On the Sell-in-May Anomaly in Germany
IS. Anfang1, supervised by dr. A. Plantinga2
Abstract
Evidence shows that returns on equity markets are significantly higher during the period from November to April than during May to October, a phenomenon labeled the "Sell in May" or "Hal-loween effect", challenging the efficient market hypothesis. Examining the Hal"Hal-loween effect for the German market reveals that this particular market anomaly seems to be systematic rather than industry or size related. While a significant effect is indeed found for industries classified as "cyclicals", it disappears when correcting for general market movements. Possible explanations for this market-wide phenomenon are explored, but eventually the effect is left unexplained. Al-though the Halloween effect seems to weaken subsequent to its first academic documentation, a trading strategy that goes into equities over the winter period and into a risk-free position over the summer still offers investors an improved risk-return trade-off over a buy-and-hold approach. Keywords: Stock Market Anomaly, Halloween Effect, Market Efficiency
1. Introduction
According to the Efficient Market Hypothesis (EMH) as popularized by Fama (1970), changes in asset prices are serially random. Hence, no predictable and exploitable inefficiency should be present in financial markets. However, well documented stock market anomalies such as so-called calendar effects challenge the validity of the EMH. Calendar effects describe the "tendency of financial assets’ returns to display systematic patterns at certain times of the day, week, month, or year" (Brooks, 2014). Empirical evidence suggests that returns at specific times or periods are higher (lower) than normal. Widely known calendar effects include the "January - effect", "Turn-of-the-month/year/quarter - effect", "Day-of-the-week-effect", and the "Sell in May - effect", also called "Halloween - effect", among others. The latter one is perhaps the most remarkable of the aforementioned calendar effects among both academics and practitioners. Every year at the same
IMaster’s thesis MSc Finance, University of Groningen, January 2018 1Student number: S2412330.
2Department of Economics, Econometrics and Finance, Faculty of Economics and Business, University of
time, the old market maxim "Sell in May and go away" is omnipresent in relevant market and financial media. According to Hirsch (2012) the origin of this old saying dates back to the year 1776 and was established in England in its original form: "Sell in May and go away, come back on St. Leger day". St. Leger stakes is the last race of a series of horse races and scheduled each year in September3. While at that time it had probably little to do with stock markets, it may have insinuated that people return to "business as usual" after the horse race season and was taken over by stockbrokers once stock exchanges were established all around the continents. Later on, this adage became popular with a slight variation as "..., but remember to be back in September". Jacobsen and Zhang (2010) report that it was first documented in 1935 in a clear stock market context. However, academic research has begun to deal with it only since the beginning of the 21st century with Bouman and Jacobsen (2002) publishing a pioneering study, in which according to the "Sell in May" maxim, they splitted the year into two six months periods and labeled it the "Halloween effect". Ever since, findings of this particular stock market seasonality, though, are not completely consistent among countries and over time.
Previous studies regarding the "Halloween effect" were mainly conducted on the basis of a countries’ largest stock market index. In contrast to that, this paper aims at providing a compre-hensive study, in which the Halloween-, and at the same time the January- effect are examined for several industries and size categories taking the German market as an example. The idea stems from the fact that by only taking into account broad market-level data, one might ignore the role of stock market heterogeneity in determining the estimation outcomes. Consequently, Sharma and Narayan (2014) claim that "testing any hypothesis one should consider as homogeneous a set of stocks/firms as possible". Furthermore, different industries may display different effects, as they may be differently affected by economic cycles. In order to examine that, three German stock indices are taken into account, namely the DAX, MDAX, and SDAX, representing large-, mid-, and small-caps, respectively. Furthermore, 17 different industry baskets are considered. The results might provide insights about the manifestation of calendar effects beyond broad stock market indices that represent only the largest, and normally most traded companies.
This paper resembles previous studies in terms of methodology, and yet, contributes to the existing literature by examining not only the possible existence of calendar effects but also inves-tigating whether these are consistent over sizes and industries. After a brief literature review, the data which is used and the methodology that is applied will be presented. Subsequently, both the Halloween- and January effect will be examined. In a first step, a standard approach prevailing in literature will be applied. Secondly, the effects will be investigated relative to the market in
3See http://www.tbheritage.com/TurfHallmarks/Gazeteer/GazeteerYorks.html#sls for further information
order to find out if the anomalies manifest in a pattern among different sectors, or whether it is a rather systematic, market-driven, phenomenon. Next, the results will be presented, followed by a discussion and examination of possible explanations. Finally, as to investigate its economic significance, it will be shown whether a trading strategy based on the Halloween effect yields higher returns in absolute terms and in terms relative to risk.
2. Related Literature
Since the influential paper of Fama (1965) about the behavior of stock prices, the existence and persistence of calendar effects in a broad range of stock markets and asset classes have been an in-tensively investigated topic in the finance domain. This chapter gives a brief overview about pre-vious studies related to the calendar effects that are examined in this thesis, namely the "January-", and the "Halloween effect". The former refers to the observed tendency of stock returns to be sig-nificantly higher in January than in other months of the year. The Halloween effect describes the theory of stock returns being significantly higher from November to April than from May to October (hereafter referred to as "winter period" and "summer period", respectively).
The study of monthly seasonalities has received a lot of attention in previous decades. Rele-vant studies date back to the seventies and eighties, such as Rozeff and Kinney (1976), Gultekin and Gultekin (1983), Thaler (1987), Ariel (1987) and Jaffe and Westerfield (1989), documenting evi-dence of the January effect in different countries. More recent studies include Haug and Hirschey (2006), Lucey and Zhao (2008), further confirming the existence of a January effect. Main ex-planations for this anomaly include tax-loss selling (Starks et al 2006) and window dressing of institutional investors (Lakonishok and Smidt 1988; Ritter 1988). The former refers to the sale of bad performing equities in order to claim tax losses at the end of the fiscal year, which, in most countries, falls on December. In January, Investors buy those equities back which leads to high returns during this month. Window dressing refers to the action of investment managers selling losing positions before disclosure date in order to present a better looking portfolio. However, while evidence for the January effect seems to be consistent in most studies, Giovanis (2009) finds no evidence for a January effect in the 55 stock markets that are examined in his study.
