Analysis of the January Effect in Time Series of
Mexican Stock Market Indexes
Análisis del Efecto Enero en las Series Temporales de los Índices
Bursátiles Mexicanos
Mariana
Garay Alvarado
Universidad Autónoma de Querétaro (México)
http://orcid.org/0000-0002-0019-500X
mgaray107@gmail.com
Michael Demmler
Universidad
Autónoma de Querétaro (México)
http://orcid.org/0000-0002-1629-5814
michael.demmler@uaq.mx
Received: January, 2019
Accepted: May, 2019
ABSTRACT
The current article has the research
objective to search for empirical evidence of the January effect within the
time series of the IPC and the sector indexes of the Mexican stock market using
econometric GARCH analysis. The dataset is formed by the log returns of the
daily closing prices corresponding to the IPC as well as the sector indexes
covering the period from 01/01/2010 to 12/31/2018. The main results of the
article are as follows: Based on the January effect the Efficient Market
Hypothesis in its weak form sense cannot be rejected for the Mexican stock
market as the results do not provide significant evidence of the existence of
the respective calendar anomaly within the analyzed time series of the IPC and
the different sector indexes.
Keywords: Efficient Market Hypothesis;
calendar anomalies; January effect; Mexican stock market.
Jel Code: G11, G12, G14.
RESUMEN
El presente
artículo tiene el objetivo de investigación de buscar evidencia empírica del
efecto enero en las series temporales del IPC y los índices sectoriales
analíticos del mercado bursátil mexicano utilizando modelos econométricos tipo
GARCH. La muestra de datos está conformada de los rendimientos logarítmicos de
los precios de cierre diarios correspondientes al IPC así como los índices
sectoriales analíticos y se abarca el período 01/01/2010 a 31/12/2018. Los
principales resultados del artículo son los siguientes: basado en el efecto
enero la Teoría de los Mercados Eficientes en su forma débil no se puede
rechazar para el mercado bursátil mexicano, ya que los resultados no muestran
evidencia significativa de la existencia de dicha anomalía de calendario en las
series de tiempo analizadas del IPC y de los diversos índices sectoriales
analíticos.
Palabras clave: Teoría
de Mercados Eficientes; anomalías de calendario; Efecto Enero; mercado bursátil
mexicano.
Código Jel: G11, G12, G14
INTRODUCTION
The Efficient Markets Hypothesis is
still nowadays one of the most influential theories existing in finance as demonstrated
by the Nobel Prize in Economics for its founder Eugene F. Fama
in 2013. Fama (1970, 1991) himself differentiates
between the three different levels of market efficiency – weak form,
semi-strong form and strong form efficiency.
Empirical tests of the different
market efficiency levels have a long tradition within financial literature.
According to Fama (1991) return seasonality studies
as for example tests of the January effect can be considered as tests of the
EMH in its weak form sense. Numerous studies using a variety of methodological
approaches reach differing results of the degree of existing market efficiency
depending on variables such as the analyzed market, period or country.
However, there exists just a small
amount of studies relating the January effect and the Mexican stock market
(e.g. Cabello and Ortiz, 2003; López and Rodríguez, 2010; Rodríguez and
Morales, 2009; Rojo, 2013). In fact, a study using
current datasets and taking into account not just the IPC but also the 2009 established
sector indexes of the Mexican stock market is not existent.
A study of this type would provide
an up-to-date and comprehensive picture of the existence or non-existence of
the January effect in time series of the Mexican stock market. Therefore, the
present article has the research objective to search for empirical evidence of
the January effect within the time series of the IPC and the sector indexes of
the Mexican stock market using econometric GARCH analysis.
In order to achieve the outlined
research objective, the present article is divided into five main sections.
After this introductory part, the second chapter (Theoretical Background)
introduces the theoretical fundamentals with respect to the Efficient Market
Hypothesis and the January effect as one example of calendar anomalies.
The third part (Methodology)
presents the underlying dataset and the methodological approach of the study.
The fourth section (Presentation and Analysis of Results) presents and
interprets the results of the test and subsequently chapter five concludes.
THEORETICAL BACKGROUND
Efficient Market Hypothesis
Theory and
Assumptions
In 1970, Eugene F. Fama published an article on so-called efficient markets.
Since then the Efficient Market Hypothesis (EMH) has had a strong impact on the
world of finance. The article defines that a financial market in which prices
always fully reflect available information can be called "efficient" and refers to a random process of asset
pricing that behaves like a "fair game"
where the results cannot be systematically predicted.
