,. |'I ... , 3;”; 5&5 v gv ’- ”4ft. , 9%,”. *‘ Tb." ., .-.‘l— I :97 :32: ' ‘ff‘ ! m EMPIRICAL EVALUATION? ». . THE RELATiONSHiP BETWEENE‘RRORS . : j * m ANALYSTS’ FORECASTS‘GF EARNINGS _ I pm SHARE AN-DSIOCK PRICES ' M W t“ W 0? Ph 9 :~;i:-,5ifié;'?-S:t - V mm mm: UNWERSEW .- 3 1293 10100 5159 , LIBRARY Michigan Sm: Umvcrsi .-.=_ _ . " .5 _. This is to certify that the 'a thesis entitled AN EMPIRICAL EVALUATION OF THE RELATIONSHIP BETWEEN ERRORS IN ANALYSTS' FORECASTS OF EARNINGS PER SHARE AND STOCK PRICES presented by Paul Andrew J anell has been accepted towards fulfillment of the requirements for Ph.D Business — Accounting degree in flag/”W Major professor 1 3'0 74 Date I 3/. 0-7639 ABSTRACT AN EMPIRICAL EVALUATION OF THE RELATIONSHIP BETWEEN ERRORS IN ANALYSTS' FORECASTS OF EARNINGS PER SHARE AND STOCK PRICES BY Paul Andrew Janell The purpose of this research was to examine the rela— tionship between errors in analysts' forecasts of earnings per share and subsequent stock price changes and, thereby, provide empirical evidence as to the utility of these forecasts. A second area for consideration was an assess— ment of the effectiveness of revisions in these forecasts made over a period of time. It has been established, both theoretically and empirically, that a strong association exists between earnings and stock prices. Previous empirical work demonstrates that an apprOpriate methodology for the assessment of the utility of an event is the observation of subsequent stock price reactions to that event. This study examined the relationship between errors in analysts' forecasts and subsequent stock price returns, Paul Andrew Janell adjusted for market effects. Analysts' forecasts were obtained from the Standard and Poor's Earnings Forecaster. Fifty firms in 1970 and fifty firms in 1971 were randomly selected from the relevant population. In establishing the utility of analysts' forecasts it must be shown that the relationship between errors in analysts' projections of earnings and subsequent stock price returns is statistically greater than can be found between forecasts made by other models and stock price returns. Thus, six naive forecast models were selected to provide projections which would serve as a control group. The results of this study are reported in two sec— tions. The first section presents the results of two preliminary test statistics which describe the predictive accuracy of the forecast models included in the study. Several conclusions were drawn from this aspect of the study. First, it was shown that as the forecast horizon was reduced, the mean prediction errors decreased for both the analysts' forecasts and the projections made by the naive models. Secondly, it was noted that analysts tended to be overoptimistic since approximately 70% of their forecasts were overpredictions. The Wilcoxon signed— rank test was then employed to test whether differences in Paul Andrew Janell accuracy of the forecast models were statistically sig- nificant. The best naive model yielded lower forecast errors than analysts in 1970 but greater errors in 1971, although neither difference was statistically significant. The second part of the study presents the results concerning the utility of the forecasts as perceived by investors. The Spearman rank correlation coefficient was utilized to measure the relationship between errors in the forecasts and subsequent cumulative stock return residuals. At the .05 level of significance it was found that two of the three annual naive models did not differ significantly in their association with stock price returns than did errors in the analysts' estimates. The conclusion drawn, therefore, was that analysts' projections do not have greater utility for investors than do forecasts generated by simple naive forecast models. It was also found at the .05 level of significance that there was no statistical difference in the associa— tion between errors in the analysts' annual forecasts and subsequent stock price returns than existed between errors in the analysts' revisions and the cumulative stock price returns. The conclusion drawn was that the analysts' revisions were not perceived to possess greater utility Paul Andrew Janell than the analysts' annual forecasts. These conclusions imply that the cost incurred by analysts in the preparation and dissemination of their forecasts is not justified in terms of the utility derived by the market. AN EMPIRICAL EVALUATION OF THE RELATIONSHIP BETWEEN ERRORS IN ANALYSTS' FORECASTS OF EARNINGS PER SHARE AND STOCK PRICES BY Paul Andrew Janell A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting and Financial Administration 1974 0010/3) COpyright by PAUL ANDREW JANELL 19 74 ACKNOWLEDGMENTS This author is indebted to many people for their contributions that resulted in the completion of this research and the doctoral program. First, I express my appreciation to the members of my dissertation committee, Dr. Roland F. Salmonson (Chairman), Dr. Melvin C. O'Connor, and Dr. Maryellen McSweeney for their invaluable sugges- tions and encouragement in completing this dissertation. Two other faculty members at Michigan State Univer- sity offered helpful suggestions for this research. They are Dr. Alden C. Olson and Dr. Daniel W. Collins. To Dr. Gardner M. Jones, Chairman of the Department of Accounting and Financial Administration, I express my thanks for the guidance and assistance that aided in com- pletion of the doctoral program. I am indebted to Merrill Lynch, Pierce, Fenner and Smith Inc. for supplying some of the data necessary for thistresearch. I am also indebted to Josephine McKenzie for her expert typing of this thesis. iii To my parents, Albert and Catherine Janell, and to the parents of my wife, Sebastino and Adeline Lemmo, I express my sincere appreciation for their love and encouragement throughout my academic career. And to my wife, Mary, without whom this research would never have been accomplished. I will forever be indebted to Mary for her typing the many rough drafts of this dissertation and her love and encouragement through— out the doctoral program. And to my sons, ”P.J.", and Craig Steven, whom have been the purpose for all my efforts. iv TABLE OF CONTENTS ACKNOWLEDGMENTS. . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . Chapter I INTRODUCTION. . . . . . . . . . . . . . . Purpose of the Research . . . . . . . Significance of Earnings in Investor Expectation Models . . . . . . . . . . Associations of Earnings and Stock Prices . . . . . . . . . . . . . Approach and Organization of the Study . . . . . . . . . . . . . II REVIEW OF EXISTING LITERATURE CONCERNING ANALYSTS' FORECASTS OF EARNINGS PER SHARE. . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . Survey of the Literature Concerning the Reliability and Accuracy of Analysts' Forecasts of Earnings. . . . . . . . . Survey of the Literature Concerning the Accuracy of Analysts' Estimates of Earnings Per Share and Stock Prices. Summary . . . . . . . . . . . . . . . . III HYPOTHESES AND METHODOLOGY. . . . . . Introduction. . . . . . . . . . . . . . Theoretical Considerations. . . . . . . General Research Hypotheses . . . . Research Hypothesis-l . . . . . . . Research Hypothesis—2 . . . . . . . Research Hypothesis-3 . . . . . . . V Page iii viii 12 12 13 21 32 38 38 39 46 46 48 50 Chapter Page Methodology . . . . . . . . . . . . . . . 51 POpulation Criteria. . . . . . . . . . 51 Sample Selection Criteria and Procedures. . . . . . . . . . . . . . 52 Selection of Naive Forecasting Models. . . . . . . . . . . . . . . . 53 Identification of Actual Earnings Per Share and Their Announcement Dates . . . . . . . . . . . . . . . . 57 The Market Model . . . . . . . . . . . 58 Evidence Supporting the Use of the Market Model. . . . . . . . . . . . . 66 Preliminary Descriptive Test Statistics. . . . . . . . . . . . . . 66 Statistical Hypotheses and Tests. . . . . 69 Research Hypothesis-l . . . . . . . . 69 Research Hypothesis-2 . . . . . . . . 73 Research Hypothesis—3 . . . . . . . . 75 The Level of Significance . . . . . . . . 78 Limitations of the Methodology. . . . . . 79 Summary . . . . . . . . . . . . . . . . . 80 IV RESULTS OF THE STATISTICAL TESTS. . . . . . 88 Introduction. . . . . . . . . . . . . . . 88 Results of the Preliminary Descriptive Test Statistics. . . . . . . . . . . . . 88 Results of the Wilcoxon—Signed Rank Tests . . . . . . . . . . . . . . . 107 Results of the Statistical Test Concerning the First Research Hypothesis . . . . . . . . . . . . . . . 119 Results of the Statistical Test Concerning the Second Research Hypothesis . . . . . . . . . . . . . . . 124 Results of the Statistical Test Concerning the Third Research Hypothesis . . . . . . . . . . . . . . . 128 Summary . . . . . . . . . . . . . . . . . 131 Appendix A Spearman Rank Correlation Coefficients for the Forecast Models for 1970 and 1971. . . . . . . . . . . . 135 vi Chapter V SUMMARY, CONCLUSIONS, IMPLICATIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH Summary . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . Implications of the Empirical Results. . . . . . . . . . . . . . Recommendations for Further Research . . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . vii Page 141 141 143 147 149 151 Table LIST OF TABLES Relative Prediction Errors (|A-F|/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over-And-Underpredictions by Years for Naive Model #1. . . . . . . . . . . Relative Prediction Errors (IA-FI/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over-And—Underpredictions by Years for Naive Model #2. . . . . . . . . . Relative Prediction Errors (lA-F|/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over—And-Underpredictions by Years for Naive Model #3. . . . . . . . . . . Relative Prediction Errors (IA-FI/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over—And—Underpredictions by Years for Naive Model #4. . . . . . . . . . . Relative Prediction Errors (IA-FI/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over-And-Underpredictions by Years for Naive Model #5. . . . . . . . . . . Relative Prediction Errors (IA—FI/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over—And-Underpredictions by Years for Naive Model #6. . . . . . . . . . . viii Page 91 92 93 94 95 96 Table Page 7 Relative Prediction Errors (|A-F|/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over-And-Underpredictions by Years for Analysts' Annual Predictions. . . . . . . 97 8 Relative Prediction Errors (|A-Fl/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over-And-Underpredictions by Years for Analysts' First Quarterly Revision. . . . 98 9 Relative Prediction Errors (|A-F|/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over—And-Underpredictions by Years for Analysts' Second Quarterly Revision . . . 99 10 Relative Prediction Errors (lA-FI/F) Classified by Range of Relative Errors, Mean Relative Error, and Distribution of Over-And—Underpredictions by Years for Analysts' Third Quarterly Revision. . . . 100 11 Summary of the Relative Predictive Accuracy of the Naive Forecast Models and Analysts' Forecast for the Period 1970-1971. . . . . . . . . . . 101 12 Mean and Adjusted Mean Prediction Errors Normalized by Price (IA-Fl/P) for the Years 1970 and 1971 . . . . . . . . . . . . . 105 13 Results of the Wilcoxon Signed-Rank Test Comparing Naive Forecast Models for 1970 and 1971 Utilizing lA-FI/F and IA-FI/P as Measures of Predictive Accuracy . . . . . . . 109 14 Results of the Wilcoxon Signed—Rank Test Comparing Analysts' Annual Forecasts with Analysts' Quarterly Revised Forecasts for 1970 and 1971 Utilizing lA-Fl/F and |A~F|/P as Measures of Predictive Accuracy. . . . . . 111 ix Table 15 16 17 18 19 20 21 Results of the Wilcoxon Signed-Rank Test Comparing Analysts' Annual Forecast Models with the Annual Naive Forecast Models for 1970 and 1971 Utilizing lA-FI/F and lA-Fl/P as Measures of Predictive Accuracy. . . . . Results of the Wilcoxon Signed-Rank Test Comparing Analysts' Quarterly Revised Forecasts with the Naive Quarterly Fore- cast Models for 1970 and 1971 Utilizing |A-F|/F and |A-F|/P as Measures of Predictive Accuracy . . . . . . . . . . . . Spearman Rank Correlation Coefficients for the Annual Forecast Models. . . . . . . Significance Levels for Rejection of the First Research Hypothesis . . . . . . . . . Spearman Rank Correlation Coefficients for Analysts' Forecasts . . . . . . . . . . Spearman Rank Correlation Coefficients for the Interim Forecast Models . . . . . . Significance Levels for Rejection of the Third Research Hypothesis . . . . . . . . . Spearman Rank Correlation Coefficients for the Annual Forecast Models for 1970 and 1971 . . . . . . . . . . . . . . . Spearman Rank Correlation Coefficients for the Analysts' Forecasts for 1970 and 1971 . . . . . . . . . . . . . . . Spearman Rank Correlation Coefficients for the Interim Forecast Models for 1970 and 1971 . . . . . . . . . . . . . . . Page 113 114 122 122 127 130 130 136 136 138 CHAPTER I INTRODUCTION Purpose of the Research It has been fairly well—established in the financial literature that a strong relationship exists between earn- ings and stock prices.1 Because of this relationship, a considerable amount of effort in the investment community has been devoted to the prediction of earnings per share. This can be evidenced by the many publications which recommend various stocks to buy—and-sell. These recom— mendations are substantially supported by projections of the firm's earnings.2 Recently, academic researchers have begun to examine the accuracy of analysts' projections of earnings per share and have raised several questions. How accurate are these forecasts of earnings? Does the accuracy of these forecasts influence investor decisions? Is the accuracy of these forecasts such that it justifies the lFootnotes appear at the end of each chapter. 1 2 cost of their preparation and dissemination? Will inaccu— rate forecasts be ignored by investors, or will they mis- lead investors and increase the volatility of stock prices and disrupt the allocative efficiency of the stock market? The present research was directed primarily at deter— mining whether an association exists between analysts' forcasts of earnings per share and stock prices. If investors do utilize analysts' projections then their reactions to the forecasts can be ascertained by an exam- ination of subsequent stock price movements. Specifically, stock price changes were related to forecast errors over a period of time. However, it is not sufficient to merely determine that an association between analysts' forecasts of EPS and stock prices exists. Since analysts devote a signifi- cant amount of time in preparation of these forecasts there is a substantial cost attached to them. To justify this cost, there should be a significantly greater association between analysts' forecasts and stock prices than between alternative forecast models, which are obtainable at a lesser cost, and stock prices. One method of examining this "cost-benefit" question is to compare the analysts' predictions with naive forecast models to determine which is more highly associated with stock prices, since 3 forecasts from naive models can be Obtained at a relatively negligible cost. This "cost-benefit" analysis represents a second primary area of this research. A third, but no less important, area for considera— tion in this research was an investigation of the improve- ment of the forecasting accuracy of analysts and any in- creased association between analysts' estimates and stock prices as the forecasting horizon is reduced. The purpose was to ascertain how effective the analysts' revisions are over time. Significance of Earnings in Investor Expectation Models Cohen and Zinbarg, authors of a well-known investment text have stated that: Common stock has value for only three pos- sible reasons. First, the ownership of common stock confers a claim to a corpora- tions' net income. This claim bears fruit when the corporation's board of directors declares dividends. Second, if the corpo- ration enjoys growing success, earnings and dividends will rise, and the price of the stock may rise also. The third, and least significant, source of common stock value is that if a corporation is liqui— dated, the common stock owner has a pro rata claim to any asset value that may remain after all creditors and preferred stockholders have been paid. The third reason is only of significance when a cor- poration is about to be liquidated. Since most investors 4 are concerned with investing in corporations that are going concerns, they will be most interested in dividend payments and price appreciation of their stock. Thus, according to Cohen and Zinbarg the two factors that give stock value are earnings and dividends. Latane' and Tuttle offer a similar explanation. A stock's value is thought of as based on the present value of the future stream of payments to be received either by the company (earnings) or from the company's earnings stream by the stockholder (cash dividends).4 Theoretically, it is the cash payment (cash dividends) that give stock value. However, without earnings there would be no dividends. Since dividends are a function of earnings, authors of investment texts have suggested the use of earnings rather than dividends in various invest- ment models. Bolten points out: ...dividends tend to lag earnings, in many cases, by relatively long and un— predictable lengths of time, and the direct forecasting of dividends over the infinite time horizon of a stock is often very difficult and inaccurate. Nearer term earnings estimates, however, imply an expected dividend stream;....5 Latane' and Tuttle state: ...Since dividend payout rate is so vari— able and non-comparable, and since divi— dends seem to be related to the more 5 comparable earnings figures, we shall concentrate on earnings, because a growing earnings trend must eventually result in an increased stream of divi— dend payments to the investor.6 An even stronger case for the use of earnings in investor models has been made by Modigliani and Miller. They assert that, given the investment decision of the firm, the dividend pay- out ratio is a mere detail. It does not affect the wealth of shareholders. M.M. argue that the value of the firm is deter- mined solely by the earning power on the firm's assets or its investment policy and that the manner in which the earnings stream is split between dividends and retained earnings does not affect this value.7 The above excerpts from financial literature confirm the importance of earnings in investor expectation models. To come to firm conclusions regarding the outlook for a particular security investors must employ estimates of future earnings as inputs to their models. One obvious source of these inputs are projections of earnings per share provided by professional security analysts. A priori, one could, therefore, expect that analysts' estimates of earnings per share are a potential source of valuable information to investors.8 6 Associations of Earnings and Stock Prices To assess whether analysts' projections do in fact furnish information to investors, an operational defini- tion of information must be provided. Beaver9 has shown that the information content of an event can be ascertained by observing the stock price adjustment to the announcement of that event. In the context of the present study, if an event (i.e. analysts' projections) changes the expecta— tions of investors such that it leads to a change in the equilibrium price of the stock, that event is said to possess information content. In the previous section