(2004), Doeswijk (2008), Jacobsen and Visaltanachotti (2009) and Haggard and Witte (2010). While Bouman and Jacobsen (2002) could not provide an explanation for the Halloween effect, Kam-stra et al (2003) linked it to the effect of Seasonal Affective Disorder (hereafter SAD). SAD, also referred to as winter depression or winter blues4, is a type of depression that most commonly occurs as a result of the shortening of the days in fall and winter, which in turn leads to increasing risk aversion among investors, and hence declining equity prices followed by abnormal high re-turns as days become longer again. Contrary to the findings in Kamstra et al (2003), Jacobsen and Marquering (2008) show that inference from studies that try to explain the Halloween anomaly by mood shifts of investors as a result of weather changes might be data driven. Doeswijk (2008) crit-icizes, that it is well-known beforehand, that SAD is most pronounced during the winter months, and hence the findings may be a result of data mining. Instead, Doeswijk (2008) puts forward the so-called "optimism-cycle hypothesis" as a possible explanation for the Halloween effect. Accord-ing to this, investors become overoptimistic durAccord-ing the last months of the year with respect to the economic outlook and earnings as they are looking forward to the begin of a new year. As the new year’s months pass by and investors expectations are not met, they realize that they were too optimistic, which in turn leads to declining equity prices. Investor optimism is proxied by first day IPO performance in this study. Further, Doeswijk (2008) provides evidence by showing that the strategy of overweighing equities during the winter period and underweighing them during the summer period yields excess returns in two out of every three years. Marbely and Pierce (2004) provide evidence that once adjusted for outliers in turbulent financial times, in their study period the equity price crash in October 1987 and the fall of the hedge fund Long Term Capital Management in August 1998, the Sell in May effect disappears. Those findings are countered by Haggard and Witte (2010), who prove that even considering outliers and transaction costs, trad-ing on Sell in May would have outperformed a buy and hold strategy. In turn, Dichtl and Drobetz (2014; 2015) show that a trading strategy based on the Halloween effect since the first publication about it, would not have outperformed and additionally, provide evidence for a weakening or even disappearance of the effect in recent years.
While most of the aforementioned studies are conducted on broad index level, there are only few studies carried out on a sectoral level. Such studies include Mills and Coutts (1995), Jacobsen and Visaltanachotti (2009), Sharma and Narayan (2014), Hui and Chan (2015) and Carrazedo et al (2016). Mills and Coutts (1995) investigate the presence of calendar effects in varios FTSE stock indices and several industries. Their findings suggest that some industries do indeed mimic the behavior of broad UK market indices, displaying similar calendar effects, while other industries,
4Generally, SAD refers to mood changes that occur in seasonal patterns, not especially during the winter. However,
e.g. Industrials, do not. Jacobsen and Visaltanachotti (2009) show that the Halloween effect is sta-tistically significant in two third of the American industries they studied, with large differences among sectors and industries. They conclude that the Halloween effect is indeed related to dif-ferent sectors, with consumer sectors outperforming the market during the summer months and production sectors showing an outperformance during the winter. Hui and Chan (2015) test for calendar effects on securitized real estate indices on major global stock markets. Their findings show that there is not only no Halloween or January effect, but that these effects are even reverse in some cases. In other words, the real estate sector tends to show higher returns during the sum-mer than during the winter period. For German securitized real estate, however, no significant effect was found at all. Finally, Carrazedo et al (2016) study the Halloween effect on European sectoral level. Their findings reveal statistically significant differences in returns between the pe-riod from November until April and May until October in 23 out of the 37 indices they examine, giving strong evidence for the existence of Halloween effects on both index and sector level. The findings of the aforementioned studies underline that, as sectors differ in nature, they may also exhibit different patterns with respect to calendar effects.
3. Methodology and Data
3.1. Data
The data sample used in this study comprises monthly total return data of three main German stock indices and the accompanying industry baskets in order to allow for comparability among size and industries. Table 1 gives an overview about these indices.
Table 1: Monthly total return index series, provided by Deutsche Boerse and collected from Datastream.
Size:DAX, MDAX, and SDAX
Industries:Automobiles, Banks, Basic Resources, Chemicals, Construction, Consumer, Financial Services, Food & Beverages, Industrial, Insurance, Media, Retail, Software, Technology, Telecommunication, Transport & Logistics, and Utilities
All time series are provided by Deutsche Boerse and are collected from Thomson Reuters Datastream. Except for the DAX, all the series cover the time period from January 1988 up to and including August 2017. The DAX time series stretches from January 1965 until August 2017. Re-turns are calculated as rt = ln
p t
pt−1
companies, ranging from ca. EUR 1.7bn (pbb) to ca. EUR 64.5bn (Airbus) in market capitaliza-tion with an average value of EUR 7.5bn. Similarly, the SDAX is composed of the 50 “small cap” companies that rank directly below those included in the MDAX with values of market capital-ization between EUR 0.46bn (Gerry Weber) and EUR 6.4bn (Delivery Hero) with an average value of ca. EUR 1.8bn5. Hence, comparing those three indices may provide insights about how stocks in different size categories differ (or not) with respect to seasonal patterns in returns. The sector indices are composed of all listed stocks that are classified to belong to the respective industry. On average, the industry indices include 17 constituents with a median of 12. All industry indices are classified into superordinate MSCI sectors and assigned to one of the two main sectors "Cyclicals" and "Defensives" according to the Global Industry Classification Standard developed by MSCI and Standard & Poor’s as shown in Table A.1 in the Appendix. An industry is said to be cyclical, if its performance is affected by economic cycles, whereas defensive industries are those whose demand and supply are assumed to remain equal, independent of economic cycles6.
In the course of this paper, Fama & French’s (1993) three factors, namely the "market" factor, the "small minus big" (SMB) factor, and the "high minus low" (HML) factor, plus Carhart’s (1997) so called "momentum factor" (MOM) will also be made use of. For consistency’s sake, the fac-tors that are specifically calculated for the German market will be taken into account. The data is prepared, maintained and provided by the School of Business and Economics at Humboldt University Berlin (Brueckner et al 2015): Here, the market portfolio is a market value weighted portfolio of all listed stocks in Germany. The average of one month money market rates that were reported by banks in Frankfurt until 2012 is used as the risk free rate, followed by the one-month EURIBOR as of mid 2012. The SMB, HML, and MOM factors are constructed in the style of Fama and French (1993) and Carhart (1997). Accordingly, SMB is a portfolio that is long in stocks with a small market capitalization and short in stocks with a large market capitalization. HML is a portfolio that is long in stocks with a high book-to-market ratio and short in stocks with a low book-to-market ratio. Similarly, MOM is a portfolio that is long in winner stocks and short in loser stocks as determined by returns in the previous twelve months. As the time horizons of the DAX and Industry Indices and the time series from Humboldt University differ in their ending date, the final dataset used in this study starts in May 1988 and ends with the last trading day of April 2016, as to maintain consistency. Finally, the dataset consists of 336 monthly observations.
Table 2 shows the basic characteristics of yearly returns from both the afore-described indices and factors that are relevant for the forthcoming analysis. Mean and standard deviation of yearly returns are reported and splitted into a winter and summer period. The second last column shows
5All aforementioned values as of November 2017.
Table 2: Basic characteristics of yearly returns for the period from May 1988 to April 2016 based on 336 monthly observations. Yearly means and standard deviations are reported in column three and four, respectively. Prob. denotes the probability that mean winter returns and mean summer returns are equal. The last column reports in how many of the 28 seasons considered the winter returns outperformed summer returns.
