Journal of Technical Analysis (JOTA). Issue 33 (1989, August)

~IIII~~~IIANS ASSOCIATION

JOURNAL Issue 33 August 1989

I

MARKET TECHNICIANS ASSOCIATION JOURNAL

Issue 33 August 1989

Editor

John R. McGinley Technical Trends

Wilton, Connecticut

Manuscript Reviewers

Arthur T. Dietz, Ph.D. Graduate School of Business Administration

Emory University Atlanta, Georgia

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

Kansas City, Missouri

Frederick Dickson Management Asset Corporation

Westport, Connecticut

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

Anthony W. Tabell Delafield, Harvey, Tabell

Princeton, New Jersey

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

San Francisco, California

Frank D. Korth Value Line Asset Management

New York, New York

Printer

Fidelity Press Inc. 655 Plains Road

MiIford, Connecticut 06460

Publisher

Market Technicians Association 71 Broadway, 2nd Floor

New York, New York 10006

MTA JOURNAL ! AUGUST 1989 1

Benefits of MTA

MARKETING TECHNICIANS ASSOCIATION, INC.

Member and Affiliate Information

ELIGIBILITY: REGULAR MEMBElzsHIp 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.”

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STYLE SHEET FOR THE SUBMISSION OF ARTICLES

MTA Editorial Policy

The MARKET TECHNICIANS ASSOCIATION JOURNAL is published by the Market Technicians Associa- tion, 71 Broadway, 2nd Floor, New York, NY loo06 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. Publication dates are February, May and November.

Style For The MTA Journal

All papers submitted to the MTA Journal are re- quested to have the following items as prerequisites to consideration for publication:

should be put at the end of the article. Submis- sion 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 affiiation will be shown under the title.

5. Two submission copies are necessary.

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

Manuscript of any style will be received and ex- amined, 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 BV’2 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 references

Mail your manuscripts to:

Dr. Richard Orr John Gutman Investments 35 Meriam Street Lexington, MA 02173

MTA JOURNAL i AUGUST 1989 3

MARKET TECHNICIANS ASSOCIATION Board of Directors, 1989-90

President 1 Vice-President/Long Range Vice-President/Seminar Philip Roth Dermis Jarrett Philip Erlanger Shearson Lehman Hutton Kidder, Peabody & Co., Inc. Fidelity Management World Firrl. Center, Amex Tower 10 Hanover Square, 15th Fl. 82 Devonshire Street-N9A New York, NY 10285-1100 New York, NY 10005 Boston, MA 02109 2X2/640-8900 2l2/510-3751 617 /570-7248

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Committee Chairpersons

programs Membership Ken Tower Robert Prechter, Jr. Delatield, Harvey, Tabell New Classics Library 600 Alexander Road P.O. Box 1618 Princeton, NJ 08543-5209 Gainesville, GA 30503 609/987-2300 404/536-0309

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Journal Dr. Richard Grr John Gutman Investments 35 Meriam Street Lexington, MA 02173 617 /861-1544

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MTA Office Manager Shelley Lebeck Market Technicians Association 71 Broadway, 2nd Fl.. c/o NYSSA New York, NY 10006 2l2/344-1266

4 MTA JOURNAL / AUGUST 1989

TABLE OF CONTENTS

ARTICLES

PAGE

Membership and Subscriber Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Style Sheet For The Submission of Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

MTA Officers and Committee Chairpersons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Editors Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Financial Manias By Charles D. Kirkpatrick II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Institutional Buying Power and the Stock Market By R. David Ranson and William G. Shipmun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chaos I: Time Series Forecasts in Markets By Richard C. Orr, Ph.D. .,..................................................... 29

Retracement Percentage By Arthur A. Merrill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Warning Signs For Market Peaks By Roger Williams .,............................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Day of the Week and Intraday Effects in Stock Returns By Michael Smirlock and L.uuro Starks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

MTAJOURNAL! AUGUST 1989 5

Editor’s Comments

John R. McGinley, Editor

This issue marks an inflection point in the long history of this Journal. We have altered its appearance by typesetting almost all of it. Before long, if costs per- mit, the final format (rule lines around pages, two column articles, etc.) and what will be its distinctive “look” will be in place for every issue.

We will request authors to submit articles on disk wherever possible to reduce costs. Inasmuch as most articles are prepared on word processors already, this should be no imposition. We hope you like our ini- tial steps. (For contrast, one article has been left typewritten.)

Articles in this issue I am particularly proud of the lead article, which

I coaxed out of MTA historian par excellance, Charlie Kirkpatrick. His analysis of panics is required reading, especially now in the late ‘80’s which contain the very seeds of which he writes. His original speech-which I sat through spellbound-also covered the accompany- ing drop in money velocity. He tells me that’s another whole article. Charlie?

The next article, reprinted by permission of the Financial Analysts Journal, is a blockbuster: it dem- onstrates the Funds Cash Percentage, one of our most beloved sentiment/supply/demand indicators, is for most purposes, useless. The cash figures have no, re- peat no, correlation with the market! It does not, in fact measure sentiment. The article explains in detail why. Analysts relying too heavily on this indicator are innocently using the market to measure the market, a specious undertaking.

While the article definitively shows this indicator does not measure its intended target, i.e. sentiment, Arthur Merrill has shown it does have one remaining use: because the indicator’s denominator is for all purposes the market and the market is a good indicator of itself because of the long-term cycles present, it can be used to predict the averages, but not sentiment. However, it is far easier to monitor these cycles by simply using the market itself, without the intermediate step of collecting and calculating the Funds Cash Percentage.

Dick Orr’s well attended breakfasts at the Seminar were for those of us intrigued with Chaos, one of the Seminar’s highlights. This is Dick’s second article on the subject for the Journal. (You’ll no doubt find it easier to understand if you have read James Gleick’s book, Chaos.) In reading the article, I personally developed a list of questions and suspect many others will as well. We plan to submit a list of questions to Dick for further discussion and clarification in an up- coming Journal. Please submit yours to the Journal; the discussion should be fascinating. Those interested in joining the Chaos Resource Group should contact Hank Pruden at PO Box 1348, Ross, CA 94957.

Arthur Merrill’s article was the first submitted for acceptance in fulfillment of CMT II requirements. We are delighted his was also the first to be printed. The 50% principle and some of the Fibbonacci ratio numbers appear to have some explaining to do faced with the raw statistics and analysis in this article. But then exploring fact and fiction (what he calls anecdotal evidence) in the market has been Arthur’s passion for over 30 years.

Roger Williams has done yeoman’s work in codi- fying the turning points of many indicators at some of the past inflection points in the market. This useful study could be the jumping-off point for others interested in both updating and backdating the work he has begun.

The last article-on the days of the week-is yet another study in this important area. The Journal published an later article on the subject in February 1985 (“Day-of-the-Week Effects” by Robert Wood & Thom- as McInish). Curiously neither of these studies quote or even reference the most definitive early work done on the subject by Arthur Merrill (“Behavior of Prices on Wall Street”, 1966, rev. 1984), to which we also refer the interested reader. You’ll find it in the MTA Library.

CMT II Articles Much of the work as Editor this year has been

in attempting to clarify the requirements for CMT II papers. Many members feel they want to point with

6 MTA JOURNAL 1 AUGUST 1989

pride to what they accomplished in achieving their CMT ticket: “That’s what I did to get my CMT.” They want it to be something of lasting worth for future technicians to read, a veritable point of pride. We en- courage you to get yours in as soon as possible. You have three years from the time you passed CMT I. (Ar- ticles not specifically for CMT II are also sought, of course.)

Toward this end, at the Seminar we hammered out a definitive document spelling out the CMT II article requirements in hopes of clearing the air, ending the confusion and encouraging articles. If eligible, you should be receiving your copy about the time you receive this Journal. Those of us on either the Certifica- tion or Journal Committees will be glad to discuss your article ideas; please give us a call.

MTA JOURNAL 1 AUGUT 1989 7

FINANCIAL MANIAS

Charles D. Kirkpatrick II Kirkpatrick & Company, Inc.

Charlie Kirkpatrick, longtime member of the MTA, is president of Kirkpatrick & Company, Inc., a consulting firm to institutional investors.

The following paper is an edited and updated version of a speech given by the author to the Society for the Investigation of Recurring Events in New York, February 25, 1987.

FORWARD:

This paper is about financial manias - economic events rather than market events. As such, you may ask why it is included in a technical analysis journal. But from reading financial market history as a technician, I noticed certain economic patterns seemed to precede fmancial manias. While financial manias were relatively infrequent and the preceding patterns not absolutely precise, as are most technical patterns, the recurrence of economic and political events was so consistent that it formed the basis for a technical theory of financial manias.

Technical work is not necessarily limited to specific chart patterns, ratios or indicators. In its broadest sense, technical work includes all observable price behavior, be it chaotic, Elliott, cyclical, patterned, or simply random. The most difficult aspect of technical work for non- practitioners to accept is the lack of causal relationships implied by technical theory. Not knowing the ‘ ‘reason’ ’ for a price move bothers many people. For example, no one has come up with a satisfactory “reason” as to why a ‘head-and-shoulders’ pattern will often foretell a price move. The technician cares more about the foretelling than about the cause. In return, this non-causal perspective allows the technician to observe historical phenomena more clearly. He is not inhibited by the bound of finding a “reason.”

The principal difference between economic patterns and market price patterns, aside from cause, is that unlike specific stock or commodity prices, economic patterns often develop in related data, not directly connected with that which the technician hoped to predict. We see this in stock market analysis when we look at non-price data such as put/call ratios, advisory sentiment, and monetary statistics. Even then we tend to simplify the relationship to one-on-one, i.e., advisors are bearish, therefore the market is low.

In studying longer term economic data to find a technically suitable means of analyzing financial manias, I found plenty of the one-on-one relationships - debt/equity ratio is high, therefore the stock market is high, or money velocity is high, long-term rates are high, and so on - but more interestingly, I also found that financial manias develon through a nrogression of sequential events which. if accomplished in order. seem to guarantee the mania’s OcCurrenCe.

Certain prerequisites were necessary, certain sequentialevents had to occur, andcertain elements were present along the way, causal or not. This necessary sequence differs from conventional, technical price-patterns. Still, the complexity and lack of necessary cause is perhaps why only

MTA JOURNAL / AUGUST 1989 9

a technical study, in its effort to simplify and predict rather than to necessarily understand, is able to see even the slightest bit of order leading up to such a long and ultimately devastating economic event as a financial mania.

ANCIAT, MAN-&

What are they and what do they require? How do they arrive? When have they occurred? Are we in one now?

A mania is characterized by intensely enthusiastic, mass psychological behavior; it is a craze stimulated principally by exaggerated emotion rather than logic. Gun control, ALAR on apples, and abortion all qualify as a mod- em-day manias. There can be a religious mania (some would say religion itself is a mania) as we see affecting the followers of Khomeini, Jim Jones or Reverend Moon, and there can be political manias like communism or fascism. In short, a mania occurs when coi- lective reasoning is abandoned.

THE 1920’S AND NOW

DOW JONES INDUSTRIAL

1917- 1932 1976 - PRESENT 400 4WJO

FLORICA LAND WUAPSE(l=Q

One visionoftenpaintedin history books is that during a mania people behave in odd ways (“maniacs”?) - i.e., they are wide- eyed, speak in strange tongues, perhaps gy- rate their bodies and use obscene gestures. However, this is rare. Leading up to 1929, for example, freakish behavior did not increase. More commonlv. manias are very subtle. Basicallv. thev are neriods of unsound reasoning covered bv emotionalism. Like alco-

1917 1920 1923 1926 1929 1932 1970 1961 1964 1967 1990 1993

lNlTULlDllDAT*ALUUSrrDTOEOU*Llel,

holics justifying drinks on a seemingly rea- VERTICAL LINES = 36-MONTH LOWS JIWlKiLConp~.Inc.

sonable appeal for sympathy, people in a mania often convince themselves that they

CHART I

are completely rational. It is only later they discover their thoughts have been absurd. This is especially true in financial manias.

We remember financial manias for their aftermath. You have heard of the South Sea Bubble, the Tulip Bulb and 1929 stock market manias because the subsequent economic contractions were obvious, measurable (in suffering, anyway) and worldwide. The panic following these manias brought back reality to those caught up in the preceding popular thought. That earlier emotional period, when followed by a financial panic, is called a “financial mania.”

This is not to say that all panics are preceded by financial manias. Panics are different; they


can occur for other reasons. For example, the 1980 Hunt stock market panic was small and short- lived, due to the insolvency of a few speculators.

Panics are also relatively frequent, catching people off guard during periods of general op- timism. In most instances they are halted either by the action of a specific financial leader, like Alexander Hamilton in 1792, J. P. Morgan in 1893, 1901 and 1907, and more recently, Paul Volcker in 1980 (and Alan Greenspan in 1987), or by the liquidity of the financial system itself, as in 1962,197O and 1974.

On the other hand, those panics following financial manias occur relatively infrequently and cause changes to the entire economic and political system, sometimes forever. The panic following the Mississippi Bubble (1720), for example, created an embedded French distrust in bonds and paper currency still evident today and is one reason why France has never been able to develop the capital base necessary to competitively expand its productivity. Look at how the 1929 mania crash still influences public opinion today. It is probably why you are here (reading this paper). Financial mania panics cause permanent damage.

