINAL SERIES CORRELATION DIMENSION ESTIMATES 12

u EMBEDDlrdG DIM=9 q EMBEDDING DIM= 10

7 10 - 0 z

5 8- > E

z 6- :,.:‘:.’ ‘.

F

; .“.““.. ,. .:r ,,. ..,:, y .’

4 1

E

4- ‘:: :::. : . . .:. ,:. i

E 0 2- ..:

0 MD GQ GD BA

1

COMP

Figure 2

have been conducted using these techniques, therefore, a more thorough investigation seemed prudent. The analysis, so far, has not been successful in the detection of nonlinearities for individual stock price series. Scheinkman and LeBaron believe that the behavior of individual stocks might contain idiosyncracies or be too noisy, thereby hiding a possible nonlinear structure. Cognizant of this belief, a composite series was constructed from the selected individual stocks, to see if some of the idiosyncracies and noise might be “washed out”, thereby increasing the nonlinear deterministic signal, if one exists, relative to the noise (higher signal to noise ratio.)

Four individual New York Stock Exchange issues were selected from the aerospace/defense industry: 1) McDonnell Douglas, 2) Grumm an, 3) General Dynamics, and 4) Boeing. Each data set consisted of 104 weekly closing prices from 22 February 1985 to 13 February 1987. Aerospace/defense stocks were selected with the hypothesis that the “smart money” and “ordinary” investor effect postulated by Schiller (19841, might be stronger due to factors that are unique to the industry. Some of the “smart money” assessment factors relative to the “ordinary” inves-

tor that could contribute to this effect include: 1) the ability to properly evaluate the future effect of an advanced technology breakthrough; 2) more accurate projections of the future level of defense spend- ing; 3) proper assessment of the effect of catastrophes (e.g., airline crashes) and defense related scandals; 4) knowledge of foreign competition.

Analysis Procedure The first step in the analysis is to take first dif-

ferences for each of the five weekly closing stock price series (see Figure I), resulting in a time series of weekly price changes, then estimate a model for each of the time series using your favorite linear regression technique. The purpose of this technique is to remove long term linear dependency due to stock price appreciation. In this analysis, the Box-Jenkins Autoregressive Moving Average (ARMA) (Box and Jenkins, 1970, Hoff, 1983) modeling process has been implemented. Using this estimated model and the associated time series, a residual time series is calculated for each stock and the composite. The residuals will then be checked for significant autocorrelation coefficients in the lags. If significant

MTA JOURNAL. / SPRING 1991 31

ORIGINAL AND SCRAMBLED SERIES CORRELATION DIMENSION ESTIMATE COMPARISON

12

MD GD BA COMP

Figure 3

coefficients exist, the ARMA modeling process is repeated. After completion of this process, each residual series now satisfies the IID assumptions of the random walk hypothesis. Correlation estimates for each of the resultant residual series are calculated according to the method described in Scheinkman and LeBaron (1988).

Three independent but similar measures of nonlinear dependence using correlation dimension estimates were applied: 1) Correlation dimension estimates that continue to grow with the corresponding embedding dimension indicate no nonlinear dependence; 2) Correlation dimension estimates that are small relative to the associated embedding dimension imply the presence of nonlinear dependence in the data; and 3) Scheinkman and LeBaron (1988) developed a test called the shuffle diagnostic This procedure consists of forming a “scrambled” residual data set by sampling from the residual time series at random with replacement, and then comparing the relative correlation dimension estimates of the original and “scrambled” residual series. If

the correlation estimates for the original series are significantly smaller than the “scrambled” series, then we can conclude that original series contains nonlinear dependence.

Correlation Dimension Analysis Results The estimates of correlation dimension at

embedding dimensions 9 and 10 (Figure 2) for all stock return series show no clear indication of nonlinear dependency relative to the first measure, since the estimates of correlation dimension for all time series increase with the embedding dimension. However, the absolute correlation dimension estimate of the composite series is small relative to the corresponding embedding dimension, implying the possibility of nonlinear dependency. The comparison of the original to the scrambled residual series (Figure 3), we observe no significantly higher scrambled series estimates for the individual stocks, but the composite series estimates for the scrambled data are significantly higher than the original series at embedding dimensions 9 and 10.


COMPOSITE SERIES CORRELATION DIMENSION ESTIMATES 14

ORIGINAL SERIES SCRAMBLED SERIES A .-.-~.‘-.-.

7 l2 ,,Q ,’ ,’ ,’

0 ; .’ .’ u>

,’ ,’ ,’ 7 ‘0 -

,’

g

&” ,a-* _,a-

E a- _.-’

//o...=*~‘-’

g

./*

0 I I I I I I 6 7 8

EMBED;ING DIMENSION’

12 13

Figure 4

Additional correlation dimension estimates were calculated for the composite series data at embedding dimensions 7,8,11, and 12 to substan- tiate the initial findings. Estimates of correlation dimension for the original and scrambled data at embedding dimensions 7 through 12 (Figure 4) support the hypothesis that nonlinear dependence exists in the original series for all three measures: 1) the scrambled series estimates continue to grow with the embedding dimension, while the original series levels off at about 5.5; 2) the original series estimates are small relative to the associated embedding dimension; and 3) the estimates are significantly different between the scrambled and original series at all embedding dimensions.

excessively small. Even data sets containing 6000 observations are considered, by most researchers, to be too small to obtain accurate estimates of correlation dimension. Second, the estimation process might not have removed enough linear dependence (due to long term appreciation of the stock price) in the data, and the process itself could have induced some dependence in the residuals. Finally, the evidence of nonlinearity could be due to the presence of nonstationarities (the statistical properties of the data set are not uniform) and heteroscedasticity (the variance of the data is not constant as a function of time) in the residual series.

Nevertheless, the results and processes of the analysis did indicate some avenues of further research. Conducting an analysis for a much larger

Conclusions data set of the stocks considered, giving special at- Apparent indications of nonlinearities in the tention to the problems of the estimation process and

composite stock time series data are encouraging, residual structure, will provide a better basis for the however, the evidence could be challenged for a num- formulation of any conclusions about the data. Lower ber of important reasons. First, and most important, estimates of correlation dimension for the composite the number of observations in the data sets are relative to the individual series indicate the possi-


bility that idiosyncracies and noise of individual series were removed, implying that an analysis of comprehensive industry indices might produce some interesting findings.

Knowledge of the existence of nonlinear dependency in the data alone is not sufficient to capital- ize on market price fluctuations. Research and development of nonlinear prediction and classification techniques applied to market price data can potentially provide the most promising prospects for characterizing a significant portion of the time series that has been traditionally referred to as pure random error. Application of nonlinear regression and neural network techniques have great potential. For instance, by fitting a nonlinear model, that is in the form of a simple or complex difference equation, the estimated value of the coefficients can provide information on the cyclical state of the system (i.e. 1 cycle, 2 cycle,. . . , n cycle,. . . , chaos) and potentially predict near term price magnitude and direction. Neural net models, which are inherently nonlinear in their computational elements, provide potentially the greatest opportunity for exploiting time series with low correlation dimension estimates. Combina- tions of these methods along with other emerging nonlinear techniques, and the availability of low cost high speed processors should produce some significant breakthroughs in the next five years.

REFERENCES

Alexander, S. S., “Price Movements in Speculative Markets: Trends or Random Walks.” In P H. Cootner, editor, The Random Character ofStock Market Prices, Cambridge: M.I.T. Press, 1964.

Box, G. E. P., and G. M. Jenkins, Time Series Analysis, Forecasting and Control, Holden-Day, 1970.

Brock, W. A. (1986), “Distinguishing Random and Deterministic Systems: Abridged Version,” Journal of Economic Theory 40, 168195.

Brock, W. A. “Nonlinearity and Complex Dynamics in Econom- ics and Finance.” In I! W. Anderson, K. J. Arrow, and D. Pines, editors, The Economy us an Evolving Complex System, Addison Wesley, 1988.

Brock, W. A., W. D. Dechert, and J. Scheinkman (1988), “A Test for Independence Based on the Correlation Dimension,” Depart- ment of Economics, University of Wisconsin, Madison, Universi- ty of Houston, and University of Chicago, unpublished.

Brock, W. A., and C. L. Sayers (1988), “Is the Business Cycle Characterized by Deterministic Chaos?’ Journal of Monetary Economics 22, 71-90.

Bunow, B., and G. H. Weiss (1979), “How Chaotic is Chaos? Chaotic and Other “Noisy” Dynamics in the Frequency Domain,” Mathematical Biosciences 47, 221-237.

Cootner, l? H. (ed.), The Random Character of Stock Market Prices, Cambridge: M.I.T. Press, 1964.

Fama, E. F. (1965), “The Behavior of Stock Market Prices,” Jour- nal of Business 38, 34-105.

Farmer, J. D., and J. J. Sidorowich (1988a), “Exploiting Chaos to Predict the Future and Reduce Noise,” Theoretical Division and

Center for Nonlinear Studies, Los Alamos National Laboratory.

Farmer, J. D., and J. J. Sidorowich. “Can New Approaches to Nonlinear Modeling Improve Economic Forecasts?’ In P W. Ander- son, K. J. Arrow, and D. Pines, editors, The Economy as an Euolu- ing Complex System, Addison-Wesley, 1988b.

Grassberger, P and I. Procaccia (19831, “Measuring the Strange- ness of Strange Attractors,” Physicu 9D, 189-208.

Hoff, J. C., A Practical Guide to Box-Jenkins Forecasting, Wadsworth, 1983.

Levy, R. A. (1967), “Random Walks: Reality or Myth,” Financial Analysis Journal 23, 69-77.

Ramsey, J. B., and C. L. Sayers, and I? Rothman (19881, “The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications,” New York University, and University of Houston.

Sayers, C. L. (1988), “Diagnostic Tests for Nonlinearity in Time Series Data: An Application to the Work Stoppages Series,” Department of Economics, University of North Carolina.

Scheinkman, J., and B. LeBaron (1986, revised 1988), “Nonlinear Dynamics and Stock Returns,” University of Chicago; Journal of Business, forthcoming.

Scheinkman, J., and B. LeBaron (1987), “Nonlinear Dynamics and GNP Data,” University of Chicago, and CEREMADE (Universi- ty of Paris IX), unpublished.

Shiller, R. J. (1984), “Stock Prices and Social Dynamics,” Brook- ings Papers on Economic Activity 2, 457-498.

‘B&ens, E (19831, “Invariants Related to Dimension and Entropy,” Proceedings of the Thirteenth Coloquio Brasileino de Matematica.

Peter Mulieri has spent several years in aerospace and advertising holding operations research, systems analysis, and programmer analyst positions. This paper is a summary of his master’s thesis work fir an M.S. degree in applied mathematics and statistics from the State University of New York at Stony Brook. He is currently a member of the Investment Technology Group at Jef- feries and Company, Inc.


The Use of Price-Volume Crossover Patterns in Technical Analysis S. Kris Kaufman and Marc Chaikin

Abstract: Background and Methods. The routine use of price-volume crossover signals as a means of forecasting future stock or commodity price movement has been gaining popularity lately due to the availability of software to simplify the analysis. In this study we tested 24 unique crossover patterns and identified their forecasting performance. Cross- overs are classed by both pattern and the elapsed time for the pattern to develop. For each pattern, we analyzed how much better one could forecast price direction 5,10,15, and 20 days in the future, given that the elapsed time for the cross to develop spanned

TITLE: Price-Volume Crossover Derivations

the same number of days. We used approximately one hundred and twenty five thousand days of daily stock and commodity data bundled together in our evaluation. At least 100 occurrences for each crossover pattern were used in the analysis.