No. Winter Summer No. of years
of obs. Mean S.D. return return Prob. RW >RS
Market 336 8.41% 22.10% 8.73% -0.32% 1.36% 22 SMB 336 -4.67% 11.84% -2.61% -2.05% 78.58% 15 HML 336 6.21% 15.54% 3.83% 2.38% 56.86% 16 MOM 336 12.49% 13.19% 5.31% 7.18% 55.66% 10 Rf - Rate 336 3.45% 2.60% 1.70% 1.74% 91.98% 13 DAX 336 8.05% 23.74% 9.34% -1.29% 0.98% 20 MDAX 336 10.36% 23.93% 9.48% 0.88% 3.59% 20 SDAX 336 7.29% 24.88% 8.66% -1.37% 1.88% 18 Automobiles 336 9.05% 27.51% 9.78% -0.74% 4.63% 18 Banks 336 0.11% 31.28% 5.28% -5.16% 7.68% 18 Basic Resources 336 9.37% 34.95% 11.18% -1.81% 2.24% 19 Chemicals 336 11.13% 22.39% 12.01% -0.88% 0.18% 22 Construction 336 7.85% 31.66% 10.77% -2.92% 1.38% 20 Consumer 336 9.53% 22.98% 10.29% -0.76% 0.51% 20 Financial Services 336 8.90% 30.16% 8.66% 0.24% 9.31% 19
Food & Beverages 336 4.48% 23.67% 4.14% 0.35% 40.75% 14
Industrial 336 13.16% 33.11% 13.71% -0.55% 1.21% 21 Insurance 336 6.65% 30.77% 6.14% 0.51% 28.46% 17 Media 336 4.72% 50.38% 7.50% -2.78% 21.46% 15 Retail 336 4.34% 23.53% 4.77% -0.42% 20.81% 17 Software 336 18.07% 38.76% 13.98% 4.10% 13.98% 18 Technology 336 7.02% 38.06% 11.58% -4.55% 1.28% 19 Telecommunication 336 2.75% 32.56% 4.71% -1.97% 23.82% 14
Transport & Logistics 336 6.57% 30.21% 9.34% -2.78% 2.21% 20
Utilities 336 5.73% 23.50% 5.35% 0.38% 19.37% 19
higher than average summer returns of the risk-free rate. The average difference in winter and summer mean returns happens to be 9.87% with the lowest being 3.79% for the Food & Beverages industry and the highest being 16.13% for the Technology industry. The general market portfolio shows an average yearly return of 8.41%, with a negative average summer return of -0.32% while over the winter period on average 8.73% are earned. For all three size indices, as well as for 10 out of 17 industry indices plus the general market, the difference in means is statistically significant. On average, the general market and the size and industry indices show higher returns during the winter period in around two-thirds of the seasons under consideration. Table A.2 and Table A.3 in Appendix A show the basic characteristics of yearly returns for the period before and after the first academic documentation of the Halloween effect by Bouman and Jacobsen (2002) in December 2002. Winter returns among the indices outperformed summer returns in around 75% of the time during the period from May 1988 to April 2003, whereas this number reduces to ca. 60% for the period thereafter. This summary statistics give a first indication that trading on the Halloween anomaly, meaning to invest in equities over the winter period and switch into a risk-free position during the summer period, may have the potential to serve as a profitable market timing strategy.
3.2. Methodology
Following Bouman and Jacobsen (2002), the Halloween effect will now be examined account-ing for a possible January effect that could drive the results, by estimataccount-ing an OLS regression of the form:
rt =µ+β1Jt+β2Ht+εt (1)
where rtis the continuously compounded monthly return, H is the "Halloween" dummy variable taking a value of one for the months in the period from November until April, with the exception of January, and zero otherwise. J is a dummy variable taking a value of one if the observation falls on January and zero otherwise. The constant term µ captures the monthly mean return over the period from May to October, µ+β2represents the monthly mean return over the November -April period, excluding the January return, which is given by β1. Hence, β2captures the additional monthly mean return for the months over the November - April period, excluding January. εt represents the usual error term. In fact, equation (1) tests the mean returns during the summer period, January and the winter period and the results show if mean returns during a specific time of the year are statistically significant higher than in the others.
(1987)7. To add further statistical robustness to the results, equation (1) will be estimated with the time series winsorized at the 2.5% and 97.5% level in order to assure that the results are not driven by extreme outliers8.
In a next step, the January and Halloween effect will be investigated relative to the market in a CAPM-like framework, following the approach of Jacobsen and Visaltanachoti (2009):
rst−rtf =µ+α1Jt+α2Ht+β(rmt −rtf) +εt (2) where the constant plus the Halloween term capture returns during the winter period, the con-stant captures summer returns, and the January term captures returns during January, relative to general market returns. Beta, as usually, measures the sensitivity of the observed index to market movements. As a robustness test, all indices are regressed on the Fama and French (1993) and Carhart (1997) factors in the following fashion:
rst−rtf =µ+aHt+β(rmt −rtf) +sSMB+hHML+mMOM+εt (3) As Jacobsen and Visaltanachoti (2009) highlight, the "small minus big (SMB) and the high minus low factor (HML) are partially driven by the January effect". Hence, regression three does not include a January dummy. Similar to the procedure in equation (1), HAC standard errors are used in regression (2) and (3).
4. Results
In Table 3, the results of equation (1) are reported. With the exception of 6 out of 20 indices, a statistical significant Halloween effect is found even when controlling for a possible January effect. Surprisingly, the latter is only found in 4 out of the 20 indices. Hence, it seems that there is no January effect driving the Halloween effect. For all three superordinate size indices the Halloween effect is strongly significant. DAX, MDAX, and SDAX, representing large-, mid, and small-cap companies, all show a significant effect at the 1%, 5% and 1% level, respectively, with mean monthly returns of 2.02%, 1.42% and 1.62%. Additionally, the SDAX also shows a January effect that is significant at the 10% level. The Chemicals sector shows the highest mean monthly returns during the winter period, namely 2.69%, whereas the Media sector earns the highest mean
7Note that in more recent literature such as Jacobsen and Zhang (2012) or Dichtl and Drobetz (2015), residuals are
modelled as a GARCH (1,1) process as a robustness test. This is not done in this study as the number of monthly observations in the present data set does not exceed 500 to 1000 observations, which are necessary in order not to obtain biased results as pointed out by i.a. Hwang and Valls Pereira (2006).
8Common practice is to winsorise at 1% and 99%. However, winsorising at those values would not sufficiently
Table 3: Results from the regression rt=µ+β1Jt+β2Ht+εtwhere J is a dummy variable that takes the value of one if
the observation falls on January and zero otherwise. The Halloween dummy H takes the value of one for months in the period from November to April (excluding January) and zero otherwise. The constant µ denotes mean monthly returns over the summer period. β1denotes the additional January return, and β2denotes the additional mean monthly return
over the winter period. The sample comprises 336 observations for monthly returns over the period from 1988 to 2016. The t-values are based on Newey-West heteroskedasticity and autocorrelation (HAC) adjusted standard errors. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.