We also note that financial manias are a relatively new event in the course of human history. There were panics in Roman times and earlier, defaults on bonds and so forth, usually from natural events rather than emotional excess (Pompeii pasta futures?), but the permanent change induced by the more modern version appears to have originated around the time of the Tulip Bulb mania in Holland in 1634. The “reason” it took so long for financial manias to develou is because other maior economic factors had to develou first. Principal among these was the Industrial Revolution (requiring large capital pools), company shares (the concept of readily transferable ownership in an ongoing entity), fiat money and credit (a standard medium of exchange and negotiable paper representing a promise to deliver), exchanges (a central marketplace), and perhaps even double-entry bookkeeping (to quantify return on investment)

Industrial Revolution and Currency

Obviously, the Industrial Revolution required capital. To finance the increased productivity from new plant and equipment, a potential manufacturer needed purchasing power beyond what the local knight or duke could supply. Paper money, credit, stock shams, and financial exchanges developedout of the need for these financial resources. Coinage was first used around 700 B.C., but paper money, substitute money, was not invented until the 9th century in China. In Europe, paper money, originally bills of exchange, became negotiable instruments around the 1 lth century.

Another subtle change occurred during the slow transfer from agrarian to industrial economies. This was the change in consumer choice from a few decisions in an agricultural, supply-limited economy to a large number of alternatives in a demand-driven, industrial economy. Keynes outlined this fundamental psychological change in his refutation of Say’s Law (“goods supplied on the markets will regularly stimulate the demand for them.“)

In an agrarian society there is little surplus. Economic growth and productivity are related to the limited supply of crops. Numerous consumption decisions are impossible because the economy is supply-driven. On the other hand, the surplus produced through the increased

MTA JOURNAL / AUGUST 1989 u

productivity of the Industrial Age created a demand-driven economy. As Keynes noted, a prospering individual then could decide whether to (1) keep his money, (2) spend it, or (3) invest it (read “speculate”). In the agrarian economy, a person could not get caught up in a financial mania because neither the means nor opportunities to speculate were available. Only in the Industrial Age has he been given the opportunity to make the wrong choice.

Corporate Shares, Exchanges and Credit

Credit, we know, has been around a long time. Sumerian documents from about 3000 B.C. reveal the use of credit and interest charges to finance grain and metal production. Credit default is presumably just as old. The earliest known municipal default, for instance, occurred in 337 B.C. (when two out of thirteen municipalities of the Attic Maritime League defaulted on loans from the Delos Temple). To speculate in financial markets, specifically the stock market, however, the concept of a corporation and an exchange in which to trade corporate shares is also necessary.

We know that companies existed in Babylon, nineteen centuries before Christ. These were participations in specific projects. The Code of Hammurabi included the first recorded wage and price controls (they were just as unsuccessful then as now) and limits on interest rates, suggesting that credit also existed 4,000 years ago. (It was in mortgages on houses and seasonal financing of crops.) In Rome and renaissance Italy, partnerships were sold in associations, usually to bid on government contracts, finance a ship, or divide risk as in an insurance policy. Each of these agreements broke up after the project was completed. Not until the second millennium did the concept of a permanent entity develop and shares in that corporation become negotiable instruments. Some were long lasting. Sydney Homer reports that as late as 1957, a 2 l/2 percent perpetual annuity, issued in 1624, was traded on the New York Stock Exchange in Lekdyk Bovendams Company, chartered in 1323.

As the development of corporations was slow, so was the organization of exchanges. Early in the middle ages local merchants and traveling traders would meet in specific places to discuss crops, prices, make arrangements and learn the news:

In Dunkerque,“all businessmen [meet daily] at the hour of noon, on the square infront ofthe town house [i.e., the town hall]. And it is there, within sight and hearing of everyone that these bigwigs (gross bonnets) quarrel and insult each other.” Archives Nationales, Paris, Section G7,698,24.

These town meetings developed into trading centers in the major cities and eventually became organized into exchanges. The first is thought to have been assembled in Bruge, France in 1409 but even earlier informal exchanges met regularly:

Barcelona, 1393 - In Gothic Hall “u whole squadron of brokers [could be seen] moving in andout of its pillars, and the people standing in little groups were brokers (corredorsd’orella) by ear’whose job it was to listen, report and put interested parties in touch. ” Charles Carriere, Negociants Marseillais au XVIIIe siecle, 1973, I, p. 51.

The earliest major exchange, which proportionally would dwarf the New York Stock Exchange or Chicago Mercantile Exchange of today, was the Amsterdam Exchange, built in

It MTA JOURNAL I AUGUST 1989

163 1 but organized much earlier. It included trading posts for specific instruments, and a clearing house in which certificates were registered on special ledgers. Commodities, curren- cies, shareholdings in specific ventures, maritime insurance, government annuities (bonds) and private company obligations (the Dutch East India Company was founded as a stock venture in 1602) were traded here. Over 4,500 people crushed inside the building each day. The public sat in coffee houses outside the exchange building, and brokers would come out to buy and sell shares, hoping to turn a profit on returning inside. Individual speculation was common. A Joseph de la Vega (Confusion de confusiones, Amsterdam, 1688) kept notes and wrote of being successively ruined five times in markets such as wheat futures and herring forwards.

This hectic pace culminated in 1634 with the Tulip mania when a Semper Augustus bulb sold for 2500 florins (a business suit cost only 80 florins). It collapsed, reportedly, when a visiting sailor bit into a rare bulb (‘which could be exchanged for a new carriage, two grey horses, and a complete harness’) thinking it was an onion, and not a very good onion at that. The subsequent collapse in tulip bulb prices ended the first financial mania.

.

Pow do thev arrive l

3

One perturbing problem in investigating financial manias is the scarcity of historic economic data. We know who killed whom and who slept with whom, but we know very little about the economic forces which drove political, religious and social life. After the major financial manias in the early 1700’s, the South Sea Bubble inEngland and the Mississippi Bubble in France, we must look to American, post-Revolution, economic history. American economic data is better than most, and it improves until very recently when it has been “adjusted” for seasonality and inflation.

From looking at financial manias in the past, we can outline the principal stages which the economic pattern seems to follow. Those stages are outlined below. Following that outline is a brief description of each of the three major manias after the Tulip mania, showing how the stages fit a common pattern.

Stage A. (Price inflation mania1

I. An unpopular war in a foreign land, initiated by a belief in an abstract threat, never a direct one, is financed in tandem with a prosperous economy.

II. Inflation in commodity prices accelerates, usually due to the increased demand for goods by the military and by the domestic economy, and total debt increases.

III. A coincident rise in interest rates, due to borrowing for the war and to uncertainty about the future value of the currency, causes debt holders to lose purchasing power but gain higher yields in short-term instruments. Of the Industrial Age consumer choices, spending outweighs keeping or investing.

Stage B. (Price and interest rate peak1

I. When the war ends, inflation and interest rates peak. The demand for

MTA JOURNAL i AUGUST 1989 u

goods declines. Money supply contracts over the short but sharp transition recession period from inflation to deflation. Commodity producers lose, debt holders begin to regain principal as lower rates push up intangible asset prices (stocks and bonds).

I. Credit expands (a necessary requirement for a financial mania). The sovereign is pressured into credit expansion or other means of credit expansion become available, and rules about owning and speculating in intangible assets become more relaxed.

II. Commodity markets decline and financial assets continue to rise as interest rates decline. Debt holders gain principal but new purchasers increas- ingly derive less and less current income.

Stage D. (Financial mania)

I. Debt quality declines as new purchasers lessen quality constraints in order to maintain current income in the declining interest rate environment.

II. Increased total debt is issued to accommodate lesser quality constraints and to cover earlier non-productive debt in tangibles (real estate, oil).

III. Rise in principal value of financial assets masks few defaults. P/E’s in stocks expand.

IV. Enthusiasm generated from profits made in financial assets generates more enthusiasm and, because few defaults occur, a false feeling of safety. Of the three Industrial Age consumer choices, investment (speculation) outweighs spending and keeping.

Stage E. (The collapse]

I. Financial markets collapse, specifically the stock market and lower quality debt market. Causes are usually either the exhaustion of speculative buying (the sailor and the onion), governmental restrictive action, an increase in interest rates, or the pullout from the markets by foreigners.

Of these stages, the most critical and necessary are (1) the commodity inflation and interest rate bulge, fueled by expanding credit, and (2) the continued credit expansion after an inflation peak. Without mice inflation first, a financial mania has never developed. Second, when inflation and interest rates peak, money supply and credit must continue to expand in spite of the difficulties encountered in the transition from inflation to deflation. If monev SUDD~V is curtailed at this iuncture or credit is unavailable, the financial mania never develops,

Because these two important junctures appear to be necessary for a financial mania to

14 MTAJOURNALi’ AUGUST 1989

develop, you would think modern government with its power through the central bank (Federal Reserve) would have the means to prevent such a calamity by curtailing inflation and by restricting credit expansion. Unfortunately, at those important moments, political pressures force the central bank to behave oppositely. Pressure to keep alive those weakened economic sectors which suffered from the commodity price change “shock” and to support an insolvent, debt-ridden credit system, keeps the financial machine going, laying the foundation for and later fueling the financial mania. Ironically, it is also the sovereign power which usually initiates the final collapse either by instigating programs damaging to the financial structure (trade resnic- tions, for example) or by restricting credit too late when speculation has reached an excess. Rather than solving the problem, the sovereign almost always contributes to it.

have thev occurredZ

Rather than delve explicitly into each of the many stages and minor similarities as they have occurred throughout each mania, the charts will demonstrate only the apparent connection between commodity manias and financial manias. There are many, many more detailed similarities between financial manias but a large book would be needed to catalog them. The most important pattern, as stated before, is the connection between a financial mania and an earlier inflation and interest rate bulge.

CHART II

DOW JONES INDUSTRIAL AVERAGE (recreated from other historical price

data prior to 1870)

10000 ::::::::::::::::~:::::::::::::::::!:::.:::::::::~:~~:::::::~:::::::~:~::::.::'::~:::.:~::: E. ::::::::::::::,:::: ::::::::::::: i :::::: :: ::::::::j::.:::::::::::: ::; ::::::.:::::::::j::: 3 ;ii;;;:;' . . . . . . . . . . . . ..'.................~................~.................~................~... ..:... Ll ,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~........ a:::::

1700 1750 1800 1850 1900 1950

5 YEAR INTERVALS (c)1999 Kirkpdrick 8 Company, Inc.

MTA JOURNAL ! AUGUST 1989 fi

Inflation, Financial Manias and Wars

“Inflation is always and everywhere a monetary phenomenon,” says Milton Friedman, When an increase in demand versus supply is fueled by expanded credit, prices of goods will rise. The expanded credit and abnormal demand for goods rises faster than usual during a war. Thus, most inflationary binges, aside from those produced by blatant printing of money, occur during war time (and generally during an unpopular war when both domestic wants and war needs compete). This has been true in every inflation peak prior to a financial mania.

The enclosed chart II (previous page) identifies the financial mania peaks on a reconstructed series of stock prices dating back to 1700 in Great Britain and the U.S. The level of prices at each period is unimportant. What is important is the accelerated price curve leading up to the peak and the long, severe, protracted decline afterward. This structure identifies a financial mania peak. They occurred in 1720, 1835, and 1929. For cycle buffs, the interval between peaks averaged 104.5 years (98.3 years, including the Tulip mania). This is not a Kondratief wave which coincides with economic depressions approximately every 50 years. It has taken two Kondratief cycles to make a Mania wave cycle, so far. Economic depressions am not always preceded by manias, but manias always end in depressions.

CHART III

BRITISH STOCK PRICES & INFLATION 1700-1800

CPI STOCK PRICES

200 j

4000 ................................. - ............. 1.. ................. _

_...................L...................L...................L ..................................... ..~

INFLATION PEAK. (71 I _......... . . . . . . ..)...................~...................I......

20 1 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 rTl I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I i I I I I I f I I I I I I I I I I I I i I I I I I I I 400

1700 1720 1740 1760 1780 1800

- CPI - STOCK MARKET

(c)1989 Kirkpatrick & Company, It-c.


1700-1800 British stock m-ices and consumer prices

Statistics about inflation, stock prices, and interest rates during the Tulip mania are scarce and don’t cover enough consecutive years to be useful. This leaves us with the South Sea Bubble (or the Mississippi Bubble in France) in the early eighteenth century as the first financial mania with somewhat reliable data.

Chart III (previous page) shows one important aspect of a financial mania - a war-induced inflationary peak always precede it. In 1700, the grandson of Louis IVX, of France was offered the succession to the Spanish throne. The French King decided that this ally would be enough to finally overthrow the Hapsburgs. Although not a direct threat to England, this action was enough to convince the British to side with the Dutch and Austria against the French in a long, bloody and indecisive war called the “Warof Spanish Succession.” Finally, in 1710, the Tory’s replaced the Whigs on a peace platform, and the war ended with the peace treaty of Utrecht in 1713. The wartime spike in British consumer prices peaked in 17 11. At the same time, interest rates also peaked, British Government long-term bonds at 8.7 percent were later to decline to 2.83 percent by 1737. This peak in both consumer price inflation andinterestrates occurred nine years prior to the South Sea Bubble peak in 1720.

CHART IV

AMERICAN STOCK PRICES & INFLATION 18004900

DJIA EQUIV. PPI 100 ~.................-...............-.......................;...................~...................~ 700

FINU(ClAL MANIA PEW. ,835

PEAK IN INFLATION i 70 BUT NO SUBSEQUENT - 4 .......... . . , ................ f .......

INFLATION PM. ,814

.........

,:::::;:.:::::I-/ 1

..)...................~ .......