Uribe and Ulloa (2011) interpret the
efficient market definition as follows: Even though the information that occurs
in the financial markets is extensive, it is absorbed and reflected at any time
by the market prices of the assets. The reason that some future information is
not yet reflected in the market prices is simply that it is still unknown by
the market participants and its occurrence depends on a random process. Hence,
if financial markets are efficient, it is impossible to systematically gain
excess profits from the prediction of market prices, regardless of the type of
information or prediction techniques used.
Following the previously outlined
hypothesis, according to Fama (1970), the following
assumptions have to be fulfilled in order to classify a market as efficient:
Economic agents can be characterized
by rationality what implies that they correctly use the available and relevant
information to formulate rational expectations and thus, establish by their
buying and selling decisions correct market prices of the financial assets. In
addition, market participants are defined homogeneously according to the model
of the Economic Man (homo œconomicus) and therefore
also homogeneously take the same (correct) investment decisions.
Market participants have free and
instant access to all available information. However, only new, unexpected,
fundamental information can change the market price of a financial asset. In
this sense, the term fundamental information can be defined as information that
changes the real economic prospects for example of company (in case of a
stock). According to the EMH investors interpret new (fundamental) information
rationally and quickly, and use their knowledge to establish “fair” market prices which reflect
fundamental values. As all market participants possess the same information and
take the same correct investment decisions, consequently, no individual
investor could systematically gain excess returns above the average market
return level.
By not having to consider taxes or
transaction costs, market participants are able to respond easily and quickly
to new, relevant information and incorporate this information instantly into
the market prices of the asset by their buying and selling decisions.
Given the outlined assumptions
above, one reaches one of the following main findings of the EMH: In the medium
and long-term inefficiencies in the form of differences between the market
price of an asset and its fundamental value cannot exist. Possibly existing
inefficiencies in the short run would be immediately eliminated by the rational
investors using a perfectly functioning arbitrage process (Barberis
and Thaler, 2002; Demmler, 2017).
Types of Information Efficiency
According to Fama
(1970, 1991) it can be differentiated between the three following levels of
efficiency according to the type of information:
The current market prices of an
asset reflect the totality of the existing historical information represented
by the historical price movements of the asset. Hence, analysis methods which
are based on the analysis of historical prices (technical analysis) are
obsolete and cannot result in excess returns.
Departing from weak form efficiency,
the semi-strong efficiency additionally incorporates all public information
available (i. e. corporate publications,
any type of news media coverage, analysts’ publications, etc.). Thus,
forecasting techniques as the fundamental analysis, which depends on the
analysis and interpretation of public information, are not necessary as its use
cannot result in above average investment returns.
The strong form information
efficiency is the most complete one as it takes into account the previous two
types of information efficiency and, furthermore, considers non-public
information (insider information). As within this type of information
efficiency market prices reflect all the existing information, it is not possible
for any investor to systematically gain excess investment returns. Hence,
within this type of market the only adequate investment strategy is a passive
portfolio management approach that results in investors constantly obtaining
the average market return.
Figure 1
Types of information efficiency
Source: Own elaboration (Jensen, 1978).
As can be seen in Figure 1 the
different levels of information efficiency are related in a way that the weak
form efficiency forms part of the semi-strong form, and this one in return is
an essential component of the strong form efficiency type. Thus, the rejection
of the EMH in its weak form sense for a specific market automatically
eliminates the possibility that this market could be semi-strong and strong
form efficient. Hence, the negation of the weak form EMH results in the
rejection of the other two forms. However, it is possible that a specific
market can be characterized as weak form efficient but semi-strong form
inefficient. Consequently, there also exists the possibility of a semi-strong
form efficient and strong form inefficient market (Demmler,
2017).
Criticism
of the Efficient Market Hypothesis and Implications for Investors
The EMH has been controversially discussed since its publication. For
example, it seems impossible that its assumptions can be fulfilled in reality.
In real markets information is costly and the vast majority of investors have a
limited access to it. Moreover, investors are heterogeneous and face problems,
for example, in the form of limited liquidity, taxes and transaction costs. León
(2013) highlights some important implications for the case that the EMH would
be a mirror image of real financial markets:
Another argument against the EMH is a paradox, proposed by Grossman
(1976), where he argues that if there exists a general awareness that the
capital market is efficient, its participants would begin to act passively, and
thus, stop to collect information what would result automatically in an
inefficient market.
In addition, Grossman and Stiglitz (1980) added that expected investment
returns need to be higher than information cost because otherwise the interest
in investing would disappear. Subsequently, Shiller (1981) questioned the EMH
with the concept of excess volatility. The author concludes that the volatility
of stocks is too high to be explained by models of market efficiency.
