Mark Your Calendar:
An Analysis of Calendar Anomalies across US
Sectors
Paulrich Lawrence C. Tan
University of Amsterdam
Amsterdam Business School
Master in International Finance
Thesis Supervisor:
drs. Dennis Jullens
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C
ONTENTS
Abstract ... 4 1 Introduction ... 5 1.1 Market Efficiency ... 5 1.2 Market Models ... 5 1.3 Calendar Anomalies ... 7 2 Literature Review ...102.1 Literature on the Halloween Effect ...10
2.2 Literature on the January Effect ...12
2.3 Literature on the TOM Effect ...13
2.4 Other Integrated Studies ...14
3 Methodology and Hypothesis ...15
3.1 Main Hypothesis ...15
3.2 Data Requirements ...16
3.3 Statistical Relationship and Definition of Variables ...16
4 Data and Descriptive Statistics ...20
4.1 Data and Data Source ...20
4.2 Descriptive Statistics – Monthly Returns ...20
4.3 Descriptive Statistics – Daily Returns ...22
5 Results ...23
5.1 Means Test ...23
5.2 Means Test Halloween/ January Effect ...23
5.3 Means Test – Turn of the Month Effect ...25
5.4 Regression Results for the Halloween Effect ...27
5.5 Regression Results for the Tom Effect ...29
6 Robustness Checks ...32
6.1 Robustness Check – Halloween Effect (Four Factor Model) ...32
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6.3 Robustness Check – More Recent Time Period ...34
7 Conclusion ...37
7.1 Results Summary ...37
7.2 Application and Further Research...38
References ...41
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A
BSTRACT
By extending the time horizon and research scope of an earlier publication by Jacobsen and Visaltanachoti (2006), the thesis aims to examine the effects of various calendar anomalies across sectors in the US stock market. First, the research finds that the Halloween Effect remains strong (but have weakened in recent years) for cyclical sectors, and at the same time negative for some defensive sectors. These findings are consistent with earlier research. Second, some sectors exhibit both positive and negative performance versus the market during Turn of the Month days. Unlike the Halloween Effect where the “Optimism Cycle” has been cited as the primary reason for the return difference, the same cannot be said for the Turn of the Month Effect. The results indicate that seasonal anomalies remain an interesting enigma in the financial markets. It provides equity investors an opportunity to take sector decisions to enhance portfolio returns by taking advantage of return differences during specific points of a calendar year.
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1
I
NTRODUCTION
1.1 M
ARKETE
FFICIENCYOutperformance versus the general stock market has always been one of the primary objectives of investors and active managers alike. Alpha is becoming more and more elusive as market participants exploit strategies that have proven to outperform the market consistently. Intuitively, alpha should not be sustainable over the longer-term since arbitrageurs will immediately take advantage of market opportunities, thereby reducing the possibility of consistent outperformance. Otherwise, market participants can infinitely achieve riskless profits. The natural adjustment of prices prevents investors from making prolonged risk-free profits by implementing certain trading strategies. This is especially true for developed markets such as the United States, where the market breadth and depth are high, as investors all over the world trade in and out of the stock market in large volumes.
The notion that all market information should be reflected in the prices of securities is known as the Efficient Market Hypothesis (EMH). Three forms of EMH have been observed, namely, weak, semi-strong, and strong. The weak EMH theory states that all information on trading data is already present in the price of securities and therefore there is no added value of performing technical analysis. The semi-strong form, on the other hand, states that all publicly available information on company fundamentals is already reflected in prices. Lastly, the strong form EMH states that prices reflect all information that is relevant to a company, public or private (information that is only available to insiders of a company) (Bodie, et al. 2010).
1.2 M
ARKETM
ODELSOver the years, various models have been developed in order to explain the required rate of return of different asset classes. It started with the Capital Asset Pricing Model (CAPM) which first
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appeared in articles written by William Sharpe, John Lintner and Jan Mossin in 1964. They demonstrated that the expected return on assets is derived predominantly from non-diversifiable risk or market risk when introduced to a well-diversified portfolio. The theory itself had many assumptions. First is the ability of investors to buy and sell all securities at competitive market prices (without incurring taxes and transaction costs) and can borrow and lend at the risk free interest rate. Second, investors hold only efficient portfolios of traded securities; portfolios that yield the maximum expected return for a given level of volatility. Finally, investors have homogenous expectations regarding the volatilities, correlations, and expected returns of securities. (Berk and DeMarzo 2011).
The idea behind CAPM is that investors holding a portfolio of investments only want to be compensated for the risk that an asset contributes to a portfolio. The systematic risk or beta risk created by the correlation between the asset’s return and the returns of other investments. The CAPM therefore expresses the cost of equity as the sum of the required return on riskless asset plus a premium for beta or systematic risk (Palepu, et al, 2013). The relationship is expressed as:
𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟏: 𝐸(𝑟𝑒) = 𝑟𝑓+ 𝛽[𝐸(𝑟𝑚)− 𝑟𝑓]
Where 𝛽 represents systematic risk, 𝒓𝒎 represents market return, and 𝒓𝒇 represents the risk free
rate. It should be noted that the CAPM is an ex-ante model. However, in order to test the theoretical basis of the CAPM, ex-post data are used (Reddy and Thomson 2010).
Despite the unrealistic assumptions specifically on frictionless markets and homogenous expectations of investors stated above, the model remains widely used in Finance and have been extended by several academics. Fama and French (2004) concluded that the empirical record of the CAPM itself is quite poor. Other researchers expanded the theory and included more fundamental factors in an attempt to better explain expected returns. More recently, the model was updated by Fama and French (1993), where they identified two fundamental stock market factors related to (1) firm size and (2) book-to-market equity. These two factors are called the Small Minus Big (SMB) factor, which is the return of a portfolio of small stocks in excess of the
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return on a portfolio of large stocks, as well as the High Minus Low (HML), which is the return of a portfolio of stocks with a high book-to-market ratio in excess of the return on a portfolio of stocks with a low market ratio. Fama and French argued that firms, which have a high book-to-market ratio are more likely to be in financial distress, and small stocks may be more sensitive to changes in business conditions. These characteristics, all other things being equal, make these firms riskier than others. Later, an additional momentum factor was added to the model by Carhart (1997). The momentum factor essentially takes the difference between the returns of the highest performing firms and the lowest performing firms. It is also described as the tendency of security prices that went up in the recent past to go up further, while the reverse is true for losers. By adding the momentum factor, Carhart concluded that the updated model almost fully explains the persistence of equity mutual funds’ mean adjusted returns.