1800 1820 1840 1860 1880 1900

(c)l 989 Kirkpatrick 8 Company. Inc.


1800-1900 US.

Later in the 19th century, we see a demonstration of where an inflationary binge was not followed by a financial mania. But again, as in the South Sea Bubble, the one financial mania which did occur was preceded by a war-induced inflationary peak. Notice that again, long-term interest rates peaked coincident with commodity prices and that both followed a generally unpop& war, the War of 18 12. The commodity price peak preceded the mania peak by twenty- one years, During that time, Jacksonian democracy allowed the Bank of the United States charter to expire and permitted countless unregulated country banks to issue specie. The stock market mania centered on canal, railroad and bank stocks with names like Morris Canal and Banking Company, but the bulk of speculation was in public land. The end came when Jackson issued the Specie Circular in 1836 which allowed payment for government land only in gold, silver and some Virginia script. The subsequent run on gold forced England to raise its rediscount rate to stem the gold flow. A depression set in which bankrupt many English companies and pulled speculative money out of the U.S.

Again an unpopular war erupted in 1860, the Civil War, and it, too, generated an inflationary binge and arise in long-term interest rates. Notice, however, that following the peak in inflation in 1866, no noticeable financial mania developed in the stock market. The economy

CHART V

AMERICAN STOCK PRICES & INFLATION 1900-PRESENT

/& _..___.._..____.__ _ .____.____..._....~ . j . . . . . . . . . . ~..::,I........... li i- .._....._..___.___ _

FINANCIAL MANIA PEAK. 1929

1900 1920 1940 1960 1980 2000

(c)1989 Kirkpabick 8 Company, Inc.

18 MTA JOURNAL ! AUGUST 1989

suffered from a severe economic depression in the 1870’s to 1890’s, probably the worst ever, including the 1930’s, but no mania developed before it. Why? Probably because, unlike the 1820’s and the 1920’s, the dollar was tightly tied to gold and credit expansion was discouraged. In addition, the Federal Reserve had not been organized, leaving the banking system without a “lender of last resort.” This vacuum tends to force bankers and other lenders of credit to behave more prudently.

19OOPresent

Again, an unpopular war, the “war to end all wars,” the First World War, stimulated prices andinterestrates into aninflationary bubble which burst on the armistice in 1919. Ten years later the financial mania ended with the 1929 stock market crash. The availability of credit after the War, thanks to the new Federal Reserve, and the declining post-war commodity prices and interest rates had fueled a speculation in intangible assets. The sequential pattern of previous manias developed on schedule.

. Are we in one now, 3

Many of the requirements for a financial mania have been met today. We have had an unpopular war in Vietnam, a commodity price binge which ended in 1979-80 after the war, and a coincident peak in interest rates in 1981. Since then intangible asset prices have risen as investors scrambled to maintain high yields by purchasing lessor quality debt, and at the same time, total debt increased as a percentage of GNP while the Federal Reserve supplied credit, even to the point of buying “junk” bonds and corporate loans from insolvent banks and permitting commercial banks to underwrite corporate issues. In vogue are such absurd notions of corporate finance as the belief that the low failure rate in “junk” bonds is an indication of low risk. And the academics have joined in by telling us that high debt/equity ratios are irrelevant and, indeed, desirable so long as debt cost (interest) is tax deductible and equity cost (divi- dend) is taxable. (This argument, t&en to its absurd extreme, suggests that an infinite debt equity ratio is ideal.) In other words, we have passed through most of the necessary stages for a financial mania.

CHART VI

JAPANESE MARKETS CONSUMER PRICE CHANGE ANC

THE STOCK MARKET

STOCK MARKET 100~ 4 :::::::::: : :.:

CPI PERCENT CHANGE 100

^ _ ..__._.........,......,.. M ..-.... .y-.: 10~~~

Alternatively, from a cyclical point-of- view, we are not due for a mania until 2020 (100 years from 1920); commodity prices have not declined absolutely; the Federal Reserve has not blatantly expanded credit because it is still worried about inflation (when it should be worried about speculation); the mania in “junk”

MTA JOURNAL / AUGUST 1989 fi

bonds or the stock market has not yet developed into a public hysteria. (It may have been nipped in the bud by the crash in 1987.) This would suggest that if we are now in a financial mania, it is not yet over.

One could also argue that the “maniacal” aspects of the current financial mania are more pronounced in Japan where the stock market and real estate market are more overpriced than here and the public is more deeply involved. Certainly, a collapse in financial markets would be pro- portionately more damaging to Japan than to us because their financial markets are so much more excessively over-valued.

What should you watch if the world is currently in a financial mania? The center of speculation has definitely moved to Japan and the Pacific rim, and for this reason, these markets should be monitored closely. As earlier stated, the level of inflation and interest rates is not as important as the direction. In spite of lower over-all interest rates and inflation, Japan has followed the standard stages leading to a financial mania (see chart VI). Inflation and interest rates peaked in 1974, and their stock market is now following an upwardly accelerating curve. It takes no great revelation to understand the perils existing in current Japanese markets.

But markets may react to other events, often governmental, which can create restrictions detrimental to the mania’s continuance. The Smoot-Hawley tariffs initiated in 1929 have been suggested as the potential cause for the stock market crash then. In 1835, it was the Specie Circular, Since the financial speculation in lesser quality intangibles is fueled by declining interest rates, a potential cause for disruption is a rise in rates. In February, 1929, the Federal Reserve, fearing that too much money was entering the speculative financial markets, and again in 193 1, fearing the loss of dollars from the banking system, restricted credit. Ultimately, they were right, but in reacting too late, they helped create the stock market crash and the depression.

In conclusion, there seem to be three major areas to watch: (1) the speculative markets, principally Japan, (2) governmental action which restricts trade, and (3) central bank action which restricts credit. When and if any one of these three areas changes for the worse, the current mania will be nearing its end.

Sources

Bolles, Albert, The Financial History of the United States, New York, 1896. Braudel, Fernand, The Structures of Everyday Life, Volume 1, Civilization and Capitalism, lSth-

18th Century, Braudel, Femand, The Wheels of Commerce, Volume 2, Civilization and Capitalism, 15th- 18th

Century, Business Conditions Digest, U.S. Department of Commerce, Tables 94 & 96, April &December

1988, & April 1989 Farrell, Maurice L. (ed.), The Dow Jones Averages 1885-1970, New York, 1972. Foundation for the Study of Cycles, Cycles, July 1965. Friedman, Milton 8z Schwartz, A., A Monetary History of the United States 1867-1960,

Princeton, 1963. Hillhouse, A. M., Municipal Bonds, New York, 1936.


Table I Relative Size of Mutual Fund and Pension Fund Stock Holding

Matud Fund Stock Holdings

Billions of Dollars

As a Pefcentagc of

Stock Held Total by All Stock

fnst~tutms Outstanding

1955 196.5 1975 1977

$ 6.9 9.5% 2.2% 30.9 15.1 4.3 33.7 10.8 4.5 31.7 9.3 3.2

Pension Fund Stock Holdings

As a Percentae of

Billions of Dollars

Stock Held Total by All Stock

Instrtutums Outstanding

1955 $ 6.1 8.4% 2.0% 1965 4Q.a 19.9 5.7 1975 86.6 20.3 11.7 1977 101.9 29.1 10.2

So-: Row of Funds Accounts. Federal Revrve Board.

doubled, the major shift was from individuals to institutional investors.

Significant changes have also taken place within the institutional category itself. In 1955, pension funds and mutual funds accounted for 8.4 and 9.5 per cent, respectively, of stock owned by institutional investors. As Table I shows, about four per cent of all stock outstanding was held by these two institutional investor groups. By 1977, respective market shares had changed dramatically: Pension funds accounted for 29.1 per cent and mutual funds 9.3 per cent of the equity of all institutional investors. Together, they held more than 13 per cent of all stock outstanding.

These figures indicate the significant im- portance of mutual fund and pension fund portfolio decisions. Moreover, pension funds enjoy a substantial and increasing cash flow, estimated at $22 billion in 1979. Their influence in the institutional market will undoubtedly increase. The equity assets of mutual funds peaked in 1972 at $52 billion, before falling to the 1979 level of about $32 billion. Although non-income mutual funds have lost market share, they remain an important investor category. By convert- ing their liquid assets into stock, they can harness three to four billion dollars in buying power.

The Cash-Asset Ratio Mutual fund liquid assets are considered by Some to phy a Causd role in the determination of

stock prices. “As a general rule, the greater the cash position of funds, the more bullish the market outlook. . . the lower the cash position, the more bearish the outlook is believed to be.“* In this context, the “cash position” refers to the cash-asset ratio -that is, liquid assets divided by total assets. Figure A compares the cash-asset ratio with the Standard & Poor’s (S&P) 500 index.

One would expect funds to be fully invested when portfolio managers expect the market to rise and lightly invested when they expect the market to fall. If mutual funds were able to an- ticipate market turns, then a low cash-asset ratio would tend to coincide with a market trough and a high ratio with a market peak. Figure A shows, however, that the cash-asset ratio tends to be loiv at market peaks and high at market troughs. In fact, the correlation between percentage changes in the ratio and in the S&P 500 index is negative and statistically significant.

Two general interpretations ha,ve emerged to explain the fact that stock prices have tended to move in a direction opposite to that suggested by the ratio. One is that “mutual funds appear to have acted in a fashion generally attributed to amateurs-that is, reaching a fully invested position at the top of the market cycle and having the most reserve buying power at the bottom.“‘That is, they have been consistently wrong at market extremes, and other investors can exploit their errors.

The other interpretation holds that the low cash position at market peaks, per se, keeps stock prices from rising further, since there is little buying power left. And, at market bottoms, “when the uninvested funds are put back into the market, stock prices will be driven ~p.“~ From this perspective, too, other investors can improve their market timing by observing the mutual fund cash-asset ratio.

Neither interpretation is reconcilable with the concept of an efficient market. In the first case, it is just as difficult to be consistently wrong at market turning points as it is to be consistently right. And, with respect to the second, stocks are priced based upon perceptions of the after-tax present value of all future returns accruing to the investor. Stock price movements reflect a reas- sessment in these perceptions. However, changes in buying power per se do not necessarily imply changes in perceptions.

An Alternative There is another explanation for the negative

MTA JOURNAL 1 AUGUST 1989 23

by R. David Ranson and Wi&arn G. Shipman

Institutional BuySng Power and the Stock Market

The ratio of mutual funds’ cash to their assets tends to be low at market peaks and high at market troughs. One explanation is that mutual funds have been consistently wrong at market extremes. Another is that variations in mutual fund liquid asset balances cause stock price levels to change; for example, the funds’ low cash position at market peaks keeps stocks from rising further, since there is so little buying power left. Either explanation implies that changes in institutional “buying power” signal changes in the market level.

Unfortunately, both explanations run counter to efficient market theory. The first ignores the fact that it is as difficult to be consistently wrong at market turning point as it is to be consistently right. And the second rests on the tacit assumption that the funds initiate the trading decision while the investors they trade with play a passive role. Without information about both buyers’ and sellers’ preferences, no analysis of a tran&tion can indicate the direction in which price will change, if indeed it changes it all. In fact, evidence shows no association between pension fund stock purchases and stock price changes.

There is a third and more reasonable explanation for the negative relation between the level of the stock market and funds’ cash-asset ratios: Changes in the denominator of the ratio-total assets -are caused by changes in the level of the stock market. The market value of the stocks institutional investors own rises and falls with the market.

C ORRECT timing of stock market turns is critical to investors, who have spared little

effort in the pursuit of reliable indicators of market change. “Buying power” is one such indicator. Conceptually, buying power is the amount of cash and cash equivalents held or received by investors that could be committed to the stock market at their discretion. The buying power hypothesis may be summarized as follows: Since the supply of stocks is essentially fixed, variations in the liquid asset balances and cash flows that constitute the significant sources of demand are prime determinants of stock price changes.

Is buying power a reliable indicator? This article examines the relation between stock market

R. David Ranson and William Shipman are General Partners of H.C. Wainwright 6 Co., Economics.


prices and buying power as measured by the liquid assets of non-income mutual funds and the positive cash flow of private pension funds. Our results suggest that information concerning the deployment of assets or cash flows is of little value in forecasting stock price changes.

Historical Perspective U.S. common stock is held by U.S. institutions and individuals and by foreigners. In 1955, American institutional investors owned 24 per cent, American individuals 73 per cent and foreigners three per cent of outstanding stock. By 1976, institutions held 40 per cent, individuals 54 per cent and foreigners six per cent.’ Although the fraction of common stock held by foreigners 1. Footnotes appear at end of article.

Figure B Changes In Total Assets of ken-income Mutual Funds vs. Stock Price Movements

Percentage Chanp

-r 40

.30

20

10

0

-10

-20

-30

-40

I I I I I I I I I I I I 1 I I I I

on-Income Fund Total Assets

L \ \ \ \ \ I I \

i

\ I

\ \ \ \

Source H C Wamwrlght & Co.. Economics

1 I I I II III II I I I I I I 1961 62 63 64 65 66 67 68 69 70 7l 72 73 74 75 76 77

S&P change and the change in total assets associated with the same S&I’ change.

Each of the three expressions in the equation can be estimated separately. Table II presents these estimates (known as regression coefficients) along with relevant measures of strength of the statistical relationships. The negative correlation between changes in the cash-asset ratio and in the S&P 500 is fullv accounted for by the almost tautologous relation between total assets and the market index. The association between the cash position and the market index is positive and, therefore, although it is weak, tends to mute rather than strengthen the overall negative

relation between the cash-asset ratio and the market. These results are consistent with our alternative interpretation and cast doubt on the two conventional views described above.