A critique of the research area of behavioral finance is that the EMH
assumes market domination by perfectly rational investors. However
in reality, the formation of expectations and the behavior of market
participants can be characterized by limited rationality (Simon, 1955) or even
irrationality. In real financial markets, irrational market participants could
gain significant importance in the short, medium and long-term asset pricing
process (Demmler, 2017).
An additional point of criticism on the EMH is the existence of
so-called capital market anomalies. According to Lo (2007) an anomaly can be
defined as "a regular pattern in an asset´s returns which is reliable,
widely known, and inexplicable." Calendar anomalies are an example of
these capital market anomalies and will be presented in the subsequent section.
Return Seasonality in Stock Markets
Calendar Anomalies
The presence of calendar anomalies,
also known as stock market seasonality, has been the subject of multiple
research studies. According to Fama (1991)
seasonality studies can be classified as tests of the EMH in its weak form
sense. Calendar anomalies reflect abnormal return patterns within the stock
market in certain periods as for example days, weeks, months or even years. Nageswari and Selvam (2011) define calendar anomalies as
regular and repetitive patterns in time series of stock returns which lead to
systematically higher or lower returns in certain periods compared to other
periods.
The Monday effect, for example,
exists when on this day the average return is consistently lower, and the
volatility is systematically higher than on the other days of the week. Also,
the change of month effect indicates that stock prices tend to increase over
the last four days of the present month and the first three days of the
subsequent one (Kristjanpoller and Muñoz, 2012; Quantpedia, 2015).
In general, existing calendar
anomalies have been attributed to various factors as for example government and
investor decisions, business conditions, economic indicators and international
events. Nevertheless, regardless of their origin or cause, the existence of
calendar anomalies calls into question the EMH as they permit to forecast
future market prices based on past returns – a reality that should not exist
according to the EMH. In particular, one of the most analyzed stock market
calendar anomalies is the so-called January effect which will be presented in
detail in the following section.
The January Effect
The January effect refers to the
observation of abnormally high returns in the first month of the year compared
to all the other months. Ritter (1988) defines the January effect as the return
phenomenon where stock companies have abnormally high returns during the period
that starts on the last day of December and continues during the following
month of January. Multiple scientific studies in financial literature have reach
mixed results with respect to its existence or non-existence.
In general, the results of these
studies vary depending on the specific asset, portfolio, country or market,
applied model and analyzed period. For examples, different results are often
obtained by evaluating the same index or asset in one original study and in a
subsequent one years later.
Asteriou and Kavetsos
(2006) search empirical evidence of calendar effects in the stock markets of
the Czech Republic, Slovakia, Slovenia, Hungary, Lithuania, Poland, Romania and
Russia during the period 1991-2003, using regression models proposed by
Gultekin and Gultekin (1983) and Jaffe and Westerfield
(1989). Their results show statistically significant evidence of the January
effect in Hungary, Poland, Romania and Slovakia.
At the global level, Giovanis (2009) uses GARCH models to analyze 55 stock
markets around the world and does not find strong statistical evidence of the
existence of the January effect. In fact, the author just finds a very weak January
effect appearing in only 7 stock markets. In contrast, Giovanis
(2009) also finds that the month of December shows a stronger calendar effect,
as 12 stock markets of the sample present relatively higher returns in
this month compared to the rest of the year. Based on the results of his study
the author finally rejects the EMH as every stock market of the sample
presents, in some way or another, systematic monthly return patterns.
Marrett and Worthington (2011) search for
potential differences in the average monthly returns of various industrial
sectors of the Australian stock market. At the market level, they find that
average returns are significantly higher (almost three times) in April, July
and December. Furthermore, they also provide special evidence for small
businesses which show significantly higher returns in January, August and
December in comparison to other months. In addition, Marrett
and Worthington (2011) identify a January effect for the financial and energy
sectors as well as telecommunications and transport. On the other hand, they do
not find any evidence for a January effect in the industries of health and
insurance, materials and communication.
The study concludes that the high
level of seasonality implies a non-efficiency of the Australian stock market in
the weak form sense – a result that can be explained according to Marrett and Worthington (2011) by tax payments and
liquidity restrictions for especially small enterprises.
One can also find some studies
concerning calendar anomalies and the January effect in particular for the
Mexican stock market. For example, Cabello and Ortiz (2003) analyze the returns
of the Mexican stock market in Mexican Pesos and U.S. Dollars and detect a
January effect for the period 1986-2001. Later Rodríguez and Morales (2009)
search for the day of the week effect and the January effect using ARCH models.
In a total of 23 companies listed on the Mexican stock market the study
identified the day of the week effect in 7 and the January effect in 10 companies.