1.3 C
ALENDARA
NOMALIESAcademic evidence shows that certain anomalies have persisted over the years. They are termed anomalies since they deviate from the existing theories on EMH and the market models presented in the previous section. These include “seasonal anomalies”, wherein the performance of certain markets and securities have demonstrated evidence of moving in a certain pattern depending on specific days or periods within particular calendar year. Bordeaux (1995) indicated that the existence of calendar or time anomalies is a contradiction of the weak form of EMH because it infers that stock returns should be time invariant, that is, no identifiable short-term basis pattern should exist.
Equity return patterns that are linked to time are known as calendar anomalies. These anomalies include, among others, the January effect, the Halloween effect, and the Turn of the Month (hereafter “TOM”) effect. Over the years, academics have demonstrated that calendar anomalies are prevalent in global markets including the US.
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The research will attempt to answer how persistent seasonal effects were through time until the end of 2013, and more interestingly, include the Global Financial Crisis period (2008 to 2011). Secondly, the research will examine whether all sectors within the US market exhibit seasonality. Lastly, it will test whether certain sectors exhibit abnormal returns relative to the general market under the different seasonal anomaly scenarios.
As mentioned, the three calendar anomalies that will be examined in this research are the (1) January effect, (2) Halloween Effect, as well as (3) The TOM effect. The January effect is a theory that stock prices rise more in January than any other month. The Halloween Effect, on the other hand, is a phenomenon where returns in winter months exceed those of summer months. Lastly, the TOM effect anomaly looks at the excess returns exhibited by stocks on the last day of the month until the first few days of a month compared to other days of the month. These calendar anomalies will be discussed in more detail in the Literature Review section.
Several studies have examined the performance of different sectors to test for the Halloween effect. Specifically for the Halloween effect, this thesis will extend data beyond the Global Financial Crisis and will perform other tests to see whether abnormal sector returns can be explained. The study will also extend the same sector analysis methodology used for the Halloween effect to the TOM effect calendar anomaly, which was to the best of the author’s knowledge, has not been done previously.
The topic remains interesting and relevant in the context of equity portfolio management concerning US stocks. For instance, an investor can simply tweak his exposure over a certain period in a calendar year based on the seasonal patterns observed. By doing so, the investor should be able to outperform the general market index over the full calendar year. Moreover, if persistent excess return of certain sectors versus the market were to be demonstrated, investors should be able to implement a trading strategy of switching from one sector to another to achieve excess returns. This can be achieved while still maintaining a somewhat diversified exposure to
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the market by investing in sectors that can be shown to outperform over a specified period. These will be further examined in the sections to follow.
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2 L
ITERATURE
R
EVIEW
Various studies on seasonal anomalies have been documented for decades. The review below summarizes the key publications that are relevant to this specific thesis.
2.1 L
ITERATURE ON THEH
ALLOWEENE
FFECTWhile the seasonal effect has already been captured by the media several years back, the first academic study was only completed recently by Bouman and Jacobsen (2002) in which they concluded that unlike most other calendar effects, they find that the effect is present and persistent in both developed and emerging markets including the US. The effect is also present in thirty six (36) out of the thirty seven (37) markets in the sample that were examined.
Several reasons were stated in the study that attempted to explain the anomaly, including the effect of interest rate movements and trading volume, and they find no conclusive evidence. One factor that they found significant is the length of time as well as the timing of vacations. They indicated that these may be due to a shift in the number of investors, and therefore the capacity in the economy decreases, and will finally result in higher expected returns. In addition, they highlighted another explanation: investors may have been financially constrained because they spent more money during their summer holidays than during the months that they are working, which in turn results to investors asking for a higher liquidity premium during winter months. However, they finally concluded that arbitrage should have made both effects disappear. Moreover, they further mentioned that if summer vacations were indeed the reason for this anomaly, the effect would have been the reverse for countries in the Southern Hemisphere. However, in their research, this was the case only for New Zealand, and the findings related to this were not statistically significant.
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Kramer, Kamstra and Levi (2002) meanwhile, found links between the Seasonal Affective Disorder (SAD) effect, where they tested the length of days and stock market returns all over the world. Contrary to the conclusion above by Bouman and Jacobsen (2002), they indicated that daylight has been shown in numerous clinical studies to have a profound effect in people’s moods, and in turn people’s moods have been found related to risk aversion.
Other behavioral-related findings include a study by Cao and Wei (2004) where they found that temperature affects mood and in turn affect risk-taking behavior. The main finding is that lower temperatures can result in aggression while lower temperatures can result in either aggression or apathy. They then linked lower temperatures to higher stock returns and higher temperatures to lower or higher stock returns, depending on the trade-off between the two competing effects (of aggression and apathy). Finally, they concluded that there is a significant negative correlation between temperature and stock returns across different markets.
However, Doeswijk (2004) refuted these earlier studies and indicated that factors such as the SAD effect and temperature have an inherent disadvantage. The reason is that these factors are known in advance to have cycles that are parallel to the Halloween seasonal pattern in the stock market. For instance, it is known that temperatures are lower in winter than in summer months, and it is also known that the amount of daylight is also much less in winter than during the summer months. As such, the appearance of data mining in academic papers of this nature cannot be excluded. He suggested another more interesting reason for the seasonal effect in stock markets which he called the “Optimism Cycle”. This cycle is linked directly to observed behavioral patterns of investors. The theory states that investors start to look towards the end of the year, often, with overly optimistic expectations. These expectations wane as the year progresses, resulting to a summer lull. In addition, he indicated that the outlook for cyclical stocks are much better during the winter months as they benefit most from the anticipated rosy macroeconomic environment. The reverse is true for defensive stocks as they are relatively stable and are less affected by fluctuations in the economic cycle. He concluded that according to the “Optimism Cycle” hypothesis, investors’ preferences are biased towards cyclical stocks during winter and
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towards defensives during the summer. IPOs were used as a proxy for the degree of optimism in the model. The “Optimism Cycle” was in the end a significant factor in explaining away the return differences of certain sectors versus the actual market.
Further to the study above, Jacobsen and Visaltanachoti (2006), also performed a cross-sector study of the Halloween effect in the US market. While they did not directly mention the “Optimism Cycle” effect, they both indicated the same conclusions that the Halloween effect was absent in defensive sectors as well as consumer consumption but is strong in production sectors and industry sectors. The researchers mentioned that previous studies such as the SAD effect and temperature changes that cause a change in risk aversion are difficult to reconcile with the negative excess returns that were exhibited by some sectors. They were not able to identify a particular reason why the effect is stronger for certain sectors than the others. This was later criticized by Doeswijk, indicating in a comment to the research that the “Optimism Cycle” should have been stated as the reason for the observed sector differences.
