journal of technical analysis (jota). issue 15 (1983, may)

MARKET TECHNICIANS ASSOCIATION

JOURNAL Issue 15

MARKET TECHNICIANS ASSOCIATION JOURNAL

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MARKET TECHNICIANS ASSOCIATION JOURNAL Issue 15 May, 1983

Editor: James M. Yates Bridge Data Company 10050 Manchester Road St. Louis, Missouri 63122

Contributors: Walter L. Eckardt Arthur A. Merrill Robert J. Nurock Richard C. Orr Robert R. Prechter, Jr. Robert F. Vandell

Publisher: Market Technicians Association 70 Pine Street New York, New York 10005

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@Market Technicians Association 1983

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MTA JOURNAL - MAY, 1983

TABLE OF CONTENTS

Title

MEMBERSHIP AND SUBSCRIPTION INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

MTA LE-lTER FROM THE EDITOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . James M. Yates

AN EXPLANATION OF THE WALL $TREET WEEK TECHNICAL MARKET INDEX . . . . . . . . . . . . . . . . . . . . Robert J. Nurock

A RISING TIDE: THE CASE FOR WAVE V IN THE DOW JONES INDUSTRIAL AVERAGE . . . . . . . . . . . . Robert R. Prechter, Jr.

THE USE OF VOLUME AS AN EARLY WARNING SIGNAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Richard C. Orr, Ph.D.

TRENDS AND THE LOG SCALE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arthur A. Merrill

CENTERFOLD: MAJOR MARKET INDEX (XMI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

STOCK INDEX FUTURES: TECHNICAL ANALYSIS AND ARBITRAGE OPPORTUNITIES . . . . . . . . . . Walter L. Eckardt

APPLIED MODERN PORTFOLIO THEORY: ITS FUNDAMENTAL AND TECHNICAL ASPECTS . . . . . . . . Robert F. Vandell

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MEMBERSHIP AND SUBSCRIPTION INFORMATION

REGULAR MEMBERSHIP - $50 per year plus $10 one-time application fee.

Receives the MTA Journal, the monthly MTA Newsletter, invitations to all meetings, voting member status, and a discount on the Annual Seminar fee. Eligibility requires that the emphasis of the applicant’s professional work involve technical analysis.

SUBSCRIBER STATUS - $50 per year.

Receives the MTA Journal and the MIA Newsletter, which contains shorter articles on technical analysis. The subscriber receives special announcements of the MTA meetings open to The New York Society of Security Analysts and/or the public, plus a discount on the Annual Seminar fee.

ANNUAL SUBSCRIPTION TO THE MTA JOURNAL - $35 per year.

SINGLE ISSUES OF THE MTA JOURNAL (including back issues) - $15

The Market Technicians Association Journal is scheduled to be published three times each fiscal year in approximately November, February, and May.

An ANNUAL SEMINAR is held each Spring.

Inquiries for REGULAR MEMBERSHIP and SUBSCRIBER STATUS should be directed to:

John Greeley Greeley Securities, Inc. 120 Broadway New York, New York 10005

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MTA LETTER FROM THE EDITOR

As you have already noticed, the MTA Journal -- May, 1983, looks a little different. Saddle stitched, the printer’s term for folded and stapled, and typeset copy, along with a new cover design, set it apart from its predecessors. The content, as always, is meant to stir the gray matter.

We have also instituted the Market Technician’s centerfold. A suggestive (?) naked (uncovered) listing of bare (?) data (rounding bottoms?) in chart and/or tabular form. The contributor gets worldwide notoriety (his or her name is printed next to the creation) in 11 point type. A single page is available for explanation of the various curves and other intricacies of the presentation.

The American Stock Exchange has developed an index of twenty blue chip stocks and is trading options on this index. A full listing of the daily values from January 2, 1973, through March 8, 1983, is available as the centerfold. (Tony Tabell eat your heart out.) Other information in regard to this index is available directly from the American Stock Exchange.

The production of the MTA Journal would not have occurred without the valuable assistance of the following very valuable people: Pam Hollrah, who typed every word; Sheldon Hoffman, who wrote the program to set the type and do the text-editor-to-typeset conversions; Buzz Eckardt, who proofread the entire book; Sally Ruppert, who co-ordinated the entire effort and made it work; Fred Zaegel, who added his valuable printing experience; and all those brave enough to contribute written material for public inspection.

We thank you one and all for talking the time to read our modest effort.

As always, comments, suggestions and just friendly phone calls are welcome.

James M. Yates, Editor

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AN EXPLANATION OF THE WALL $TREET WEEK TECHNICAL MARKET INDEX

Robert J. Nurock Investor’s Analysis, Inc.

The Wall $treet Week Technical Market Index is a consensus index of stock market indicators created by Robert J. Nurock, President-Market Strategist of Investor’s Analysis, Paoli, PA, an independent investment consultant’origi- nator of stock market research, and a regular panelist of Wall $treet Week, with Louis Rukeyser, since its inception in 1970.

The Index, which was introduced to the Wall $treet Week audience on October 6, 1972, and is updated weekly for presentation on the program, reflects the influence of a wide variety of factors -- not necessarily related to the economy, corporate earnings, or dividends -- on stock prices. These data, when reduced to index form, facilitate the per- ception of changes in investor psychology, market action, speculation, and monetary conditions that are usually present at key market turning points. The Index does not attempt to identify short term swings, but rather intermediate to long term (3-6 months or longer) market moves. It is of value in confirming the continuation of a current trend (when the majority of its components are neutral) and in providing early warning of a change in a prevailing trend (when the net majority of its components are bullish or bearish).

Technical analysts, who study this type of data, which reflect the potential supply of/or demand for stocks, have been nicknamed “elves” by host Louis Rukeyser. “Chief ELF” Bob Nurock points out that technical analysis, like all forms of stock market research, can be fallible in its predictions and is best used as an adjunct to other forms of analysis.

HOW THE INDEX IS CONSTRUCTED

In preparing his Index, Bob constantly monitors the statistics used in constructing ten well-known technical indicators. These are:

1. DOW JONES MOMENTUM RATIO. This indicator measures the point differential between the Dow Jones Indus- trial Average and its 30-day moving average. It may be compiled by maintaining a running total of the closing DJIA for the past 30 days; dividing that total by 30 to obtain a daily average; then comparing the Dow’s latest close with its most recent 30-day average.*

SIGNIFICANCE: This indicator flashes a warning when stock prices have reached an extreme of momentum typically found as the market approaches important turning points.

2. NYSE HI-LO INDEX. This indicator compares the average number of stocks making new highs and new lows on a daily basis over the last 2 weeks. Ten-day moving averages of both new highs and new lows are computed (in a manner similar to that used for the 30-day moving average of the DJIA above), and are compared to one another.*

SIGNIFICANCE: This indicator measures the strength of the market leaders, and the ability of the market to advance to higher ground, or its inability to resist going into lower ground. At an intermediate-term bottom, every stock should have corrected, and therefore few new highs are made. At an intermediate-term market top, investor psychology tends to be onesidedly bullish, thus few new lows are registered. A reversal from either extreme tends to confirm a change in market direction.

3. MARKET BREADTH INDICATOR. This indicator is a lo-day moving average of advances minus declines. An algebraic total of net advances to declines is computed daily and then smoothed into a 1 O-day average reading.*

SIGNIFICANCE: This indicator measures the underlying strength of market moves by indicating whether or not the majority of stocks are moving in the same direction as the market averages, confirming market strength or weakness.

4. TRADING INDEX. This indicator is a lo-day moving average of the ratio of volume going into advancing stocks versus the volume going into declining stocks on the NYSE. It is computed by dividing the number of issues advancing by the number of issues declining and dividing the resulting quotient by the quotient of the division of volume in advancing stocks by the volume in declining stocks.*

SIGNIFICANCE: This indicator measures overenthusiasm or over- pessimism on a short term basis, as represented by excessive volume flowing into stocks as they reach their extremes.

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5. PRICES OF NYSE STOCKS VERSUS THEIR MOVING AVERAGES. This indicator reflects the percentage of NYSE stocks selling above their lo-week and 30-week moving averages. (Compiled by INVESTOR’S INTELLIGENCE, One West Avenue, Larchmont, New York 10538.)

SIGNIFICANCE: This indicator measures the percentage of stocks which have moved too sharply in one direction, and thus signals that the market may be overbought or oversold and ready for a reaction in the opposite direction.

6. PREMIUM RATIO ON OPTIONS. This indicator compares the average premium on all listed put options to the average premium on all listed call options on a weekly basis. It is compiled by dividing the average premium on puts by the average premium on calls. (Raw data from the OPTIONS CLEARING CORP., 141 W. Jackson Blvd., Chicago, IL 60604.)

SIGNIFICANCE: When the premium ratio is high it indicates investors are overly pessimistic and bidding put prices up excessively. When the ratio is low, it indicates investors are overly optimistic and bidding call prices up excessively.

7. ADVISORY SERVICE SENTIMENT This indicator categorizes the forecasts of leading advisory services as bullish, bearish, or as expecting a market correction. (As reported by INVESTOR’S INTELLIGENCE.)

SIGNIFICANCE: Advisory service sentiment tends to follow a trend rather than anticipate a change in trend. There- fore, when sentiment as measured by this indicator becomes distinctly one-sided, a contrary move in the market may be anticipated.

8. LOW-PRICE ACTIVITY RATIO. This indicator relates the level of activity in more speculative stocks to that in more seasoned issues. (Available weekly on the Market Laboratory page in BARRON’S.)

SIGNIFICANCE: Speculative activity is usually high at market tops and low at market bottoms.

9. INSIDER ACTIVITY RATIO. This indicator is a ratio of insider sell transactions relative to buy transactions on a weekly basis. (Computed by STOCK RESEARCH CORP., 50 Broadway, New York, NY 10004.)

SIGNIFICANCE: The higher the ratio of sellers to buyers, the stronger the belief of key corporate insiders that their stocks are overvalued and that a downward price reaction is likely. The lower the ratio, the stronger the belief that their stocks are undervalued and that an upward move is likely.

10. FED POLICY. This indicator provides a guide to the direction of Federal Reserve Board policy as reflected by the level of the Federal Funds Rate relative to the Discount Rate. It is compiled by taking the ratio of the closing bid price for Fed Funds to the Discount Rate on a daily basis, and computing a four-day average of the ratios for Friday, Mon- day, Tuesday and Thursday each week. Wednesday readings are omitted as they are unusually volatile due to end of the bank week transactions.’

SIGNIFICANCE: A high Fed Funds rate relative to the Discount Rate signifies that money is “tight” and borrowing is being discouraged. The effect of this is to slow down the growth of business. A low Fed Funds rate relative to the Discount Rate indicates that money is “easy” and borrowing is being encouraged. Under such conditions the expansion of business is encouraged.

*raw data is available daily from major financial publications

HOW THE INDEX IS CALCULATED

The Index is based on an evaluation of weekly trends in the foregoing ten indicators in accordance with the criteria outlined in Table 1. It is calculated every Friday using the most current data available at the market’s close the previous Thursday.

When an indicator reaches an extreme usually registered at market bottoms, it is assigned a plus (+).

When an indicator reaches an extreme usually registered at market tops, it is assigned a minus (-).

Indicator readings between extremes are designated neutral (0).

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The first time an indicator moves directly from one extreme to another (i.e., from positive to negative or vice versa), it is assigned a neutral (0) reading which is maintained until a plus or minus reading is confirmed (same reading for two consecutive weeks).

Once this evaluation is completed, the net algebraic total of the number of positive ( + ) and negative ( - ) indicators is the Technical Market Index reading for the week.

HOW THE INDEX IS INTERPRETED

The Technical Market Index readings are interpreted as follows:

+ 5 or higher +4 +3 +2 +1

0 -1 -2 -3 -4 -5 or lower

Extremely bullish. Buy now. Strongly bullish. Get ready to buy. Bullish. Mildly bullish. Neutral. Neutral. Neutral. Mildly bearish. Bearish. Strongly bearish. Get ready to sell. Extremely bearish. Sell now.

As an example, the following is the Index reading for August 27, 1982:

4 indicators positive = + 4 5 indicators neutral = 0 1 indicator negative = -1 Index Reading: +3

Interpretation: Bullish

THIRD REVISION 1 O/1/82

TABLE I

WALL STREET WEEK TECHNICAL MARKET INDEX

INDICATOR INTERMEDIATE

BOTTOM INDICATOR (Positive Reading)

INTERMEDIATE TOP INDICATOR (Negative Reading)

1. DOW JONES MOMENTUM RATIO -30 or below (DJIA VS. 30-day moving average)

+30 or above

2. NYSE HI-LOW INDEX An expansion of the An expansion of the 0$ new daily highs/new new highs from less new lows from less

than 10 to a figure than 10 to a figure exceeding the exceeding the average number of average number of new lows is positive new highs is negative

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3. MARKET BREADTR INDICATOR (lo-day moving average of net advances or declines)

4. TRADING INDEX (lo-day moving average of volume in advancing stocks/volume in declining stocks >

5. % OVER MOVING AVERAGES (% NYSE stocks selling above their lo- and 30-week moving averages)

6. PREMIUM RATIO ON OPTIONS (Weekly average premium puts/calls)

7. ADVISORY SERVICE SENTIMENT (Percentage services bearish)

8. LO-PRICE ACTIVITY RATIO (Weekly ratio of volume in Barron’s Lo-Price Stock Index/Volume in DJIA stocks >

9. INSIDER ACTIVITY RATIO (Weekly ratio of insider sell transactions/buy transact ions >

10. FED POLICY (Weekly ratio of Fed Funds rate/Discount rate)

An expansion of this index from below +lOOO to the point where it peaks out and declines 1000 points from this peak is positive. Readings between +lOOO and -1000 are neutral.

lo-day average above 1.20

A lo-week reading below 30% AND a 30-week reading below 40%

Ratio above 128%*

Above 45.6%*

Below 12%

Below 1.5

Below 103%

A contraction of this index from -1000 to the point where it bottoms out and rises 1000 points from this trough is negative. Readings bewteen -1000 and +lOOO are neutral.

10 day average below 0.80

A lo-week reading above 70% AND a 30-week reading above 60%

Ratio below 40X*

Below 26.0X*

Above 18%

Above 2.5

Above 125%

* Readings in excess of standard deviation from mean of most recent historical readings. Exact criteria will be updated annually to reflect actual experience.

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ROBERT J. NUROCK

MARKET ANALYST AND MARKET STRATEGY SPECIALIST

“Emotions play a larger role in decision-making than move investors are willing to admit. That’s why understanding current investor psychology is so important to understanding where the market is and where it might go,” says Robert J. Nurock, President/Market Strategist of Investor’s Analysis of Paoli, PA.

Mr. Nurock is responsible for the formulation and recommendation of investment strategy to numerous investment institutions, as well as a select group of individual investors. He brings to this assignment a strong background in translating abstract theoretical research data into practical working terms. For example, he developed the Maryland Regional Stock Index while working as an invesment executive in Baltimore. This index, which is published daily by the Baltimore Sunpapers, enables investors to compare the performance of local stocks to that of the market as a whole.

Television viewers have also benefited from Mr. Nurock’s ability to express hard data in terms that the layman can understand. Mr. Nurock aided in the initial production of Public Broadcasting’s WALL $TREET WEEK, and has served as a regular panelist since its inception. The Technical Market Index he developed for WALL $TREET WEEK has been nationally recognized as an effective way to forecast stock market trends and prices.

Currently, Mr. Nurock writes a MARKET STRATEGY REPORT for clients of Investor’s Analysis, Inc. His report ana- lyzes economic and stock market trends as well as helpful expectations regarding the future course of stock prices, information which is helpful to investors concerned with improving their market timing and performance. In addition, he consults with and advises clients personally on the most appropriate courses of action for their own particular investment objectives.

Mr. Nurock completed his undergraduate studies at Pennsylvania State University and did postgraduate work at Johns Hopkins University. He is a member of the Analysts Club, past vice president of the Market Technicians Association, and a member of the New York Society of Security Analysts, Inc.

Prior to launching Investor’s Analysis, he was First Vice-President-Market Strategy, Butcher & Singer, Inc., Phila- delphia, PA, which he joined after leaving Merrill Lynch, where he was vice president in charge of the Investor Support Group. In this position, he acted as a liaison between the research and economic divisions and the sales force, aiding the latter in making timely investment recommendations.

He has been quoted widely by such financial publications as BARRON’S, WALL STREET JOURNAL, BUSINESS WEEK, NEW YORK TIMES, DUN’S REVIEW, and in major newspapers throughout the United States, Canada, and Europe. He has been a guest lecturer at the Wharton School of Business at the University of Pennsylvania and at Goucher College in Baltimore, where he created and taught a seminar course in investments and securities. He has also been a featured speaker at investment seminars conducted for both professional and lay groups.

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ROBERT J. NUROCK

BORN: May 25, 1937

EDUCATION: Pennsylvania State University - B.A., 1958 John Hopkins University - Post Graduate Studies

CAREER DATA: 1982-Present: President, Market Strategist - Investor's Analysis, Inc., Paoli, PA 19301

Consultant and advisor to numerous investment institutions, as well as a select group of individual investors, on the stock market.

Recommends specific investment strategy, industry groups and stocks appropriate to current economic, monetary, and stock market conditions and the future outlook.

Writes biweekly MARKET STRATEGY REPORT, and conceptual investment commentary, OBSERVATIONS, when timely and appropriate. Also issues timely AN IDEA! reports with specific stock suggestions.

1979-1982: First Vice President-Market Strategy, Butcher & Singer, Inc., Philadelphia,PA.

Responsible for the formulation and recommendation of investment strategy for institutional investors and the firm's Account Executives. Wrote biweekly MARKET LETTER. Member Investment Policy Committee.

1977-1979: Vice President-Investor Support Group, Merrill Lynch, Pierce, Fenner 6 Smith, Inc., New York, NY

Responsible for the development and marketing of securities research-based products and services to the individual investor.

1974-1977: Market Specialist-Product Supervisor, Market Analysis Dept., Securities Research Division, Merrill Lynch, Pierce, Fenner & Smith, Inc., New York NY

Developed new products and devised market strategies for the use of them. Wrote explanatory booklet on Market Analysis, and how to make better investment decisions.

1967-1974: Account Executive, Merrill Lynch, Pierce, Fenner & Smith, Inc., Baltimore, MD

ACCOMPLISHMENTS: Aided production of first live Public Broadcasting network TV series on stock market, Wall Street Week,

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ACTIVITIES:

viewed on over 200 stations, and appeared as regular panelist. Designed nationally recognized W$W TECHNICAL MARKET INDEX to forecast stock prices and trends.

Recognized as investment authority by, and has spoken before, the New York Society of Security Analysts, National Securities Traders Association, Securities Industry Association, National Association of Investment Clubs, and Market Technicians Association.

Appeared as guest expert on various television and radio shows including Cable News Network's "Moneyline", WNEW-TV and the CBS radio network.

Wrote weekly column analyzing economic and stock market trends , published by Merrill Lynch.

Created and taught Seminar Course in Investments and Securities for Goucher College. Guest Lecturer, The Wharton School, University of Pennsylvania.

Developed Maryland Regional Stock Index (MARSI) which compares performance of local stocks to that of the market as a whole and is published daily by the Baltimore Sunpapers.

Cited as authoritative market analyst in HOW TO MAKE MONEY ON WALL STREET, by Louis Rukeyser, a Literary Guild Selection, published by Doubleday & Co., Inc.

Quoted in BARROW'S, WALL STREET JOURNAL, BUSINESS WEEK, NEW YORK TIMES, DUN'S REVIEW, FINANCIAL WORLD, and in other major publications throughout the United States, Canada, and Europe.

Analysts Club Market Technicians Association, past Vice President New York Society of Security Analysts Pennsylvania State University Alumni Fund

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A RISING TIDE:

THE CASE FOR WAVE V IN THE DOW JONES INDUSTRIAL AVERAGE

Robert R. Prechter, Jr.