of this chapter the theoret- ical importance of earnings in investor expectation models was established. It remains to be demonstrated that in the real world earnings themselves possess information content. Beaver examined this issue by observing stock price and volume reaction to 506 earnings announcements. He concluded: ...The behavior of the price changes uni— formly supports the contention that earn— ings reports possess information content. Observing a price reaction as well as a volume reaction indicates that not only are expectations of individual investors altered by the earnings report but also the expectations of the market as a whole, as reflected in the changes in equilibrium prices.10 7 Ball and Brown have also investigated the markets' reaction to accounting income numbers and concluded: Of all the information about an indi- vidual firm which becomes available during a year, one—half or more is captured in that year's income number. Its content is therefore considerable.ll Both of the above studies indicate that earnings do have information content in the sense that the market re- acts (as measured by price changes) to the income numbers. Further evidence between the association of earnings and stock prices, although in a more indirect way, has been provided in several studies by Latane' and Tuttle. In one of their research efforts they computed growth rates for several variables during the period 1956—66 for 68 industries and then calculated intercorrelations among the variables. Commenting on the results they state: /\-« / Perhaps the most significant (relation— ship) is the high correlation of growth in prices with earnings and Operating profits growth as well as the high cor- relation between these latter two mea— sures of earnings. This relationship between price growth and earnings growth is at the heart of security analysis and explains why security analysts spend such a large part of their time trying to forecast earnings.12 The above excerpt not only gives support to the con— tention that stock prices and earnings are contemporane- ously related but also some credence as to why analysts' 8 forecasts of earnings and stock prices should also be related. Such a relationship is the underlying foundation for the present research. Additional support has also been provided by Ball and Brown, who were earlier quoted as saying that the current income number has considerable content. They further state: However, the annual income report does not rate highly as a timely medium, since most of its content (about 85 to 90 percent) is captured by more prompt media which perhaps include interim reports. Since the efficiency of the capital market is largely determined by the adequacy of its data sources, we do not find it disconcerting that the mar— ket has turned to other sources which can be acted upon more promptly than annual net income ....... This study raises several issues for further investigation. For example, there remains the task of identifying the media by which the market is able to anticipate net income ..... 13 It seems plausible to hypothesize that one possible medium by which the market is able to anticipate earnings would be analysts' projections of net income. Approach and Orggnization of the Study The approach of this study was to first obtain analysts' predictions of earnings per share from the Standard and Poor's "Earnings Forecaster." For each 9 firm included in the study, monthly abnormal returns were computed from the forecast date through the month that actual earnings were announced. Then the associa- tion between the analysts' forecast errors and stock return residuals was established. The study also in- cluded a comparison of naive models with the analysts' forecasts and assessed the cost and benefits of each. Finally, an investigation of the effect of revisions in the analysts' forecasts was performed. Chapter II contains a review of the literature dealing with analysts' projections of earnings per share. This review is concerned with the available empirical evidence on the accuracy of analysts' forecasts and their association with stock prices. Chapter III contains a detailed discussion of the hypotheses to be tested, the data used, and the method— ology employed. A theoretical discussion of the method— ology utilized is also presented. Chapter IV contains a discussion of the findings of the study. The hypotheses are restated and the evidence with which to accept or reject these hypotheses is also presented. Finally, Chapter V contains a brief summary of the study, lists the major conclusions, and presents several recommendations for future areas of study. 10 FOOTNOTES 1The empirical evidence demonstrating that a strong relationship exists between earnings and stock prices is discussed in the third section of this chapter. 2Many investment research firms and research divi— sions of brokerage firms (e.g., Shearson, Hammil & Co., Inc., Merrill Lynch, Pierce, Fenner and Smith, Bache & Co., to name a few) publish lists of stocks to buy, hold, or sell. Often, their recommendations are supported by their estimates of future earnings per share for the firm in question. 3Cohen, Jerome B., and Zinbarg, Edward D., Investment Analysis and Portfolio Management, Homewood, Illinois: Richard D. Irwin, Inc., 1968, p. 260. 4Latane', Henry A., and Tuttle, Donald L., Security Analysis and Portfolio Management, New York, New York: The Ronald Press Company, 1970, p. 270. 5 . Bolten, Steven E., Security Analysis and Portfolio Management, New York, N.Y.: Holt, Rinehart and Winston, Inc., 1972. 6Latane' and Tuttle, op. cit., pp. 277-8. 7Van Horne, James C., Financial Management and Policy, Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1971, p. 245. 8This statement, of course, is a primary issue underlying this research project. 9Beaver, William H. "The Information Content of Annual Earnings Announcements," Empirical Research in Accounting: Selected Studies, 1968, a supplement to Volume VI of The Journal of Accounting_Research, p. 68. lOIbid., p. 82. 11Ball, Ray and Brown, Philip, "An Empirical Evalu- ation of Accounting Income Numbers," Journal of Accounting Research, VI (Autumn, 1968), p. 176. ll 12 , . Latane and Tuttle, Op. c1t., p. 385. 13Ball and Brown, 92, cit., pp. 176—7. CHAPTER II REVIEW OF EXISTING LITERATURE CONCERNING ANALYSTS' FORECASTS OF EARNINGS PER SHARE Introduction The literature pertaining to analysts' projections of earnings per share can be classified into two principal categories: 1. Research focusing on the accuracy of analysts' estimates of earnings. For the most part this research is concerned with the comparison of analysts' projections with estimates computed using various naive or mechanical forecasting models. 2. Research concerned with the accuracy of analysts' forecasts of earnings and the relationship of the forecasts with stock prices. The studies to be reviewed and falling under the above categories are of an empirical rather than a theo— retical nature. Since these works possess varying degrees of similarity to the present study, they will be explicated in considerable detail. 12 13 Survey of the Literature Concerning the Reliability and Accuracy of Analysts' Forecasts of Earnings One of the first studies dealing with the analysis of earnings predictions was conducted by Cragg and Malkiel.1 Their research examined the expected growth of earnings per share for 185 corporations as of the end of 1962 and 1963. The data for these corporations were collected from five investment firms and consisted of an average annual rate of growth expected to occur for each of the 185 sample firms}2 Cragg and Malkiel indicated that each of the five participating firms was trying to predict the same growth rate, specifically ”the long—run average ("normalized") earnings level, abstracting from cyclical or special circumstances."3 Although each participating firm may have a somewhat different perception of growth and how it should be calculated, Cragg and Malkiel con— tended that any such differences among the participating firms did not appear to show up in the predicted growth 4 Furthermore, the growth rates provided by the rates. investment firms were given as point estimates and no confidence intervals surrounding these estimates were provided. Cragg and Malkiel were primarily interested in deter— mining the degree of agreement among the five investment 14 firms in their predictions of expected growth rates as well as determining the accuracy of these predictions. A review of the results of the relevant aspects of their study will be presented below. By use of an intercorrelation matrix, Cragg and Malkiel demonstrated that considerable agreement existed among the investment firms in their growth-rate predic- tions. Kendall's coefficient of concordance for ranks of companies by different predictors was .79 for 1963. How- ever, Cragg and Malkiel recommend some caution in inter- preting the statistic by stating that ”...the lack of agreement it also reveals can hardly be considered negligible."5 Decomposition of the correlation coefficients into two components indicated that agreement concerning industry growth was not the major factor in accounting for the agreement in predictions among the participating firms. Further testing provided some evidence that certain industry groups (oil and cyclicals) were more difficult to forecast than other groups (electric utilities) in the ex ante sense. The extent of agreement among the predicting firms was also examined by a comparison of the predicted growth rates of earnings. This analysis revealed that the 15 predictions of 1963 were highly correlated with those of 1962. Finally, Cragg and Malkiel correlated the forecasted growth rates with P/E ratios. Actually, they used the in- verse of the P/E ratios as surrogates for market—expected growth rates. Although the correlations presented were generally high, they also demonstrated a degree of dis- parity among the forecasting firms. The second aspect of their study was concerned with the accuracy of the predictions made by the five investment firms. However, in assessing the abilities of the fore— casters, Cragg and Malkiel encountered a major difficulty in that the five years for which the projections were made had not yet elapsed. Thus, they used the realized growth of actual and normalized earnings (as estimated by firms 1 and 2) through 1965.6 The methods of evaluation utilized by the authors were "simple correlations and the inequality coefficient, U2 = (Pi - Ri)2 T— (l) 1 where Pi is the predicted and Ri the realized growth rates for the ith company. It will be noticed that the inequal— ity coefficient, in effect, gives a comparison between perfect prediction (U2=O) and a naive prediction of zero 16 growth for all corporations (U2=1)."7 Note, however, that an underprediction would appear to be superior to an overprediction of the same magni- tude. This can be illustrated by the use of the following example: P R Case 1 6% 4% Case 2 4% 6% Both cases have an absolute forecast error of 2%” Using equation (1) and solving for U2, case 1 would have a U2=.25 whereas, case 2 would have a U2=.ll. Thus, the use of the inequality coefficient leads to a bias, which is impossible to assess without an indication of the number of over—and-under—predictions. Commenting on the results of the over—all accuracy of the forecasts, Cragg and Malkiel state: First, the forecasts based on perceived past growth rates, including even growth over the most recent year, do not per- form much differently from the predic— tions. There seems to be no clear—cut forecasting advantage to the careful and involved procedures our predictors employed over their perceptions of past growth rates either in terms of correla— tion or of the inequality coefficient.8 By reference to "their perceptions of past growth rates" Cragg and Malkiel are referring to historic growth rates provided by the participating firms themselves. As a final step of their study, Cragg and Malkiel 17 examined the forecasting ability of several naive models based on historic data. The findings indicated that the investment firms did not have significantly superior ability in forecasting. In concluding, the authors state that: ...the careful estimates of the security analysts participating in our survey, the bases of which are not limited to public information perform little better than these past growth rates. We must be cautious, however, in over- generalizing these results. We did not have data to investigate directly whether the performance of the predictions of growth in the period considered were atypical of the usual forecasting abilities of such forecasts. The question is impor- tant, however, since it can be argued that the peculiarities of the expansion that occurred after the date of the forecasts made the period especially difficult to forecast. Moreover, our work is hampered by the fact that only a few firms were able to participate in our survey. It may also be that shorter-term earnings predictions are considerably more successful relative to naive forecasting methods.9 In evaluating and comparing Cragg and Malkiel's work to the present study several points should be emphasized. First, they dealt with predicted growth rates of earnings over a five year period, whereas the present study em- ployed forecasts of earnings per share for a one—year period. This eliminated the difficulties of dealing with growth rates and the problem that the period had not 18 entirely elapsed when comparisons were made. Secondly, the effect of revisions in the forecasts was examined. A final distinction is that Cragg and Malkiel did not directly relate the forecasts to stock price changes, a procedure which is of central importance to the present study. A second empirical research effort dealing with the accuracy of analysts' estimates was conducted by Edwin J. Elton and Martin J. Gruber.lo The purpose of this research was to test the performance of alternative mechanical fore- casting techniques in predicting earnings per share and to compare the results of these models with predictions made by security analysts. Nine mechanical techniques, which were variations of exponentially weighted moving averages, naive models, simple moving averages, and re- gressions, were employed in their project. Analysts' estimates were obtained from a large pension fund, an investment advisory service, and a large brokerage house. The mechanical forecasting techniques were "used to estimate earnings for the period 1962-67 on a stratified random sample of 180 firms selected from the Standard and n 11 one I two ' and three-year fore‘ Poor's Compustat Tape. casts were made. The majority of the article was devoted to a l9 discussion of these mechanical forecasting techniques in terms of their prOperties and predictive accuracy. To evaluate the accuracy of the forecasts two methods were employed: (1) The square of the forecast error (i.e. (actual - forecast)2)12 and (2) a variation of the standard error of estimate in the form: _ 2 13 U — 2i (actuali — forecasti) 2i (actuali)2 First, the accuracy of the nine mechanical forecast- ing techniques for a one—year period was examined. The results indicated that the additive exponential with no 14 trend in trend out performed every other technique at a l15 was statistically significant level. The naive mode outperformed by only three of the four exponential models, but even for these only the additive exponential with no trend in trend exhibited a statistically significant dif- ference and this was at the 10% level of significance. In comparing the performance of the mechanical tech— niques to the analysts' forecasts, the performance was measured for only those firms common to the participating firms and the random sample, and covered the period 1964— 66. Actually, only the additive exponential model was used in the comparison. Commenting on their results, Elton and Gruber state: 20 The average data show that the best mech— anical technique outperforms the security analysts at one financial institution, but is outperformed by the analysts at two others. However, none of the three differ— ences is significant at even the 20%.leve1.... In short, there is no statistically signifi— cant evidence to indicate that the forecasts made by analysts are different from those made by an exponentially weighted moving average employing an additive trend. In- sofar, as better forecasts lead to better valuation models, the lack of such evidence would seem to indicate that mechanical tech- niques exist which can provide valid inputs to financial models and that these techniques (given their low cost) should be employed at least as a bench mark against which to judge analysts' performance.l6 Although the results of Elton and Grubers' study appear to somewhat discredit analysts' performance, three points should be noted. First, two of the firms did per— form better than the mechanical model. Next, one must question whether the method of evaluation utilized was appropriate (see footnote 12). Finally, in a footnote, the authors, themselves, issue the following caveat: One must exercise care in generalizing these results, since, to the extent that the superior performance of the additive exponential was peculiar to our sample, the results may be biased against the analysts' performance.17 Elton and Grubers' study is somewhat more comparable to the present study in that analysts' projections of earnings were compared to a mechanical forecasting 21 technique. The results are interesting and were useful in selecting mechanical forecasting techniques utilized for comparative purposes in the present study. However, there are some notable differences between Elton and Gruber's research and the present research effort. First, a broader group of analysts' estimates was utilized. Secondly, revisions in forecasts were examined. Lastly, forecast errors were related to stock prices. Both of the above studies discuss the accuracy of analysts' estimates but fail to relate these predictions to subsequent stock price changes. The next section of this chapter reviews several studies that relate analysts forecasts and stock prices. Survey of the Literature Concerning the Accuracy of Analysts' Estimates of Earnings Per Share and Stock Prices Richard W. McEnally18 employed a sample of 100 com— panies to evaluate the usefulness of earnings estimates in selecting common stocks. Earnings estimates for the year ended 12/31/66 were obtained from the three leading investment advisory services. McEnally examined several investment strategies that could be used as models for testing the usefulness of the earnings estimates. The first strategy examined was one 22 that advocates buying stocks that sell for a low price— earnings ratio. To test the validity of this P/E model, the author divided the 100 firms into 5 portfolios of 20 stocks each on the basis of the ratio of April 1 prices to e.p.s. for the same year. This was done for the five year period 1961—1965. The results indicate that purchase of the lowest P/E stocks, Portfolio 1, would have yielded the highest returns, 38% before commissions, while the pur— chase of the highest P/E stocks, Portfolio 5, would have yielded the lowest returns. To insure that the results were not due to the fact that low P/E stocks perform better, McEnally repeated the study using historical rather than future earnings per share. Few meaningful differences were found between the portfolios.19 The second investment strategy organized the 100 stocks into five portfolios on the basis of the magnitude of