Allocation of Cash Flow The hypothesis that “money going into the market” causes stock prices to rise also can be analyzed using pension fund cash flows. Pen- sion fund flows were $19.6 billion in 1978 alone, and in the first quarter of 1979 reached $22.2 billion at an annual rate. In 1946, corporate equities comprised only 7.6 per cent of total financial assets of pension funds. In 1972, the


Figure A S&P 500 and Mutual Fund Cash-Asset Ratio

S&P500 Cash-Asset Ratlo

120

110

loo

90

80

70

60

50

U’

30

20

10

0 I I I I I I I ! I ! Ill

1960 61 62 63 64 bj 66 67 68 69 70 ;I -2 7 74 75 76 7:

13 0

12 3

7.5

5.0

2 5

0.0

relation between the stock market and the cash- asset ratio: Changes in the denominator of the ratio - total assets - are closely related to changes in the level of stock prices, as Figure B shows. Careful examination of the data indicates that the negative relation between changes in the cash-asset ratio and changes in the stock market arises from this fact alone.

In mathematical terms, let C/A be the cash- asset ratio of non-income mutual funds, where C is the aggregate cash position and A total assets. The percentage change in the cash-asset ratio can be split into two components-the percentage change in total cash and the percentage change

in total assets?

A%(CIA) = A%C - A%A.

Each of the components has its own relation to percentage changes in the S&P 500 (S). These relations are connected as follows:

A?‘o(UA) _ A%C A%A ---- A%S AYOS A%S

This equation states that the change in the cash- asset ratio that corresponds to a given percentage change in the S&P equals the difference between the change in cash position associated with the


Figum E Stock Prices and the Fraction of Private Pension Fund Assets Invested in Corporate Equities

S&P Sal

120

110

IOU

90

au

70

60

50

S&P so0

(Year-End) W

/v

I’

I

I. ! /\ 1 Pension Fund \ I ‘u \ ,

’ I Equity OwnershIp

v (Year-End)

Source: H.C. Wamwnght h Co.. Economtcs

I I I I I I I I I I I I I I I I II I

1960 61 62 63 64 65 66 67 68 69 70 7l 72 73 -4 3 76 7 78

6S

60

55

50

45

40

Assuming that stock prices will rise because pension funds increase their commitment to equities is analogous to analyzing the above transaction from the viewpoint of investor A alone. While it is possible that stock prices will rise if pension funds place a greater proportion of their cash flows into the equity market, it is equally possible that prices will stay the same or fall.

Empirically, the allocation of cash flow by private pension funds is not significantly correlated with either the size or direction of stock price changes. Figure C shows the scatter-plot relation between changes in stock prices during a given

calendar year and the fraction of cash tlow that pension funds allocated to equities in that year. Figure D compares changes in stock prices with the dollar purchase of corporate equities by pension funds. Neither reveals any association between pension fund activity and stock price changes, and statistical computations confirm the lack of a relationship.

Yet Figure E shows a close positive correlation between the S&P 500 and the fraction of total assets that pension funds hold in stocks. Why? Once again, the reason is a near mathematical tautology: Two closely related variables -stock assets and the S&l’ 500-are the corresponding

MTA JOURNAL ; AUGUST 1989 27

Table II Decomposlhon of the Relation Between Stock Price Figure C Allocation oi Penwn Fund Cash Flow< to Changes and Changes m the Cash-Asset Raho Equltles md Stock Market Prices

Measure of h&sure of Rekttlon udl Statntlcal 2 Ido”“-

0 Variabk S&P 500’ Signlficanceb :

1’0 -

(1) Cash balances 0.087 (2) Total assets 0.959

0.72’ f $ - 0

Minus 48.m 1; Equals (3) Cash-asset raho -0.872 7.29t t-100 -

;2 It 0

a. Regression coefficient of percentage change in vanable on c 3 percentage change VI S&P 500. <= aAl - . 0

b. T-value. -c: 0 l Not statistically slpvficant. : 5 0 l o t Statistically sguficant. -2 M) -

7:t 0. l

z$ 0 .

0 00 peak, stocks accounted for as much as 73 per cent 0 of pension fund assets. By 1979, the ratio had $7 40 -

zg l .*.. l

fallen to about 51 per cent-a 14-year low. Assume that, for whatever reasons, pension ;

funds decide to maintain the present asset mix of j about SO per cent stocks to 50 per cent all other assets, and in so doing invest one-half their posi-

-40 -20 0 20 4

Percentage Change in S&P XXI tive cash flow in stocks and one-half in other assets. With about $22.2 billion in flows in 1979, $11.1 billion would go to the equity market-an

Figure D Pension Fund Equity Purchases

increase of $9.4 billion over 1978. Would this and Stock Market Prices

increase stock prices? The buying power hypothesis suggests that,

with a limrted supply of stock outstanding, an additional $9.4 billion in demand would of necessity cause prices to rise. Furthermore, as sellers learned of the pension funds’ decision, they would be more reluctant to relinquish their stock. According to this view, it might take a substantial rise in prices to bring about equilib- rium between supply and demand.

This view essentially rests on the assumption that pension fund managers initiate the trading decision; the investors from whom they purchase their stock are implicitly relegated to a passive role. But there is no u priori reason to attrib- ute the initiative to the buyers.

For example, if two investors, A and Z, hold all the shares of a public company and are content with the number of shares they hold, their combined level of demand will lead to neither transactions nor price changes. If preferences for holding the security change, such that investor A wishes to hold one million dollars more and investor Z wishes to hold less by precisely the same amount, a transaction will occur, but no price change will result.

Analyzing the transaction solely from the viewpoint of the buyer, it would appear that the one’ million dollar increase in demand should raise the price of the fixed supply of stock. Con-

59.0

a0 p 2 2 70 II

0

w

versely, however, if the transaction is analyzed solely from the viewpoint of the seller, it would appear that the one million dollar decrease in demand should lower the stock price. Without information about preference changes, no analysis of this transaction can indicate the direction in which the price will change, if indeed it changes at all.


Chaos I: Time Series Forecasts in Markets

Richard C. Orr, Ph.D.

Introduction

This paper and one to follow expand on some ideas presented at two informal breakfast meetings of the Chaos Group at the 1989 MTA Seminar. The group, which was formed at the 1988 seminar, consists of people with an interest in the possible application of chaos theory to the financial markets. Preliminary discussions are already underway to make this area of investigation a more formal part of next years seminar. Although I have tried to make the contents of this paper understandable to the reader with no background in chaos theory, I would nonetheless suggest that Dr. Henry Pruden’s interview with me in this journal earlier this year (see 1) would be helpful additional reading. James Gleick’s marvelous account of the development of chaos theory over the past twenty-five years (see 2) is also a terrific resource for the non- scientist seeking to discover what it is about this new science that has so many people excited.

In my view, chaos theory, as it applies to the financial markets, splits into two broad areas. The area with which this paper deals is the use of time series to forecast future price behavior. Its purpose is two-fold. The first is to provide the reader with a better understanding of chaos theory and its impact on forecasting. The second is to show how, under the right conditions, three consecutive price changes can be used to forecast the fourth price change with reasonable success. A sequel to this paper, to appear in a later edition of this journal, will cover the second area to which I referred: the fractal structure of markets. Market technicians are uniquely equipped to understand this structure, and I believe that much of technical analysis currently in practice will be made rigorous from the viewpoint of fractals, with many technical tools being refined through this perspective. This is the future of technical analysis, and it will cast a giant shadow across the traditional business school curricula in this country.

Phase Spaces and Strange Attractors

In the interview mentioned above, I referred to the phase space of a process as a mathematical picture which can completely describe all future values of the process. An attractor for the space is some part of the space: a point, a simple curve, or something more complex, which tends to capture and then dominate all future motion of the system. The phase space of a pendulum will serve as an example.

Suppose you wind a clock which has a pendulum and let it start to run by pulling the pendulum to the right and releasing it. The following diagram represents the phase space for this situation. Starting at point S we have a representation of the extreme right of center position of the pendulum and, as it is stopped, its zero velocity. Releasing the pendulum, it swings left and its velocity increases. It reaches maximum velocity at the bottom of its swing, and now as the motion continues to the left the velocity decreases. At the extreme left position the velocity is again zero. Now the

MTA JOURNAL ! AUGUST 1989 29

numerators of the ratios being compared. Since the market value of stocks owned naturally goes up and down with rises and falls in the index, the two ratios automatically display a strong positive correiation.

Genesis of the Buying Power Hypothesis Large price movements in the stock market fre- quently are associated with unusually large dollar transactions and volume. Indeed, some analysts have found a meaningful relation between the size of price movements and volume fluctua- tions.6 This observation appears to support the buying power hypothesis by advancing the no- tion that heavy volume, conceptualized as buying power or selling pressure, is the causal factor and price change the result.

The idea that the size of cash balances “on the sidelines” can influence market prices may be a natural extension of the evidence, but it is incon- sistent with the concept that stock prices closely approximate the discounted value of expected future returns. The efficient market perspective focuses on price movements as symptomatic of new information reaching the market. The size of any movement is strictly limited to the change in the discounted present value implied by the new information. Major pieces of new information imply major price movements. Volume fluctua- tions are merely the result of these factors, not the cause. In other words, when information reaching the market is important enough to create large price adjustments, it may well be important enough to induce large numbers of investors to trade. l

Footnotes

1. Securities and Exchange Commlssion. 2. Jerome 8. Cohen, Edward D. Zinbarg and Arthur

Zeikel, lnucstnwnt Analysis and Po@lio Management (Homewood, IL: Dow Jones-Irwin, Inc., 1973), p. 534.

3. Ibid, pp. 535-536.

4. Ibid. p. 534. 5. The formula shown is exact if percentage changes

are computed on a continuously compounded (i.e., logarithmic) basis. Otherwise, it is approximate.

6. See Robert L. Crouch, ‘The Volume of Transac- tions and Price Changes on the New York Stock Exchange,” Finamal Analysts loumal, July/August 1970.


An infinite non-self-intersecting path contained within a bounded region will start to fill that region, so we get places where the path is very tightly packed. It might look like this:

This example is in three dimensions, so the path does not intersect itself even though it appears to in our two dimensional representation.

A number of economists and “chaologists” are seriously researching the possibility that markets are governed by strange attractors. For reasons discussed in my earlier interview, the presence of a strange attractor would mean that almost all time-specific price forecasts would be impossible. Without attempting at this point to find a strange attractor, we will proceed to investigate one day forecasts which may be made possible by the warping of the phase space of the market due to such an attractor.

A View from Two Dimensions - Simple Correlation

Early work by Louis Bachelier (see 3) at the turn of the century seemed to imply a lack of correlation between successive price changes. This led eventually to the random walk hypothesis and its refinement, the efficient market hypothesis. In an article published in this journal (see 4) almost ten years ago, I showed that with extremely high probability the market does not strictly move in a random fashion. I used the Indicator Digest Average as my database, because I had access to it at the time, but Tony Tabell replicated my experiments using 50 years of daily Dow Jones Industrials

Last year, John Bollinger indicated to me that he had found a highly significant correlation (r=.215) between successive percent price changes for just over four thousand NYSE index prices from January 5, 1970 through May 2, 1986. This is a quite surprising result, given the work of Bachelier and many others. It implies that the change of price of an index on one day does have a direct influence on the change of price for that index on the next day.


pendulum begins to swing to the right, and we develop negative velocity. In my example, I have chosen not to continually wind the clock, and hence both the extreme position and velocity decrease over time and the phase space spirals in toward the center point. The center point is the attractor for this space.

I POSITIVE VELOCITY (LEl7)

PENDULUM PHASE SPACE

*

POSITION RIGHT

POSITION LEFT

1 NEGATIVE VELOCITY (RIGHT)

A phase space with a strange attractor is considerably more complex. For our purposes, think of a bounded space of two, three, four or whatever dimensions containing some kind of infinitely long curve which never intersects itself. Once the phase space gets close enough to a strange attractor, it is locked to it and must follow it forever. The reason that the phase space must never intersect itself is that it completely describes all future behavior of the system. One never has a choice as to what path to follow. An intersection in the phase space would cause the following problem:

30 MTA JOURNAL I AUGUST 1989

For reasons that will become clearer as we progress, I believe that some relationship like this does hold. The work in the previous section already suggests that, for price changes, DELTAt = g (DELTAt-1) works at some level of reliability.

In Chaos, (see 2) James Gleick devotes a chapter to the Dynamical Systems Collective, a group of physics graduate students at the University of California, Santa Crut.. Robert Shaw, one of its members, may have given us the most useful product yet in attacking problems like one-day forecasting. It is called phase space reconstruction. I will describe the process in the context in which it will be used here. Given a single stream of data (in our case price changes):

DELTAI, DELTA2, DELTA2;-

suppose we hypothesize that there is some relationship allowing a given DELTA to be forecast in some cases by previous DELTAS.

DELTAk = f(DELTA1, DELTA2;-,DELTAk_l)

Without knowing what the relationship is, if we can just view the data in the appropriate dimensional space (in this case k dimensions) the relationship will become more apparent. If a strange attractor is present, the space will be warped somehow, while the absence of such a relationship should be indicated by a random looking mass of points. In three dimensions, the spaces might look like this:

:.- ..-: ..*. /

- . . . . ,.*: . . . . -.* .- . .*. .. * - . . .-* /r

. . * --.. . . . *. . . a. . *,.- . ..-.-. ,. ’ ‘:. *

..a**. .*. . * .:.‘.*I. . -. ’ * . ’ . .

