Seasonality in the cross section of stock returns: Advanced markets versus emerging markets
Fengyun Li, Huacheng Zhang* and Dazhi Zheng
This version: November, 2017 Abstract We extend the studies of stock return seasonalities by Heston and Sadka (2008, 2010) to a comprehensive sample of 42 international markets, including 21 advanced markets and 21 emerging markets. Our results show that there is a large variation in stock seasonality across markets and this pattern mainly exists in the advanced markets but is weak in the emerging markets. The response of stock returns to the same-month returns five or longer years in the past , in general, becomes less pronounced for all markets. A winner-loser portfolio approach employed to examine the economic significance of stock return seasonality consistently suggests that winner-loser strategy can deliver high returns only in advanced markets but not in emerging markets. We conduct statistical, rational and behavioral analyses to explore the potential reasons that cause the seasonality in advanced markets and find that regression bias, January effect, and Fama-French-Carhart type risk premium all have partial explanatory power on this difference.
Keywords: Asset pricing; Market efficiency; Seasonality; International financial markets JEL Classification: G12, G14, G15
___________________________________________________________ * Fengyun Li is from Renming University of China, Huacheng Zhang from Southwestern University of Finance and Economics, and Dazhi Zheng from West Chester University. Corresponding author: Huacheng Zhang, email:
[email protected], phone: +86-28-87099049.
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1. Introduction Existing studies show that stock returns are serially correlated. For example, Jegadeesh and Titman (1990, 1993) document a negative first-order serial correlation in monthly stock returns and positive higher-order serial correlations. Buying stocks that have performed well in the past and selling stocks that have performed poorly generates significant positive returns over subsequent 3 to 12 months. Moreover, according to Heston and Sadka (2008), the relative performance of stocks in one month is related to their relative performance in the same month in previous years. Winner stocks of the same--month in past years back up to past 20 years significantly outperform loser stocks in the same calendar month. More recently, Keloharju, Linnainmaa, and Nyberg (2016) report a strategy that selecting stocks based on their historical same-month returns earns an average return of 13% per year. In international markets, Heston, and Sadka (2010) extend their study to Canada, Japan, and 12 European countries and find that firms that outperform their domestic market peers in a particular month in the past up to 5 years continue to outperform in the same calendar month, suggesting that international stock markets may share similar patterns found in the U.S. stock market. Existing studies on the same-month return pattern, however, mostly focus on the U.S. market (e.g. Heston and Sadka, 2008; Keloharju et al., 2016) or certain advanced markets (Heston, and Sadka, 2010). The question whether emerging markets exhibit similar return patterns has not been well examined.
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Furthermore, among the limited studies on emerging
markets, the majority of them focus on stock market indexes rather than individual stocks to investigate stock return patterns. Emerging markets are considered less efficient and suffer
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Ho (1990) studies the stock return seasonality in Asia Pacific markets; Fountas and Segredakis (2002) study the January-effect anomaly in eighteen emerging stock markets for the period 1987β1995, Al-Saad and Moosa (2005) study the stock return seasonality in Kuwait Stock Exchange and Pandey (2002) studies the Malaysian stock market.
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severer behavioral biases. 2 To investigate whether the same-month return pattern exists in emerging markets and whether this pattern is different from that in advanced markets, this study adopts a large dataset out of 42 markets outside the U.S., including 21 advanced markets and 21 emerging markets. Our dataset covers all five main regions of international financial markets, including North America, South America, Europe, Asia-Pacific, and Middle-East markets. To our knowledge, this is the most comprehensive study on stock return seasonality in international markets. We follow Heston and Sadka (2008, 2010) to test whether stock returns exhibit seasonality in advanced and emerging markets, respectively. The Fama-MacBeth regression results suggest that seasonal patterns strongly exist in the advanced markets but very weakly in the emerging markets (Table 2). In advanced markets, stock returns are statistically positively related to the same-month returns in past 1, 2, 3, 4, and 5 years. In emerging markets, however, stock returns are only significantly positively related to the same-month returns two years from now and negatively related to the same-month returns 5 years from now. We further test whether this difference is economically meaningful. Following DeBondt and Thaler (1985), Jegadeesh and Titman (2001), Heston and Sadka (2008, 2010), we perform portfolio analysis to test whether stock return seasonality is economically significant. We allocate stocks into 10 docile portfolios according to their historical same-month returns over various historical time intervals, and form a seasonal portfolio by longing the historical same-month winner stocks and shortselling the historical same-month loser stocks. Portfolios are created over all markets in the whole sample as well as for each international market. We compute the next-month total returns as well as returns in excess of the local market portfolio returns of all stocks.
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For example, the herding behavior (Chiang and Zheng, 2010).
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The average excess return of the winner-minus-loser portfolio out of all advanced markets is as high as 0.53% (t=3.37) when the portfolio is formed based on the same-month returns in past year 1, 0.27% (t=1.77) when based on the same-month returns in past year 2-3, and 0.21% (t=1.10) when based on the same-month returns in past years 4-5. The average excess return of the winner-minus-loser portfolio out of all emerging markets is 0.11% (t=0.43) when formed based on the same-month returns in past year 1, and becomes -0.23% (t=-0.75), and -0.24% (t=-0.82) when based on the same-month returns in past years of 2-3 or 4-5. Investment strategy of buying the same-month winners and selling the same-month losers in the past one year works (i.e. delivers significant positive returns ) in 9 out of the 18 advanced economies but only in 3 out of the 19 emerging markets. 3 Moreover, this strategy can cause investors to lose money in several emerging markets (Table 4). This pattern remains when the winner-minus-loser portfolio is formed based on the same-month returns in past years of 2 or 3, consistent with the findings in Table 3 that winner-minus-loser portfolios deliver positive returns when investing in the advanced markets and fail to deliver positive returns in the emerging markets. In sum, the results suggest that stock return seasonality is not a universal phenomenon and mainly exists in advanced markets but not in emerging markets, which is also different from Heston and Sadka (2010), which focus on 14 advanced markets. It is also interesting to explore what reasons cause this difference. First, Kamstra (2017) shows that the statistical test of FamaMacBeth procedure for seasonality test may suffer severe implementation biases. We implement fixed-effect models proposed by Kamstra (2017) by controlling firmsβ expected return level. Consistently, we find that the implementation bias of the Fama-MacBeth procedure might be one
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Some markets were dropped due to data availability and reliability.
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of the reasons that cause the difference in seasonality patterns between advanced and emerging markets. After adjusting for this bias, the t-statistics of the coefficients on the same-month returns in advanced markets become insignificant or marginally significant (between 0.76 and 1.85). The t-statistics of the coefficients on the same-month returns in past year 2-3 in emerging markets, however, are almost unchanged and still significant, suggesting that implementation bias cannot be the sole reason causing this difference. We then turn to explore other possible reasons proposed in literature based on portfolio analysis. We consider both behavioral and rational theories proposed in the literature to explore the significant reasons for this difference. Keloharju et al. (2016) suggest that seasonality anomaly is intertwined with other return anomalies through shared systematic factors. We test if the winnerminus-loser gain can be explained by local Fama and French (1993) and Carhart (1997) type risk factors. In addition to factor models, the literature has proposed alternative explanations for stock return seasonality and correlation. Lewellen (2002) finds that stocks excess covariance rather than under- or over-reaction, explains momentum in the portfolios. Cooper, McConnell and Ovtchinnikov (2006) document that the returns in January have power in predicting market returns over the next 11 months of the year. We test whether the above reasons can be used to explain seasonality pattern difference between advanced and emerging markets using portfolio analysis approach. The performance difference in seasonal portfolios between the advanced markets and the emerging markets cannot be explained by the local market risk factors such as size, book-tomarket and momentum formed following Fama and French (1993) and Carhart (1997) (Table 7). The winner-minus-loser portfolios based on the same-month returns in past one year are able to deliver significant positive risk-adjusted returns (alphas) in 6 out of the 19 advanced markets and 5
only in 2 out of the 15 emerging markets. The number of advanced markets, which the winnerloser portfolios constructed on the same-month returns over past years of 2 and 3, and past years of 4 and 5 could deliver significantly positive alphas, increases to 13 and 10, respectively. The number of emerging markets increases to 4 in both cases. We then examine whether the global risk factors formed similarly to those by Fama and French (1993) and Carhart (1997) can explain the performance difference of the seasonal winner-loser portfolios between the emerging and the advanced markets and find that the local risk factors are better than the global factors in explaining local returns. 4 We find that the Fama and French type risk factors have power to explain the short-term return seasonality patterns. The fact that the seasonality patterns exist in the advanced markets but not in the emerging markets can be partly attributed to the difference in firm characteristics between the two types of stock markets. Specifically, there is significant difference in seasonality between the small firms in the advanced markets and those in the emerging markets, while little difference is found in large firms (Table 5). The empirical results also suggest that the winner-loser strategies produce significantly positive returns in January and December in the advanced markets, but not in the emerging markets (Table 6). To sum up, we find that the existence of seasonality in advanced markets and not in emerging market can be attributed to statistical, rational and behavioral reasons and beyond. The fact that we do not find a perfect answer implies that other unknown reasons driving this phenomenon are worth further analysis.
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The results are not reported, but are available upon request. For example, difference in investorβs rationality and risk aversion across countries as proposed by Kamstra, Kramer, Levi and Wang (2014) and Hirshlerfer, Jiang and Meng (2017), difference in culture, regulation and law environments Houston, Lin, Lin and Ma (2010), Houston, Lin, and Ma (2012), and Li, Griffin, Yue, and Zhao (2013), among others, are the additional potential sources worth exploring in future studies.
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The remainder of this paper is organized as the follows. We introduce the methodology, variable definitions, and data sources in Section 2. The main empirical findings are in Section 3 and Section 4 wraps up the whole paper.
2. Methodology and Data 2.1 Methodology Following Heston and Sadka (2008), the stock return seasonality test can be specified as the following two-step Fama-MacBeth (1973) regression: ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ ,
(1)
where ππππ,ππ,π‘π‘ is the return on stock i from market n in month t, the coefficient π½π½ππ,π‘π‘ represents the cross-sectional response of returns in one month to returns in the kth lagged month. For each lagged month, π½π½ππ,π‘π‘ is computed as the average of all stocks slope coefficients.