In 1978, A. J. Frost and I wrote a book called ELLIOTT WAVE PRINCIPLE, which was published in November of that year. In the forecast chapter of that book, we made the following assessments:

1. That wave V, a tremendous bull market advance, was required in order to complete the wave structure which began in 1932 for the Dow Industrial Average.

2. That there would be no “crash of ‘79” and in fact no ‘69-‘70 or ‘73-‘74 type decline until wave V had been completed.

3. That the 740 low in March 1978 marked the end of Primary wave@and would not be broken.

4. That the bull market in progress would take a simple form, unlike the extended advance from 1942 to 1966.

5. That the Dow Industrial Average would rise to the upper channel line and hit a target based on a 5x multiple of the wave IV low at 572. then calculated to be 2860.

6. That, if our conclusion that 1974 marked the end of wave IV was correct, the fifth wave peak would occur in the 1982-l 984 time period, with 1983 being the most likely year for the actual top.

7. That “secondary” stocks would provide a leadership role throughout the advance.

8. That after wave V was completed, the ensuing crash would be the worst in U. S. history.

One thing that continuously surprised us since we made those arguments was how long it took the Dow Jones In- dustrial Average finally to lift off. The broad market averages continued to rise persistently from 1978, but the Dow, which appeared to mirror more accurately the fears of inflation, depression and international banking collapse, didn’t see its corrective pattern, dating from 1966, until 1982. (For a detailed breakdown of that wave, see THE ELLIOTT WAVE THEORIST September 1982 issue.) Despite this long wait, it fell only briefly beneath its long-term trendline, and the explosive lift-off finally began when that downside break failed to precipitate any significant further selling.

If our overall assessment is correct, the forecasts Frost and I made based on the Wave Principle back in 1978 will still occur, with one major exception: the TIME TARGET As we explained in our book, R. N. Elliott said very little about time, and in fact, our estimate for the time top was not something that the Wave Principle required, but simply an educated guess based on the conclusion that wave IV in the Dow ended in 1974. When it finally became clear that the long sideways wave IV correction hadn’t ended until 1982, the time element had to be shifted ahead to com- pensate for that change in assessment. At no time was there a doubt that wave V would occur; it was only a matter of when. and after what.

I would like to take this space to answer three important questions:

1. Has the sideways correction in the Dow which began in 1966 actually ended?

2. If so, how big a bull market can we expect?

3. What will be its characteristics?

1) IN 1982 THE DJIA FINISHED A CORRECTION OF VERY LARGE DEGREE. The evidence for this conclusion is overwhelming.

First, as those who take the Wave Principle seriously have argued all along, the pattern from 1932 is still incomplete and requires one final rise to finish a five-wave Elliott pattern. Since a Supercycle crash was not in the cards, what

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HAS occurred since 1966 is more than adequate for a correction of Cycle degree (the same degree as the 1932- 1937, 1937-l 942,1942-l 966 and 1966-l 982 waves).

Second, the sideways pattern from 1966 (or arguably 1964 or 1965, if you enjoy talking theory) pushed to the ab- solute limit the long-term parallel trend channel from 1932. As you can see in illustration 3, from Elliott’s own “Nature Law”, it is an occasional trait of fourth waves that they will break beneath the lower boundary of the uptrend channel just prior to the onset of wave 5. The price action in 1982 simply leaves no more room for the correction to continue.

Third, the pattern between the mid-‘60’s and 1982 is another wonderful real-life example of standard corrective formations outlined by Elliott over 40 years ago. The official name for this structure is a “double three” correction, which is two basic corrective patterns back-to-back. In this case the market traced out a “flat” (or by another count, a “de- scending triangle”) in the first position and an “ascending triangle” in the second, with an intervening simple 3-way advance, labeled “X”, which serves to separate the two simpler patterns. Elliott also recognized and illustrated the occasional propensity for the final wave of a triangle to fall out of the lower boundary line, as occurred in 1982. The doubling of a correction is moderately rare, and since the 1974 low had already touched the long term uptrend line, Frost and I weren’t expecting it. Moreover, a “double three” with a TRIANGLE in the second position is so rare that in my own experience it is unprecedented.

Fourth, the pattern has some interesting properties if treated as a single formation, that is, one correction. For instance, the FIRST wave of the formation (966 to 740) covers almost exactly the same distance as the LAST wave (1024 to 777). The advancing portion, moreover, takes the same time as the declining portion, 8 years. The symmetry of the pattern prompted Frost and me to come up with the label “Packet Wave” in 1979 to describe a single pattern starting at “rest”, going through wider, then narrower swings, and returning to the point from which it began. (This concept is detailed in the December 1982 issue of THE ELLIOTT WAVE THEORIST) Using the alternate count of two triangles, it happens that the middle wave (wave C) of each triangle covers the same territory, from the 1000 level to 740. Numerous Fibonacci relationships occur within the pattern, many of which were detailed in a Special Report of THE ELLIOTT WAVE THEORIST dated July 1982. Far more important, however, is the Fibonacci relationship of its STARTING and ENDING points to part of the PRECEDING BULL MARKET Hamilton Bolton made this famous observation in 1960:

Elliott pointed out a number of other coincidences. For instance, the number of points from 1921 to 1926 were 61.8% of the points of the last wave from 1926 to 1928 (the orthodox top). Likewise in the 5 waves up from 1932 to 1937. Again the wave from the top in 1930 (297 DJIA) to the bottom in 1932 (40 DJIA) is 1.618 times the wave from 40 to 195 (1932 to 1937). Also, the decline from 1937 to 1938 was 61.8% of the advance from 1932 to 1937. SHOULD THE 1949 MARKET TO DATE ADHERE TO THIS FORMULA, THEN THE ADVANCE FROM 1949 TO 1956 (361 POINTS DJIA) SHOULD BE COMPLETE WHEN 583 POINTS (161.8% OF THE 361 POINTS) HAVE BEEN ADDED TO THE 1957 LOW OF 416, OR A TOTAL OF 999 DJIA.

So in projecting a Fibonacci relationship, Bolton forecast a peak which turned out to be just three points from the exact hourly reading at the top in 1966. But what was largely forgotten (in the wake of A. J. Frost’s successful forecast for the wave IV low at 572, which was borne out in 1974 at the hourly low of 572.20) was Bolton’s very next sentence:

ALTERNATELY, 361 POINTS OVER 416 WOULD CALL FOR 777 IN THE DJIA.

Needless to say, 777 was nowhere to be found. That is, until August 1982. The exact orthordox low on the hourly readings was 776.92 on August 12. In other words, Bolton’s calculations defined the exact beginning and end of wave IV in advance, BASED ON THEIR RELATIONSHIPS TO THE PREVIOUS PRICE STRUCTURE. In price points, 1966 1982 is .618 of 1957-l 982 AND of 1949-l 956, each of which, being equal, is .618 of 1957-l 966 -- all within 1% error! When weekly and monthly patterns work out time after time to Fibonacci multiples, the typical response from Wall Street observers is, “another coincidence.” When patterns of this size continue to workout, it becomes a matter of faith to persist in believing that Fibonacci multiples are NOT characteristic of the stock market. As far as I know, Bolton is the only dead man whose forecasts continue to fit the reality of Wall Street.

From these observations, I hope to have established that Cycle wave IV in the DJIA, which the “Constant Dollar Dow” clearly supports as a single bear phase, ended in August 1982.

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Illustration 1

BOLTON’S FIBONACCI CALCULATIONS, 1960 (hourly extremes in brackets where different)

Illustration 2

COUNT BASED ON 1978 INTERPRETATION (Still probable for broad indexes)

600 t 522 I

4001 .-----.

HI A15 1415)

2) THE ADVANCE FOLLOWING THIS CORRECTION WILL BE A MUCH BIGGER BULL MARKET THAN ANY- THING SEEN IN THE LAST TWO DECADES. Numerous guidelines dealing with normal wave behavior support this contention.

First, as Frost and I have steadfastly maintained, the Elliott Wave structure from 1932 is unfinished, and requires a fifth wave advance to complete the pattern. At the time we wrote our book, there was simply no responsible wave interpretation that would allow for the rise beginning in 1932 already to have ended. The fifth wave will be of the same degree and should be in relative proportion to the wave patterns of 1932-l 937, 1937-l 942, 1942-l 966, and 1966-l 982.

Second, a normal fifth wave will carry, based on Elliott’s channeling methods, to the UPPER CHANNEL LINE, which in this case cuts through the price action in the 3500-4000 range in the latter half of the 1980’s. Elliott noted that when a fourth wave breaks the trend channel, the fifth wave will often have a throw-over, or a brief penetration through the same trend channel on the other side.

Third, an important guideline within the Wave Principle is that when the third wave is extended, as was the wave from 1942 to 1966, the first and fifth waves tend toward equality in time and magnitude. This is a tendency, not a necessity, but it does indicate that the advance from 1982 should resemble the first wave up, which took place from 1932 to 1937. Thus, this fifth wave should travel approximately the same percentage distance as wave I, which moved in nearly a 5x multiple from an estimated (the exact figures are not available) hourly low of 41 to an hourly peak of 194.50. Since the orthodox beginning of wave V was 777 in 1982, an equivalent multiple of 4.744 projects a target of 3686. If the exact hourly low for 1932 were known, one could project a precise number, Bolton-style, with some confidence. As it stands, the “3686” number should be taken as probably falling within 100 points of the ideal projection (whether it comes true is another question).

Fourth, as far as TIME goes, the 1932-l 937 market lasted five years. Therefore, one point to be watching for a possible market peak is 5 years from 1982, or 1987. Coincidentally, as we pointed out in our book, 1987 happens to be a Fibonacci 13 years from the correction’s low point in 1974,21 years from the peak of wave III in 1966, and 55 years from the start of wave I in 1932. To complete the picture, 1987 is a perfect date for the Dow to hit its 3686 target since to reach it, the Dow would have to burst briefly through its upper channel line in a “throw-over”, which is typical of exhaustion moves (such as the 1929 peak). Based on a 1.618 time multiple to wave I and on equality to the 1920’s fifth Cycle wave, an 8-year wave V would point to 1990 as the next most likely year for a peak. It would be particularly likely if the Dow is still substantially below the price target by 1987. Keep in mind that in wave forecasting, time is a consideration which is entirely secondary to both wave form, which is of primary importance, and price level.

Fifth, while the Dow Industrial Average is only in its FIRST Primary wave advance within Cycle wave V, the broader indexes began wave V in 1974, and are already well into their THIRD Primary wave. These indexes, such as the

21

Value Line Average, the Indicator Digest Average and the Fosback Total Return Index, are tracing out a traditional extended third, or middle wave, and have just entered the most powerful portion. Estimating conservatively, 60% of five-wave sequences have extended third waves, so this interpretation is along the lines of a textbook pattern, whereas attempts to interpret the broader indexes as being in their fifth and final wave are not. With a third wave extension underway in the broad indexes, a good deal of time will be necessary to complete the third wave, and then trace out the fourth and fifth waves. With all that ahead of us, the size of the current bull market will have to be substantial.

3) Now that the likelihood of wave V OCCURRING has been established and its size and shape estimated, it might be helpful to assess its probable CHARACTERISTICS.

First, the advance should be very selective, and rotation from one group to another should be pronounced. BREADTH during wave V should be unexceptional, if not outright poor relative to spectacular breadth performance in the mon- olithic markets of the ‘40’s and ‘50’s. As a long-term study in the April 1983 issue of THE ELLIOTT WAVE THEORIST shows, breadth performance in Primary and Cycle fifth waves is demonstrably poorer than that in the prior first and third waves. This characteristic is true even in daily wave formations and typically sets up technical momentum divergences at fifth wave tops of all degrees.

Second, this bull market should be a simple structure, more akin to 1932-1937 than to 1942-1966. In other words, expect a swift and persistent advance, with short corrections, as opposed to long rolling advances with evenly spaced corrective phases, Large institutions will probably do best by avoiding a market timing strategy, and concentrating on stock selection, remaining heavily invested until a full five Primary waves can be counted.

Third, the wave structure of the Dow and that of the broader indexes should fit together. If the count based on our 1978 interpretation is still the correct one, then it is the same as that for the broad indexes, and their waves will co- incide. If the preferred count is the correct one, then I would expect the third wave in the broad indexes to end when the Dow finishes its FIRST wave, and the fifth wave in the broad indexes to end when the Dow finishes its THIRD wave. That would mean that during the Dow’s fifth wave, it would be virtually alone in making new highs, as market breadth begins to thin out more obviously. At the ultimate top, then, I would not be surprised to see the Dow Industrials in new high ground, unconfirmed by both the broad indexes and the advance-decline line, creating a classic technical divergence.

Finally, given the technical situation, what might we conclude about the psychological aspects of wave V? The 1920’s bull market was a fifth wave of a THIRD Supercycle wave, while Cycle wave V is the fifth wave of a FIFTH Supercycle wave. Thus, as the last hurrah, it should be characterized, at its end, by an almost unbelievable institutional mania for stocks and a public mania for stock index futures, stocks options, and options on futures. In my opinion, the long- term sentiment gauges will give off major trend sell signals two or three years before the final top, and the market will just keep on going. In order for the Dow to reach the heights expected by the year 1987 or 1990, AND in order to set up the U. S. stock market to experience the greatest crash in its history, which according to the Wave Principle is due to follow wave V, investor mass psychology should reach manic proportions with elements of 1929, 1968 and 1973 all operating together and, at the end, to an even greater extreme.

22

Illustration 3

All illustrations taken fmm ELLIOTT WAVE PRINCIPLE and THE MAJOR WORKS OF R.N. ELLIOTT.

Rule of AlternatiOn. 5

Y.“e II VI. 198? Ia”8 IV. I 9

wave I: Bxtended 5th

1937 5

wove Iv: Double correction (Symbolic representation)

1932 1952

1953 Most typical wwe structure: Extended 3rd of extended 3rd.

L

I 1942

I 1932

Throw-over particul*rly comon after Y.“B 4 trendline break.

Elliott noted thrt trendline breek can occur in rave 4.

/

/ 1942

3

A

1 4

1932 2

wave 11: zigzag 1937

1942

Wave III: Extended 3rd

throw-over

1967 \ 1970

Intervening “X” WeYe

1973

f 1970

second part of wave IV (ascendlng triangle)

1973 1976 1981

1974

Elliott recognized occasional occurtence of trendline break by final wave in triangles

1952

23

Illustration 4

@ THE ELLIOTT WAVE THEORIST, P.O. Box 1618. Gainesville. GA 30503

8 I too lm I I I -m I

Plyrs ; I c -SO

I I c

/.L.\ 1 I

’

-

24

BIOGRAPHY

Robert R. Prechter, Jr. is editor of THE ELLIOTT WAVE THEORIST financial letter of Gainesville, Georgia. He co-authored ELLIOTT WAVE PRINCIPLE -- KEY TO STOCK MARKET PROFITS with A. J. Frost, and edited THE MAJOR WORKS OF R. N. ELLIOTT, a collection of Elliott’s original writings.

25

THE USE OF VOLUME AS AN EARLY WARNING SIGNAL

Richard C. Orr, Ph.D Contratrend, Inc.

This article is based on notes for an invited address which was given to the Technical Security Analysts of San Fran- cisco on December 14,1982.

I. Introduction

While what follows is primarily a discussion of two new indicators based on NYSE advancing and declining volume, the manner in which the data for these indicators is smoothed is also important. Rather than use the traditional n-day moving average for some number “r-r”, we will rely on a somewhat similar process referred to as exponential smoothing.

At the outset, it should be pointed out that there are instances where the use of a regular moving average is preferable to exponential smoothing. If one is dealing with data that is periodic - that is, data with a precise cyclical nature such as 29 days - then a 29 day moving average should be used. When data is only “somewhat cyclical”, e.g. an average cycle length of 29 days, but ranging from 26 to 32 days, then the advantage of the 29 day moving average no longer outweighs the advantage of exponential smoothing.

II. Exponential Smoothing

Exponential smoothing is based on the premise that the importance of data declines at a uniform rate over time, the same way that radioactive material decays. For example, yesterday’s data may be only 90 percent as important as today’s; the day before yesterday’s data may be only 90 percent as important as yesterday’s (or (.90)(.90) = .81, 81 percent as important as today’s data); and so forth. Use of a regular moving average - say, 10 days - is based on the premise that all data for the previous 10 days is equally important and that all data older than 10 days is of no importance. As a result, a 10 day moving average can be changed substantially by the addition of an unusually large or small piece of data on day 1 or the deletion of a similar piece of data on day 11.

Figure 1 gives a visual comparison of these two smoothing techniques. A constant of 10 has been chosen for the exponentially smoothed moving average so that in each case the most recent piece of data accounts for 10 percent of the total in the moving average. In the case of the .lO day moving average, days 2 through 10 each account for another 10 percent of the total, but the weights on the exponentially smoothed data continue to decrease indefinitely at a uniform rate. In practice, these weights eventually become so small that they disappear in the round-off error during computation of the average. In the exponentially smoothed moving average shown in Figure 1, the importance of a given piece of data is diminished by the factor of .90 each day. Hence, approximately every 6.5 days the importance of any piece of data has been cut in half.

The general formula for any exponential smoothing process is:

New Average = (1 -A)(Old Average) + (A)(New Value)

where A is any number between 0 and 1.

27

FIGURE 1.

10 DAY MOVING AVERAGE

1 - 10

ox,+ 1 - 10

*x2+ 1 - 10

l x,+ . . l + +j l x,,+o~x,,+o~x,,+o~x,,+~ l l

. ..------- 1111111111 .10

.05

.oo

CALCULATION: (.l) l (SUM OF LAST 10 DAYS’ VALUES)

OR) 1. KEEP INDIVIDUAL VALUES AND A RUNNING

TOTAL FOR THE LAST 10 DAYS.

2. DELETE THE LAST DAY AND ADD A NEW FIRST DAY

3. DIVIDE BY 10.

.IO EXPONENTIALLY SMOOTHED MOVING AVERAGE

CALCULATION: (.9) l (YESTERDAY’S AVERAGE) + (.l) l (TODAY’S VALUE)

HALF-LIFE OF DATA: ABOUT 6’/2 DAYS.

28

In the remainder of this section we illustrate the technique of exponential smoothing and compare the results with those of the more traditional moving average. Fictitious data has been created for XYZ Corporation. This data has then been smoothed using both the 10 day moving average and the .lO exponentially smoothed moving average previously discussed. One can verify, using the table on the next page, that each value of the 10 day moving average has been calculated by averaging the closing values for the most recent 10 days, and each value of the .lO exponentially smoothed moving average has been calculated by adding 90 percent of the previous value of the average to 10 percent of the current closing value for the stock. All results have been rounded to the nearest tenth. The graph in Figure 2 begins on day 10, the first day for which we can compute the 10 day moving average.

Notice that the exponentially smoothed moving average behaves more and more like the 10 day moving average over time. If we were to repeat the particular pattern of this data continually, the shapes of these two moving averages would be almost identical. The major difference, however, would be that the exponential moving average would always lead the regular moving average. It would turn down sooner and it would turn up sooner. This is because an exponentially smoothed moving average must always move in the direction of the most current piece of data. If the last data point is below the average then the average must be falling, while if the last data point is above the average, then the average must be rising. The fact that this property does not hold for regular moving averages is illustrated in Figure 2. Notice that the 10 day moving average continues to rise after the closing price has fallen below it, and that the same average continues to fall after the closing price has risen above it.

In summary, the two main advantages of exponentially smoothed moving averages are their ability to systematically remove previous data, a little at a time rather than all at once, and their responsiveness to a move in the data from above to below the moving average, or vice versa.

FIGURE 2. XYZ CORPORATION DATA FOR FIGURE 2.

n

20 :

L

CLOSE 10 DAY M.A. 30 SMOOTHED M.A.