I . . . * . RANDOM SPACE * : . : * .


What follows is a replication of Bollinger’s experiment using different data. In order to test over a wide range of conditions, I chose S&P500 data over two successive bull and bear markets as defined by a 1.25 multiplicative filter on daily closing prices. Any rise of 1.25 or more constitutes a bull market while any decline of (l/l .25)= .80 constitutes a bear market. From a multiplicative perspective, a 25 percent rise and a 20 percent decline are offsetting moves. The period used was from May 26, 1970 to August 12, 1982.

S&P500 Extrema Usina A 1.25 Multiplicative Filter

Fxtmum IzfiGe

700526 LOW 69.29 730111 HIGH 120.24 741003 LOW 62.28 801128 HIGH 140.52 820812 LOW 102.42

There are 3087 days in this period. If DELTA is defined by:

DELTA = TODAY’S PRICE - YESTERDAY’S PRICE

YESTERDAY’S PRICE ,

we have 3086 DELTAS and, hence, 3085 pairs of successive DELTAS to compare. The result is a correlation of rz.221, confirming John Bollinger’s powerful result. As we shall soon see, we can do better. Much of the behavior of the market is hidden when viewed from a two dimensional perspective, but begins to show itself at higher dimension.

Phase Space Reconstruction - Three Dimensions

The classical approach to modeling the market, or any other process, is to find some variables which might be useful in predicting behavior and then try to logically or statistically combine them into some sort of predictive formula. If yt is the variable to be predicted at time t and at, bt, ct, dt”- are the explanatory variables, we symbolically have:

Suppose, however, one feels that past values of y can be used to predict its future value. This is known as a recurrence relation, and might be represented symbolically by:

yt = S(Yt-1 P Yt-29 Yt-3*“‘).


INTERPOLATION FOR SLICE

POINT BEFORE CROSSING

POINT AFfER CROSSING L\

The following table of correlation coefficients for these various cases shows the improvement we have when compared to our earlier results:

4 Uatq Coefficient

Correlations

Samde S tze

DELTAI, DELTA2 3085 .221

DELTAI, DELTA2 after DELTA3 + + to - 651 .233

DELTAI, DELTA2 after DELTA3 4 - to + 650 .314

DELTAI, DELTA2 interpolation as + + to - 651 .443

DELTAi, DELTA2 interpolation as DELTA3 + - to + 650 .501

This is, of course, just one slice of an infinitude of possible slices, but clearly more is going on in three dimensions than was in two dimensions.

Four Dimensions Aren’t All That Bad - The Main Result

If price movement in the market is chaotic, then the utility of any information we have regarding price on a given day diminishes rapidly. With this in mind, we now look at our most promising result in four dimensions: forecasting tomorrow’s price change, given the last three day’s price changes. When viewed as a four dimensional problem, the points now look like:

(DELTAI, DELTA2, DELTA3, DELTA4).


Suppose we take our 3086 DELTAS created previously and place them as points in three dimensions as follows:

point 1: (DELTAI, DELTA2, DELTA3) point 2: (DELTA2, DELTA3, DELTA4)

point 3084: (DELTA3084, DELTA3085, DELTA3086)

If one plots these 3084 points in three dimensions and looks at the shape of the graph one finds that it has become more warped that its two-dimensional counterpart. If a plotting capability in three dimensions is not available, a two dimensional slice can be obtained like cutting a disk out of a sphere. If we look at the second and third coordinates at times when the first coordinate changes from positive to negative or negative to positive, we have essentially taken two slices of the three dimensional picture. Almost no points will have first coordinates equal to zero, so we have several choices as to how we view this new data. We can take the last two coordinates of the point prior to crossing the plane DELTAl=O. We can also take the last two coordinates of the point after crossing that plane. A sharper result is obtained by interpolation of these two points which actually places a point on the plane DELTAl=O.


Forecast Results

Neutral

NDUU 32 NDUN 17 NDUD 13 NNDD 64 NNDN 32 NNDU 17 NNUU 57 NNUN 41 NNUD 24 NUDD ,4p NUDN -24 NUDU IQ

193 110 64

As can be seen this is a very strong result with good forecasts occurring three times more often than do bad forecasts. In fact, a bad forecast is made only 17.4% of the time.

Conclusion

We have seen that a standard two-dimensional investigation of price changes produces some insights, but fails to uncover much that is hiding at higher dimensions. We have seen that, under the rules for three consecutive DELTAS given in the previous section, it is possible to forecast the fourth DELTA not with certainty, but with a much better than random level of accuracy. James Gleick mentions in &IQS that a number of economists are investigating the possibility that stock market data may have dimension 3.7 or 5.3. This would imply the need to go to 4 or 6 dimensions, respectively. While other results remain to be discovered, the four dimensional investigation above may give the flavor of the limits of investigations of this type. In

s II: The F actal St ucture of M&Q& I hope to show that prospects are much brighter, once time specirfic forecasts are abandoned. If one deals instead with the structure of a situation, much more may be possible. Filters, trendlines and trading ranges are but three examples of structures which are not locked in to a specific time frame. They exist until they are completed. This could lead to some very powerful applications. For example, it may be possible to recast all of Elliot Wave Theory from this viewpoint of fractals.

Bibliography

1. Orr, Ft. and Pruden, H., -china for C&X in the Mark& MTA Journal 31 (1989)

2. Gleick, James, Chaos (Viking Press, 1987)

3. Bachelier, Louis, Theorie de la Sbecw (Gauthier-Villars, 1900)

4. Orr, Richard, The Timelv Demise of the Random Walk. MTA Journal 7 (1980)

Dr. Richard C. Orr is Vice President for Research, John Gut- man investment Corp., a frequent contributor to this Journal. and a member of the MTA Board.


If this space is warped sufficiently, we should be able to find regions of it where DELTAI, DELTA2, and DELTA3 can do a reasonable job of forecasting DELTA4.

Rather than using multiple regression or correlation techniques or slicing the space as we did in the previous section, suppose we just group all the DELTAS into three sets. Over the period we have been using (700526 to 820812) one-third of the DELTAS were less than -.00292, while one-third of the DELTAS were greater than +.00326. Let

D = {all DELTAS c -.00292} N = {all DELTAS 2 -.00292 but 5 .00326} U = {all DELTAS > .00326}.

Each point in our space now has one of 34 = 81 designations:

(D, D, D, D) (D, D, D, N) (D, Q D, U) (D, D, N, D)

(U, u, u, U). We now create a logical model to describe a piece of this space. As a trade-off between a volatile situation: (U, D, U, +), an overbought situation: (U, U, U, l ) and a dead-in-the-water situation: (N, N, N, l ), where l is tomorrow’s price change, we create a model based on the following rules:

DELTA3 = U or D DELTA1 = N DELTA2 # DELTA3.

Obviously other models are possible, but this one yields the following:

(N D, U, +) (N, N, D, l I (N, N, U l ) (N U, D, *It

where we must forecast l in each of these four cases. If we take all points that fall into one of these four categories and look at the correlation between the third and fourth coordinates we get coefficient r=.451, much better than the non-interpolated three dimensional case we observed earlier. Since we have limited ourselves to these cases, we have only 12 outcomes to count. Under these conditions we expect a strong up move, U, to produce another U, while a strong down move, D, should produce another D. Therefore, a forecast is good if the last two coordinates are the same. It is neutral if the fourth coordinate is N. A forecast is bad if the last two coordinates are different (U,D or D,U). A count of the 367 points which qualify is as follows:


for support or resistance is the entire area from 25% to 55 % . There are interesting bulges, also, at 73 % and from 92% to 98%.

Of course, this check is based on the averages and not on individual stocks. But if support came in at the traditional levels of the individual stocks, it would appear in the averages. Also, those who watch individual stocks are influenced quite often by the action of the averages.

Market “wisdom” also tells us that a slight retracement is a good sign for the continuation of a trend. Is this so? Does the size of a retracement predict the size of the following move or retracement? If this is the situation, smaller and smaller retracements should be followed by larger and larger retracements. In Fig- ure 6, the typical situation should be A rather than B. As technicians, we know this is so, and that trends tend to continue.

To check it out, I took the retracement file and looked at adjacent pairs, and compared the second retracement (which could be a primary swing) with the first retmcement in the pair. The result is in Figure 7. The vertical scale is the first retracement; the horizontal scale is the following retracement. For example, at point A a retracement of 28 % was followed by one of 210%. This would be similar to A in Figure 6. The resulting swarm of 780 retracements (count ‘em!) certainly has a downward slant. as we would expect, although the correlation isn’t high. The straight line is a least square regression that I fitted to the logarithms. (log Y = 6.94-0.507*log X)

The conclusion of this part of this study is that market wisdom is correct; smaller and smaller retracements tend to be followed by larger and larger retracements. This is another nail in the coffin of the random walk.

To end on a constructive note, I’ve marked the location of the quartiles (Q) and medians (M) on Figs. 3 and 4. These points divide the data into four equal quarters. One quarter of the data points are in the low- est quartile, three fourths are above. In a bull market, then, if a secondary reaction is more than a blip, the odds are three to one that it will continue until it has retraced at least 38% of the preceding upswing. The odds are even money that it will reach 64% (the me- dian) and three to one that it will find support and be reversed before 97% is reached.

Similarly, in a bear market, if in a rally the retracement exceeds 5 % , the odds are three to one that the rally will continue and retrace at least 45% of the preceding swing; even money that it will retrace 74% ; three to one that it will find resistance and be reversed before 109% of the preceding primary.

Anhur A. Mem’ll. recipient of the 4th Annual MZA .b+wd. also afrequent contributor to this Journal. founded his letter. Tech-

and articles on the market. and has advanced the research on mduztors and indicator testing by giant steps over the Iears.


Retracement Percentage

Arthur A. Merrill

After a swing in either direction, stock prices reverse and “retrace.” In a bull market. a secondary reaction usually retraces only a portion of the preceding primary upswing, while an upward primary upswing retraces more than 100% of the preceding secondary.

First, some definitions of the terms used in this paper:

Swing: Any move of more than 5 % . This elim- inates the “blips”. To make rises and declines comparable, the bottom of both rises and declines is called 100%. For example, a decline from 105 to 100, which is certainly comparable to a rise from 100 to 105, is called a 5% swing, and not, a 4.76% decline.

Bull and Bear Markets: Any swing of more than 30%. The bottom of both upswings and downswings is called 100%. This simple definition does a good job of fitting the markets called bull or bear by financial histories.

Primary swing: A swing in the direction of the bull or bear market. In a bull market, the primary swing is upward: in a bear market it is downward.

Seconda? reaction: A downward swing in a bull market.

Rally: .4n upswing in a bear market. Retracement percent: This is the total travel of

a swing in percent of the preceding swing. If prices are zig-zagging, the retracement percent is the zag in percent of the zig.

Market “wisdom” tells us that we should expect support in a secondary reaction at one third, one half, and two thirds of the preceding upswing. Elliott Wave analysts tell us to expect support at the 38 % and 62 % Fibonacci levels. In a bear market rally, we should expect resistance at the one third, one half, two thirds, 38% and 62 % levels.

This market “wisdom” is presumably based on experience, but I have never seen supporting evidence. I’m a curious type; perhaps some of my ancestors were from Missouri. Anyway, to get a factual count I asked my computer to review the data base developed for the book “Filtered Waves.” This data base gives the terminal points for all swings of the Dow of more than 5 % . It ignores smaller swings. I asked the computer to check all of the retracements of secondary reactions

in bull markets and all rallies in bear markets. The data bank extends back to 189’7; including 182 secondaries and 181 rallies.

The results are in Figure 3 (retracements in bull markets), Fig. 4 (rallies in bear markets), and Fig. 5 (secondaries and rallies combined). In the left hand part of the charts, each percentage retracement is marked with a spot. Note that the scales are reversed. The scale for secondaries has zero at the top; the scale for rallies has zero at the bottom. Also note that in a number of cases the retracement exceeded the preceding primary swing.

Since the data varies considerably between the percentage points, I tried a five point centered average, which is shown at the right of Figs. 3, 4 and 5. For example, in Fig. 3 note the clustering around the 71% point. No secondaries stopped at 69, one turned at 70, seven at 71, two at 72, zero at 73. The five point average, located at 71, is (0+1+7+2+0)/5=2.0.

How do the benchmarks for support and resistance stand up? Not too well:

33 % : This a low point in bull market secondaries (Fig. 3), but does show a peak in bear market rallies (Fig. 4). In Fig. 5, overall there’s no sign of special activity.

67 % : This is a low area both in bull secondaries and bear rallies. No special support or resistance is evident.

50%: This is certainly a time honored bench mark. However, the bull market secondaries show no special peak; it’s a low spot in bear market rallies. Overall, in Fig. 5, it’s a negative. A little farther on, though, at 55% the bear market rallies found real resistance. Overall. in Fig. 5. 55% was the highest point.

38 %: This is a fibonacci point. It does show a support point in bull market secondaries, but not much resistance in rallies. Overall, it isn’t an unusual point.

62%: This is the other fibonnacci benchmark. This is a negative for both bull secondaries and bear rallies.

The score for these benchmarks certainly isn’t im- pressive. If you will look at Figure 5. the strongest area

38 MTAJOURNAL; AUGUST 1989

*Lo RETRAGEMENT BULL MARKET

C IO NDA SE RIES , O/o

-- -

39 ABOVE IlOok

TOTAL = 182.