For the economic significance analysis, at the beginning of each month, stocks are
equally sorted into ten groups based on their historical seasonal (raw or excess) returns, i.e. the same-month returns in the past years of 1, 2 and 3, or 4 and 5. We form a winner portfolio by buying all stocks within the top group (highest historical seasonal returns) and a loser portfolio by buying all stocks within the bottom group. We also compute the return spread between the winner portfolio and the loser portfolio in each month. The portfolios are formed for both individual markets and all markets together throughout all available lagged months. In addition to evaluate the raw returns, we calculate the risk-adjusted portfolio performance by the following Fama-French -Carhart type four-factor model to test if the seasonality pattern can be explained by local and global risk factors: 7
ππππ,ππ,π‘π‘ β ππππππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + π΄π΄π‘π‘ οΏ½π
π
ππππ,π‘π‘ β ππππππ,π‘π‘ οΏ½ + π΅π΅π‘π‘ ππππππππ,π‘π‘ +πΆπΆπ‘π‘ π»π»π»π»π»π»ππ,π‘π‘ + π·π·ππ,π‘π‘ ππππππππ,π‘π‘ + ππππ,ππ,π‘π‘ ,
(2)
where π
π
ππππ,π‘π‘ is the monthly value-weighted return of the market portfolio in the nth market in
month t and ππππππ,π‘π‘ is the risk free rate for the nth market in month t approximated by the return of one-month U.S. Treasury Bills. ππππππππ,π‘π‘ , π»π»π»π»π»π»ππ,π‘π‘ and ππππππππ,π‘π‘ represent the return differences
between the small size stock portfolio and the large size stock portfolio, between the high book-
to-market (B/M) equity stock portfolio and the low B/M stock portfolio, and between the past winner stock portfolio and the past loser stock portfolio for the nth market in month t. 6 2.2 Data The data in this paper, including stock prices for individual firms, market price indexes, trading volumes, market capitalizations, book-to-market values and the risk-free interest rates for all international markets, are collected from the Datastream International. As noted by Ince and Porter (2006), the Datastream International data suffers several issues in relation to data coverage, classification, and integrity for international markets. In addition, according to Brennan, Huh, Subrahmanyam (2011), extreme returns may generate large illiquidity and affect the validity of the model. Therefore, to compile the data, we set a firmβs observations over a whole month to be missing if its stock returns and trading volumes by the end of each month are in the extreme the top or the bottom 1% of the cross-section in each market. To fix the massive stale data problem, we follow Ince and Porter (2006) and drop observations with security prices and trading volumes that have zero variance for more than three months during the periods. Moreover, we require 50 or more stocks for each market in each month to ensure meaningful
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See Appendix for the details of Fama-French (1993) portfolio formation.
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analysis, which means the starting date of our sample varies across markets. Because the sample is ended by June 2013, the whole data spans from January 1995, to June 2013. 7 We end up with 21 advanced markets and 21 emerging markets. 89 Monthly data are used to construct FamaFrench (1993) and Carhart (1997) risk factors. 10 Monthly stock return is defined as R t = (log(P t ) β log(P 0 )) Γ100, where P t denotes the closing price in the end of month t and P 0 the closing price in the end of month t-1. Table 1 reports summary statistics of the data, including starting date, average number of firms per month, average return per month, and total observations for each market. India stock market has the most stocks (on average 4074 per month) out of 42 markets, and stocks in Romania stock market have delivered, on average, the highest average return of 4.55% per month in the past 18 years. Hungary market, on the other hand, has the least number of stocks of average 51 per month; Italy markets performed the worst with an average return of only 0.10% per month during the sample period. In general, the average stock returns in emerging markets are larger than those in advanced markets in the past two decades. However, most advanced markets have longer sample periods, implying that analysis on emerging market may suffer small sample bias. For example, the starting point for both Bulgaria and Ukraine is May 2006. [Table 1] 3. Empirical Analysis
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Starting and ending dates varies from market to market. Data for emerging markets tend to have shorter periods. The 21 advanced markets are: Australia, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, and United Kingdom; and the 21 emerging markets are: Argentina, Brazil, Bulgaria, China, Egypt, Hungary, India, Indonesia, South Korea, Mexico, Malaysia, Morocco, Philippine, Poland, Romania, Russia, South Africa, Saudi Arabia, Turkey, Taiwan, and Ukraine. 9 According to MSCI world index in 2013, we categorize South Korea as an emerging market and Greece as an advanced market. 10 For detailed information on data and Fama-French portfolio formation, please refer to the Appendix. 8
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3.1 Statistical Analysis We start with the Fama-MacBeth (1973) two-pass procedure to test the cross-sectional correlation between returns in current month and returns in the same calendar month in previous years. We first conduct empirical analysis for model (1) with 16 lags of months examined (k=1, 2, 3β¦ 12, 24, 36, 48, 60) separately for each individual stock in our sample. To better understand the difference in seasonality patterns between advanced markets and emerging markets, we split the whole data into two groups with each group contains 21 markets (advanced and emerging) and then calculate the average π½π½ππ,π‘π‘ for both groups.
The estimation results are reported in Panel A of Table 2. The first column is the time
series averages of cross-sectional seasonal coefficients for all markets, the second column shows the time series averages for all advanced markets, and third column shows the time series averages for all emerging markets. [Table 2] For emerging markets, the seasonality coefficients are significant for lags of 1, 2, 9, 10, 12 and 24 months. The seasonality coefficient signs with lags of 1 and 2 are negative (t = -7.97 and -2.72), indicating that a short-term reversal pattern exists in emerging markets and consistent with short-term reversal literature (e.g. Lehmann, 1990; Lo and MacKinlay, 1990; and Jegadessh, 1990). More interestingly, although the signs of the coefficient on lags of 12, and 24 are positive and statistically significant (t =1.70 and 2.71), the coefficients on lags of 36 and 48 are small and insignificant and the coefficient on lag of 60 is negative, indicating that return seasonality only weakly exists in emerging markets. For the advanced markets, the seasonality coefficients are significant for lags of 1, 3, 12, 24, 36, 48 and 60 months (t =-7.14, 3.16, 3.06, 1.67, 2.62, 2.19 and 2.90). It shows significant evidence of return seasonality in these markets and is consistent 10
with Heston and Sodka (2010). For the whole sample, the coefficients are significant for lags of 1, 9, 10, 12, and 24 months (t =-9.47, 2.42, 1.98, 3.07 and 2.58), evidence of short-term reversal and seasonality. To examine the difference across individual markets, we conduct the same regressions for each country. The distribution of the t-statistics of all market-based response coefficients for the whole sample is illustrated in Figure A.1, the distribution for advanced markets in Figure A.2, and the distribution for emerging markets in Figure A.3. The average t-statistics across all markets, advanced markets, and emerging markets are plotted in Figure 1. The plots support the findings in Table 2 that the seasonality pattern at annual frequency (longer annual lags) is more significant in advanced markets and the short term momentum and return reversal (shorter lags) are more significant in emerging markets. [Figure 1] To address the misspecification concern in single regression, we conduct multivariate analysis to examine the robustness of the above findings. Specifically, we test the following augmented Model (1β): ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + β12 ππ=1 π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + π½π½24,π‘π‘ ππππ,ππ,π‘π‘β24 + π½π½36,π‘π‘ ππππ,ππ,π‘π‘β36 + π½π½48,π‘π‘ ππππ,ππ,π‘π‘β48 + π½π½60,π‘π‘ ππππ,ππ,π‘π‘β60 + ππππ,ππ,π‘π‘ ,
(1β)
The independent and dependent variables are defined in section 2, under Model (1). The estimation results of Model (1β) are reported in Panel B of Table 2, which are, in general, consistent with those in Panel A of Table 2 that the seasonality pattern at annual basis is more significant in advanced markets (seasonality coefficients are positive and significant for lags of 12, 36, 48, and 60 months) than in emerging markets (seasonality coefficients are positive 11
and significant for lags of 12 and 36 months and negative and significant for lag of 60 months). For the short-term return reversal, the coefficients are more significant for emerging markets (negative and significant for lags of 1 to 5 months) than that for advanced markets (negative and significant for 1 month only). The multivariate regression results suggest that our findings are robust when more lagged returns are included. 3.2 Portfolio Analysis 3.2.1 Whole Market Analysis The return seasonality patterns in previous section imply that exploiting these patterns may be economically meaningful. We test this by forming winner-loser portfolio strategies based on distinct annual intervals. Following Heston and Sadka (2008) and to separate our study from short-term momentum studies (Jegadeesh and Titman, 1993 and 2001), we form portfolios based on three same-month intervals: past 1 year (year 1), past years of 2 and 3 (years 2-3), and past years of 4 and 5 (years 4-5). Decile portfolios are formed based on the average same-month raw returns over each lagged interval and the portfolio performance over the next month is evaluated. For example, the winner decile portfolio of years 2-3 held in January 2013 would be an equally weighted combination of stocks that delivered the highest 10% average returns in January 2010 and January 2011. Both decile portfolio raw returns and market excess returns are calculated. 11 To save space, we only report the returns of the winner (stocks with the highest 10% samemonth returns) and the loser (stocks with the lowest 10% same-month returns) decile portfolios and the return differences between the winners and losers (Table 3) [Table 3]
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Market excess return equals to individual stock return minus value-weighted market return: ππππππππππππππ,ππ,π‘π‘ = ππππ,π‘π‘ β π
π
ππ,π‘π‘ ,
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Panel A of Table 3 reports the performance of the winnerβloser strategies formed with stocks in all markets; Panel B reports the performance of the winnerβloser strategies formed with stocks in all advanced markets; Panel C reports the performance of the winnerβloser strategies formed with stocks in all emerging markets. In general, Table 3 shows that exploiting stock return seasonality is economically significant in advanced markets but not in emerging markets. The top 10% same-month winner stocks in advanced markets outperform significantly the bottom 10% same-month loser stocks by 53 basis points (t=3.37) when stocks are sorted on same-month returns in past year 1, and 27 basis points (t=1.77) when stocks are sorted on samemonth returns in past years 2-3. The top 10% stocks in advanced markets based on the samemonth return over past years 4-5 still outperform the bottom 10% stocks while this outperformance is not significant (t=1.10). The top 10% same-month winner stocks in emerging market, however, fail to outperform the bottom 10% same-month loser stocks significantly in each case. As a result, the top 10% same-month winner stocks out of the whole sample do not outperform the bottom 10% same-month loser stocks. To sum up, Table 3 shows that stock return seasonality is economically meaningful in advanced markets but not in emerging markets, consistent with the statistical analysis results in the previous section. 3.2.2 Individual Market Analysis It is interesting and important to investigate why winner-loser strategies work in advanced markets but not in emerging markets. There are several potential reasons. One is that the results could be driven by the dominance of some specific markets in which stock return seasonality does not exist as documented in literature. 12 It is well known that there are significant differences in culture, legal system, and information environment across emerging markets but
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For example, Fountas and Segredakis (2002) and Ratner and Leal (1999).