current years' earnings appreciation (i.e. Portfolio 1 consists of the 20 stocks having the highest ratio of Cur- rent Year's Earnings/Prior Year's Earnings). The results of this experiment indicated that Portfolio 1 would have had an average annual compounded rate of return of approxi- mately 43% while Portfolio 5 would have declined about 7% 23 in value. The above tests manifest the importance of the poten- tial use of earnings estimates as well as demonstrating the strong relationship between earnings and stock prices. In order to examine the usefulness of earnings esti- mates the above tests were repeated substituting the mean of the investment advisory firms' estimates for actual earnings for the April 1, 1966—March l, 1967 period. The results showed an absence of any pattern in the returns among the different portfolios. The author presents and discusses several reasons why the earnings estimates did not prove meaningful. First, the investment strategies may have been inapprOpriate. However, this was quickly dismissed since it was demon— strated that the two strategies could differentiate be— tween the weak and strong performing stocks. Secondly, the earnings estimates may not have been useful since they were poor approximations of actual earnings. McEnally states, however, that the earnings estimates were quite close to actual earnings. Finally, the esti— mates of 1966 could have been representative of investor expectations and, thus, the stock prices on April 1, 1966 fully discounted the expected earnings changes. Although McEnally's results may seem to conclusively 24 demonstrate the uselessness of earnings estimates, caution must be exercised in evaluating and generalizing these re— sults. It was not stated whether the sample was selected randomly or not. Thus, the results may be peculiar to these particular companies. Also, the study investigated earnings estimates for one year only, 1966, which may again limit the generalizations of McEnally's results. McEnally did not employ any statistical tests, thus, it is possible that some of the differences he found could have occurred by chance. This fact is somewhat substantiated by the fact that in one of the tests Portfolio 2 performed better than Portfolio 1, which McEnally rationalized by examining the performance of two of the companies contained in Portfolio 1. But perhaps, the results he did achieve could have been eXplained by a similar rationalization. Another notable deficiency in his study was a lack of adequate control. No attempt was made to control for general market effects, or control the level of risk among the different portfolios. Finally, the use of price- earnings ratios may be justifiably questioned since P/E ratios are affected by several variables.20 There are also notable differences between McEnally's study and the present research. The present study ex— amined the relationship of stock prices and forecast 25 errors over time. In investigating this issue general market effects were removed from the stock prices. Secondly, analysts' estimates were compared to estimates provided by naive models. A final important distinction was that the present study also examined the effect of revisions in the forecasts on subsequent stock price changes. A second study relating earnings forecasts and stock prices was done by Victor Niederhoffer and Patrick J. Regan.21 The purpose of this research was to provide some empirical evidence to support the hypothesis that stock price fluctuations are closely associated with changes in earnings. For their study, Niederhoffer and Regan selected the 50 best and 50 worst price performers on the NYSE for 1970. A random sample of 100 firms also selected from the NYSE served as a control group. Earnings projections were obtained from the 3/31/70 edition of Standard and Poor's ”Earnings Forecaster." In the cases where more than one prediction was provided for a company the authors arbitrarily chose the estimate of the institution with the largest number of forecasts in the "Earnings Forecaster.”22 Eight stocks were rejected from the original top 50 and 17 from the bottom 50 because the authors limited the study to only those firms with 26 23 fiscal years ending between September and February. To evaluate the earnings changes and forecasting errors the authors normalized the data by price. This was primarily done because of the many companies which had small or negative earnings making the use of percentage changes misleading. The following three variables were computed for each company: (1) F - Al P = estimated earnings change per dollar of price ———————-= actual earnings change per dollar of price -—————- = error in forecast per dollar of price where A1 1969 actual earnings per share A2 1970 actual earnings per share 1970 forecasted earnings per share 1969 year-end stock price24 A non—parametric discriminant analysis was utilized to contrast the tOp 50, random 100, and bottom 50. Report— ing on the results of the distribution of actual earnings changes per dollar of price (equation 2) Neiderhoffer and Regan state: ...for all companies with actual earnings gains of four cents or more per dollar of price, the odds were 14 to one that the company would finish in the top 50 rather than in the random 100, with virtually no 27 chance of ending up in the bottom 50. But for earnings losses of eight cents or more,25 the odds were 20 to one that the stock would land in the bottom 50 rather than in the random 100. In this case, there was no chance of finishing in the tOp 50. A similar phenomenon emerged in the distribution of forecasting errors, .... we can see that when the forecast was overestimated by eight cents or more per dollar of price, the odds were nearly 17 to one that the stock would finish in the bottom 50 rather than in the random 100. At the other extreme, an underestimate of one cent or more per dollar of price almost guaranteed that the stock would finish in the top 50 rather than in the random 100, since the chances were 24 out of 25.26 But the table does seem to vindicate the analysts' position as seers, since half of the estimates for the 100 random stocks were within one cent (normalized) of actual earnings and two- thirds were within two cents.27,28 Considerable caution should also be exercised in assessing and generalizing the results of this study. Only forecasts for 1970 were subjected to analysis, which limits the generalizations of the study to that particular year. Many will agree that 1970 was an atypical year, one in which the stock market suffered a dramatic drOp as evi— denced by the dip in the Dow Jones Industrial Average to 631.16.29 In such a year as 1970 corporations also have the tendency to increase expenses since net income will probably be below expectations at any rate. In this way corporations shift expenses into one year so future years' 28 reported incomes will be increased. These deficiencies could have been partially allevi— ated by removing general market effects from the stock prices and associating the estimates with these residual returns, a procedure that was utilized in the present study. Nevertheless, Niederhoffer and Regan do confirm the fact that a strong relationship exists between earn— ings changes and stock prices. The final work to be reviewed in this chapter is an unpublished paper completed at Portland State University by Richard H. Gassner and Roger D. Williams.30 They selected 100 firms, not on a random basis, and examined the relationship of stock returns to changes in analysts' weekly estimates. The source for these forecasts was the 1967 edition of the Standard and Poor's "Earnings Fore- caster". Two separate models were use to detect significant changes in analysts' estimates. The first model was designated the mean relative change model (MR), since it was based upon a change in the mean of the analysts' projections of earnings per share. For their analysis, only changes considered as significant, arbitrarily set at 5%.or more, were utilized. Using the MR model, returns, or price relatives, were computed for various holding 29 periods. For example, if there was a mean change in the analysts' estimate of e.p.s.;5%.the stock was "purchased and held" for a given holding period (e.g. one week, 2 weeks, 3 weeks, or 6 months). Then a return was computed by dividing the initial price of the stock into the price at the end of the holding period. The second model utilized in the analysis was called the cluster model. A cluster was defined as a group of estimates which had a boundary of plus or minus one standard deviation around the mean. In order for a signal to be produced for this model an analyst's estimate first had to be within the cluster and then move out of the cluster. To evaluate the results of these models two measures were utilized (1) the standard deviation of returns, em— ployed as a surrogate for risk and (2) a control index of performance. This control index was similar to an index developed by Fisher and, in fact, employed the same weighting factors as did Fisher. However, the index was not a market index since it was constructed only for the stocks employed in the study.31 The authors summarize the overall results of their study as follows: 30 In general, the results of the study were not as significant as was hoped, although the results could be generally classed as encouraging and warranting further research. The central prOblem is one of a lack of consistency in the results. Although both models produced impressive returns for selected condi- tions, few patterns of returns or con- sistency of upward and downward signals were produced. The mean relative change model produced annualized percentage returns after commissions for most of the weekly holding periods in excess of the returns for the control index. The returns on the 100 stock sample for the 6—month holding period were slightly below the control index. In general the standard deviations were of the same magnitude for both the up and down signals over the shorter holding periods. However, for the 6 month holding period the standard deviation was significantly greater. With regard to the mean relative change model Gassner and Williams state: Although certain specific results of the mean relative change model as discussed above seem promising, it should be care— fully noted that the model as applied here does not clearly distinguish between up- ward and downward signals, i.e., positive results were indicated by both upward and downward changes. This factor does not necessarily mean that the model has no value, but it should point out that these results should be carefully interpreted and considered at best as promising results and thus indicative of a need for further research.33 31 In general, the cluster model did not perform as well as the mean relative change model. There were no partic- ular patterns of results and "there was little distinction between upward and downward signals as predictors of price movement."34 There are several limitations of this study that the authors acknowledged. Since the data base was not ran- domly selected and the study covered only one time period, the generalizations of this study are limited. The method- ology is also limited in that only week by week changes were examined, "whereas, the changes that may be signifi— cant may occur slowly over a long period of time".35 Another limitation is that the control index and the results of the model are not strictly comparable because they were not compared at the same level of risk. There are some other limitations that the authors failed to acknowledge. Since no statistical tests were employed it is difficult to assess whether any of the results would have been significant in a statistical sense. Secondly, the price relatives did not include any dividend payments. This may not be too serious since dividends were also absent in the control index. Finally, the methodology utilized did not adequately control for general market effects since the control index was not a 32 market index. In spite of these limitations, this research effort indicates that analysts' estimates of earnings per share may be useful in some investor valuation models and the relationship between analysts' projections and stock price changes warrants further research. In the present study this relationship was examined from a different perspec— tive and with a different methodology. Summary This chapter has reviewed previous works dealing with the accuracy of analysts' estimates and the attempts made to relate them to stock price changes. These studies do confirm that there is a strong relationship between earnings and stock prices. However, there is some contradictory evidence regard- ing the usefulness and accuracy of analysts' estimates. On one hand, Gassner and William's project and Niederhoffer and Regan's study provide some evidence that analysts' forecasts of earnings per share are meaningful data for investors. On the other hand, it was also demonstrated that certain mechanical forecasting techniques may be as good at predicting earnings as are security analysts. Because of certain deficiencies and limitations of these 33 studies, such evidence is not conclusive. In the present study an attempt was made to remove these weaknesses, and, thereby establish conclusively the relationship that exists between analysts' forecasts and stock prices. The present research effort (1) examined the associ- ation between analysts' estimates and stock prices from a different perspective and with a different methodology (2) incorporated several aspects of the previous studies into one study (3) improved upon the previous works by removing some of their deficiencies and limitations and (4) investigated some areas that have previously been unexplored. 34 FOOTNOTES lCragg, J. G. and Malkiel, Burton G., "The Consensus and Accuracy of Some Predictions of the Growth of Corpo— rate Earnings," Journal of Finance (March, 1968), pp. 67— 84. 2Actually only two of the five participating firms could provide data for all of the 185 sample corporations. 3Ibid., p. 68. 4It should be noted that any bias introduced by the way the participating firms calculated expected growth rates is indeed difficult to assess. Thus, one can not say how such differences in calculations would affect the results of their study. 5Cragg and Malkiel, op. cit., p. 71. 6Although the authors logically argue that since the firms are predicting normalized earnings, the use of an estimate of normalized earnings may be a valid standard of comparison, such a procedure certainly detracts from the conclusions of the study. 7Cragg and Malkiel, op. cit., p. 76. 81bid., p. 77. 91bid.. pp. 83—84. 10Elton, Edwin J. and Gruber, Martin J., "Earnings Estimates and the Accuracy of Expectational Data," Management Science, Vol. 18, No. 8 (April, 1972) Appli- cation Series, pp. B409-B429. lllbid., p. B—414. 12Note that this method weights differences of the same magnitude equally. Thus, an error of 20¢ per share would be given equal weight regardless of whether the difference originated from actual e.p.s. of $2.00 and a forecast of $1.80 or from actual e.p.s. of $.40 and a forecast of $.20. However, there could be a wide dis- parity in terms of percentage error as the foregoing 35 example illustrates. Because of such a disparity the results of the study must be interpreted with a great deal of caution. 13Note that this equation is the same as Cragg and Malkiel's inequality coefficient, which was discussed earlier, and is, thus, subject to the same bias. Because of these biases, the conclusions of this study are suspect. l4An additive trend effect means that earnings per share are expected to grow at a constant amount per year. The term "no trend in trend" indicates that there is no trend in this growth rate for this model. 15The naive model utilized in this study was of the following form: Et, T = Et + (Et - Et_l). This equation states that estimated earnings are equal to earnings of the prior period plus the prior change that had occurred in earnings. 16Elton and Gruber, 0p. cit., p. B—419. l7 lEiQ-I p. B—4l9, footnote 26. 18McEnally, Richard W., "Using Earnings Estimates in Selecting Common Stocks," Trusts and Estates, Volume 109 (January, 1970), pp. 35-38. 19It should be noted that there is some evidence to support the fact that low P/E stocks perform better than high P/E stocks. The reader is referred to Nicholson, S. Francis, "Price Ratios in Relation to Investment Results," Financial Analysts Journal, Volume 24, No. l (January-February 1968), pp. 105—109. 20The price-earnings ratio is a shorthand formulation of the present discount valuation (PDV) model. The PDV model discounts dividends (or earnings) at a particular discount rate r. Theoretically, the PDV model considers dividends (or earnings), their expected growth, and the discount factor r, which is composed of interest rate risk, purchasing power risk, business risk, and financial risk. For a further discussion see Bolten, Steven E., Op. cit., Chapter III, pp. 39—48. 36 21Niederhoffer, Victor and Regan, Patrick J., "Earning Changes, Analysts' Forecasts and Stock Prices," Financial Analysts Journal, Volume 28, No. 3 (May—June 1972), pp. 65-71. 22Upon review of the "Earnings Forecaster" for a period of some 26 months (including 1970) it is this writer's Opinion that the institution providing the greatest number of forecasts is, in fact, Standard and Poor's. If this Observation is correct then Niederhoffer and Regan are testing Standard and Poor's Forecasts rather than a representative sample of security analysts. 23It is possible that the elimination of these 25 firms could have biased the results of this study. Furthermore, since the companies were limited to those With fiscal year ends between September and February and the authors did not separately disclose the results by length of forecast (i.eq 6 months, 7 months, etc.), an additional bias of unknown dimension detracts from the results of this study. 24Another potential bias in this study relates to the use of the 1969 year-end stock price for two reasons. First, the price could have been unusually high or low at that time. Secondly, since the forecasts were selected from the March 31, 1970 "Earnings Forecaster" it would seem that a more current price or a recent months' average should be used so as to reflect the events transpiring up to that time. 25It is interesting to note that 86% of the tOp 50, 98%.of the random 100, and 80% of the bottom 50 had earnings changes within + $.04 and -$.08 limits discussed by the authors. 26It is also interesting to note that 100%.of the bottom 50 companies, 79% of the random 100 companies and only 11.4% of the top 50 companies were characterized by overestimates. 27These percentages are difficult to assess because of the method of computation, as well as, the potential bias that exists in this methodology. See footnote 24. 28Niederhoffer and Regan, op. cit., pp. 70-71. 37 29This was the lowest point since 1962. 3OGassner, Richard H., and Williams, Roger D., "The Relationship Between Changes in Analysts' Earnings Per Share Estimates and Ensuing Price Movements for Individual Stocks." Unpublished paper, Portland State University, 1969. 31The use of the same weighting factors as Fisher may be somewhat inapprOpriate in this case since Fisher developed a market index to be used as a standard of com- parison for long periods of time. Fisher states that over shorter periods of time the results of his index are somewhat erratic and have a downward bias. See Fisher, Lawrence. "Some New Stock Market Indices," Journal of Business, Volume 34 (Supplement, January, 1966), pp. 226-41, especially page 201. 