30 30.0

29 29.9

28 29.7

25 29.2

22 28.5

21 22%

20 220

21 26.4

22 25.9

25 24.3 25.9

28 24.1 26.1

29 24.1 26.4

30 24.3 26.7

29 24.7 220

28 25.3 27.1

25 25.7 26.9

22 25.9 26.4

21 25.9 25.8

20 25.7 25.2

21 25.3 24.8

22 24.7 24.5

25 24.3 24.6

2% 24.1 24.9

29 24.1 253

30 24.3 25.6

29 247 26.1

28 25.3 26.3

25 25.7 261

22 25.9 25.6

21 25.9 25.3

20 25.7 24.8

21 25.3 244

22 247 241

25 24.3 24.2

26 24.1 24.6

29

III. Volume Momentum Divergence as a Market Indicator

In the early 1960’s the NYSE began to record separately the volume of advancing issues and the volume of declining issues on a daily basis. This data has given rise to a number of indicators over the years, but none as interesting, in our opinion, as the two that are discussed in this section and the next. Under the premise that healthy markets need expanding volume, we move easily to the assumption that healthy markets need expanding up volume. In order to detect any strengthening or weakening of the volume of advancing issues in the market, one can set up the following ratio. After applying a rather slow exponential smoothing process (with a coefficient of .042, the importance of any piece of data is halved every 16 days) we look at:

UP VOLUME - DOWN VOLUME

UP VOLUME + DOWN VOLUME

While the divergence analysis to be applied could be done using only the numerator of the above ratio, the notion of what constituted a significant divergence would have to be continually modified over the years as total volume continued to expand. The introduction of the denominator in the above ratio standardizes this indicator so that over the past 20 years it has rarely moved outside of the range from -.20 to + .20.

Figures 3 and 4 show the behavior of the above indicator just prior to the October Massacres of 1978 and 1979. The two lines cd on Figure 3 and the two lines ab on Figure 4 are not trendlines, but rather they are lines drawn at the same points in time on both the graphs of the Dow Jones Industrial Average and the graphs of the above ratio. Notice that in 1978 line cd on the DJIA slopes slightly upward, while the corresponding line cd on the ratio slopes downward rather significantly. This indicates the deterioration of up volume in the market over a period of almost two months prior to the first October Massacre. In 1979, the divergence is even more dramatic. Notice that during the entire month of September line ab on the DJIA shows a rising market, while line ab on the ratio shows an accompanying loss of momentum measured by up volume.

Such divergence, then, often provides an early warning of an impending correction. It is perhaps worth mentioning that in December, 1982, while this article was being written, we again were experiencing this same kind of divergence. By the time this is read, we will know if the warning was correct.

FIGURE 3. FIGURE 4.

c * 900

850

SW

a\ s:;

\ 800

DOW JONES INDUSTRIAL AVERAGE DOW JONES INDUSTRIAL AVERAGE

UPVOLUME - DOWN VOLUME ( 042 SMOOTHED,

UP VOLUME + DOWN VOLUME

1978 A s 0 ,979 A s 0

30

IV. A Non-Traditional Volume Oscillator

Such oscillators involving advancing and declining volume are computed by taking a fairly responsive 10 or 25 day moving average of up minus down volume and determining whether or not this average has moved above or below an established netural range. If it has moved above this range, we are said to have an overbought condition, but a move below this range yields an oversold condition. A problem alluded to earlier now resurfaces: since volume tends to expand over the long term, the boundaries of the neutral range would have to be continually expanded. In order to remedy this problem, we consider the ratio of two different exponentially smoothed moving averages of up volume. This ratio will move within the same range over the years since expanding volume will affect both the numerator and denominator of the ratio by essentially the same factor.

The coefficient of the “faster” exponentially smoothed moving average is ,083 (giving the data an 8 day “half-life”), and the coefficient of the “slower” smoothing process is .042 (the same as we used in the previous section, giving the data a 16 day “half-life”). The ratio we use is:

.083 SMOOTHED UP VOLUME

.042 SMOOTHED UP VOLUME

The important parameters for this ratio seem to be .94, 1.06, and 1.20. The ratio oscillates above and below 1 .OO - the number arising anytime the two averages cross - which is the center of the range for this oscillator. Most of the time the ratio remains in a range from .80 to 1.20. A rise above 1.20 during a bear market generally signals the beginning of a bull market. Although the market may test its old lows, there is generally not much downside risk below these previous levels. Figures 5 and 6 illustrate two instances of this signal, one in 1974 and the other in 1982. Notice that in one case the old lows were tested, while in the other they were not.

The band from .94 to 1.06 for the above ratio gives us a much more near-term perspective on the market. Any strong move, whether bullish or bearish, for which the ratio enters the band should allow it to move through the band and out the other side. Failure to do this indicates weakness. Should the ratio move below 1.06 but fail to continue on below .94, we have an indication of weakness for the near-term bearish case, i.e. near-term strength. Conversely, should the ratio rise above .94 but fail to rise as high as 1.06, a weakness for the near-term bullish case, which would be bearish, is evident. Referring again to Figures 5 and 6, we find near-term strength signaled in October, 1974, and again in October, 1982, while near-term weakness is signaled in November, 1974.

FIGURE 5.

083 SMOOTHED UP VOLUME


FIGURE 6.

DOWJONES NDUSTRlAL AVERAGE



,982 J A s 0

V. Conclusion

Technical analysts need to be contrarians to some degree. In this spirit we have discussed two market indicators which, it can be safely said, not everybody uses. We have also taken a careful look at the exponential smoothing process. We do not advocate that the reader rush off to abandon the more standard moving average in favor of the exponentially smoothed moving average, but he or she should be aware of the strong points of such a smoothing technique and not be hesitant to use it when the need arises. Much more than up volume or down volume data can be smoothed exponentially. For example, we use a 29 exponential smooth for sentiment data such as the public to specialist short ratio, rather than using the more conventional 4 week moving average.

What is important is not that the reader’s approach to market timing be the same as our approach. Indeed, it is quite the contrary. The successful technician must create as many tools as possible for market timing or stock selection which will set him or her apart from the crowd. Remember, when buying or selling, one should strive to “go through the door” just ahead of the crowd.

32

TRENDS AND THE LOG SCALE

ARTHUR A. MERRILL Merrill Analysis, Inc.

04102183

In these notes, trends are compared on arithmetic and logarithmic scales. Exactly the same data are presented in the left and right-hand charts of each pair.

When stock price changes are considered, percent change is much more important, of course, than change in points. A move from 10 to 12 is more important than a move from 100 to 110.

Figure 1.

‘ARITH METIG:

60 t

50

40

30 /

I- 20%

20

IO F

&20%

100

60

6C

50

46

LOGAR ITH MIG:

I- 20%

%- 20%

The arithmetic scale exaggerates moves at the higher price levels. The log scale keeps moves in proportion. A certain percent change is the same vertical distance anywhere on a log chart.

33

Constant Points Change - Figure 2.

ARITHMETIG IO01 IC

8

E

5

4

3

2

I

LOGARITHMIC IO-

IO -

io -

io -

*o -

O-

O-

1 1 I I , 1 1 I I

A straight line on an arithmetic chart is deceptive. It presents a steady rise; the log chart shows that the rate of price change has been slowing down. When you are looking at a chart with an arithmetic scale, think twice before you reach for a ruler.

Constant Percent Change - Figure 3.

ARITHMETIC: LOGARITHM I C: IOC

8C

60

50

40

This is called a geometric trend. The arithmetic scale gives a deceptive skyrocket effect. The log scale gives the true picture of steady sustainable growth.

34

Parabolic Trend - Figure 4.

ARITHMETIC: lOOI

60’

50 -

40’

30 -

70-

E-

30-

20-

IO :

7-

5- 4-

3-

2-

LOGARITHMIC: IO

This curve (y = axxx) doesn’t make much sense on a stock chart, but we occasionally hear the term.

The chart, though, illustrates the danger of the trends drawn on an arithmetic scale. The left-hand chart is euphoric; actually, the growth rate has been slowing down.

Beware trends on an arithmetic scale!

35

MAJOR MARKET INDEX (XMI) Daily values from January 2, 1973

through March 8, 1983

DATE

2 JAN 73 99.295 3 JAN 73 100.217 4 JAN 73 100.050 5 JAN 73 100.823 8 JAN 73 100.934 9 JAN 73 100.906

10 JAN 73 100.478 11 JAN 73 101.350 12 JAN 73 101 .ooo

15 JAN 73 100.189 16 JAN 73 100.239 17 JAN 73 100.895 18 JAN 73 101.417 19 JAN 73 101.895 22 JAN 73 101.512 23 JAN 73 102.112 24 JAN 73 100.700 26 JAN 73 100.384

29 JAN 73 99.706 30 JAN 73 99.434 31 JAN 73 99.328

1 FEB 73 98.078 2 FEB 73 98.195 5 FEB 73 98.345 6 FEB 73 98.962 7 FEB 73 98.228 8 FEB 73 98.162

9 FEB 73 99.678 12 FEB 73 100.712 13 FEB 73 101.184 14 FEB 73 99.728 15 FEB 73 98.862 16 FEB 73 99.267 20 FEB 73 99.878 21 FEB 73 99.062 22 FEB 73 98.873

23 FEB 73 97.384 26 FEB 73 96.623 27 FEB 73 95.695 28 FEB 73 96.589

1 MAR 73 95.512 2 MAR 73 97.262 5 MAR 73 97.750 6 MAR 73 98.834 7 MAR 73 99.645

VALUE DATE

8 MAR 73 9 MAR 73

12 MAR 73 13 MAR 73 14 MAR 73 15 MAR 73 16 MAR 73 19 MAR 73 20 MAR 73

21 MAR 73 22 MAR 73 23 MAR 73 26 MAR 73 27 MAR 73 28 MAR 73 29 MAR 73 30 MAR 73

2 APR 73

3 APR 73 4 APR 73 5 APR 73 6 APR 73 9 APR 73

10 APR 73 11 APR 73 12 APR 73 13 APR 73

16 APR 73 17 APR 73 18 APR 73 19 APR 73 23 APR 73 24 APR 73 25 APR 73 26 APR 73 27 APR 73

30 APR 73 1 MAY 73 2 MAY 73 3 UAY 73 4 MAY 73 7 MAY 73 8 MAY 73 9 MAY 73

10 MAY 73

37

VALUE DATE VALUE

99.373 11 MAY 73 93.636 98.895 14 MAY 73 91.467 99.023 15 MAY 73 92.224 99.889 16 MAY 73 92.401

100.450 17 MAY 73 91.381 99.634 18 MAY 73 89.793 99.178 21 MAY 73 89.104 97.856 22 MAY 73 90.094 97.717 23 MAY 73 90.607

96.456 24 MAY 73 93.961 94.995 25 MAY 73 94.445 95.200 29 MAY 73 93.938 95.845 30 MAY 73 92.557 97.428 31 MAY 73 91.722 97.712 1 JUN 73 90.613 98.456 4 JUN 73 89.819 97.350 5 JUN 73 91.680 95.717 6 JUN 73 91.627

94.823 7 JUN 73 93.239 94.489 8 JUN 73 94.317 94.550 11 JUN 73 93.926 95.478 12 JUN 73 95.461 97.267 13 JUN 73 94.614 98.656 14 JUN 73 93.713 98.695 15 JUN 73 92.439 98.556 18 JUN 73 91.129 98.123 19 JUN 73 91.905

97.462 20 JUN 73 92.243 96.989 21 JUN 73 90.969 97.734 22 JUN 73 91.757 98.006 25 JUN 73 90.145 97.395 26 JUN 73 91.609 95.412 27 JUN 73 92.065 94.017 28 JUN 73 93.245 94.678 29 JUN 73 93.037 93.017 2 JUL 73 91.763

93.112 3 JUL 73 90.352 93.462 5 JUL 73 90.104 94.745 6 JUL 73 89.689 96.323 9 JUL 73 90.827 96.873 10 JUL 73 91.911 95.950 11 JUL 73 93.660 96.773 12 JUL 73 92.913 95.589 13 JUL 73 91.473 94.673 16 JUL 73 93.221

DATE VALUE

17 JUL 73 92.616 18 JUL 73 93.144 19 JUL 73 93.280 20 JUL 73 93.517 23 JUL 73 93.535 24 JUL 73 94.033 25 JUL 73 95.491 26 JUL 73 95.864 27 JUL 73 95.835

30 JUL 73 95.592 31 JUL 73 94.643

1 AUG 73 93.588 2 AUG 73 93.582 3 AUG 73 93.316 6 AUG 73 93.594 7 AUG 73 93.511 8 AUG 73 92.539 9 AUG 73 92.634

10 AUG 73 92.178 13 AUG 73 91.455 14 AUG 73 90.376 15 BUG 73 90.667 16 AUG 73 90.169 17 BUG 73 89.813 20 AUG 73 89.226 21 BUG 73 88.563 22 AUG 73 88.337

23 AUG 73 89.363 24 AUG 73 88.924 27 AUG 73 89.926 28 AUG 73 90.198 29 AUG 73 90.868 30 AUG 73 90.341 31 AUG 73 90.524 4 SEP 73 90.501 5 SEP 73 90.198

6 SEP 73 90.495 7 SEP 73 89.973

10 SEP 73 88.983 11 SEP 73 88.491 12 SEP 73 88.509 13 SEP 73 88.853 14 SEP 73 89.736 17 SEP 73 88.865 18 SEP 73 88.183

19 SEP 73 89.896 20 SEP 73 90.305 21 SEP 73 90.394

DATE VALUE

24 SEP 73 90.489 25 SEP 73 91.081 26 SEP 73 91.615 27 SEP 73 91.828 28 SEP 73 91.123

1 OCT 73 90.714

2 OCT 73 90.998 3 OCT 73 90.584 4 OCT 73 89.997 5 OCT 73 92.338 8 OCT 73 92.865 9 OCT 73 92.723

10 OCT 73 92.486 11 OCT 73 93.956 12 OCT 73 94.323

15 OCT 73 93.387 16 OCT 73 93.719 17 OCT 73 93.417 18 OCT 73 93.541 19 OCT 73 94.027 22 OCT 73 93.156 23 OCT 73 94.063 24 OCT 73 94.655 25 OCT 73 95.200

26 OCT 73 95.852 29 OCT 73 95.645 30 OCT 73 93.594 31 OCT 73 92.741

1 NOV 73 92.492 2 NOV 73 91.994 5 NOV 73 90.738 6 NOV 73 90.234 7 NOV 73 90.981

8 NOV 73 91.858 9 NOV 73 90.181

12 NOV 73 89.884 13 NOV 73 89.932 14 NOV 73 88.403 15 NOV 73 88.491 16 NOV 73 89.955 19 NOV 73 87.182 20 NOV 73 85.694

21 NOV 73 86.565 23 NOV 73 85.896 26 NOV 73 83.543 27 NOV 73 82.920 28 NOV 73 84.586 29 NOV 73 84.177

38

DATE

30 NOV 73 83.152 3 DEC 73 81.664 4 DEC 73 81.208

5 DEC 73 80.147 6 DEC 73 82.345 7 DEC 73 83.709

10 DEC 73 84.983 11 DEC 73 83.140 12 DEC 73 81.151 13 DEC 73 80.144 14 DEC 73 80.831 17 DEC 73 80.132

18 DEC 73 82.320 19 DEC 73 82.115 20 DEC 73 81.301 21 DEC 73 80.289 24 DEC 73 79.602 26 DEC 73 82.459 27 DEC 73 84.472 28 DEC 73 83.935 31 DEC 73 83.923


10 JAN 74 77.745 11 JAN 74 79.662 14 JAN 74 79.584


28 JAN 74 81.886 29 JAN 74 81.856 30 JAN 74 82.820 31 JAN 74 82.067

1 FEB 74 81.217 4 FEB 74 79.523 5 FEB 74 79.168 6 FEB 74 79.656 7 FEB 74 79.692

VALUE

DATE VALUE DATE VALUE DATE VALUE



1 MAR 74 80.072 4 MAR 74 79.921 5 MAR 74 81.826 6 MAR 74 82.447

7 MAR 74 81.416 8 MAR 74 82.109

11 MAR 74 83.260 12 MAR 74 83.718 13 MAR 74 84.309 14 MAR 74 84.297 15 MAR 74 84.026 18 MAR 74 82.850 19 MAR 74 82.187

20 MAR 74 82.603 21 MAR 74 82.754 22 MAR 74 83.013 25 MAR 74 83.550 26 MAR 74 83.760 27 MAR 74 82.416 28 MAR 74 80.958 29 MAR 74 79.915

1APB 74 79.391

2APR74 79.879 3 APR 74 81.072 4APR 74 81.181 5 APR 74 79.867 8 APR 74 79.053 9APR74 79.776

10 APR 74 79.234 11 APR 74 79.144 15 APR 74 79.168

16 APR 74 80.542 17 APR 74 81.000

18 APR 74 81.157 19 APR 74 80.150 22 APR 74 80.090 23 APR 74 78.987 24 AFR 74 78.047 25 APR 74 77.577 26 APR 74 77.866

29 APR 74 77.818 30 APR 74 78.221

1MAY 74 79.566 2 MAY 74 79.427 3 MAY 74 78.812 6 MAY 74 78.903 7 MAY 74 79.439 8 MAY 74 79.807 9 MAY 74 81.494

10 MAY 74 79.867 13 MAY 74 79.403 14 MAY 74 79.764 15 NAY 74 79.578 16 MAY 74 79.023 17 MAY 74 77.733 20 NAY 74 77.480 21 MAY 74 77.601 22 MAY 74 76.932

23 MAY 74 77.263 24 MAY 74 78.577 28 NAY 74 78.288 29 MAY 74 76.962 30 MAY 74 77.745 31 MAY 74 77.818

3 JUN 74 79.813 4 JUN 74 80.475 5 JUN 74 80.544

6 JUN 74 82.261 7 JUN 74 82.992

10 JUN 74 83.605 11 JUN 74 82.774 12 JUN 74 82.767 13 JUN 74 83.105 14 JUN 74 82.168 17 JUN 74 81.012 18 JUN 74 80.781

19 JUN 74 80.319 20 JUN 74 79.869 21 JUN 74 79.313 24 JUN 74 79.750 25 JUN 74 81.100

39

26 JUN 74 79.750 27 JUN 74 78.463 28 JUN 74 78.082

1 JUL 74 78.413

2 JUL 74 76.639 3 JUL 74 76.639 5 JUL 74 76.002 8 JUL 74 73.715 9 JUL 74 74.403

10 JUL 74 73.060 11 JUL 74 72.747 12 JUL 74 75.902 15 JUL 74 76.296


29 JUL 74 30 JUL 74 31 JUL 74

1 AUG 74 2 AUG 74 5 AUG 74 6 AUG 74 7 AUG 74 8 AUG 74

9 AUG 74 12 AUG 74 13 AUG 74 14 AUG 74 15 AUG 74 16 AUG 74 19 AUG 74 20 AUG 74 21 AUG 74

72.073 72.029 70.911 70.192 69.774 70.298 71.685 74.015 72.604

71.816 70.473 69.268 67.856 67.562 66.831 65.888 66.406 64.720


3 SEP 74 61.802

DATE VALUE DATE VALUE

8 NOV 74 63.033 11 NOV 74 63.039 12 NOV 74 61.559 13 NOV 74 61.502 14 NOV 74 61.103 15 NOV 74 59.778 18 NOV 74 57.329 19 NOV 74 56.274


2 DEC 74 55.930 3 DEC 74 55.237

4 DEC 74 55.493 5 DEC 74 54.137 6 DEC 74 53.313 9 DEC 74 54.131

10 DEC 74 55.755 11 DEC 74 56.036 12 DEC 74 56.011 13 DEC 74 55.624 16 DEC 74 54.974


31 DEC 74 56.667 2 JAN 75 57.717 3 JAN 75 57.854 6 JAN 75 57.842 7 JAN 75 57.760 8 JAN 75 56.911 9 JAN 75 58.035

10 JAN 75 59.122 13 JAN 75 58.341

14 JAN 75 57.710 15 JAN 75 58.160 16 JAN 75 58.004 17 JAN 75 56.761

40

DATE VALUE

4 SEP 74 60.066 20 JAN 75 56.986 21 JAN 75 56.286 22 JAN 75 57.392 23 JAN 75 57.529 24 JAN 75 58.210

5 SEP 74 62.571 6 SEP 74 62.552 9 SEP 74 60.815

10 SEP 74 60.465 11 SEP 74 59.847 12 SEP 74 57.929 13 SEP 74 56.336 16 SEP 74 57.742 17 SEP 74 58.810

27 JAN 75 61.290 28 JAN 75 61.303 29 JAN 75 62.927 30 JAN 75 61.902 31 JAN 75 62.627 3 FEB 75 63.633 4 FEB 75 63.477 5 FEB 75 65.132 6 FEB 75 64.688