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the difference is small among advanced markets. 13 The second possible reason is that strong heterogeneity across emerging markets weakens the economic value of seasonality when we pool all stocks and ignore heterogeneity difference. To address these concerns, we first perform the same analysis for each individual market to test whether the difference in return spread between same-month winner stocks and loser stocks across individual markets leads to, at the aggregate level, the significant difference in return seasonality between the advanced and emerging markets found in previous section. Given the facts that the sample period for some emerging markets is short, we form same-month portfolios based on three shorter time intervals: past year 1, past year 2, and past year 3 to include as many markets in the sample as possible. The top decile portfolio (winner) and bottom decile (loser) portfolio returns and the return differences are reported in Table 4. 14,15 [Table 4] Panel A of Table 4 shows the winner-loser strategy performance in advanced markets and Panel B of Table 4 shows the winner-loser strategy performance in emerging markets. It is evident that the winner-loser strategies generate significant positive returns for more advanced markets than for emerging markets. Specifically, when portfolios are formed on the same-month returns in past year 1, winners outperform losers in 9 out of 19 advanced markets, including Belgium, Finland, Japan, Netherlands, New Zealand, Norway, Spain, Switzerland, and United Kingdom, while only in 3 out of 18 emerging markets show the same pattern which are Poland, Romania, and South Africa. When portfolios are formed on the same-month returns in past year
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For example, Millar et al. (2005) We only report the portfolio raw returns to save space. The excess returns show similar patterns, and are available upon request. 15 A few markets were dropped because either they donβt have three-year data to form portfolios or there are too many stale data. 14
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2, winners outperform losers in 6 advanced markets and 1 emerging market, respectively. When portfolios are formed on the same-month in past year 3, winners outperform losers in 5 advanced markets but not in any emerging market. The results also indicate that the stock returns are more likely to respond to recent past same-month returns than with distant seasonal returns, which is consistent with our findings in section 4.2.1. In short, the results above suggest that stock return seasonality is not everywhere in the world and stock returns show significant seasonal patterns mainly in advanced markets but not in emerging markets. The difference in stock return seasonality between advanced and emerging markets is both statistically and economically significant. In the following analyses, we try to explore the underlying reasons for this difference and focus on the reasons that causes seasonal pattern in advanced markets. 3.3 Potential Explanations for Return Seasonality Previous studies proposed several explanations for the existence of stock return seasonality in U.S. from both the statistical and the economic perspective. Kamstra (2017) show that that statistical bias exists in the seasonality regressions. Keloharju et al. (2016) suggest that seasonality may be explained by multiple risk factors. The studies by Bouman and Jacobsen, (2002), Kamstra, Kramer, and Levi, (2003), and Cooper, McConnell and Ovtchinnikov (2006) suggest that stock return seasonality can be partially driven by Calendar effect on stock prices. Bogousslavsky (2016) introduces a model in that investors rebalance portfolios at different frequencies, and the empirical evidence shows that the variation in expected returns is correlated with the frequency of traderβs rebalancing horizon, which generate seasonality in the cross-
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section of stock returns. 16 In this section, we test the above potential explanations with our data and focus on the existence of seasonality in advanced markets. 3.3.1 Implementation bias and seasonality Kamstra (2017) argues that stock return momentum and the time-series autocorrelation from Fama-MacBeth regressions have been exaggerated due to a common implementation bias. Specifically, he shows via simulations that the findings in Heston and Sadka (2008, 2010) are problematic as the lagged returns are spuriously correlated with time t returns and they could have different expected values. Since our research follows Heston and Sadka (2008, 2010), we revise Model 1 and Model 1β to a fixed effect model by forming the firm expected return (average historical returns are used as the proxy) into deciles as suggested by Kamstra (2017)17 and re-run the following fixed effect models: ππππ,ππ,π‘π‘ = β10 ππ=1 πΌπΌ0,ππ π·π·ππ,ππ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ ,
(3)
12 ππππ,ππ,π‘π‘ = β10 ππ=1 πΌπΌ0,ππ π·π·ππ,ππ + βππ=1 π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + π½π½24,π‘π‘ ππππ,ππ,π‘π‘β24 + π½π½36,π‘π‘ ππππ,ππ,π‘π‘β36 + π½π½48,π‘π‘ ππππ,ππ,π‘π‘β48 +
π½π½60,π‘π‘ ππππ,ππ,π‘π‘β60 + ππππ,ππ,π‘π‘ ,
(3β)
where j represents the decile of the firm iβs expected return, which is calculated by the average of the firmβs past 12 month returns, and π·π·ππ,ππ equals 1 when firm i is in the expected return decile j, 0 otherwise. All other variables are defined in section 2, under Model (1).
The model estimations are reported in Table 5, where Panel A shows single lag regression results and Panel B shows multiple lags regression results. Firstly, the results show that seasonality patterns still exist in international markets, especially for shorter time horizon
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We will skip investigating this reason because we do not have trading data. We also tested an alternative model by including average past returns in the equation as proposed by Kamstra (2017), and the results are similar with the fixed effect model. The results are available upon request.
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(12th and 24th lags) in both advanced and emerging markets, which is consistent with our main findings in this research. However, they also suggest that the model specification bias found by Kamstra (2017) has significant impact on stock return seasonality, especially for advanced markets. Compared to the results in Panel A of Table 2, less lag coefficients are significant in Panel A of Table 5. Specifically, only the coefficients of 12th and 36th lags are positive and significant for advanced markets (coefficient of lag 36 is only marginal significant at 10%), while all coefficients of 12th, 24th, 36th, 48th, and 60th lags are positive and significant for advanced markets in Table 2. The results for all markets and advanced markets are similar between Table 2 and Table 5, where the coefficients of two of the seasonal lags (12th and 24th) are significant in Table 2 and the coefficients of three of the seasonal lags (12th, 24th, and 36th) are significant in Table 5. The results in Panel B are similar to those in Panel A of Table 5. When we use multiple regressions, the seasonality patterns still exist, but the difference between advanced markets and emerging markets is largely disappeared. The results in Table 5 also imply that the estimation model bias suggested by Kamstra (2017) might be one of the reasons but cannot be the only reason that cause significant seasonality patterns in advanced markets. [Table 5] 3.3.2 Seasonality and Firm Size Another explanation for the different seasonality patterns between advanced markets and emerging markets might be the characteristics of firms. As emerging markets tend to have weaker legal environment than advanced markets and less strict requirements for companies going public, 18 public firms in emerging markets might be smaller and more diverse compared to those in advanced markets. Therefore, in this section, we allocate all firms into two groups in 18
For example, Klapper and Love (2004) and Fan, Wei, and Xu (2011).
17
each market at the beginning of each month based on firm size defined as the market capitalization of common stocks outstanding and then form decile portfolios based on three time intervals: past year 1, past years 2-3, and past years 4-5, within each size group. The top decile portfolio (winner) and bottom decile (loser) portfolios excess returns and return differences are reported in Table 6. [Table 6] Panel A of Table 6 reports the performance of the winner-loser strategies based on large firms in all markets, advanced markets, and emerging markets; Panel B reports the performance of the winner-loser strategies based on small firms in all markets, advanced markets, and emerging markets. The results confirm our conjecture that the difference in stock return seasonality between advanced and emerging markets is more pronounced with small firms than large firms. For the large firm group, stock return seasonality is strong in year 1 but not in other lagged years for both markets and there is little difference between advanced markets and emerging markets (Panel A). The winner-loser strategies generate positive and significant returns (52 basis points for advanced markets and 54 basis points for emerging markets) based on the same-month returns in past year 1 but not based on the same-month returns in distant time intervals. The differences in return seasonality between the advanced markets and the emerging markets in small firms, however, are prominent. For advanced markets (Panel B), the excess returns delivered by past same-month winners in all three time intervals are positive and negative by past same-month losers while the excess returns by both past same-month winners and losers in emerging markets are negative. In addition, the winner-loser strategies sorted on the samemonth returns in past years 2-3 generate positive and marginally significant (at 10% level) returns in advanced markets, but negative and insignificant returns in emerging markets. The size 18
effect will be further investigated in next section when we control for the Fama-French factors to test seasonality alphas. 3.3.3 Calendar Effect and Seasonality For each calendar month, equally weighted stock returns are sorted into ten groups based on their historical same-month returns in past year 1, years 2-3, or years 4-5, respectively. Winners are stocks within the top group (highest 10% historical same-month returns) and losers are stocks within the bottom group. Table 7 presents the portfolio returns of winner and loser groups and the performance of winner-loser strategies (longing winner stocks and shorting loser stocks) in each calendar month. Panel A reports the results for advanced markets group and Panel B reports emerging markets group. 19 [Table 7] The calendar effect on stock returns is more prominent in advanced markets, especially in January and December. The winner-loser strategies sorted on all three time intervals deliver significantly positive returns in January, 82 basis points (t=1.77) by portfolios sorted on the same-month return in past year 1, 125 basis points (t=2.13) in past years 2-3, and 184 basis points (t=3.93) in past years 4-5. In December the same-month winner-loser strategies deliver a return of 160 basis points (t=3.36) when stocks are sorted on same-month returns in past year 1, 147 basis points (t=2.60) when sorted on past years 2-3, and 86 basis points (t=1.77) when sorted on past years 4-5. One the other hand, there is no obvious pattern for emerging markets, the winner-loser strategies produced significantly positive returns in March (significantly negative returns for May) when stock are formed on the same-month returns in past year 1, in February
19
A few markets were dropped because either they donβt have three-year data to form portfolios or there are too many stale data.
19
when formed on same-month returns in past years 2-3, and in August when formed on samemonth returns in past years 4-5. The results are in line with the studies on January effect (Bouman and Jacobsen, 2002; Kamstra, Kramer, and Levi, 2003) that stock return patterns tend to be different in January than other months, especially in advanced markets. It is also consistent with our previous findings that stock return seasonality is stronger in advanced markets than in emerging markets. It is likely that tax loss selling is one of the major driving factors for the different results between advanced markets and emerging markets in calendar effect of seasonality. In an early study, Gultekin and Gultekin (1983) examine stock market seasonality in major advanced countries and they find that that there are disproportionately large January returns in most countries and April returns in the U.K., and these months are also the beginning of a tax year in each country. For many emerging markets, however, accounting standards and tax laws had not been well developed and strictly enforced especially at individual level. For example, among the many, Claessens et al. (1995) and Fountas and Segredakis (2002) both find very limited or little evidence in favor of the turn-of-the-tax-year effect and the tax-loss selling hypothesis in emerging markets. 3.3.4 Risk-Adjusted Returns Fama and French (1993) introduce a three-factor (market risk premium, size, book-tomarket ratio) model to price asset returns. Carhart (1997) proposes an additional momentum factor and argue that the four-factor model can better explain cross-sectional stock returns. In this section, we construct the four risk factors for each market and investigate whether the
20
seasonality pattern still remains after being adjusted for these risk premiums. 20 Specifically, in each month we sort stocks into ten groups based on their historical same-month returns respectively in past years of 1, 2, or 3, and calculate portfolio returns for next month and apply Model 2 to adjust the risk premiums in portfolio returns (alpha). 21
22
Table 8 presents the risk-
adjusted portfolio returns of winner and loser groups and the performance of winner-loser strategies (longing winner stocks and shorting loser stocks) in each market. Panel A is for advanced markets and Panel B is for emerging markets. 23 [Table 8] The results of Table 8 are consistent with those in Table 4 that the seasonality patterns exist, in terms of portfolio returns after being adjusted by the four risk factor premiums, in advanced markets but not in emerging markets. In particular, for portfolio formed on the samemonth returns in past year 1, the winner-loser strategies produce significantly positive profit in Germany, Japan, New Zealand, Singapore, Switzerland, and United Kingdome out of the advanced markets, and only in China, Romania out of the emerging markets; for portfolio formed on the same-month returns in past year 2, the winner-loser strategies work well in Canada, Finland, France, Greece, Italy, Norway, and Spain of advanced markets, and in Korea, Malaysia, Turkey and Taiwan of emerging markets; for portfolio formed on the same-month returns in past year 3, the winner-loser strategies work in 10 advanced markets and in 4 emerging markets, most of which show the same pattern when portfolios are formed on the same-month returns in past year 2. The evidence indicates that the return seasonality patterns are more 20
For details on how Fama-French-Carhart factors are formed, please see Appendix. See detailed explanation of the model in section 2. 22 It can also be interesting to include other variables in the specification such as weather in each market while we do not have these data. We thank to an anonymous referee for making this point. 23 A few markets were dropped because either they donβt have three years data to form portfolios or there are too many stale data. 21
21
prominent in advanced markets than in emerging markets after being adjusted for risk premiums, and the seasonality patterns are more prominent for Asian emerging markets. There is also a major difference in the results from those in Table 4 that return seasonality, in terms of riskadjusted returns of winner-loser portfolio, exists in more markets when portfolios are formed on the same-month returns over remote years. In particular, the strategies work in 13 and 10 advanced markets when portfolios are respectively formed on the same-month returns in year 2 and year 3, in 6 advanced markets when on the same-month returns in year 1. These numbers of emerging markets become 4, 4 and 2. The evidence indicates that risk factors might be able to explain part of short-term seasonality patterns in international stock returns. In an unreported diagnosis, we replace the local Fama-French-Carhart risk factors with global Fama-French-Carhart risk factors to compute risk-adjusted returns and the risk-adjusted returns delivered by the winner-loser strategies are almost unchanged relative to the raw returns, indicating that the global risk factors have less power in explaining stock return seasonality patterns compared to local risk factors. 24 4. Conclusion This paper investigates stock return seasonality patterns in international markets. We collect data from 42 international markets, including 21 advanced markets and 21 emerging markets. Those markets cover all five regions of international financial markets from North America, South America to Europe, Asia-Pacific, and Middle-East. The data span from January 1995, to June 2013. Following Heston and Sadka (2008), we apply the Fama-MacBeth (1973) methodology to estimate the seasonal coefficients that represent cross-sectional response of returns at one date to returns in the same-month in previous years. The results reveal that stock 24
The results are available upon requests.