2.2 L
ITERATURE ON THEJ
ANUARYE
FFECTThe January effect, meanwhile, was first cited by Wachtel (1942) where he indicated that January returns seem to be greater than that of other months. Further work by Rozeff and Kinney (1976) showed that seasonal patterns in an equal-weighted index of the NYSE showed that average returns for January was about 3.5%, and only 0.5% in other months. Additionally, Kleim (1983) concluded that the January effect seems to be more significant for small firms and not on the general market. More recent studies by Easterday et al. (2008) indicate that there was a time period between 1963-1979 where the January effect seemed to have declined, but has since reverted back to previous levels.
As indicated by Kleim (1983) and Wachtel (1942), tax loss selling is one of the reasons for the existence of the January effect. Tax-loss selling is essentially selling securities in order to benefit from netting effects of tax losses against taxes on gains. In a more recent paper by Singal and
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Chen (2001), they tested several other hypotheses and arrived at the same conclusion. They have shown that past losers are more likely to be sold in December to realize capital losses and at the same time past winners are more likely to be sold in January to postpone the payment of taxes.
2.3 L
ITERATURE ON THETOM
E
FFECTThe TOM effect has also been widely documented. Lakonishok and Smidt (1988) documented various anomalies, and under the TOM effect, they showed that using data for the Dow Jones Industrial Average (DJIA) from the period 1897 to 1986, the returns are much higher from the last trading day of the month until the first three trading days of the next month. These four trading days had average returns of 11.8 basis points (“bps”) per day, while other days only had a return of 1.5 bps.
McConnell and Xu (2006), meanwhile extended the earlier study and concluded that the TOM effect remains pronounced by extending the data to 2005. They made the same conclusion that all positive returns that occurred in the equity market within the DJIA occurred during the TOM days. Several possible explanations including higher volatility, an increase in the risk-free rate, and the concentration of buying activity during month-end (such as pension funds buying in the market or salaries being paid out during the end of the month that increased demand) were tested. They concluded that all these factors failed to explain the anomaly, and furthermore found that the net flow of liquidity into mutual funds are no higher than the other days of the month. This is a clear signal that month end cash flows do not necessarily translate to more investments during month end.
In an earlier study, Jacobs and Levy (1988) also concluded that investor psychology and behavior during these turning points of the calendar seem to be the most plausible explanation for their
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existence. They also state that while calendar anomalies have little economic significance (as most observed effects have relatively small differences between the control group and the non-control group), they apparently still evoke special investor behavior.
These studies indicate that thus far, there has been no conclusive evidence on the possible reason on why this phenomenon exists.
2.4 O
THERI
NTEGRATEDS
TUDIESMany more studies have been written on calendar anomalies but one particular study by Swinkels and Van Vliet (2011) identified the interaction effects of the various anomalies and narrowed down the number of true market anomalies to two. By looking at five different calendar effects, namely, Halloween effect, January effect, TOM effect, the Weekend effect (stocks tend to decline on Monday than the previous Friday), and the Holiday effect (stocks go up immediately after a Holiday weekend), they found that only the Halloween and the TOM effect are the strongest and these two effects alone fully eliminate or diminish the other effects. Prior to this, Bouman and Jacobsen (2002) also found in their research the January effect does not fully explain or influence the return differences of winter versus summer returns.
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3 M
ETHODOLOGY AND
H
YPOTHESIS
3.1 M
AINH
YPOTHESISThe result of the Literature Review shows that a selected number of seasonal anomalies have persisted through time. As concluded by Swinkels and Van Vliet (2011), the seasonal anomalies can be narrowed down to the TOM Effect as well as the Halloween Effect. These anomalies are the main focus of this study. Furthermore, Jacobsen and Visaltanachoti (2006) also concluded that while the Halloween Effect has persisted in the general market, there have been differences across various industry groups within the general market. Doeswijk (2004) also performed a similar research on US sectors and the “Optimism Cycle” has been cited as the main reason for identifying such differences for the Halloween Effect.
Building on these studies, the following hypotheses are formulated:
1. The Halloween Effect in the US market and in different industry groups within the US market has persisted even after including data post-2006.
1.1. Cyclicals and production-related sectors in the US outperform the general market in winter months and underperform in summer months in the US market, while the reverse is true for defensives (even with extended data).
1.2. The January effect is not a main driver of return for the Halloween Effect (even with extended data) for US markets as the anomaly is only present for small-cap firms.
2. The TOM Effect has persisted across the US market as well as different industry groups within the broader market.
2.1. Similar to the observation for the Halloween Effect, certain US sectors also exhibit a pattern of outperformance or underperformance versus the US market under the TOM effect.
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2.2. Certain sectors outperform or underperform the market on the basis of a short-term optimism or sentiment cycle
3.2 D
ATAR
EQUIREMENTSIn order to test whether anomalous returns have persisted over time, a key requirement is return data: monthly for the Halloween Effect and daily for the TOM effect. The returns per sector also need to be specified through time. In addition, to test the various hypotheses relating to excess return, the risk free rate and all inputs from the Fama-French-Carhart model are required. Variables used are described and defined further below.
3.3 S
TATISTICALR
ELATIONSHIP ANDD
EFINITION OFV
ARIABLESFor return data used, they are grouped differently using dummy variables depending on the anomaly being tested. For the Halloween effect, the Hal dummy variable is used to identify Winter Months of November to April (except January), while Hal2 is used to identify Winter Months of November to April (including January). This is similar to the approach performed by Jacobsen and Visaltanachoti (2006), where January returns were isolated from the Halloween effect in order to determine whether the January effect indirectly influences the Halloween effect. Jan is the dummy variable used for the January month in the monthly return data analyzed. For the TOM Effect, the last day of the month, as well as the first three days of the month are labelled as “TOM” days with TOM used as the dummy variable in the analysis. In addition, the Relative Strength Index (RSI) is used as a proxy for a short term sentiment indicator to test hypothesis 2.2.
Other terms used are Rf, which represents the risk-free rate, Mkt or Rm, which represents the market return, and HML, SMB, and MOM, which are the other three factors of Fama-French-Carhart, namely, “High Minus Low”, “Small Minus Big”, and Momentum.
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To test whether the seasonal anomalies identified are significant, first, a means test will be performed. As an example, the means test formula for the Halloween effect for the general market is shown below:
𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟐: 𝑀𝑘𝑡 − 𝑟𝑓 = 𝐶 + 𝛼𝐻𝑎𝑙2 + 𝜀
Where Hal2 takes the value of 1 for winter months (November to April) and 0 for summer months (May to October). The coefficient 𝛼, in this case shows the difference between the return on winter months versus summer months. The test will then be performed to see whether the general market performance differs significantly from all the sectors being tested. For this example, a positive coefficient means that there is a positive return for winter versus summer months. Conversely, negative coefficient means that there is a negative return for winter versus summer months (which is contrary to what was observed in the general market).