5. PT.AVG.

7 I ,

I J

,t’,-‘- ------

I I ,

t , ’

H

I

I I FIG.3

I L ’ I

MTA JOURNAL i AUGUST 1989 ill

- RETRAGEMENT IN BULL

PR I MARY SWING

SEGONDARY

-PRIMARY SWING

REACTION

MARKETS -

O/O RETRAGEMENT = 100(13/A) FIG. I

- RETRACEMENT IN BEAR MARKETS-

-PRIMARY SWI I’JG

IMARY SWING

O/o RETRACEMENT = 100(8/A)

FIG. 2


7. RETRAGEMENT

BULL AI’JD BEAR MARKETS

3- ir !OOOOO --i -

4r-

40.

I I 4 1 ’ .33-

. 38-

1 -- ,- - -

c I I --I ’ J-e-

JO-

.62-

.67-

I 1 1 ( I


95, RETRAGEM ENT

BEAR MARKET

RALLI ES

O/o 48 ABOVE 110%

p-M

70 ‘% .67-t- - -7 7%~-- -

-3

FIG.4

52-k- - m- --

60

i

b

JO+-50, p- -- -

-+o

TOTAL ISI.

5 PT. AVG.

-me --

-4Esx----- I

I 1

I ’

--I - - --


100

300 ‘GO

600

500

400

300

200

100

80 ?C

60

50

40

30

RE’IRAGEMENT PAIRS . .

. .

.

. :

4 I- cl3 (I:

LL

. . . . .

. - l . .

.

* .’ . . .

.

.

.

.

. * : :

.

.

.

. *

. * . ‘,‘I . *. . . . . . .

. ‘xv*: , . ‘. .

. . ; .

. . *+ . -

.

. : .

. . . ‘. -a.*

. . .

- I * . . * . . .

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‘, . - .* *

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. ,*. . -* . ’ .

. -._ .

. . .

. ‘. .a . .

. . . 1

. .

.

.

. 0

I 20 30 40 50 60 80 I00 200 300 400 600 800

- SECONO -+ FIG.7


0 A

SMALL RETRACEMENT

FOLLOWED BY A

LARGE RETRAGEMENT

SMALL RETRAGEMENT

FOLLOWED BY A

SMALL RETRACEMENT.

0 B

FIG.6


TABLE I

MARKET PEAKS STANDARD AND POOR’S 500 INDEX

MONTHLY DAILY

May 1946

June 1948

January 1953

July 1956

July 1959

December 1961

January 1966

December 1968

January 1973

September 1976

February 1980

November 1980

August 1987

May 29, 1946

June 15, 1948

January 5, 1953

August 2, 1956

August 3, 1959

December 12, 1961

February 9, 1966

November 29, 1968

January 11, 1973

September 21, 1976

February 13, 1980

November 28, 1980

August 25, 1987

MTA JOURNAL I AUGUST I989 47

Warning Signs For Market Peaks

Roger Williams

The October 19, 1987 market crash caught many off guard. Numerous well-known market analysts were taken by surprise and did not give advance warning. In our view, over-valuation, rising interest rates, and a slowdown in monetary growth were the principal contributing factors. The 1987 market peak was similar to other market tops in some respects, but different in others.

We have listed the major stock market peaks in Table I from 1946 through 1987. The Standard and Poor’s 500 stock index has been used in preference to the much narrower Dow-Jones Industrial Average. In the future, analysts may wish to shift to something much broader such as the Wilshire index, or to something equally weighted such as the Value Line index.

Major market peaks are not proclaimed in advance with thunder and lightning clarity. A gradual process or corrosion occurs, and then the major peak comes on us like a “thief in the night.”

Over-valuation helps to explain some market peaks and not others. For rough guidelines, we suggest that a price-earnings ratio (S&P 500-Trailing earnings) at 18 and up is in risky territory, and anything above 20 is very dangerous. P.E. ratios above 18 were noted prior to the peaks of 1946, 1959, 1961, 1966, 1968, 1973 and 1987. For yields on the S&P 500, anything below 3.6% is risky, and anything below 3.0% is quite haz- ardous. In 1987, we clearly went beyond the hazard lights of a P.E. ratio of 20 and a yield of under 3.00%.

While over-valuation can give a warning signal. it does not provide a clear indication of danger im- mediately ahead. Market analysts have often looked at advances and declines, trading volume, number of new highs and other internal market indicators of potential difficulty. These are useful but not necessarily conclusive or compelling. We turn to such underly- ing influences as prices, costs, and profit margins; monetary factors and other economic indicators.

Prices, Costs and Profit Margins Rising unit labor costs often bring pressure on

profit margins. This series is available in Business Con- ditions Digest on a monthly basis for manufacturing companies. A rise in the lagging indicator composite (Department of Commerce) tends to reflect rising costs and declining profit margins.

A pickup in the rate of inflation is usually serious. Selling prices usually rise slower than buying prices (cost elements), which means lower profit margins. Higher inflation tends to push up interest rates, a harm- ful influence for the stock market. Finally, a rise in

inflation often leads the Federal Reserve toward monetary restraint.

Monetary Factors Although one can argue over the choice of M-l,

M-2, and other monetary aggregates, a marked slowdown in monetary growth has often been followed by major market peaks. We clearly had such a slowdown in the pre-crash months of 1987.

Perhaps the most dangerous sign of all is a noticeable and continuing rise in interest rates, something which happened in pre-crash 1987. A rise in interest rates means heavier discounting applied to future eam- ings per share and higher costs for both business and consumer borrowers. A significant rise in interest rates has been one of our most consistent advance indicators of major market peaks.

Other Economic Warnings When economic expansion slows down ap-

preciably, this cuts into future growth of earnings and private spending. Several long-leading indicators have been helpful in predicting slowdowns on downturns in economic activity. Their leads are usually long enough to also give advance warning for the stock market. These indicators include building permits, rate of change in the coincident indicator composite (De- partment of Commerce), and the percentage rising of the Commerce leading indicator components.

Track Record The track record of our various indicators is shown

in Table II. An “X” means that advance warning was given for that particular market peak. No means no warning and NA means data not available. Over-valuation, interest rates, and inflation are the best three in our view, but other indicators are also helpful. Of the various market peaks, 1959 was best advertised in advance, while 1961 was the most difficult to predict.

We have not attempted to formulate very specific timing and quantitative rules. These are probably best left to the inidvidual user.

Dr. Roger Williams is Professor of fionomrcs at Tiffin Uwer- sity. Ohio and President of Investment Horizons. an investment advisoyfirm. He aas formerly Chief Economist for Standard and Poor’s Corporation. He has published a month1.v letter ’ ’ Wiiams 7’rend Indicators ’ 1 has appeared on rhe TV .Vightly Business Repon. and has been cued in the Xew York 7imes. the WI Street Journal. and Lotus Rukqvser ‘s sydtcated column. His work has emphasrzed Integration of monefay

economic, and technical indicators m the analysis of the market. indusrry groups, and individual stocks.


Day of the Week and Intraday Effects in Stock Returns

Michael Smirlock'

Laura Starks

*Assistant Professors of Finance at the Wharton School (University of Pennsylvania) and Washington University, respectively. We are grateful to Don Keim, Terry Marsh, Richard Rogalski and Jay Ritter for comments and suggestions that have improved the quality of this paper. This is a revised version of .the paper we presented at the Western Finance Association meeting in Vancouver, June 1984. We would also like to thank Jay Merves and David Mook for excellent research assistance.


-

TABLE II

ADVANCE WARNING SIGNS

STOCK MARKET PEAKS

BATTING

AVERAGE 1946 1946 1953 1956 1959 1961 1966 1966 1973 1976 1960 1960 1967

PRICE-EARNING RATIOS

Level 7-13 X NO NO NO X X X X X NO NO NO X

Fast growth 2-13 X NO NO NO X NO NO NO NO NO NO NO NO

PRICES, COSTS & PROFIT MARGINS

Change in Inflation 11-13 X X NO X X NO X X X x x x x

Change in Lagging Index 8-10 NA NA X X X NO NO X X X X X NA

Change in Unit Labor Costs 6-12 NA NO NO X X NO X X NO NO X X NO

Change in Profit Margins 5-13 NO NO NO X X NO NO X MIXED X X NO NO

MONETARY FACTORS

Change in Money Supply 9-13 x x X x X NO X NO NO NO X X X

Change in Interest Rates 11-13 NO X X X X X X X X NO X X X

OTHER ECONOMIC WARNINGS

Rising Leading Economic Indicators 7-11 NA NA X X X NO NO NO X NO X X X

Change in Building Permits 9-12 NA X X X X NO X NO X NO X X X

Change in Coincident Index 8-11 NA NA X X X NO X X X X X NO NO

Warning Cases 4 4 6 9 11 2 7 7 7 4 9 7 6

No Advance Warning 2 4 5 2 0 9 4 4 4 9 3 5 6

Not Available 5 3 0 0 0 0 0 0 0 0 0 0 1

Mixed Picture 0 0 0 0 0 0 0 0 1 0 0 0 0

____-__

they are positive on the other weekdays. On all weekdays, the mean returns

over this trading interval are between five and ten times as large as returns

a&ruing later in the day.

These conflicting results are significant for several reasons. First,

these analyses differ on where research emphasis should focus--trading or

nontrading periods --in investigating the weekend effect. Indeed, Rogalski's

conjecture that the nontrading weekend effect characterizes sample periods

other than his own is not supported by the Prince or Smirlock and Starks

findings, nor is it confirmed by Harris's results. Second, given the

disparate time periods used in these studies, the results are suggestive of

instability in the return generating process. By thoroughly examining

intraday returns over a longer sample period, additional insight into the

nature of the weekend effect and the return generating process can be gained.

A third issue concerns the trading time hypothesis, which asserts that

returns are generated only during active trading and the expected return is

the same for each trading day. While French (19801 rejects this hypothesis

using daily returns, both Oldfield and Rogalski (1980) and Rogalski accept the

trading time hypothesis using open to close returns. The latter studies use

considerably smaller sample periods and also do not consider differences in

returns across trading days for any intraday period, which Harris (1984) shows

may characterize intraday returns. 3 A strict interpretation of the trading

time hypothesis might imply, for example, equal returns across days over some

intraday period.

The purpose of this paper is to further investigate day of the week

effects and these related issues using hourly return data from the DJIA over

the 21 year period 1963 t!!rough 1983. This paper is divided into four

sections. In section II we investigate the distributions of DJW returns,


I. Introduction

Convincing evidence has been provided that there are day of the week

effects in stock returns, characterized by negative Monday returns. Although

documentation of this "weekend" effect is extensive, researchers have been

unable to adequately explain its cause.' These studies have concentrated

entirely on daily returns; i.e., returns measured from close to previous

close. More recently, Prince (19821, Smirlock and Starks (19831, Roqalski

(1984) and Harris (1984) have employed intraday data in an attempt to provide

additional insight into the characterization of the weekend effect. These

latter studies all find a weekend effect using closing returns, but report

very different results when daily returns are decomposed into their component

parts.

Prince and Smirlock and Starks use hourly Dow Jones Industrial Average

(DJIA) data over two different five-year periods from the 1960s. Al though

Prince uses 24-hour moving return windows while Smirlock and Starks compute

hourly returns, both studies provide evidence that the weekend effect occurs

during active trading time on Monday. Roqalski, using DJIA data from 1974 to

1984,2 decomposes returns into open to previous close and close to open.

Unlike the aforementioned authors, he concludes that the entire weekend effect

is contained in the Monday open to previous Friday close returns and that

Monday returns over the active trading day are not unusual. Rogalski refers

to this as the nontradinq weekend effect. Harris employs transaction-by-

transaction data for the 14 months ending January 1983 for all NYSE stocks.

Although Harris finds evidence of a nontrading weekend effect for large firms,

his findings are not nearly as strong as those of Rogalski. Further, he also

reports a significant difference between Monday and other days in the first 45

minutes of trading. Over this interval, Monday return; are negative, while

50 Ml-A JOURNAL i AUGUST 1989

obtained from the Wall Street Journal. As is well known, the calculation of

the DJIA contains several methodological shortcomings relative to other stock

return indices. Nonetheless, it is used in this study since hourly DJIA

values are, relatively easy to obtain and the active trading of the constituent

firms substantially mitigates nontrading problems associated with other

indices (Gibbons and Hess (1981)). Additionally, the correlation between the

DJIA and more appropriate stock return indices (such as the S&P 500 utilized

by French and Gibbons and Hess) is quite high over long time periods.

For the empirical analysis, the entire sample period was divided into

three subperiods. These subperiods were chosen based on institutional

characteristics and previous analyses. The most recent subperiod runs from

October 1, 1974 through 1983 and was selected to correspond to the sample

period used by Rogalski. The October 1 starting date was selected because on

that date the NYSE expanded trading time by one-half hour from 3:30 to 4:00

p.m.

The earliest subperiod extends from January 1, 1963 through February 9,

1968. The end of this subperiod coincides with the last day of the four

business day settlement period and thus avoids any difficulties associated

with the change in settlement periods. The hourly return data has several

minor problems. The closing value of the DJIA actually corresponds to 3:3O

and not 4:00 p.m., since the earlier time was the actual market close.