22
returns show significant seasonality patterns in advanced markets but not in emerging markets. The findings remain with multivariate analyses including multiple seasonal returns. We further perform portfolio analysis to test whether winner-loser portfolio strategies based on the same-month returns in past years generate significant profits. We sort stocks based on the same-month returns in three time intervals: past year 1, years 2-3, and years 4-5. Decile portfolios formed on the average monthly raw return over all months in each lagged interval and the portfolio returns are measured over the next month. The results show that stock return seasonality is economically significant in advanced markets but insignificant in emerging markets. Specifically, based on past year 1 seasonal return, winners outperform losers by 51 basis points in raw returns in advanced markets while the significance decreases for portfolios sorted on more distant past seasonal returns (more than 12 months). We breakdown the whole market groups into individual market and find that winners outperform losers in 9, 6, and 5 advanced markets when portfolios are formed by the same-month returns in past year 1, 2, or 3, respectively. On the other hand, winners outperform losers in 3, 1, and 0 emerging markets when portfolios are formed by the same-month returns in past year 1, 2, and 3, respectively. We further investigate the possible explanations for the difference in stock return seasonality patterns in international markets and find that this difference can be attributed to various reasons, including regression bias, size, risk premium and Calendar effect. Our alternative test following Kamstra (2017) suggests that the difference in seasonality pattern between advanced and emerging markets might be partially attribute to the implementation bias of the Fama-MacBeth procedure. After we control firmsβ lagged returns (proxy of the cross-sectional dispersion of mean returns), the difference between advanced markets and emerging markets is largely weakened. The detailed reasons are worth further 23
investigation. The different patterns between the advanced markets and the emerging markets can also be partly attributed to the difference in firm characteristics such as size. For large firms, the winner-loser strategies generate similar profits in both the advanced the and emerging markets based on past returns (52 basis points in advanced markets and 54 basis points in emerging markets based on past year 1 return, but not for more distant time intervals). For small firms, however, the differences in return seasonality between the advanced markets and the emerging markets are prominent. Specifically, the winner-loser strategies can generate positive excess returns particularly when the strategies are formed on the same-month returns in past years 2-3, but the winnersβ portfolio cannot generate consistently higher excess returns than the losersβ portfolios in emerging markets. Third, we find significantly January and December effects on the returns of the seasonal portfolios formed based on all three formation intervals (past year 1, years 2-3, and years 4-5) in advanced markets, but no effect on seasonal portfolios in emerging markets. The results are in line with the extensive studies on January effects (Bouman and Jacobsen, 2002; Kamstra, Kramer, and Levi, 2003) that stock return patterns tend to be more profound in January than other months, it is especially true for advanced markets whose tax year starts in January. Lastly, we test if the Fama-French-Carhart risk factors can explain the stock return seasonality patterns. For emerging markets, the seasonality patterns exist prominent in Asian markets. Specifically, the seasonal winner-loser strategies produce significantly positive profit in 6, 13, and 10 advanced markets when portfolios are formed on seasonal returns in past year 1, 2, and 3, respectively, and in 2, 4, and 4 emerging markets. However, the fact that the winner-loser strategies work in more markets when portfolios are formed by distant past seasonal returns indicates that Fama-French-Carhart risk factors might be
24
able to explain more of the short-term seasonality patterns than the long term seasonality patterns in international stock returns. In terms of future research, it is interesting to investigate other possible explanations for this seasonality in advanced markets, including investorβs sentiment, risk aversion, literature, regulation, and so on.
25
Appendix: Data and Fama-French-Carhart Portfolio Formation
The data used in this study is from Datastream International, including stock price, trading volume, market capitalization, and book-to-market value. Formation of size, book-to-market, and momentum portfolios follows the procedure in Fama-French (1993). Portfolios are rebalanced every month and evaluated in subsequent one month. To form portfolios, all firms must have book-value data for December in year t and equity data (stock price and market capitalization) from the starting date of year t. Stocks are independently divided into five groups by size (large/small market capitalization), book-to-market ratios (High/Low), and momentum. The size portfolios are formed by on firmβs capitalization at the end of June of year t-1. The book-tomarket and momentum portfolios are formed at the end of December of year t-1. Then we calculate the value-weighted returns for each portfolio, and form the Fama-French and momentum factors as the return difference between the corresponding top portfolio and the bottom portfolio.
26
Figure A.1: Distribution of Seasonality Coefficients for All Markets. This figure plots the distribution of the t-statistics of the time series averaged coefficients of cross-sectional return response from one month to up to 60 months for each country. In each month and for each country, return seasonal coefficient is estimated from the following specification: ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ , ππ = 1,2, . . πΌπΌ, ππ = 1,2 β¦ 60; π‘π‘ = 1, 2, β¦ ππ, where i denotes ith stock, n denotes nth country, and ππ denotes the kth lag. The sample period is from January 1995 to December, 2013. 6
T-statisratics of Seasonality Coefficient
4
2
0
-2
-4
-6 0
6
12
18
24
30
36
Month lag
27
42
48
54
60
arg
aus
bel
brl
bul
can
chn
den
egy
fin
fr
ger
gre
hk
hug
ind
ine
ire
isr
it
jp
kor
mex
mly
mor
net
nez
no
phl
po
pol
rom
rua
saf
sau
si
sp
sw
tur
tw
uk
ukr
Figure A.2: Distribution of Seasonality Coefficients across Advanced Markets. This figure plots the distribution of the t-statistics of the time series averaged coefficients of cross-sectional return response from one month to up to 60 months for each advanced market. In each month and for each market, return seasonal coefficient is estimated from the following specification: ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ , ππ = 1,2, . . πΌπΌ, ππ = 1,2 β¦ 60; π‘π‘ = 1, 2, β¦ ππ, where i denotes ith stock, n denotes nth country, and ππ denotes the kth lag. The sample period is from January 1995 to December, 2013. 6
aus bel can
T-statistics of Seasonality Coefficients
4
den fin fr ger
2
hk ire isr
0
it jp net
-2
nez no po si
-4
sp sw uk
-6 0
6
12
18
24
30 Month lag
28
36
42
48
54
60
Figure A.3: Distribution of Seasonality Coefficients across Emerging Markets This figure plots the distribution of the t-statistics of the time series averaged coefficients of cross-sectional return response from one month to up to 60 months for each emerging market. In each month and for each market, return seasonal coefficient is estimated from the following specification: ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ , ππ = 1,2, . . πΌπΌ, ππ = 1,2 β¦ 60; π‘π‘ = 1, 2, β¦ ππ, where i denotes ith stock, n denotes nth country, and ππ denotes the kth lag. The sample period is from January 1995 to June, 2013. 6
arg brl
T-statistics of Seasonality coefficient
bul chn
4
egy gre hug
2
ind ine kor mex
0
mly mor no
-2
phl pol rom rua
-4
saf sau tur
-6
tw
0
6
12
18
24
30 Month lag
29
36
42
48
54
60
ukr
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Heston, Steven L., and Ronnie Sadka, 2010. "Seasonality in the cross section of stock returns: the international evidence." Journal of Financial and Quantitative Analysis 45(5): 1133-1160. Ho, YanβKi, 1990. "Stock return seasonalities in Asia Pacific markets." Journal of International Financial Management & Accounting 2 (1): 47-77. Houston, Joel F., Chen Lin, Ping Lin, and Yue Ma (2010). βCreditor rights, information sharing and bank risk taking.β Journal of Financial Economics 96 (3): 485-512. Houston, Joel F., Chen Lin, and Yue Ma, 2012. βRegulatory arbitrage and international bank flows.β Journal of Finance 67 (5):1845-1895. Ince, Ozgur S., and R. Burt Porter, 2006. "Individual equity return data from Thomson Datastream: Handle with care!" Journal of Financial Research 29 (4): 463-479. Jegadeesh, Narasimhan, and Sheridan Titman, 1995. "Short Horizon Reversals and the Bid-Ask Spread." Journal of Financial Intermediation 4 (2):116-132. Jegadeesh, Narasimhan, and Sheridan Titman, 1993. "Returns to buying winners and selling losers: Implications for stock market efficiency." The Journal of finance 48 (1): 65-91. Jegadeesh, Narasimhan, and Sheridan Titman, 2001. "Profitability of momentum strategies: An evaluation of alternative explanations." The Journal of Finance 56 (2): 699-720. Kamstra, Mark. J. 2017. Momentum, Reversals, and other Puzzles in Fama-MacBeth CrossSectional Regressions. Working Paper, York University. Kamstra, Mark J., Lisa A. Kramer, and Maurice D. Levi, 2003. "Winter blues: A SAD stock market cycle." The American Economic Review 93 (1): 324-343. Keloharju, Matti, Juhani T. Linnainmaa, and Peter Nyberg, 2016. "Return seasonalities." The Journal of Finance 71 (4):1557-1590. Klapper, F. Leora and Love, Inessa, 2004. Corporate governance, investor protection, and performance in emerging markets. Journal of corporate Finance, 10(5): 703-728. Lewellen, Jonathan, 2002. "Momentum and autocorrelation in stock returns." Review of Financial Studies 15 (2): 533-564. Li, Kai, Dale Griffin, Heng Yue, and Longkai Zhao, 2013. βHow does culture influence corporate risk-taking.β Journal of Corporate Finance 23: 1-22. Millar, CJM Carla., Eldomiaty, Tarek I., Choi, Chong Ju, and Hilton, Brian, 2005. Corporate governance and institutional transparency in emerging markets. Journal of business ethics, 59(1):163-174. Pandey, I. M, 2002. "Seasonality in the Malaysian stock market: 1992-2002."Journal of Financial Management & Analysis 15 (2): 37.