Again, similar to the approach performed by Jacobsen and Visaltanachoti (2006), a test will be performed based on the formula for Jensen’s alpha to test whether the difference in returns versus the general market is significant. Using the Halloween effect and TOM effect examples in the formula below, the degree and significance of the outperformance of a specific sector can be determined:
𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟑: 𝑅𝑠− 𝑅𝑓 = 𝐶 + 𝛼(𝐻𝑎𝑙2) + 𝛽(𝑀𝑘𝑡 − 𝑟𝑓) + 𝜀 𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟒: 𝑅𝑠− 𝑅𝑓 = 𝐶 + 𝛼(𝑇𝑂𝑀) + 𝛽(𝑀𝑘𝑡 − 𝑟𝑓) + 𝜀
The formula will essentially indicate how much additional winter return is generated (represented by the 𝛼coefficient) compared to the summer months (represented by the Constant, C) and the associated significance levels. A positive coefficient means a positive return contribution, while a negative coefficient translates to a negative return contribution. Performing this test would address Hypotheses 1.1 and 2.1.
In order to identify and isolate the effect of the January Effect on the Halloween Effect, the equation below will be used:
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𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟓: 𝑅𝑠− 𝑅𝑓 = 𝐶 + 𝛼(𝐻𝑎𝑙) + 𝛾(𝐽𝑎𝑛) + 𝛽(𝑀𝑘𝑡 − 𝑟𝑓) + 𝜀
The difference between the results under Equation 3 and Equation 4, will then be analyzed.
The above model will be extended to the test for TOM effect based on daily returns, and equation 2 will be used to test the difference in return of TOM days versus non-TOM.
In reference to Doeswijk (2005) where he indicated that the (calendar year) “Optimism Cycle” is the reason for the Halloween effect difference for Cyclicals and Non-cyclicals, this concept will be extended to the TOM effect as well. For the TOM effect, the Relative Strength Index (RSI) will be used as a proxy for the short term “Optimism Cycle”. This is a commonly used technical market indicator.
Celov and Grigaliuniene (2012) used the RSI as one of the measures of short term sentiment in their study in order to measure the relationship of sentiment and volatility in the stock market. The RSI is essentially an index reflecting the price of a security in relation to itself. When the RSI exceeds 70, the security or index is said to be overbought, which is an indicator for selling the stock, and when the index is below 30, the index is in an oversold territory, thereby creating a buying opportunity. The calculation of the RSI follow a definition used by Taran-Morosan (2011) using the classic form of RSI:
An upward daily change is defined (U) while a downward daily change is defined as (D), and these are calculated on a daily basis.
Equation i:1 𝑈
𝑐𝑙𝑜𝑠𝑒 = 𝑐𝑙𝑜𝑠𝑒𝑡𝑜𝑑𝑎𝑦− 𝑐𝑙𝑜𝑠𝑒𝑦𝑒𝑠𝑡𝑒𝑟𝑑𝑎𝑦
Equation ii: 𝐷𝑐𝑙𝑜𝑠𝑒 = 𝑐𝑙𝑜𝑠𝑒𝑡𝑜𝑑𝑎𝑦− 𝑐𝑙𝑜𝑠𝑒𝑦𝑒𝑠𝑡𝑒𝑟𝑑𝑎𝑦
If U takes a positive value on that day, then D takes a value of zero for that day, and vice versa. After which, an exponential moving average (EMA) is calculated using a multiplier (α). The α is
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determined in relation to the number of days. This is used to decrease the effect of older data versus newer data. The multiplier is calculated as:
Equation iii: 𝛼 =𝑁+12
In order to calculate EMA, however, a simple moving average (SMA) of the first N days until the day where RSI is being calculated must be obtained, according to Equation iv. Note: X denotes either U or D depending on the value being calculated.
Equation iv: 𝑆𝑀𝐴𝑁 =𝑋1+𝑋2+𝑋𝑁3…+𝑋𝑁
The EMA can then be determined according to Equation v.
Equation v: 𝐸𝑀𝐴𝑁+1= α × 𝑋1+ (1 − α) × 𝑆𝑀𝐴𝑁
The RSI is then calculated as:
Equation vi: 𝐸𝑀𝐴𝑁+1= α × 𝑋1+ (1 − α) × 𝑆𝑀𝐴𝑁
After calculating the RSI, the factor will be included in the regression equation below, in an attempt to test whether hypothesis 2.2 holds.
𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟔: 𝑅𝑠− 𝑅𝑓 = 𝐶 + 𝛼(𝑇𝑂𝑀) + 𝛾(𝑅𝑆𝐼) + 𝛽(𝑀𝑘𝑡 − 𝑟𝑓) + 𝜀
As a next step, a robustness check will be performed by adding the Fama French factors to
Equations 3, 4, and 5, above. This is to include, as much as possible, other explanatory variables
that contribute to alpha of a sector versus the general market. As an example, the test for the equation for the Halloween effect is shown below.
𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝟕: 𝑅𝑠− 𝑅𝑓 = 𝐶 + 𝛼(𝐻𝑎𝑙2) + 𝛽(𝑀𝑘𝑡 − 𝑟𝑓) + 𝛾(𝐻𝑀𝐿) + 𝛿(𝑆𝑀𝐵) + 𝜇(𝑀𝑂𝑀) + 𝜀
The same will be performed for the TOM effect. Lastly, a final robustness test will be performed to check whether results are different for the more recent period (1986 to 2013).
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4 D
ATA AND
D
ESCRIPTIVE
S
TATISTICS
4.1 D
ATA ANDD
ATAS
OURCEData used in this research can be obtained from the website of Fama and French2. The data used
are based on the value-weighted daily returns 17-sector classifications. The 17-sector classification is a narrowed down version of a bigger 49-sector classifications of Fama and French. The sectors are the following: (1) Food, (2) Mines (Mining and Minerals), (3) Oil (Oil and Petroleum Products), (4) Clothes (Textiles, Apparel and Footwear), (5) Durables (Consumer Durables), (6) Chemicals, (7) Consumer (Drugs, Soaps, Perfume and Tobacco), (8) Construction (Construction and Construction Materials), (9) Steel Works, (10) Fabricated Parts, (11) Machinery (Machinery and Business Equipment), (12) Cars (Automobiles), (13) Transportation, (14) Utilities, (15) Retail, (16) Financials (Banks, Insurance Companies, and Other Financials), (17) Others (Other sectors that cannot be classified under the 16 other sectors specified above).