Nonetheless, we refer to the return from 3:00 p.m. to close over this period

as an hourly return and treat the close as if it were 4:00 p.m. Additionally,

until November of 1963 the Journal did not report 3 o'clock DJL4 values and

for the last several weeks of this subperiod the exchange closed at 2

o'clock. Accordingly, for these days there are no hourly returns for 3 and 4

o'clock. The final subpericd is from February 10, 1968 through September 30,


decomposing these returns into closing, close to open and open to close, for

several sample periods. Our results for the 1974-83 period concur with those

of Rogalski. For the two sample periods prior to 1974, our results reverse

themselves. There is no nontrading weekend effect: the entire weekend effect

is observed during active trading time. These results also imply a rejection

of the trading time hypothesis using closing returns in both subperiods, as

well as open to close in the pre-1974 period. Section III extends the

investigation to hourly returns across trading days. Our results show that

for a majority of these intraday trading periods the trading time hypothesis

is rejected over the subperiods. In the pre-1974 period, the hourly returns

on Monday are generally lower than their counterparts on other trading days,

regardless of the hour of the day. in the post-1974 period, however, there is

nothing unusual about Monday hourly returns when compared to other weekdays.

The hourly returns, however, suggest that the weekend effect is "moving up" in

time: that is, in the earlier period almost all of Monday hourly returns were

negative, but the nontrading weekend returns were not, while in the later

period, only Monday morning and t!!e nontrading weekend had negative returns.

The negative Monday morning returns in the post-1974 subperiod is swamped by

positive afternoon returns, yielding no apparent weekend effect in trading

time. Section IV formally examines whether hourly returns are t!!e same within

a day. This hypothesis is generally rejected and a further examination

suggests that there is no consistent reason for this rejection across

subperiods. These findings raise the issue as to why stock returns should

differ by hour of the day. Section V contains our conclusions.

II. Data and Analysis

The data employed in this section consist of hourly observations of the

DJIA for each trading day between January 1, 1963 through December 31, 1983,


opening return is over twice the magnitude of that of any other day and is

significantly less than zero while Monday's intraday return is positive and

close to the mean across all days. Nontrading periods also appear important

for other days as well. For every day but Friday, nontrading and trading

period returns are of opposite sign and, except for Wednesday and Friday, the

magnitude of nontrading returns exceed those of trading period returns.

For the 1968-1974 period, the results are quite different. Although the

Monday opening return is negative, its magnitude is not unusual compared to

other days. The most prominent return value is the Monday inttaday, which is

over four times the magnitude of either R" t

or Rt for any other weekday and is

significantly less than zero. Nontrading periods also appear leSS important

over this sample period. For all days but Thursday, the magnitude

of Rd 0 and Rd are t exceeds that of Ri and for all weekdays the mean values of R t t

the same sign.

The 1963-1968 period results are different from the other subperiods.

The mean value of RE is positive and significantly different from zero, while

the mean of Rt is negative but insignificant. This implies that most of the

return in the !XIA for any day is captured in the opening. Further, the mean

of R" ' t 1s positive and exceeds the mean value of Rt for every day of the

week. The values of RE and Rt, however, do not support Rogalski's finding

that the negative weekend effect is contained in the opening return on

Monday. Quite the opposite, we find that the opening on Monday yields a

positive return that is overwhelmed by the large negative return from open to

close. 6 The value of Rt for Monday is close to four times the magnitude of

that for any other day and is significantly less than zero at the five percent

level, while Rz is small and positive for Monday.

MTA JOURNAL / AUGUST I989 55

1974. Over part of this period, the market closed at 2:00 p.m. and/or was

closed on Wednesday.

From these data, nine different return series are denoted and calculated

as follows: Rz measures daily returns and is calculated as the percentage

change in the DJf from the close of day t-l to the close of day t; RE measures

opening returns and is calculated as the percentage change in the DJI from the

close of day t-l to the open of day t; Rt measures intraday returns and is

calculated as the percentage change in the DJI from the open of day t to the

close of day t; R:, where i = 11, 12, 1, 2, 3, 4, measures hourly returns and

is calculated as the percentage change in the DJI from hour t-l to hour t.4

We begin the analysis by examining closing returns, RF, and its two

component parts, Ry and Rz. Days after market holidays are omitted. Average

daily percent returns and associated t-values are reported in Table 1. The

distribution of Ri over the pre-1974 subperiods is similar to that reported

for the S&P 500 for similar time periods by French (19801, Gibbons and Hess

(19811, and Keim and Stambaugh (1984). Monday returns are negative and almost

twice as large in absolute magnitude as the next highest weekday. The t-

statistics indicate that Monday returns are significantly below the mean value

of R"t across all days of the week. Over the post-1974 period, however, while

Monday returns are negative, they are not significantly different from the

mean across all weekdays.

for the DJIA and with the

Gibbons and Hess and Keim

periods.

This finding is consistent with that of Rogalski

findings of French, Lakonishok and Levi (19821,

and Stambaugh for other indices over similar sample

More striking are the results of decomposing Ri into two component

parts, RT and Rt. Consider first the post-1974 period. There appears to be,

just as Roqalski and Harris found, a nontrading weekend effect. The Monday


the market opening and not during the trading day. Indeed, there is no

significant difference in daily returns during active trading periods. The

earlier subperiods are exactly opposite this and, as a resuit, provide no

support for the Rogalski conjecture that the nontrading weekend effect is

robust beyond his sample period. We find that the opening on Monday yields a


close. Further, while the trading time hypothesis receives support during the

post-1974 period, the earlier subperiods provide clear evidence against this

hypothesis. There is a strong trading time effect during active trading that

is characterized by negative and significant returns on Monday. Finally, the

substantial changes in return patterns across trading and nontrading periods

suggest that the return process for common stocks is not constant over time.

The rejection of equality of R: across days in the pre-1974 subperiods

provides specific evidence against the multiple component jump process

expounded by Oldfield and Rogalski, although the post-1974 results are

consistent with their stochastic return generating process. 6

III. Day of the Week Effects in Intraday Returns

Over the pre-1974 sriod, the weekend effect occurred during the trading

day and not from Friday close to Monday open. Thus, one important issue is

whether the negative Monday return characterized the entire trading day or was

contained in some specific part of the day. Over the post-1974 period, the

weekend effect can be described as a nontrading weekend effect. This should

not be taken as implying that active trading on Monday is no different than

other days. It is possible, for example, that significant negative returns

accrue .over part of Monday and are cancelled out by large positive errors over

the rest of the day. In this case, there might be no difference between

Monday and other days over t!!e entire trading day, but significant differences


To more formally test whether there is a weekend effect, we estimate the

following model:

a ‘-liDl t, + a2iD2t + a3$D3t +a .D 41 4t + aSiDSt + tit (1)

where '$ is the return measure i (i = c, o, d) in period t, Dtt is a dummy

variable for Monday (i.e., Dlt = 1 if observation t falls 'on a Monday and zero

otherwise), D2t is a dummy variable for Tuesday, etc. and zit is a disturbance

term. The coefficients of (1) are the mean returns for Monday through

Friday. The equality of these coefficients can be investigated with an F-

test. These test statistics and associated probability values are reported in

the last two columns of Table 1. F5 values are from tests of equal

coefficients across all five weekdays. F4 values exclude Monday and test

coefficient equality of Tuesday through Friday. For RC t the equality of all

coefficients is rejected for the pre-1974 subperiods but not the post-1974

subperiod. For none of the subperiods, however, does the F4 value allow us to

reject the null hypothesis that the mean returns for all days but Monday are

equal.

More dramatic are the results utilizing RF and Rd t* For the Tao pre-1974

subperiods, the null hypothesis of equality of Rt across days is rejected at

the five percent level, while a similar test employing RF accepts the null of

equal returns. For the post-1974 period, the results are just the opposite.

There is no difference in Rt across days but a significant difference in R 0

t*

Finally, for either return measure and any subperiod, the equality of mean

returns excluding Monday is always accepted. 5

The results in Table 1 indicate a significant shift in the weekend effect

and, by implication, tie return generating process. The results of the post-

1974 period mirror that of Rogalski and suggest t??e weekend effect occurs at


return. Additionally, over the entire sample period the nontrading weekend

returns change from slightly positiue to significant and negative and are

responsible for the entire Monday effect over the post-1974 period. This

evidence suggests the weekend effect has been "moving up" in time, from

characterizing virtually the entire Monday trading day to being due to a non-

trading weekend effect.

The pattern of intraday returns also suggests that there may be day of

the week effects in hourly returns. To formally test this proposition,

equation (1) is estimated employing the six hourly return measures as

dependent variables. The F-statistics testing the null hypothesis that the

mean returns for any hour across all days are equal, are reported in the

column labeled F5 in Table 2, while the F-statistic testing equality of hourly

returns for all days excluding Monday is reported in column F4.

For the earliest subperiod, the null hypothesis of equal returns across

days is only rejected for the first two and the last hour of trading. When

Monday is excluded, the null hypothesis. is not rejected for all hours except

the last one. The results are similar for the second subperiod. For the

first two hours, equality of mean returns across all days is rejected, while

for the other trading hours the null is never rejected. When Monday is

excluded, the null hypothesis of equal returns is not rejected for all trading

hours. Over the post-1974 period, F5 again allows rejection of the null only

for the first two trading hours while F4 allows rejection of the null only for

xl2 .

These results are surprisingly consistent across subperiods, especially

given the different characterization of the Monday effect. The evidence

indicates that, regardless of subperiod, Monday morning return characteristics

are different from those of other days. Most notably, the first hour of


.-- across hourly returns. If this pattern describes returns, it would not be

appropriate to describe Monday as similar to other days. Accordingly, it

might also be inappropriate to assert that the trading time hypothesis is a

valid description of 'active trading over the post-1974 period.

To address these issues, we report the summary statistics for the six

hourly return measures across days for each subperiod in Table 20 For the

earliest subperiod, this table shows that, for any hour, mean Monday returns

are lower than their counterpart on any other day with one exception (R: on

Tuesday). Further, except for the first hour of trading, Monday's hourly

returns are always negative. Over the second subperiod, the pattern of

returns is somewhat different. The largest hourly returns in absolute

magnitude are the negative returns that characterize the first two hours of

trading on Monday. These two hours account for virtually the entire Monday

'effect over this subperiod. The post-1974 hourly return pattern is quite

different from the earlier subperiods. There is a significant negative return

in the first hour on Monday, while opening hour returns for all other days are

positive. Further, the magnitude of Monday's negative opening hour return

matches that of the nontrading period from close Friday to open Monday.

Although the mean of R12 is also negative on Monday, the remaining hourly

returns are all positive and swamp the earlier negative returns so that mean

returns over the active trading day are positive.

These intraday results reveal a shift in the pattern of hourly returns

over Monday. In the earliest subperiod, returns are negative almost

throughout the entire trading day. In the next subperiod there are

significant negative returns over Monday morning, but afternoon returns are

slightly positive. In the post-1974 subperiod, morning returns are still

negative but afternoon returns are positive and easily swamp the morning


weekdays. in the post-1974 period, however, the null is always rejected. The

summary statistics in Table 2 suggest this finding in differences in hourly

returns is not attributable to any specific hour across days. Although the

trading time hypothesis ik not rejected, using open to close returns over the

post-1974 period, it is difficult to put much confidence in this finding when

hourly returns are significantly different both within ani3 across days over

this time period.

V. Cone lusions

This paper has investigated day of the week and intraday effects in stock

returns for the DJIA. Several observations emerge from the analysis. First,

we provide additional evidence that there is a daily seasonal characterized by

negative returns on Monday. Second, we have found that the weekend effect has

changed over time. From 1963-1968, the return from Friday close to Monday

open was positive, as well as the return in the opening hour. This return was

swamped by the negative return over the remainder of the trading day,

resulting in a negative return over the entire day. Over the 1968-1974

subperiod, the nontrading veekend return is slightly negative, but the weekend

effect is primarily attributable to the significant negative opening hour

returns. Although returns over the latter part of the trading day are

positive, returns over the entire trading day are significant and negative.

Over the post-1974 period, trading period returns on Monday are positive,

although opening hour returns are significant and negative. Over this time

interval, there is a nontrading weekend effect characterized by significant

negative returns from Friday close to Monday open. Third, the trading time

hypothesis is rejected over the post-1974 period using open to close (and

close to close) returns. Although open to close returns support the trading

time hypothesis over this same period, the variability of the hourly returns

MTA JOURNAL 1 AUGUST 1989 61

the market opening and not during the trading day. Indeed, there is no

siqnificant difference in daily returns during active trading periods. The

earlier subperiods are exactly opposite this and, as a result, provide no

support for the Rogalski Conjecture that the nontrading weekend effect is

robust beyond his sample period. We find that the opening on Monday yields a


close. Further, while the trading time hypothesis receives support during the

post-1974 period, the earlier subperiods provide clear evidence against this

hypothesis. There is a strong trading time effect during active trading that

is characterized by negative and significant returns on Monday. Finally, the

substantial changes in return patterns across trading and nontrading periods

suggest that the return process for common stocks is not constant over time.