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Figure 1: Statistical Significance of Seasonality Tests. This figure plots the distribution of the average t-statistics of time series averaged coefficients of cross-sectional return response from one month to up to 60 months for all markets, advanced markets or emerging markets. In each month and for each country, return seasonal coefficient is estimated from the following specification: ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ , ππ = 1,2, . . πΌπΌ, ππ = 1,2 β¦ 60; π‘π‘ = 1, 2, β¦ ππ, where i denotes ith stock, n denotes nth country, and ππ denotes the kth lag. The sample period is from January 1995 to December, 2013. Average t-statistics of Seasonality Coefficients
2 1 1 0 -1 -1 -2 -2 -3
All market
Advanced markets
Emerging markets
-3 -4 1
6
11
16
21
26
31 Month lag
33
36
41
46
51
56
Table 1: Summary Statistics This table reports summary statistics of stocks for each market and across all 42 markets. Markets are grouped into advanced and emerging markets. The former includes Australia, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Switzerland, and United Kingdom, and markets in the latter groups are Argentina, Brazil, Bulgaria, China, Egypt, Hungary, India, Indonesia, Korea, Mexico, Malaysia, Morocco, Philippine, Poland, Romania, Russia, South Africa, Saudi Arabia, Turkey, Taiwan, and Ukraine. Number of stocks, number of observations and average monthly returns are reported. We require 5 or more stocks in each month for each market to be included in the sample. The starting month for each market is reported in the first column. The sample period is ended by June 2013. Country Argentina Australia Belgium Brazil Bulgaria Canada China Denmark Egypt Finland France Germany Greece Hong Kong Hungary India Indonesia Ireland Israel Italy Japan Korea Mexico Malaysia Morocco Netherlands New Zealand Norway Philippine Portugal Poland Romania Russia South Africa Saudi Arabia Singapore Spain Switzerland Turkey Taiwan United Kingdom Ukraine Emerging Advanced Total
Starting date
Number of firms
Average returns (%)
Total Observations
1995.1 1995.1 1995.1 1995.7 2006.5 1995.1 1997.7 1995.1 1996.11 1995.1 1995.1 1995.1 1995.1 1995.1 2006.1 1995.1 1995.1 1999.1 1995.1 1995.1 1995.1 1995.1 1995.1 1995.1 1998.9 1995.1 1995.1 1995.1 1995.1 1995.2 1997.9 1997.1 2003.5 1995.1 2002.8 1995.1 1995.1 1995.1 1995.1 1995.1 1995.1 2006.5 NA NA NA
85 183 241 194 353 995 250 173 133 215 805 959 337 1289 51 4074 427 75 479 268 2529 1698 120 902 77 243 123 226 238 90 793 189 244 247 158 480 283 435 383 1659 454 249 12861 10545 23406
1.45 0.63 0.56 2.08 2.32 1.75 1.04 0.61 1.47 0.58 1.07 0.85 0.53 1.56 0.47 2.44 2.37 0.98 1.14 0.10 0.45 1.71 1.40 0.78 0.30 0.60 0.58 0.71 2.29 0.83 0.62 4.55 1.93 1.65 1.02 0.92 0.42 0.72 3.34 0.82 0.78 3.22 1.72 0.79 1.28
15794 24720 34065 19058 25943 135773 24640 29408 18455 34303 121068 139768 50818 179907 3123 584896 55346 8932 80813 38725 463767 236790 20258 138333 9312 38353 17665 27053 42717 14148 49315 26370 17105 38632 24508 61083 40411 64631 56839 206562 71052 15809 1680623 1612782 3293405
34
Table 2: Statistical Test of Stock Return Seasonality This table reports the results of stock return seasonality using the Fama-MacBeth two-pass approach. Panel A reports the results of seasonal test by single regression specified as: ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ and Panel B reports the results by multiple regression specified as : ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + β12 where ππ=1 π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + π½π½24,π‘π‘ ππππ,ππ,π‘π‘β24 + π½π½36,π‘π‘ ππππ,ππ,π‘π‘β36 + π½π½48,π‘π‘ ππππ,ππ,π‘π‘β48 + π½π½60,π‘π‘ ππππ,ππ,π‘π‘β60 + ππππ,ππ,π‘π‘ ππππ,ππ,π‘π‘ is the return on stock i from market n in month t, the slope coefficient π½π½ππ,π‘π‘ represents cross-sectional response of returns at one month to returns at a previous month k. We first conduct cross-sectional linear regression in each month and report the averages of time series coefficients (in parentheses). We conduct analyses for all, advanced and emerging markets, respectively. The t-statistics are adjusted for heteroskedasticity and autocorrelation. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively. The sample period is from January 1995 to June 2013. Return lag ππ
All markets Coefficient
t-stat
Advanced markets Coefficient t-stat
Emerging markets Coefficient t-stat
Panel A. Single regression results 1 2 3 4 5 6 7 8 9 10 11 12 24 36 48 60
-0.043*** -0.005 0.004 0.005 0.001 0.006 0.004 0.002 0.008** 0.006** 0.003 0.008*** 0.007** 0.003 0.009 0.001
(-9.47) (-1.29) (1.09) (1.32) (0.36) (1.31) (1.22) (0.73) (2.42) (1.98) (1.03) (3.07) (2.58) (1.39) (1.59) (0.49)
-0.040*** 0.008 0.011*** 0.005 0.002 0.004 0.005 0.004 0.002 0.002 0.002 0.009*** 0.004* 0.007** 0.012** 0.007***
35
(-7.14) (1.67) (3.16) (1.04) (0.41) (0.88) (1.22) (0.96) (0.49) (0.37) (0.65) (3.06) (1.67) (2.62) (2.19) (2.90)
-0.044*** -0.013*** 0.002 0.003 0.000 0.007 0.004 0.001 0.011** 0.008** 0.004 0.006* 0.012*** 0.002 0.001 -0.006
(-7.97) (-2.72) (0.3) (0.68) (-0.1) (1.15) (1.11) (0.2) (2.26) (2.12) (0.89) (1.70) (2.71) (0.68) (0.23) (-1.18)
Panel B. Multiple regression results 1 2 3 4 5 6 7 8 9 10 11 12 24 36 48 60
-0.049*** (-10.76) -0.009** (-2.52) 0.001 (0.48) 0.003 (0.85) 0.002 (0.77) 0.004 (1.17) 0.003 (1.19) 0.003 (0.95) 0.008** (2.59) 0.006** (2.37) 0.004 (1.61) 0.008*** (3.71)
-0.039*** (-8.67) -0.014*** (-3.78) 0.004 (1.24) -0.005* (-1.76) 0.003 (1.09) 0.002 (0.53) 0.000 (0.11) 0.001 (0.42) -0.002 (-0.92) 0.002 (0.84) 0.011*** (3.71) 0.000 (0.03) 0.002 (1.26) 0.008*** (4.05) 0.004*** (2.51) 0.001 (0.67)
-0.046*** (-8.40) 0.003 (0.64) 0.009*** (2.72) 0.003 (0.93) 0.001 (0.35) 0.004 (1.01) 0.004 (1.23) 0.002 (0.63) 0.001 (0.38) 0.001 (0.35) 0.005 (1.63) 0.010*** (3.82)
36
-0.048*** (-7.63) -0.001 (-0.17) 0.006* (1.71) 0.004 (1.08) 0.001 (0.45) 0.004 (0.92) 0.001 (0.34) 0.001 (0.18) 0.003 (0.70) 0.000 (0.08) 0.007*** (2.18) 0.011*** (3.03) 0.002 (1.01) 0.006*** (3.32) 0.010*** (2.34) 0.008*** (2.94)
-0.051*** (-9.40) -0.019*** (-4.47) -0.003 (-0.75) 0.000 (-0.02) 0.000 (-0.03) 0.004 (0.87) 0.004 (1.36) 0.002 (0.74) 0.011** (2.59) 0.008*** (2.66) 0.005 (1.28) 0.006** (2.30)
-0.034*** (-5.41) -0.027*** (-6.07) -0.010*** (-2.99) -0.010*** (-3.81) -0.007*** (-2.39) -0.002 (-0.39) -0.001 (-0.32) -0.002 (-0.62) 0.000 (-0.09) -0.001 (-0.34) 0.004 (1.36) 0.007* (1.85) 0.003 (1.40) 0.007*** (2.78) 0.001 (0.39) -0.007*** (-2.20)
Table 3: Economic Significance of Stock Return Seasonality This table reports the economic value of stock return seasonality. In each month we allocate all stocks into decile groups based on historical seasonal return over three rolling windows: past year 1, past years 2-3, or years 4-5 and calculate the equal-weighted portfolio returns over subsequent one month for each decile. We report the portfolio returns of winner stocks (highest historical seasonal return decile) and loser stocks (lowest historical seasonal return decile) and spread between the two groups. Panel A reports the results using the whole sample; Panel B reports the results with stocks in the advanced markets, and Panel C with stocks in the emerging markets. The associated Newey-West t-statistics with 4 lags are in parentheses. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively. The sample period is between January 1995 and June 2013. Panel A: All Markets
Winners Losers Winners-losers
Winners Losers Winners-losers
Panel B: Advanced Markets
Total Return (%)
Excess return (%)
Total Return (%) Seasonality basis: past year 1 1.55***
1.94***
0.43***
(5.31)
(4.31)
(4.32)
1.83***
0.16
(4.63)
Panel C: Emerging Markets
Excess return (%)
Total Return (%)
Excess return (%)
0.57***
2.46***
0.42***
(4.97)
(5.46)
(3.08)
1.04***
0.03
2.51***
0.32*
(1.33)
(2.75)
(0.28)
(5.01)
(1.72)
0.11
0.27
0.51***
0.53***
-0.06
0.11
(0.63)
(1.59)
(3.14)
(3.37)
(-0.22)
(0.43)
Seasonality basis: years 2-3 1.81***
2.17***
0.33***
0.50***
2.31***
0.10
(5.81)
(3.04)
(4.80)
(4.36)
(4.65)
(0.38)
2.11***
0.15
1.63***
0.24*
2.64***
0.33**
(5.58)
(1.32)
(4.06)
(1.84)
(5.74)
(1.96)
0.05
0.18
0.18
0.27*
-0.34
-0.23
(0.36)
(1.34)
(1.14)
(1.77)
(-1.06)
(-0.75)
Seasonality basis: years 4-5 Winners Losers Winners-losers
1.76***
0.08
1.25***
0.27**
2.34***
-0.05
(4.37)
(0.81)
(3.14)
(2.29)
(4.75)
(-0.26)
1.96***
0.10
1.11***
0.06
2.72***
0.19
(4.77)
(0.86)
(2.89)
(0.49)
(5.15)
(0.93)
-0.21
-0.02
0.140
0.21
-0.38
-0.24
(-1.11)
(-0.11)
(0.72)
(1.10)
(-1.29)
(-0.82)
37
Table 4: Economic Significance of Stock Return Seasonality by Stock Market This table reports the economic value of stock return seasonality for each stock market. In each month and for each market we sort stocks into decile groups based on historical seasonal return over three rolling windows: past year 1, year 2, or year 3 and calculate the equal-weighted portfolio returns over subsequent month for each decile. We report the portfolio returns of the winner stocks (highest historical seasonal return decile) and loser stocks (lowest historical seasonal return decile) and spread between the two groups. Panel A shows the results for each individual advanced market, and Panel B for each individual emerging market. The associated Newey-West t-statistics with 4 lags are in parentheses. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively.