Results: The results suggest that several patterns are significant and could be used to improve a stock or commodity price forecast. The most negative cross within the test window was II-B, which occurs when price drops on decreasing volume, rises on light volume and then drops again on increasing volume. It was interesting that the converse pattern

PRICE-TIME VIEW

A 2 4

P Fi

I 0 P C E 1

o,,j$, 3

PRICE-VOLUME VIEW

4 2

IIIIII II>

TIME \

P R

VOLUME-TIME VIEW f

’ X>

C 1

E ’ 3

VOLUME

TIME

Figure 1: DERIVATION OF PRICE-VOLUME CROSSOVER


I-B is not as bullish as II-B is bearish. The I-B results show that you will generally move up immediately after the cross, only to fall later. The utility of this technique is its ease of use by computer and the in- tegration of price and volume which is achieved.

Introduction Market technicians usually study time-based

charts in order to identify price and volume patterns. There is a large body of technical knowledge about the combinations of price and volume behavior that lead certain types of market price action [Bring et al.]. The price-volume chart provides a different way of viewing the data. In fact, the two major reasons for using this view are that it leads to a single indicator integrating price and volume and the data can be easily tracked by computer. The identification of these patterns on the price-volume chart has been

linked to the crossing of two price-volume lines. Ben Cracker, for one, has long been a proponent of price- volume charting and has studied some of the basic patterns as well as pattern groupings. In this study we will test each of the 24 basic single cross patterns on four time periods using very diverse stock and commodity data.

Crossover Patterns The price-volume view is formed by plotting

the closing price on a vertical axis versus volume on a horizontal axis (Figure 1). Each day a new point is added and then connected to the previous days point by drawing a line. For this discussion we will refer to the “final” segment as the most recent price-volume line. The “initial” segment is the one which occurred further back in the past and is crossed by the final segment. Crossover patterns are

TITLE: PriceVolume Crossover Patterns I

P FINAL SEGMENT: PRICE INCREASES R

VOLUME INCREASES I

C I

i”

E VC .Ij:J(E

5 I -0.2 5 I -1.4 5 I -1.6

A 10 I 0.8

15 I 0.4

~ y-2.1 lB lg~-~~~ : ,viiii

VOLUME VOLUME VOLUME


Figure 2


classified by the direction of the initial and final segments, and by the elapsed time between them. The pattern shown in figure 1 shows price rising on increased volume (1 to 21, then declining with the same level of volume (2 to 31, before finally rising on decreasing volume (3 to 4) to complete the pattern. The dashed line indicates that an unknown number of days may have elapsed between the initial and final segments. There are 24 patterns in all (Fig- ures 2 through 5). The patterns have been divided into four groups based on the direction of the final segment. Each of the figures shows one of the four final segment possibilities with all possible initial segment choices.

Analysis The best way to judge the benefit of using cross-

over signals is to analyze the actual price action

following a certain crossover. Within a particular time frame, more than one crossover pattern may complete They have different initial segments with the same final segment, but they still occur together in terms of the evaluation. We have chosen a simple least-squares approach to solve for the relative importance of the crossovers. This approach neatly sep- arates each pattern by assigning it a weight as part of a linear sum. Figure 6 shows the least-squares matrix equation Aij * Wj = Bi, where the A’s are zeros or ones depending on whether one of the 24 crossovers occurred within the analysis window, the W’s are the unknown pattern weights, and the B’s are the answers to what happened next in the market. If the market went up after 5 days (or any fmed num- her), a plus one is entered. Otherwise, a minus one is used. Since we have so much data (roughly 125,000 days), the problem is very well constrained. The re-

TITLE: Price-Volume Crossover Patterns II

FINAL SEGMENT: PRICE DECREASES

VOLUME INCREASES

P

R I

C E

I

\

VOLUME

5 I -3.9 5 I -8.3 5 I -0.2

A 10 I -0.7 8 10 I -5.5

C 10 I -1.7

15 I -1.1 15 I -3.8 15 I -2.8

20 I -0.5 20 I -2.3 20 I -2.0

; L+ ; ix 1 ‘\


5 I -4.6 5 I -4.1 5 I -8.1

10 I -1.3 10 I -0.8 10 I -0.9

D 15 I -2.9

20 I 1.6

~ \ iE g:i:l iF gi


Figure 3


sulting weights will tell us whether a pattern is bearish (W < 0) or bullish. Also note that we added a constant term to the weighted sum model to pick up any price trend bias over the whole data set. This turned out to be positive 1 to 2% which is due to the 80’s bull market.

The equation was solved for four cases. All crossovers occurring within 5 days coupled with the resulting price behavior 5 days out, and the same for 10,15, and 20 days. The results are shown in the upper right hand corner of each pattern on figures 2 through 5. The weights may be interpreted as an average percentage deviation from the random case. In other words a 5.2 weight indicates that the pattern predicted higher prices about 5% better than random. When the weights flip-flop between positive and negative without any clear pattern, the crossover has little or no significance in forecasting.

In evaluating the results it is apparent that all patterns with the same final segment do not have the same forecasting utility (see Figure 7). One might expect that days following a move higher on increasing volume (figure 2 patterns) would always be more positive, independent of the crossover. Our results show that patterns I-C and I-F predict very negative price action 5days out, before turning and becoming very positive later. Other members of that group, including I-A, I-B, and I-C show no clear pattern, while I-D is positive early and negative late, the opposite of I-C and I-F. Group II however, does show universally negative behavior, but there are two patterns which are much more negative than the rest. Table 1 is a summary of the signiticant results.

Discussion The results suggest that several of the price-

TITLE: Price-Volume Crossover Patterns Ill

P FINAL SEGMENT: PRICE DECREASES R

VOLUME DECREASES

II- C /

E VOLUME

5 I -7.0 5 I -6.4 5 1 -6.2

10 I -0.9 10 I -2.5 10 I -5.6

iA +-= iB kii:- / Jjl:::


5 1 -0.8 5 I -0.9 5 I -5.4

10 I 1.2 10 I -0.2 10 I -4.8

iD j-t:: iE g=- ~ F &Ii::


Figure 4


volume crossover patterns are significant and could be used to improve a stock or commodity price forecast by generally +/- 5%. It is interesting to note that down moves are much more easily forecast using price-volume patterns than up moves. Also, the group II pattern results suggest that any time one sees a price drop on heavy volume, a hasty exit is in order.

The most negative cross within the test window was II-B, which occurs when price drops on decreasing volume, rises on light volume and then drops again on increasing volume. It was very interesting to note that the converse pattern I-B is not as bullish as II-B is bearish. The I-B results show that you will generally move up immediately after the cross, only to fall later.

The use of the price-volume crossover technique is a practical way of integrating two charts into one for analysis. Since a computer can easily be programmed to pick out these patterns, this indicator should continue to gain in popularity over time. Fur- ther study should be devoted to combining crossover patterns with other technical indicators, analyzing weekly and monthly data, and also to special se- quences of these patterns.

REFERENCES

Cracker, Benjamin B., The Computerized Investor, The Cracker Report, 320 West California Blvd., Pasadena, CA 91105, Volume M.

Pring, Martin, Technical Analysis Explained, McGraw-Hill, Second Edition, 1985.

TITLE: Price-Volume Crossover Patterns IV

PRICE INCREASES FINAL SEGMENT: VOLUME DECREASES

P

R

I/ C

T

E VOLUME

5 I -3.1 5 I -0.8

A 10 I 2.5 B 10 I 4.4 C 10 I 0.8

15 I 2.6 15 I 2.8 15 I 0.0

20 I 2.5 20 1 3.1 20 1 1.4

; \ ; x ; .p,102


5 1 -9.2 5 1 -3.9 5 I 5.2

D 10 I -2.8

15 I -2.5

; x-1.3 iE gy= (F <-ii:

6

VOLUME VOLUME

Figure 5

VOLUME


r TITLE: Crossover Evaluation using Lea3bSqwre~~

MATRIX EQUATION:

125,000 Days of Data

24 Patterns >

- 0 0 1 0 0 0 1 o....

A IS THERE A NO. 3 CROSSOVER TODAY

1 = YES O-NO

-

PAlTERN WEIGHTS

-- Wl w2 w3

--

=

WAS THE MARKET HIGHER OR LOWER 5 DAYS IN THE

/

FUTURE?

IL --

1 1

-1 -1 1

-1

--

-1 = LOWER 1 = HIGHER

Figure 6: LEAST-SGUARES EOUAllON TO SOLVE FOR CROSSOVER WEIGHTING

TITLE: Crossover Pattern Evaluation

P R

I c 2

SET OF ALL MARKET DAYS WHEN

PRICE WAS UP ON DECREASED

VOLUME FROM THE PRIOR DAY

VOLUME

ON INCREASED VOLUME

Flgure 7: PATTERN EVALUATION: HOW DIFFERENT ARE CROSSOVER CASES FROM THE NORM 3

40 MTA JOUFWAL I SF’FLING 1991

TABLE 1

Price Action Pattern Description Early Late

I-C Price is up strongly on increased volume followed later by price up less with more volume. DOWN UP

I-D Price is down strongly on slightly decreased volume followed later by price moving up strongly with increasing volume. UP DOWN

I-F Price is up somewhat on greatly increased volume followed later by price up more on less volume DOWN UP

II (all) Price decreases on increasing volume. Note that II-B and II-F are very

negative patterns within the group. DOWN DOWN

III-A Price is up slightly on large volume increase followed later by a strong price decrease on decreased volume. DOWN UP

III-B Price moves down on increased volume followed by price drop on decreased volume. DOWN DOWN

III-C Price is down strongly on slightly lower volume followed later by smaller decline on much lower volume. DOWN DOWN

III-F Price is down slightly on much lower volume followed by greater decline on slightly decreased volume. DOWN DOWN

IV-A Price is down slightly on increased volume followed by a higher price on decreased volume. DOWN UP

IV-B Price increases on increased volume followed by a price increase on decreasing volume - UP

IV-D Price decreases strongly on slightly higher volume followed by a rising price on much lower volume. DOWN DOWN

Kris Kaufman is a senior geophysicist with a leading oil exploration software company and president of Parallax Financial Research. Parallax publishes the PRECISION TURN trend change indicator quarterly and provides computer research and consulting services to several Wall Street firms.

Marc Chaikin graduated from Brown University with a degree in Finance He was the head of the Options Department at Tucker Anthony fir five years Later Marc joined Drezel Burnham Lambert and for five years he worked with technically oriented traders and investors. Two years ago he, along with his partner Bob Brogan, firmed Bomar Securities, L.P, a technical research bou- tique with a computer-based product which gives buy- side portfolio managers and block trading desks quick and easy access to technical data. Marc is a frequent guest analyst on FNN, is often quoted in Investor’s Daily and recently wrote an article fir Wall Street Computer Review’s July issue titled “Technical Analysis Systems: A User’s Perspective’:


Pattern Recognition Signal Filters David R. Aronson

Derived with a statistically based artificial intelligence technique, they can significantly enhance the perfbrmance of mechanical trading systems, but prop er development is precarious.