32Gassner and Williams, Op. Cit, p. 21. 33Ibid., p. 21 and 25. 34Ibid., p. 25. 35Ibid., p. 34. CHAPTER III HY POTHESES AND METHODOLOGY Introduction Chapter III is concerned with three major tOpics. First, the theoretical considerations that provide the foundation for the research hypotheses tested and the methodology utilized are presented. Second, the general research hypotheses concerning the association of forecasts and stock prices are set forth. Finally, the methodo- logical structure of the research is presented. This structure included an identification of the pOpulation of firms under study, a description of the sample selection criteria and procedures, a discussion of the selection of the naive forecasting models, and a development of the model utilized to abstract market—wide effects from stock returns. This section also included a discussion of some preliminary descriptive test statistics as well as the statistical hypotheses and statistical tests utilized in this study. The chapter concludes with a discussion of the limitations of this methodological structure. 38 39 jgheoretical Considerations In Chapter I the theoretical importance of earnings :in investor expectation models was established. That cihapter also contained a brief discussion of empirical srtudies made by Beaverl and Ball and Brown2 which sub~ sirantiated the contemporaneous association of stock (pr:ices and earnings data. Because these two studies were iristrumental in establishing a theoretical construct and £1 slalid research methodology for investigating investor acijldstment to new information, this section of Chapter III vviJ_1 present a more detailed discussion of these research efforts . Beaver examined both price changes and the physical ‘Kiltune of securities traded associated with the announce- merrt n by defining the information content of a event to be . at stock price adjustment to that particular event. 40 Beaver hypothesized that if the earnings report had information content then the stock price adjustment during the week of the earnings announcement would be larger than in other weeks. To test this hypothesis some method was required to abstract out effects which were not related to the earnings announcement but, nevertheless, might cause a change in stock prices. To abstract from market—wide events that tend to affect all stock prices, Beaver employed the following linear regression model: . . A 4 Rjt ’ ajt + bjt Rmt + ejt where: Rjt = the return of security j for week t ajt' bjt = regreSSion parameters that vary from security to secu- rity and relate past security returns to market returns. Rmt = the return on a market index for week t. éjt the residual return for firm j in week t. Since the residual return (éjt) reflects events unique to a particular firm, Beaver analyzed the behavior of the éjt during the week of the earnings announcement as well as the behavior of these éjt for several weeks both before and after the earnings announcement. Beaver pre— dicted that the éjt during the week of the earnings announcement would be greater than for non—report weeks. 41 Based on the results Obtained from this test, he con— cluded that "the behavior of price changes uniformly supports the contention that earnings reports possess information content."5 With respect to the present study, Beaver's research effort is very significant. First, he has demonstrated that earnings reports possess information which leads to a change in the equilibrium value of the current market price of the securities. This result confirms the fact that a strong contemporaneous relationship exists between earnings and stock prices. Furthermore, his research pro- vides support for the utilization of the market model as a means of abstracting market—wide effects from a secu- rity's total return. A second study that also investigated the information content of annual earnings reports, but from a different perspective than Beaver, was the pioneering effort of Ball and Brown. In their study they were concerned with both the content and the timing of earnings reports. They contend that: An empirical evaluation of accounting in- come numbers requires agreement as to what real—world outcomes constitute an appro- priate test of usefulness. Because net income is a number of particular interest to investors, the outcome we use as a predictive criterion is the investment 42 decision as it is reflected in secu- rity prices. Both the content and timing of existing annual net income numbers will be evaluated since use- fulness could be impaired by defici- encies in either.6 The authors examined a total of 261 firms over the period 1957-1965 and constructed "two alternative models of what the market expects income to be and then investi— gate(d) the market's reactions when its expectations prove(d) false".7 The first model was constructed by regressing each firm's income on the average of all firms' income in the market. The expected income change for a particular firm was "then given by the regression prediction using the change in the average income for the '8 The difference between the actual and ex- market...‘ pected income change was defined as the forecast error. It was this forecast error, or unexpected income change, which the authors assumed to represent the information to be conveyed by the income number. The second model constructed was a simple naive model which predicted that income for the current year would be the same as that of the previous year. Ball and Brown elected to use the investment deci— sion as it is reflected in security prices as their pre- dictive criterion. Their choice was justified by both 43 theory and empirical evidence as they indicated in their study: Recent developments in capital theory provide justification for selecting the behavior of security prices as an Oper— ational test of usefulness. An impres— sive body of theory supports the proposi- tion that capital markets are both effi- cient and unbiased in that if information is useful in forming capital asset prices, then the market will adjust asset prices to that information quickly and without leaving any opportunity for further abnormal gain. If, as the evidence indicates security prices do in fact adjust rapidly to new information as it becomes available, then changes in security prices will reflect the flow of information to the market. An Ob— served revision of stock prices associ— ated with the release of the income report would thus provide evidence that the infor— mation reflected in income numbers is use— ful.9 To examine the stock price adjustments to the infor- mation conveyed by the income forecast errors, Ball and Brown had to first abstract the market-wide effects from each security's overall return. Like Beaver, they employed the market model to abstract from these effects and to obtain a measure of the return attributable to each specific security. These stock return residuals were computed for each firm and for each month for a period of 11 months prior to the month of the earnings announce— ment. The importance of these residual returns is 44 conveyed by the following statement: ...since the market has been found to adjust quickly and efficiently to new information, the residual must repre— sent the impact of new information, about firm j alone, on the return from holding common stock in firm j.lO Next the authors separated their sample of firms into two categories according to the sign of the forecast error. Firms that had positive forecast errors (i.e. actual earnings > predicted earnings) were designated as good news firms and those with negative forecast errors (i.e. actual earnings < predicted earnings) were desig— nated as bad news firms. Ball and Brown hypothesized that the firms with posi— tive forecast errors should have positive stock return residuals and the firms with negative forecast errors should have negative stock return residuals. The ration- ale supporting this hypothesis assumes that investors utilize the authors' models to form expectations about earnings and also act according to these expectations in establishing an equilibrium price for each security. For the good news firms investors will gradually realize that their predictions of earnings were underestimated and, 11 thus, will act to bid the price of these stocks up (more precisely it is the residual return that should 45 increase). A similar reaction but in the Opposite direc- tion should occur for the firm conveying bad news. To test this hypothesis a chi—square statistic for a two-by—two classification by sign of forecast error and sign of stock residual was computed. The results of their study indicate not only that earnings numbers possess information content but also that most of this information was anticipated prior to the earnings announcement date. However, the authors did not investigate what media the market was utilizing to anticipate the information con- tained in the annual income number. The significance of Ball and Brown's study is three- fold. First, it confirms Beaver's results by also demon- strating that earnings reports do possess information con— tent. Secondly, it provides additional support for the utilization of the market model as a valid method of abstracting market—wide effects from the overall return of a security. Finally, it suggests the existence of other media by which investors are able to anticipate the information conveyed by the annual earnings report. 46 General Research Hypotheses Research Hypothesis-l The previous section of this chapter has demonstrated that a valid predictive criterion for examining the use— fulness of an event (e.g. the announcement of earnings reports) is the investment decision as it is reflected in security prices. Beaver has utilized this criterion to show that annual earnings reports cause significant changes in stock prices in the week of their announcement relative to stock price adjustments in other weeks. Ball and Brown's research also utilized this criterion to confirm Beaver's results. They further demonstrated that much of the information content of these earnings reports is anticipated by the market prior to their actual release. However, the media utilized by the market to anticipate the annual income numbers were not established. As stated in Chapter I it seems plausible to hypothe- size that one possible medium by which the market is able to anticipate earnings would be analysts' projections of net income. Since professional security analysts devote a considerable amount of time in developing their projec— tions, it is reasonable to assume that these forecasts are worthwhile. If analysts' forecasts of earnings per share do 47 possess information content (in the operational sense as utilized by Beaver and by Ball and Brown), then stock price adjustments should be associated with errors in these fore— casts. Furthermore, since there is a substantial cost in preparing these forecasts, a priori, it is expected that there would be a greater degree of association be- tween analysts' forecasts and stock prices than between forecasts made by some naive model (with a relatively negligible cost) and stock prices. A comparison of projections provided by security analysts and predictions generated from naive models was made in the present study. This comparison was somewhat akin to a cost—benefit analysis. However, since the costs and benefits of each prediction method were not fully assessed, a complete cost—benefit analysis was not made. In this study benefits were assessed by the associ— ation between forecasts (more specifically, forecast errors) and stock return residuals. Thus, it was assumed the greater the association, the greater the benefits. Also, no attempt was made to determine the exact cost of the earnings projections. Rather, it was assumed that forecasts generated from the naive models examined in this study were Obtained at a lesser cost than forecasts provided by the analysts. Because of these restrictions 48 on the cost—benefit analysis, conclusive results are forthcoming only if the forecasts generated by the naive models have the greatest association with the stock return residuals. The first hypothesis of this study dealt with the issue of cost—benefit analysis in the limited sense as described above. The hypothesis concerned with the asso— ciation between stock price returns and errors in fore- casts iS: . l . . Null HypotheSis, HO: The assoc1ation that exists between errors in analysts' forecasts of earnings per share and stock price returns does not differ from the association that exists between forecast errors generated by selected naive models and stock price returns. Alternative Hypothesis, Hi: The association that exists between errors in analysts' forecasts of earnings per share and stock price returns lg greater than the associ- ation that exists between forecast errors generated by selected naive models and stock price returns. Research Hypothesis—2 The first research hypothesis was concerned with the association between stock price returns and errors in fore- casts of earnings per share which were made at a time when 49 only the previous year's earnings data were available. Generally, this meant that at the time the forecasts were made there were nine to ten months remaining in a firm's fiscal year. However, as the year progresses many events may occur that cause such forecasts to become outdated and unrealistic. One such event is the issuance of the cor— porations' quarterly earnings reports. If any of these events (including the quarterly earnings reports) possess information content, then in- vestors will revise the inputs to their expectation models and act accordingly, which will result in stock price adjustments. Analysts will also react to these events by revising their forecasts. It is, therefore, reasonable to expect that errors in such revisions should have a greater association with stock price returns than errors in the analysts' original forecasts made at a time when only the previous years earnings were known. Specifically, errors in annual analysts' forecasts were compared to errors in analysts' predictions made after the quarterly earnings reports were published. The statement of the hypothesis contrasting annual analysts' forecasts and analysts' revised forecasts is: Null Hypothesis, Hg: The association that exists between errors in annual analysts' 50 forecasts of earnings per share and stock price returns does not differ from the association that exists between errors in analysts' quarterly re— vised forecasts and stock price returns. Alternative Hypothesis, Hi: The association that exists between errors in analysts' quarterly re- vised forecasts and stock price returns is greater than the association that exists between errors in annual analysts' fore- casts of earnings per share and stock price returns. Research Hypothesis-3 As mentioned above, one primary event that may pro- vide additional information about expected earnings per share is the issuance of quarterly earnings reports. These interim reports not only allow analysts the Oppor- tunity to revise their forecasts but also furnish addi— tional data that could be used in various naive models. The final research hypothesis of this study is concerned with a comparison of errors in analysts' forecasts revised on a quarterly basis to naive models employing quarterly earnings data. This final hypothesis is: Null Hypothesis, Hg: The association that exists between errors in analysts' quarterly revised forecasts of 51 earnings per share and stock price returns does not differ from the asso- ciation that exists be— tween forecast errors generated by selected quarterly naive models and stock price returns. Alternative Hypothesis, Hi: The association that exists between errors in analysts' quarterly re— vised forecasts of earn- ings per share and stock price returns is greater than the association that exists between forecast errors generated by selected quarterly naive models and stock price returns. Methodology ngulation Criteria The population of firms considered in this research met the following criteria: 1. The firms appear in the 1970 and 1971 editions of Standard and Poor's Earnings Forecaster. The firms are listed on the New YOrk Stock Exchange (NYSE), except for firms leaving the NYSE because of delisting, merging, or listing on other exchanges. The firms have a fiscal year-end on December 31. The firms meeting the first three criteria have a minimum of three analysts' estimates per month for at least ten months prior to the announce— ment of the annual earnings by the corporation in the Earnings Forecaster. 52 The Standard and Poor's Earnings Forecaster12 was selected as a data base because it provides a broad com- pilation of analysts' forecasts made by leading Wall Street researchers on over 1800 leading corporations. Over sixty investment, research, and/or brokerage firms contribute their forecasts to this publication. Criteria two and three were imposed to put the firms on a comparable basis with regard to the time horizon of the forecasts, to facilitate the data collection proce- dures, and to facilitate the hypotheses testing. Criterion four was imposed to give added validity to the analysts' forecasts. A mean of the analysts' esti- mates was computed and it was assumed in the present study that this mean estimate was a valid representation of the analysts' eXpectations regarding the earnings. The utilization of the above criteria limited the pOpulation of firms to 296 in 1970 and to 251 in 1971. Sample Selection Criteria and Procedures From the relevant population described above, fifty firms in 1970 and fifty firms in 1971 were randomly 13 selected using a table of random numbers. For each firm selected the following additional criterion had to be met. 1. At a minimum, sixty months of price data prior to the month of forecast must have been available. 