70- 13,980 BENTZ, William Frederick, 1940- THE MEASUREMENT OF COMMON STOCK PRICE RELATIVE f UNCERTAINTY: AN EMPIRICAL STUDY. f I I The Ohio State University, Ph.D., 1969 | Accounting £ University Microfilms, Inc., Ann Arbor, Michigan j t ....... .____ ...... _...... -i <© Copyright by William Frederick Bentz I1970i I i THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED THE MEASUREMENT OF COMMON STOCK PRICE RELATIVE UNCERTAINTY: AN EMPIRICAL STUDY DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By William Frederick Bentz, B.A., M.Acc. ****** The Ohio State University 1969 Approved by Adviser Department of Accounting PLEASE NOTE: Not original copy. Some -pages have very light type. Filmed as received. University Microfilms ACKNOWLEDGMENTS I gratefully acknowledge the constructive criticisms and suggestions provided by my dissertation reading committee, Professors Thomas J. Burns (chairman), Diran Bodenhorn and Melvin Greenball. They have never failed to give prompt attention to this work in spite of the many demands on their time. Professor Burns deserves special thanks for creating a very favor­ able environment in which I could improve my research skills and pursue my research interests. As a dissertation advisor, he has been instrumental in obtaining data, computer time, financial assistance, and all the other resources necessary to undertake an extensive empirical study. As an aca­ demician, Professor Burns has constantly demanded that I improve the rea­ soning behind each step in the dissertation, as well as suggesting ways in which the exposition of theory and results could be improved. Professor Bodenhorn is responsible for much of the improvement in logic and internal consistency which distinguish the dissertation from earlier drafts. Pro­ fessor Greenball has made many substantive and methodological suggestions which have improved the dissertation, even though it was well in progress when he joined the committee. Helpful suggestions have been received from Professors Cunnyngham, Cole Nestel, and Lyle during various stages of the development of the disserta­ tion. Preliminary analyses of the data were run on the Ohio State University 7094 system, with the assistance of the College of Administrative Science ii Data Center staff. Jim Boltz, Anita Gehr, and Marjorie Brundage provided programming assistance as well as technical information. Final computations and statistical analyses were run at the Kansas University Computation Center. Jeff Bangert has provided assistance in the use of the program library, and in the operation of the GE 635 system. Financial assistance has been provided by the Department of Accounting at The Ohio State University in the form of teaching opportunities and re­ search appointments. Support during much of my dissertation work was pro­ vided by The Haskins & Sells Foundation in the form of two Faculty Assis­ tance Grants (1965-66 and 1966-67). Some financial support was also pro­ vided by the Ohio Society of Certified Public Accountants in an award called the Herman Miller Price (1966). The financial aid provided by these sources is gratefully acknowledged since a doctoral degree would not have been feasible without this support. The secretarial assistance provided by the School of Business of The University of Kansas is gratefully acknowledged. Mrs. Betty Bovee has typed the dissertation with great care and cheerfulness. Mrs. Marcia Brown typed many of the tables, and was responsible for duplication of the dis­ sertation. Without the cooperation of Mrs. Bovee and Mrs. Brown, the dis­ sertation would have been a much more difficult undertaking. I am most thankful to my wife, Janet, and our children, Michael and Jennifer, who provided encouragement and understanding throughout my grad­ uate studies. In terms of unfilled needs, a family's investment in a doc­ toral degree is never quite repaid. iii VITA June 14, 194C . Born - Dayton, Ohio 1962 ....... B.A., Economics, The University of Cincinnati, Cincinnati, Ohio 1964 ........ Public Accounting Internship, Ernst and Ernst, Columbus, Ohio 1964 ........... Internship, General Motors Corporation, Detroit, Michigan 1965 ....... M.Acc., The Ohio State University, Columbus, Ohio 1965-1967 ..... Teaching Associate, Department of Accounting, The Ohio State University, Columbus, Ohio 1967-1968 ........ Research Associate, Department of Accounting, The Ohio State University, Columbus, Ohio 1968-1969 ........ Assistant Professor of Business, School of Business, The University of Kansas, Lawrence, Kansas PUBLICATIONS Magazine Review: "The Mathematical Content of the Business School Curriculum" by David Novick, California Manage­ ment Review, Spring, 1966, which was reviewed in Management Services, July-August, 1966 Magazine Review: "Capital Budgeting of Interrelated Projects: Survey and Synthesis" by H. Martin Weingartner, Management Science, March, 1966, which was re­ viewed in Management- Services, September-October, 1966. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ................................................ ii VITA ................................................ iv LIST OF TABLES ........................................ vii Chapter I. INTRODUCTION AND SUMMARY ................................... 1 A Statement of Objectives Outline of the Study Summary of the Results II. THE INVESTMENT PROCESS ..................................... 28 Individual Investment: A Postulated Process III. UNCERTAINTY AND PREDICTION MODEL ERROR ..................... 45 Uncertainty: Some General Notions Uncertainty and Prediction Uncertainty Defined A Measure of Uncertainty Price Relative Variance as a Measure of Uncertainty Analytical Arguments for Attempting to Predict Price Relatives Summary IV. THE PREDICTIVENESS OF COMMON STOCK PRICES AND PRICE RELATIVES 75 Introduction The Random Walk Hypothesis: A Review The Potentiality of Stock Price Prediction Naive Prediction Models An Economic Model of Stock Value V. ANALYSIS AND INTERPRETATION OF THE PREDICTION MODEL’S PERFORMANCE ............................................ 122 Performance of the Exponential Smoothing Models Performance of the Growth Model v Page Implications for Measuring Uncertainty Potential Improvements in the Growth Model Predictions APPENDIX A .................................................. 156 B .............................................................. 159 BIBLIOGRAPHY .................................................... 230 vi LIST OF TABLES Table Page 1. Naive Prediction Model No. 1 - Prediction. Results for the Years 1958 Through 1967 Using the Best Smoothing Constant for the Ten Years Preceding the Year for which a Prediction is Being M a d e ............................. 162 2. Naive Prediction Model No. 2 - Prediction Results for the Years 1958 Through 1967 Using the Best Smoothing Con­ stant for the Ten Years Preceding the Year for which a Prediction is Being Made ..... ................... 164 3. Naive Prediction Model No. 3 - Prediction Results for the Years 1958 Through 1967 Using the Best Smoothing Con­ stant for the Ten Years Preceding the Year for which a Prediction is Being M a d e ................... 166 4. Naive Prediction Model No. 1 - Prediction Results for the Years 1958 Through 1967 Using the Smoothing Constants I n d i c a t e d ............................................ 168 5. Naive Prediction Model No. 2 - Prediction Results for the Years 1958 Through 1967 Using the Smoothing Constants I n d i c a t e d ............................................ 170 6 . Naive Prediction Model No. 3 - Prediction Results for the Years 1958 Through 1967 Using the Smoothing Constants Indicated ........................................... 172 7. Price Relative Prediction Performance with Respect to Mean-Squared Error for Sixty-one Companies over the Ten Year Period 1958 Through 1967 Using Three Exponen­ tial Smoothing Models with Both Shifting Smoothing Constants and Fixed Smoothing Constants ........ 174 8 . Price Relative Prediction Performance with Respect to Constant Bias for Sixty-one Companies over the Ten Year Period 1958 Through 1967 Using Three Exponen­ tial Smoothing Models with Both Shifting Smoothing Constants and Fixed Smoothing Constants ................ 176 vii Table page 9. Price Relative Prediction Performance with Respect to Proportional Bias for Sixty-one Companies over the Ten Year Period 1958 Through 1967 Using Three Expo­ nential Smoothing Models with Both Shifting Smooth­ ing Constants and Fixed Smoothing Constants ............ 178 10. Price Relative Prediction Performance with Respect to Correlation for Sixty-one Companies over the Ten Year Period 1958 Through 1967 Using Three Exponen­ tial Smoothing Models with Both Shifting Smoothing Constants and Fixed Smoothing Constants ................ 180 11. Price Relative Prediction Performance Ranking of Three Exponential Smoothing Models, Incorporating Shifting as Well as Fixed Smoothing Constants, by Industry for the Ten Year Period 1958 Through 1967 182 12. Comparative Price Relative Prediction Results Using Fixed Smoothing Constants versus Shifting Smoothing Constants for Sixty-one Companies from 1958 Through 1967 ....................... 184 13. Comparative Absolute Prediction Errors Using Fixed Smoothing Constants versus Shifting Smoothing Con­ stants for Sixty-one Companies from 1958 Through 1967 .................................................. 186 14. Kolmogorov-Smirnov One Sample Test for the Normality