Introduction Unprofitable trading signals, particularly when they arrive in strings, are the bane of all traders who employ mechanical trading systems (MT’S). This has led many systems traders to attempt the development of signal filters, supplementary criteria designed to eliminate signals with a high probability of loss. An ideal filter would reject all loss signals and accept all profitable ones. Though this is an impossible goal, a filter that eliminates significantly more losers than winners is an achievable goal, provided proper statistical methods are employed.

The attempt to develop filters is not new. The basic approach involves an analysis of prior signals to discover the characteristics that distinguish winners from losers. Unfortunately these well motivated efforts often go astray, producing overfitted or (curve fitted) filters. The key symptom of overfit is excellent discrimination on the analyzed signals which is not evidenced when the filter is applied to an independent set of signals. In other words the filter was so highly “tuned” to a particular set of prior trades that it lacked sufficient generality to be effective on other (i.e., future) signals. They are the filter developer’s version of “fools gold”.

This article espouses a new approach to filter development that overcomes the overfitting problem. It utilizes a highly computer intensive technique called statistical pattern recognition (SPR), a branch of artificial intelligence (AI). The AI aspect permits SPR to “learn” through trial and error the distinguishing characteristics of unprofitable and profitable signals. Should none exist that is discovered as well. More importanly, SPR is able to discern the proper degree of fit thus greatly reducing the overfit problem. Therefore, when a filter is produced, it is likely to discriminate well when applied to an independent set of signals, provided however, they are statistically similar to historical ones (i.e., charac-

terized by indicator readings that are similar to some of the analyzed signals).

In an operational mode, SPR signal filters qualify new trading signals by determining if the current indicator pattern (i.e., set of indicator readings) is similar to those associated with prior unprofitable signals. Signals matching the “unprofitable” pattern would be rejected.

Tests of SPR signal filters on out-of-sample data (i.e., data other than that used to develop them) have demonstrated both enhanced profitability and reduced risk. Typical SPR filters eliminate about one third to two thirds of all signals. However, those signals qualified as acceptable are of a much higher merit. In terms of the Profit Factor, an effective index of MTS performance improvements of over 50% have been attained. In addition, the magnitude of equity draw-downs has been reduced as much as 65%. The enhanced signal quality afforded by SPR filters permits the trader to deploy capital more ag- gressively, thereby enhancing net trading profits with no more risk than the unfiltered system.

Mechanical Trading Systems A mechanical trading system @ITS) is a set of

definitive rules that generates clear-cut buy and sell signals in a given financial market. A well known example is the “four-week” break-out system which signals long positions when prices exceed the high- est price established in the preceding four weeks and short positions when prices trade below the low of the prior four weeks.

MTS vary in terms of their underlying philosophy. Three broad categories are trend-following sys- terns, counter-trend systems, and cycle systems. Trend-following systems, based on the assumption that price trends, once established will continue, assume long positions upon initial evidence of advancing prices and short positions upon initial evidence of declining prices. Counter-trend systems assume that extended price trends will reverse and signal positions opposite to the recent trend. Cycle sys- terns assume recent periodic behavior in prices will persist and attempt to position the trader at antici-

42 MTA JOURNAL I SPRING 1991

pated crests and troughs in prices. Hybrid systems blend a number of these approaches. MTS also display a wide range in their degree of complexity, with some based on a few simple rules such as the four- week break-out system, while others are based upon much more complex signaling criteria.

MTS are attractive for several reasons. In futures trading trend-following MTS have been hand- somely profitable demonstrating real-time com- pounded returns in excess of 30% per year over 10 or more years. Even after adjustment for risk (i.e., equity volatility, draw-downs, etc.) , few investment strategies can boast such results. In addition, they provide a consistent strategy that eliminates emotional trading decisions. Moreover, their exact nature allows for computer based design, optimization and testing on historical data. Finally, their definitive historical signals make MTS ideally suited for filtering via SPR.

But despite their successful track records over the long-term, MTS often try the patience and pock- ets of traders over the short-term, because a significant fraction, typically over 50%, of the signals result in losses. To make matters worse, the false signals tend to be concentrated in strings rather than being randomly intermixed amongst the profitable signals. A succession of losers, can produce a dramat- ic decline in account equity known as a “draw-down”. Draw-downs of 30 to 50% of trading capital are not unheard of, and may cause the trader to abandon the MTS altogether, thus missing out on its long-term profit potential.

Such periods of sub-par performance occur when markets fluctuate, for extended periods, in a manner that is at odds with the MTS’ underlying philosophy. Trend-following system suffer in trend-less choppy markets, while counter-trend systems will be hurt during strong trends. In 1988 one major futures advi- sor who relied on MTS was not only required to close two public futures funds due to large declines in equity, but gave up on money management altogether. Research described in this article suggests that SPR signal filters can ameliorate equity draw-downs by rejecting a majority of signals occurring during the environment for a given MTS.

Fundamental Weakness of MTS Why don’t MTS have higher levels of signal ac-

curacy and better overall performance? Two answers seem reasonable, one based on cybernetics, and a second based on the efficient market hypothesis.

Cybernetics, is concerned with the analysis and synthesis of complex systems of all types. One of its fundamental principles, The Law of Requisite Variety (LRV), reveals a design flaw in most MTS

that would lead to an expectation of low signal accuracy. LRV states that mechanisms designed to predict or control the behavior of a complex system are required to embody a degree of complexity that approaches that of the system itself. Therefore, complex financial markets can not be beaten with simplistic MTS. In this context complexity refers to a “rich” variety of properly integrated information.

Financial markets are examples of complex systems. Yet the vast majority of MTS are relatively simple. Trading signals are typically generated solely from price data, massaged in a limited number of ways (i.e., averaging, differencing, etc.). Low degree of signal accuracy are not surprising. Yet, at the same time, LRV suggests how to improve a pre- scription for enhancing MTS signal accuracy; aug- ment it with additional information found in other data series and indicators. Signal filters do just this.

A second reason to expect low MTS performance is the so-called Efficient Market Theory (EMT). It implies that the performance of an investment strategy will suffer if too many employ it because its information content has been discounted. Since many traders use similar MTS, degraded performance is the natural consequence. To attain superior performance one must employ strategies built on valid information that has not yet been discounted. Since, to date, few traders are exploiting SPR signal filters the concept offers significant potential. In addition, because the development of effective signal filters is fraught with pitfalls, many who attempt it will fail, thus maintaining the edge for those who are successful at it.

Signal Filters Signal filters are supplementary rules (models)

that operate in conjunction with an MTS. The rules define conditions under which signals ought to be rejected, due to an above normal probability of loss.

The concept of employing signal filters is not new, however, the use of SPR to develop them is. Moreover, it is the author’s contention that SPR, properly applied, is a superior method of producing filters. Less rigorous methods tend to produce filters with better historical (in-sample) than future (out-of-sample) performance. SPR filters have demonstrated accuracy on both prior and future signals.

Filter development via SPR involves a computerized analysis of a representative sample of prior trading signals, each characterized by an array of statistical data. The statistical data includes the signal type (long or short), its date of occurrence, its outcome (i.e., the gain or loss ultimately realized upon close-out of the trade initiated by the signal), and the values for a list of candidate filtering indicators.


The indicators are typically designated by the let- ter “X” (X,, X,, X,, . . . . . X,,). The indicator values used are those known as of the date of the signal’s occurrence. This is crucial because this is the date on which the trader must decide whether to accept or reject the signal. It should be emphasized that the greater the number of signals the better, with 100 or so being the bare minimum. In addition, the historical sample should include a range of market environments (up-trend, down-trend, congestion) and system performance (good and bad). SPR analysis does not require knowledge of the MTS’s underlying rules or trading logic A sample of the data matrix required for filter development is illustrated below:

Date Type Outcome X, X, X, XN

750206 Long -20,600 +.25 -.17 -.7 -3.2 750218 Short +3250 +.49 -.67 +.76 +.24

SPR analysis is performed by specialized software that permits the computer to discover the set of indicator characteristics (i.e., the pattern) that tended to be present at the time unprofitable signals were issued, but not typically present for profitable signals. In other words, the software searches for the indicators characteristics, which to some degree, validly discriminate profitable from unprofitable signals. The operative word is “validly”.

Typically tens or hundreds of indicator candi- dates need to be evaluated to find a few, that individually or in combination, serve this purpose. An indicator can be any variable, technical or fundamental, that can be represented by a number. Ex- amples are the popular “RSI” indicator, the 5 day change in tbill rates, indicators invented by the analyst, signals from other MTS, etc. In filter development projects conducted by the author’s firm, as many as 400 candidate indicators have been evaluated to find a few that can be used to filter signals.

Statistical Pattern Recognition Statistical Pattern Recognition (SPR), the ap-

proach advocated by this article for filter development, is a branch of artificial intelligence (AD. AI is the frontier of computer science whose objective is endowing computers with abilities that qualify as intelligent. The particular aspect of intelligence rep- licated by SPR is inductive generalization, (i.e., inductive reasoning), the act of inferring a principle or rule from an examination of numerous specific examples. The key to valid inductive logic is the ability to avoid rules that are overly tailored to the examples analyzed. Sound inductive inference pro-

duces rules that apply to examples other than those analyzed.

More specifically, SPR is concerned with the discovery of rules that differentiate one class of items from another based on various characteristics. In other words SPR permits the computer to discover class distinguishing attributes and formulate classification rules. For example, given the problem of discovering a rule to discriminate basketball play- ers (class l), from jockeys (class 2), and a set of data on fifty of each, including their height, eye color, neck size, IQ etc, an SPR system would discover that the attribute “height” is a useful distinguishing indicator, but “eye color” is not. In the process, an SPR system would generate a classification rule:

If height is greater than 6 feet, then class = basketball player, If height is less than 6 feet, class = jockey,

Once formulated, the rule can be used to classify individuals whose class is unknown but whose height is known. For example the rule would classify an individual whose height is 6’ 5” as a basketball player.

Signals from an MTS can be viewed as falling into one of two classes:

CLASS 1: signals that are profitable at time of close out

CLASS 2: signals that are unprofitable at time of close out

To give the reader some idea of what a rule (i.e., pattern) might look like, consider the following pattern involving two indicators:

If on the day of a signal the following conditions are present, then do not act on the signal:

1. The 20 day % change in open-interest is less than -2.5 and,

2. The prior days’ close was in the lower half of the daily range.

A computer “armed” with SPR software discovered that this pattern of characteristics had a stronger tendency to be present when unprofitable signals were issued. In other words, the pattern was correlated with a higher than probability of signal failure. For example the unfiltered MTS might have 50% probability of issuing an unprofitable signal, the signals given in the presence of the above pattern might have a 65% probability of loss, while signals given in absence of the pattern might have 35% loss probability.

The reader may wonder why a computer “armed” with SPR is necessary to discover such a

‘id MTA JOURNAL /SPRING 1991

pattern. Why not just leave it to the unaided human mind? While the mind has an unparalleled ability to deal with sight and sound patterns, experiments performed by cognitive psychologists have revealed it is not adept at sensing patterns or detecting pre- dictive relationships in factual and statistical data. An example of a fact pattern is illustrated by the problem of determining if a set of indicator values correlates significantly with a signal’s outcome. The brain’s upper limit seems to be three factors, though we do much better with two or one. Other experiments have shown that not only does the mind fail to detect significant patterns, but often “perceives” patterns that are not valid.