53 This criterion was imposed to assure that sufficient observations were available for the market model, which was employed to abstract the general market effects from a security's overall return. Selection of Naive Forecasting Models The primary criteria utilized in the selection of naive forecasting models were (1) their ability to gener— ate accurate forecasts according to previous testing, (2) ease of computation, and (3) ease of data collection. All of the models selected are capable of generating fore- casts at a minimum of cost, thus, insuring that they could be widely used by any investor. After a review of the pertinent literature the following models were selected for inclusion in the present study. Model 1. The current year's earnings per share (EPS) is equal to the prior year's earnings per share. Mathematically, this forecast is computed as follows: EPSt = EPS where t = the current year t—l Model 2. The current year's earnings per share is equal to the previous year's earnings per share plus any change that occurred from the year before. Mathematically, this forecast is computed as follows: EPSt = EPSt_l + (EPSt_l - EPSt_2) or EPS where t = the EPS = 2(EPSt_1) - t_2 current year t 54 Model 3. The current year's earnings per share is equal to the previous year's earnings times the percentage change in earnings per share from the year before. Mathe- matically, this forecast is computed as follows: or EPst = EPSt_1 x (EPSt_1/EPSt_2) _ 2 = EPSt — (EPSt_l) /EPSt_2 where t the current year The association of forecast errors from these models and stock price returns was compared in this study with the association between errors in analysts' forecasts of earnings per share and stock price returns. All three of the annual naive forecast models were used by COpeland and Marionil4 who tested them against forecasts made by corporate executives. Of these three models, model 1 exhibited the best predictive accuracy in terms of the lowest total relative and absolute errors, summed and averaged, over the sample of firms employed in their study. However, as these models were only tested for the prediction of 1968 earnings per share, the results of Copeland and Marioni's study may well be peculiar to this particular year. There appears to be some indirect evidence that this might be the case. 15 Elton and Gruber conducted a study, which was 55 reviewed in Chapter II, that evaluated the predictive accuracy of several mechanical forecasting techniques. Their results demonstrate that their naive model was out- performed by only three of the four exponential models evaluated; but even for these exponential models only the additive exponential with no trend in trend was superior to the naive model in terms of a statistically signifi- cant difference, and this was at the 10% level of signifi- cance. The naive model employed by Elton and Gruber was equivalent to model 2 of the present study. Since Copeland and Marioni found that model 1 was superior to model 2, one can infer that either the results of the two works are peculiar to the years Observed, or that the difference between model 1 and the more SOphisticated exponential models may be minor.16 The association between forecast errors derived from three additional naive forecast models was compared with the association between errors in analysts' quarterly revised forecasts and stock price returns. These models were designated as the quarterly naive forecast models, since they utilized quarterly earnings per share data. These quarterly naive forecast models are listed below: Model 4. Earnings per share of the current year equals four times the first quarter earnings per share of the current year. Model 5. Model 6. 56 Mathematically, this forecast is com- puted as follows: EPS = 4 EPS t ( tql) where: t = the current year ql = the first quarter Earnings per share of the current year equals two times the combined earnings per share of the first two quarters of the current year. Mathematically, this forecast is computed as follows: EPS = 2(EPS t ) + EPS tql tq2) where: t = the current year ql the first quarter q2 = the second quarter Earnings per share of the current year equals four-thirds times the sum of the first three quarters of earnings per share of the current year. Mathe- matically, this forecast is computed as follows: = + + EPSt 4/3 (EPStql EPStq2 EPStq3' where: t = the current year ql = the first quarter q2 the second quarter q3 the third quarter Of the above three quarterly naive forecast models, only model 4 was evaluated by COpeland and Marioni. They concluded that of the six naive models they evaluated, model 4 was the superior predictor in terms of the lowest total relative and absolute errors. Models 5 and 6 were formulated so that comparisons could also be made with analysts' revisions made when second and third quarter 57 earnings reports were available. Identification of Actual Earnings Per Share and Their Announcement Dates Actual annual and quarterly earnings per share data and their announcement dates were obtained from the W311 Street Journal Index. The annual earnings per share were also verified against the actual earnings reported in the Standard and Poor's Earnings Forecaster. On the rare occasions when either the annual or quarterly earnings per share data were not reported in the Wall Street Journal Index, these data were Obtained from either the Standard and Poor's Earnings Forecaster or the Standard and Poor's Stock Market Reports.17 Where necessary appropriate adjustments were made in the earnings data to reflect stock splits and stock dividends. It was necessary to obtain the earnings announcement dates to assure that the analysts could have had access to the actual reported earnings of the previous year prior to forming their estimates of current year's earnings per share. Analysts' estimates made at the end of the month of the earnings announcement were selected for inclusion in this study. In this way the analysts' predictions and the forecasts generated by the naive models comprised the same time horizon. Consider the following example: 58 1969 EPS 1970 EPS Date Amount Date Amounp Firm A 2/12/70 2.00 1/28/71 2.30 Firm B 3/ 5/70 4.00 3/ 8/71 3.80 For firm A actual 1969 EPS was reported in February 1970, whereas the actual 1969 EPS for firm B was reported in March of 1970. Thus, the analysts' projections made at the end of February 1970 for firm A and the analysts' projections made at the end of March 1970 for firm B would be utilized in the present study. The purpose of this procedure was to put the naive forecast models and the analysts' forecasts on a comparable time-period basis so that investors would have had the Opportunity to apply either the naive models or the analysts' forecasts in obtaining inputs for their particular stock price models. The earnings announcement dates also dictated the period over which the stock return residuals were computed. For firm A, stock return residuals would be computed for each month beginning with March 1970 and terminating with January 1971. On the other hand, the stock return resid— uals for firm B would be computed for each month beginning with April 1970 and terminating with March 1971. The Market Model In the first section of this chapter the theoretical considerations underlying the information content of an 59 event were discussed. It was asserted that an apprOpri— ate predictive criterion for establishing the usefulness of an event was the investment decision as it is reflected in security prices, since they adjust rapidly to new in— formation as it becomes available. Thus, an observed revision in stock prices to the release of some event suggests the utility of that particular event. It was also stated that the market model was an apprOpriate specification of the process generating indi- vidual security returns. This model asserts that secu— rity returns are a linear function of a general market factor. Empirical support of this model was established in a study by King18 who demonstrated that stock prices and, thus, rates of returns of holding stocks tend to move together. He established that over the period from March 1944 through December 1960 that approximately 30 to 40 per cent of the variability in a stock's monthly rate of return could be related to market—wide effects. He also demonstrated that for the same period approxi— mately 10 per cent of the variability in a stock's monthly rate of return could be accounted for by industry effects. Thus, a security's overall return is a result of three main factors: The first is common to all 60 securities and is known as the market effect; the second is common to particular industries and is called the industry effect; and the third factor is unique to each specific security and is designated as the residual effect (or residual return). It is this residual return that is of special significance in establishing the information content of an event. The significance of this residual return is substantiated by Ball and Brown who state that: Since the market has been found to adjust quickly and efficiently to new informa— tion, the residual must represent the im- pact of new information, about firm j alone, on the return from holding common stock in firm j. Thus, to ascertain whether an event possesses infor— mation content, it was necessary to abstract from the market—wide effects and concentrate on the effects unique to the firm. The industry effect was not removed from a security's overall return because the amount of vari— ability accounted for by the industry effect relative to the market effect was believed to be minor. Specifically, the increase in precision by removal of the industry effect does not outweigh the cost of data-gathering and computational problems. Furthermore, Ball and Brown refer to a study by Blume20 which suggests that the industry effects could be somewhat less than the 10% found by King. 61 The market model was the method utilized in the present study to abstract the market-wide effects from the individual security's return. This model is of the form: Rjt where: jt where: A jt A A R + e. (1) + . bjt mt jt the return of firm j in month t and is equal to mt Pjt + Djt -121 P j, t—l — the closing price per share of firm j at the end of month t, the cash dividend paid per share of firm j in month t that the share went ex-dividend, the closing price at the end of month t-l, adjusted for stock splits and stock dividends, - the regression parameters that vary from security to security which relate past changes in a security's price to past changes in the market index. Bjt has a special meaning since it mea- sures the response of a security's return to the overall market's return and "it serves as a relative measure of the risk of holding the ith security."23 the return of the market index in month t and is equal to: (SP)t 24 -l (SP)t—l 62 where: SP = the closing value of Standard and t , . Poor 3 Price Index at the end of month t, SPt_1 = the closing value of Standard and Poor's Price Index at the end of month t-l, éjt = the residual return in month t and incorpo— rates the effects unique to the firm. The error term (ejt) is assumed to satisfy the assumptions of a linear regression model. That is, l. éjt has zero expectation. 2. The variance of éjt is constant over time. 3. The ejt are serially independent. The residual return (ejt) is equal to the overall return of a security less the return attributable to market-wide events, which can be represented in equation form as follows: ejt = Rjt ‘ ajt ‘ bjt Rmt (2) Equation (2) is not a strict transformation of equa- A t' bjt) are tion (1) since the regression coefficients (aj estimated from time periods that differ from the period in which the effect of the unique factor (éjt) is being studied. For example, in computing the residual term (éjt) for each month in 1970, five years of monthly price data terminating with December 1969 were used in the 63 linear regression model to Obtain estimates of ajt and bjt. Then these estimates were substituted in equation (2) along with the actual monthly returns (Rjt' and the actual market return (Rmt) to obtain each é. 3t. The rea- son for deleting 1970 monthly price data from the compu— tation of the regression parameters (ajt' bjt) was that otherwise the first assumption (i.e., E (éjt)=0) of the regression model would have been violated if the forecasts possessed information content. In the present study the estimates of the regression parameters were provided by the Securities Research Divi- sion of Merrill Lynch, Pierce, Fenner and Smith, Inc.25 An explanation of the methodology utilized by Merrill, Lynch to compute these regression parameters is warranted since its procedures differ somewhat from that discussed above. Merrill, Lynch used simple linear regression analysis to relate monthly price returns on an individual security to monthly price returns on the Standard and Poor's 500 Stock Index26 for a period of sixty months. Standard regression analysis was selected over other methods (e.g. curvilinear regression or exponential smoothing) because there is no empirical evidence to demonstrate that any other method is statistically superior. Monthly price returns were chosen rather than 64 weekly or daily returns, because this interval has been the most thoroughly tested and there is some evidence to indicate that weekly and daily intervals contain some bias. The actual price data used to compute the security and market price relatives was obtained from the ISL Daily Stock Price Index.27 A major difference in the procedure used by Merrill, Lynch from that discussed previously is that it excludes dividends from the calculations of both the individual and the S & P 500 returns. It states that: In the calculations, returns on the stocks and on the S&P 500 are represented by per— centage price changes, excluding dividends. Studies have shown that betas based on simple price returns are almost identical to those based on total returns (prices and dividends). A study by Sharpe and Cooper at Stanford University showed that the r2 on regressions of total—returns beta against price—return betas is above .99. Because dividends are usually stable, it can also be shown that the two methods yield statistically as well as empiri- cally, an almost identical beta.28 To be useful for estimation purposes the regression parameters (ajt' bjt) should be stable from period to period. Several researchers29 have examined the stability of the beta coefficient by measuring and comparing betas on individual stocks from one period to another. Although a relation was found between betas for successive time 65 periods, the betas for some stocks did vary from one period to the next. The variations in the betas can be caused by statistical or sampling error, or by changes in the actual value of a security's beta. Such variations suggest that some type of adjustment to the beta is war- ranted. Merrill, Lynch makes such an adjustment in its calculation of the betas to allow for the statistical 30 It states that this: phenomenon called regression bias. ...adjustment makes use of an empirical Bayesian approach to determine the amount of measurement error in the pOpulation of betas. One makes an a priori assumption that all betas are equal to one. Using the statistical error information (standard error of beta) provided by the regression, it is possible to gauge the over—all accuracy of the betas vis-a-vis the prior estimates. Adjusted betas are obtained by taking an apprOpriately weighted average of the unadjusted and the a priori estimates of beta. Because the degree of adjustment depends on the estimated reliability of a priori assump- tions, no change is made in the betas if the a priori estimates prove to be useless. Statistical theory indicates that under certain conditions these modifica— tions can never result in worse predic- tions than those indicated by the un- adjusted betas.31 It is these adjusted betas that were substituted in equa- tion (2) to Obtain estimates of the residual returns (ejt)° 66 Evidence Supporting the Use of the Market Model Fama, epggl,in their study which investigated the information effect of stock splits examined the validity of the market model (which they refer to as equation (1)) as a means of removing the general market effects from a security's return. They contend that: ...the estimates of equation (1) for the different securities conform fairly well to the assumptions of the linear regres- sion model. For example, the first order auto—correlation coefficient of the esti— mated residuals from (1) has been com- puted for every twentieth split in the sample (ordered alphabetically by secu— rity). The mean (and median) value of the forty-seven coefficients is - 0.10, which suggests that serial dependence in the residuals is not a serious prOblem ..... In sum we find that regressions of security returns on market returns over time are a satisfactory method for abstracting from the effects of general market conditions on the monthly rates of return on individual securities... Further support for the market model may be inferred from the many studies33 that have utilized this model to abstract from general market effects. Preliminary Descriptive Test Statistics For each forecasting model examined in this study two descriptive statistics were computed to present a pre— liminary evaluation of each model's predictive ability. These two statistics are also presented since they are 67 somewhat comparable to statistics utilized in previous studies. However, they are still deficient since they do not relate the forecasts to stock price adjustments, which is the predictive criterion employed in the present study. The first measure of predictive accuracy was of the form: where: F = Forecasted earnings per share Actual earnings per share This measure relates absolute forecast errors (IA-Fl) to the forecasted earnings rather than to the actual earnings per share because they will be easier to use by investors in this form. Since actual earnings are not known when the prediction is made, any adjustments that an investor desires to make to adjust for past tendencies to over-or- underpredict will be easier, if the prediction errors are expressed relative to predicted earnings.34 It was previously demonstrated that expressing pre— diction errors relative to actual earnings results in a 35 In a similar fashion bias favoring underpredictions. the measure (|A-F|/F) results in a bias favoring over- predictions. This bias can be illustrated by the 68 following example: Forecast Actual (IA-FI)/F Firm A 1.80 2.00 11% Firm B 2.20 2.00 9% In this example the absolute earnings forecast error for both firms is $.20. Note, however, that the error rate is 11% for the underprediction while it is only 9% for the overprediction. The second measure of predictive accuracy used in this study was of the form: where: . F = Forecasted earnings per share - Actual earnings per share 3’ l P = Average closing price of the most recent three months prior to the forecast. Since this model normalizes the errors by price, it pro— vides a more meaningful measure when earnings are small or negative. An average closing price of the most recent three months was used to alleviate any undue influence of extreme prices in any particular month. This measure also is void of any differential bias of under-or-over- estimates and thus serves as a control on the first measure. These two measures provide only preliminary evidence of the predictive accuracy of the forecast models 69 investigated in this study. What is more important is the association that exists between the forecasts and stock prices. Statistical Hypotheses and Tests Research Hypothesis-l The first hypothesis of this research was: Null Hypothesis, Hi: The association that exists between errors in analysts' forecasts of earnings per share and stock price returns does not differ from the association that exists between forecast errors generated by selected naive models and stock price returns. Alternative Hypothesis, Hi: The association that exists between errors in analysts' forecasts of earnings per share and stock price returns is greater than the association that exists between forecast errors generated by selected naive models and stock price returns. To Operationalize this hypothesis, a statistical hypothesis which tests for the degree of correlation between errors in the forecasts of earnings per share and the stock price returns was required. The measure of cor- relation utilized in the present study was the Spearman 70 rank correlation coefficient (sometimes designated as Spearman's Rho). This test is a measure of association which requires only that both variables be measured in at least an ordinal scale so that the Observations under con— sideration can be ranked. In the present study the fore— casts were ranked according to the size of the forecast errors. This was accomplished by first computing the forecast errors according to the model (A-F)/F [i.e. (actual earnings per share minus forecasted earnings per share) / forecasted earnings per share] and then ranking the forecasts by the size of the forecast errors. The largest forecast error received the lowest rank (i.e. a rank of 1). Then the monthly stock return residuals (éjt) were cumulated over time for each firm and ranked in a similar fashion (i.e. the largest negative cumulative stock return residual received a rank of l). The justification for expecting a correlation to exist between the forecast errors and stock price returns was similar to that offered by Ball and Brown. If in— vestors perceive that the forecasts offer valuable infor- mation, they will utilize them in forming their expecta— tions of future stock returns. When actual earnings per share are announced and they are greater than forecasted (i.e. there is a positive forecast error) then it is 71 expected that the stock return residuals would increase. However, as Ball and Brown have demonstrated this increase will occur gradually over time. Thus, large positive stock return residuals cumulated over time should be associated with large positive forecast errors. The con- verse should hold for negative forecast errors. The formula used to compute the Spearman rank corre— lation coefficient was: N r8 = l - 6.2 d, i=1 1 N3 - N where: d = the difference between the rankings of the two sets of data N = the number of firms for which obser- vations were made (i.e. 100) A separate rs was computed to measure the association between each forecast model and stock price returns. Thus, four separate correlation coefficients were com- . l 2 3 puted and deSignated as rS , rS , rS for the three - . 