Seasonality
Winners
Year 1 Losers
WML
Winners
Year 2 Losers
WML
Winners
Year 3 Losers
WML
0.78 (0.67) 0.92* (1.64) 0.09 (0.18) 0.44 (0.84) 0.93* (1.67) 0.59 (1.53) 0.62 (1.43) -0.56 (-0.76) 0.14 (0.31) -0.20 (-0.38) -0.20 (-0.35) 0.69*** (3.11) 1.17* (1.83) 1.74* (1.78) 1.30* (1.82) -0.15 (-0.26) 0.98** (2.16) 1.24*** (3.26) 1.11*** (2.99)
0.54 (0.64) 1.37** (2.41) 3.18*** (4.88) 0.87 (1.55) 1.38** (2.39) 2.04*** (4.96) 1.59*** (3.76) -0.13 (-0.15) 1.95** (2.28) 1.14** (2.04) -0.01 (-0.01) 1.18** (2.45) 1.24** (2.06) 2.41*** (3.43) 0.72 (0.85) 0.98 (1.41) 0.97* (1.84) 1.78*** (3.61) 1.45*** (3.27)
0.28 (0.35) 0.69 (1.10) 2.28*** (3.16) 1.20** (2.33) 0.56 (0.89) 2.27*** (4.18) 1.58*** (3.17) -0.49 (-0.59) 2.40*** (2.62) 1.54** (2.57) -0.34 (-0.54) 0.38 (0.78) 0.09 (0.14) 1.34 (1.01) 0.14 (0.13) 1.55** (1.96) 0.20 (0.36) 0.55 (1.21) 1.07** (2.41)
0.26 (0.32) 0.68 (1.14) 0.89* (1.70) -0.34 (-0.57) 0.82* (1.83) -0.23 (-0.45) 0.01 (0.02) 0.36 (0.64) -0.45 (-0.91) -0.40 (-0.89) 0.33 (0.80) 0.80*** (3.80) 1.15** (2.22) 1.07 (0.74) 0.59 (0.81) -0.57 (-1.22) 0.77** (2.04) 1.22*** (3.62) 0.38 (1.19)
0.65 (0.53) 1.14 (1.61) 2.46*** (3.16) 1.46** (2.25) 1.69*** (2.93) 1.90*** (4.18) 1.37*** (3.02) 0.18 (0.22) 2.15*** (2.77) 1.70*** (2.60) 0.19 (0.32) 1.15** (2.45) 1.83*** (2.80) 1.81** (2.11) 1.30 (1.28) 2.09** (2.48) 0.81 (1.36) 1.57** (2.58) 1.38*** (3.25)
-0.47 (-0.55) 0.94 (1.46) 2.82*** (3.69) 0.47 (0.83) -0.33 (-0.59) 1.49*** (3.12) 1.00** (2.17) -0.28 (-0.37) 2.71*** (2.93) 1.34** (2.38) -0.63 (-1.15) 0.33 (0.75) 0.48 (0.80) 1.69 (1.03) 0.96 (1.11) 1.50* (1.80) 0.47 (0.77) 0.57 (1.42) 1.50*** (2.75)
1.12 (0.93) 0.20 (0.24) -0.36 (-0.71) 0.99 (1.57) 2.03*** (4.75) 0.40 (0.83) 0.37 (0.84) 0.47 (0.85) -0.56 (-1.25) 0.37 (0.78) 0.82** (2.24) 0.82*** (4.35) 1.34** (2.38) 0.12 (0.07) 0.34 (0.40) 0.58 (0.89) 0.34 (0.76) 1.00** (2.10) -0.11 (-0.27)
Panel A: advanced countries Australia Belgium Canada Denmark Finland France Germany Greece Hong Kong Israel Italy Japan Netherlands New Zealand Norway Singapore Spain Switzerland United Kingdom
2.23** (1.94) 0.94* (1.93) 3.25*** (4.68) 1.08** (2.41) 0.78 (1.28) 2.14*** (5.00) 1.58*** (3.48) 0.81 (0.91) 2.15*** (2.70) 1.58*** (2.82) -0.05 (-0.10) 0.95*** (2.17) 1.14* (1.73) 1.34* (1.67) 1.17 (1.44) 1.62** (2.03) 1.19** (2.26) 1.76*** (3.90) 1.84*** (4.54)
1.45* (1.94) 0.02 (0.03) 3.17*** (4.59) 0.64 (1.10) -0.15 (-0.25) 1.55*** (3.15) 0.96* (1.87) 1.37 (1.35) 2.01** (2.29) 1.78*** (2.97) 0.15 (0.21) 0.26 (0.53) -0.03 (-0.05) -0.40 (-0.49) -0.13 (-0.15) 1.78* (1.91) 0.21 (0.35) 0.52 (1.06) 0.73 (1.49)
38
Panel B: Emerging markets Brazil Bulgaria China Egypt India Indonesia Korea Mexico Malaysia Philippine Poland Romania Russia South Africa Saudi Arabia Turkey Taiwan Ukraine
0.27 (0.21) 2.63*** (2.86) 1.66* (1.67) 0.40 (0.27) 3.29*** (4.48) 2.42*** (3.31) 1.84** (2.51) 1.99 (1.61) 0.93 (1.39) 3.09*** (3.73) 2.90*** (3.48) 5.95*** (5.09) 3.71* (1.90) 3.32*** (5.65) 0.20 (0.20) 3.78*** (4.05) 0.46 (0.71) 0.27 (0.21)
1.97 (1.44) 1.63* (1.77) 0.91 (0.88) -0.54 (-0.39) 3.12*** (3.99) 2.96*** (3.26) 1.74* (1.94) 0.87 (0.87) 0.64 (0.83) 2.05*** (2.74) 1.47 (1.71) 3.52*** (3.66) 3.40** (2.40) 1.94*** (3.28) 1.29 (0.89) 2.82*** (3.05) 0.94 (1.48) 1.97 (1.44)
-1.69* (-1.66) 1.00 (1.17) 0.74 (1.30) 0.94 (0.80) 0.17 (0.44) -0.54 (-0.69) 0.10 (0.17) 1.12 (0.97) 0.29 (0.79) 1.03 (1.58) 1.44** (2.25) 2.43* (1.94) 0.31 (0.15) 1.38* (1.91) -1.09 (-1.11) 0.96 (1.90) -0.48 (-1.31) -1.69* (-1.66)
-1.18 (-1.11) 2.68*** (2.60) 1.77 (1.45) 0.15 (0.11) 3.69*** (5.09) 2.43*** (3.39) 2.01** (2.53) 1.98*** (2.80) 1.10 (1.52) 2.27** (2.55) 2.15** (2.52) 3.31*** (2.93) -1.34 (-1.40) 3.72*** (5.36) 1.19 (1.11) 3.48*** (3.67) 1.31* (1.89) -1.18 (-1.11)
39
0.62 (0.42) 1.74* (1.91) 2.33* (1.91) -0.13 (-0.09) 3.61*** (4.39) 2.41*** (2.86) 1.38* (1.78) 0.90 (1.20) 0.55 (0.64) 2.30*** (2.71) 1.76** (2.12) 3.15** (2.44) -1.09 (-1.39) 3.25*** (5.40) 1.65 (1.33) 3.08*** (3.05) 0.55 (0.82) 0.62 (0.42)
-1.79 (-1.50) 0.95 (0.71) -0.55 (-0.84) 0.27 (0.44) 0.09 (0.24) 0.02 (0.03) 0.63 (1.62) 1.08 (1.25) 0.55 (1.58) -0.03 (-0.05) 0.38 (0.60) 0.16 (0.13) -0.25 (-0.28) 0.47 (0.59) -0.46 (-0.46) 0.41 (0.98) 0.76* (1.90) -1.79 (-1.50)
-2.08 (-1.49) 4.78 ** (2.28) 0.67 (0.48) 0.99 (0.50) 3.32*** (4.24) 2.71*** (3.35) 1.99*** (2.96) 1.19 (0.85) 1.51** (2.46) 2.69*** (3.08) 1.14 (1.28) 4.35** (2.59) -2.44*** (-3.50) 1.93*** (3.49) 1.45 (1.31) 2.95*** (3.03) 1.06 (1.49) -2.08 (-1.49)
-3.74** (-2.18) 3.02* (1.71) 0.05 (0.04) 2.02 (0.88) 3.52*** (4.42) 3.53*** (4.30) 1.73** (2.39) 2.60 (1.57) 0.93 (1.54) 2.33*** (3.34) 2.72** (2.34) 3.04** (2.30) -3.54** (-2.25) 2.29*** (3.85) 0.40 (0.46) 3.09*** (3.14) 0.52 (0.73) -3.74** (-2.18)
1.66 (0.75) 1.76 (0.59) 0.61 (0.88) -1.03 (-0.90) -0.20 (-0.47) -0.81 (-1.40) 0.26 (0.73) -1.41 (-0.75) 0.57 (1.89) 0.36 (0.53) -1.58** (-2.45) 1.32 (0.75) 1.10 (0.84) -0.37 (-0.57) 1.05 (1.38) -0.13 (-0.31) 0.54 (1.76) 1.66 (0.75)
Table 5: Robustness test for Stock Return Seasonality This table reports the robustness test results for stock return seasonality using the fixed effect model by forming the firm expected return into deciles as suggested by Kamstra (2017). Panel A reports the results of seasonal test by single regression specified as: ππππ,ππ,π‘π‘ = β10 ππ=1 πΌπΌ0,ππ π·π·ππ,ππ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + ππππ,ππ,π‘π‘ , Panel B reports the results of seasonal test by multivariate regression specified as: ππππ,ππ,π‘π‘ = 12 β10 ππ=1 πΌπΌ0,ππ π·π·ππ,ππ + βππ=1 π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + π½π½24,π‘π‘ ππππ,ππ,π‘π‘β24 + π½π½36,π‘π‘ ππππ,ππ,π‘π‘β36 + π½π½48,π‘π‘ ππππ,ππ,π‘π‘β48 + π½π½60,π‘π‘ ππππ,ππ,π‘π‘β60 + ππππ,ππ,π‘π‘ , where j represents the decile of the firm iβs expected return, which is calculated by the average of the firmβs past 12 month returns, and π·π·ππ,ππ equals 1 when firm i is in the expected return decile j, 0 otherwise. ππππ,ππ,π‘π‘ is the return on stock i from market n in month t, the slope coefficient π½π½ππ,π‘π‘
represents cross-sectional response of returns at one month to returns at a previous month k. We first conduct cross-sectional linear regression in each month and report the averages of time series coefficients (in parentheses). We conduct analyses for all, advanced and emerging markets, respectively. The tstatistics are adjusted for heteroskedasticity and autocorrelation. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively. The sample period is from January 1995 to June 2013. Return lag ππ
All markets Coefficient
t-stat
Advanced markets Coefficient t-stat
Emerging markets Coefficient t-stat
Panel A. Single regression results 1 2 3 4 5 6 7 8 9 10 11 12 24 36 48 60
-0.029*** -0.005 0.006 0.006 0.002 0.006 0.005 0.004 0.01*** 0.003 0.005 0.007** 0.010*** 0.009*** 0.001 0.002
(-7.79) (-1.25) (1.65) (1.38) (0.57) (1.39) (1.52) (1.26) (2.60) (1.06) (1.46) (2.22) (2.84) (3.33) (0.31) (0.42)
-0.037*** -0.002 0.011** - 0.002 -0.0003 0.005 0.006 0.001 0.002 -0.003 -0.001 0.011*** 0.003 0.006* 0.002 0.004
40
(-7.88) (-0.46) (3.18) (-0.30) (-0.11) (1.62) (1.54) (0.32) (0.56) (-0.99) (-0.35) (2.85) (1.25) (1.70) (0.76) (1.25)
-0.03*** -0.008 0.006 -0.002 0.002 ** 0.003 0.007 0.006 0.02* 0.006 0.008 0.008* 0.012** 0.01*** -0.0002 0.0005
(-6.13) (-1.58) (1.18) (-0.30) (0.48) (0.60) (1.58) (1.46) (2.73) (1.45) (1.63) (1.80) (2.58) (3.03) (-0.07) (0.12)
Panel B. Multiple regression results Return lag ππ 1 2 3 4 5 6 7 8 9 10 11 12 24 36 48 60
All markets Model 1 Model 2 -0.029*** -0.043*** (-7.89) (-9.12) -0.006 -0.013*** (-1.36) (-4.18) 0.005 -0.000 (1.58) (-0.15) 0.005 -0.006* (1.83) (-1.76) 0.004 -0.005 (1.14) (-1.10) 0.006* 0.002 (1.83) (0.55) 0.006** 0.002 (2.18) (0.85) 0.006** 0.005 (2.07) (1.32) 0.001*** 0.005* (2.76) (1.23) 0.006** 0.007** (2.08) (2.28) 0.007** 0.007** (2.22) (2.32) 0.009** 0.011*** (2.96) (3.11) 0.006** (2.21) 0.008*** (2.24) 0.003 (0.79) 0.000 (0.12)
Advanced Model 1 Model 2 -0.039*** -0.042*** (-8.70) (-8.70) -0.004 -0.004 (-1.02) (-0.98) 0.009** 0.006 (2.51) (0.16) -0.001 0.003 (-0.28) (0.60) -0.001 -0.002 (-0.32) (-0.58) 0.003 0.004 (0.83) (1.22) 0.004 0.002 (1.06) (0.73) 0.001 -0.001 (0.44) (-0.29) 0.000*** 0.005 (0.18) (1.23) -0.004 0.002 (-1.19) (0.62) 0.000 0.006* (0.46) (1.79) 0.011** 0.013*** (3.28) (3.14) 0.002 (0.67) 0.006* (1.84) 0.007* (1.78) 0.005* (1.85)
