UUnniivveerrssiittyy ooff TTeennnneesssseeee,, KKnnooxxvviillllee TTRRAACCEE:: TTeennnneesssseeee RReesseeaarrcchh aanndd CCrreeaattiivvee EExxcchhaannggee Masters Theses Graduate School 12-2010 UUnnddeerrssttaannddiinngg tthhee SSoouurrcceess ooff AAbbnnoorrmmaall RReettuurrnnss ffrroomm tthhee MMoommeennttuumm SSttrraatteeggyy.. Yu Zhang [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the Arts and Humanities Commons RReeccoommmmeennddeedd CCiittaattiioonn Zhang, Yu, "Understanding the Sources of Abnormal Returns from the Momentum Strategy.. " Master's Thesis, University of Tennessee, 2010. https://trace.tennessee.edu/utk_gradthes/847 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Yu Zhang entitled "Understanding the Sources of Abnormal Returns from the Momentum Strategy.." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science, with a major in Mathematics. Charles Collins, Major Professor We have read this thesis and recommend its acceptance: Henry Simpson, George C. Philippatos Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official student records.) To the Graduate Council: I am submitting herewith a thesis written by Yu Zhang entitled “Understanding the Sources of Abnormal Returns from the Momentum Strategy.” I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science, with a major in Mathematics. Charles Collins, Major Professor We have read this thesis and recommend its acceptance: Henry Simpson George C. Philippatos Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official student records.) Understanding the Sources of the Abnormal Returns from the Momentum Strategy A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Yu Zhang December 2010 Copyright © 2010 by Yu Zhang. All rights reserved. ii ACKNOWLEDGEMENTS Thanks to Dr. Charles Collins and Dr. Henry Simpson. This thesis would not be possible without you. Special thanks to Dr. George C. Philippatos whose support makes my pursuit in math possible. iii ABSTRACT This thesis studies the sources of the returns from the momentum strategy and attempts to find some hints for the heated debate on the market efficiency hypothesis over the past twenty years. By decomposing the momentum returns from a mathematical model, we investigate directly the contributors and their relative importance in generating these momentum returns. Our empirical results support that autocorrelation of own stock returns is one of the driving forces for the momentum expected returns. The magnitude of the autocorrelation decreases as the ranking period becomes more remote. The second important source comes from the cross-sectional variation of the expected returns in the winner and loser portfolios at a given time. The third important source is the difference of the expected returns between the winner and loser portfolios. To our surprise, the cross-autocovariance does not contribute much to the momentum expected returns. Thus, the lead-lag effect can cause momentum returns, but its impact is not as significant as we had anticipated. More importantly, by changing the weights of the winner and loser portfolios, we find that the own-autocovariance of the winner portfolio is almost negligible, compared to that of the loser portfolio. The returns of the winners are much more random than those of the losers. This asymmetric own-autocovariance found in the return decomposition provides another underlying explanation to the recent finding that the contribution of the winner and loser portfolios to the momentum returns is asymmetric, and it is the losers, rather than the winners, that drive the momentum returns. Therefore, the market may not be as efficient as we believed before. iv TABLE OF CONTENTS Chapter Page CHAPTER I .................................................................................................................................... 1  INTRODUCTION .......................................................................................................................... 1  I. Background .............................................................................................................................. 1  II. Stock Trading Strategies ........................................................................................................ 3  2.1 Short-term contrarian strategy ......................................................................................... 3  2.2 Intermediate momentum strategy ...................................................................................... 4  2.3 Long-term contrarian strategy .......................................................................................... 4  III. Motivation ............................................................................................................................. 5  CHAPTER II ................................................................................................................................... 8  CHAPTER III ............................................................................................................................... 20  DECOMPOSITION OF MOMENTUM RETURNS ................................................................... 20  I. Theoretical Model.................................................................................................................. 20  II. Model Comparison ............................................................................................................... 26  2.1. The momentum expected return with Lo and MacKinlay (1990) weighting scheme ..... 27  2.2 The momentum expected return with our weighting scheme .......................................... 27  2.3. Difference in returns between the two models ............................................................... 27  III. Circumstances in Generating Positive Momentum Returns ............................................... 28  3.1Returns follow random walk with starting point (cid:2020) .......................................................... 28  U CHAPTER IV ............................................................................................................................... 30  EMPIRICAL RESULTS ............................................................................................................... 30  I. An Empirical Appraisal of Momentum Returns .................................................................... 30  1.1Return decomposition ...................................................................................................... 30  1.2 Empirical comparison of our model and model in Lo and Mackinlay (1990) ................ 36  CHAPTER V ................................................................................................................................ 37  CONCLUSION ............................................................................................................................. 37  LIST OF REFERENCES .............................................................................................................. 39  VITA ............................................................................................................................................. 53  v LIST OF TABLES Table Page Table 1. Return Decomposition with All Stocks in the U.S. Market ............................................ 42  Table 2. Return Decomposition with NYSE & AMEX Stocks Only ........................................... 47  Table 3. Return Decomposition with Change of Weights ............................................................ 49  Table 4. Return Decomposition following Lo & MacKinlay (1990) ........................................... 51  vi CHAPTER I INTRODUCTION I. Background In the 1970s the efficient market hypothesis was widely accepted among finance researchers. It has been commonly believed that information spreads in the market very quickly and, hence, the prices of the securities can quickly reflect the information with minimal delay. Thus, neither the technical analysis of past stock-price behavior nor fundamental analysis of firm specific information can help investors beat the market and earn returns higher than those of randomly selected portfolio with comparable risk. As stated in Malkiel (2003), in efficient financial markets, no investor can earn above-average returns without accepting above-average risks. This efficient market hypothesis has been engrained in much of the modern theoretical and empirical research in financial economics. However, two decades ago, researchers found that simple investment strategies based on stocks’ past returns may realize consistently positive profits. These rejections of martingale behavior of stock prices have seriously challenged the foundation of even the weak-form efficient market hypothesis. Stock return predictability based on past returns alone, has attracted a lot of attention in finance. The literature has documented three stock trading strategies categorized in terms of time horizons: (a) short-term reversal (Jegadeesh, 1990, and Lo and Mamaysky, 1990); (b) intermediate momentum (Jegadeesh and Titman (JT), 1993); and (c) long-term reversal (Debondt and Thaler, 1985, and Fama and French, 1988). As evidence opposing the efficient market hypothesis, these stock trading strategies are typical examples of exploiting stock return predictability. The debate on the abnormal profits from the momentum strategy that sells the 1