µ t-value β1 t-value β2 t-value
DAX -0.0022 -0.3994 0.0055 0.4403 0.0202*** 3.1912 MDAX 0.0015 0.2665 0.0148 1.259 0.0142** 2.4306 SDAX -0.0023 -0.4219 0.0195* 1.7164 0.0162*** 2.8479 Automobiles -0.0012 -0.1917 0.0058 0.3030 0.0199** 2.1623 Banks -0.0086 -1.0721 -0.0082 -0.3668 0.0225** 2.4751 Basic Resources -0.0030 -0.5505 0.0255* 1.7636 0.0209** 2.5708 Chemicals -0.0015 -0.2646 -0.0058 -0.4022 0.0269*** 4.3211 Construction -0.0049 -0.6679 0.0161 0.9001 0.0241*** 2.9683 Consumer -0.0013 -0.2493 0.0045 0.3079 0.0212*** 3.6237 Financial Services 0.0004 0.0674 0.0231 1.2899 0.0122* 1.7668 Food & Beverages 0.0006 0.1154 0.0014 0.0789 0.0073 1.0386 Industrial -0.0009 -0.1355 0.0278* 1.8165 0.0230*** 2.6989 Insurance 0.0009 0.1211 -0.0112 -0.7156 0.0135 1.5693 Media -0.0046 -0.4971 0.0544*** 2.8450 0.0097 0.8300 Retail -0.0007 -0.1340 -0.0038 -0.2814 0.0111* 1.8628 Software 0.0068 0.8761 0.0428** 2.1347 0.0112 1.0719 Technology -0.0076 -0.9427 0.028 1.6238 0.0266*** 2.7924 Telecommunication -0.0033 -0.5284 -0.0033 -0.1552 0.0140 1.4318 Transport & Logistics -0.0046 -0.6300 0.0219 1.3287 0.0199** 2.4311 Utilities 0.0006 0.1268 -0.0023 -0.0127 0.0104* 1.6915
Table 4: Results from the regression rst−rtf = µ+α1Jt+α2Ht+β(rmt −rtf) +εt where J is a dummy variable that
takes the value of one if the observation falls on January and zero otherwise. The Halloween dummy H takes the value of one for months in the period from November to April (excluding January) and zero otherwise. The constant µ denotes mean monthly returns over the summer period. α1denotes the additional January return, and α2denotes the
additional mean monthly return over the winter period. The β-coefficient corrects for general market movements. The sample comprises 336 observations for monthly returns over the period from 1988 to 2016. The t-values are based on Newey-West heteroskedasticity and autocorrelation (HAC) adjusted standard errors. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level,respectively.
µ t-value α1 t-value α2 t-value β t-value
DAX -0.12% -1.24 -0.49% ** -2.13 0.19% 1.55 1.12*** 61.72 MDAX 0.15% 0.58 0.69% 1.22 0.03% 0.10 0.86*** 16.65 SDAX -0.27% -0.91 1.28% * 1.74 0.44% 1.22 0.73*** 14.39 Automobiles 0.01% 0.03 -0.57% -0.56 -0.03% -0.04 1.24*** 18.93 Banks -0.71% -1.57 -2.00% -1.42 0.19% 0.30 1.27*** 15.24 Basic Resources -0.29% -0.60 1.74% 1.41 0.66% 1.03 0.88*** 13.84 Chemicals -0.10% -0.39 -1.48% -1.60 1.11% *** 3.10 0.97*** 24.73 Construction -0.47% -1.32 2.02% * 2.04 0.77% 1.37 1.10*** 20.59 Consumer -0.18% -0.53 -0.19% -0.18 0.99% ** 2.19 0.69*** 9.92 Financial Services 0.05% 0.16 1.49% 1.15 -0.22% -0.47 0.89*** 13.06 Food & Beverages -0.10% -0.23 -0.22% -0.13 0.10% 0.15 0.39*** 4.80 Industrial 0.00% 0.00 1.76% * 1.90 0.49% 1.08 1.11*** 20.52 Insurance 0.21% 0.64 -2.25% ** -2.25 -0.63% -1.08 1.22*** 10.75 Media -0.42% -0.61 4.54% *** 2.86 -0.62% -0.64 0.97*** 8.94 Retail -0.08% -0.24 -1.15% -1.28 -0.23% -0.56 0.83*** 13.81 Software 0.82% 1.44 3.13% 1.60 -0.91% -1.06 1.25*** 9.06 Technology -0.56% -1.17 1.53% 1.47 0.35% 0.60 1.42*** 14.97 Telecommunication -0.34% -0.65 -1.07% -0.53 0.11% 0.13 0.80*** 8.73 Transport & Logistics -0.38% -0.95 1.20% 1.13 0.24% 0.43 1.07*** 20.77 Utilities 0.02% 0.07 -0.90% -0.78 -0.14% -0.31 0.73*** 10.48
even accounting for extreme outliers, the results hardly change and the Halloween effect remains highly pronounced in cyclical sectors. After accounting for outliers, no significant effect remains for indices that are classified as defensives.
certain sectors out- or underperforming during the winter or the summer period.
In Table 5, the results of the Halloween effect when controlling for the three Fama and French (1993) and the Carhart (1997) factors are reported for the different industry and size indices. As can be seen, the results from Table 4 hardly change. For most indices, the signs remain equal. Thus the relative outperformance and underperformance during the summer and winter period can not be accounted for by the additional factors. Worthy mentioning is that including the Fama and French (1983) and Carhart (1997) risk factors, statistically significant and positive returns over the summer period can be observed for the MDAX and Software indices, while a statistically sig-nificant negative return over the winter period can be seen in the insurance industry, which is important to take into account, especially for factor investors seeking specific industry exposure. In general, however, no clear pattern with respect to defensive or cyclical sectors can be detected. In fact, the results may suggest that the Halloween effect is not a sector or size dependent phe-nomenon but rather systematic: While considered individually, almost all sector and size indices show a significant Halloween effect. However, in a single index and multiple factor model, which puts the Halloween effect in terms relative to the market, almost no significant effect can be found. Almost all industry baskets seem to follow the market with mean summer returns that are mainly negative or close to zero relative to the market portfolio.
In the following section, some possible explanations for the Halloween effect will be explored and discussed. The January effect will not be taken into further consideration, as it is shown not to be substantially significant.
5. Discussion
A. Systematic Risk
As the results from section four suggest, the Halloween effect is neither a size nor a sector spe-cific anomaly. In a single index and a four factor model, it is shown that industries do not signifi-cantly outperform the market on a risk-adjusted basis, neither during the summer nor the winter period with the exception of the Chemicals and Consumer indices. Hence, if the Halloween effect is systematic, it may well be that high mean monthly returns during the winter period are a result of higher systematic risk during the winter than during the summer. In other words, we would simply observe a risk premium due to higher sensitivity to market movements between Novem-ber and April. In order to be in line with that, systematic risk should be lower during the summer than during the winter. This idea is tested by estimating the following formula:
rst−rtf =µ+α1Jt+α2Ht+D1β1(rmt −r f
t) +D2β2(rmt −r f
Table 6: Estimates of the β coefficient separated into a Summer and Winter Beta resulting from equation (4) and the β coefficient from equation (2). The sample comprises 336 observations for monthly returns over the period from 1988 to 2016. The t-values are based on Newey-West heteroskedasticity and autocorrelation (HAC) adjusted standard errors. Prob. denotes the probability that summer and winter betas are indifferent.