41
Emerging Model 1 Model 2 -0.031*** -0.044*** (-6.73) (-7.76) -0.010** -0.030*** (-2.42) (-4.65) 0.003 -0.005 (0.74) (-1.01) 0.005 -0.009** (1.39) (-2.43) 0.006 -0.007 (1.29) (-1.40) 0.005 -0.002 (1.03) (-0.42) 0.008** 0.003 (2.36) (0.76) 0.008** 0.004 (2.23) (0.87) 0.017*** 0.004 (2.99) (0.87) 0.009** 0.004 (2.26) (1.04) 0.009** 0.004 (2.16) (0.93) 0.011** 0.007* (2.58) (1.70) 0.007** (2.08) 0.010** (2.48) -0.002 (-0.58) -0.002 (-0.53)
Table 6: Economic Significance of Stock Return Seasonality and Firm Size This table reports the economic value of stock return seasonality for large firms (Panel A) and small firms (Panel B). In each month we first sort stocks into two groups based market capitalization, and then sort them into decile groups based on historical seasonal return over three time windows: past year 1, years 2-3, or years 4-5 and calculate the equal-weighted portfolio returns over subsequent month for each decile. We report the portfolio returns of winner stocks (highest historical seasonal return decile) and loser stocks (lowest historical seasonal return decile) and spread between the two portfolios. Panel A reports results of the large firm group; Panel B reports results for small firm group. The associated Newey-West t-statistics with 4 lags are in parentheses. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively. The sample period is between January 1995 and June 2013.
Portfolios Panel A. Large firms
Panel A1: All Markets Excess return (%)
Panel A2: Advanced Markets Excess return (%)
Panel A3: Emerging Markets Excess return (%)
Seasonality basis: year 1 Winners Losers Winners-losers
0.92*** (11.9) 0.39*** (4.46) 0.53*** (4.52)
0.93*** (11.82) 0.42*** (4.33) 0.52*** (4.18)
0.90*** (6.70) 0.37** (2.45) 0.54*** (2.68)
Seasonality basis: years 2-3 Winners Losers Winners-losers
0.67*** (7.03) 0.79*** (8.78) -0.13 (-0.96)
0.65*** (5.91) 0.73*** (8.09) -0.08 (-0.55)
0.68*** (4.37) 0.86*** (5.40) -0.17 (-0.79)
Seasonality basis: years 4-5 Winners Losers Winners-losers
0.52*** (7.02) 0.75*** (7.89) -0.23* (-1.92)
0.56*** (6.98) 0.61*** (7.02) -0.06 (-0.47) 42
0.48*** (3.79) 0.88*** (5.18) -0.41** (-1.96)
Panel B. Small firms Seasonality basis: year 1 Winners Losers Winners-losers
-0.01 (-0.16) -0.17 (-1.57) 0.16 (1.13)
0.11 (0.94) -0.01 (-0.08) 0.12 (0.64)
-0.14 (-1.00) -0.34** (-2.21) 0.20 (0.95)
0.00 (0.03) -0.31** (-2.38) 0.31* (1.77)
-0.64*** (-5.22) -0.40*** (-2.84) -0.24 (-1.34)
0.03 (0.21) -0.25** (-2.07) 0.28 (1.49)
-0.28 (-1.48) -0.32** (-2.25) 0.05 (0.19)
Seasonality basis: year 2-3 Winners Losers Winners-losers
-0.31*** (-3.67) -0.35*** (-3.70) 0.04 (0.32) Seasonality basis: year 4-5
Winners Losers Winners-losers
-0.12 (-1.04) -0.29*** (-3.06) 0.17 (1.09)
43
Table 7: Stock Return Seasonality and Calendar Effect This table reports the economic value of stock return seasonality across calendar months for advanced and emerging markets, respectively. In each month and for each market we sort stocks into decile groups based on historical seasonal return over three time windows: past 1 year, years 2-3, or years 4-5, and calculate the equal-weighted portfolio returns over subsequent month for each decile. We report the portfolio returns of winner stocks (highest historical seasonal return decile) and loser stocks (lowest seasonal return decile) and spread between the two portfolios in each calendar month. Panel A shows the results for advanced markets, and Panel B for emerging markets. The associated Newey-West t-statistics with 4 lags are in parentheses. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively. The sample period is between January 1995 and June 2013. Year 1 Winners Losers Panel A: Advanced markets 1.88 1.06 January February March April May June July August September October November December
(5.17) 0.63 (1.22) 0.59 (2.08) 1.06 (2.64) 0.53 (1.49) 0.21 (0.95) -0.12 (-0.44) 0.34 (1.11) -0.04 (-0.11) 0.82 (1.96) 0.47 (0.94) 0.58 (1.92)
WML
Winners
Year 2-3 Losers
WML
Winners
Year 4-5 Losers WML
(3.72) 0.45 (1.12) -0.25 (-0.72) 0.53 (1.13) 0.32 (0.74) -0.59 (-1.52) -0.13 (-0.32) 0.04 (0.08) -0.17 (-0.35) 0.24 (0.57) 0.57 (1.21) -1.02 (-2.60)
0.82* (1.77) 0.18 (0.29) 0.84* (1.80) 0.53 (1.15) 0.21 (0.40) 0.81* (1.91) 0.01 (0.02) 0.30 (0.56) 0.13 (0.21) 0.58 (1.15) -0.10 (-0.18) 1.60*** (3.36)
2.04 (4.68) 1.01 (1.67) 0.14 (0.42) 0.57 (1.81) 0.41 (0.93) 0.24 (0.48) -0.02 (-0.12) -0.30 (-1.26) 0.04 (0.10) 0.46 (1.83) 0.51 (0.95) 0.30 (0.93)
0.78 (1.63) 1.26 (2.18) 0.49 (1.46) 0.48 (0.92) 0.99 (1.76) -0.44 (-1.12) -0.40 (-1.09) 0.08 (0.2) -0.05 (-0.09) -0.35 (-0.72) 0.69 (1.12) -1.17 (-3.34)
1.25** (2.13) -0.25 (-0.50) -0.35 (-0.64) 0.09 (0.21) -0.57 (-1.21) 0.68 (1.62) 0.38 (1.47) -0.38 (-0.86) 0.09 (0.11) 0.81 (1.55) -0.17 (-0.23) 1.47** (2.60)
1.90 (5.82) 1.23 (2.11) 0.46 (1.18) 0.18 (0.78) -0.34 (-0.72) -0.18 (-0.38) 0.13 (0.35) -0.30 (-0.76) 0.66 (1.46) -0.02 (-0.04) 0.15 (0.49) 0.40 (2.04)
0.06 (0.15) -0.28 (-0.43) 0.17 (0.47) 0.15 (0.32) 0.63 (1.40) 0.10 (0.30) -0.19 (-0.57) -0.01 (-0.02) -0.03 (-0.05) 0.59 (1.15) 0.12 (0.37) -0.46 (-1.03)
1.84*** (3.93) 1.51 (1.33) 0.29 (0.44) 0.02 (0.04) -0.97 (-1.28) -0.28 (-0.45) 0.31 (0.68) -0.29 (-0.52) 0.69 (0.87) -0.61 (-0.70) 0.02 (0.05) 0.86* (1.77)
2.43 (1.41) 1.82 (1.51) -1.00 (-0.64) 3.89 (1.77) 3.81 (1.56) 1.90 (0.92) 3.42 (2.29)
1.69 (1.10) 0.18 (0.12) 3.54** (2.68) 0.42 (0.22) -2.20* (-1.66) 0.25 (0.17) -1.51 (-1.53)
4.33 (2.90) 4.31 (3.04) -2.23 (-0.72) 5.70 (3.24) 1.71 (0.88) 1.04 (0.8) 3.76 (2.63)
2.98 (1.50) 1.30 (1.27) -0.90 (-0.57) 5.44 (3.1) 3.35 (1.77) 1.26 (0.74) 3.24 (2.65)
1.35 (0.88) 3.01** (2.73) -1.34 (-0.47) 0.26 (0.19) -1.64 (-0.98) -0.21 (-0.25) 0.51 (0.56)
1.17 (0.87) 0.45 (0.38) 1.55 (1.12) 4.94 (2.99) 1.81 (0.65) -0.34 (-0.19) 3.07 (2.53)
1.08 (0.42) 1.43 (1.54) -1.02 (-0.59) 4.56 (3.21) 2.80 (1.60) 2.65 (1.25) 3.55 (2.26)
0.10 (0.04) -0.97 (-0.89) 2.57 (1.54) 0.38 (0.36) -0.99 (-0.60) -2.99** (-2.41) -0.48 (-0.46)
Panel B: Emerging markets January February March April May June July
4.11 (2.12) 2.00 (1.62) 2.54 (1.85) 4.31 (2.81) 1.61 (0.88) 2.14 (1.12) 1.92 (1.48)
44
August September October November December
3.09 (1.47) -0.19 (-0.14) 0.37 (0.20) 3.01 (1.54) 6.26 (3.18)
0.11 (0.07) -0.34 (-0.17) 0.46 (0.26) 6.11 (1.81) 4.13 (2.04)
2.98 (1.56) 0.15 (0.12) -0.09 (-0.09) -3.10 (-1.04) 2.13 (1.43)
3.38 (1.86) 1.03 (0.61) 0.53 (0.28) 4.04 (2.43) 5.24 (2.34)
45
0.67 (0.51) 0.19 (0.13) 0.44 (0.21) 2.09 (1.37) 4.23 (2.03)
2.71 (2.29) 0.85 (1.05) 0.10 (0.13) 1.96 (1.50) 1.01 (0.41)
4.10 (2.38) -0.05 (-0.02) 1.27 (0.64) 4.38 (2.15) 7.13 (2.43)
1.89 (1.54) 0.94 (0.59) 0.42 (0.22) 5.56 (3.18) 4.16 (1.87)
2.21** (1.98) -0.99 (-0.82) 0.86 (1.60) -1.18 (-0.94) 2.97 (0.91)
Table 8: Adjusted Seasonality Returns by Local Risk Factors This table reports the risk-adjusted returns of high and low seasonal stock portfolios and return spread between the two groups. We construct Fama-French-Carhart type of four risk factors and adjust each stock returns accordingly. Specifically, we apply the following model to adjust stock returns (alpha): 25 26 where ππππ,ππ,π‘π‘ = πΌπΌππ,π‘π‘ + π½π½ππ,π‘π‘ ππππ,ππ,π‘π‘βππ + π΄π΄π‘π‘ (π
π
ππ,ππ,π‘π‘ β ππππππ,π‘π‘ ) + π΅π΅π‘π‘ ππππππππ,π‘π‘ + πΆπΆπ‘π‘ π»π»π»π»π»π»ππ,π‘π‘ + π·π·ππ,π‘π‘ ππππππππ,π‘π‘ + ππππ,ππ,π‘π‘ π
π
ππ,ππ,π‘π‘ is the equal-weighted market monthly return for market n in month t and ππππππ,π‘π‘ is the risk free rate for market n in month t. ππππππππ,π‘π‘ , π»π»π»π»π»π»ππ,π‘π‘ and ππππππππ,π‘π‘ denote the size, book-to-market (B/M) and momentum factors. In each month and for each market we sort stocks into decile groups based on historical seasonal returns over three time windows: past year 1, year 2, or year 3 and calculate the equalweighted risk-adjusted returns over subsequent month for each decile. We report the risk-adjusted portfolio returns (alpha) of winner stocks (highest historical seasonal return decile) and loser stocks (lowest seasonal return decile) and spread between the two portfolios in each calendar month. Panel A shows the results for advanced markets, and Panel B for emerging markets. The associated Newey-West t-statistics with 4 lags are in parentheses. ***, ** and * indicate significance at the 1%, 5% and 10% levels, respectively. The sample period is between January 1995 and June 2013.