In contrast, computerized SPR has no such limits. The machine can tirelessly and objectively search through numerous indicators individually and in multitudinous combination to find valid filtering criteria. Clearly, computer based SPR, not the brain, is the tool of choice in filter development.

How Does SPR Work? The following section will describe how the

SPR process discovers patterns and though it involves complex mathematics, it has key concepts that can be readily grasped by non-mathematicians with the aid of diagrams. The key concepts are:

1. Indicator Spaces 2. Proximity & Similarity 3. Discrimination & Classification 4. Classification of a Current Signal

Indicator Spaces An indicator space (also referred to as a vector

space, state space parameter space, etc.), is a mathematical convention for representing data and detecting patterns. The space is a grid of one or more axes, with each axis, or dimension representing an indicator. In spaces of two or more dimensions axes are mutually perpendicular. A specific set of indicator readings are represented by a set of coordinates that define a point in the space. Therefore, each trading signal is represented by a point whose location is determined by the indicator values existing at the time of the signal.

While we will illustrate this concept with sev- era1 graphical diagrams, SPR does not utilize graph- its. Rather, the indicator space is represented inside the computer’s memory by strings of numbers called vectors. In this way patterns, should they exist, can be detected mathematically rather than visually. This is crucial in problems with many potential dimensions, or high levels of noise (randomness) that render visual recognition inadequate.

The simplest indicator space is one-dimension-

al (1-D) and is composed of a single axis. Such a space would be employed if only a single indicator were being evaluated for its signal filtering ability. This is illustrated in Figure 1. Consider indicator X,, which can assume values from - 10 to + 10. At the time of a particular signal, X, had a value of -7.5. That signal is depicted by a data point positioned at a value “ -7.5” on the indicator axis in figure 1. If our MTS signal history consisted of 100 signals, they would be depicted by 100 data points, each plotted at the axis location corresponding to the indicator’s value at the time of the signal.

However, in real-world analysis the analyst wants to evaluate the filtering potential of several indicators used in combination. In such instances higher dimensional spaces, consisting of two or more indicators are required. Yet, regardless of the number of dimensions, each signal is still represented by a single data point. For example, if each signal were to be characterized by two indicator values, it would be represented by a point in two-dimensional or 2-D space An example is a piece of ordinary graph paper, consisting of two mutually perpendicular axes (see Figure 2). The data point labeled “A”, positioned at coordinates (-7.5, +3.2), indicates that at the time of that signal, indicator X, had a value of “-7.5” and indicator X, had a value of “+3.2”.

Were three indicators being considered, each signal would be depicted by a point in a 3-D space, defined by three mutually perpendicular indicator axes. If four indicators were being evaluated for their conjoint filtering power, each signal would be represented by a point in a 4-D space and so on. Though 4-D spaces, and spaces of higher dimensionality can not be visualized, they are easily represented with the indicator space paradigm. In fact there is no theoretical limit to the number of dimensions (e.g., 4,5,10 or even 100) that can be used, though there are limits imposed by the number of historical signals available for analysis. The greater the number, the more dimensions (i.e., indicators) one can consider in combination.

Proximity = Similarity A very important property of indicator spaces

is that the distance separating two data points reveals their degree of similarity in terms of their indicator values. Two data points with similar indicator values will have similar coordinates and will be located close to one another. Highly dissimilar data points will be separated by large distances. Figure 3 illustrates this idea. Three MTS signals are represented by the three data points, A, B and C plotted in a 2-D space. A and B have similar indicator characteristics and therefore are located near each


Figure 1

A 1-D indicator Space

The dot positioned at -7.5 in Xl space indicates that at the time of that MT5 signal indicator, Xl had a value

Figure 2

A 2-D Indicator Space

A 2-D space composed of indicators Xl and X2. On the day of the signal Xl’s value was -7.5 and X2’s was +3.2. The dot’s position on the grid illustrates this.

other. In contrast, point C, which is characterized by very different indicator values, is found far removed from both A and B. This property allows degrees of similarity between data points to be measured in terms of the distance separating them.

When a whole set of points are characterized by similar indicator values, they will cluster in a relatively compact region of indicator space called a “neighborhood”. Points A and B in figure 3 lie in the same neighborhood, while point C does not.

Classification and Discrimination Things really become interesting when infor-

mation about the class membership of each data point is added. This is accomplished in our illustrations by identifying all members belonging to the

Figure 3

Proximity = Similarity

Signals represented by points A & B in Xl, X2 space were characterized by very similar Xl, X2 indicator readings and thus lie near each other in the space.

The signal represented by point C occurred within a context of Xl, X2 values very different from signals A and B, and thus is far removed from them in the indicator space.

same class with the same symbol. In filter development the two classes of interest are: signals that produced profits, and signals that produced losses. In the illustrations profitable signals are denoted by a “+” symbol, while unprofitable signals are designated by a “0” symbol. The class information enables the SPR program to evaluate the ability of a given indicator space to discriminate (i.e., separate) profitable from unprofitable signals.

A space is said to discriminate well if unprofitable signals tend to concentrate in regions that are relatively distant from regions populated with profitable signals. In other words the “0” symbols tend to be segregated from the I‘+” symbols. In contrast spaces that lack discrimination information display a random intermixture of the two classes. Of course, how well a given space discriminates depends upon the information content of the indicators that compose it. The goal of an SPR system is the discovery of spaces (indicator combinations) with the best discrimination power amongst a large set of possible spaces.


Figure 4A shows a two dimensional indicator space with very strong discrimination . The neighborhood concentrated with “o”symbols is far removed from and easily separable from the neighborhood populated with “+” symbols. In contrast Figure 4B displays a 2-D space composed of two indicators that do not contain good discrimination power as evidenced by the intermixture of gain and loss trades. In cases like this no simply shaped region (boundary) can segregate the bad trades from the good.

It should be pointed out that the illustrations used in this article are idealized, showing patterns that are much clearer and stronger than any likely to be encountered in actual filter development. This is done to make the concepts readily understandable. However, SPR employs a very sensitive criterion that can detect useful discrimination information even if very weak. In a very real sense, it is much like the search for gold, that even in the richest ores is hard to see.

An important aspect of SPR is the com- binatorial search problem. In its pursuit of spaces with good discrimination power, the SPR program must evaluate a huge number of indicator combinations. For example, given 100 candidate indicators, there are 100 1-D spaces, 4,950 possible 2-D spaces, 161,700 3-D spaces, almost 4 million 4-D spaces, etc This very large number of spaces creates two problems. First, significant computing resources are required to evaluate all of them. Second, when the number of spaces is large relative to the number of signals available for analysis, many spaces that appear to discriminate, do so only by chance. This bogus discrimination is a mere statistical accident, and is unlikely to reappear if another set of trading signals were to populate the space. This phenomenon is an aspect of overfitting, a very severe problem that often thwarts neophytes in their entire effort to develop useful signal filters. Fortunately sound SPR methods use techniques such as cross-validation and significance testing to avoid overfitting. We discuss these below.

After the search is over, the SPR system will come to one of two possible conclusions: None of the indicators are useful discriminators, or one or more spaces contain valid filtering information and a Cl- ter rule can be formulated.

Classification of a Current Signal Of course the ultimate objective of SPR is be-

ing able to determine the most probable class of a newly issued signal before the trader acts on it. Will it be profitable or not. . . . That is the question. This is referred to as signal classification. Though true class can not be known until after the position ini-

Figures 4A & 46

A Space with Good Discrimination Power and a Space with Poor

Discrimination Power

Xl

Fig. 4A Indicator space Xl, X2 has strong discrimination power evidenced by the spatial separation of profiible from unprofitable signals.

Fig. 46 The intermixture of profitable and unprofitable signals in X4, X5 space indicates that this pair of indicators is devoid of useful filtering information.

+ = profitable signal 0 = unprofitable signal

tiated by the signal is closed out, the values of the filtering indicators are known when the signal is generated. These values define a point in the indicator space.

Probable class is determined by comparing the current signal’s location in indicator space with those of prior signals whose class is known. The fundamental assumption is that the current signal’s class is most probably the same as the signals most heavily represented in the immediate vicinity of


indicator space. Consider the following example: Suppose today the MTS issues a signal. If current indicator values define a point in the space that is located in or near a region that is dominated by loss trades, the signal is most likely to be a loser and would therefore be rejected by the filter. This concept is illustrated in Figure 5. The trading signal of unknown class is depicted with a “?” symbol.

The Overfitting Problem & Its Avoidance

Despite the intuitive appeal of SPR concepts, the proper development of SPR filters is fraught with a significant pitfall. . . overfitting. Truly useful SPR methods must safeguard against this ever present problem.

All data modeling involves fitting. But it is when this process is carried too far that overfitting occurs. Properly fitted models (trading systems, filter, equations, etc) capture the data’s valid patterns, and are therefore likely to hold true in other samples of data. In contrast, overfitted models have been forced to be so specific to the analyzed data that they inadvertently capture random effects as well. To be sure, such a model will appear to predict well (fit> in that data set, but that performance will not hold up in another sample.

The neophyte data analyst often fails to realize how easy it is to be seduced by the desire to fit. The truth is high degrees of fit can always be achieved with sufficient effort, misguided though it may be. If enough different models without limit on their complexity are tested, a perfect fit will be found. Developers of MTS, utilizing optimizable system development “tool-boxes”, are often guilty of this. In their desire to produce the “ultimate” trading system that catches every turning point with no false signals, they keep adding rule upon rule. The in- evitable result is merely a complex description of the analyzed data that is guaranteed to work like the “Holy Grail” in that specific data set. But also guaranteed is the failure of the MTS to repeat this brilliant performance when applied to new data. This often leads to the erroneous conclusion that the markets somehow changed just as the MTS was being installed for actual trading. The hard truth is the MTS was flawed with overfit from its inception. The only way to develop a model, be it an MTS or a filter, that will perform well in the future is to halt the growth of rule complexity prior to falling into the over& trap.

The key to avoiding overfit is to be aware of how it can come about. Overfit can result in two ways. One type results from allowing the class separating boundaries to assume any contorted shape necessary

Figure 5

Classification of a Current Signal

Xl

The current MTS signal, whose outcome is not yet known, is depicted by the “7” symbol positioned at the Xl, X2 values at the time of the signal’s occurran- As these coordinates place it in a region of Xl, X2 space dominated by previous loss signals, it is likely to be a loser as well. An SPR filter would reject such a signal.


to segregate profitable from unprofitable signals. In Figure 6A good and bad signals are highly intermixed, yet the strangely shaped boundary imposed on the same data sample in Figure 6B does separate the unprofitable from the profitable signals. However the shape of the unprofitable region is likely to be unique to that particular sample of signals and lack- ing in sufficient generality to filter a new set of signals accurately.

Another, even more insidious form of overfit results from testing too many spaces. This will produce spaces in which winning and losing signals are separable with simply shaped boundaries. The cause is the large number of possible spaces relative to the number of trading signals available for analysis. As mentioned previously, given 100 candidate indicators, there am over four million possible l-D, 2-D, 3-D and 4-D indicator spaces. The number of prior trading signals typically available for analysis (100


Figures 6A & 6B

An Overfitted (Invalid) Discrimination Boundry

Fig. 6A This 2-D indicator space, based on indicators X4 and X5, has no valid filtering information as evidenced by the random intermixture of profitable and unprofitable signals throughout the space.