18 SEP 74 59.522 19 SEP 74 61.559 20 SEP 74 61.271 23 SEP 74 60.034 24 SEP 74 58.822 25 SEP 74 58.341 26 SEP 74 57.204 27 SEP 74 55.012 30 SEP 74 54.168


1 OCT 74 53.962 2 OCT 74 53.487 3 OCT 74 52.363 4 OCT 74 52.151 7 OCT 74 54.431 8 OCT 74 54.043 9 OCT 74 56.992

10 OCT 74 58.604 11 OCT 74 59.891

21 FEB 75 69.111 24 FEB 75 67.962 25 FEB 75 66.500 26 FEB 75 67.200 27 FEB 75 67.387 28 FEB 75 68.237 3 MAR 75 69.717 4 MAR 75 69.948 5 MAR 75 69.530


6 MAR 75 70.611 7 NAB 75 70.779


25 OCT 74 59.110 28 OCT 74 59.204 29 OCT 74 62.346 30 OCT 74 63.826 31 OCT 74 62.783

1 NOV 74 62.758 4 NOV 74 62.027 5 NOV 74 64.101 6 NOV 74 62.933

19 MAR 75 70.298 20 MAR 75 69.461 21 MAR 75 69.417 24 MAR 75 67.856 25 MAR 75 68.662 26 MAR 75 70.073 27 MAR 75 70.148 7 NOV 74 63.527


5JUN75 77.101 6 JUN 75 76.870 9 JUN 75 75.740

10 JUN 75 75.365 11 JUN 75 75.546 12 JUN 75 74.765 13 JUN 75 75.102 16 JUN 75 75.889 17 JUN 75 74.977

18 JUN 75 74.790 19 JUN 75 76.296 20 JUN 75 76.733 23 JUN 75 77.939 24 JUN 75 78.157 25 JUN 75 78.494 26 JUN 75 78.638 27 JUN 75 78.445 30 JUN 75 78.732

1 JUL 75 78.326 2 JUL75 77.814 3 JUL 75 77.832 7 JUL 75 77.020 8 JUL 75 76.939 9 JUL75 78.051

10 JUL 75 77.645 11 JUL 75 77.076 14 JUL 75 77.576


28 JUL 75 73.010 29 JUL 75 72.822 30 JUL 75 73.478 31 JUL 75 73.110

1 AUG 75 72.541 4 AUG 75 71.879 5 BUG 75 71.285 6 AUG 75 71.548 7 AUG 75 71.685

8 AUG 75 71.392 11 AUG 75 72.085 12 AUG 75 72.235

DATE VALUE

31 NAR 75 69.705 1 APR75 69.036

13 AUG 75 70.998 14 AUG 75 70.723 15 AUG 75 71.573 18 AUG 75 71.035 19 AUG 75 69.755 20 AUG 75 68.512

2APR 75 68.886 3 APR75 67.606 4APR75 67.112 7 APR75 66.812 8APR75 67.606 9APR75 69.655

10 APR 75 70.642 11 APR 75 71.167 14 APR 75 72.591


2 SEP 75 70.480 3 SEP 75 71.242

15 APR 75 73.434 16 APR 75 73.541 17 APR 75 73.709 18 APR 75 72.710 21 APR 75 73.453 22 APR 75 73.378 23 APR 75 72.560 24 APR 75 72.222 25 APR 75 72.747

4 SEP 75 71.492 5 SEP 75 71.135 8 SEP 75 71.392 9 SEP 75 69.924


28 APR 75 72.322 29 APR 75 71.998 30 APR 75 74.078

1MAY 75 74.902 2 MY 75 76.133 5 MY 75 77.233 6 MY 75 75.421 7 MY 75 75.996 8 MAY 75 76.027


9 MY 75 76.995 12 MY 75 77.145 13 MY 75 78.051 14 MY 75 78.776 15 MY 75 77.689 16 MY 75 76.745 19 MY 75 76.920 20 MY 75 76.495 21 MY 75 75.477

30 SEP 75 68.930 1 OCT 75 68.156 2 OCT 75 69.499 3 OCT 75 71.429 6 OCT 75 72.335 7 OCT 75 72.260 8 OCT 75 73.597 9 OCT 75 74.134

10 OCT 75 73.915

22 MY 75 75.652 23 MY 75 76.795 27 MY 75 76.408 28 MY 75 75.452 29 MY 75 75.246 30 MY 75 76.639

2 JUN75 77.845 3 JUN75 77.689 4JUN75 77.070


41


21 OCT 75 76.439 22 OCT 75 76.770 23 OCT 75 77.301

30 DEC 75 76.427 31 DEC 75 76.539


12 JAN 76 82.018

8 MAR 76 84.485 9 MAR 76 84.692



3 NOV 75 74.521 4 NOV 75 75.084 5 NOV 75 75.671

17 MAR 76 83.942 18 MAR 76 83.636 19 MAR 76 83.936 22 MAR 76 84.117 23 MAR 76 85.541 24 MAR 76 86.753 25 MAR 76 85.929 26 MAR 76 86.147 29 MAR 76 85.729


6 NOV 75 76.214 7 NOV 75 76.139


30 MAR 76 85.429 31 MAR 76 86.247

1 APR 76 85.904 2 APR 76 85.997 5 APR 76 87.303 6 APR 76 87.040 7 APR 76 85.960 8 APR 76 85.391 9 APR 76 84.610

26 JAN 76 84.954 27 JAN 76 84.111 28 JAN 76 83.761 29 JAN 76 85.672 30 JAN 76 86.216

2 FEB 76 86.035 3 FEB 76 86 .241 4 FEB 76 86.391 5 FEB 76 85.035


1 DEC 75 78.126 2 DEC 75 77.020


6 FEB 76 84.354 9 FEB 76 84.254

10 FEB 76 84.916 11 FEB 76 85.073 12 FEB 76 84.379 13 FEB 76 83.780 17 FEB 76 83.024 18 FEB 76 83.561 19 FEB 76 84.960

3 DEC 75 75.552 4 DEC 75 75.802 5 DEC 75 74.653 8 DEC 75 75.084 9 DEC 75 75.415

10 DEC 75 76.239 11 DEC 75 75.740 12 DEC 75 75.665 15 DEC 75 75.996

26 APR 76 85.616 27 APR 76 84.941 28 APR 76 85.316 29 APR 76 85.185 30 APR 76 84.767

3 MAY 76 84.198 4 MAY 76 84.829 5 MAY 76 84.161 6 MAY 76 84.510

20 FEB 76 85.854 23 FEB 76 85.360 24 FEB 76 85.722 25 FEB 76 84.991 26 FEB 76 83.705 27 FEB 76 83.336

1 MAR 76 84.004 2 MAR 76 84.273 3 MAR 76 83.830


7 MAY 76 85.079 10 MAY 76 86.266 11 MAY 76 86.003 12 MAY 76 85.660 13 MAY 76 85.098

4 MAR 76 83 .Oll 5 MAR 76 83.174

42


84.916 28 SEP 76 86.755 29 SEP 76 86.031 30 SEP 76 85.990


14 MAY 76 84.111 17 MAY 76 83.954 18 MAY 76 84.161 19 MAY 76 84.211

23 JUL 76


2 AUG 76 84.189 3 AUG 76 85.090 4 AUG 76 85.076 5 BUG 76 84.365

20 NAY 76 84.941 21 NAY 76 84.248 24 NAY 76 82.936 25 NAY 76 83.124 26 MAY 76 82.505 27 NAY 76 82.518 28 MAY 76 83.274

1 JUN 76 82.830 2 JUN 76 83.099


6 AUG 76 84.352 9 AUG 76 83.979


3 JUN76 82.781 4 JUN 76 81.778 7 J-UN 76 81.327 8 JUN 76 81.505 9 JUN 76 79.751

10 JUN 76 82.042 11 JUN 76 83.142 14 JUN 76 84.013 15 JUN 76 83.659


1 NOV 76 83.979 3 NOV 76 83.079 4 NOV 76 83.106

19 AUG 76 84.622 20 AUG 76 83.925 23 AUG 76 83.851 24 AUG 76 83.031 25 AUG 76 83.925 26 AUG 76 83.072 27 AUG 76 83.404 30 AUG 76 83.925 31 AUG 76 84.304


5 NOV 76 81.339 8 NOV 76 80.472 9 NOV 76 80.181



10 SEP 76 85.807 13 SEP 76 85.299 14 SEP 76 85.029

29 JUN 76 84.772 30 JUN 76 84.844

1 JUL 76 84.294 2 JUL 76 84.785 6 JUL 76 84.347 7 JUL 76 84.654 8 JUL 76 84.654 9 JUL 76 85.715

12 JUL 76 86.612

18 NOV 76 82.070 19 NOV 76 81.779 22 NOV 76 82.348 23 NOV 76 81.833 24 NOV 76 82.117 26 NOV 76 82.822 29 NOV 76 82.070 30 NOV 76 81.596

1 DEC 76 81.576


13 JUL 76 86.082 14 JUL 76 86.154 15 JUL 76 85.636 16 JUL 76 85.296 19 JUL 76 84.936 20 JUL 76 84.622 21 JUL 76 84.530 22 JUL 76 84.903

43



10 DEC 76 82.456 13 DEC 76 82.503 14 DEC 76 83.045


29 DEC 76 83.891 30 DEC 76 84.575 31 DEC 76 84.846

3 JAN 77 84.243 4 JAN 77 83.194 5 JAN 77 82.612 6 JAN 77 82.469 7 JAN 77 82.469

10 JAN 77 82.578



1 FEB 77 79.883 2 FEB 77 79.626 3 FEB 77 79.084 4 FEB 77 78.895

7 FEB 77 78.976 8 FEB 77 78.610 9 FEB 77 77.839


17 FEB 77 78.448 18 FEB 77 78.197 22 FEB 77 78.637 23 FEB 77 78.482 24 FEB 77 77.994 25 FEB 77 78.062 28 FEB 77 78.326

1 MAR 77 79.037 2 MAR 77 78.773


10 MAR 77 79.491 11 MAR 77 79.545 14 MAR 77 80.377 15 MAR 77 80.811


29 MAR 77 30 MAR 77 31 MAR 77

1 APR 77 4 APR 77 5 APR 77 6 APR 77 7 APR 77

11 APR 77

12 APR 77 13 APR 77 14 APR 77 15 APR 77

78.407 77.141 77.053 77.744 76.552 76.579 76.349 76.715 77.216

78.082 77.988 78.502 78.468

44



2 MAY 77 75.923 3 MAY 77 76.275 4 MAY 77 76.728 5 MAY 77 76.891

6 MAY 77 76.153 9 NAY 77 75.733

10 MAY 77 75.895 11 MAY 77 74.941 12 MAY 77 74.968 13 MAY 77 75.266 16 MAY 77 75.510 17 MAY 77 76.017 18 MAP 77 76.369

19 MAY 77 75.990 20 MAY 77 75.428 23 MAY 77 74.291 24 MAY 77 74.081 25 MAY 77 73.309 26 MAY 77 73.695 27 MAY 77 72.774 31 MAY 77 72.781

1 JUN 77 73.553

2 JUN 77 73.128 3 JUN 77 74.068 6 JUN 77 73.595 7 JUN 77 74.152 8 JUN 77 74.590 9 JUN 77 74.388

10 JUN 77 74.444 13 JUN 77 74.702 14 JUN 77 75.767

15 JUN 77 75.502 16 JUN 77 75.655 17 JUN 77 75.739 20 JUN 77 76.261 21 JUN 77 76.505 22 JUN 77 76.372 23 J-UN 77 76.518


24 J-UN 77 76.922 27 JUN 77 76.860

28 JUN 77 75.989 29 JUN 77 75.899 30 JUN 77 76.010


11 JUL 77 74.785


26 JUL 77 76.255 27 JUL 77 75.103 28 JUL 77 75.181 29 JUL 77 75.366

1 AUG 77 75.729 2 AUG 77 75.309 3 AUG 77 75.366 4 AUG 77 75.665 5 AUG 77 75.395

8 BUG 77 74.769 9 AUG 77 74.968


19 AUG 77 75.551 22 AUG 77 76.170 23 BUG 77 75.878 24 AUG 77 75.544 25 AUG 77 74.762 26 BUG 77 74.755 29 AUG 77 75.530 30 AUG 77 75.011 31 AUG 77 75.380


12 SEP 77 74.364 13 SEP 77 74.478 14 SEP 77 74.670


28 SEP 77 73.838 29 SEP 77 74.215 30 SEP 77 74.634 3 OCT 77 74.975 4 OCT 77 74.094 5 OCT 77 73.781 6 OCT 77 74.229 7 OCT 77 74.051

10 OCT 77 73.923

11 OCT 77 12 OCT 77 13 OCT 77 14 OCT 77 17 OCT 77 18 OCT 77 19 OCT 77 20 OCT 77 21 OCT 77

24 OCT 77 25 OCT 77 26 OCT 77 27 OCT 77 28 OCT 77 31 OCT 77

1 NOV 77 2 NOV 77 3 NOV 77

73.227 72.480 72.310 72.480 72.558 72.388 71.485 71.748 71.435

71.002 71.009 72.082 72.416 72.544 72.174 71.314 70.483 70.660

4 NOV 77 7 NOV 77 8 NOV 77

45

71.300 72.018 71.947


17 NOV 77 73.426 18 NOV 77 73.667 21 NOV 77 73.596 22 NOV 77 74.421 23 NOV 77 74.627 25 NOV 77 74.734 28 NOV 77 74.300 29 NOV 77 73.106 30 NOV 77 73.376

1 DEC 77 73.219 2 DEC 77 73.042 5 DEC 77 72.772 6 DEC 77 71.698 7 DEC 77 71.719 8 DEC 77 71.847 9 DEC 77 72.359

12 DEC 77 72.203 13 DEC 77 72.238


28 DEC 77 73.838 29 DEC 77 74.023 30 DEC 77 73.959

3 JAN 78 72.402 4JA.N 78 72.437 5 JAN78 71.378 6 JAN 78 70.746 9 JAN78 70.554

10 JAN 78 70.106


DATE

19 JAN 78 70.291 20 JAN 78 69.999 23 JAN 78 69.423


1 FEB 78 69.793 2 FEB 78 69.736 3 FEB 78 69.082

6 FEB 78 69.082 7 FEB 78 69.757 8 FEB 78 69.971 9 FEB 78 69.608


17 FEB 78 67.305 21 FEB 78 67.163 22 FEB 78 67.134 23 FEB 78 67.348 24 FEB 78 67.774 27 FEB 78 67.184 28 FEB 78 66.516 1 MAR 78 66.566 2 MAR 78 66.509


10 MAR 78 67.248 13 MAR 78 67.063 14 MAR 78 67.376 15 MAR 78 66.950


VALUE DATE VALUE

30 MAR 78 66.672 31 MAR 78 66.246 3APR78 65.841 4APR78 66.168 5APR78 66.957 6 APR 78 66.978 7 APR 78 67.269

10 APR 78 67.646 11 APR 78 67.419


25 APR 78 73.575 26 APR 78 73.881 27 APR 78 73.191 28 APR 78 74.293

1MAY 78 74.911 2 MAY 78 74.456 3 MAY 78 73.525 4MAY 78 73.198 5 NAY 78 73.390

8 MAY 78 72.935 9 NAY 78 72.757

10 MAY 78 72.580 11 MAY 78 73.916 12 MAY 78 74.442 15 MAY 78 75.224 16 NAY 78 75.672 17 MAY 78 75.729 18 NAY 78 74.869

19 NAY 78 74.428 22 MAY 78 75.551 23 MAY 78 74.556 24 NAY 78 74.051 25 NAY 78 73.738 26 NAY 78 73.397 30 NAY 78 73.767 31 MAY 78 73.923

1 JUN 78 74.008

2 JUN 78 74.790 5 JUN 78 76.418

46

DATE

6 JUN 78 76.575 7 JUN 78 76.241 8 JUN 78 76.255 9 JUN 78 76.034

12 JUN 78 75.665 13 JUN 78 76.006 14 JUN 78 75.743


28 JUN 78 72.828 29 JUN 78 72.693 30 JUN 78 72.366

3 JUL 78 71.940 5 JUL78 71.535 6 JUL78 71.783 7 JUL78 72.345

10 JUL 78 72.992 11 JUL 78 73.219



1 AUG 78 77.286 2 AUG 78 79.788 3 AUG 78 79.511 4 AUG 78 79.923

7 AUG 78 79.240 8 AUG 78 79.788 9 AUG 78 79.894

10 AUG 78 79.141 11 AUG 78 79.724

VALUE

DATE VALUE

14 AUG 78 79.397 15 AUG 78 79.553 16 AUG 78 80.335 17 AUG 78 80.570


31 AUG 78 78.658 1 SEP 78 79.077 5 SEP 78 80.108 6 SEP 78 81.089 7 SEP 78 81.046 8 SEP 78 82.667

11 SEP 78 82.390 12 SEP 78 82.439 13 SEP 78 81.345


27 SEP 78 77.534 28 SEP 78 77.890 29 SEP 78 78.075


10 OCT 78 79.745 11 OCT 78 81.060 12 OCT 78 80.285 13 OCT 78 80.165 16 OCT 78 78.842 17 OCT 78 77.797 18 OCT 78 77.470 19 OCT 78 76.411

DATE VALUE

20 OCT 78 76.141

23 OCT 78 76.312 24 OCT 78 75.587 25 OCT 78 75.494 26 OCT 78 74.833 27 OCT 78 73.774 30 OCT 78 75.096 31 OCT 78 72.821

1 NOV 78 76.553 2 NOV 78 75.231

3 NOV 78 75.707 6 NOV 78 74.762 7 NOV 78 73.760 8 NOV 78 74.407 9 NOV 78 74.115

10 NOV 78 74.321 13 NOV 78 72.992 14 NOV 78 72.743 15 NOV 78 72.700


30 NOV 78 74.364 1 DEC 78 75.679 4 DEC 78 75.572 5 DEC 78 76.745 6 DEC 78 76.703 7 DEC 78 76.290 8 DEC 78 75.999

11 DEC 78 76.553 12 DEC 78 76.098

13 DEC 78 75.572 14 DEC 78 75.743 15 DEC 78 75.245 MAY 80 79.706 27 MAY 80 79.905 28 MAY 80 80.272 29 MAY 80 78.782

30 MAY 80 79.369 2 JUN 80 78.872 3 JUN 80 78.624

47

DATE

4 JUN 80 80.014 5 JUN 80 79.875 6 JUN 80 80.223 9 JUN 80 80.421

10 JUN 80 81.087 11 JUN 80 82.051

12 JUN 80 81.931 13 JUN 80 81.921 16 JUN 80 82.160 17 JUN 80 82.170 18 JUN 80 82.488 19 JUN 80 81.037 20 JON 80 80.829 23 JUN 80 81.286 24 JUN 80 81.504

25 JUN 80 82.478 26 JUN 80 81.842 27 JUN 80 81.772 30 JUN 80 80.372




1 AUG 80 86.093


11 ATJG 80 88.547

VALUE

DATE VALUE DATE VALUE DATE

12 AUG 80 87.613 13 AUG 80 87.107 14 AUG 80 88.448


28 AUG 80 84.991 29 AUG 80 85.070 2 SEP 80 85.795 3 SEP 80 86.759 4 SEP 80 86.103 5 SEP 80 85.398 8 SEP 80 83.868 9 SEP 80 84.524