The sector return data used for analysis is from 1926 to the end of 2013. For the test of Halloween effect and January effect, monthly returns are used. On the other hand, daily returns are used to perform tests on the Turn of the Month Effect.
The historical data of Fama-French factors of Market Return – Risk Free Rate (Rm-Rf), Small Minus Big (SMB), as well as High Minus Low (HML) were all likewise obtained from the website of Fama and French. These factors will be used for testing the various hypotheses of this thesis as well as for performing robustness checks.
4.2 D
ESCRIPTIVES
TATISTICS–
M
ONTHLYR
ETURNS
2 The website can be accessed through: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. The website contains information related to different sector returns as well as the Fama-French factors on a daily and monthly basis. The information is updated and extended on a regular basis.
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Table 1. above shows the descriptive statistics for monthly excess returns of the seventeen sector and the general market from 1926 to 2014. The maximum gain for any sector in the market in a one-month period was Steel (80.70%) while the lowest maximum gain was in the Mining (31.68%) sector. The largest monthly maximum drop was with seen in the Financial sector (-39.62%), which was registered on September 1931 during the great depression era (surprisingly, not during the fall of Lehman in September 2008). On the other hand, “Others” sector had the lowest monthly decline (25.30%). The market had an average monthly return of 0.63% and a volatility of 6.14%. It is interesting to note that Utilities had the lowest mean return (0.57%) while the Oil sector had the highest monthly return (0.81%). Meanwhile, the highly cyclical sector Steel had the highest volatility (8.58%) while the Food sector, which is regarded as a defensive sector, had the lowest monthly volatility (4.83%). More interestingly, the kurtosis of return data show significant difference across sectors. Kurtosis is a measure by which is a measure to test whether a distribution is more peaked or more flat that the normal distribution. The return data distribution exhibit leptokurtosis, which as defined by Haas and Pigorsh (2007), is a distribution that is more peaked in the center and thicker tailed than normal distribution. This indicates that the probability of gains and losses is much higher than would be implied by the normal distribution. The Consumer Durables sector exhibited the largest kurtosis (19.44) while the Mining sector exhibited the lowest kurtosis (5.20). This would mean that the probability of having outliers is largest and smallest for the Consumer Durables and Mining sectors, respectively.
Cars Chems. Clothes Const Consum. Durables Finan. Fab. Parts Food Machn Mining Market Oil Others Retail S teel Trans Utils.
M ean 0.80 0.71 0.62 0.70 0.72 0.66 0.70 0.65 0.69 0.78 0.65 0.63 0.81 0.59 0.71 0.63 0.67 0.57 M edian 0.69 0.72 0.65 0.79 0.89 0.81 0.86 0.75 0.83 1.11 0.57 1.02 0.77 0.87 0.81 0.71 0.83 0.76 M aximum 80.41 46.51 43.99 42.11 38.02 70.72 59.75 42.52 33.12 49.26 31.68 38.04 38.97 33.43 42.21 80.70 62.14 42.82 M inimum (34.90) (33.20) (32.07) (31.64) (26.00) (36.36) (39.62) (29.95) (28.44) (32.73) (32.88) (29.10) (29.61) (25.30) (30.32) (32.60) (33.18) (32.88) Std. Dev. 7.87 6.41 6.27 6.93 4.94 7.82 6.92 6.11 4.83 7.18 6.92 5.45 6.14 5.14 5.99 8.58 7.12 5.60 Skewness 1.14 0.29 0.38 0.38 0.25 1.32 0.55 0.14 (0.01) 0.18 (0.13) 0.17 0.27 (0.18) (0.01) 1.31 0.99 0.12 Kurtosis 16.43 9.36 8.21 8.41 9.35 19.44 14.20 9.06 9.63 8.57 5.20 10.34 6.84 6.68 8.79 16.09 15.19 10.69 Observations 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031 1031
Table 1. Descriptive Statistics - Monthly Excess Returns (Rs-Rf) per Sector including Market Return (Rm-Rf) (July 1926 to December 2013) The table below shows the descriptive statistics of the monthly excess return data used for Halloween and January effect. Highlighted in blue are the maximum values and in orange are the minimum
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4.3 D
ESCRIPTIVES
TATISTICS–
D
AILYR
ETURNSLooking at daily returns, the overall observation is slightly different from the previous monthly return table presented. The average overall market return was 0.0284% on a daily basis with a standard deviation of 1.07%. The Steel sector stands out with the high median daily return (0.013%), highest maximum one-day gain (30.53%), the worst single-day loss (-23.98%), highest daily volatility (1.67%), most positively skewed (0.60) and the highest kurtosis (30.14), all of which indicate the highly cyclical nature of the industry. Not surprisingly, the Utilities sector, which is considered as a defensive sector, showed the lowest average daily return and the lowest maximum daily decline among all sectors. The food sector, which is also a defensive sector, meanwhile, showed the lowest daily volatility.
Cars Chems. Clothes Const Consum. Durables Finan. Fab. Parts Food Machn Mining Market Oil Others Retail S teel Trans Utils.
M ean 0.0370 0.0337 0.0296 0.0265 0.0335 0.0264 0.0289 0.0306 0.0312 0.0351 0.0295 0.0284 0.0266 0.0370 0.0315 0.0276 0.0286 0.0256 M edian 0.0155 0.0365 0.0470 0.0490 0.0450 0.0435 0.0400 0.0500 0.0520 0.0550 0.0270 0.0600 0.0500 0.0370 0.0490 0.0130 0.0490 0.0440 M aximum 27.46 18.43 22.56 15.23 13.40 20.48 13.97 19.83 16.00 21.23 23.73 15.64 11.93 19.28 17.76 30.53 18.52 17.62 M inimum (19.32) (21.09) (18.45) (18.40) (18.75) (19.96) (15.63) (17.45) (16.00) (20.06) (15.83) (17.44) (17.68) (19.92) (17.67) (23.98) (17.34) (15.21) Std. Dev. 1.56 1.30 1.28 1.08 0.96 1.41 1.20 1.31 0.93 1.43 1.48 1.07 1.03 1.28 1.12 1.67 1.31 1.09 Skewness 0.42 (0.11) 0.06 (0.29) (0.05) (0.05) (0.04) 0.21 (0.00) 0.19 0.22 (0.12) (0.20) 0.12 (0.02) 0.60 0.06 0.32 Kurtosis 17.70 20.43 21.22 21.20 20.43 17.84 14.55 25.39 24.56 16.30 19.69 19.71 18.40 17.98 17.32 30.14 16.41 26.38 Observations 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120 23120
Table 2. Descriptive Statistics - Daily Excess Returns (Rs-Rf) per Sector including Market Return (Rm-Rf) (July 1926 to December 2013) The table below shows the descriptive statistics of the monthly excess return data used for the Turn of the M onth Effect. Highlighted in blue are the maximum values and in orange are the minimum
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5 R
ESULTS
5.1 M
EANST
ESTIn order to test whether returns under the different calendar anomaly scenarios are significantly different from the excluded period, a sample means test3 is done to show the difference in returns
between the control group and the excluded group. As previously discussed, this is similar to the approach performed by Bouman and Jacobsen (2002). By doing a simple linear regression against a dummy variable, the difference between the control group and non-control group can be shown. A means test is performed for the Halloween, January as well as the Turn of the Month effect. The results below show the difference between winter and summer returns (for the Halloween effect), January versus non-January months (for the January effect), and the TOM days versus non TOM days for the TOM effect. The variables used below are defined under Section 3.3.4
5.2 M
EANST
ESTH
ALLOWEEN/
J
ANUARYE
FFECT
3 The means test is a used as a regression technique used to determine the difference between a control group and a non-control group in statistics. This methodology was used by Bouman and Jacobsen (2002) but is also widely used in other studies. This is explained better in the link:
http://www.medicine.mcgill.ca/epidemiology/joseph/courses/EPIB-621/dummy.pdf
4 Note: All p-values and T-statistic of uses the Heterokedasticity and Autocorrelation Consistent (HAC) standard errors.
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α t-Statistic p-Value α t-Statistic p-Value
General Market 0.6998 0.1840 0.1840 0.6620 1.9839 0.0475 Cars 1.2876 0.1101 0.1101 0.8116 1.6722 0.0948 Chemicals -0.2504 0.7018 0.7018 1.1102 3.0794 0.0021 Clothes 2.2933 0.0019 0.0019 1.2359 3.3314 0.0009 Construction 1.1680 0.1212 0.1212 1.3025 3.3504 0.0008 Consumer 0.2420 0.6277 0.6277 0.2954 1.1072 0.2685 Durables 1.6595 0.0316 0.0316 1.0157 2.2575 0.0242 Fabricated Parts 0.8807 0.1440 0.1440 1.1496 3.1759 0.0015 Financials 1.0607 0.1313 0.1313 0.7162 1.8167 0.0695 Food 0.2742 0.5816 0.5816 0.3581 1.3477 0.1780 Machineries 1.2682 0.0843 0.0843 1.2041 2.8962 0.0039 Mining 1.9909 0.0091 0.0091 1.1515 2.7269 0.0065 Oil -0.4874 0.4346 0.4346 0.5983 1.7520 0.0801 Others 0.8581 0.1082 0.1082 0.7498 2.6297 0.0087 Retail 0.3594 0.5851 0.5851 0.5827 1.6676 0.0957 Steel 1.7532 0.0382 0.0382 1.3770 2.7140 0.0068 Transportation 1.9729 0.0077 0.0077 0.9820 2.3232 0.0204 Utilities 1.0954 0.0698 0.0698 0.0437 0.1363 0.8916
Table 3. Means Test - January Effect/ Halloween Effect
January Effect
Sector Halloween Effect (Hal2)
The ta ble below shows the result of a mea ns test performed using the formula indica ted in regression Equa tion 2 on return da ta from 1926 to 2013. The coefficient α shows the difference of Ja nua ry returns versus non-Ja nua ry returns for the Ja nua ry effect, a nd the difference between Winter over Summer months for the Ha lloween Effect. Highlighted in grey a re the P-va lues of the sectors tha t ha ve exhbited a return difference tha t is significa nt a t the 10% level. The ca lcula ted T-sta tistic uses HAC sta nda rd errors.
From the table above, we observe that January returns are not significantly different from non-January months for the general market. This is consistent with previous research done which concluded that the January effect is mostly present in small cap stocks only. Notable differences are the Clothing, Mining, and Transportation sector, which shows a highly significant difference between January and non-January months.
For the Halloween effect, taking Hal2 as the variable (which means January is included as one of the winter months), more consistency across different sectors is observed. Steel, Construction, and Clothing have the highest significant winter return over summer returns. Steel and Construction are considered as highly cyclical industries. Another interesting observation consistent with earlier research is that only three sectors do not exhibit greater winter returns over summer returns – consumer, food, and utilities. These sectors are considered defensive in nature and therefore returns over the winter months, while slightly greater than the summer months, show no significant difference.
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For illustration purposes, the sectors that have demonstrated significant difference at the 10% level are shown below:
5.3 M
EANST
EST–
T
URN OF THEM
ONTHE
FFECT0.0000 0.5000 1.0000 1.5000 2.0000 2.5000
Chart 1. Difference between January and non-January returns (1926-2013) 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 Ge n eral Ma rk et Ca rs Ch em ical s Clo th es Co n st ru ct io n D ur able s F ab rica te d Pa rt s F in an cial s M ac h in erie s M in in g O il O th er s R et ail St ee l T ran p o rt at io n
Chart 2. Difference between Halloween and Non-Halloween (1926-2013)
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Unlike the January effect and the Halloween effect, the TOM effect shows a significant difference across all the seventeen (17) sectors analyzed. Instead of monthly return, daily returns are shown above. The general market for example, has a return difference of (+0.13%) compared to non-TOM days. The sectors that exhibit the highest difference are Cars, Steel, and Transportation, which are considered largely as cyclical sectors, while sectors that had the least difference are again Food, Consumer and Utilities.
The result of the means test performed above show that the Halloween Effect and the Turn of the Month effect remain present. It also indicates that cyclicals exhibit a higher difference between the control and the non-control group. For the January effect, the results show inconsistency across sectors, and the general market itself does not exhibit significantly different returns. Moreover, only a limited number of sectors demonstrate that January returns are higher than other months. For this reason, the regression equation as described in Equation 3 will not be
α t-Statistic p-Value General Market 0.1346 7.5158 0.0000 Cars 0.1884 7.2148 0.0000 Chemicals 0.1349 6.2535 0.0000 Clothes 0.1278 6.7118 0.0000 Construction 0.1280 5.8957 0.0000 Consumer 0.1062 6.2567 0.0000 Durables 0.1407 5.9995 0.0000 Fabricated Parts 0.1511 7.5777 0.0000 Financials 0.1459 6.6806 0.0000 Food 0.1040 6.7056 0.0000 Machineries 0.1329 5.4603 0.0000 Mining 0.1281 5.0950 0.0000 Oil 0.1392 6.2098 0.0000 Others 0.1181 6.7254 0.0000 Retail 0.1293 6.6756 0.0000 Steel 0.1936 6.8263 0.0000 Transportation 0.1520 6.8033 0.0000
Sector TOM Effect
Table 4. Means Test - TOM Effect
The table below shows the result of a means test performed using the formula indicated in regression Equation 2 on daily return data from 1926 to 2013. The coefficient α shows the difference of TOM versus non-TOM days. Highlighted in grey are the P-values of the sectors that have exhbited a return difference that is significant at the 10% level. The calculated T-statistic uses HAC standard errors.