Fig. 66 Despite the lack of discrimination found in Xq X5 space, an overfitted boundry can be found that partitions profit and loss signals into separate regions. Such a boundry is invalid and unlikely to be effective on future signals.


to 1,000). By chance alone some spaces will appear to classify well, yet this is a merely statistical accident. If such spaces were to be populated with another sample of signals, the discrimination would evaporate.

So proper fit, not perfect fit, is the real objective. The key question is how can we know when proper fit has been achieved and additional fitting will result in over-fit? There are two methods: cross-validation and significance testing.

Cross-validation makes use of two sets of data. One set, referred to as the “learning set” is used ini- tially to search for spaces with “potential” classification power. A second set, called the “test set” is used to validate or confirm the discrimination power found in the “learning set”. Only spaces that show similar classification boundaries in both the “learning set” and “testing set” are given a favorable rat- ing. Most spaces fail this acid test.

The concept of cross-validation is illustrated in the Figures 7A, 7B, 7C, and 70. Figure 7A shows a 2-D indicator space populated with signals from the “learning set”. The pure neighborhoods give some hope that the space is a good signal discriminator. If the signals from the test set show a similar degree of class segregation, such as that seen in figure 7B, we have good evidence that the space contains valid information. If, however, the test set shows up looking like figure 7C, with the class pure neighborhoods but with the good and bad signal clusters having shifted locations, or as in 7D with class pure neighborhoods failing to appear, the SPR pro- g-ram would reject the space.

Despite its importance, being confirmed by cross-validation is not certain evidence of validity, as validation in the test set can be seen if enough spaces are tested. Therefore, additional safeguards based on specialized significance tests are employed to increase the level of certainty that a space is a valid discriminator. Sophisticated significance tests can determine if the degree of confirmation in the “test-set” is large enough such that it is unlikely to be due to chance. The precautions that need to be taken to avoid overfitting can not be overemphasized.

Reliability to Future Trading Signals The key question is how reliable will SPR

signal filters be when applied to previously unseen signals, even if the over-fit problem has been success- fully avoided? The simple answer is, if future signals are statistically similar in terms of their indicator characteristics, then similar levels of discrimination should be seen. By statistically similar, we mean that the indicator values characterizing new signals are within the range associated with previous signals. For example if indicator X,, has taken on values of - 100 to + 100 in the historical data, but sud- denly is at a value of +300 at the time of a new signal, the SPR filter prediction is not likely to be reliable. In other words SPR methods don’t extrapo- late well to signals that reside regions of the indicator space that are sparsely populated with historical samples. However, this is true of any intelligent system confronted with a situation for which is has no prior experience to make a judgement. With re-


Figures 7A, 7B, 7C & 7D

Cross-Validation Detects Ovetfitted Spaces

Fig. 7A In the “learning” data this space shows good discrimination of profit and loss signals.

Fig. 7B I f the “test” data shows clusters of profit and loss signals similar to the “learning data”, as shown here, the space is validated for filtering.

Fig. 7C If the “test” data shows pure clusters of profit and loss signals as shown here, but their locations have shifted significantly relative to the learning data, the space is graded invalid.

Fig. 7D I f the “test” data fails to show easily separable clusters of profit and loss signals, as shown here, the space is graded invalid.

spect to SPR filter development, this is not as big a problem as it might seem at first blush, for the candidate indicators can be designed to stay within well defined ranges.

gestion), for it is only in this manner that the SPR system has the opportunity to examine a range MTS performance conditions (good and bad).

Another more significant issue in SPR filter Results reliability has to do with the historical data set pro- To display the efficacy of the SPR filtering tech- vided. It is important that it contain as wide a range nique, we report below the results of two analyses

of market conditions as possible. If the historical sig- carried out by the author’s firm. These analyses were nal sample is comprised entirely of a steeply trend- performed utilizing PRISM, a proprietary pattern ed bull market, the SPR system will be unable to recognition system developed by Raden Research learn the distinguishing characteristics of profitable Group, Inc.. The first case relates to the development signals in all types of markets (bull, bear, and con- a filter developed for an MTS designed to trade the


Deutsche Mark for the foreign exchange department of a large money center bank. In a second case, a filter was developed for an MTS used to trade T-Bond futures.

Deutsche Mark Filter A sample of 208 historical signals issued by an

MTS for Deutsche Mark trading covering the period January 1975 through November 1987, were supplied by the client. The logic of the MTS were not disclosed.

The MTS user also supplied historical data on approximately 100 raw economic and market data series including Euro interest rates, balance of trade figures, employment data, GNP data, industrial pro- duction data, money supply data, stock prices, retail sales, spot currency rates for four countries: U.S., England, Germany and Japan. In a cooperative effort, the client and the author’s firm defined a set of 300 candidate indicators (i.e., transformations of the raw data); for example, the ten-day chance in the difference between the Euro dollar rate and the Euro Yen rate. These indicators were programmed and generated with PRISM. All indicators were lagged to take into account reporting and revision lags associated with the data, PRISM was then used to determine which, if any, had valid filtering information. Three indicators proved useful, and filter rules were formulated.

Below, the table compares the performance of the “raw” (i.e., unfiltered) trading system with the filtered version. These results include all trades, and is therefore a mixture of both cases used for learning and testing of the filter:

lated filter rules. Performance of the filter on the historical data indicated that signals accepted by the filter would be profitable 58% of the time compared with 44% profitable signals from the unfiltered system. The profit factor was increased by over 200%. In addition, the filter reduced the magnitude of draw-down by over 65%. The system and SPR filter were then used in actual trading for the period April 1986 through July 1987. The trading, which was conducted on behalf of a large international bank, produced profits exceeding 200% on invested capital with 62% of all trading signals profitable. Over the same period the unfiltered system would have had 51% profitable trades and experienced a draw-down 33% larger than the filtered system. Thus in actual trading, the filter performed in line with historical expectations. After July 1987, trading was ceased due to factors unrelated to the effectiveness of the trading system.

Conclusion SPR has been shown to be an effective method

for developing filters to improve the performance of MTS. The method appears to offer a number of ad- vantages over more traditional methods of analysis that often fall prey to over-fitting. Actual results of employing SPR signal filters have shown significant increases in MTS performance and such filters may offer a new lease on life to existing MTS.

David Aronson is president of Raden Research, a New York firm that specializes in applying pattern recogni-

; twn to financral markets. The firms PRISM system has developed signal filters for several trading firms.

Performance Unfiltered Filtered Indicator MTS MTS % Improvemt.

Total Profits $1,578,000 $1,854,00 +17.5

% Profit Trades 50% 56% +12

Profit Factor .39 .57 +47

The Profit Factor is the log of the ratio of all gains from profitable trades divided by all losses on unprofitable trades. Alternatively it is the log of:

% signals profitable x Avg gain on profit signal % signals unprofitable Avg loss on unprofit signal

T-Bond Ml73 Filter The sample of historical signals used for analy-

sis were 670 trading signals issued by a short-term volatility breakout MTS used to trade T-Bonds. The signals covered the period August 1977 through De- cember 1985. The author’s firm developed a list of 360 candidate indicators. PRISM identified four as containing valid filtering information and formu-


The Dow Jones Industrial Average Alternative Computation Methods Walter J. Marullo

Introduction Whenever one inquires about the performance of the U.S. stock market, one usually receives an answer in terms of the Dow Jones Industrial Average (DJIA). Although other indices contain many more components and therefore provide much broader coverage, the DJIA, an average of thirty relatively high-grade and well-followed stocks, has become synonymous with the “market.” Many members of the investment community, however, take issue with the DJIA’s lofty distinction. They insist that for a variety of reasons, the average is at best an imperfect indicator of the overall market and one that is sub- ject to a number of biases and distortions. The purpose of this paper is to probe and to analyze the DJIA’a purported limitations and to suggest ways in which the average could be improved in the future.

History of the DJIA “The Dow Jones Industrial Average is the con-

tinuous price index of the U.S. stock market from the late nineteenth century to the present.“’ Charles H. Dow, one of the founders of the Wall Street Journal, constructed the original DJIA in 1896 from a list of twelve major industrial stocks! In computing his index, Dow simply averaged the prices of the twelve component stocks. If any of the stocks had split or paid a stock dividend of at least a hundred percent since its incorporation in the index, however, its price was first adjusted by a cumulative split factor. For example, if one of the component stocks was selling at $50 per share but had undergone a 2-1 split some- time after its inclusion in the index, Dow assigned that stock a price of $100 before averaging it with the prices of the other eleven stocks. Reflecting the expansion of the U.S. economy, Dow expanded his index to include twenty stocks in October of 1916.5

In October of 1928, Peter Hamilton, Dow’s suc- cessor as editor at the Wall Street Journal, not only expanded the DJIA to include thirty stocks but also changed the method of its calculation? Hamilton continued the practice of averaging the components’ stock prices, but rather than accounting for stock splits in the numerator of the calculation, he ad-

justed for splits and large stock dividends (greater than 10 percent) by changing the divisor “Specifical- ly, when a DJIA stock splits, the divisor is changed so that the value of the index at the moment of the split is the same, using either the new price and new divisor or the old price and old divisor.“5 For example, suppose the index comprised only two stocks, both of which were selling for $100. In this case, the index would have a value of 100 ( 1100 + 1001/2 = 100). If one of the stocks then underwent a 2-1 split, the divisor would have to change from two to 1.5 so that the value of the index would remain at 100 ( 1100 + 50]/1.5 = 100). Under the original method for computing the DJIA, the adjustment for the split would have occurred in the numerator, and the divisor would have remained constant ( [lo0 + 2 x 50112 = 100).

The need for simplicity and easy calculation was the primary reason that Hamilton changed the manner in which the index was computed! Know- ing updated stock prices of the 30 industrials and the current divisor’, one could easily calculate the DJIA by hand or with a simple adding machine. Thus, with his new method of calculation, Hamil- ton could provide hourly quotes of the DJIA using only the crude technology available in 1928. Al- though many changes have been made in the stocks that comprise the present-day DJIA, the average is still calculated using Hamilton’s flexible-divisor method.

Criteria for Evaluating Stock Indices Before evaluating any stock index, one must

consider the purposes for which it is being used. In general, an index can serve as (1) an indicator of aggregate market movement&’ and/or (2) a benchmark for measuring the performance of an investment portfolio? Different indices will better serve one of these two main functions. For example, someone interested in assessing overall market changes would generally prefer to use a broad, market-value-weighted index. On the other hand, someone evaluating the performance of a portfolio manager may rather use an index in which the individual components were equally weighted, because such a benchmark is a

52 M’J!A JOURNAL / SPRING 1991

more “accurate representation of a typical investment portfolio at its inception, that is, one in which approximately equal dollar amounts would be invested in each stock.“1° Other criteria one may consider in assessing a stock index include the ease of calculation (although less relevant in the age of high- speed computers) and the longevity of the index, i.e., the extent to which one is able to make comparisons between today’s stock market and those that existed in the distant past. All things considered, “it is pret- ty well recognized among analysts that there is no such thing as the perfect stock index and that the search for one is doomed to failure.“”

Evaluation of the Present DJIA The strong points of the DJIA are its simplici-

ty, longevity, and timeliness. As mentioned above, the index is very simple to calculate, and it allows one to make comparisons with stock markets as far back as 1896. Because each of the DJIA’s component stocks trades very frequently, the average is much more timely than other indices, whose constituent stocks trade in a less liquid manner. “The DJIA gives one of the few accurate indications of the market valuation process as it evolves I31 is an extremely useful index for representing short-tern market movements.“12

As a long-term indicator of the stock market, the DJIA has many theoretical limitations and biases. Most of these problems arise from (1) the fact that the average is a price-weighted index and (2) the manner in which the average adjusts for stock splits and stock dividends.