10 SEP 80 84.991



1 OCT 80 85.577 2 OCT 80 85.557 3 OCT 80 86.521 6 OCT 80 87.951

7 OCT 80 87.415 8 OCT 80 87.713 9 OCT 80 86.610



31 OCT 80 84.365 3 NOV 80 85.676 5 NOV 80 86.799 6 NOV 80 85.011 7 NOV 80 85.120

10 NOV 80 85.458 11 NOV 80 86.233 12 NOV 80 88.001 13 NOV 80 89.411


28 NOV 80 1 DEC 80 2 DEC 80 3 DEC 80 4 DEC 80 5 DEC 80 8 DEC 80 9 DEC 80

10 DEC 80

11 DEC 80 12 DEC 80 15 DEC 80 16 DEC 80 17 DEC 80 18 DEC 80 19 DEC 80 22 DEC 80 23 DEC 80

91.219 88.855 89.769 89.580 89.620 87.981 86.233 86.233 84.484

84.206 85.209 85.150 86.610 87.603 87.276 87.891 89.799 89.789

24 DEC 80 90.236 26 DEC 80 90.683

48

29 DEC 80 90.077 30 DEC 80 90.285 31 DEC 80 90.434

2 JAN 81 91.279 5 JAN 81 92.997 6 JAN 81 94.100 7 JAN 81 92.381

8 JAN 81 91.030 9 JAN 81 91.259

12 JAN 81 91.319 13 JAN 81 91.189 14 JAN 81 91.229 15 JAN 81 91.617 16 JAN 81 91.954 19 JAN 81 91.646 20 JAN 81 89.699

21 JAN 81 89.352 22 JAN 81 88.646 23 JAN 81 88.855 26 JAN 81 89.014 27 JAN 81 89.938 28 JAN 81 89.203 29 JAN 81 89.401 30 JAN 81 89.342

2 FEB 81 87.872


10 FEB 81 89.590 11 FEB 81 89.093 12 FEB 81 88.438 13 FEB 81 88.050




9 MAR 81 92.312 10 MAR 81 92.014 11 MAR 81 91.368 12 MAR 81 93.871

15 MAY 81 91.512 22 JUL 81 86.746 23 JUL 81 87.215 24 JUL 81 88.516 27 JUL 81 89.418 28 JUL 81 88.762 29 JUL 81 88.586 30 JUL 81 89.430 31 JUL 81 90.450

3 AUG 81 89.899

18 NAY 81 92.027 19 MAP 81 91.904 20 MAY 81 91.540 21 MAY 81 91.188 22 MAY 81 90.648 26 MAY 81 91.948 27 MAY 81 92.906 28 NAY 81 93.303 29 MAY 81 93.182


4 AUG 81 89.899 5 AUG 81 90.403 6 AUG 81 90.016 7 AUG 81 89.278


lJUN81 93.821 2 JUN 81 92.906 3 JUN 81 93.083 4 JUN 81 93.171 5 JUN 81 94.174 8 JUN81 94.096 9 JUN 81 93.766

10 JUN 81 93.898 11 JUN 81 95.143

26 MAR 81 94.736 27 MAR 81 93.459 30 MAR 81 92.996 31 MAR 81 93.716

1APB 81 94.283 2 APR 81 94.108 3 APR 81 93.531 6 APR 81 92.501 7 APR81 92.429



8 APR 81 92.934 9 APR 81 93.572

10 APR 81 93.789 13 APR 81 93.160 14 APR 81 92.717 15 APR 81 93.716 16 APR 81 94.036 20 APR 81 94.952 21 APR 81 93.737

28 AUG 81 84.671 31 AUG 81 83.710


10 SEP 81 82.702

25 JUN 81 94.075 26 JUN 81 93.563 29 JtJN 81 92.756 30 JUN 81 91.903

lJUL81 90.789 2 JUL 81 90.133 6 JUL81 89.055 7 JUL81 89.336 8 JUL 81 89.348

22 APR 81 93.840 23 APR 81 94.283 24 APR 81 94.942 27 APR 81 95.509 28 APR 81 94.633 29 APR 81 93.366 30 APB 81 92.769

1MAY 81 92.542 4 NAY 81 91.430

11 SEP 81 84.003 14 SEP 81 83.382 15 SEP 81 82.843 16 SEP 81 82.479 17 SEP 81 81.307 18 SEP 81 81.167 21 SEP 81 82.057 22 SEP 81 81.835 23 SEP 81 81.2%


5 MAY 81 90.606 6 MAY81 90.740 7 MAY 81 91.152 8 MAY 81 91.152

11 MAY 81 89.731 12 MAY 81 91.059 13 MAY 81 90.462 14 MAY 81 90.843

49

DATE


1 OCT 81 83.194 2 OCT 81 83.780 5 OCT 81 83.663 6 OCT 81 83.476

7 OCT 81 84.753 8 OCT 81 86.043 9 OCT 81 85.433




10 NOV 81 84.238 11 NOV 81 84.788 12 NOV 81 85.046


27 NOV 81

VALUE

87.074

DATE VALUE

30 NOV 81 87.344 1 DEC 81 87.437 2 DEC 81 86.312 3 DEC 81 86.793 4 DEC 81 87.648 7 DEC 81 87.015 8 DEC 81 86.465 9 DEC 81 86.992



4 JAN 82 86.382 5 JAN82 84.648 6 JAN 82 84.437

7 JAN 82 84.472 8 JAN82 84.906

11 JAN 82 83.441 12 JAN 82 83.288 13 JAN 82 82.081 14 JAN 82 82.784 15 JAN 82 83.265 18 JAN 82 84.249 19 JAN 82 83.429

20 JAN 82 83.183 21 JAN 82 83.734 22 JAN 82 83.464 25 JAN 82 83.476 26 JAN 82 83.347 27 JAN 82 83.652 28 JAN 82 85.585 29 JAN 82 86.640

1 FEB 82 84.660

2 FEB 82 84.765 3 FEB 82 83.734 4 FEB 82 84.179 5 FEB 82 84.941

50

DATE

8 FEB 82 83.101 9 FEB 82 82.397

10 FEB 82 83.065 11 FEB 82 82.550 12 FEB 82 82.421



10 MAR 82 80.381 11 MAR 82 80.370


25 MAR 82 83.007 26 MAR 82 82.046 29 MAR 82 82.327 30 UAR 82 82.597 31 MAR 82 82.386

1APR 82 83.652 2 APR 82 84.355 5 APR82 83.956 6 APR 82 84.495

7 APR82 84.308 8 APR 82 85.035


VALUE


19 APR 82 85.199 20 APR 82 84.437

21 APR 82 84.742 22 APR 82 85.691 23 APR 82 86.828 26 APR 82 87.086 27 APB 82 85.984 28 APR 82 85.410 29 APR 82 84.495 30 APR 82 84.812

3 MAY 82 85.222

4uAY 82 85.820 5 MAY82 86.019 6 MAY 82 86.793 7 MAY 82 87.414

10 MAY 82 86.675 11 MAY 82 87.332 12 MAY 82 86.957 13 MAY 82 86.218 14 MAY 82 85.902

17 MAY 82 84.835 18 MAY 82 84.366 19 MAY 82 83.769 20 MAY 82 83.710 21 MAY 82 84.156 24 MAY 82 84.179 25 MAY 82 83.968 26 MAY 82 83.323 27 MAY 82 83.019

28 MAY 82 82.233 1 JUN82 81.987 2 JUN 82 82.561 3 JUN 82 82.690 4JUN82 81.495 7 JUN82 81.565 8 JUN82 81.413 9 JUN82 80.932

10 JUN 82 81.284


24 JUN 82 81.999 25 JUN 82 81.155 28 JUN 82 81.823 29 JUN 82 81.811 30 JUN 82 81.530

1 JUL 82 80.616 2 JUL 82 79.936 6 JUL82 79.983 7 JUL 82 80.100

8 JUL 82 80.815 9 JUL 82 81.753

12 JUL 82 83.054 13 JUL 82 82.972 14 JUL 82 83.663 15 JUL 82 83.652 16 JUL 82 84.249 19 JUL 82 84.003 20 JUL 82 84.683


2 AUG 82 82.960

3 AUG 82 82.304 4 AUG 82 80.756 5 AUG 82 79.913 6 AUG 82 78.740 9 BUG 82 78.553

10 AUG 82 78.588 11 BUG 82 78.447 12 AUG 82 78.354 13 AUG 82 79.479


27 AUG 82 30 AUG 82 31 AUG 82

51

89.078 90.063 91.235




1 OCT 82 92.864 4 OCT 82 92.548 5 OCT 82 92.653

6 OCT 82 96.732 7 OCT 82 98.619 8 OCT 82 100.963





9 NOV 82 108.347 10 NOV 82 106.554 11 NOV 82 107.703


26 NOV 82 102.967 29 NOV 82 102.440 30 NOV 82 106.812


9 DEC 82 10 DEC 82 13 DEC 82 14 DEC 82 15 DEC 82 16 DEC 82 17 DEC 82 20 DEC 82 21 DEC 82

22 DEC 82 23 DEC 82 27 DEC 82 28 DEC 82 29 DEC 82 30 DEC 82 31 DEC 82

3 JAN 83 4 JAN 83

5 JAN 83 107.808 6 JAN 83 109.707 7 JAN 83 109.625


107.093 106.050 106.355 104.503 103.003 102.932 104.808 103.835 106.554

106.730 107.503 110.316 108.793 109.015 107.785 107.902 105.804 107.867


31 JAN 83 110.047 1 FEB 83 107.902 2 FEB 83 108.007 3 FEB 83 108.359 4 FEB 83 109.426 7 FEB 83 110.551 8 FEB 83 109.086 9 FEB 83 108.617

10 FEB 83 110.527

11 FEB 83 110.332 14 FEB 83 111.378 15 FEB 83 111.129 16 FEB 83 110.617 17 FE8 83 110.665 18 FEB 83 111.129 22 FEB 83 109.725 23 FEB 83 111.550 24 FEB 83 114.425

25 FEB 83 114.300 28 FEB 83 113.363

1 MAR 83 115.588 2 MAR 83 115.788 3 MAR 83 115.700 4 MAR 83 115.825 7 MAR 83 115.838 8 MAR 83 113.313

52

STOCK INDEX FUTURES: TECHNICAL ANALYSIS AND ARBITRAGE OPPORTUNITIES

Walter L. Eckardt, Jr.

Bridge Data Company and

Associate Professor of Finance Southern Illinois University at Edwardsville

(April, 1983)

INTRODUCTION

In February, 1982, the Kansas City Board of Trade initiated trading in futures on the Value Line Index. Shortly there- after, futures on the Standard and Poor’s 500 Composite and the New York Stock Exchange Index came into existence. Investor interest in these contracts has been substantial.

In this study, I examine the statistical properties of daily returns for four stock index futures contracts and the underlying indexes. I apply two well known filter rule trading strategies to each of the return series in a preliminary effort to infer the likelihood that technical analysis can be successfully utilized in this area. The rules work quite well on the stock index series, but fail miserably on the futures.

If markets were frictionless and dividends were certain and paid continuously, it is easy to show that arbitrage activity would force the difference between the futures price and the spot price of the index to the product of the spot prices and the differences between the riskless rate and the dividend yield on the index over the life of the contract.’ If this value, known as the basis, was too small, alert traders could purchase the future, short the index, and harvest a return in excess of the riskless rate on this riskless position. The operation would work in reverse if the basis was too large.

I compute the “proper” value of the basis for the four futures according to the arbitrage restrictions. This number fluctuates little from day to day, although it decays steadily toward zero as the settlement date approaches. Therefore, with an approximately constant basis, the filter rules that worked well for the indexes should work nearly as well for the futures. The fact that they do not implies that the basis must diverge substantially from its “proper” (i.e. no arbitrage) value. I compare the actual basis with the corresponding proper basis and find significant differences throughout my sample. It follows that profitable arbitrage opportunities may exist.

It is a straightforward matter to compute the riskless return implicit in the basis of a stock index futures contract. If this rate is less than the riskless rate available elsewhere, then a short hedge (i.e. short the index, buy the future) can be used to capture this advantage. If the implicit rate exceeds the riskless rate, then a long hedge may be prof- itably employed. I tabulate (annualized) implicit rates for the futures in this study. The results indicate potential substantially profitable positions on both sides of the market.

THE DATA

The data for this study consists of daily observations of four stock index futures contracts and two underlying indexes. The time period is 9-15-82 through 4-12-83 for the futures and 2-l-73 through 4-l 2-83 for the indexes. Table 1 provides details for each time series.

I performed a runs analysis for each futures contract, each index over the period 9-15-82 through 4-12-83, and each index over the period l-2-73 through 4-l 2-83. This test utilizes the sign of the daily price change in an effort to determine if the time series is random. Nonrandomness may be present in two forms. If too few runs (positive or negative) are found, then the series has a tendency for persistence; if too many runs occur, the series has a propensity for reversal. The first condition is favorable for the potential success of technical trading rules such as filter tests, while the second condition offers less justification for optimism. Of course, an inference of randomness is not encouraging. Table 2 presents a summary of the runs analysis.

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The futures displayed a strong tendency toward reversal, while the indexes exhibited a weaker tendency toward reversal since 9-l 5-82. However, the indexes showed an extremely strong inclination toward persistence over the extended sample period from l-2-73. A preliminary inference from these results is that classical technical rules applied to the indexes over a long period of time have a good chance of favorable outcome, while similar application to futures and to the indexes recently do not promise great success.2

Of course, a runs analysis is only one of many possible tests of randomness. A series that appears random on the basis of a runs test may have other properties that offer possibilities of economic exploitation. For example, the size of the daily returns, ignored by the runs analysis, may open the way to the establishment of a favorable technical trading rule. I leave these deliberations to another time.

TRADING RULES

I applied two filter rules to each of the eight time series that appear in Table 2.

RULE 1: Buy the security when it rises 50 basis points or more in 1 day; sell (and move into a riskless asset) when the security declines 50 basis points or more in 1 day.

RULE 2: Cover short and buy the security when it rises 50 basis points or more in 1 day; sell and sell short when the security declines 50 basis points or more in 1 day; no earnings on short sale proceeds.

No commissions are assessed and it is assumed that transactions can be accomplished at the closing price of e day.

Before I present the results, two comments are in order. First, the above rules are very simple versions of the class of filter rules. I do not imply that more favorable results could not have been achieved with different parameters or more sophisticated decision criteria. However, the rules are representative to the extent that reasonable inference about the success potential of similar strategies can be made from these results. No other variations were attempted, so my output is not compromised by selection bias. Second, the commission and price specification assumptions favor success for the filter rules somewhat unfairly. Controversy over this issue dates back to the pioneering work of Alexander[l]. In addition, the indexes are not directly tradeable (yet!) and definitely not shot-table (ever?), which re- duces the meaningfulness of the results somewhat. Again, however, I think that these rules can give a reasonable directional indication of the potential exploitability of these time series.

Trading rule results appear in Table 3 (rule 1) and Table 4 (rule 2). The long-only filter generated returns comparable to buy and hold for each index since 9-15-82. This seems satisfactory in view of the fact that the market rose strongly throughout the entire observation period. It is a bit surprising that a momentum rule was this successful when applied to time series that exhibited a tendency toward reversal (i.e. positive Z-scores). The long-short filter returns for the indexes since 9-l 5-82 were positive, but fell far short of buy and hold. This is reasonable in light of the market trend over the period. Both trading rules performed splendidly over the longer period from l-2-73. The long-short filter did best, given the opportunity to actively exploit a number of severe down markets.

The fate of the filter trading applied to the futures was a sorry one indeed. The long filter lost money in a period of rapidly rising stock prices, while the long-short filter threatened to wipe out investor capital altogether.

The disparate results of filter trading for futures and the underlying indexes indicate that the time series of returns for each of these groups differ in an important way. Does such a difference make a statement about the possible existence of arbitrage profits? This is the subject of the next section.

ARBITRAGE PROFITS

The no-arbitrage relationship between the futures price and the spot price can be written

F = Se@-W (1)

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where F = futures price, S = spot price, R = riskless return per unit time, D = dividend yield on the index per unit time, and t = time until settlement date.3 The basis, B = F-S, can thus be formulated as

B = S(e(R-W-1) (2)

Given values of R and D, the no-arbitrage basis for a futures contract can be computed using equation (2). Note that the value of B is moderately sensitive to S and declines toward zero as t moves to zero. The change in B from day to day is quite small. Hence, the daily return on a futures contract should mainly reflect the return on the underlying index. The time series of daily returns for the future should closely parallel that of the index. Otherwise, equation (1) fwill be violated and arbitrage profits could result.

For example, on 9-22-82, the NYSE Composite Index closed at 71 .lO, while the March-83 future closed at 70.70. If we assume R = 9% and D = 4.5% (annual values), equation (2) indicates that the basis should be 1.685. We observe a value of -.40. If we form a short hedge by shorting the index at 71 .lO and buying the future at 70.70, we effectively borrow 71 .l 0 for 190 days, at which time we must repay 70.70 plus a dividend at a 4.5% annual rate (roughly 1.67). The annualized interest on such a loan is approximately 3.4%, quite a bargain in a 9% market.

In the last section, the trading rule results implied that the futures return series and the index return series were quite dissimilar. It is clear that the dissimilarity must principally be a result of violations of equation (2). Table 5 presents monthly highs and lows for basis deviation from proper value. It is clear that substantial violations of equation (2) occurred frequently. Table 6 displays monthly highs and lows for the (riskless) interest rate implicit in the basis under the assumptions of a 9% riskless rate and a 4.5% annual dividend yield on each index. Implicit interest values under (over) 9% indicate profitable arbitrage borrowing (lending) opportunities may exist. The extreme values for QQQAH and QQUCH in 2-83 and 3-83 correspond to short term loans because settlement was near. The rates in Table 6 underscore the potential for successful arbitrage against basis values that deviate substantially and often from the proper values indicated by equation (2).

DISCUSSION

The results of this study imply:

1. There is the potential for substantial filter returns in the stock indexes.

2. The futures returns do not support the probable existence of favorable filter returns.

3. The deviations of the stock index and the futures return series are due mainly to departure of the basis from its no-arbitrage value.

4. Worthwhile arbitrage opportunity may exist between futures and underlying indexes.

Many nagging questions remain. If arbitrage opportunities exist, why don’t market participants with low costs exploit them and thereby force the basis into line? Perhaps the lack of a satisfactory market proxy stymies this operation. Restrictions on full use of short sale proceeds and associated short selling difficulties could destroy most of the advantages of the short hedge possibilities. The thinness of the market might cause potential big (low cost) players to lose interest and the remaining participants might be deterred by high trading costs.

Suppose that arbitrage activity eventually keeps the basis close to its no-arbitrage value. Will the filter rules that work for the indexes now work for the futures? The leverage available from the futures will allow small return advantages to be increased manyfold. Perhaps the favorable filter returns on the indexes resulted from the fact that the indexes were not tradeable and that tradeable proxies carried transactions costs and other unpleasant characteristics that neutralized the apparent advantage. If this is so, will the index proxies that may be developed display virtually random return series, which, in conjunction with the elimination of arbitrage profits, will render the filter rules useless for both the proxies and the futures?

This study is an attempt to outline some practical implications of the relationship between stock indexes and stock index futures. The market will supply the answers to the questions raised here.

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FOOTNOTES

1. See Eckardt[2] and Moriarty, Phillips, and Tosini[3].

2. The tendency toward reversal in the futures series is the strongest such property I have ever observed in a security return series.

3. This is the relationship stated in words in the introduction for the case of continuous compounding.

REFERENCES

1. Alexander, S. “Price Movements in Speculative Markets: Trends or Random Walks.” Industrial Management Review, 2 (May, 1961) 7-26.

2. Eckardt, W. “A Characterization of Options on the Value Line Index.” Kansas City Board of Trade, 1982.

3.Moriarty, E., Phillips, S., and Tosini, P. “A Comparison of Options and Futures in the Management of Portfolio Risk.” Financial Analysts Journal, 37 (January-February, 1981), 61-7.