The rejection of equality of Rt across days in the pre-1974 subperiods

provides specific evidence against the multiple component jump process

expounded by Oldfield and Rogalski, although the post-1974 results are

consistent with their stochastic return generating process. 6

III. Day of the Week Effects in Intraday Returns

Over the pre-1974 period, the weekend effect occurred during the trading

day and not from Friday close to Monday open. Thus, one important issue is

whether the negative Monday return characterized the entire trading day or was

contained in some specific part of the day. Over the post-1974 period, t!!e

weekend effect can be described as a nontrading weekend effect. This should

not be taken as implying that active trading on Monday is no different than

other days. It is pssible, for example, that significant negative returns

accrue .over part of Monday and are cancelled out by large positive errors over

the rest of the day. Ln this case, there might be no difference between

Monday and other days over the entire trading day, but significant differences

60 MTA JOURNAL/ AUGUST 1989

TABLE 1

SUU.SC~ statlstlca Car RC, R” and R* by

Day of the Week and Sample Period”

Sample

PacLOd variable StatAstlc Monday mesday Wednesday Thursday Friday

All

Daye

1963-1968 It=

R0

l-8

1960-1974

1974-1981 RC

R0

la*

Hean

t-value

nean

L-value

Wan

t-value

Observations

Hean

t-value

Mean

t-value

Mean

t-value

ctmervatlons

t&an

t-value

Mean

t-value

nean

t-value

Observatlone

-.1536

t-4.16).

.oofJ2

(.34)

-.I619

(-4.40)’

251

.Of320

(2.21).

.0314

(1.94)

.0477

(1.41)

263

.0709

(5.61 I*

.0815

(2.78)*

.0458

0.17).

-.0261

t-.63)

-.2152

f-4.08)*

-.0264

t-1 -05)

-.1933

(-4.53).

305

.0414

(1 .Of3)

.0253

(1.35)

.0160

( .51)

258

-.0207

f-.40)

-.0328

(-1.33)

.0119

f.28)

316

.0448

1.31

.0696 .0368

(1.33) ( .69)

.0114 .0363

(.70) (1.44)

.0522 .0004

(1.24) ( .Ol)

313 305

.0356

(1.29)

255

.0271

( -53)

.0169

t.68)

.OllO

(-26)

317

-0203

1.27

.0365

14.65).

-.0167

(-1.15)

1288

-.0195

(--al)

.0022

(.20)

-.0226

(-1.19)

1556

-.0153 .0047 -0764 .0115 .ot330 .0331

t-.48) t.26) (1.70) f-68) (1.96) (1 .64)

-.0114 .0086 -.0174 .0319 .0137 -.0060

t-3.131 (.38) t-.01 1 (1.46) ( .62) t-.61)

.0551 - .0039 .0939 - .0203 .0692 .039

(1.34) (-.09) (2.41*) t-.51 1 (I.731 (2.18)*

422 437 473 463 449 2244

7.69*

1.80

. 40

1.35

6.87’ 1 .Ol

4.60. -51

1.47 1 .I2

5.21.

.97

3.20.

1.52

.2Y

.es

.BY

1 .Yl

at-value based on null hypothesis that the mean equals zero.

*t-value oc P-etatlstlc algnificant at the five percent level.

both within and across days vitiates any conclusions based on open to close

returns. Taken together, these findings indicate that the conjecture by

Rogalski. that the nontrading weekend effect and trading time hypothesis

characterize the pre-1974 period is inappropriate. The pre-1974 results,

however, are consistent with the findings presented in Prince and Smirlock and

Starks. Finally, the differences in hourly returns and their pattern across

subperiods suggest that the return generating process may not be stable. This

instability in the return generating process is also suggested by the shift in

the weekend effect.

Additional work needs to be done to further document and validate the

above findings, especially as regards the shift in the weekend effect and the

trading time hypothesis. One obvious extension is to use an index more

representative of the market, such as the S&P 500. Transactions data would

also be useful if the sample period were long enough. This research should

investigage both trading and nontrading periods, and not focus on one at the

expense of the other. Finally, any explanation of the Monday effect should

also be able to explain its shift from a trading to largely a nontrading

effect over the last Wenty years.


TABLE 3

Tests for Intraday Effects, by Sample Period

Sample Null F-Statistics for Hypotheses Tests by Dependent Variable Period Hypothesis Monday Tuesday Wednesday Thursday Friday

1963-1968

1968-1974

a,,= a,*= a,= a2= a3= a4 2.74* 5 .oe* 10.00* 8.06* 5.89’

a,2= a,= a2= a3= a4 1.87 .76 1.05 1.55 .96

a,,= a,2= a,= a2= a3= a4 9.77* 1 .oo 1 .ll 1.57 2.80L

a,2= a,= a2= a3= a4 5.22* 1 .26 .77 .B3 2.20

1974-1983 a,,= a,2= a,= a2= a3= a4 9.92* 5.75* 3.77* 8.72’ 3.43’

a,2= a,= a2= aj= a4 5.11* 6.53* 4.52* 9.77* 4.27*

*F-statistic signiEicant at the five percent level.

summary Statletlce for ltourly Returne by

Day of the Week and Saapls Periodaeb

sample

Period Variable statlstlc Monday Tuesday Wednesday l?lursday Friday,

All

Days

1963-1968 R”

“‘2

R’

“2

II’

II’

1968-1974

1974- 1983

II’ ’

‘7’2

It’

‘42

II’

R’

R”

R’2

R’

R2

i-2

R4

Mean

t-value

Wean

t-value

Hean

t-value

Hean

t-value

Mean

t-value

Mean

t-value

ObservatIonsb

Uean

t-value

Mean

t-value

nean

t-value

Man

t-value

usan

t-value

Uean

t-value

Cbservationsb

nean

t-value

‘lean

t-value

blean

t-v.3 lue

Mean

t-value

Hem

t-value

llean

t-value

ObservatLona

.0052 .0595* .0059~ .0567* .0527’ .0524*

t.241 0.49) (6.53) (4.56) (4.f-30) (7.52)

-.0557@ .0032 -.Oll8 - .0258 -.Ol57 - .0209&

(-3.501 t.241 t-.931 (-1.89) (-1.53) (-3.52)

- .0303* -.01oa .0016 -.0190 - .0070 -.0131

(-2.81) (-.98) t.16) (-1.94) f-.07) (-2.90)

- .0034 -.0096 .OOl9 .0040 .0047 - .ooo*

t-.371 (-.9e1 ( .2t3) l.361 (.51) (.‘O) -.0375* .0027 so067 -.0159 .0034 - . ooeo

(-2.931 l.17) t.401 (-I -18) t.301 (-1 .25)

-.0414* -.026-l* - .0265 - .0369 .ooao - .0248

(-4.331 C-2.20) I-1 -74) (-3.04) t.771 (-4.56)

251 258 263 260 265 12!38

-.1049* .OOl4 .0328 .0310 -.02at -.0132

l-6.21) I .091 (1.48) (1.47) (1.36) (-1.59)

-.0669 - .0060 .0134 -.0242 -.0201 -.0253*

(-4.54) (-.35) f.791 (-1.41) t-1.27) t-2.291

- .0402 - .0037 -.0077 -.0071 .0051 -.0106

(-2.73) (-.29) t-.58) t-.501 t.471 (-1.57)

.OOlS .0323* .0232 .0171 .03I32* .0227*

f.10) (2.17) (1 .a71 (1 .60) (3.111 (2.32)

.0099 - .0059 .0014 - .0094 .0000 -.0006

t.64) f-.39) t.191 (.97) ( .03) t-.67)

.OOLll -.0003 -.0141 - .0109 .019s - .0009

t.531 t-.691 (-1.36) (-.I391 (1.78) f-.73)

305 316 313 305 317 1556

-.0626* .0227 .0279* .0250 -0004 .0166

(5.17) (1.81) (1.98) (1.72) t.911 (1.921

- .0275* - .0269* .0164 - .0320* .0068 -.0337*

t-2.13) (-2.21) (1.49) f-2.71) t.391 (-4.75)

.0219. .0247* .0260* .0300* .0220* .0250*

(1.97) (2.17) (2.61) (2.47) (2.03) (5.00)

.0630* -0329. .0391* .0445* .0109 .0379*

(5.47) (2.79) (2.91) 0.291 (1.43) (7.15)

.0371* - .0656 -.043t3* - .0663. -.0231 -.0121

(2.41) I-4.71) l-3.191 (-4.79) (-1.63) (-1.96)

.0239 .0069 .0274* .0207 .0466* .0053

(1.91) (.I?) (2.00) (1.61) (2.81) t.e11

422 437 473 463 440 2239

F5 p4

3.51. .95

2.72. .83

I .42 .72

.40

1.72

2.52.

.50

.s3

2.61.

8.61.

3.01.

2.28

.99

1.77 .21

1 .ll .47

.18

1.17

.09

1.37

6.55. .35

2.69. 3.11.

.OB .08

2.49 I .57

6.90. 1.56

1.74 2.27

‘t-value based on null hypothesie that the uzan equals zero.

bFor the 1963-1968 period, R’ and R’ have 204, 208, 214, 211 and 204 observatlona for Monday, Tuesday, Wednesday, Thursday and Friday,

raepectlvely. ¶%a total number of obeervatlons for R3 a;#d R4 Is 8041. This is because, as noted in the text, over pact of the period the

prkat closed at 2 o’clock and, for some observatlone, no 3 o’clock DJIA was reported in the Journal.

t-value or F-statistic slgnlflcant at the five percent level.

For the 1960-1974 period, R’ (R*) hae 283 (2451, 290 (2501, 284 (2411, 277 (237). 292 (253) obsarvatlong for Monday, Tuesday, Wednesday,

Thursday end PrIday. Thls Is for the sams reasons a8 noted In the text end above.

*‘t-value of F-statlstlc slqnlflcant at the flvc percent level.

BIBLIOGRAPHY

Cross, F. "The Behavior of Stock Prices on Fridays and Mondays," Financial -- Analysts Journal (November - December 19731, 67-69.

Fama, E. "me Behavior of Stock Prices," Journal of Business 38 (Jan. 19651,

383-417.

French, K. "Stock Returns and the Weekend Effect," Journal of Financial Economics 8 (March 19801, 55-70.

Gibbons, M. and P. Hess. “Day of the Week Effects and Asset Returns," Journal of Business 54 (October 19811, 579-596.

Harris, L. ‘A Transaction Data Study of Weekly and Intradaily Patterns in Stock Returns," unpublished manuscript, University of Southern California, 1984.

Keim, D. and R. Stambaugh. "A Further Investigation of the Weekend Effect in Stock Returns," Journal of Finance 39 (May 19841, forthcoming.

Lakonishok, J. and M. Levi. "Weekend Effects on Stock Returns--A Note," Journal of Finance 37 (June 19821, 883-889.

Oldfield, G. and R. Rogalski. “A Theory of Coinmon Stock Returns over Trading and Non-Trading Periods," Journal of Finance 35 (June 19801, 729-751 l

Prince, P. "Day of the Week Effects: Hourly Data,” unpublished manuscript, University of Chicago, 1982.

Rogalski, R. "New Findings Regarding Day of the Week Returns over Trading and Non-Trading Periods," unpublished manuscript, Dartmouth College, 1984.

Scholes, M. and J. Williams. "Estimating Betas from Nonsynchronous Data,” Journal of Financial Economics 4 (December 19771, 309-327.

Smirlock, M. and L. Starks. “Day of the Week in Stock Returns: Solne Intraday Evidence," unpublished manuscript, University of Pennsylvania, 1983.

Reprinted with rhe kind permission of the authors.

MTA JOURNAL ! AUGUST 1989 6:

FOOTNOI'ES

'See French (19801, Gibbons and Hess (19811, Lakonishok and Levi (19821, and Keim and Stambaugh (1984). Also see Cross (1973) and Fama (1965) for further evidence on the .day of the week effect. Explanations for the observed weekend effect that have been rejected include the calendar time hypothesis, which asserts that the expected return for Monday is three times the expected return for other days of the week (French (198011, the delay between trading and settlement due to check clearing (Lakonishok and Levi (19821, Gibbons and Hess (198111, measurement error in returns (Gibbons and Hess (1981) and Keim and Stambaugh (7984)) and specialist-related biases (Keim and Stambaugh (1984)).

2Rogalski also examines the S&P 500 and the NYSE index and reports similar to those obtained using the DJIA.

3The Oldfield and Rogalski study examines the trading and nontrading returns for five stocks for the 39 month pericd October 1, 1974 through December 31, 1977.

4Specifically, Rr = en(DJIA /DJIA 1 l 100, where i = CI

1, 2, 3, 4. All the Return seriis weret-Checked for significant 0, d, 11, 12,

autocorrelations. According to Scholes and Williams (19771, significant autocorrelations in returns may be due to nontrading problems, which Gibbons and Hess (1981) cite as a possible explanation of the weekend effect. For RC, the observed autocorrelation at lag 1 is about .04 and for the other return measures never exceeds .lO for any subperiod, indicating that nontrading problems are not significant for the MIA.

'The evidence in Table 1, as well as previous work by Faata (19651,

indicates that Honday returns have a higher variance relative to other days. To avoid heteroscedasticity, equation (1) was standardized by the estimated standard deviations for each day of the week. As with Gibbons and Hess' (p. 5861, we found that 'the heteroscedasticity adjustment has no important impact on the conclusions* in either a quantitative or qualitative sense.

6Rogalski has presented evidence that RC, R" and Rd are positive in January and, accordingly, that the weekend eEfe& does kot characterize January. To examine this proposition, we segmented our results into January and non-January results. The latter results are, not surprisingly, quite similar to those for all months and the qualitative conclusions concerning trading and non-trading periods, the weekend effect and the trading time hypothesis are the same as reported in Table 1. The results for January, however, do not allow rejection of the null hypothesis of constant returns across weekdays, regardless of return measure or subperiod. These findings concur with the January results presented by Rogalski.


Journal of Technical Analysis (JOTA). Issue 33 (1989, August)

Economy & Finance

Transcript of Journal of Technical Analysis (JOTA). Issue 33 (1989, August)