As a price-weighted index, the DJIA is influenced more by its higher-priced components than by its lower-priced components. Consider the situation at the end of 1989, when Navistar sold for $3.875 per share, while DuPont sold for $123 per share. If the price of Navistar’s stock had risen 10 percent, the DJIA would have increased by only 0.66 points ( 10.1 x 3.8751 divided by the then-current divisor of 0.586). On the other hand, if DuPont’s stock price had risen 10 percent, the DJIA would have increased by 20.99 points ( 110.1 x 1231/0.586), illustrating how the index can become dominated by a few, very high-priced stocks. Moreover, although great care has been taken to ensure that a variety of major industries are represented in the DJIA, changing stock prices can dramatically alter the relative weightings of those industries.

Most criticism of the DJIA focuses on the theoretical biases resulting from the manner in which the index adjusts for stock splits and stock dividends. Interestingly, some critics claim that the average has an upward bias, while other critics maintain that the

index has a downward bias. Proponents of the upward-bias argument insist

that the price of a stock tends to increase abnormal- ly during the interval between when a company announces a stock split and when the split actually takes effect. According to these critics, “a proportionate decline in the price of the split stock after the split will not ‘wash out’ the run-up. It will fail to do this simply because the post-split stock has relatively less weight in the DJIA than the pre-split stock.“13 Although the increase in the price of the stock is temporary, the change in the DJIA divisor at the time of the split is permanent. As a result of the cumulative effect of past stock splits, the DJIA would become upwardly biasedT4

To illustrate this phenomenon, consider a hypothetical index of two stocks, A and B, both of which are currently selling for $100 per share. Assume that Company B announces a 2-1 split and that the price of Stock B increases to $120 just before the split date Also assume that the price of Stock B falls from $60 per share to $50 per share shortly thereafter. The following tables show how the pre-split run-up in Stock B causes an upward bias in this hypothetical DJIA.

DJIA With Stock B Run-up

After Before After split split

Announcement Announcement Date Date

Stock A 100 100 100 100 Stock B 100 120 60 50 Divisor 2.00 2.00 1.45 1.45 DJIA 100.00 110.00 110.00 103.13

DJIA Without Stock B Run-up

After BefOlV? After split split

Announcement Announcement Date Date

Stock A 100 100 100 100 Stock B 100 100 50 50 Divisor 2.00 2.00 1.50 1.50 DJIA 100.00 100.00 100.00 100.00

Although in both scenarios the ending prices of Stocks A and B are $100 and $50, respectively, the ending index value is higher in the scenario with the temporary run-up of Stock B than it is in the scenario without the temporary run-up. Thus, a pre- split, abnormal increase in the price of Stock B would cause an upward bias in the DJIA.

The theoretical underpinning of the upward- bias argument is reasonable; however, proponents have not provided much tangible data to support their contention. On the other hand, E. Eugene Carter and Kalman J. Cohen, in a study covering the period from June 1948 to January 1963, found no empirical


evidence to support the notion that the DJIA is upwardly biased?5

Those who argue that the DJIA has a downward bias focus on the facts that (1) when a stock splits, it has less influence on the value of the DJIA because the average is a price-weighted index and (2) succesful, high-growth stocks tend to split more often than unsuccessful, low-growth issues!6 Accord- ing to the proponents of the downward-bias theory, the DJIA becomes more and more influenced by its poorer performing components.

Consider, for example, a hypothetical index of two stocks, A and B, both of which originally sell for $100 per share. Assume that Stock A remains at $100 per share for three years. Also assume that Stock B rises to $200 per share in Year 2, splits 2-1, rises again to $200 in Year 3, and than once again splits 2-l. The following tables show how the splitting of the high-growth stock causes the index to be lower than it otherwise would have been.

DJIA With Stock B Splits

Stock A Stock B Divisor DJIA

Year 2 Year 2 Year 3 Year 3 Before After Before After

Year 1 Split split split split

100 100 100 100 100 100 200 100 200 100 2.00 2.00 1.33 1.33 0.89

100.00 150.00 150.00 225.00 225.00

DJIA Without Stock B Splits

Stock A Stock B Divisor DJIA

Year 1

100 100 2.00

100.00

Year 2

100 200 2.00

150.00

Year 3

100 400 2.00

250.00

In the scenario in which its stock twice splits 2-1, Company B ends up contributing 50 percent of the index’s value at the end of Year 3; however, in the scenario in which its stock never splits, Company B ends up contributing 80 percent of the index’s value at the end of Year 3.

A real-life example of this reduction in the weighting of a high-growth stock is provided by the case of Merck & Co. during the lo-year period from June 1979 to December 1989. On June 29, 1979, Merck’s stock was selling at $67.50 per share, and it contributed 5.47 percent of the DJIA’s value. Over the next ten years, Merck’s stock split twice, once at 2-l and again at 3-1. On December 29, 1989, Merck’s stock was selling at $77.50 per share, and its weighting in the DJIA had dropped to 4.59 percent. If Merck and the other DJIA stocks had not split at all during those ten years, Merck theoretically would have sold for $465.00 per share and would

have contributed 12.38 to the value of the DJIA. Stock splits and anything else that causes

large changes in relative stock prices significantly influence the differential weightings of the DJIA’s individual components. Some critics of the index have concluded that “the DJIA is neither a reliable indicator of market sentiment nor an accurate benchmark for use in measuring market performance, since its characteristics change randomly over time.“”

Alternative Computation Methods The present method used in calculating the

DJIA creates many theoretical problems for the index. On an empirical level, I therefore wanted to see how different computation methods would have changed the value of the DJIA over a particular test period. Using data from volumes of the Daily Stock Price Record, I calculated four alternative, monthly ending DJIAs for each month during the period from June 1979 through December 1989 (test period). The alternatives were (1) a market-value-weighted index, (2) an equal-weighted index using arithmetically calculated returns, (3) an equal-weighted index using geometrically calculated returns, and a (4) constant-divisor index.

Market-Value Weighting Most of the well-known stock market indices

such as the S&P 500, the NYSE composite, the NASDAQ composite, and the AMEX composite are market-value-weighted indices, i.e., the current index is computed according to the following formula:

Total Market Value of All Components Today

Total Market Value of All Components on Base Day

x

Index on Base Day

(Market Value = Price/Share x Shares Outstanding)

Critics of value-weighted indices point out that they can become dominated by a few major stocks. They insist that although these indices may be representative of the overall market, they are less useful as benchmarks for evaluating investment performance, because few portfolios would have such a heavy emphasis on a handful of stocks. Critics also maintain that value-weighted indices have a long- term upward bias because the weighting of the more successful stocks continually increases over time?

In calculating a value-weighted DJIA for each month of the test period, I used June 29, 1979, as my base day and 841.98, the closing DJIA on that day, as my base index. On four occasions during the test period, individual stocks were added and deleted


from the DJIAlg, and it therefore was necessary to multiply the simple, value-weighted DJIA by an adjustment factor so that the value of the index just before the substitution equaled the value of the index just after the substitution. The adjustment factor was carried forward and used in the computation of subsequent month’s indices until a further substitution of components necessitated its revision.

The results of those calculations are tabulated in Appendex A and are portrayed versus the actual monthly closing DJIAs in Graph 1. Critics of value- weighted indices maintain that such averages are upwardly biased, and the data for the period between September 1981 and June 1986 support that contention. For 58 straight months, the value-weighted DJIA exceeded the actual average. This apparent upward bias reversed in later months, causing the value-weighted DJIA to be less than the actual DJIA in 67 of the 126 months of the whole test period (53.2 percent of the test months). Moreover, the value- weighted DJIA at the end of 1989 was 2478.34, while the actual DJIA finished 1989 at 2753.20. The poor relative performance of the value-weighted index since August 1987 is largely the result of IBM’s falling from $168.375 per share on August 31,1987, to $94.125 per share on December 29, 1989-a per- annum price depreciation of 22.1 percent. As indicated in Appendix B, IBM’s stock price increased at a per-annum rate of only 2.4 percent throughout the entire test period, and this may explain why the value-weighted DJIA was more often less than the actual DJIA. These results demonstrate the extent to which large-capitalization stocks can influence a value-weighted index.

weighted index value was equal to 100 in Year 1, the following table shows the different ending index values that would result from using arithmetically and geometrically calculated indices?l

Returns Arithmetically Calculated

Year 1 Year 2 Year 3

Stock A 100 50 100 Return on A -50% 100% Stock B 50 100 50 Return on B 100% -50% Average Return 25% 25% Index 100.00 125.00 156.25

Returns Geometrically Calculated

Year 1 Year 2 Year 3

Stock A 100 50 100 Return on A -50% 0% Stock B 50 100 50 Return on B 100% 0% Average Return 25% 0% Index 100.00 125.00 100.00

Notice that with an arithmetically calculated, equal-weighted index, the base period index value is simply the index of the previous period, while with a geometrically calculated, equal-weighted index, the base period index value is the index that prevailed at some fixed point in the past (Year 1 in this hypothetical example). Considering that the prices of Stocks A and B in Year 3 are no different than they were in Year 1, one can see why the geometrically calculated Year 3-index of 100.00 is more accurate than the arithmetically calculated Year 3-index of 156.25.

Although an equal-weighted index using geometrically calculated returns is more accurate than one using arithmetically calculated returns, I con-

Equal Weighting strutted monthly, equal-weighted DJIAs for each In an equal-weighted index, no stock has a dis- month of the test period using both computation

proportionate influence on the overall average. Such methods. an index is generally calculated by taking the aver- In calculating an arithmetic, equal-weighted age percentage return of the individual component DJIA, I took the monthly closing price of each compo- stocks and applying it to some base period index val- nent stock, adjusted for any previous splits during the ue. Two types of equal-weighted indices are possible test period, and divided it by the split-adjusted price depending on whether the individual component per- of the previous month. This ratio was then averaged centage returns are arithmetically or geometrical- with the ratios derived from the prices of the other 29 ly computed. An arithmetically calculated, equal- components, and the resulting mean ratio was weighted index is easier to compute, but it tends to multiplied by the previous month’s index to produce overstate actual performance; a geometrically cal- the new equal-weighted DJIA. As I had done with the culated, equal-weighted index is more difficult to value-weighted computations, I chose 841.98, the ac- compute, but it is more accurateTo tual DJIA at the end of June 1979, as my beginning

Consider two hypothetical stocks, A and B. In index. Year 1, Stock A sells for $100 per share, and Stock The results of those calculations are listed in Ap- B sells for $50 per share. In Year 2, Stock A falls to pendix A and are pictured versus the actual monthly $50, and Stock B rises to $100. In Year 3, the prices closing DJIAs in Graph 2. The arithmetic, equal- of Stocks A and B return to their original values of weighted DJIA was greater than the actual DJIA in $100 and $50, respectively. Assuming that the equal- 98 of the 126 months of the test period (77.8 per-


Graph 1

ACTUAL DJIA VS. VALUE-WEIGHTED DJIA Jum 1979 through D~c~mbw 1989

2.800

2.700

2.600

2.500

2.400

2.300

0 2.200

! 2.100

d >- 2.000

B 1.900

fi 1.800

0 J GO 1.700

= *b 1.600

i 1 so0

‘r : 1.400

1.300

1.200

1.100

1 .ooo

0.900

0.600

0.700 m

1980 1981 1982 1963 1964 1985 1966 1987 1988 1989

0 Actual DJIA + Valua-Walghted DJIA

Graph 2

ACTUAL DJIA VS. EQUAL-WT.(ARITH.) DJIA Juna 1979 through Oacambar 1989

2.800

2.700

2.600

2.500

2.400

2.300

it 2.200

d2 5

2.100

2.000

g 0: TV

1.900

1.800

a ii 52 1.700

1 .600 1

1.500

1.400

1.300

1.200

1.100

1 .ooo

0.900

0.800

0.700 m

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989

0 Actual DJIA t Equal-Wt.(Arlth.)

56 hfTA JOURNAL ! SPRING 1991

cent of the test months). In addition, the equal- weighted average finished 1989 at 2763.31, slightly higher than the actual DJIA of 2753.20. These results are consistent with the notion that an equal- weighted index calculated from arithmetic returns tends to overstate actual performance.