4 annual naive forecast models, respectively, and r for s the analysts' forecasts. The following statistical hypotheses were then tested to determine which forecast model had the greatest association with stock price returns: 72 Hla : r4 = r1 0 s s H1a . r4 > r1 a S s Hlb : r4 = r2 0 S S lb H : r4 > r2 a s s ch : r4 = r3 o S s ch : r4 > r3 a s s The statistic used to test for differences in the population correlation coefficients (001 — 002) is stated as: V5l r4 a 8 2b 2 4 H : rq = r O S S H2b : rq2 > r4 a S S 2c 3 4 H : rq = r O S S H2C : rq3 > r4 a S S Research Hypothesis—3 The third research hypothesis of this study was: Null Hypothesis, H3: The association that 0 exists between errors in analysts' quarterly revised forecasts of earnings per share and stock price returns does not differ from the association that exists between forecast errors generated by 76 selected quarterly naive forecast models and stock price returns. Alternative Hypothesis, H3: The association that a exists between errors in analysts' quarterly re- vised forecasts of earnings per share and stock price returns lg greater than the asso- ciation that exists be— tween forecast errors generated by selected quarterly naive forecast models and stock price returns. Forecast errors were computed using the same model as for research hypotheses one and two. Cumulative stock return residuals were obtained for each naive quarterly model in the same manner as they were obtained for the analysts' quarterly revised forecasts. Again, the Spear— man rank correlation coefficient was computed to measure the association between each forecast model and the stock price returns. For the quarterly naive models these cor— . . . . N l N 2 relation coeffiCients were deSignated as rs q , rS q , Nq3 . and rS to represent naive models 4, 5, and 6, respec— tively. The following statistical hypotheses were then tested to ascertain which forecast model had the greatest association with stock price returns: Fama, H3a . rql = qul O S S 3a ql qu H : r > r a S 8 3b 2 N 2 H : rq = q 0 S S : r r a S S H3C : rq3 = qu3 O S S H3C : rq3 > qu3 a S S et.al. have stated that the distributions of returns are better approximated by the non-Gaussian mem- bers of the stable Paretian family than the normal distri— bution.37 Thus, the Spearman rank correlation coefficient was chosen as the apprOpriate test statistic for this study since it makes no assumptions regarding the distri- butions of the forecast errors nor the stock return residuals. below: The efficiency of this statistic is described The efficiency of the Spearman rank cor- relation when compared with the most powerful parametric correlation, the Pearson r, is about 91 per cent. (Hotelling and Pabst, 1936). That is, when rS is used with a sample to test for the existence of an association in the population, and when the assumptions and requirements underlying the prOper use of the Pearson r are met, that is, when the pOpulation has a bivariate normal 78 distribution and measurement is in the sense of at least an interval scale, then rS is 91 per cent as efficient as r in rejecting HO. If a correlation between X and Y exists in that population, with 100 cases rS will reveal that correlation at the same level of si nificance which r attains with 91 cases.3 This means that the probability of showing no corre- lation when one in fact does exist in a bivariate normal population is somewhat less when utilizing the Spearman rank correlation coefficient than when using the Pearson's product moment correlation. The probability of showing that a correlation does exist when in fact none exists depends upon the level of significance chosen (i.e. the alpha level). The Level of Significance The level of significance chosen for which to reject or not reject the null hypotheses in the present study was equal to .05. This means that the probability of a Type I error, rejecting the null hypothesis when in fact it is true, is .05. The significance level was set at .05 to conform to conventional standards. However, the actual significance levels are also reported to allow the reader to draw his own conclusions. The second type of error which can occur in hypoth- esis testing is known as the Type II error, not rejecting 79 the null hypothesis when in fact it is false. To deter— mine the probability of a Type II error, several alterna- tive distributions of the possible correlations would first have to be formulated. This procedure is beyond the sc0pe of this research. However, it is believed that a sample size of 100 and an alpha level of .05 are large enough to limit the prObability of a Type II error to a reasonably low level.39 Limitations of the Methodology The most Obvious limitations of the proposed study relate to the criteria used to specify the pOpulation. The first limitation is that the results of this study are strictly applicable to only the population of firms included in the study. This population was restricted to New York Stock Exchange firms with December 31 fiscal year-ends that appeared in the 1970 and 1971 editions of the Standard and Poor's Earnings Forecaster. A further restriction was that a minimum of three analysts' esti- mates per month for at least ten months prior to the annual earnings announcement had to be available for the firm to be included in the study. Although it was assumed that the mean of the analysts' estimates was a representa- tive forecast for all analysts, this may not be the case. 80 However, there are no a priori reasons to believe that these limitations are critical. The definition of the population criteria and sample selection procedures provides an Opportunity for the reader to judge for him— self whether or not he can safely infer the results of this study to forecasts made by analysts in general. Summary This chapter was concerned with three major topics. The first tOpical area dealt with the theoretical consider- ations that provided the necessary foundation for the formulation of the research hypotheses and the methodology that was utilized in this study. Two major empirical research efforts that examined the information content of the annual earnings report were reviewed. The first article, by Beaver,4O demonstrated that the information content of an event could be assessed by observing the market's response in terms of stock price adjustments to the announcement of that event. The second study con— ducted by Ball and Brown,41 also employed as a predictive criterion the investment decision as it is reflected by security prices. In these studies the authors utilized the market model which asserts that a security's return is a linear function of a market factor. The use of 81 this model was necessary to remove the market-wide effects so that the residual returns, which represent the impact of new information about those firms alone, could be Oh- tained. Both works indicated that the annual earnings report possesses information content. However, Ball and Brown further demonstrated that much of the information content was anticipated prior to the release of the earn- ings report. The significance of these two studies for the present research was three~fold. First, they demon— strated that there exists a strong relation between earn— ings and stock prices. Second, they provided a valid criterion and methodology for examining the information content of an event. Finally, it was suggested that the media which allow the market to anticipate the information content of the earnings report deserve investigation. The second section of this chapter sets forth the general research hypotheses. These hypotheses are con— cerned with whether there exists a greater association between analysts' forecasts of earnings per share and stock price returns than exists between forecasts gener- ated by selected naive models and stock price returns. They are also concerned with any improvement that may be Obtained in this association as the forecast horizon is reduced. 82 The final topical area of the chapter presents the methodological structure of the research. This structure includes an identification of the pOpulation of firms studied, a description of the sample selection criteria and procedures, and a discussion of the selection of naive forecast models. Also included in this section was a detailed discussion of the market model and the manner in which it was utilized in this research. Evidence support- ing the use of this model was also cited. Furthermore, there was a discussion of some preliminary descriptive statistics as well as the statistical hypotheses and statistical tests employed in the study. The statistical model used to measure the association between each model's forecast errors and the cumulative stock return residuals was the Spearman's rank correlation coefficient. The chapter concludes with a discussion of the limitations of the methodological structure. 83 FOOTNOTES 1Beaver, William H. "The Information Content of Annual Earnings Announcements," Empirical Research in Accounting: Selected Studies, 1968, a supplement to Volume VI of The Journal of Accountinngesearch, pp. 67- 92. 2Ball, Ray and Brown, Philip, "An Empirical Evalu- ation of Accounting Income Numbers," Journal of Accounting Research, Volume VI (Autumn, 1968), pp. 159-178. 3Beaver, Op. cit., p. 68. 4Since the market model is also employed in the present study to abstract from market—wide effects, a detailed discussion of it is deferred to a subsequent section of this chapter. 5Beaver, op. cit., p. 82. 6Ball and Brown, 0p. cit., p. 160. 7Ibid., p. 161. 8 . Ibid., p. 162. 9Ibid., pp. 160—1. For a discussion of the theory and empirical evidence referred to see Fama, Eugene "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, Vol. 25 (May, 1970), pp. 383-420. lOIbid., p. 163. 11There are other events that could cause stock prices to go up or down. However, the market model was employed to remove the confounding effects of such events. 12The importance of this data source is further mani- fested by Standard and Poor's assertion that the estimates of earnings per share "represent the best estimates of leading analysts at the moment and therefore have a sig— nificant bearing on current stock values." 13This table of random numbers was obtained from the 84 following source: Clark, charles E., Random Numbers in Uniform and Normal Distributions, San Francisco, Calif— ornia: Chandler Publishing Company, 1966. 14COpeland, Ronald M. and Marioni, RObert J., "Executives' Forecasts of Earnings Per Share Versus Fore~ casts of Naive Models," Journal of Business, Volume 45, No. 4 (OctOber, 1972), pp. 497—512. 15Elton, Edwin J. and Gruber, Martin J., "Earnings Estimates and the Accuracy of Expectational Data," Management Science, Vol. 18, No. 8 (April, 1972) Appli- cation Series, pp. B409-429. 16The primary purpose of this research is not a com— parison of the predictive accuracy of various mechanical forecasting techniques. Thus, the exponential models were not included in this study. They were also omitted since they require computer computation which means they would not be readily accessible to all investors. Further— more, some naive models (e.g. model #1) may be capable of producing forecasts equivalent in accuracy to the more sephisticated exponential models. 17A few discrepancies in reported earnings per share data were noted between The Wall Street Journal Index and the Standard and Poor's sources. These discrepancies were eliminated by utilizing the data in the corporations annual report. 18King, Benjamin F. "Market and Industry Factors in Stock Price Behavior," Journal of Business, Volume 34 (Supplement, January, 1966), pp. 139-90. 19Ball and Brown, 6p. cit., p. 163. 20Blume, Marshall E. "The Assessment of Portfolio Performance" (unpublished Ph.D. dissertation, University of Chicago, 1968). 21Subtracting one from the monthly price relatives yields the discrete monthly rate of return. Discrete rather than continuous compounding was chosen because this was the method utilized to compute the alpha and beta estimates which were supplied by Merrill, Lynch, Fenner and Smith Inc. Ball and Brown, who also utilized dis— crete compounding, performed tests on the continuous 85 compounding model and noted that the results of both com— pounding models corresponded closely. See Ball and Brown, op. cit., p. 162. 22For the method of adjustment see Fisher, Lawrence, "Outcomes for Random Investments in Common Stocks Listed on the New York Stock Exchange," Journal of Business, XXVIII (April, 1965), pp. 149-161. 23Pettit, Richardson R., "Dividend Announcements, Security Performance and Capital Market Efficiency," IRE Journal of Finance, Volume XXVII, No. 5 (December, 1972), pp. 993-1007. 24See footnote 21. 25The author expresses his gratitude to Merrill, Lynch and especially to Mr. Gilbert Hammer and Mr. Lawrence Tint for providing the data necessary to com- plete this dissertation. 26Fama, et.al., found that the results using Standard and Poor's Composite Price Index as a measure of market conditions in the linear regression model were in agreement with those obtained by using Fisher's "Com- bination Investment Performance Index." See Fama, et.al. "The Adjustment of Stock Prices to New Information,” International Economic Review, Vol. 10, No. 1 (February, 1969), p. 4. 27Investment Statistics Laboratory, Inc., ISL Daily Stock Price Index: New York Stock Exchange (Palo Alto, California: Investment Statistics Laboratory, Inc.), volumes for the years 1969—1972. 28Merrill, Lynch, Fenner and Smith Inc., Securities Research Division, "Security Risk-Evaluation Service," Technical Addendum, March, 1972, p. 3. 29The issue concerning the stationarity of beta remains unresolved. On the one hand, Sharpe and COOper have concluded "there is substantial stability over time even at the level of individual securities." On the other hand, Myers indicated that "the beta coefficient was stationary for no more than about 75 per cent and possibly as few as 50 per cent of the stocks on the NYSE between 1950 and 1967." Sharpe and Cooper's conclusions 86 were based on the ability of betas calculated over a five-year period using monthly data to predict betas for the next year (a method similar to the one utilized in the present study) whereas Myers conclusions were based on the ability of betas calculated over one 7-year period to predict betas over the next 7-year period. Further- more, Blume had indicated that the usefulness of beta can be improved by correcting for regression toward the mean. It has been assumed that the stationarity assumption has not been violated for the purposes of the present study, since the methodology utilized in computing betas was similar to Sharpe's and the betas were corrected for regression toward the mean. For further discussion con- cerning the issue of stationary betas see Blume, Marshall B. "On the Assessment of Risk," The Journal of Finance (March 1971), pp. 1-10. Myers, Stephen L. "The Station- arity Problem in the Use of the Market Model of Security Price Behavior," The Accounting Review (April 1973), Vol. XLVIII, No. 2, pp. 318-322. Sharpe, W. F. and COOper, G. M., "Risk-Return Classes of New York Stock Exchange Common Stocks, 1931—67," Financial Analysts Journal (March—April 1972), pp. 46-54. 3ORegression toward the mean is a function of errors in measurement and the degree of correlation. Generally, the more deviant the estimate is from the mean the greater is the measurement error contained in the esti— mate. Also, the lower the degree of correlation, the greater the regression toward the mean. Thus, a stock with an observed beta of 2.0 (assuming that the Observed beta for all stocks was between 0 and 2.0 with a mean of l) is mostly likely overestimated and its beta will tend to move toward one. The reverse will apply to stocks with beta estimates less than one. 31Merrill, Lynch, op. cit., p. 4. 32Fama, et.al., 0p. cit., pp. 5-7. 33For example, See Beaver, Op. cit., pp. 67-92; Ball and Brown, pp; cit., pp. 159-178; Pettit, op. cit., pp. 993-1007; and Brown, Philip and Kennelly, John W., "The Information Content of Quarterly Earnings: An Extension and Some Further Evidence," The Journal of Business, Vol. 45, No. 3 (July, 1972), pp. 403-15. 87 34This point was made by Charles L. McDonald. See McDonald, Charles L., "An Empirical Examination of Pub— lished Predictions of Future Earnings." Unpublished Ph.D. dissertation, Michigan State University, 1972, p. 55. 35See Chapter II, p. 13. 36Olkin, Ingram and Siotani, M. "Asymptotic Distribution Functions of a Correlation Matrix." Stan- ford, California: Stanford University Laboratory for Quantitative Research in Education, Report No. 6, 1964. 37Fama, et.al., Op. cit., p. 7. 38Siegel, Sidney. NOQparametric Statistics for the Behavioral Sciences, New YOrk, New York: McGraw— Hill Book Company, Inc., 1956, p. 213. 39For a given value of the parameter being tested, the power of a test increases as the sample size, and the significance level increases. Since the power of a test is equal to one minus the Type II error, this means that under the above conditions the probability of a Type II error would decrease. 4OBeaver, William H., op. cit., p. 67-92. 