Summer Winter
Beta t-values Beta t-values Beta t-values Prob.
Dax 1.12 61.72 1.13 50.93 1.11 42.94 46.46% MDax 0.86 16.65 0.92 14.47 0.76 9.39 12.77% SDax 0.73 14.39 0.80 12.16 0.62 8.52 4.80% Automobiles 1.24 18.93 1.17 10.98 1.34 12.20 38.99% Banks 1.27 15.24 1.26 11.01 1.28 12.67 88.05% Basic Resources 0.88 13.84 0.95 9.30 0.77 8.13 24.13% Chemicals 0.97 24.73 1.01 20.57 0.91 12.21 29.12% Construction 1.10 20.59 1.08 11.22 0.92 4.97 40.95% Consumer 0.69 9.92 0.77 10.06 0.57 5.24 9.56% Financial Services 0.89 13.06 0.86 11.58 0.93 7.77 57.74% Food & Beverages 0.39 4.80 0.52 6.46 0.18 1.13 6.05%
Industrial 1.11 20.52 1.12 13.23 1.10 13.12 90.31% Insurance 1.22 10.75 1.28 11.67 1.11 5.08 46.86% Media 0.97 8.94 1.04 5.93 0.88 5.08 55.57% Retail 0.83 13.81 0.86 11.07 0.79 8.82 57.24% Software 1.25 9.06 1.28 7.42 1.19 5.45 74.37% Technology 1.42 14.97 1.35 11.55 1.53 11.14 29.79% Telecommunication 0.80 8.73 0.76 7.29 0.85 5.32 62.65%
Transport & Logistics 1.07 20.77 1.17 15.22 0.92 8.97 8.23%
Utilities 0.73 10.48 0.79 8.28 0.64 5.61 35.35%
B. Bonds and Interest Rates
Another possible explanation may originate from returns on bonds and interest rates during the summer period. If for some reason, the central bank uses to rise interest rates during the sum-mer period (or to lower interest rates during the winter) compared to interest rates observed dur-ing the winter (summer), investors may be tempted to take advantage of that and move (partly) into risk-free positions. In the same way, investors may for some reason switch from equities to bonds for the summer period, which would to some extent explain lower equity returns during the summer months. For this explanation to hold, higher returns on bonds and/or higher interest rates should be observed empirically during May to October. In other words, bonds and interest rates should display a reversed Halloween effect. Consequently, mean returns for the winter and summer period for the RDAX, REX, and eb.rexx, and mean monthly risk-free interest rates for winter and summer months are compared and tested for statistical differences. REX is a synthetic index that reflects the market for German government bonds based on notional bonds9. RDAX was an index that consisted of all corporate bonds of the 30 DAX companies that met certain con-ditions such as minimum investment grade of BBB and a volume of at least Eur 500m. Bonds in the index were weighted with a maximum weight of 20 percent. Its calculation, however, was stopped in 201410. The eb.rexx index also reflects the market for German government bonds, but as opposed to REX, it is based on baskets of actually traded bonds11. Table 7 shows the results for mean monthly returns during the winter and summer period. Prob. denotes the probability that mean returns are equal in both periods.
Table 7: Winter and summer returns of RDAX, REX, and eb.rexx for the years 1999 to 2014, 1988 - 2016, and 2001 to 2015, respectively, and the mean for the monthly risk-free interest rate as described in section three.
Mean Winter Return Mean Summer Return Prob.
RDAX 5.14% 4.54% 73.14%
REX 2.51% 3.04% 46.51%
eb.rexx 1.74% 2.72% 23.77%
Risk-free Interest Rate 0.28% 0.29% 91.98%
While the REX and eb.rexx indices indeed show higher returns during the summer period, this does not hold for the RDax. Furthermore, the differences in means are not statistically significant. Mean monthly interest rates happen to be almost equal during winter and summer. Hence, both interest rates and returns on bonds cannot explain the anomaly either.
9More information available at
http://deutsche-boerse.com/dbg-en/about-us/services/know-how/glossary/glossary-article/REX- -German-bond-index-/2561258
C. Liquidity
Another attempt to explain the Halloween effect is to look at liquidity over the winter and summer period. If trading volume as a measure for market liquidity happens to be lower during the winter period, the higher returns are earned as a compensation for bearing higher liquidity risk. In other words, investors are rewarded with a liquidity premium for holding equities during the winter months. In order to test whether the difference in returns can by explained by a differ-ence in market liquidity, trading volume during the winter and summer periods will be compared and tested for statistical difference. All trading volume data is collected from Datastream and cov-ers the period from 2003 to 2010 with the exception of the DAX series, which continues until 2016. As can be seen in the last three columns of Table 8, trading volume happens to be slightly lower during summer in 11 out of the 20 indices. However, if the Halloween effect is explained by a liquidity premium, it should work the other way around. In any case, no statistically significant difference in trading volume is found.
D. Risk
Table 8: Mean monthly return variances during winter and summer periods calculated on basis of daily observations from 1988 to 2016 and trading volume in percentage during winter and summer periods from 2003 to 2010 in percent-age. Dax trading volume data ranges from 2003 to 2016. Prob. denotes the probability that Winter and Summer means are indifferent.
Variances Trading Volume
Winter Summer Prob. Winter Summer Prob.