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SYMBOL A. FUTURES

QQQB QQQM

QQUCH QQUCM

B. INDEXES NYSE SAP

SERIES

QQQ@ QQQAM

QQUCH QQUCM

NYSE SAP

NYSE SAP

NOTES:

TABLE 1 DATA FOR THE STUDY

DESCRIPTION

NYSE March-83 NYSE June-83

S&P March-83 S&P June-83

DATES OBS

g-15-821 3-31-83 139 g-15-8214-12-83 146

g-15-8213-17-83 129 g-15-8214-12-83 146

NYSE Composite l-2-7314-12-83 2681 S&P 500 Composite l-2-7314-12-83 2681

TABLE 2 RUNS ANALYSIS

DATES O-RUNS E-RUNS Z-SCORE

g-15-8213-31-83 86 69.4 2.85 g-15-8214-12-83 86 72.7 2.24

g-15-82/3-17-83 73 68.8 1.65 g-15-8214-12-83 82 71.9 1.72

g-15-8214-12-83 80 72.8 1.21 g-15-8214-12-83 80 72.3 1.30

l-2-7314-12-83 1113 1298.5 -7.28 l-2-7314-12-83 1141 1298.5 -6.18

O-RUNS = observed number of runs. E-RUNS = expected number of runs for a random series. Z-SCORE = statistic ( O=> random, negative=> trends,

positive=> reversals).

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TABLE 3 TRADING RULE 1

SERIES DATES RETURN B-H TRADES %-GAIN X-IN

QQQm 9-15-8213-31-83 -14.0 24.2 35 20 51 QQQM 9-15-8214-12-83 -12.8 24.0 36 25 45

QQUm g-15-8213-17-83 -6.0 19.8 30 23 50 QQUCH g-15-82/4-12-83 -6.5 23.9 35 26 48

NYSE 9-15-8214-12-83 22.6 25.7 24 54 55 SAP 9-15-8214-12-83 21.8 25.4 24 50 55

NYSE l-2-73/4-12-83 789.2 37.5 295 49 53 SAP l-Z-7314-12-83 636.4 30.8 314 48 51

NOTES: B-H = buy-and-hold return (no dividends for indexes). TRADES = number of trades. %-GAIN = percentage of profitable trades. %-IN = percentage of time in the security. All returns are unannualized.

TABLE 4 TRADING RULE 2

SERIES RETURN B-H TRADES %GAIN-S XGAIN-L

QQQB -45.5 24.2 69 17 21 QQQm -43.8 24.0 71 28 26

QQua -30.5 19.8 60 33 23 50 QQUCM -34.8 23.9 69 31 26 48

NYSE 10.0 25.7 47 29 56 SAP 8.2 25.4 47 29 52

NYSE* 2068.4 37.5 588 42 49 sAP* 1402.5 30.8 626 43 48

%-L

51 45

55 55

53 51

NOTES: See notes to Table 3. %GAIN-S = percentage of profitable short trades. %GAIN-L = percentage of profitable long trades. X-L = percentage of time in long position. * = period from l-2-73.

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TABLE 5 BASIS DEVIATIONS

MONTH

9-82

lo-82

11-82

12-82

l-83

2-83

3-83

4-83

QQQm QQQm

-.29 -2.12

.34 -2.24

1.20 -1.90

.62 -1.47

.79 -.74 1.18 -.50 1.20 -.94

-.72 -2.53

-.18 -2.70

.83 -2.34

.29 -1.37

.28 -1.24

.95 -.89

.96 -1.67

-.63 -1.17

-.68 -3.91

.31 -4.01

1.30 -2.74

1.11 -2.42

1.23 -.93 1.86 -.49 1.32 -.98

QQUCM

-1.38 -4.54

-.70 -4.72

.47 -3.47

.24 -2.74

.43 -1.71

1.34 -1.31

1.02 -2.57 -1.02 -2.31

NOTES: Upper value is high for the month. Lower value is low for the month. All numbers are in dollars. Deviation = actual basis-proper basis.

MONTH

9-82

lo-82

11-82

12-82

l-83

2-83

3-83

4-83

TABLE 6 IMPLIED INTEBEST BATES

QQQm QQQU QQUCH QQUCM

na 2.9 9.3 2.6

13.6 2.1

11.7 2.7

13.7 4.3

23.2 5.2

40.7 -17.5

na 4.3 na 3.9

10.9 4.1 9.7 6.0 9.8 5.7

12.2 6.4

12.4 2.4

i”l

na 2.4 9.6 1.9

11.6 2.6

12.6 2.1

15.1 4.7

25 .O 6.2

62.6 -41.7

na 4.1 na 3.6 9.6 4.5 9.4 5.2 9.7 6.1

11.9 6.6

11.3 1.1 na 1.0

NOTES: Upper value is high for the month. Lower value is low for the month. All numbers are in annual percent. na = no rate above 9% available (i.e. no long hedges).

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Walter L. Eckardt, Jr. is an Associate Professor of Finance. He holds two bachelor of engineering degrees from Vanderbilt Universitv and three degrees from Washington University: M.S. in Applied Mathematics and Computer Science, 1971; MBA, 1974; and the Doctor of Science in Applied Mathematics and Computer Science, 1973. Professor Eckardt joined the Southern Illinois University at Edwardsville faculty in 1973. He has been active in the areas of research and consulting, and has published in Journal of Finance, Journal of Financial and Quantitative Analysis, Financial Management, Journal of the American Statistical Association, Financial Review, Decision Sciences, and other academic and professional journals. Professor Eckardt has worked on a consulting basis for the American Stock Exchange, Stanford Re- search Institute, Dean Witter and Company, the Automobile Club of Missouri, the American Optometric Association, Bridge Data Company, and other local and national firms.

BIOGRAPHY

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APPLIED MODERN PORTFOLIO THEORY: ITS FUNDAMENTAL AND TECHNICAL ASPECTS

Robert F. Vandell Professor of Business Administration

University of Virginia

Modern Portfolio Theory, predicated as much of it is on markets that are either efficient or perfectly efficient, should not be warmly received as a subject for discussion by technical forecasters, whose reason for being is to discover potential price inefficiencies in the market and, on balance, be right often enough to provide extra market profits for their clients. A growing number of practitioners have seen in modern portfolio theory something that academics had ignored: the theory’s potential for helping to identify pricing anomalies in the market place. It is my purpose here to review some of the more important ways practitioners are using modern portfolio theory for pragmatic money-making ends. As you will see, the applications involve a curious admixture of fundamental and technical analysis. You, I hope, will also see that some of the shortcomings or limitations of applied modern portfolio theory occur in the technical areas. These limitations or gaps may provide new kinds of opportunities for technicians to exploit.

Applied Modern Portfolio Theory employs a premise alien to academics: the markets are not now efficient but they will tend to become so over time. To the extent inefficiencies can be correctly identified, the tendency toward effi- ciency will provide exploitable, superior profit-making opportunities for clients. Identifying inefficiencies requires analytical skill and judgment, and these come largely from superior fundamental analysis. Applied Modem Portfolio Theory merely provides a systematic, disciplined basis for translating the analysis of individual securities into a market-wide referencing system that facilitates identifying under and overvalued securities and for measuring explicitly the degree of the estimated inefficiency. Even a security that has been correctly identified as significantly undervalued may not be an attractive one to buy. Undervaluation must also be recognized by others, and as interest mounts in the security, increased demand must--if benefits are to be realized--bid up prices and create excess profits in the wake. The extent to which and the rapidity with which undervaluation is recognized by others affects the magnitude of excess returns. Timing and market momentum thus become important considerations in deciding which undervalued opportunities should be exploited.

One might also hypothesize that the markets are not now efficient and they won’t be efficient at the end of normal holding periods either. The character of the inefficiency, however, will be dramatically different at the beginning and end of the holding period. It is in this direction, I believe, that Applied Modern Portfolio Practice will tend to move over the next decade. Both increased and changed fundamental and technical forecasting will be necessary if active managers are to pursue this next and logical step in capitalizing upon inefficiencies in the market place.

There are two intrinsic limitations to Applied Modern Portfolio Theory in its current form. First, the system in the hands of astute, skillful poeple does tend to differentiate between securities or classes of securities that should be purchased or not purchased. It does not, however, indicate when purchases should be sold. Stocks tend to be pushed out of portfolios because they are no longer as attractive to purchase as are alternative securities. The system lacks a disciplined basis for timely selling and the sales discipline may be more critical to investment success than the purchase decision. Technical considerations may be more important here.

Second, analysts will not always be right; bias, ignorance, and limitations of the system of evaluation itself may contribute to misidentifying under and overvalued securities. Can supplementary screens be developed to help eliminate incorrectly analyzed security valuations? This too may be an area where technicians have tools that may add insight to the valuation process.

There is still another villain to the problem of building attractive portfolio performance from skilled analysis: diversification. How should skillful managers diversify? Academic optimal diversification models, predicated on market ef- ficiency theory but patched up to let some skill into the portfolio composition process, may provide very distorted over-diversification solutions. Again, technical understanding of market conditions may provide a basis for gaining improved return performance without increasing adverse risk.

The principal point of departure from theory to Applied Modern Portfolio Practice is the capital asset pricing model as developed by Sharpe, Lintner, Mossin and others from the theoretical insights of Markowitz. I presume knowledge of how this theory came to be, and concentrate on the implications for exploitation in a world where securities are not always priced efficiently for all participants. My first task is descriptive. How does the application work for such

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active management tasks as security selection, group rotation, portfolio tilting, market timing and portfolio composition? At the interface between fundamental and technical analysis, I draw upon some empirical examples that are designed to illustrate but not to prove. Here, I am endeavoring to show how technical analysis may help reduce the intrinsic limitations of Applied Modern Portfolio Practice. As a survey, this paper must omit a good many interesting variations and supplementary analyses that enrich practice.

THE CAPITAL ASSET PRICING MODEL

Deduced logically by assuming perfect market conditions, the capital asset pricing model states that all securities should be priced along the security market line which is defined by the risk-free rate of return and the rate of return expected for the market portfolio. Specifically,

E(R) = R, = B,E(R,)

where:

E(Ri) = the expected total rate of return for any security, i.

R, = the current risk free rate of return, often assumed to be the go-day treasury bill rate.

Bi = the volatility of security i relative to the market’s volatility, known as beta.

E(R,) = the expected total rate of return for a market-weighted index of the market portfolio, comprising all risky assets.

The assumptions from which the model is deduced are quite controversial and are the focus of considerable practitioner attention in modifying the theory for practical ends. These assumptions are:

1. All investors seek to maximize the expected value of the utility of their terminal wealth at the end of a single period.

2. Investors choose the portfolio they must want on the basis of their risk and return expectations. Risks and return are measured by the variance and the mean of expected results for alternative portfolios.

3. All investors have homogeneous expectations of risk and return for each security among all those available. All investors have uniform time horizons.

4. Information is freely available.

5. There is a risk-free asset with a uniform rate of return for all. Investors can borrow at the risk-free rate of return in sufficient quantitites to meet their risk objectives. Short selling is feasible for all.

6. There are no taxes, transactions costs, or other market imperfections.

7. Investors are price-takers.

8. The total quantity of assets is fixed and all assets are perfectly divisible.

While there are many other aspects of importance to capital asset pricing theory, this list of assumptions will suffice for our purposes.

THE EMPIRICAL SECURITY MARKET LINE

The security market line (SML) is an expectational representation of market equilibrium. Using analyst estimates of future risk and returns for individual securities, practitioners can create an empirical SML by least square regression techniques as illustrated in Chart 1 below.

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Chart 1 Empirical Security Market Line

E(Bi)

Each dot represents an analyst’s forecast of the total rate of return and beta risk for a security. Returns are usually calculated using a variable-growth dividend-discount model and are equivalent to conventional internal rates of return. Security betas are developed by a variety of means but the means simply reflect the approach that the firm has found to be most useful in measuring the relative volatility of a security. The security market line summarizes the risk/ return central tendency of individual analysts’ estimates.

Almost always, the intercept of the empirical SML line is well above its theoretical counterpart, the risk-free rate of return. The SML slope, too, is usually less steep than it should be and may - disturbingly - slope downward. Historical tests of CAPM show these same tendencies, and are properly referred to as misspecification. The coefficients of determination of the regression equation tend to be modest, indicating a considerable scatter of points around the SML.

Stocks that plot well above the empirical SML are considered undervalued. They promise more than market returns for a given level of risk. Similarly, stocks that plot below the line are considered overvalued. The vertical distance between the dot for a security and the empirical SML is called the security’s alpha. Dots above the line have positive alphas; below it, negative. Alphas provide a basis for ranking a universe of stocks by relative attractiveness.

Alphas are a measure of the long-term excess returns potential for a stock. Similarly, the weighted average of the alphas of a portfolio reflect the analyst’s estimate of the risk-adjusted return potential for the portfolio. Alphas describe what is called the long-term game.

It is a short-term game, however, that attracts the interests of many professionals. If an analyst correctly identifies an undervalued security, others recognize the security’s attractiveness subsequently, and in the process of pur- chasing it, they drive up the price. A substantial excess return, well above the initial alpha estimate, will be realized. Note that - other factors equal - the plot for this undervalued security will gravitate in the direction of the “efficient” security market line as prices rise. This phenomenon is called ‘correction. ” Analysts, of course, will not always be right in their assessments. Nevertheless, the rewards from a tendency to be correct, reflecting analytical skills, can be quite attractive.

It is important to bear in mind that when market price changes cause a dot to shift downward, capital gains are being realized. The reverse is true for an upward shift in the locus of a dot: the change reflects capital losses. The downward shift in a dot, however, does not automatically create excess returns. For example, if all dots shift in the same direction, then the relative movement of the dots becomes a better, although incomplete, indication of excess positive or negative returns.

What factors besides market price changes can cause dots to shift? With a rising dividend stream forecast and a constant market price, the passage of time will tend to move the locus of a dot upwards. In the short run, these time- movement changes tend to be very small because of the infinite-life characteristics of equities. An analyst could change his risk assessment (beta) for the stock and thus cause its plot to change. Most methods of estimating beta, however, tend to assure that beta changes will be relatively small in the short run. Finally, an analyst can change his/her es-

63

timate of the security’s dividend stream. Note, however, that even significant adjustments to earnings per share estimates for a security for the next twelve months will not change the dividend discount model’s rate of return by very much unless the analyst also changes his long-term assessment of prospects for that stock. Aside from market prices, changes in estimates of long-term prospects are the factor most likely to affect dot movement. In the short-run, these reassessments are not likely to affect a large number of securities.

Although the empirical SML system for identifying potential over and undervalued securities is initially driven by fundamental analysis, the shift in dots over the short run is determined by changing market conditions. In this regard, the security market line analysis of changes from period to period has a high degree of technical overtones.

Money is made by owning undervalued securities that correct towards the SML and by not owning overvalued securities that also correct. Leaving out analysts’ errors for the moment, there is a counter-migration towards inefficiency Some undervalued stocks will become more undervalued from one period to the next and hence will be relatively unattractive investments in the interim.

Similarly, some overvalued securities will become more overvalued, and hence be relatively attractive interim investments. The counter-migrations toward inefficiency (reflected in a continued wide scatter of plots around the period SML over many time periods) cloud the effectiveness of SML interpretation. Can the favorable migrations be separated from the unfavorable ones? We shall return to this question shortly after we establish a larger perspective.

Alphas are affected by the same forces that cause dots to move. A change in parameters of the ex ante security market line from one period to the next can also change the alpha measure for any security.

A change in the ex ante slope of the SML has powerful implications for interim return performance of securities. Con- sider the illustration in Chart 2.

Chart 2

Effects of Changes in Ex Ante Expectations on Ex Post Results -- --

Ex Ante Ex Post

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The slope and intercept of the ex ante SMCs are assumed to have changed from A at the beginning of the period, to 6 at the end of the period. The effect of this change on the interim realized SML (ex post) is dramatic as the chart on the right shows. Similarly, if we went from B to A we would have found a steeply upsloping SML with a negative intercept. Changes in the expectational locus of the SML can have a potentially much greater impact on which stocks prove attractive buys over the interim period. A low-alpha, low-beta stock would be much more attractive stock to own, generally, in this illustration than a high-alpha, high-beta one. In the short-term game, alphas have limited value because the migration of the ex ante SMCs tends to be overpowering.

Note that the exceptional SML can be defined by two parameters E(t?,,,) and 6, (the slope coefficient). Both are subject to technical and fundamental analysis. In Table 1, I have recorded these SML parameters for sixty months from the beginning of 1974 to the end of 1978, as developed from data provided by one company. These parameters appear to be responding to systematic cyclical changes with much less random influence than one might have anticipated. If changes in these parameters can be forecasted, then analysts will have very powerful insights into the character of the ex post security market line, and from that persepective, on the potential price changes for individual securities.

If we could forecast the SML three months hence, we would have considerable insight into interim price movements. We could make the heroic assumption that all stocks will be priced efficiently on the forecasted SML line on that date. Given an estimate of the beta for a security on that date, one could estimate a discount rate applicable to the security; this rate could be applied to the existing dividend stream forecast to estimate the most likely market price for the security three months hence. Prospective price changes (or total rates of return) from today’s price can be measured for each security and be used as a second method of ranking a stock’s potential.’ The alpha potential of the stock will be built into this calculation. We simply assume that dots on today’s SML chart will gravitate towards tomorrow’s estimate of the SML.

If the security analysts have forecasting skill, the current alphas derived from a SML analysis will have some forecasting value. They will suggest stocks to buy (high positive alphas) and stocks to avoid (high negative alphas). Un- fortunately, no automatic indicator tells when a stock that has previously been purchased should be sold. SML is buy- driven. Stocks are sold to make room for new buys. There is no criteria that establishes which stocks should be sold. One might throw out the stock with the lowest alpha, for example. No established analysis validates that this-or other similar decision rules has economic value. Sell decisions may be more important than buy decisions in building portfolio performance.

Why is the absence of a selling discipline a risk? An undervalued stock may become hot and undergo such a significant price change that it becomes overvalued before its price movement has peaked out. If the stock is sold while its alpha is low, but still positive, perhaps only one-third of its potential price movement will be captured. Can we avoid selling stocks with high momentum potential? Technical analysis, designed to provide both buy and sell signals, should be helpful.

Of greater concern, the SML security selection system works because of a tendency for the analyst to be right. It also works despite the fact that an analyst is occasionally wrong. The analyst can be wrong because he has misestimated either the risk or return potential of a security’s potential (called bias), or because other analysts do not see the same potential for a protracted period. Can these issues be addressed?

Two forecasts, each with a tendency to have some information content and each developed by independent means, are more valuable than one. It is important that each set of forecasts have four properties: (1) they encompass a diverse and relatively large universe of securities; (2) they are subject to scaling so that better is distinguished from worse; (3) they have information content; and (4) they are based upon independent types of analysis. Certain types of technical analysis should meet these specifications when used with SML alphas.

The relative value of two or more forecasts can be assessed as follows (using least square multiple regression techniques):

fi = a + bF,, + cF,, + e,

where:

a = ex post rate of return for security i over an appropriate period immediately following the forecast (say, one year)2

F,, = forecast for security i by the first method of analysis

65

Fzi = forecast for security i by the second method of analysis

e, = error factor

Positive signs for the b and c coefficients would indicate that each forecast was providing information of value.

Evaluation of one forecasting period might be misleading. If the measurement were repeated, say, quarterly over a market cycle, the average coefficient (a, 6, C) would begin to take on some meaning.3 A revised forecast (RF) could be constructed as follows.

RF, = Z + 6F,, + CF,,

The various coefficients might also be subject to a time series technical analysis in order to predict what they will be (above or below the mean) in the next period, t, and this might lead to a further forecast revision. The revised forecast would then be used for security selection.

Once we have established basis for scaling one or more forecasts so that over time they tend to be more realistic predictors of actuals, the data can be used to evaluate analyst’s bias by reevaluating history using the following equation:

e,, = Rit - RF, -

If the average error term (e,) for a security over the course of a cycle is materially different from zero, this is an indication of analyst bias. Should e, be negative, the analyst has tended to overestimate the potential for a security on balance; the reverse would be true if e, were positive. The time series of forecast errors for a security is also ana- lyzable by technical means. Errors due to bias, once they are identified, can be eliminated from the forecasts to make them more reliable (assuming, perhaps dangerously, predictably stable and analytical bias).