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tested since the general market itself failed to show significant difference between January and the other months of the year. The January effect will subsequently be observed in conjunction with the Halloween effect because the January month falls within the interval of the Halloween months.
To determine whether the sector returns shown above are significantly different from the return of the market, a regression test is performed on Equation (3) for the two other anomalies to be tested.
5.4 R
EGRESSIONR
ESULTS FOR THEH
ALLOWEENE
FFECTSummer Return (C) T-statistic P-value Hal. Return including January (Hal2) ( γ) T-statistic P-value Cars 0.037 0.20 0.840 0.028 0.290 0.922 Chemicals (0.143) (1.16) 0.246 0.437 0.168 0.010 Clothes (0.265) (1.54) 0.124 0.645 0.245 0.009 Construction (0.309) (2.68) 0.007 0.531 0.174 0.002 Consumer 0.365 2.91 0.004 (0.181) 0.177 0.307 Durables (0.221) (1.37) 0.172 0.166 0.235 0.482 Fabricated Parts (0.194) (1.50) 0.133 0.503 0.185 0.007 Financials 0.018 0.15 0.884 (0.065) 0.166 0.695 Food 0.297 2.56 0.011 (0.150) 0.158 0.343 Machineries (0.177) (1.50) 0.133 0.402 0.174 0.021 Mining (0.175) (0.77) 0.442 0.590 0.327 0.071 Oil 0.232 1.51 0.132 0.016 0.245 0.948 Others (0.056) (0.85) 0.394 0.172 0.106 0.105 Retail 0.153 1.26 0.209 (0.067) 0.192 0.728 Steel (0.464) (2.37) 0.018 0.480 0.278 0.085 Transportation (0.170) (1.19) 0.235 0.225 0.214 0.294 Utilities 0.324 2.05 0.040 (0.474) 0.215 0.028
Table 5. Result of regression for Hallow een Effect (including January in the Hal Effect)
Equation 3: Rs-Rf=C+α(Hal2)+β(Mkt-rf)+ε is regressed. The values shown below are the coefficients shown below are the respective alpha contribution of the Halloween Effect (α) and the January Effect (γ). Highlighted in grey are the P-values of the sectors that have exhibited a significant excess return contribution at the 10% level. The calculated T-static
used the HAC standard errors.
The table above shows that cyclicals exhibit the most alpha versus the market during the winter months with Clothing, Mining and Construction taking the lead. Monthly alpha versus the
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market of 0.65%, 0.59%, and 0.53%, were observed respectively, for these sectors. Utilities on the other hand, underperform the market during winter months (-0.47%). Food, Retail, Consumer, and Financials (surprisingly), also have negative alpha but are not significant at the 10% level. This is consistent with the previous literature despite extending data beyond 2006 and including the financial crisis years.
To test whether the January effect contributes to the returns in the Halloween Effect, the two variables are separated and the results are shown below.
Compared to the previous test, there are fewer sectors that exhibit positive alpha versus the market during the winter months when the January month is taken out of the Halloween effect. A comparison of the results for the two previous tests are shown below.
Summer Return (C) P-value Hal. Return ex January ( α) P-value January Return ( γ) P-value Cars 0.064 0.730 (0.072) 0.814 0.404 0.405 Chemicals (0.122) 0.327 0.642 0.001 (0.688) 0.079 Clothes (0.256) 0.135 0.395 0.112 1.837 0.000 Construction (0.311) 0.007 0.521 0.005 0.591 0.096 Consumer 0.374 0.003 (0.156) 0.402 (0.338) 0.361 Durables (0.245) 0.130 0.058 0.809 0.804 0.057 Fabricated Parts (0.210) 0.104 0.522 0.008 0.439 0.231 Financials 0.006 0.958 (0.106) 0.523 0.197 0.605 Food 0.292 0.012 (0.110) 0.502 (0.306) 0.303 Machineries (0.179) 0.125 0.366 0.049 0.587 0.123 Mining (0.171) 0.451 0.392 0.264 1.572 0.013 Oil 0.219 0.154 0.226 0.367 (0.992) 0.047 Others (0.052) 0.427 0.137 0.223 0.301 0.150 Retail 0.140 0.249 0.000 0.998 (0.311) 0.447 Steel (0.464) 0.017 0.382 0.195 0.979 0.029 Transportation (0.169) 0.235 0.032 0.885 1.185 0.007 Utilities 0.325 0.039 (0.623) 0.007 0.264 0.568
Table 6. Result of regression for Halloween Effect (excluding Jan. in the Hal Effect)
Equation 5: [Rs-Rf=C+α(Hal)+γ(Jan)+β(Mkt-rf)+ε is regressed. The coefficients shown below are the respective alpha contribution of the Halloween Effect (α) and the January Effect (γ). In bold are the
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The chart above seems to indicate that much of the contribution from the Halloween effect in certain sectors (Clothes, Mining, and Steel) is due to the January effect. However, this will be tested later in the robustness checks to see whether the January effect can be explained away by other factors in the Four Factor Model.
5.5
R
EGRESSIONR
ESULTS FOR THET
OME
FFECT-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Chart 3. Excess Retun in Halloween Months by Isolating January Effect
Page 30 of 43 Non-TOM Days Return (C) T-Statistic P-value TOM Days Return ( α) T-Statistic P-value Cars (0.002) (0.391) 0.696 0.023 1.502 0.133 Chemicals 0.005 0.965 0.335 (0.007) (0.635) 0.525 Clothes 0.000 0.026 0.979 0.025 2.031 0.042 Construction 0.002 0.531 0.596 (0.013) (1.154) 0.249 Consumer 0.011 2.530 0.011 0.010 0.888 0.375 Durables (0.003) (0.499) 0.618 (0.004) (0.306) 0.760 Fabricated Parts (0.002) (0.358) 0.721 0.025 2.328 0.020 Financials (0.000) (0.024) 0.981 0.001 0.058 0.954 Food 0.009 2.494 0.013 0.005 0.548 0.584 Machineries 0.006 1.524 0.128 (0.031) (3.023) 0.003 Mining 0.003 0.365 0.715 0.019 0.903 0.366 Oil 0.008 1.372 0.170 0.014 0.944 0.345 Others 0.002 0.591 0.554 (0.003) (0.430) 0.668 Retail 0.004 1.025 0.305 0.007 0.714 0.475 Steel (0.013) (1.936) 0.053 0.020 1.178 0.239 Transportation (0.003) (0.701) 0.483 0.006 0.509 0.611 Utilities 0.004 0.685 0.494 (0.005) (0.399) 0.690
Table 7. Result of regression for TOM Effect
Equation 4: Rs-Rf=C+α(TOM)+β(Mkt-rf)+ε. The values shown below are the coefficient shown below is the alpha contribution of the TOM effect. Highlighted in grey are the P-values of the sectors that have exhibited a significant
excess return contribution at the 10% level. The calculated T-static used the HAC standard errors.