Dax 10.77% 10.95% 73.81% 50.03% 49.97% 97.93% MDax 9.20% 9.70% 36.25% 48.54% 51.46% 51.79% SDax 8.23% 8.35% 79.76% 52.68% 47.32% 25.35% Automobiles 12.06% 12.20% 82.81% 51.23% 48.77% 55.44% Banks 12.00% 12.03% 97.20% 49.43% 50.57% 78.97% Basic Resources 11.71% 11.59% 87.50% 49.82% 50.18% 95.35% Chemicals 11.31% 11.39% 87.67% 50.46% 49.54% 83.14% Construction 11.06% 11.38% 63.33% 49.34% 50.66% 83.38% Consumer 9.88% 10.11% 59.72% 50.39% 49.61% 89.56% Financial Services 10.14% 10.45% 66.86% 49.49% 50.51% 84.99% Food & Beverages 10.38% 10.35% 96.97% 48.74% 51.26% 68.82%
Industrial 11.19% 11.54% 54.70% 51.27% 48.73% 52.06% Insurance 11.38% 11.63% 73.34% 51.01% 48.99% 56.79% Media 12.08% 11.94% 78.84% 51.47% 48.53% 57.22% Retail 10.28% 10.42% 75.27% 47.97% 52.03% 54.77% Software 12.77% 13.03% 71.75% 50.55% 49.45% 82.75% Technology 12.49% 12.61% 88.31% 49.75% 50.25% 89.51% Telecommunication 12.83% 12.93% 88.98% 51.03% 48.97% 54.70% Transport & Logistics 12.02% 12.41% 39.39% 48.65% 51.35% 48.02%
Utilities 10.92% 10.90% 97.13% 50.36% 49.64% 88.82%
E. Seasonal Affective Disorder (SAD)
As mentioned before, Kamstra et al (2003) relate the Halloween anomaly to the so-called SAD, also referred to as the Winter Blues, a form of depression which causes investors to become more risk averse as days get shorter. Their theory states that investors’ increasing risk aversion leads to declining equity prices as the hours of light per day decreases, leading to the materialization of a risk premium in terms of higher returns during the winter months. This theory will be tested by estimating the following formula which shows the returns of each month of the year:
returns do indeed become negative in August and September, followed by positive returns over the winter period. Regarding returns during the winter period, the argumentation in support or contrary to the SAD theory is twofold: On the one hand, the theory does not allow for positive average returns in October, November and December, as light hours per day in Germany still de-crease during those months12and a risk premium should materialize subsequently. On the other hand, the risk premium may already materialize after a large price decline observed in August and September, months, in which according to SAD, investors should still display increasing risk aversion due to the shortening of days. One could argue that investors already get rewarded with high returns for staying in the market at a time at which aggregate risk aversion is assumed which theoretically should drive prices downwards. Large, and mostly statistically significant mean returns in April are in line with both argumentations.
However, international evidence as in Bouman and Jacobsen (2002) shows that the Halloween effect is also found for countries in which daylight hours do not substantially differ over the year such as Mexico13, Thailand14, and Singapore15, just to name a few. Hence, even though it may somehow or other be in line with monthly returns in Germany, it is highly unlikely that SAD serves as a general explanation for the anomaly.
F. Optimism-Cycle Hypothesis
Doeswijk (2008) relates the Halloween effect to what he labeled the "optimism-cycle". In-vestors are assumed to exhibit a positive optimism bias with respect to the economic outlook as the calendar year approaches its end. Once the new year runs its course, they get caught up by reality as their overoptimistic expectations do not materialize. As a result, equities ex-perience a price increase before the turn of the year, and decrease again soon thereafter. While Doeswijk (2008) used initial returns on IPOs as a proxy for investors’ optimism, here the Ifo Busi-ness Climate Index is used in order to test whether the Halloween effect can be explained by the optimism-cycle hypothesis. The index is regarded as a leading indicator for economic activity in Germany and is compiled from actual data and survey data on the subject of business climate, current business situation, and business expectations, data that is also made available separately in index form16. Hence, the sub-index that only takes into account perceived business expecta-tions serves as a good proxy for optimism and will be used in order to account for such. If a seasonal pattern in optimism accounts for the Halloween effect, then monthly changes in the Ifo
12See https://www.timeanddate.com/sun/germany/berlin for weather information for Germany. 13See https://www.timeanddate.com/sun/mexico/mexico-city for weather information for Mexico. 14See https://www.timeanddate.com/sun/thailand/bangkok for weather information for Thailand. 15See https://www.timeanddate.com/sun/singapore/singapore for weather information for Singapore.
16See http://www.cesifo-group.de/ifoHome/facts/Survey-Results/Business-Climate.html for a precise
Business Climate Index should display a pattern similar to the Halloween effect in stock prices. Table A.6 in Appendix A shows the estimation results for testing for the Halloween effect in the Ifo Business Climate Index time series. The results, however, show that no seasonal effect with respect to changes in expectations regarding the future state of the economy is found. Note that the survey does not address investors in particular, and yet presents a good proxy for investors’ optimism as also analysts follow it closely and interpret its results as signals for future bearish or bullish sentiment on stock markets.
G. Persistence over Time and Economic Significance
A widely-held and quite intuitive assumption in the field of finance is that once an anomaly is discovered and attention is paid to it both from academics and practitioners, an anomaly is expected to disappear. As the Halloween anomaly seems to be a very profitable one, investors might have taken advantage of their knowledge about it, leading to its disappearance since the first publication by Bouman and Jacobsen (2002). Consequently, the persistence of the Halloween effect is tested by re-estimating regression (1), only taking into account the time period starting in January 2003. Table A.5 in the Appendix shows the results. The Halloween effect seems to have weakened after its first academic discovery. While signs have not changed compared to when considering the whole time period, here it remains statistically significant only for 3 out of the 17 industry baskets, namely, Chemicals, Construction and Consumer. The SDAX is the only of the three main size indices that still displays a weak Halloween effect. Moreover, the Telecommunication industry shows a reverse Halloween effect with returns during the summer period being statistically significant higher than during the winter period in which on average negative returns are earned.
Table 10: Buy-and-Hold vs Halloween Strategy. 1988-2016 Buy-and-Hold Halloween Mean SD RRR Mean SD RRR Market 9.64% 19.49% 0.49 11.36% 12.63% 0.90 Dax 10.32% 20.94% 0.49 12.03% 13.58% 0.89 MDax 12.14% 18.49% 0.66 11.93% 11.71% 1.02 SDax 8.79% 17.03% 0.52 11.01% 10.72% 1.03 2003-2016 Buy-and-Hold Halloween Mean SD RRR Mean SD RRR Market 11.58% 18.79% 0.62 9.36% 13.41% 0.70 Dax 11.21% 19.17% 0.58 8.93% 13.74% 0.65 MDax 16.27% 19.85% 0.82 13.02% 13.70% 0.95 SDax 14.04% 18.19% 0.77 13.03% 12.40% 1.05
Note: SD denotes standard deviation and RRR denotes Risk Return Ratio
The results covering the whole time period are consistent. A Halloween strategy shows a strong outperformance for all indices when considering the Risk and Return Ratio. Trading on the Halloween strategy only yields slightly lower absolute returns in case of the MDAX. When looking at the performance of the Halloween strategy in the time period between 2003 and 2016, two findings are apparent: First, the Halloween strategy underperformance a Buy-and-Hold ap-proach in all four cases in terms of absolute returns. However, the Risk Return Ratio is also higher for all four indices, even though the difference in Risk Return Ratio is by far not as large as when considering the whole sample. Hence, although a Halloween strategy underperformed a Buy-and-Hold strategy when looking at mean yearly returns over the time period since the first academic documentation of the Halloween effect in the end of 2002, it still would have helped investors to achieve a better risk-return trade-off and can therefore still be seen as economically significant.
6. Concluding Remarks
are much smaller (or even negative) than those in the period from November until April. Their findings are mainly consistent among both developed and emerging countries and time. Previous research for the U.S. and on European basis has shown that the Halloween effect differs among sectors, leading to a similar expectation for the German market.