41Ball and Brown, pp. cit., p. 159—178. CHAPTER IV RESULTS OF THE STATISTICAL TESTS Introduction Chapter IV is concerned with the findings of this research study. First, the results of the preliminary test statistics which describe the predictive accuracy of the forecast models are presented and then subjected to a brief statistical analysis. This section also con- tains a comparison of these results with the findings of some of the empirical works reviewed in Chapter II. In the last section of this chapter the research hypotheses are restated and the evidence obtained to reject or not reject these hypotheses is presented. Results of the Preliminarnyescrippive Test Statistics As discussed in Chapter III, two descriptive test statistics were computed for each forecasting model to privide a preliminary evaluation of each model's predic— tive ability. The first measure of predictive accuracy was of the form: 88 89 A-F F where: F = Forecasted earnings per share A = Actual earnings per share The results for this measure are given for each forecast model in Tables 1 through 10. Each table includes a range of relative prediction errors, the mean relative prediction error, and the distribution of over—and-under— predictions for each year and the period under study. In addition, an adjusted mean relative error is also included in the tables. The adjustment was made by excluding the largest deviate from the observations and then recalcu— lating the mean. This adjusted mean error appears to be a better representation of the average error rate since the deviate tended to have an unusually large influence on the results. The deviates that were removed (one from 1970 and one from 1971) were two firms that had reported positive earnings for the first three quarters of their fiscal years but reported large negative earnings for their entire fiscal year. A summary of the data contained in Tables 1 through 10 is presented in Table 11 to facilitate comparisons between the forecast models. In addition the models have been grouped by forecast horizon. Thus, naive models 1, 9O 2, and 3 were classified with the analysts' annual fore— casts since each of these models provides forecasts that cover the same time period. Several general observations should be made about the predictive power of the forecast models using the first measure of predictive accuracy (i.e., IA—FI/F). Reference to Table 11 reveals that of the three annual naive fore— cast models, model 1 was the superior predictor for the period under study. Model 1 had an adjusted mean predic— tion error of 19.14% for the period under study as com- pared to adjusted mean errors of 24.70% and 25.31% for models 2 and 3 respectively. Furthermore, 40% of the forecasts produced by model 1 yielded errors of less than 10% and 68% of the forecasts yielded errors of less than 20%. In fact, model 1 also proved to be superior to model 4 which utilized first quarter earnings. This latter model had an adjusted mean error of 26.75%“ The success of model 1 appears to be somewhat attrib- utable to the period under study. It was noted previously that the economy was somewhat depressed in 1970 which means that earnings were also depressed. Since model 1 predicts that current year earnings will be the same as prior year earnings, this model produced earnings esti- mates that were smaller in magnitude relative to models 2 91 TABLE 1 RELATIVE PREDICTION ERRORS (lé%glj CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVEReAND-UNDERPREDICTIONS BY YEARS Model 1 (EPSt = EPSt-l) Period Range of Errors 1970 1971 1970-1971 0.00% to 9.99% 17 23 40 10.00% to 19.99% 17 ll 28 20.00% to 29.99% 7 5 12 30.00% to 39.99% 4 3 7 40.00% to 49.99% 2 3 5 Over 50.00% _;; _§_ __§_ Totals .29 .29 100 Mean Error (all observations) 20.46% 21.30%* 20.88% Mean Error (largest deviate excluded) 16.98% 21.30% 19.14% Underpredictions 20 35 55 Overpredictions 39_ .12 ._32 Totals 50 22_ (£99 *One prediction was omitted from this computation since the forecast was a negative amount. 92 TABLE 2 RELATIVE PREDICTION ERRORS (15%219 CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVER-AND-UNDERPREDICTIONS BY YEARS Model 2 (EPSt = EPSt-l + (EPSt-l - EPSt_2) ) Period Range of Errors 1970 1971 1970-1971 0.00% to 9.99% 13 22 35 10.00% to 19.99% 14 5 19 20.00% to 29.99% 11 7 18 30.00% to 39.99% 6 6 12 40.00% to 49.99% 2 1 3 Over 50.00% _fi_ _2_ ._13 Totals _5_Q __Q _l_0 Mean Error (all observations) 24.15% 35.67% 29.91% Mean Error (largest deviate excluded) 20.76% 28.64% 24.70% Underpredictions ll 26 37 Overpredictions §2_ _j¥i _2_4_ Totals 50 59. 100 93 TABLE 3 RELATIVE PREDICTION ERRORS clééfil) CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVEReAND-UNDERPREDICTIONS BY YEARS Model 3 (EPSt = EPSt_1 x EPSt_1/EPSt_2) Period Rgpge of Errors 1970 1971 1970-1971 0.00% to 9.99% 13 20 33 10.00% to 19.99% 12 7 19 20.00% to 29.99% 12 9 21 30.00% to 39.99% 6 4 10 40.00% to 49.99% 2 3 5 Over 50.00% __5 ._Z __12 Totals _2 _§_Q_ 190 Mean Error (all observations) 25.57% 48.10% 36.84% Mean Error (largest deviate excluded) 22.21% 28.41% 25.31% Underpredictions ll 27 38 Overpredictions 39 23 62 Totals 50 50 100 94 TABLE 4 RELATIVE PREDICTION ERRORS (14%219 CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVER-AND-UNDERPREDICTIONS BY YEARS Model 4 (EPst = 4(EPStq1) ) Period Rppge of Errors 1970 1971 1970-1971 0.00% to 9.99% 19 20 39 10.00% to 19.99% 6 8 14 20.00% yo 29.99% 14 5 19 30.00% to 39.99% 3 6 9 40.00% to 49.99% 4 4 8 Over 50.00% _44 _1_ _11 Totals 20 29 199 Mean Error (all observations) 31.64% 34.48% 33.06% Mean Error (largest deviate excluded) 24.63% 28.86% 26.75% Underpredictions 26 29 55 Overpredictions 24 20 44 Exact Predictions _Q_ ._l __1_ Totals .59 50 .100 95 TABLE 5 RELATIVE PREDICTION ERRORS (1A%El) CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVER—AND-UNDERPREDICTIONS BY YEARS Model 5 (EPSt = 2(EPSt + EPS ) ql tq2 Period Range of Errors 1970 1971 1970—1971 0.00% to 9.99% 21 29 50 10.00% to 19.99% 13 9 22 20.00% to 29.99% 9 5 14 30.00% to 39.99% 4 3 7 Over 40.00% _3_ _4_ ___Z Totals .59 §__ 19__ Mean Error (all observations) 24.83% 18.73% 21.78% Mean Error (largest deviate excluded) 18.72% 14.18% 16.45% Underpredictions 23 28 51 Overpredictions 26 21 47 Exact Predictions _41 _l_ __; Totals ‘59 59_ 199 96 TABLE 6 RELATIVE PREDICTION ERRORS (lé§zl) CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVER-AND-UNDERPREDICTIONS BY YEARS Model 6 (EPSt = 4/3(EPSt + EPSt + EPS ) ) ql q2 tq3 Period Range of Errors 1970 1971 1970—1971 0.00% to 9.99% 33 32 65 10.00% to 19.99% 11 10 21 20.00% to 29.99% 3 5 8 30.00% to 39.99% 1 0 1 40.00% to 49.99% 1 2 3 Over 50.00% _yl __l ___2 Totals 59. .59 199_ Mean Error (all observations) 17.22% 13.84% 15.53% Mean Error (largest deviate excluded) 9.63% 8.97% 9.30% Underpredictions 22 26 48 Overpredictions 28 22 50 Exact Predictions _Q_ _i; __2_ Totals 59_ 50 .lQQ 97 TABLE 7 RELATIVE PREDICTION ERRORS (léfigl) CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVERrAND-UNDERPREDICTIONS BY YEARS ANALYSTS' ANNUAL PREDICTIONS Period Range of Errors 1970 1971 1970-1971 0.00% to 9.99% 16 30 46 10.00% to 19.99% 15 7 22 20.00% to 29.99% 8 5 13 30.00% to 39.99% 6 4 10 40.00% to 49.99% 0 1 1 Over 50.00% __5 .EE __§ Totals 29_ 59_ 199’ Mean Error (all observations) 22.10% 16.46% 19.28% Mean Error (largest deviate excluded) 18.78% 12.76% 15.77% Underpredictions ll 15 26 Overpredictions 39 34 73 Exact Predictions _Q. '_2 __41 Totals 59_ 59_ 199 98 TABLE 8 RELATIVE PREDICTION ERRORS ('AZE') CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATI ERROR, AND DISTRIBUTION OF OVER-AND-UNDERPREDICTIONS BY YEARS ANALYSTS' FIRST QUARTERLY REVISION Period Range of Errors 1970 1971 1970-1971 0.00% to 9.99% 17 30 47 10.00% to 19.99% 15 ll 26 20.00% to 29.99% 8 1 9 30.00% to 39.99% 5 5 10 40.00% to 49.99% 1 O 1 Over 50.00% _44 __3 ___7 Totals 5__ ._Q .190 Mean Error (all observations) 20.84% 15.31% 18.08% Mean Error (largest deviate excluded) 17.47% 11.55% 14.51% Underpredictions ll 16 27 Overpredictions 37 32 69 Exact Predictions ‘_2 ._2 __44 Totals _Jl ‘50 199_ 99 TABLE 9 RELATIVE PREDICTION ERRORS (IA?!) CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVER—AND-UNDERPREDICTIONS BY YEARS ANALYSTS' SECOND QUARTERLY REVISION Period Range of Errors 1970 1971 1970—1971 0.00% to 9.99% 26 35 61 10.00% to 19.99% 13 7 20 20.00% to 29.99% 6 2 8 30.00% to 39.99% 0 3 3 40.00% to 49.99% 1 l 2 Over 50.00% ._4 _;2 ___§ Totals _59 §_- .19_ Mean Error (all observations) 17.27% 13.60% 15.44% Mean Error (largest deviate excluded) 13.55% 9.74% 11.65% Underpredictions 14 19 33 Overpredictions 35 29 64 Exact Predictions ._l __2 ___3 Totals 50 .59 199_ 100 TABLE 10 RELATIVE PREDICTION ERRORS (IAP'Q—Fl) CLASSIFIED BY RANGE OF RELATIVE ERRORS, MEAN RELATIVE ERROR, AND DISTRIBUTION OF OVEReAND-UNDERPREDICTIONS BY YEARS ANALYSTS' THIRD QUARTERLY REVISION Period Range of Errors 1970 1971 1970—1971 0.00 % to 9.99% 34 37 71 10.00% to 19.99% 7 6 13 20.00% to 29.99% 5 4 9 30.00% to 39.99% 2 2 4 40.00% to 49.99% 1 0 1 Over 50.00% _1’ ._1 __i§ Totals _5_(_)_ _5__ _l__9_ Mean Error (all observations) 15.80% 11.49% 13.65% Mean Error (largest deviate excluded) 9.83% 7.43% 8.63% Underpredictions 12 17 29 Overpredictions 38 32 Exact Predictions lo 70 __1_ __.1. Totals 50 59_ 100 101 mummumuom vmmfi>wm haumuumso vufina .muwmama< u mo< m vaoz u m2 mummomuom vmma>mm maumuumso vaoomm .mumkama4 u No< q kuoz u «z mummowuom wmmfi>mm uaumuumao umufim .muwhamn< u HO¢ m Howe: u m: mcofiuOfiwmum Hmaca< .mumhamc< u H< N Hmwoz N NZ 0 Hmwoz u 02 a Hmvoz u H: "muw53 H oh am am a“ Nmo.w Nmo.ma mo< N om we ow no Nom.m Nmm.mH 0: m so mm am am Nmo.HH qu.ma «ca N me an mm om qu.oa Nmm.HN m2 q mo mm mm nq Nam.o we * shows: mo * muoupm mo m muouum mo * uouum com: cams HanIONmH OOHmmm mmH mom mamHUHHoHQmmm M>HH r a S S lb 4 2 H : r = r O S S lb 4 2 H : r > r a S 8 1c 4 3 H : r = r O S S 1c 4 3 H : r > r a S S At the .05 level of significance the null hypothesis, 1a . . 1a . . . Ho was rejected in favor of Ha . This indicates that the association that exists between errors in annual analysts' forecasts and stock returns is greater than the association that exists between the forecast errors generated by model 1b 1 and stock returns. However, the null hypotheses, HO and Hie, could not be rejected at the .05 level of signifi- cance. Thus, there is no statistical difference between the association that exists between the annual analysts' forecasts and stock returns and the association that exists between the forecast errors generated by model 2 and 3 and stock returns. The actual p values at which the null hypotheses could be rejected are reported in Table 18. 122 TABLE 17 SPEARMAN RANK CORRELATION COEFFICIENTS FOR THE ANNUAL FORECAST MODELS l = = * Model 1 (EPSt EPSt_1) rS .207494 2 = _ = ** Model 2 (EPSt 2EPSt_l EPSt_2) rS .200068 2 3 = = *** Model 3 (EPSt (EPSt—l) /EPSt_2) rS .183691 Analysts Annual Forecasts r: = .319957**** *Significantly different from zero at the p = .02 level **Significantly different from zero at the p = .025 level ***Significantly different from zero at the p = .04 level ****Significantly different from zero at the p = .001 level TABLE 18 SIGNIFICANCE LEVELS FOR REJECTION OF THE FIRST RESEARCH HYPOTHESIS Null hypothesis would be rejected at Hla r4 = r1 0 s s H1a . r4 > r1 a s s Hlb r4 = r2 0 s s Hlb r4 > 1.2 a s s ch . r4 = r3 0 s s ch r4 > r3 a s s p = .045 p = .135 p = .115 123 It is not Obvious from Tables 17 and 18 why the null 1b 1c . . hypotheses, HO and Ho , were not rejected when the dif- ference between the correlation coefficients for the analysts' annual model and model 1 (i.e., r: and ri) was actually less than the difference between the correlation coefficients for the analysts' annual forecasts and model 2 and 3 (i.e., between r: and r:, r2) . The explanation is found in the correlation of each naive forecast model with the analysts' annual model. The association of the forecast errors of model 1 were more highly correlated with the forecast errors of the analysts (r: = .849) than the correlations that existed between the analysts' model and naive models 2 and 3 (r: = .679, r: = .675, respectively). Because of the strong association of the analysts' model and model 1, a smaller difference between the correlation coefficients measuring the association of . 4 l forecast errors and stock returns (i.e., rS and rs) was . la . . lb needed to reject Ho than was required to reject HO and 1c H . o The outcome of the statistical tests of the first research hypothesis implies that the market does not per- ceive analysts' forecasts to have greater utility than forecasts generated by simple naive models. Furthermore, since the results indicate that the forecasts do not 124 differ in regard to benefits, as measured by the associa- tion of forecast errors and stock price returns, this im- plies that the additional cost of preparation of forecasts by security analysts is not warranted. One final point should be made about the association of the forecast errors with stock prices. Table 17 demonstrates that a statistically significant relationship exists between the forecast errors of all the models and the cumulative stock return residuals. Although these associations were all in the predicted direction and statistically greater than zero at the .05 significance level, the magnitude of the Spearman rank correlation coefficients suggest that the strength of the relation- ships was fairly weak. This implies that the market does not rely heavily on these forecasts when forming its expectations about future earnings. Results of the Statistical Test Concerning The Second Research Hypothesis The second research hypothesis of this study states: Null Hypothesis, Hi: The association that exists between errors in annual analysts' forecasts of earnings per share and stock price returns does not differ from the asso- ciation that exists between errors in 125 analysts' quarterly revised forecasts and stock price returns. Alternative Hypothesis, Hi: The association that exists between errors in analysts' quarterly revised forecasts and stock price returns is greater than the asso- ciation that exists be— tween errors in annual analysts' forecasts of earnings per share and stock price returns. Three separate Spearman rank correlation coefficients, designated as rql, rq2, and r s s :3, were computed for each of the analysts' quarterly revised forecasts to measure their association with the cumulative stock price resid— uals. Table 19 presents the Spearman rank correlation coefficients for the quarterly forecasts and the analysts' annual forecasts. The following statistical hypotheses were then tested to determine whether any of the errors in analysts' quarterly revised forecasts had a greater association with the stock price residuals than the errors in analysts' annual forecasts: H2a : rql = r4 0 s 5 2a 1 4 H : rq > r a S S 2 H b : rq2 = r4 O S S 2 2 4 Hb : rq > r a s s H2c : rq3 = r4 O U) U) :1: H v 2c q3 r4 s At the .05 level of significance none of the null hypotheses, Hga, H2b, and Hie, could be rejected. This indicates that the association that exists between errors in analysts' forecasts and the cumulative stock return residuals does not improve as the forecast horizon is reduced. Actually, it can be observed from Table 19 that the Spearman rank correlation coefficient for the analysts' annual forecasts is greater than the correlation coeffi— cients for the analysts' quarterly revised forecasts. Rather than the association between the forecast errors and the stock returns increasing as the forecasts horizon is reduced the relationship actually decreases. In fact, it was found that no relationship exists between the analysts' third quarterly revised forecasts and the sub— sequent cumulative stock return residuals. The results obtained from testing the second research hypothesis imply that investors do not perceive the quarterly 127 TABLE 19 SPEARMAN RANK CORRELATION COEFFICIENTS FOR ANALYSTS' FORECASTS Analysts' Annual Forecasts r: = .319957* Analysts' First Quarterly Revised Forecasts r21 = .310431** Analysts' Second Quarterly Revised Forecasts rq2 = .303349** Analysts' Third Quarterly Revised Forecasts r(13 = .0307223 128 revised forecasts to possess greater utility than the analysts' annual forecasts. Furthermore, the lack of any correlation between errors in the third quarterly revised forecasts and the cumulative stock return residuals seems to indicate that the market has already discounted the final quarter's earnings. Results of the Statistical Test Concerning The Third Research Hypothesis The third and final research hypothesis of this study stateS: Null Hypothesis, Hi: The association that exists between errors in analysts' quarterly revised forecasts of earnings per share and stock price returns does not differ from the association that exists between forecast errors generated by selected quarterly naive forecast models and stock price returns. Alternative Hypothesis, H3: The association that a exists between errors in analysts' quarterly revised forecasts of earnings per share and stock price returns is greater than the asso— ciation that exists between forecast errors generated by selected quarterly naive fore- cast models and stock price returns. 129 Again, Spearman rank correlation coefficients were com- puted and designated as rqu, rng, and rgq3 to represent the naive quarterly models 4, 5, and 6, respectively. These coefficients along with the correlation coefficients for the analysts' quarterly revised forecasts appear in Table 20. The statistical hypotheses that were tested are stated as: H3a : rql = qul o s s H3a : rql > qu1 a s s H3b : rq2 = qu2 o s 5 3b H : rq2 > qu2 a s s H3c : rq3 = qu3 o s 5 3c q3 Nq3 H : r > r a s s As can be seen from Table 21 none of the three null hypotheses could be rejected at the conventional .05 sig— nificance level. Thus, the conclusion must be that there is no statistically significant difference in the associ- ation between the stock price returns and the forecast errors generated by the naive quarterly models or the errors in analysts' quarterly revised forecasts. 