Regression results for the TOM effect seem to indicate that only the Clothes (+2.5 bps) and Fabricated Parts (+2.5 bps) sector show a significant positive alpha versus the market. Machineries sector, has surprisingly shown a significant negative alpha. Another observation is that for non-TOM days, Consumer and Food sectors both posted a higher relative performance versus the market of (+1.1 bps) and (+0.9 bps) respectively, while Steel showed a significant underperformance of around (-1.3 bps). Unlike the Halloween Effect, there seems to be less of discernible pattern that cyclicals outperform during TOM days, while defensives outperform during the non-TOM days. Overall, most sectors exhibit more or less the same return as the general market during the last day of the month and the first three days of the next month
Next, the result of the regression test for the short-term “Optimism Cycle” using RSI as a proxy is shown.
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The results above show that by using RSI as a proxy for short-term “Optimism Cycle”, the indicator does not explain the positive/ negative alpha demonstrated by the sectors under the TOM effect. The conclusion is therefore that the extension of the “Optimism Cycle” to the TOM effect does not hold and the reason for the observable differences in returns remains open. Other reasons stated by previous literature indicate that cash flows that occur towards the end of the month do not necessarily change the liquidity situation in the market, and therefore this factor is not tested in this research.
TOM Days Return ( α) T-Statistic P-value Cars 0.023 1.511 0.131 Chemicals (0.007) (0.634) 0.526 Clothes 0.025 2.018 0.044 Construction (0.013) (1.168) 0.243 Consumer 0.009 0.885 0.376 Durables (0.004) (0.318) 0.751 Fabricated Parts 0.025 2.323 0.020 Financials 0.001 0.055 0.956 Food 0.005 0.546 0.585 Machineries (0.031) (3.019) 0.003 Mining 0.018 0.895 0.371 Oil 0.014 0.948 0.343 Others (0.003) (0.436) 0.663 Retail 0.007 0.710 0.478 Steel 0.020 1.181 0.238 Transportation 0.006 0.507 0.612 Utilities (0.005) (0.394) 0.693
Table 8. Result of regression for TOM Effect (with RSI)
Equation 6: [Rs-Rf=C+α(TOM)+γ(RSI)+β(Mkt-rf)+ε. The values shown below are the coefficient shown below is the alpha contribution of the TOM effect. Highlighted in
grey are the P-values of the sectors that have exhibited a significant excess return contribution at the 10% level. The calculated T-static used the HAC standard errors.
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6 R
OBUSTNESS
C
HECKS
6.1
R
OBUSTNESSC
HECK–
H
ALLOWEENE
FFECT(F
OURF
ACTORM
ODEL)
The results of the robustness test by expanding the model to include the Fama-French-Carhart factors are shown below.
Comparing the results of Table 5 and Table 9, we see consistent except for a few sectors where the return difference are no longer significant. The difference versus the market for Mining and Steel, for example, is no longer significant at the 10% level as the difference is explained away by the other factors that were introduced. However, the general conclusion remains that cyclicals outperformed defensives during winter months. This shows that the result remains consistent with earlier findings of Jacbosen and Visaltanachoti (2006). The results of this research is shown on Appendix 1. Summer Return (C) P-value Hal. Return (α) P-value Market ( β) P-value HML (γ) P-value Mom. (μ) P-value SMB (δ) P-value Cars 0.078 0.673 0.048 0.868 1.140 - 0.179 0.017 -0.142 0.001 0.022 0.748 Chemicals -0.130 0.308 0.487 0.005 1.060 - -0.015 0.821 -0.035 0.427 -0.165 0.005 Clothes -0.211 0.204 0.486 0.039 0.796 - 0.040 0.709 -0.061 0.415 0.462 0.001 Construction -0.289 0.010 0.420 0.011 1.116 - 0.042 0.461 0.007 0.866 0.218 0.001 Consumer 0.325 0.006 -0.061 0.711 0.793 - -0.085 0.211 0.024 0.561 -0.234 -Durables -0.169 0.257 -0.024 0.917 1.136 - 0.235 0.002 -0.077 0.122 0.364 0.000 Fabricated Parts -0.171 0.166 0.503 0.008 0.934 - -0.009 0.895 -0.053 0.197 0.097 0.269 Financials 0.025 0.821 -0.021 0.895 1.109 - 0.234 - -0.135 0.000 -0.071 0.160 Food 0.254 0.025 -0.138 0.381 0.780 - 0.049 0.336 0.028 0.423 -0.111 0.019 Machineries -0.053 0.639 0.461 0.007 1.203 - -0.304 - -0.089 0.023 0.112 0.007 Mining -0.198 0.388 0.375 0.247 0.800 - 0.078 0.326 0.072 0.144 0.318 -Oil 0.090 0.558 0.034 0.889 0.915 - 0.268 - 0.119 0.018 -0.236 -Others 0.013 0.836 0.197 0.047 0.892 - -0.205 - -0.031 0.131 0.069 0.014 Retail 0.207 0.087 -0.017 0.927 0.947 - -0.116 0.031 -0.060 0.106 0.037 0.606 Steel -0.435 0.022 0.339 0.221 1.238 - 0.314 - -0.090 0.047 0.227 0.008 Transportation -0.191 0.135 0.085 0.614 1.035 - 0.438 - -0.066 0.090 0.166 0.006 Utilities 0.226 0.120 -0.476 0.021 0.777 - 0.317 - 0.009 0.829 -0.176 0.001
Table 9. Result of regression for Halloween Effect (excluding Jan. in the Hal Effect)
Equation 7: [Rs-Rf=C+α(Hal2)+β(Mkt-rf )+γ(HML)+δ(SMB)+μ(MOM)+ε is regressed. The coefficient α shown below shows the alpha contrubution of the Halloween Effect (Hal2) per sector. The Fama-French Carhart factors are added as explanatory variables in the equation. In