In a simple dummy variable approach it is shown that the Halloween effect is present in most of the industries considered and that it is statistically significant for all three size indices that represent large-, mid-, and small-cap companies. When industries are classified into defensives and cyclicals, a pattern becomes apparent: The Halloween effect is only pronounced in cyclicals; defensives do not show a significant effect. Furthermore, it is shown that there is no possible January effect that may drive the high returns during the winter period. In accordance with Giovanis (2009) it is shown that in general no substantial January effect among size and industry can be found. When examining the anomaly corrected for general market movements, it is found that there is no sector specific out- or underperformance in neither of the periods suggesting that the Halloween effect is rather systematic (country specific) than sector specific. This is in contrast to the findings of Jacobsen and Visaltanachoti (2009) for the US, showing that consumer sectors outperform the market during the summer while production sectors outperform during the winter.
Moreover, consistent with the previous literature, risk-premium based explanations such as systematic risk, risk measured by variance, or liquidity fail to account for the anomaly. Neither is a reverse Halloween effect found for returns of bond indices and the risk-free rate that may to some extent explain why investors might have an incentive to sell off equities in the first place, resulting in lower returns on equity markets during the summer. Seasonal Affective Disorder, also referred to as the "Winter Blues", has previously been linked to the Halloween effect. Positive returns observed in October, November, and December, however, are not in line with the the-ory, according to which returns drop as a result of investors’ increasing risk aversion due to the shortening of days. Finally, Optimism, as proxied by the German Business Climate Index, which reflects expectations towards the future economic outlook, can not explain the anomaly either. Changes in expectations are not in line with the Halloween effect.
of observations taken into account in the period after the first academic publication, namely 13 years only.
A Halloween strategy that goes into equities during the winter period and into the risk-free rate during the summer period would have outperformed a buy-and-hold strategy when the whole time period in this study is considered. Taking into account the time period after 2003 only, the outperformance is not seen in absolute terms anymore. And yet, it still consistently outper-forms in terms of risk-return ratio. Therefore, the Halloween effect seems to remain economically significant, offering investors an improved risk-return trade-off over a buy-and-hold approach timing the market accordingly.
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Appendix A.
Table A.1: GICS industry classification and assignment to main sectors.
Dax Industry MSCI Sector Main Sector
Automobiles Consumer Discretionary Cyclicals Consumer
Media Retail
Banks Financials Cyclicals
Financial Services Insurance
Industrials Industrials Cyclicals
Transport & Logistics
Software Information Technology Cyclicals Technology
Chemicals Materials Cyclicals
Construction Basic Resources
Food & Beverage Consumer Staples Defensives Telecommunication Telecommunication Services Defensives
Table A.2: Basic characteristics of yearly returns from May 1988 to April 2003 based on 180 monthly returns. Yearly means and standard deviations are reported in column three and four, respectively. Prob. denotes the probability that mean winter returns and mean summer returns are equal. The last column reports in how many of the 15 seasons considered the winter returns outperformed summer returns.
No. Winter Summer No. of years
of obs. Mean S.D. Return Return Prob. RW>RS
Market 180 7.39% 23.94% 10.01% -2.62% 2.06% 13 SMB 180 -8.15% 12.20% -6.30% -1.85% 14.27% 5 HML 180 5.77% 19.85% 5.53% 0.24% 21.97% 13 MOM 180 14.13% 15.67% 6.89% 7.23% 94.03% 6 Rf - Rate 180 5.13% 2.16% 2.56% 2.56% 99.91% 7 DAX 180 6.84% 26.61% 11.14% -4.30% 1.51% 12 MDAX 180 7.11% 21.69% 8.05% -0.94% 7.45% 11 SDAX 180 3.56% 21.65% 6.87% -3.31% 4.76% 11 Automobiles 180 5.99% 29.86% 12.68% -6.68% 1.08% 11 Banks 180 4.90% 24.86% 7.71% -2.81% 10.82% 11 Basic Resources 180 5.79% 26.56% 11.97% -6.18% 0.38% 13 Chemicals 180 8.22% 21.24% 12.81% -4.59% 0.29% 13 Construction 180 1.06% 30.27% 6.58% -5.52% 7.92% 11 Consumer 180 6.52% 23.66% 9.34% -2.82% 3.73% 11 Financial Services 180 6.15% 32.95% 7.86% -1.72% 19.86% 10
Food & Beverages 180 5.30% 18.53% 4.47% 0.82% 34.59% 8
Industrial 180 15.54% 38.41% 17.40% -1.86% 2.22% 11 Insurance 180 3.76% 37.62% 4.96% -1.21% 45.09% 10 Media 180 -2.87% 56.57% 6.16% -9.03% 20.92% 8 Retail 180 3.73% 19.12% 4.47% -0.75% 23.90% 9 Software 180 24.13% 50.49% 21.10% 3.03% 12.50% 10 Technology 180 5.88% 34.83% 13.20% -7.31% 1.39% 11 Telecommunication 180 -1.26% 41.55% 8.94% -10.20% 4.54% 12
Transport & Logistics 180 4.84% 31.57% 9.48% -4.64% 5.46% 11
Table A.3: Basic characteristics of yearly returns from May 2003 to April 2016 based on 166 observations. Yearly means and standard deviations are reported in column three and four, respectively. Prob. denotes the probability that mean winter returns and mean summer returns are equal. The last column reports in how many of the 13 seasons considered the winter returns outperformed summer returns.
No. Winter Summer No. of years
of obs. Mean S.D. Return Return Prob. RW>RS
Market 166 9.58% 20.67% 7.25% 2.33% 32.54% 9 SMB 166 -0.64% 10.43% 1.64% -2.28% 12.14% 10 HML 166 6.72% 9.12% 1.88% 4.85% 23.37% 3 MOM 166 10.60% 9.88% 3.48% 7.12% 43.33% 4 Rf - Rate 166 1.50% 1.44% 0.71% 0.79% 79.67% 6 DAX 166 9.44% 20.93% 7.26% 2.18% 33.07% 8 MDAX 166 14.10% 26.66% 11.12% 2.98% 23.58% 9 SDAX 166 11.59% 28.43% 10.73% 0.86% 17.31% 7 Automobiles 166 12.57% 25.25% 6.44% 6.13% 96.60% 7 Banks 166 -5.41% 37.66% 2.46% -7.88% 32.73% 7 Basic Resources 166 13.51% 43.48% 10.27% 3.24% 48.66% 6 Chemicals 166 14.49% 24.07% 11.08% 3.41% 19.58% 9 Construction 166 15.68% 32.59% 15.59% 0.09% 8.82% 9 Consumer 166 12.99% 22.60% 11.37% 1.62% 7.31% 9 Financial Services 166 12.07% 27.57% 9.58% 2.49% 30.38% 9
Food & Beverages 166 3.54% 29.29% 3.75% -0.20% 66.33% 6
Industrial 166 10.41% 27.00% 9.46% 0.95% 27.55% 10 Insurance 166 9.98% 21.35% 7.49% 2.49% 45.37% 7 Media 166 13.48% 42.68% 9.05% 4.43% 68.95% 7 Retail 166 5.06% 28.60% 5.11% -0.05% 49.37% 8 Software 166 11.08% 17.52% 5.76% 5.32% 93.06% 8 Technology 166 8.34% 42.90% 9.71% -1.36% 29.24% 8 Telecommunication 166 7.37% 18.12% -0.16% 7.53% 11.91% 2
Transport & Logistics 166 8.55% 29.70% 9.18% -0.63% 22.15% 9
Table A.4: Results from the regression rt = µ+β1Jt+β2Ht+εt where J is a dummy variable that takes the value
of one if the observation falls on January and zero otherwise. The Halloween dummy H takes the value of one for months in the period from November to April (excluding January) and zero otherwise. The constant µ denotes mean monthly returns over the summer period. β1 denotes the additional January return, and β2 denotes the additional
mean monthly return over the winter period. The sample comprises 336 observations for monthly returns over the period from 1988 to 2016. The t-values are based on Newey-West heteroskedasticity and autocorrelation (HAC) ad-justed standard errors. The data is winsorized at the top and bottom 2.5% level of the return distribution. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.