25 26
See detailed explanation of the model in section 3. For details on the formation of the Fama-French-Carhart factors, please see Appendix.
46
Winners
Year 1 Losers
WML
Winners
Year 2 Losers
WML
-0.63 (-1.10) -0.70 (-1.41) -2.15*** (-4.91) 0.06 (0.11) -1.39*** (-3.12) -0.85* (-1.88) -1.43*** (-4.00) -2.07*** (-3.42) -1.86*** (-3.61) -0.63 (-1.07) -1.79*** (-3.68) -1.38*** (-4.35) -0.47 (-0.94) -0.11 (-0.21) -1.32** (-2.36) -1.94*** (-3.65) -0.78* (-1.67) -1.23*** (-2.90) -1.13*** (-3.02)
0.32 (0.36) 0.59 (0.99) 2.37*** (4.71) -0.13 (-0.22) 1.61*** (3.19) 0.95* (1.82) 1.37*** (3.22) 2.20*** (3.01) 1.39** (2.63) 0.65 (1.10) 1.93*** (3.75) 1.61*** (4.92) 0.71 (1.27) 0.30 (0.42) 2.07*** (3.18) 1.86*** (3.05) 0.90* (1.79) 1.26*** (3.04) 1.19*** (2.91)
Winners
Year 3 Losers
WML
Panel A: advanced countries Australia Belgium Canada Denmark Finland France Germany Greece Hong Kong Israel Italy Japan Nether land New Zealand Norway Singapore Spain Switzer land United Kingdom
-0.93 (-1.22) -0.65 (-1.57) -1.23*** (-2.68) 0.09 (0.22) -0.59 (-1.24) -0.22 (-0.55) -1.31*** (-3.61) -1.94*** (-3.54) -1.78*** (-3.68) -0.57 (-1.06) -1.520*** (-3.53) -0.54** (-1.97) -0.24 (-0.53) 0.40 (0.85) -0.56 (-1.01) -1.26*** (-2.64) -0.07 (-0.14) -0.65 (-1.54) -0.90*** (-2.88)
-0.93 (-1.63) -1.17** (-2.25) -0.99** (-1.96) 0.032 (0.05) -1.09*** (-2.31) -0.73 (-1.48) -2.38*** (-5.73) -2.15*** (-3.49) -2.26*** (-4.22) -0.69 (-1.00) -1.82*** (-3.67) -1.17*** (-3.66) -0.40 (-0.79) -0.45 (-1.03) -1.05* (-1.69) -1.92*** (-3.47) -0.23 (-0.44) -1.49*** (-2.89) -1.59*** (-3.98)
-0.00 (0.00) 0.52 (1.15) -0.24 (-0.55) 0.06 (0.15) 0.50 (1.31) 0.51 (1.51) 1.06*** (2.83) 0.21 (0.39) 0.48 (1.30) 0.11 (0.27) 0.30 (1.12) 0.64*** (3.28) 0.16 (0.39) 0.86* (1.72) 0.49 (0.93) 0.66* (1.75) 0.17 (0.47) 0.85** (2.39) 0.70** (2.53)
-0.30 (-0.57) -0.11 (-0.38) 0.22 (0.82) -0.07 (-0.25) 0.22 (1.12) 0.10 (0.51) -0.06 (-0.30) 0.14 (0.47) -0.47** (-2.11) 0.03 (0.12) 0.14 (0.83) 0.23** (2.28) 0.24 (1.05) 0.19 (0.50) 0.75** (2.13) -0.08 (-0.35) 0.12 (0.55) 0.032 (0.19) 0.060 (0.37)
47
-0.12 (-0.27) 0.20 (0.39) -0.58** (-2.19) 0.53* (1.78) 0.55*** (3.18) -0.04 (-0.19) -0.42** (-2.00) -0.34 (-1.25) -0.22 (-0.97) 0.14 (0.51) 0.06 (0.36) 0.16 (1.55) 0.14 (0.69) -0.36 (-0.96) 0.34 (0.80) 0.06 (0.22) -0.25 (-1.28) 0.10 (0.39) -0.07 (-0.46)
-0.78 (-0.88) -0.91** (-2.03) -1.77*** (-4.03) -0.42 (-0.82) -1.47*** (-3.67) -0.62 (-1.35) -1.35*** (-3.55) -2.18*** (-3.43) -1.70*** (-2.72) -0.35 (-0.63) -1.67*** (-3.62) -0.98*** (-3.30) -0.34 (-0.68) -0.01 (-0.01) -1.43 (-2.62) -1.60 (-3.00) -0.46 (-0.95) -1.32*** (-3.25) -1.25*** (-2.87)
0.66 (0.60) 1.11 (1.55) 1.20** (2.41) 0.95 (1.63) 2.02 (4.37) 0.58 (1.09) 0.93** (2.00) 1.84** (2.46) 1.48** (2.16) 0.49 (0.83) 1.74*** (3.54) 1.14*** (3.54) 0.48 (0.86) -0.35 (-0.46) 1.77*** (2.69) 1.67*** (2.81) 0.21 (0.41) 1.42*** (3.15) 1.18** (2.42)
Winners
Year 1 Losers
WML
Winners
Year 2 Losers
WML
Winners
Year 3 Losers
WML
Panel B: Emerging markets Brazil Bulgaria China India Indonesia Korea Malaysia Philippine Poland Romania Russia South Africa Saudi Arabia Turkey Taiwan
-0.63
0.24
-0.87
-0.26
0.11
-0.38
0.09
0.46
-0.37
(-0.89) 1.51 (1.57) -0.54 (-0.91) -0.51 (-1.08) 1.65** (1.97) -0.96 (-1.72) -1.94*** (-4.72) 0.07 (0.11) -0.90 (-1.43) 1.47* (1.78) 2.19** (2.15) 0.41 (0.92) 0.14 (0.25) -0.98** (-2.15) -1.53*** (-3.80)
(0.28) 0.71 (0.78) -1.34** (-2.18) -0.94* (-1.76) 0.98 (1.18) -1.92*** (-2.99) -2.38*** (-6.02) -0.50 (-0.75) -0.90 (-1.30) -0.60 (-0.64) 0.76 (1.02) 0.38 (0.71) 0.06 (0.08) -1.38** (-2.59) -1.21** (-2.47)
(-1.12) 0.80 (0.82) 0.80* (1.84) 0.43 (1.10) 0.68 (1.11) 0.95 (1.85) 0.44 (1.35) 0.57 (1.00) 0.00 (0.01) 2.08* (2.16) 1.43 (1.47) 0.04 (0.07) 0.08 (0.13) 0.40 (1.15) -0.32 (-1.07)
(-0.45)
(0.13)
(-0.35)
(0.13)
(0.72)
(-0.41)
-0.28 (-1.34) -0.15 (-0.75) -0.28 (-0.89) 0.01 (0.06) 0.03 (0.16) -0.23 (-0.6) -0.07 (-0.19) -0.36 (-0.48) -1.05 (-1.54) 0.22 (0.57)
-1.25** (-1.99) -0.78 (-1.45) 1.52* (1.87) -1.76*** (-3.02) -2.49*** (-5.47) -0.12 (-0.2) -1.25* (-1.88) 0.90 (0.81) 2.06** (2.41) 0.53 (1.07)
0.97 (1.39) 0.63 (1.14) -1.80** (-2.04) 1.77*** (2.94) 2.51*** (5.01) -0.11 (-0.16) 1.18 (1.35) -1.25 (-0.86) -3.10** (-2.50) -0.31 (-0.44)
0.03 (0.09) -0.48** (-2.41) 0.04 (0.11) 0.11 (0.6) 0.31** (2.05) 0.10 (0.25) 0.68* (1.69) -0.22 (-0.26) -0.11 (-0.35)
-1.04 (-1.5) -0.52 (-1.09) 1.43* (1.92) -1.81*** (-3.61) -1.99*** (-5.24) -0.03 (-0.05) -1.12 (-1.72) -0.08 (-0.09) 0.62 (1.18)
1.06 (1.43) 0.04 (0.08) -1.38* (-1.65) 1.92*** (3.32) 2.30*** (5.4) 0.13 (0.20) 1.80*** (2.48) -0.14 (-0.11) -0.73 (-1.16)
-0.02 (-0.14) 0.36* (1.81)
-1.54*** (-3.06) -1.93*** (-4.26)
1.52*** (2.98) 2.29*** (4.57)
-0.17 (-0.77) 0.24 (1.40)
-0.90 (-1.63) -2.03*** (-4.55)
0.73 (1.15) 2.27*** (4.83)
48