To calculate a geometric, equal-weighted DJIA, I took the split-adjusted, monthly closing price of each component stock and divided it by the split- adjusted price of a base-period month. This ratio was then averaged with the ratios derived from the prices of the other 29 components, and the resulting mean ratio was multiplied by the base month’s index to produce the new equal-weighted DJIA. I originally set June 1979 as the base month, but as individual component stocks were added and deleted from the DJIA, I had to reset the base to the month just before the substitution occurred.

The results of the geometric, equal-weighted calculations are tabulated in Appendix A and are portrayed versus the actual monthly closing DJIAs in Graph 3. The geometric, equal-weighted DJIA was greater than the actual DJIA in 83 of the 126 months of the test period (65.9 percent of the test months). Nevertheless, the equal-weighted average finished 1989 at 2707.39, less than the actual DJIA of 2753.20. Assuming that one can use the geometric, equal-weighted index as an accurate measure of market performance, these mixed results do not provide convincing support for either those who contend the actual DJIA is upwardly biased or those who insist the actual DJIA is downwardly biased.

ican Express for Manville Corporation. I changed the divisor to 1.470 beginning with the February 1984 computation in order to adjust for the break-up of AT&l (substituting the new AT&T for the old AT&T). This divisor was changed to 1.402 beginning with my October 1985 calculation to reflect the addition of McDonald’s and Philip Morris and the deletion of American Brands and General Foods. Finally, I changed the divisor to 1.386 beginning with the March 1987 calculation to adjust for the substitution of Boeing and Coca-Cola for Into, Ltd. and Owens-Illinois Glass. Notice that had a constant-divisor system been implemented in June 1979, the divisor that would have prevailed at the end of 1989, 1.386, is much higher than 0.586, the divisor that actually existed under the present method for computing the DJIA.

The results of the constant-divisor DJIA calculations are tabulated in Appendix A and are portrayed versus the actual monthly closing DJIAs in Graph 4. The constant-divisor DJIA was less than the actual DJIA in 105 of the 126 months of the test period (83.3 percent of the test months). Moreover, the constant-divisor index finished 1989 at 2710.97, less than the actual DJIA of 2753.20. These results support the theory that the present DJIA has an upward bias, or at least that during the June 29,1979, through December 29, 1989 test period, the factors causing an upward bias in the DJIA, i.e., temporary price run-ups in stocks just before they split, out- weighed the factors causing a downward bias in the average, i.e., the declining influence of appreciating, splitting stocks in a price weighted index.

Constant-Divisor Method In addition to calculating value-weighted and Conclusions

equal-weighted indices, I computed monthly closing With the exception of the period from August DJIAs using the constant-divisor method, which had 1987 through December 1989, the four alternative actually been used prior to October 1928. Under this DJIAs yielded similar results. Consider, for exam- method, the current price of each component stock ple, Graph 5, which portrays the arithmetic, equal- is multiplied by its cumulative split factor before be- weighted index versus the value-weighted DJIA, the ing summed and averaged with the other component two most divergent averages. The graph shows that stocks. In other words, the numerator of the index prior to August 1987, the two indices tracked each calculation, not the divisor, is adjusted for stock other very closely. As mentioned earlier, the value- splits and stock dividends. Under this method, I weighted DJIA was significantly depressed after changed the divisor only when individual component August 1987 by the dismal performance of IBM. stocks were added and deleted from the DJIA. In The constant-divisor index and equal-weighted those months of the test period, I computed a new average calculated from geometric returns, which are divisor so that the value of constant-divisor DJIA depicted in Graph 6, are better than the current DJIA, before the substitution equaled the value of the in- because they are free from the potentially distorting dex after the substitution. biases associated with the present method of cal-

The initial divisor used in my constant-divisor culating the index. The geometric, equal-weighted DJIA calculations was 1.465, the actual DJIA divi- DJIA would serve as a better benchmark for evaluat- sor in existence at the end of June 1979. This figure ing portfolio performance, while the constant-divi- was changed to 1.511 beginning with my August sor DJIA would function as a better indicator of gen- 1982 calculation to reflect the substitution of Amer- era1 movements within the blue-chip sector of the


Graph 3

2.800

2.700

2.600

2.500

2.400

2.300

ii 2.200

e 2.100

“D$ 5,

2.000

1.900

c cl 1 .a00 %H ” z 2 1.700

Jz A.5 1.600

i 1.500

2 I” 1.400

1.300

1.200

1.100

1 .ooo

ACTUAL DJIA VS. EQUAL-WT.(GEOM.) DJIA Juna 1979 through Dacsmbrr 1989

0.700

1980 1981 1982 i 983 1984 1985 1986 1987 1988 1969

El Actual DJIA t Equd-Wt.(Gaom

Graph 4

ACTUAL DJIA VS. CONSTANT-DIV SOR DJIA

2.800 ,

Juna 1979 through Dwambar 1989

2.700 -

2.600 -

2.500 -

2.400 -

2.300 -

g 2.200 -

e 2.100 -

44 g,

2.000-

1.900 -

pi 1.000 -

OJ 00 1.700-

x 1 & i 2 f

.600

.500

1980 1981 i 982 1983 1984 1985 1986 1987 1988 1989

cl Actual DJIA + Cord.-Dlvlsor DJIA


Graph 5

EQUAL-WT.(ARITH.) VS. VALUE-WT. DJIA Juna 1979 through Dacmmbw 1989

0 Equal-Wt.(Arlth.) t Valua-Walghtad

Graph 6

EQUAL-WT.(GEOM.) VS. CONS.-DIVISOR DJIA

2.600

2.700

2.600

2.500

2.400

2.300

2.200

2.100

2.000

1.900

1 A00

1.700

1.600

1 so0

1.400

1.300

1.200

1.100

1 .ooo

0.900

0.800

June 1979 through Dacamber 1989

0.700

1980 1981 1982 1963 1984 1965 1986 1987 1988 1989

0 Equal-Wt.(Gaom.) + Conat.-Dlvlsor MIA


r

stock market. During the test period, the geometric, equal-weighted index exceeded the constant-divisor DJIA in 99 of the 126 months (78.6 percent of the test months). Nevertheless, the geometric, equal- weighted index finished 1989 at 2707.39, less than the constant-divisor DJIA of 2710.97.

Graph 7, which portrays the actual DJIA together with the geometric, equal-weighted and constant-divisor indices, illustrates that the empirical differences among these alternatives was very small during the test period. It therefore may be difficult to convince people of the need to change the present method used in calculating the DJIA. The calculations show, however, that there is potential for greater distortions in the future.

With this consideration in mind, I recommend changing to a constant-divisor DJIA. Such an average had been used prior to October 1928, and one therefore could argue that the original DJIA was being reinstated. A constant-divisor index would eliminate the theoretical biases associated with the manner in which the current DJIA adjusts for stock splits and stock dividends. It would be a major improvement.

FOOTNOTES

1. Hartman L. Butler, Jr. and Devon J. Allen, “The Dow Jones Industrial Average I&-Reexamined,” Financial Analysts Journal 35 (November-December 1979), 23.

2. Robert D. Milne, “The Dow Jones Industrial Average Re-examined,” Financial Analysts Journal 22 (November-December 1966), 83.

3. Ibid.

4. Ibid.

5. E. Eugene Carter and Kalman J. Cohen, “Bias in the DJIA Caused by Stock Splits,” Financial Analysts Journal 22 (Novem- ber-December 1966), 90.

6. Mime, 84.

7. When Hamilton expanded the DJIA to include thirty stocks and changed its method of calculation, the divisor was set at 16.67 so as to equate the value of the index to what it had been just before the change. The current DJIA divisor, which reflects all of the stock splits, major stock dividends, and component changes that have occurred since October 1928, is 0.555.

8. F’rank K. Reilly, Znuestment Analysis and PorybZia Management,

2nd ed. (New York: CBS College Publishing, 1985), 121.

9. Hartman L. Butler, Jr. and Richard F. DeMong, “The Chang- ing Dow Jones Industrial Average,” Financial Analysts Journal 42 (July-August 19861, 59.

10. Milne, 86.

11. Robert B. Shaw, “The Dow Jones Industrials vs. the Dow Jones Industrial Average,” Financial Analysts Journal 11 (November 19551, 37.

12. Andrew T Rudd, “The Revised Dow Jones Industrial Average: New Wine in Old Bottles?,” Financial Analysts Journal 35 (November-December 1979), 63.

13. Carter and Cohen, 90.

14. Ibid., 91.

15. Ibid., 94.

16. Another minor argument sometimes put forward by propo

nents of the downward-bias theory is the fact that the DJIA divisor is seldom adjusted for stock dividends of less than 10 percent. These critics therefore maintain that the divisor is higher and the DJIA is lower than they otherwise would be ifthe divisor were adjusted for all stock dividends.

17. Rudd, 58.

18. Milne, 86.

19. On August 31, 1982, American Express was substituted for Manville Corporation. AT&l’was broken-up on February 16,1984, and one can think of the new AT&I’ as being substituted for the old AT&T. On October 31, 1985, McDonald’s and Philip Morris were added to the DJIA, and American Brands and General Foods were deleted. Finally, on March 13,1987, Boeing and Coca-Cola were substituted for Into, Ltd. and Owens-Illinois Glass.

20. Milne, 86.

21. Ibid.

BIBLIOGRAPHY

Butler, Jr., Hartman L., and Allen, J. Devon. “The Dow Jones Industrial Average Re-Reexamined!’ Financial Analysts Jour- nal 35 (November-December 1979), 23-30.

Butler, Jr., Hartman L., and Decker, Martin G. “A Security Check on the Dow Jones Industrial Average.” Financial Analysts Journal 9 (February 19531, 3745.

Butler, Jr., Hartman L., and DeMong, Richard F. “The Chang- ing Dow Jones Industrial Average.” Financial Analysts Jour- nal 42 (July-August 1986), 59-62.

Carter, E. Eugene, and Cohen, Kalman J. “Bias in the DJL4 Caused by Stock Splits? Financial Analysts Journal 22 (November-December 19661, 90-94.

Daily Stack Price Record, New York Stack Exchange. New York: Standard & Poor’s Corporation, April 1979-December 1989.

Milne, Robert D. “The Dow Jones Industrial Average Re-examined!’ Financial Analysts Journal 22 (November-December 1966), 83-88.