µ t-value β1 t-value β2 t-value
Table A.5: Results from the regression rt = µ+β1Jt+β2Ht+εt where J is a dummy variable that takes the value
of one if the observation falls on January and zero otherwise. The Halloween dummy H takes the value of one for months in the period from November to April (excluding January) and zero otherwise. The constant µ denotes mean monthly returns over the summer period. β1 denotes the additional January return, and β2 denotes the additional
mean monthly return over the winter period. The sample comprises 160 observations for monthly returns over the period from 2003 to 2016. The t-values are based on Newey-West heteroskedasticity and autocorrelation (HAC) ad-justed standard errors. The data is winsorized at the top and bottom 2.5% level of the return distribution. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% level, respectively.
µ t-value β1 t-value β2 t-value
DAX 0.0043 0.6733 -0.0163 -0.8261 0.0106 1.5232 MDAX 0.0076 1.0766 0.0030 0.1555 0.0093 1.1396 SDAX 0.0039 0.5500 0.0152 0.7753 0.0134* 1.6947 Automobiles 0.0102 1.2687 -0.0202 -0.7238 0.0053 0.4496 Banks -0.0084 0.0106 -0.0102 0.0347 0.0134 1.1670 Basic Resources 0.0074 0.0083 0.0046 0.2164 0.0072 0.5863 Chemicals 0.0072 1.0233 -0.0305 -1.4417 0.0171** 2.1570 Construction 0.0001 0.0140 0.0010 0.0321 0.0293** 2.3626 Consumer 0.0036 0.6151 -0.0086 -0.4645 0.0205*** 2.8985 Financial Services 0.0055 0.7901 0.0023 0.0895 0.0097 1.1539 Food & Beverages -0.0003 -0.0420 -0.0165 -0.6805 0.0141 1.1985 Industrial 0.0036 0.4361 0.0053 0.2581 0.0116 1.2346 Insurance 0.0040 0.5361 -0.0349 -1.4597 0.0114 1.1280 Media 0.0111 0.9855 0.0206 0.9281 -0.0016 -0.1298 Retail 0.0019 0.2541 -0.0122 -0.5910 0.0097 1.1125 Software 0.0097 1.4870 0.0020 0.0902 0.0013 0.1816 Technology -0.0001 -0.0094 0.0033 0.1148 0.0144 1.0396 Telecommunication 0.0127** 2.4395 -0.0297 -1.4625 -0.0099 -1.2731 Transport & Logistics 0.0020 0.2196 -0.0039 -0.1582 0.0146 1.4591 Utilities -0.0006 -0.0787 -0.0085 -0.4357 0.0098 0.9939
Table A.6: Changes in expectations during winter and summer months as proxied by the component "Business Expec-tations" of the Ifo Business Climate Index. The index series ranges from May 1991 to November 2017. Prob. denotes the probability that mean changes during the summer period and means changes during the winter period as shown in the first two columns are equal.
∆ in exp. summer period ∆ in exp winter period Prob.
Table A.7: Buy-and-Hold vs Halloween Strategy for all Industries from 1988 to 2016 and from 2003 to 2016 1988-2016 Buy-and-Hold Halloween Mean SD RRR Mean SD RRR Automobiles 13.05% 27.87% 0.47 13.45% 19.33% 0.70 Banks 4.73% 30.00% 0.16 9.18% 21.02% 0.44 Basic Resources 12.46% 24.61% 0.51 14.36% 16.74% 0.86 Chemicals 13.61% 21.93% 0.62 14.89% 14.87% 1.00 Construction 11.65% 27.40% 0.43 14.13% 17.88% 0.79 Consumer 11.49% 19.48% 0.59 12.96% 13.35% 0.97 Financial Services 11.57% 23.01% 0.50 11.79% 16.62% 0.71 Food & Beverages 7.05% 22.46% 0.31 7.26% 16.38% 0.44 Industrial 16.35% 25.02% 0.65 16.98% 17.41% 0.98 Insurance 10.77% 28.61% 0.38 9.73% 19.70% 0.49 Media 9.78% 31.17% 0.31 11.56% 21.68% 0.53 Retail 6.71% 21.72% 0.31 7.59% 14.71% 0.52 Software 24.47% 35.67% 0.69 18.78% 24.86% 0.76 Technology 12.79% 34.35% 0.37 16.12% 24.37% 0.66 Telecommunication 7.04% 29.56% 0.24 8.71% 21.77% 0.40 Transport & Logistics 10.07% 26.05% 0.39 12.40% 16.08% 0.77 Utilities 8.03% 21.16% 0.38 8.09% 13.97% 0.58 2003-2016 Buy-and-Hold Halloween Mean SD RRR Mean SD RRR Automobiles 16.52% 28.44% 0.58 9.37% 20.73% 0.45 Banks 1.45% 35.64% 0.04 6.89% 26.81% 0.26 Basic Resources 16.16% 28.85% 0.56 11.53% 20.01% 0.58 Chemicals 16.54% 21.76% 0.76 12.81% 15.87% 0.81 Construction 20.54% 30.36% 0.68 18.57% 20.00% 0.93 Consumer 14.76% 17.79% 0.83 13.12% 12.56% 1.04 Financial Services 14.88% 22.86% 0.65 12.22% 18.25% 0.67 Food & Beverages 7.76% 28.55% 0.27 6.95% 21.49% 0.32 Industrial 13.04% 23.61% 0.55 11.26% 15.84% 0.71 Insurance 12.53% 30.50% 0.41 9.17% 24.50% 0.37 Media 17.05% 28.47% 0.60 10.30% 15.66% 0.66 Retail 7.81% 21.61% 0.36 7.44% 15.36% 0.48 Software 14.66% 21.42% 0.68 8.88% 14.19% 0.63 Technology 14.98% 35.79% 0.42 14.34% 27.29% 0.53 Telecommunication 8.97% 19.53% 0.46 1.58% 14.98% 0.11 Transport & Logistics 11.56% 24.37% 0.47 11.14% 16.18% 0.69 Utilities 4.82% 25.00% 0.19 5.58% 16.59% 0.34