130 TABLE 20 SPEARMAN RANK CORRELATION COEFFICIENTS FOR THE INTERIM FORECAST MODELS = qu a * Mbdel 4 (EPSt 4 EPStql) r .119198 Analysts First Quarterly Revised Forecasts r21 = .310431** = qu — *** Model 5 (EPSt 2(EPStql+EPStq2) ) rS - .151501 Analysts Second Quarterly Revised Forecasts r22 = .303349** _ Nq3 = _ **** Model 6 (EPSt 4/3(EPStq1+EPStq2+EPStq3) ) rS .161865 Analysts Third Quarterly Revised Forecasts r23 = .0307223 *Significantly different from zero at p = .12 **Significantly different from zero at p = .005 ***Significantly different from zero at p = .07 ****Significantly different from zero at p = .06 TABLE 21 SIGNIFICANCE LEVELS FOR REJECTION OF THE THIRD RESEARCH HYPOTHESIS Null hypothesis would be rejected at H28 p = .075 H33 a ugh p = .115 H3b a Hie 3c p = .11 131 It is interesting to note that there is no statis- tical relationship between the forecast errors made from model 6 and subsequent stock price returns. This result was also observed regarding the third quarterly analyst model. Apparently any information forthcoming from the third quarter earnings is rapidly consumed and discounted by the market. Summary This chapter was concerned with the findings of this research study. First, the results of two preliminary test statistics, which described the predictive accuracy of the forecast models, were presented. Tables 1 through 12 report the mean errors, adjusted mean errors, and the number of over—and underpredictions for each of the fore- cast models. Some preliminary observations were made based on the adjusted mean errors of the forecast models. The Wilcoxon signed-rank test was then employed to test whether the differences in accuracy of the forecast models were statistically significant. It was demonstrated that of the three annual naive forecast models, model 1 had the lowest mean adjusted error rate for both years under study. However, it was found that model 1 was statistically superior in terms of 132 forecast accuracy to models 2 and 3 for 1970, but not for 1971. Model 1 also yielded a lower adjusted mean error rate than model 4, which utilized first quarter earnings. However, it was shown that the difference between these two models was statistically significant only in 1970 utilizing |A-FI/P as a measure of predictive accuracy. With regard to improvement in the predictive accuracy of the naive models as the forecasting horizon was re— duced, only model 6 was statistically superior to model 1 for both 1970 and 1971. On the other hand, the analysts' quarterly revised forecasts produced statistically lower error rates than did the analysts' annual forecasts. Table 15 presented comparisons between the forecast error for the analysts' annual forecasts and the annual naive models. In general, the analysts achieved lower forecast error rates than models 2 or 3 at a statisti— cally significant level. The best annual naive model (model 1) produced lower forecast errors than the analysts' annual forecasts in 1970 but higher error rates in 1971. However, these differences were not statistically sig- nificant. Table 16 indicated that the analysts' quarterly revised forecasts were not, in general, statistically different from the quarterly naive forecast models. An 133 exception was that the analysts' first quarterly revised forecast was statistically superior to model 4 in 1971. It is also important to note that there was a dis- tinct tendency for the analysts to overpredict. Approxi- mately 70% of their forecasts were overpredictions. The second section of this chapter presented the out— come of the hypotheses testing. The first research hypothesis of this study was concerned with whether annual analysts' forecasts or forecasts generated by selected naive models had a greater association with subsequent stock price changes. The analysts' projections of earn— ings were compared to three naive models. At the .05 level of significance it was found that two of the three naive models did not differ significantly from the analysts' estimates in their association with stock price returns. The conclusion drawn, therefore, was that analysts' projections do not have greater utility for investors than do forecasts generated by simple naive forecast models. The second research hypothesis was concerned with whether any improvement in the association of forecasts and stock returns was forthcoming as the forecast horizon was reduced. Since none of the null hypotheses was rejected at the .05 level of significance, the conclusion 134 was that the market did not perceive these forecasts as possessing greater utility than the analysts' annual forecasts. The third and final research hypothesis of this study compared the association of the analysts' quarterly fore- casts and stock price returns with the association ob— tained by selected naive models utilizing quarterly data. Again none of the null hypotheses was rejected. This im- plied that the analysts' quarterly forecasts did not differ from these selected naive models as to their utility. One final conclusion pertains to the strength of the relationship observed between the various forecast models and the cumulative stock price residuals. Although many of the models were found to be positively associated with stock price returns, the magnitudes of the Spearman rank correlation coefficients were fairly small indicating a rather weak relationship. 135 APPENDIX A SPEARMAN RANK CORRELATION COEFFICIENTS FOR THE FORECAST MODELS FOR 1970 AND 1971 This appendix is presented to report the Spearman rank correlation coefficients, which measure the associ— ation between errors in forecasts and stock price returns, computed for each forecast model separately for the years 1970 and 1971. The research hypotheses of Chapter 4 are not restated in this appendix, although they were retested for each year (i.e., 1970 and 1971 were treated separately). Thus, the purpose of this appendix is to present the re- sults of retesting the research hypotheses by individual years and, thereby, ascertain whether the results are significantly influenced by the periods involved. Table A—1 presents the Spearman rank correlation coefficients classified by years for the annual forecast models. The first research hypothesis of this study was concerned with whether the association between errors in analysts' annual forecasts and stock price returns was greater than the association between forecast errors generated by annual naive models and stock price returns. It was found that even at a .20 level of significance the first null research hypothesis was not rejected for either 1970 or 1971. This indicates that there was no 136 TABLE A—l SPEARMAN RANK CORRELATION COEFFICIENTS FOR THE ANNUAL FORECAST MODELS FOR 1970 AND 1971 1970 1971 Model 1 (EPSt = EPSt_1) .264454 .326506 Model 2 (EPSt = 2EPSt_l-EPSt_2) .300511 .374856 _ 2 Model 3 (EPSt - (EPSt_1) IEPSt_2) .309491 .320920 Analyst Annual Forecasts .317415 .418085 TABLE A-2 SPEARMAN RANK CORRELATION COEFFICIENTS FOR THE ANALYSTS'FORECASTS FOR 1970 AND 1971 1970 1971 Analysts' Annual Forecasts .317415 .418085 Analysts' First Quarterly Revised Forecasts .314979 .415616 Analysts' Second Quarterly Revised Forecasts .302776 .382048 Analysts' Third Quarterly Revised Forecasts .078131 -.0918718 137 statistical difference between the association of errors in forecasts and stock price returns for any of the annual forecast models for either 1970 or 1971. This conclu- sion is in agreement with that reached when the data were analyzed for the combined period of 1970 and 1971. The Spearman rank correlation coefficients for the analysts' annual and interim forecasts are presented in Table A-2. The second research hypothesis was concerned with the improvement in the association between forecast errors and cumulative stock price returns as the forecast horizon was reduced. As can be seen from Table A-2 the association between forecast errors and stock price returns decreases over time. Thus, the second null research hypothesis could not be rejected for either 1970 or 1971, a conclusion which conforms to that obtained when the hypothesis was tested for the combined period. The third and final research hypothesis of this study was concerned with whether the association between fore- cast errors and stock price returns was greater for the analysts' interim models than for the naive quarterly forecast models. Table A—3 presents the Spearman rank correlation coefficients for these interim forecast models. There was a statistically greater association between forecast errors and stock price returns for the analysts' 138 TABLE A-3 SPEARMAN RANK CORRELATION COEFFICIENTS FOR THE INTERIM FORECAST MODELS FOR 1970 AND 1971 r s 1970 1971 Model 4 (EPSt = 4 EPStql) .148146 .140796 Analysts' First Quarterly Revised Forecasts .314979 .415616 Model 5 (EPSt = 2(EPStql+EPStq2) .133545 .211828 Analysts' Second Quarterly Revised Forecasts .302776 .382048 Model 6 (EPSt = 4/3(EPStql+EPStq2+EPStq3) ) Analysts' Third Quarterly Revised Forecasts .078131 -.0918718 -.023l469 -.278003 first quarterly revised forecasts than for model 4 in 1971 at a .05 level of significance. The association for the analysts' third quarterly revised forecasts was also sta— tistically greater than for model 6 in 1971. However, there was no statistical difference between the associa— tion of forecast errors and stock price returns for the analysts second quarterly revised forecasts and Model 5 for 1971. No statistical differences were noted for any of the comparisons for 1970. Thus, the third null research hypothesis could not be rejected for either 1970 or 1971. Again, this result agrees with that obtained when testing 139 the hypothesis for the combined period. Thus, the same general conclusions were reached by testing the research hypotheses individually by year as were obtained when the data for each year were combined into a single period. None of the three null research hypotheses could be rejected at the .05 level of sig- nificance. 140 FOOTNOTES lCragg, J. G. and Malkiel, Burton G., "The Consensus and Accuracy of Some Predictions of the Growth of Cor— porate Earnings," Journal of Finance (March, 1968), pp. 67-84. 2Elton, Edwin J. and Gruber, Martin J., "Earnings Estimates and the Accuracy of Expectational Data," Management Science, Vol. 18, No. 8 (April, 1972) Applica— tion Series, pp. B409—B429. 3Niederhoffer, Victor and Regan, Patrick J., "Earnings Changes Analysts' Forecasts and Stock Prices," Financial Analysts Journal, Volume 28, No. 3 (May-June 1972), pp. 65-71. CHAPTER V SUMMARY, CONCLUSIONS, IMPLICATIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH Summary The purpose of this research was to provide empirical evidence regarding the utility of analysts' projections of earnings. A secondary area for consideration was an assessment of the effectiveness of revisions in these forecasts made over a period of time. It has been established in the financial literature, both theoretically and empirically, that a strong bond exists between earnings and stock prices. Theoretically, it is the payment of dividends that give stock value. However, dividends are a function of earnings. Further- more, dividends tend to lag earnings and direct fore- casting of dividends is often very difficult. Thus, most academicians have recommended utilizing earnings estimates as inputs to stock price models. Empirically, it has been demonstrated that there are significant stock price reactions to the release of earnings reports. It was further shown that much of this reaction occurs 141 142 over time as investors anticipate earnings. Given these theoretical and empirical considerations there are two primary reasons why analysts' estimates of earnings per share should possess considerable utility for investors. First, the analysts devote a considerable amount of time and effort in preparing these estimates which could easily be utilized by investors in their security price models. Secondly, it seems reasonable to argue that one possible medium by which the market is able to anticipate earnings would be analysts' projections of net income. The previous empirical research also indi- cates that an apprOpriate methodology for the assessment of the utility of an event is the observation of subse- quent stock price reaction to that event. This study examined the association of analysts' forecasts and subse- quent stock price returns. Analysts' forecasts were obtained from the Standard and Poor's Earnings Forecaster, Fifty firms in 1970 and fifty firms in 1971 were randomly selected from the relevant population. In establishing the utility of the analysts' fore— casts it was deemed insufficient merely to determine that an association between analysts' forecasts and stock prices existed. Rather, it must be demonstrated that such an association is statistically greater than can be 143 found between forecasts made by other models and stock price returns. Thus, six naive forecast models were selected to provide forecasts which would serve as a control group. The results of the study are reported in two sec— tions. The first section presents the results of two preliminary test statistics which describe the predictive accuracy of the forecast models included in the study. The second section presents the outcome of the tests of the various hypotheses. These hypotheses are concerned with the strength of the relationship that exists between each of the forecast models and cumulative stock price residuals, and how this association changes as the fore— cast horizon is reduced. Conclusions The results of this research study consist of three basic parts: the preliminary test statistics that describe the predictive accuracy of the forecast models, a statistical test employed to evaluate the differences in the forecasting accuracy of the models, and the statis— tical hypotheses that test the association between the various forecasts and subsequent stock price returns. The first section described the predictive accuracy 144 of the forecast models in terms of mean errors, adjusted mean errors, and the number of over-and—underpredictions. Several conclusions were drawn from this aspect of the study. Model 1 had the lowest error rate of the three annual naive models. Secondly, it was concluded that as the forecast horizon was reduced, accuracy improved. This second conclusion pertained to both the naive and analysts' forecasts. A final conclusion drawn was that analysts' tend to be overOptimistic in their predictions since approximately 70% of their forecasts were greater than actual earnings. The Wilcoxon signed-rank test was then employed to test whether differences in accuracy of the forecast models were statistically significant. Several conclu- sions were also drawn from this aspect of the study: First, it was found that model 1 had a lower forecast error rate than either model 2, 3, or 4 in 1970 at a statistically significant level. The differences noted in 1971 were not statistically significant. Secondly, some improvement in accuracy was noted as the forecasting horizon was reduced. Model 6 was statistically superior to model 1 in both 1970 and 1971. With regard to the analysts' forecasts, a statistically significant improve— ment was obtained as the forecasting horizon was reduced. 145 It was Observed that generally the analysts' annual forecasts yielded lower error rates than either model 2 or 3 at a statistically significant level. Model 1 yielded lower forecast errors than analysts in 1970 and the analysts yielded lower errors than model 1 in 1971, although these differences were not statistically signifi— cant. Finally, it was observed that analysts' quarterly revised forecasts were not statistically different from the forecasts generated by the naive quarterly models. The second part of the study dealt with the question of the utility of the forecasts as perceived by investors. Several research hypotheses were set forth and then tested. At the .05 level of significance none of these major research hypotheses could be rejected. (This was also true when the hypotheses were tested for each year separately. See Appendix to Chapter 4.) Several conclu- sions were reached from these statistical tests. The first conclusion was that the analysts' annual forecasts apparently possess no more utility for investors than forecasts generated by simple naive models. This further implied that the cost incurred by analysts in the prepara- tion and dissemination of their forecasts is not justified in terms of the utility derived by the market. Although analysts' achieved considerable improvement 146 in their predictive ability over the subsequent quarters of the fiscal year, no statistical difference was found in the association that existed between their annual forecasts and stock price returns and the relationship that existed between their revised forecasts and stock price returns. This led to the conclusion that investors do not perceive these revisions as possessing greater utility than the original forecasts. From the test of the final research hypothesis it was further concluded that the utility as perceived by the market did not differ between these revised projections and forecasts derived from the naive quarterly models. At this point several caveats should be issued. First, the results of this study are strictly applicable only to the population of firms included in this study. ' This population was defined by the following criteria: 1. The firms appear in the 1970 and 1971 editions of the Standard and Poor's Earnings Forecaster. 2. The firms are listed on the New York Stock Exchange (NYSE), except for firms leaving the NYSE because of delisting, merging or listing on other exchanges. 3. The firms have a fiscal year end on December 31. 4. The firms meeting the first three criteria have a minimum of three analysts' estimates per month for at least ten months prior to the announcement of the annual earnings by the corporation in the Earnings Forecaster. 147 Secondly, as with all research employing statistical tests, this study is subject to the limitation of statis— tical error. This error is referred to as a Type II error, i.e., accepting the null hypothesis when the alternative hypothesis is true. In this study control over this error was achieved by a relatively large sample size and by formulating directional alternative hypotheses. The final warning pertains to the presumed validity of the forecast error model. It was assumed that a mean estimate of the analysts' forecasts for a particular firm provided an adequate surrogate of the true analysts' fore- casts. This may in fact not be the case as is eXplained in the next section. Also, the expression of relative prediction errors as a percentage of predicted earnings may result in some bias. That is, other measures may result in a better definition of forecast errors. Implications of the Empirical Results Several plausible explanations can be formulated to account for the fact that the analysts' forecasts did not possess greater utility for investors than did the fore— casts of the selected naive models. First, the projec- tions provided by the analysts' may not have been suffi- ciently more accurate than those of the naive models to 148 prove useful for investors. This is substantiated by the fact that no statistical difference was found between model 1 and the analysts' annual forecasts. A second possibility is that the market forms its expectations according to some alternative forecast model, which was not included in this research study. This would also explain why the quarterly forecasts did not exhibit an improvement in their association with stock price returns. Another explanation pertains to the use of mean estimates as a surrogate for the analysts' "true" fore- cast. Some other value may actually prove to be a better surrogate. This can be illustrated by the following hypothetical example: §E§E_l. §E§§_Z Forecast A ‘ 2.00 2.00 Forecast B 2.10 2.00 Forecast C 1420 3409 Mean Estimate 2.00 2.33 In case 1 an estimate of $2.00 is probably a reason- able estimation of what analysts expect the corporation to actually earn. Whereas, in the second case the mean estimate is likely a poor surrogate for the analysts' "true" expectations of actual earnings. Rather, a modal 149 value or some value which considers the variance of the forecasts should prdbably be utilized. Even though the analysts' forecasts did not manifest greater utility than the forecasts of the simple naive models it is important to note that the relationship between the analysts' forecasts and stock prices was in the predicted direction and was statistically different from zero. This could imply that the errors in forecast model utilized in this study actually provided a poor measurement of the forecast errors. Thus, additional investigation into the utility of these forecasts appears warranted. The next section of this chapter presents several recommendations for further research. Recommendations for Further Research Based upon the findings of this research effort, there are several areas that seem to warrant further investigation. First, the study could be extended to a broader pOpulation of firms. Specifically, the pOpulation could be expanded by inclusion of firms listed on exchanges other than the New York Stock Exchange and by including firms with other than calendar year-ends. The fact that a positive relationship, albeit fairly weak, was observed between analysts' forecasts and 150 cumulative stock price residuals suggests that a further decomposition of the data might prove useful. Such a refinement and reclassification of the data might assume many facets. For example, the data could be classified as to particular industry or risk classes to ascertain whether any improvement in the association would be forth- coming. Another possible alternative would be an examination of alternative forecast models. This could include other various naive models as well as a redefinition of the analysts' forecast models. The present study utilized mean estimates. 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