Analyst bias can also be examined by looking at a time series of alpha forecasts. Table 2 shows the time series of alphas (derived from Table 1 SMCs) for four selected stocks over 60 months. Anheuser Busch had negative alphas throughout the five-year period; yet it seems impossible that there were no buying opportunities in this stock during this interval. In contrast, Beneficial Finance had positive alphas in all but one period. Was it always to some extent undervalued? All four companies show somewhat rhythmic patterns to the alpha movement.

Alpha performance can be decomposed into two elements - a recent average and a standardized measure of var- iability around the central tendency. In Figure 1, we illustrate average trading twelve-month alphas and related standard deviations for Beneficial Finance, along with actual alphas. The Figure illustrates buy, hold, sell decision points on the theory of correction towards a central alpha tendency. These buy, hold, sell actions can be transformed into a ranking system of relative attractiveness that is probably not too dissimilar from evidence amassed by technical analysts.

66

Figure 1 Using Alphas as Buy/Sell Signals -1s

rn.-‘.l :. ! i.:j,j,:t~i:r:,j:...i. ..: .,j..;. j ..~ j. :_.:.I

I.::.I.::1I. :I ,..’

hi”‘!“” I

I ‘I! .I, : I .’ / , , , I. :-..:I

i ! : , I

.,.. I ,... ..I I / .-.

I I .!_ I r I : I ,I. .i : i

I:.. t 1 :-+ : ! ( ! . 1 j’ :I

67

There are two pieces of potentially useful information in this data set: (1) the current mean and (2) the current deviation from the mean. Do either or both have predictive value? The answer is yes in both cases as the preliminary analysis of one firm’s data base suggests. Of the two, the deviation information content is highest and more stable over time. The two together, have higher explanatory power than the initial alpha estimates.

In summary, while SML seems to help identify efficiencies in the market place and provide perspective on market dynamics, further analysis to eliminate analyst bias and to supplement alpha forecasts with new forecasts adding different types of perspective seems quite promising.

OTHER FACTORS INFLUENCING RETURN PROSPECTS

The capital asset pricing model is no longer considered to be complete, although there is still considerable debate as to what is missing and what the implications of the missing factors are. Let me touch briefly on some of the more critical missing factors that some security analysts are employing to determine the central tendency of market performance at any given moment.

PERSONAL TAXES

Personal taxes, and particularly the tax differentials between ordinary income and long-term capital gains, are a part of real world investing. Only a casual look at the pricing of municipal securities confirms that taxes affect pricing.

The SML as described may well be useful for pension funds and other non-taxed institutions. The SML, however, may not give a useful picture of value for a high-tax-bracket individual.

One simple adjustment that can prove insightful is to modify total rate of return estimates for their tax effects. Since capital gains are not taxed until realized, the adjustment can take many forms.

Chart 3

SML's Given Different Tax Circumstances

Jon Taxed Institution f3

Chart 3 compares SMCs for a non-taxed institution and a high-tax-bracket individual as of the same date, using after- tax return estimates (Ri).

Taxes reduce the after-tax benefits, obviously. The slope of the SML also changes. The reason is that yield as a percentage of total returns tends to be inversely related to beta. Low beta electric utility stocks, for example, have high yields.

Taxes create pricing anomalies. Security A - a utility, for example - is undervalued in the eyes of non-taxed investors. It is concurrently overvalued in the eyes of a high-tax-bracket investor. If non-taxed institutions enter the market and bid up the price of security A, the price changes tend to make security A more and more overvalued in the eyes of the high-tax-bracket investor. Security B has the reverse characteristics. It is undervalued in the eyes of the high- tax-bracket investor, and overvalued from the point of view of the non-taxed institution. Any price action designed to correct for the relative-value assessment by one party only makes the value condition worse for the other party.

The evidence that stocks are concurrently under and overvalued is growing. This evidence suggests that pricing in- volves persistent inefficiencies growing out of tax-related market tensions. If so, investors should always be able to find some stocks that are undervalued relative to their tax circumstances.

The mix of investor interest in the market should also influence the character of opportunities. There are times, for example, when pension funds are heavy net investors in stocks; other times their net investment activity is nominal. Similarly, the activity of high-tax-bracket investors also waxes and wanes, and not necessarily in concert. The mix of investors participating in the market will influence price.

The slope of the relative SML lines for these two classes of investors may provide important technical information:

less: slope SML High-Tax Bracket Investor slope SML Non-Taxed Investor

Difference in SML slope

If the difference in slope of two SMCs is unusually wide, this would signal that low-yield, high-beta stocks as a class are very favorably priced. A narrow spread might suggest that low-beta, high-yield stocks have more promise in the short run.

Some firms use a similar index developed from the following multiple regression:

Ri = a, + B,(kJ + gl(Yl) (5)

where

Yi = forward yield estimate for security i.

Whenever g, is unusually large, those stocks of greatest interest to high-tax-bracket investors are more likely to be undervalued relative to their promise for other investors as well.

Table 3 illustrates the effect of adding yield as an additional explanatory variable to CAPM[per formula (5)] in order to explain the pricing of risky assets. This table employs the same practitioner ex ante data used in Table 1. The resulting coefficients for yield are within the tax boundaries of the highly-taxed, non-taxed investors in all periods and are statistically significant. The coefficients of determination are substantially higher in this calculation. In general, the beta coefficients have increased in size and significance. Rhythmic patterns in the behavior of the various coefficients over time are also apparent. All these factors are encouraging.

MARKET LIQUIDITY

Market Liquidity is a measure of a stock’s ability to absorb volume without material price changes. IBM and ATT tend to be very liquid stocks. Many over-the-counter stocks tend, by contrast, to be very illiquid.

Liquidity can be measured by various means. The simplest measure is the total public market value of a firm’s stock. A better measure is the number of trading days it takes to accumulate an investment of $X absorbing no more than Y% of daily trading volume (X and Y being determined by the circumstance of the unique investor). Still other meas-

69

ures relate relative price changes to volume in order to estimate, say, how much volume can be absorbed without price changes of more than 1%. And so on.

Liquidity is clearly a very important factor influencing the assessment of value for large institutional investors. The market impact of investing in, and later divesting from, less liquid stocks can erode much of the hoped-for benefits. If timing is important, delays can also erode benefits.

In Applied Modern Portfolio Theory, liquidity is often addressed by subdividing the universe of stocks followed into three or more subgroups, each with similar market liquidity characteristics. SML’s are then calculated for each of the subgroups. Chart 4 below illustrates the nature of the liquidity pricing effect on two different dates.

Chart 4

Effects of Liquidity on Prices of Two Dates

i fii

I

i Bi

The slopes of the SMCs for low-liquidity stocks are generally well above those for high-liquidity stocks. The difference, however, in slope can be quite wide as on the left, or quite narrow as on the right.

The angle of the liquidity fan (caused by the difference in slopes) can contain potentially valuable information about prospects. An unusually wide fan, as in September 1974, should signal unusually favorable buying opportunities among the less liquid stocks. In contrast, an unusually small fan angle, as in September 1980, would signal that low liquidity stocks will probably not perform as well as high liquidity stocks in the immediate future.

The angle of the liquidity fan can be traced over time - using, say, a time series of monthly fan angles (or spreads in return prospects measured at beta equals one). These time series tends to be rhythmic, not random, suggesting that there is potentially useful information on market prospects imbedded in the size of the spreads.

OTHER FACTORS

Taxes and liquidity are but two of many elements that (1) could affect pricing of risky assets and (2) are not considered explicitly in CAPM. The techniques of analysis employed to deal with other factors are similar to those already exposited. The universe of stocks can be broken down into subparts, each subpart with similar characteristics. Sep- arate SMCs can then be constructed for each of the subgroups, and differences noted.

70

Alternatively, a variable that measures the factor being considered can be added to the CAPM equation, a multiple regression performed, and a security market plane (SMP) constructed that describes expectations along two or more dimensions.

Academics are beginning to explore persisting market inefficiencies. Some interesting work in the area of skewing, relative price-earnings ratios, inflation (interest sensitivity) and investment horizons are beginning to emerge, and still other factors have been suggested for study.

The benefits of multifactor analysis can be powerful. First, it provides a description of the current state of the market that can give clearer insights as to wnere, within the market, value opportunities are more likely to lie. Second, a study of the time series of multifactor analysis coefficients gives good advice about the dynamics of the market and about how relative values have responded to changed expectations over time. These data may, in turn, provide evidence that will facilitate forecasts of expectational trends - ones likely to continue and ones likely to reverse - that will indicate what sectors of the market are more likely to have relatively favorable price action in the intermediate future.

The limits of multifactor analysis are the same as those of the SML. Analyst or model bias can cause failure in identifying truly undervalued securities, and some way of eliminating these influences is desirable. Second, better timing information is desirable to help with buy and particularly with sell decisions.

Perhaps, the most encouraging element to SMP work arises from the diverse circumstances and investment styles of investors. Persisting pricing anomalies - caused by tax circumstances, for example - suggest that the market can- not be efficient for all. Each investor should be able to locate securities within the market that are undervalued for his or her purposes.

RISK

The risk/return and other parameters of SMP analyses must all be estimated. Each presents measurement problems and measurement opportunities for the more perceptive analyst. Risk measures illustrate ways in which new thinking can be applied with potentially productive benefits.

Academic thinking has tended to focus on betas (relative volatility) as the most complete and useful measure of security risk. Beta is an abstract theoretical concept, and somehow measurements must be made to turn the concept into estimates that have information content. The translation is causing serious problems.

Beta is usually measured from historic information. This raises a number of pragmatic measurement problems. How long should the measurement interval be (most often a month)? How many intervals should be included - a trade- off between currency and sample size (most often 5 years of data)? What form should the model take (market model, risk premium model, logarithmic vs. arithmetic, etc.)? What should be the reference market portfolio (Standard & Poor’s 500 Index, Dow Jones Industrials, Wilshire 5000, etc.)? What should be done to adjust for the properties of the input variables, which are usually not statistically well-suited for least-square regression analysis? Unfortunately, these pragmatic decisions often lead to very different measures of betas for individual securities and for portfolios of securities. Worse, the statistical reliability of any single beta measure is often disturbingly low.

Historic betas, no matter how measured, are usually not reliable forecasts of future betas. Beta drift or their mean regression tendencies are quite marked. This has led to several statistical adjustments (Bayesian, Blume corrections, etc., for bias and inefficiency) to reduce inaccuracy of measurement. Fundamental firm risk factors also have been added to reduce measurement inaccuracies to produce what are called fundamental betas.

Despite the sophistication going into this process, we find that beta forecasts have very limited information content. Quite frequently the average beta of all securities being studied is about as good and is frequently better as a forecast of future security betas than are individual measures of beta. To say the least, this development is disconcerting to practitioners.

Non-systematic risk (residual errors in beta calculations) is assumed to have no economic meaning in pure theory because these risks can be diversified away. Practitioners (notably Farrel14) have found, in contrast, information value in residual errors that have allowed them to construct “super efficient” portfolios (more return for the same risk than promised by CAPM). Alarmingly, non-systematic risk seems to have systematic components and systematic risk seems to be largely noise.

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I mention the problems practitioners are having in measuring future security risks in a meaningful way because technicians appear to be investing considerable effort into forecasting volatility, for the purpose of evaluating options, as one example. Anyone who discovers more useful measures of future security risk in the process would be in a position to contribute significantly to security evaluation.

There are two other elements of risk that may be of interest. The first concerns the composite character of beta as a risk measure. Beta risk is a composite of three other risk elements: duration (a measure of price sensitivity to interest rate or required rate of return changes), forecasting uncertainty of total return estimates for securities, and market condition uncertainty (how volatile interest rates and total rates of return requirements will be for various classes of securities in the immediate future). All these elements of security risk are undergoing changes that have little to do with historic beta measures. Can we make more progress in identifying future risks of materiality by attacking the components? The potential importance of technical analysis to parts of this process seems self-evident.

The effects of investor time horizon on risk is also a factor that deserves more attention. Below I have shown the one- year risk/reward matrix for three portfolios. Assuming $1 .OO is invested in each portfolio, I then show (assuming risk is independent over time) what wealth uncertainties are after five, ten, and twenty-year intervals. Over the longer investment span, the most risky portfolio becomes the least risky portfolio (because a higher level of wealth is more assured, despite the uncertainties).

Wealth Uncertainties

Expected Annual Portfolio Return Volatility 5 Years 10 Years 20 Years

A 7% 15% $1.403 + .335 $1.967 + .474 $3.870 + 0.671 B 9% 20% 1.539 + .447 2.367 + .632 5.604 + 0.894 C 11% 25% 1.685 + .559 2.839 + .791 8.062 + 1.118

There are a number of investors for whom there is little or no need for, or risk of, net divestment of financial assets over long periods - pension funds, where annual inflows exceed outflows both currently and prospectively, are a good example. Short-term volatility should be of less material concern to these investors. I raise these questions: what does risk really mean to investors, and how do the risks they perceive as being relevant to their circumstances affect pricing in the market place?

This problem of relevant risk is more complicated because risks in the market place seem to cancel faster than they theoretically should for two reasons. Uncertainty of returns (intermediate term risks) from one market cycle to the next is lower for equities than one would infer from looking at volatility within the cycle. Skill in well-managed portfolios also seems to reduce risks faster than theory would imply as very preliminary evidence is beginning to suggest.

Our limited understanding of risks relevant to investors, and our prospensity to define risk too simply as beta, may, in short, be impairing our ability to understand the pricing mechanism of the market place. The result is mismea- surement of over and undervalued prospects of securities.

GROUP ROTATION

What sectors of the market are the most promising in the foreseeable future? How should portfolios be overweighted or underweighted, balancing various industrial groups with, for example, the Standard and Poor’s 500 Index to improve prospective portfolio performance? SMUSMP types of analysis can also be helpful here.

The most commonly used method of addressing this issue is to aggregate and average security alphas by industry using either equal or value weightings. Industry prospects can then be ranked by their composite alpha from best to worst.

How should these data be used to decide over and underweightings? The answer depends on the relative quality of the forecasts. Group forecast quality can be analyzed and improved by the same analytical techniques already exposited for securities. Unfortunately, this information may not always be timely: it may not indicate when to buy and when to sell. Technical analysis may again be used here to amplify results.

72

PORTFOLIO TILTING

Market dynamics, as we have illustrated, cause SMP information to change. For example, the slope of the risk dimension of SMCs can be quite steep or quite flat, depending on market outlook. We have already suggested tax factors and liquidity factors that might cause the thrust of the portfolio to be shifted to emphasize or deemphasize high- yield and/or low-liquidity stocks under various conditions. Similar shifts to overemphasize high beta stocks when the slope of the risk dimension is unusually steep, or to overemphasize low-beta stocks when this slope is unusually flat, would also be useful. This activity is called portfolio tilting.

The dynamic movement of the coefficients of multiple regression analysis (e.g. risk, yield, and liquidity) or spreads between return prospects for extreme groupings of these or other factors may, as has already been suggested, provide useful information about where within the market favorable price action is more likely to occur in the future. To the technician, an analysis of tilting, industry, and security prospects may alert him to segments of the market that should be watched more closely for possible buy or sell signals. While options involve additional analytical factors - betting long or short, with rather than against - relative market prospects should enhance the prospects of winning big. Betting may also beat hedging. In short, SMP analyses can amplify and focus the work of technicians in potentially profitable ways.

MARKET TIMING

Should equity commitments as a percentage of total portfolio assets be increased or decreased, given market prospects? Data from SML analyses is also being used to market time shifts in portfolios between equities and fixed- income securities.

The return from the equity-market portfolio - say, the S&P 500 Index - can be inferred from an SML. It is simply the total rate of return associated with beta equals one on a SMUSMP chart. The total rate of return for the equity-market portfolio can then be compared with an appropriate fixed-income return measure, such as Standard & Poor’s (seasoned) AA Utility Bond Index yield to maturity. Essentially, whenever the spread proves unusually wide (Equity return - Bond return), this signals that equity commitments should be increased significantly.

To illustrate how assessing market timing might work, let me draw upon data from a case study, lllini Trust Company5 Table 4 shows the returns that could be expected if the firm maintained a 40%/60% fixed income/equity commitment, rebalanced quarterly, over the period from the beginning of 1973 to mid 1978. The quarterly rate of return for the balanced portfolio is shown in column 5. The cumulative improvement in portfolio value for the balanced portfolio is shown in column 8.

Table 5 reports the spread between this firm’s expected rate of return for the S&P 500 Index and AA Bond Interest Rate. The spread is shown in column 4. This firm makes an adjustment to the spread depending upon the bond- market outlook, an adjustment that is not material in this illustration. Column 6 translates the risk premium estimate into the desired equity commitment (scaled firm 0% to 100%).

Table 6 applies the asset-mix analysis of a portfolio with an average target asset-mix objective of 40%/60% fixed- income/equity, but where the equity proportion can be shifted from a low of 40% to a high of 80%. The cumulative value of $1 .OO invested in the market-timing strategy proved to be 1.278 over the time span analyzed. This compares with a cumulative value of 1.150 for the stably balanced portfolio. Given the poor debt-and-equity market conditions for this 5 l/2 year period, the improvement is noteworthy.

Figure 2 illustrates the relationship between the performance of the market-timed portfolio and the balanced portfolio, using a performance-characteristic line analysis. Not only are returns improved but downside risks are lowered by market timing in this illustration.

73

Figure 2

Illini Trust Company

Market timing is, of course, one of the more beneficial purposes of technical analysis. The prospect of improving on the timing of Illini’s portfolio shifts, using technical information, would seem to be a very promising area for analysis.

DIVERSIFICATION

For reasons of space, I am going to skip over a rich and increasingly useful body of theoretical literature, and practitioner modifications thereof, relating to how long-term target asset-mix objectives (for major classes of assets such as money-market, long-term fixed-income, equity, and real estate) can be determined most usefully. Asset-mix strategy is one of the most critical decisions the client must make, but its importance to technicians seems quite secondary.

I am also going to walk past a body of literature suggesting how one might best diversify a portfolio of equity managers, each one of whom tends to manage his part of the portfolio with a very different style. Here, timing of changes in asset-mix may be more material than the literature yet recognizes. SML analysis augmented by technical analysis might very well provide useful help here.

What I would like to focus on now is how a manager with forecasting skill can construct a portfolio that balances alpha return prospects with risks. For simplicity, I will limit myself at first to the implications of security selection alone. Here, I believe the literature and practice is weakest. As to practice, there is a strong propensity to overdiversify, and in the process kill much of the potential that security selection provides. Perhaps this is understandable, given the unfor- tunate emphasis on short-term results that has crept into consultant and client analysis of performance results of late.

The real issue in my mind is how should a manager with skill diversify. Skill will tend to produce two desirable results: (1) increase the expected return performance for the portfolio, and (2) decrease the uncertainty with which that performance will be realized. The trade-off is between the size of excess return prospects built into the portfolio and the uncertainty associated with achieving the level of excess return forecasted.

74

Diversification will reduce the average size of the excess return forecasted for the portfolio, and other factors equal, the result will be unattractive. To gain some offsetting advantage, diversification must take place in a way that provides the most significant reduction in forecast uncertainty per unit of forecasted excess return sacrificed. Both forecast uncertainties for individual securities and the covariance of these uncertainties are material to improving the certainty of achieving the forecasted level of excess return potential. The properties of the model that will achieve these ends are identical to those developed by Markowitz in his pioneering work. Nevertheless, the inputs required are very different.

A manager with a good deal of security-selection skill should be able to create a super efficient portfolio. The prospective and realized portfolio returns should tend to be superior to CAPM estimates for the level of risk inherent in the portfolio. More important, there is tendency for skill to affect period risks. The upside beta (good markets) tends to exceed the downside beta (poor markets) in well-managed portfolios.6 These are important factors to consider in portfolio composition, yet they tend to be ignored.

Three other elements of diversification are important to consider for the manager with forecasting skill. The first is time. With skill, forecasting uncertainties tend to cancel faster over time, if risks are independent. Thus, over immediate periods of five years, for example, there tends to be more assurance of superior results.

