This method consists of regressing the portfolio monthly returns (excess of risk-free rate) on the factors presented in section 4.3, which are: market return (excess of risk-free rate), denoted by RM-RF, size (SMB), MGMT and PERF. The regression is calculated for each portfolio separately and is given in equation 5. The monthly factors are available on the authors’ websites, which is indicated in section VII.84
5
(5)85 𝑃𝑅𝑗𝑡− 𝑅𝐹𝑡 = 𝑎𝑗+ 𝛽𝑗(𝑅𝑀𝑡− 𝑅𝐹𝑡) + 𝑠𝑗𝑆𝑀𝐵𝑡+ 𝑚𝑗𝑀𝐺𝑀𝑇𝑡+ 𝑝𝑗𝑃𝐸𝑅𝐹𝑡+ 𝑒𝑗𝑡 The interception 𝑎𝑗 characterizes the portfolio return adjusted for both mispricing factors MGMT and PERF, and for the risk factors SMB and RM-RF. The intercepts from each portfolio and their respective t-statistics are shown in Table 6.
Table 6 indicates that, for the all-months and non-annual strategies based on year 1, all average returns from portfolios 1, 10 and 10-1, for all three periods, are not significant.
This is consistent with the hypothesis that their returns are explained by the four factors.
However, this does not hold for the annual strategy, where there is only one non-significant (0.05 level) decile spread return, which is in 2000-2016 based on year 1.
Similarly, in the years 2-5, 6-10, 11-15 and 16-20, the decile spread returns of the strategies non-annual and all are predominantly not significant, whereas the annual decile spreads are significant.
Moreover, the heatmap in Table 11 in the appendix, which contains the differences between returns adjusted for mispricing and winner-loser returns including delisting, shows that the decile spreads most affected by the four factors are related to shorter-term strategies, based on returns from year 1, and to the strategies all and non-annual. The performance of the annual decile spreads is mostly greater than the returns of the all-months and non-annual decile spreads. Hence, the seasonal strategy seems to be less explained by the four factors than the other two strategies.
83 Cf. Stambaugh, Yuan, 2017, p.1271.
84 Cf. Stambaugh, Yuan, 2017, p.1275-1285 .
85 Cf. Stambaugh, Yuan, 2017, p.1283. .
26 strategies all and non-annual decrease substantially or become statistically insignificant, the adjusted decile spread performance of the annual strategy persists significant and greater than 50 basis points for almost all periods and yearly intervals.
The evidence presented so far, that annual strategies achieve mostly high returns, even after controlling them for risk and mispricing factors, raises the question which is discussed in the next section.
27
6 Why do Investors not Arbitrage Away the Abnormal Returns?
McLean and Potiff suggest in 2016, that when an academic research about trading strategies is publicized, the abnormal returns originated through the strategies tend to shrink substantially in out-of-sample and post-publication periods, partly due to greater activity from sophisticated traders.86 This is partially consistent with the results from this study, where risk-adjusted returns from 2000-2016 are compared with returns within the two previous periods (1965-1982 and 1983-1999), which are completely included in the sample originally analyzed by Heston and Sadka in 2008 (1965-2002).87 The risk-adjusted returns of the decile spreads from the annual strategies for years 1, 2-5 and 11-15, decrease in the period 2000-2016 in comparison to 1983-1999. However, those returns are still positive, larger than 50 basis points and significant. Furthermore, this does not apply for the years 16-20, where the risk-adjusted return from the annual decile spread constantly increases until it reaches 84 basis points in 2000-2016.
To explain those remaining returns, there is evidence that some momentum strategies which appear lucrative may not result in profit after the inclusion of transaction costs, especially for equally-weighted portfolios, such as the ones empirically applied in this study.88 However, for strategies that weight portfolios according to value or liquidity, the inclusion of the costs still does not exclude the abnormal effect, which remains a puzzle.89 In the case of this study, it is reasonable to assume that rebalancing the complete portfolio each month generates substantial costs, which may lead to losses even if the monthly returns reach 60 to 70 basis points.90
7 Conclusion
This study shows empirically that, for the period between 2000 and 2016, seasonal momentum effects persist when the portfolio is formed based on returns from the same calendar month from 6 to 20 years in the past. The achieved average returns from the annual decile spreads exceed 58 basis points for this period, even after controlling for risk
86 Cf. McLean, Pontiff, 2016, p.28f.
87 Cf. Heston, Sadka, 2008, p.426.
88 Cf. Korajczyk, Sadka, 2004, p.1071f.
89 Cf. Korajczyk, Sadka, 2004, p.1071f.
90 Cf. Heston, Sadka, 2008, p.443.
28 and mispricing factors. Moreover, in the two earlier periods 1965-1982 and 1983-1999, the high decile-spread returns from annual strategies persist even when the past-performance analyzed for portfolio formation occurred in shorter-term intervals, from one to five years in the past. At the same time, strategies based on past-returns from all other months present mostly low or statistically insignificant decile-spread performance.