Reilly, Frank K. Investment Analysis and Portfolio Management. 2nd ed. New York: CBS College Publishing, 1985.

Rudd, Andrew T. “The Revised Dow Jones Industrial Average: New Wine in Old Bottles?’ Financial Analysts Journal 35 (November-December 1979), 57-63.

Schellbach, Lewis L. “When Did the DJIA Top 1200?” Financial Analysts Journal 23 (May-June 1967), 71-73.

Shaw, Robert B. “The Dow Jones Industrials vs. the Dow Jones Industrial Average” Financial Analysts Journal 11 (November 19551, 37-40.

Associate with the Environmental Services Specialized Finance Unit at the Bank of Boston.


Graph 7

ACTUAL, EQUAL-WT.(GEO.), & CON-DIV DJIA

2.600 ,

Juna 1979 thr&h D.c;mbw 1989

2.700 -

2.600 -

2.500 -

2.400 -

2.300 -

ii 2.200 -

x-J F

2.100 -

2.000 -

g 0: 0

1.900 -

1 A00 -

8 5 1.700 - GO s 1 _*t.

1 f

s E

.600

so0

.400 1

.300

.200

.lOO

0.700

1980 1981 1982 1963 1964 1985 1986 1987 1966 1969

0 Actual DJIA + Eq.-Wt.(Gao.) V COllSt.-DlV.

AdUd

DJIA

841.98

e46.42

007.63

818.58

815.70

82235

838.74

675.35

663.14

785.75

817.06

85085

867.92

935.32

932.59

932.42

924.49

99334

663.99

947.27

974.58

99775

991.75

976.88

952.34

681.47

849.98

852.55

888.98

875.00

87110

824.39

822.77

e-48.36

819 54

811.93

808.60

901.31

Appendix A

VdUP

Weighted

DJIA

84198

834.90

858.16

848.86

801.48

807.51

802 78

645.67

838.11

767.67

796.18

818.51

83823

892.26

897.07

366.77

899.07

965 95

93566

936.73

950.97

949.43

94727

941.67

933.3-l

930.47

879.43

860.98

872.52

903.79

897.86

915 16

865.92

em.33

890.25

87115

858.36

864.10

954.36

Equal.

Weighted

(Arith.)

DJIA

841.98

85451

895.26

889.30

816.66

820.55

841.64

889 20

871.96

793.39

625.44

855.72

874.68

950.96

949.34

946.76

640.40

996.10

973.75

663.67

989.47

1044.82

103266

1021.05

mo5.35

980.19

901.37

859.71

660.30

897.21

677.02

867.10

818.50

817.30

841.28

80122

795.45

762.26

882.17

Equal-

WeIghted

Geom.)

DJIA

811.98

654.51

894.98

889.09

816.06

820.64

642.04

892.51

a30.86

790.53

622.70

653.66

870.11

941.13

939.60

937.22

935.48

1005.16

973.95

958.00

986.57

1029.86

1019.92

1001.15

989.83

967.96

895.33

653.36

861.83

899.50

880.46

862.33

814.91

817.69

646.41

814.18

802.34

790.13

891.05

COMstpnt

Llkisc.r

DJIA

841.98

846.50

687.37

876.33

815.27

822.18

836.14

876.19

862.80

765.64

816.55

850.68

067.49

93447

932.68

932.25

924.83

993.09

663.62

647.53

974.66

1002.05

996.e-t

986.86

974.57

954.69

ea.73

653.75

851.00

894.80

877.39

667.58

82227

622.27

646.67

819.28

81041

803.33

895.93


Appendix A (continued)

696.25 931 12

1039.28

1046.54

1015.10 1112.18 1130.03 1226.20

1199.98

1221.96

1199 22

1216.16

1233.13 1225.20

1216.02

1253.84

1220.58 1154.83 1164.89

1170.15 1104 85 1132.40 1115.28 1224.38 1208.11 1201.38 1188.94 1211.57

1286.11

1234.01

1288.73 1258.08 1315.4, 1335.48 1341.45

1334.01 1328.83 1374 31 1412.13

1548.81

1109 06

1818.81 1783.98 1818.11 1892.72

1775.31 1898.34 1181.58

1311.11

1914.23 1a95.95 2158.04 2223.99 2304.69 2283.36 2291.51

2413.53 2512.07 2662.95

2596.28

1993.53

1833.55

1938.83

1958.22

2071.82

198808

2032.33 2031.12

2141.71

2126.73 2031.85 2112.91 2143.85 2114.51 2189.51

2342.32 27.58.39

2293.82 2418.80

248015

2440.06

2880.66 2737.21 2692.82

2645.08

2106.21

2153.20

Vdllb

Weighted

JmA

954.15

1081.71

1103.28

1130.44 1198.41 1208.05 1220.81 1340.58 1285.31 1320.33 1315.38 1339.65 1353.90 1351.98

1368.14

1380.28

1341.90 1280.97 1233.60 1320.12 1245.12 1284.21 1280.98 1388.64 1398.85 1394 41

1385 31 1394.39 1495.82 1488.83 1455.44 1445.01 1505.23 1506.07

1481.87 1455 23 1529.21 1819.58 1720.48 1887.84 178&OQ 1859 18 1345.84

189l.eQ

1895.31

1165.00

1892.11 1778.91 1931.03

1992.08

1848.92 2019.28

2115.41 2217.14

2232.88 2248.74 2353.08 2416.24

2581.68

2492.51 1978.72

1784.44

1870.00

19oc.12 1981.19 1888.55 1918.83 1921.22 2021.87 2017.30 1913.88 1974.84 2011.82 1989.21 2029.40 2188.32 2095.53 2110.08 2201.52 2249.70 222115 2407.20 2428.66 2413.81 2392.36

2440.28

2418.34

EL@- Equal. Wtiphted Weighted

Wdb.) Nseom.) DJL4 DJIA

COMt.UUt.

Divisor

DJIA

871.01 678.OQ 890.39

956 12 965 88 981.88 993.12 1004.45 1022.50

1015.38 1022.02 1032.88 1058.92 1060.42 1061.55 1099.69 1105.39 1096.82 1125.64 1131.90 1119.15 1241.10 1245 12 1210.79 1238.57 1239.06 1181.94 1248.74 1246.48 1202.49 1238.82 l!u3.15 1119 a3 1260.46 1283.41 1201.52 1278.71 1281.95 1214.28 1271.97 1281.01 1204.00 1344.81 1336.66 1253.39 1311.72 13cul.11 1238.42 1292.89 1214.53 1205.41 1201.90 1185.01 1124.32 1210.59 1192.31 1134.01 1233.11 1203.21 1158.93 1151.58 1128.15 1038.30 1164.35 1153.18 1122.92 1155.93 1128 13 1104.93 1299.43 1257.99 1218.75 1282.02 1243.15 1207.14 1280.14 1228.14 1209.99 1252.81 1211.12 1189.83 123474 1241.25 1210 31 1380.28 1330.29 1234.61 1382.83 1331.82 1239.75 138423 1315.03 1271.17 1355.72 1310.19 1280.29 1423.45 1318.11 1313.03 1441.20 1395.02 1338.22 1485.90 140621 1347.02

1448.01 1392.18 1330.32 1423.43 1319.98 1315.14 1441.39 1403.17 1361.89

1552.98 1502.06 148289

1822.88 1510.40 1533.94

1650.48 159920 1550.29

1738.51 1137.98 1895.27

16aO.83 1322.31 1182.35

1813.14 1153.39 1719.11 1883.16 1828.35 1796.78 1874.50 1829.52 181370

1717.35 1894 19 1712.29

1681.62 1820.42 1332.34

1182.55 1102.74 1891.98

1881.81 1812.95 1799.88

1811.12 1337.80 1841.74

1345.98 1812.01 1832.78

2119.90 2073.39 2091.32 2198.83 2145.74 2183.07 2211.82 2222.82 2230.19

2291.50 2238.40 2203.48 2318.13 2266.88 2213.92 2435.36 2319.41 2343.43 2616.93 2570.05 2490.40 2864.72 2819.99 2588.81 2819.63 2560.65 254419 1915.49 1935.31 1967.80 1918.88 1189.29 1798.97 1950.39 1930.51 1388.18 2007.24 1987.55 1911.30 2159.43 2113.12 2013.98 2ow.90 2046.03 1923.57 2127.51 2090.58 1981.02 2124.20 2060.43 1981.58 2252.63 2209.18 2064.55 2238.93 2205.26 205801

2144.20 2089.02 1965.30 2221.66 2152.18 2085.12 2282.14 2196.28 2088.43 2221.88 2153.83 2051.40 2284.38 2213.44 2095.84 2446.48 2396.49 2215.52 2313.88 2323.29 2198.25 7.40684 2383.30 2232.59 2512.33 2449.28 2351.06

2555.19 2487.45 2408.62 2511.11 2438.58 2318.35 2133.15 2850.23 2805.01 2796.32 2108.99 2659 54

2141.48 2871.58 2830.34 2669.21 2595.06 2808.54 2127.57 2854 74 2810.05 2163.31 2101.39 2710.97


Company

Allied Signal (Formerly Allied Chemical)

Aluminum Company of America

American Express

AT&T (Before break-up) AT8lr (After break-up)

Bethlehem Steel Boeing

Chevron Corporation lIFormerly Standard Oil of California)

Coca-Cola

DuPont

Eastman Kodak EXX0n

General Electric

General Motors Goody&W

IBM International Paper

McDonald’s Corporation

Merck & Ca Minnesota Mining &

Manufacturing Ca

Navistar (Formerly International Harvester)

Philip Morris Primerica (Formerly

American Can)

Procter & Gamble

Sears Roebuck Texaco

Union Carbide

USX Corporation (Formerly us Steel)

United Technologies

Westinghouse Electric

Woolworth Corporation American Bran&s

General Foods Into, Ltd.

Manville Corporation (Formerly Johns Manville)

Owens-Illinois Glass

APPENDIX B

Portion of Test Period in which Company Was

Included in the DJIA

Whole Period

Whole Period

E/31/82 to 12/‘29/89

6/29/79 to 2/16/84 2/16/84 to 12&J/89

Whole Period 3113187 to 12/29/89

Whole Period

3113187 to 12/29/89 Whole Period

Whole Period Whole Period

Whole Period


whole Period Whole Paper

10131185 to 12/29/89


Whole Period

10/31/85 to 12/29/89 whole Period

Whole Period


whole Period

Whole Period

Whole Period

Whole Period

Whole Period 6/29/79 to 10/31/85

w29f-79 to 10/31/85 6/29/79 to 3113187

8l29/79 to 8131182

6/29/79 to 3113187

Compound Annual Price Appreciation

3.87%

10.74%

16.25%

2.02% 18.41%

-1.31% 21.02%

10.28%

19.34% 10.97%

4.70%

13.31% 16.92%

3.42% 10.08%

2.40%

9.25% 22.46%

20.18%

10.40%

-19.79%

43.77% 3.68%

13.14%

6.72% 7.47%

6.22%

4.90%

10.75%

21.14%

16.16% 10.89%

23.32% -3.69%

-40.53%

26.89%


r NOTES

64 MTA JOURNAL ! SPRING 1991

journal of technical analysis (jota). issue 37 (1991, spring)

Economy & Finance

mta journal spring

mta library

floor new york

single issue of mta

monthly mta newsletter

bohan merrill lynch

financial technical

new jersey richard orr