Second, diversity of forecasting skill helps reduce risk. If the SML forecast set happens not to be working in one period, perhaps a market momentum, an earnings momentum, or some other model will work. The lower the covariance between sets of forecasts, each made with some forecasting skill, the more assurance the manager has of achieving some positive portfolio benefits in the short run.

Finally, the manager has several ways to make money: security selection, market timing, group rotation, and portfolio tilting. If a manager has several avenues for making money from the skill levels he possesses and if the timing when each skill works best is not perfectly correlated, then the diversity of skills, in themselves, provides opportunities for diversification that will tend to increase the likelihood of positive return/risk benefits over time.

Appropriate diversification, in short, is affected by a number of factors that are not sufficiently considered in current portfolio composition models. Current models are still too closely tied to efficient market theory to provide skillful managers with the kind of concentration that will tend to perfect superior performance in the short and particularly the long run.

CONCLUSION

This paper has taken a different tack. It assumes, on the basis of limited field analysis, that managers do have skill. Moreover, efficient market theory - through SML types of analysis - seems to help managers in security selection and group rotation and in deciding how the dynamics of the market outlook should influence market timing and portfolio tilting.

If managers have skill, why is this not reflected more in portfolioperformance? Evidence suggests that if actuals when regressed against forecasts produce an average coefficient of determination of .02, this level of skill is sufficient to generate significant excess returns. The first problem arises because the use of the word “average” in relation to forecasting skill levels. Considerable variation around the average R* is observable, and variations in skill levels can lead to undesirably erratic portfolio performance.

The first task then is to improve the level and consistency of forecasting skill. This can be done in two ways: (1) by analyzing the strengths and weaknesses of existing forecasts to eliminate bias and distortion, and hence improve the level of skills associated with the forecasts; and (2) by locating supplementary forecasts of value that amplify and diversify forecasting skills. Given some of the inherent limitations of SML analysis, market-momentum models might be a particularly attractive place to search for additional useful information.

The second problem relates to the variablility of forecasting skill across the spectrum of stocks and groups of stocks followed by a firm’s analysts. Some analysts will be quite skillful; others not so skilled. Some may be more skillful in up markets than down markets. And so on. It is important to differentiate the level of skill existing in order to improve selection capability. Intuitively, the forecasts of good security analysts should be given more weight than the forecasts of poor analysts. There are some promising methods emerging that may facilitate this end.

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The next problem relates to composing a portfolio that provides clients with an attractive balance between the expected level of excess returns forecasted and the uncertainty of their delivery. Diversity of skills (stock selection, group rotation, etc.) may help this process. The fundamental question is how much to diversify the portfolio against the composite uncertainties associated with multiplicity of forecasting skills. Both the level of skill and the diversity of skills employed will affect the outcome. Higher levels of skill should lead to more concentrated portfolios and larger, more intelligent bets.

Last, the question of how portfolio risks generated by managers with skill changes over time needs to be explored. If performance risks cancel rapidly, as seems to be the case, a more venturesome portfolio posture may be desirable for many clients.

Research into these critical issues is primarily taking place in the practitioner world. This research is still at an ele- mentary level, however, and the promise of generating insights from methodological attack largely lies ahead.

FOOTNOTES

1. This procedure can also be adapted to forecasting uncertainties. Interestingly, beta proves to be a poor measure of short-term market risk. See Vandell and Finn, “Portfolio Objectives: Win Big, Lose Little!“, Journal of Portfolio Management, Summer 1982.

2. Ri might also be expressed as a risk-adjusted excess return. Chart 2 illustrates some of the problems that this alternative measure can create.

3. Coefficient stability can be improved by scaling actuals and forecasts relative to their means and standard deviation. However, the different dispersion of actuals (larger) and the forecasts must be factored back into the forecast model (4).

4. James L. Farrell, “The Multi Index Model and Practical Portfolio Analysis”, Financial Analysts Research Foun- dation, Occasional Paper 4 (1976) Charlottesville, Virginia.

5. Copyright 1979 by the Sponsors of the Colgate Darden Graduate School of Business, University of Virginia, Box 6550, Charlottesville, Virginia 22906.

6. The reasons for this statement and supporting empirical evidence will be exposited at length in a forthcoming mon- ograph entitled “Optimum Concentration for Skilled Managers in Semi-Efficient Markets”.

76

PERIOD INTERCEPT

(a,>

SLOPE

(bl) R”2

l/74 7.71 2.97 .124 2174 7.36 3.20 .169 3174 7.58 3.07 .172 4174 7.70 3.35 .168 5174 8.17 3.24 .129 6174 8.09 3.30 .121 7174 8.43 3.43 .139 8174 9.29 4.28 .143 9174 11.18 4.41 .187

10174 11.07 3.72 .118 11174 11.26 3.73 .109 12174 11.42 3.78 .082

l/75 12.12 1.73 .040 2175 12.33 1.29 .023 3175 12.90 0.55” .005 4175 13.58 - .89* .ooo 5175 13.31 -.22* .ooo 6175 12.76 0.26* .OOl 7175 13.17 0.05* .ooo 8175 13.70 -.13* .ooo 9175 13.82 0.10” .ooo

10175 14.05 -.36* .002 11175 14.24 -.71* .007 12175 13.83 -.20* .ooo

l/76 12.94 - .22* .OOl 2176 12.00 0.65* .Oll 3176 11.59 0.01 .028 4176 11.59 1.10 .034 5176 11.61 1.28 .040 6176 11.77 1.29 .038

TABLE 1

THE EMPIRICAL SECURITY MARKET LINE (SML):

Period

INTERCEPT

(a,)

SLOPE

(bl) R”2

7/76 11.70 1.21 .036 8/76 11.76 1.21 .036 9176 12.64 0.63” .Oll

lo/76 12.55 0.70* .013 11/76 11.62 1.46 .065 12176 11.47 1.34 .057

l/77 11.33 1.60 .lOl 2177 11.38 1.78 .119 3177 11.59 1.69 .102 4177 12.01 1.34 .085 5177 12.11 1.36 .084 6177 12.18 1.12 .058 7177 12.19 1.27 .067 8177 12.39 1.25 .070 9/77 12.30 1.49 .095

10177 12.47 1.61 .099 11177 12.61 1.31 .062 12177 12.57 1.40 .069

l/78 12.98 1.49 .065 2178 13.29 1.22 .057 3178 13.29 1.30 .061 4/78 13.43 0.72 .021 5/78 13.42 0.67 .106 6178 13.54 0.68 .016 7178 13.59 0.40* .006 8/78 13.61 0.27* .003 9178 13.80 0.23* .002

10178 13.71 1.17 .042

11178 13.60 1.18 .042 12178 13.67 1.22 .040

(1)

*Not statistically significant at the .05 level

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PERIOD

AMERICAN HOME

PRODUCTS ANHEUSER-

BUSCH BALTIMORE

GAS AND ELECTRIC BENEFICIAL

CORPORATION

74-l -2 .oo -1.90 1.60 -0.06 74-2 -2.53 -2.05 1.81 0.68 7 4-3 -2.59 -1.87 2.02 1.65 74-4 -2.67 -2.14 2.89 2.27 74-5 -3.29 -2.66 4.47 1.87 7 4-6 -3.31 -2.85 5.67 1.38 7 4-7 -1.81 -1.82 5.54 1.39 74-8 -2.02 -2.13 4.21 1.99 74-9 -1 .Ol -2.14 4.48 1.25 74-10 -1.95 -2.17 3.70 1.60 74-11 -1.22 -2.10 3.71 0.25 74-12 -1.72 -2.60 4.43 0.36

7 5-l -0.14 -1.91 2.08 0.15 7 5-2 -0.00 -2.58 1.99 1.32 7 5-3 -0.08 -2.35 2.17 2.03 7 5-4 -0 .oo -2.55 2.40 1.61 7 5-5 -0.11 -2 .Ol 2.40 1.16 7 5-6 -0.10 -2.24 1.79 1.15 7 5-7 -0.31 -2.02 2.24 2.13 7 5-8 -0.51 -1.74 1.35 2.05 7 5-9 -0.19 -1.47 1.82 2.05 75-10 -0.44 -1.65 1.80 2.50 75-11 -0.45 -1.71 0.69 1.38 75-12 -0.20 -1.60 1.12 1.87

76-l -0.13 -0.90 0.21 1.18 76-2 -0.13 -0.71 0.35 1.16 76-3 -0.20 -1.31 0.89 1.04 76-4 -0 .Ol -1.28 0.38 1.32 76-5 -0.14 -1.20 0.70 0.72 76-6 -0.29 -1 .Ol 0.61 1 .oo 76-7 -0.12 -1.15 -1.65 0.25 76-8 -0.46 -1.07 -0.37 0.78 76-9 -0.54 -0.99 -0.57 0.95 76-10 -0.59 -0.53 -0.58 1.18

76-11 -0.25 -0.26 -0.30 1.42 76-12 -0.09 -0.85 0.01 0.82

TABLE 2

EXAMPLES OF ALPHAS FOR FOUR COMPANIES 1974 - OCTOBER, 1978

(CONTINUED)

78

PERIOD

AMERICAN HOME

PRODUCTS ANHEUSER-

BUSCH BALTIMORE

GAS AND ELECTRIC

77-l 0.40 -0.77 0.05 77-2 0.05 -0.99 0.24 77-3 0.19 -1.05 0.58 77-4 0.60 -1.12 0.41 77-5 1.01 -1.09 -0.32 77-6 0.41 -1.15 -0.31 77-7 0.54 -1.04 -0.71 77-8 0.30 -1.04 -0.80 77-9 0.63 -0.67 -0.40 77-10 0.71 -0.30 -0.25 77-11 0.71 -0.09 -0.50 77-12 0.69 -0.13 -0.15

78-l 0.50 -0.11 0.38 78-2 0.67 -0.04 0.78 78-3 0.81 -0.69 0.73 78-4 0.57 -1 .Ol 1.03 78-5 0.27 -1.04 0.87 78-6 0.59 -1.45 0.75 78-7 0.15 -1.28 0.30 78-8 0.21 -1.19 0.14 78-9 0.41 -0.60 0.61 78-10 0.90 -1.25 1.18

TABLE 2 (CONTINUED)

EXAMPLES OF ALPHAS FOR FOUR COMPANIES 1974 - OCTOBER , 1978

BENEFICIAL CORPORATION

1.24 1.79 1.91 2.20 2.75 2.13 2.05 3.20 2.77 3.38 3.01 3.36

4.03 3.12 3.55 3.54 3.43 3.09 2.76 2.01 1.81 3.82

NOTE: Alphas may change as the result of:

1) changes in the market price of the stock, 2) changes in the "security market line", 3) changes in analysts' estimates of returns for the stock, or 4) changes in analysts' estimates of risks for the stock, 5) passage of time.

79

PERIOD INTERCEPT

(a,> (b3)

BETA SLOPE (b4) R*3 PERIOD

INTERCEPT (a,)

YIELD SLOPE (b3)

BETA SLOPE (b4) Rs2

l/74 5.17 .610 3.43 .551 7176 9.12 .358 2.28 .231 2174 5.07 .610 3.44 .595 8176 9.13 .368 2.30 .239 3174 5.62 .516 3.25 .563 9/76 8.79 .446 2.52 .257 4174 5.55 .535 3.47 .611 10.76 9.11 .397 2.40 .191 5174 5.65 .577 3.42 .600 11176 9.42 .286 2.44 .199 6174 5.40 ,617 3.48 .643 12176 9.61 .251 2.16 .164 7174 5.97 .531 3.55 .582 l/77 10.21 .149 2.09 .147 8174 5.68 .654 4.55 .681 2177 10.12 .163 2.31 .176 9174 8.60 .427 4.56 .477 3177 10.35 .156 2.23 .151

10/74 6.70 .518 5.26 .511 4177 11.21 .lOO 1.68 .lll 11174 6.53 .551 5.40 .511 5177 11.48 .078 1.63 .098 12174 6.79 .533 5.43 .441 6177 11/32 .lll 1.48 .086

l/75 8.88 .302 3.42 .168 7177 11.18 .129 1.68 .103 2175 8.91 .335 3.07 .182 8177 11.16 .154 1.75 .122 3175 8.92 .381 2.68 .236 9177 11.08 .153 1.97 .149 4175 9.80 .392 1.84 .194 10177 11.08 .173 2.15 .165 5175 9.68 .384 1.85 .196 11177 11.13 .187 1.90 .131 6/75 9.22 .381 2.06 .232 12177 10.98 .197 2.01 .150 7175 10.19 .321 1.61 .139 l/78 11.21 .212 2.15 .147 8175 9.75 .427 1.87 .239 2178 11.66 .186 1.84 .130 9175 9.73 .436 2.12 .238 3178 11.66 ,186 1.92 .132

10175 9.87 .438 1.83 .209 4178 11.41 .229 1.54 .147 11175 10.28 .424 1.39 .197 5178 10.98 .278 1.67 .177 12175 9.82 .434 1.88 .196 6178 10.92 .293 1.74 .202

l/76 10.37 .295 1.16 .104 7178 10.88 .308 1.53 .209 2176 9.36 .349 1.80 .211 8178 10.80 .319 1.46 ,238 3176 8.80 ,348 2.19 .262 9178 11.11 .297 1.40 .204 4176 9 .oo .358 2.17 .245 10178 10.43 .342 2.48 .301 5176 8.73 .393 2.41 .289 11178 10.31 .349 2.47 .315 6176 8.59 .394 2.57 ,328 12178 9.86 .402 2.71 .374

TABLE 3

THE SECURITY MARKET PLANE (SMP):

YIELD SLOPE

*All of the coefficients are significant at the .05 level.

80

TABLE 4

ILLINI TRUST COMPANY

RESULTS OF SIMULATION OF A STABLE 40/60 DEBT/EQUITY ASSET MIX

(1) (2) (3) (4) (5) (6) (7) (8) CUMULATIVE VALUE

OF $1 INVESTED IN QUALITY S&P BOND 500 BALANCED INDEX INDEX PORTFOLIO

TARGET OPENING EQUITY POSITION

RATE OF RETURN CORP. BOND PORTFOLIO

RATE OF RATE OF RETURN RETURN S&P BALANCED 500 INDEX PORTFOLIO QUARTER

-4.89% -2.90% 1.0014 .9511 .9710 -5.77% -3.61% .9980 .8962 .9360

4.81% 3.74% 1.0194 .9393 .9710 -9.16% -5.82% 1.0114 .8533 .9144

1973-1 60% 1973-2 60% 1973-3 60% 1973-4 60%

0.14% -0.34%

2.14% -0.78%

1974-1 60% 1974-2 60% 1974-3 60% 1974-4 60%

-3.50% -5.18% -3.08%

9.30%

-2.82% -3.09% .9760 .8292 .8862 3.18% -0.18% .9254 .8556 .8846

-32.96% -21.06% .8969 .5736 .6983 9.38% 9.35% .9804 .6274 .7635

1975-1 60% 1975-2 60% 1975-3 60% 1975-4 60%

4.75% 3.59%

-3.28% 9.22%

22.94% 15.63% 1.0269 .7713 .8829 15.37% 10.64% 1.0638 .8899 .9768

-10.95% -7.90% 1.0289 .7924 .8997 8.65% 8.87% 1.1238 .8610 .9794

14.97% 10.65% 1.1711 .9899 1.0838 2.48% 1.60% 1.1746 1.0144 1.1011 1.92% 3.37% 1.2400 1.0339 1.1382 3.14% 4.88% 1.333 1.0613 1.1938

1976-1 60% 1976-2 60% 1976-3 60% 1976-4 60%

4.21% 0.30% 5.57% 7.52%

1977-1 60% 1977-2 60% 1977-3 60% 1977-4 60%

-2.31% 3.86% 1.09%

-0.82%

-7.44% -5.40% 1.3025 .9870 1.1293 3.32% 3.54% 1.3527 1.0198 1.1693

-2.82% -1.26% 1.3675 .9918 1.1545 -0.13% -0.41% 1.3563 .9897 1.1498

1978-1 60% 1978-2 60%

-4.12% -0.40%

-5.00% -4.65% 1.3004 .9402 1.0963 8.40% 4.90% 1.2952 1.0192 1.1500

81

(1)

QUARTER

(2) EXPECTED

EQUITY RETURN S&P 500 INDEX

(3) (4) (5) (6)

AA BOND RISK PREMIUM ADJUSTED EQUITY INTEREST RATE EQUITY RISK PREMIUM TARGET

197 3-1 9.75% 7.43% 2.32% 2.12% 0% 1973-2 10.13% 7.53% 2.60% 2.40% 0% 1973-3 10.47% 7.59% 2.88% 2.68% 5% 1973-4 10.65% 7.96% 2.69% 2.49% 0%

1974-1 11.03% 7.91% 3.12% 2.92% 11% 1974-2 11.47% 8.13% 3.34% 2.14% 0% 1974-3 11.72% 8.54% 2.18% 2.92% 11% 1974-4 14.54% 9.08% 5.46% 5.46% 74%

1975-1 15.44% 9.01% 6.43% 6.63% 100% 1975-2 13.94% 8.88% 5.06% 5.26% 69% 1975-3 13.30% 8.80% 4.50% 4.70% 55% 1975-4 14.23% 8.96% 5.27% 5.47% 74%

1976-1 14.06% 8.80% 5.26% 5.46% 74% 1976-2 13.47% 8.34% 5.13% 5.23% 68% 1976-3 13.60% 8.52% 5.08% 5.08% 65% 1976-4 13.73% 8.09% 5.64% 5.84% 84%

1977-1 13.86% 7.94% 5.92% 6.12% 91% 1977-2 14.32% 8.00% 6.32% 6.32% 96% 1977-3 14.48% 7.96% 6.52% 6.52% 100% 1977-4 14.79% 7.90% 6.89% 6.69% 100%

1978-1 15.05% 8.30% 6.75% 6.55% 100% 1978-2 15.69% 8.73% 6.96% 6.76% 100% 1978-3 15.26% 8.93% 6.33% 6.13% 91%

TABLE 5


DETERMINATION OF RISK PREMIUMS AND TARGET EQUITY COMMITMENTS JANUARY, 1973 TO JULY, 1978

S = Stable Interest Rates Expected R= Rising Interest Rates Expected F = Falling Interest Rates Expected

82

QUARTER

OPENING SIMULATED EQUITY RATE OF RETURN POSITION ON PORTFOLIO

1973-1 40.0% 1973-2 40.0% 1973-3 42.0% 1973-4 40.0%

1974-1 44.4% 1974-2 40.0% 1974-3 44.4% 1974-4 69.6%

1975-1 80.0% 1975-2 67.6% 1975-3 62.0% 1975-4 69.6%

1976-1 69.6% 1976-2 67.2% 1976-3 66.0% 1976-4 73.6%

1977-1 76.4% 1977-2 78.4% 1977-3 80.0% 1977-4 80.0%

1978-1 80.0% 1978-2 80.0%

TABLE 6


SIMULATED PORTFOLIO RESULTS USING MR. GRANE'S ASSET-MIX STRATEGY

JANUARY, 1973 - JUNE, 1978

CUMULATIVE VALUE OF $1 INVESTED

-1.88% .9812 -2.54% .9563

3.24% .9873 -4.18% .9461

-3.23% .9155 -1.85% .8985

-16.56% .7497 9.30% .8194

19.17% .9765 11.49% 1.0887 -8.10% 1.0005

8.82% 1.0887

11.66% 1.2156 1.75% 1.2369 3.10% 1.2752 4.27% 1.3297

-6.25% 1.2466 3.42% 1.2892

-2.04% 1.2629 -0.28% 1.2595

-4.83% 1.1987 6.60% 1.2779

83

BIOGRAPHY

Robert F Vandell; Charles C. Abbott Professor, Darden Graduate School of Business Administration, University of Virginia; B.S. Yale University 1950; MBA and DBA Harvard Business School of 1952, 1957; formerly on faculties of Harvard Business School and IMEDE. Formerly Research Director, Financial Analysts Research Foundation; au- thor: several books and many academic and business papers; advisor to pension funds with assets of $3.5 billion. Principal, Management Analysts Center, Inc. (consulting); officer various academic financial associations.

84

journal of technical analysis (jota). issue 15 (1983, may)

Economy & Finance