The implications of these findings are that seasonal momentum remains a puzzle, which is not explained by factors that usually explain other types of momentum and contrarian effects. Besides, since empirical evidence indicates that strategies based solely on past-performance achieve high returns, market efficiency in its weak form might be violated.
However, some limitations of this study could be explored in a future research for more refined results. For instance, all stocks are equally weighted in each portfolio, although different weights could be implemented with the purpose of maximizing the performance.
Furthermore, transaction costs are not considered in the winner-loser strategies presented in this thesis, although they might influence the results considerably, due to the frequent portfolio rebalancing. Hence, the inclusion of transaction costs into the model can contribute to finding in which extent the high returns can be converted into profit.
29
V Appendix
Table 7.Simple cross-sectional regressions of returns: sample comparison.
1965-2002 1965-2016 2003-2016
30 Table 8. Heatmap: WL returns incl. delisting minus WL excl. delisting.
Period 1965-1982 1983-1999 2000-2016
Portfolio 1 10 10-1 1 10 10-1 1 10 10-1
Year 1
All -0.09 -0.01 0.08 -0.27 -0.03 0.24 -0.44 -0.05 0.39 Annual -0.05 -0.03 0.02 -0.18 -0.06 0.13 -0.23 -0.09 0.14 Non Annual -0.09 0.00 0.09 -0.28 -0.03 0.25 -0.43 -0.05 0.38
Years 2-5
All -0.06 -0.02 0.04 -0.24 -0.03 0.21 -0.30 -0.04 0.26 Annual -0.04 -0.05 -0.02 -0.12 -0.07 0.06 -0.15 -0.08 0.07 Non Annual -0.06 -0.02 0.04 -0.25 -0.03 0.22 -0.28 -0.04 0.24
Years 6-10
All 0.00 0.00 0.00 -0.13 -0.05 0.08 -0.10 -0.06 0.04 Annual -0.02 -0.01 0.00 -0.08 -0.06 0.02 -0.09 -0.07 0.02 Non Annual 0.00 0.00 0.01 -0.12 -0.03 0.09 -0.09 -0.06 0.03
Years 11-15
All 0.01 0.00 -0.01 -0.06 -0.05 0.01 -0.05 -0.07 -0.03 Annual 0.00 0.00 0.01 -0.05 -0.02 0.03 -0.05 -0.07 -0.02 Non Annual 0.02 0.00 -0.03 -0.06 -0.05 0.00 -0.07 -0.08 -0.02
Years 16-20
All 0.00 0.00 0.00 -0.02 -0.04 -0.02 -0.04 -0.07 -0.03 Annual 0.01 0.00 -0.01 -0.03 -0.02 0.02 -0.06 -0.07 -0.01 Non Annual -0.01 -0.01 0.00 -0.01 -0.04 -0.02 -0.04 -0.07 -0.03 Source data: CRSP
31 Table 9. Winner-loser incl. delisting returns with -100% for omitted values.
Period 1965-1982 1983-1999 2000-2016
32 Table 10. Heatmap: risk-adjusted returns minus WL-returns incl. delisting.
Period 1965-1982 1983-1999 2000-2016
Portfolio 1 10 10-1 1 10 10-1 1 10 10-1
Year 1
All -1.92 -1.37 0.55 -1.60 -1.38 0.22 -1.13 -0.77 0.36 Annual -1.62 -1.68 -0.06 -1.44 -1.50 -0.06 -1.01 -0.80 0.21 Non Annual -2.00 -1.32 0.68 -1.60 -1.37 0.23 -1.11 -0.79 0.32
Years 2-5
All -1.91 -1.15 0.75 -1.48 -1.43 0.05 -1.14 -0.75 0.38 Annual -1.51 -1.61 -0.10 -1.36 -1.48 -0.13 -0.93 -0.84 0.09 Non Annual -1.93 -1.13 0.81 -1.51 -1.43 0.09 -1.13 -0.73 0.40
Years 6-10
All -1.44 -1.39 0.05 -1.48 -1.42 0.06 -0.81 -0.90 -0.09 Annual -1.30 -1.50 -0.20 -1.44 -1.41 0.03 -0.83 -0.85 -0.02 Non Annual -1.46 -1.40 0.06 -1.46 -1.42 0.04 -0.80 -0.90 -0.10
Years 11-15
All -1.40 -1.24 0.16 -1.43 -1.45 -0.03 -0.76 -0.87 -0.11 Annual -1.24 -1.32 -0.08 -1.44 -1.39 0.05 -0.82 -0.83 -0.01 Non Annual -1.39 -1.22 0.17 -1.39 -1.45 -0.06 -0.77 -0.88 -0.11
Years 16-20
All -1.35 -1.12 0.23 -1.46 -1.44 0.02 -0.82 -0.87 -0.05 Annual -1.18 -1.27 -0.10 -1.38 -1.43 -0.06 -0.83 -0.78 0.05 Non Annual -1.39 -1.13 0.26 -1.50 -1.41 0.09 -0.79 -0.86 -0.07 Source data: CRSP; Fama/French 3 factors
33 Table 11. Heatmap: return adjusted for mispricing minus WL-return incl. delisting.
Period 1965-1982 1983-1999 2000-2016
Portfolio 1 10 10-1 1 10 10-1 1 10 10-1
Year 1
All -1.13 -2.02 -0.89 -0.78 -1.61 -0.84 0.10 -0.94 -1.04 Annual -1.50 -1.69 -0.19 -1.28 -1.33 -0.06 -0.54 -0.40 0.14 Non Annual -1.22 -1.99 -0.77 -0.75 -1.58 -0.83 0.14 -1.01 -1.15
Years 2-5
All -2.11 -0.95 1.17 -1.19 -1.15 0.04 -0.53 -0.48 0.05 Annual -1.54 -1.50 0.03 -1.22 -1.16 0.06 -0.66 -0.59 0.07 Non Annual -2.16 -0.93 1.23 -1.19 -1.09 0.09 -0.50 -0.50 0.00
Years 6-10
All -1.58 -1.28 0.31 -1.32 -1.31 0.01 -0.75 -0.59 0.16 Annual -1.31 -1.57 -0.26 -1.30 -1.24 0.06 -0.82 -0.59 0.23 Non Annual -1.61 -1.25 0.35 -1.31 -1.30 0.00 -0.68 -0.59 0.09
Years 11-15
All -1.16 -1.35 -0.19 -1.23 -1.31 -0.08 -0.62 -0.71 -0.08 Annual -1.21 -1.36 -0.15 -1.40 -1.11 0.29 -0.66 -0.67 -0.01 Non Annual -1.18 -1.32 -0.15 -1.09 -1.37 -0.28 -0.58 -0.70 -0.11
Years 16-20
All -1.33 -1.03 0.30 -1.50 -1.34 0.16 -0.62 -0.77 -0.15 Annual -1.22 -1.18 0.04 -1.36 -1.31 0.05 -0.71 -0.55 0.16 Non Annual -1.37 -1.05 0.32 -1.53 -1.36 0.17 -0.54 -0.77 -0.24 Source data: CRSP; Stambaugh-Yuan Mispricing Factors
34
VI References
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Hong, Harrison and Stein, Jeremy C., 1999, A Unified Theory of Underreaction, Momentum Trading and Overreaction in Asset Markets, The Journal of Finance 54, 2143-2184.
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Jegadeesh, Narasimhan and Titman, Sheridan, 2001, Profitability of Momentum Strategies: An Evaluation of Alternative Explanations, The Journal of Finance 56, 699-720.
Korajczyk, Robert A. and Sadka, Ronnie, 2004, Are Momentum Profits Robust to Trading Costs?, The Journal of Finance 59, 1039-1082.
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37
VII Used Tools and Datasets (Benutzte Hilfsmittel)
Tools
Microsoft Excel (2016).
Microsoft Word (2016).
R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
Datasets
Fama, Eugene F. and French, Kenneth R., 2017, Fama/French 3 Factors, available from:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.
Stambaugh, Robert, F. and Yuan, Yu, 2017, Stambaugh-Yuan Mispricing Factors, available from: http://www.saif.sjtu.edu.cn/facultylist/yyuan/.
Wharton Research Data Services, 2017, CRSP Monthly Stocks, available from:
wdrs.wharton.upenn.edu.
VIII Honorable Declaration (Ehrenwörtliche Erklärung)
„Ich versichere hiermit, dass ich die vorliegende Arbeit selbständig und ohne Benutzung anderer als der angegebenen Quellen und Hilfsmittel verfasst habe. Wörtlich übernommene Sätze oder Satzteile sind als Zitat belegt, andere Anlehnungen, hinsichtlich Aussage und Umfang, unter Quellenangabe kenntlich gemacht. Die Arbeit hat in gleicher oder ähnlicher Form noch keiner Prüfungsbehörde vorgelegen und ist nicht veröffentlicht.
Sie wurde nicht, auch nicht auszugsweise, für eine andere Prüfungs- oder Studienleistung verwendet. Zudem versichere ich, dass die von mir abgegebenen schriftlichen (gebundenen) Versionen meiner Bachelorarbeit mit der abgegebenen elektronischen Version auf einem Datenträger inhaltlich übereinstimmen.“
Ort, Datum: ________________________ Unterschrift: ________________________