As well for the Mexican stock
market, López and Rodríguez (2010) at first propose two econometric approaches
with "dummy" variables. Secondly, they evaluate the presence of ARCH
effects in the results obtained and, finally, adjust their tests by using a
GARCH model in order to take into account the volatility of the returns. López
and Rodríguez (2010), using market prices expressed in Mexican Pesos, find
evidence of the January effect and other calendar anomalies for the period
1987-2009. However, the same test does not find such evidence using a dataset
on a US Dollar basis. Moreover, Rojo (2013) cannot
confirm in her study, using ARCH models, the presence of abnormal returns in
January with respect to the other months of the year.
Considering the presented studies,
one cannot find a clear result with respect to the existence or non-existence
of the January effect in Mexico. Hence, the present study is dedicated to the
analysis of this phenomenon for the current Mexican stock market.
METHODOLOGY
Research Problem
The presence of calendar anomalies,
in particular of the January effect, has been analyzed for different stock
markets all around the world. The results of these studies are often
contradictory and differ depending on factors such as country, specific market
and analyzed period.
It needs to be mentioned that the
majority of the studies realized for Mexico focus their analysis on the IPC (Índice de Precios y Cotizaciones) which represents the leading stock index of
the Mexican market. However, since March 2009 the Mexican Stock Exchange offers
a new classification of the Mexican market using additionally to the IPC a
total of 7 sector indexes. This new classification is based on
international standards also used by other stock exchanges and presents a
starting point for a better segmentation in order to facilitate market studies
and comparative analyses (Bolsa Mexicana de Valores,
2019).
In particular, the present study
focuses on the possible identification of the January effect on the Mexican
stock market including the IPC and the sector indexes, since its existence –
like the existence of any other calendar anomaly – would reject the EMH in its
weak form sense. For this reason, the present article formulates the following
research objective: Search for empirical evidence of the January effect within
the time series of the IPC and the sector indexes of the Mexican stock market
using econometric GARCH analysis.
Dataset and Statistical Method
The dataset is formed by the daily
closing prices corresponding to the IPC as well as the sector indexes. The
prices were obtained from the database Investing (2019). As was already
mentioned, the Mexican Stock Exchange started its sector classification in
March 2009. However, in order to cover a unified period of 12 months a year the
data of the present study includes the time series of 01/01/2010 to 12/31/2018.
Hence, the logarithmic daily returns of the IPC and the 7 sector indexes
covering the period mentioned above are used for the analysis.
The present study replicates the
methodology proposed by López and Rodríguez (2010). The model for testing the
existence of seasonal effects is as follows:
Where:
1 if the return in t corresponds to
month i
0 otherwise
However, this model is adapted to
test the presence of the January effect, in such a way that this month becomes
the month of reference, leaving the model as follows:
where c represents the average
return in the month of January and the coefficients α represent the difference
between the returns of the month of January and month i.
The null hypothesis seeks to prove
that the coefficients αi are equal to 0. Thus, negative
values of the coefficients of the "dummy" variables would be the
statistical evidence of the existence of the January effect.
However, as de Arce (1998) points
out, in classical time-series theory statistical approaches are based on a
stationary stochastic process. This implies the assumption of a constant
variance of the time series – a fact that normally does not apply for financial
time series. In addition, according to Rojo (2013),
in financial time series it is common to find the following problems: lack of a
regular dynamic structure in the mean, leptokurtic distributions, volatility
clustering and volatility persistence, among others.
Therefore, the present study tests
for ARCH effects in the residuals of Equation 2. Afterwards, if necessary,
the model is estimated again by a GARCH (1,1) model in order to consider a
time-dependent variance and evaluate the existence of the January effect under
this new specification.
Autoregressive conditional
heteroscedasticity (ARCH) models, introduced by Engle (1982), aim to determine
a pattern of statistical behavior for the variance and their importance lies in
considering past information of the variable and its volatility as an
explanatory factor of the present behavior of the variable, suggesting like this
a predictable future.
PRESENTATION AND ANALYSIS OF RESULTS
Descriptive Statistics
Table 1 shows the descriptive
statistics obtained from the daily logarithmic returns of each index. Results
are expressed in percentage.
Table 1
Descriptive statistics
Source: own elaboration.
Note: The meanings of the
variables are as follows: Price and Quotation Index (IPC), Materials Sector
Index (SE2), Industrial Sector Index (SE3), Consumer Discretionary Sector Index
(SE4), Consumer Staples Sector Index (SE5), Health
Care Sector Index (SE6), Financial Sector Index (SE7), Telecommunication
Services Sector Index (SE9).
One can find similarities between
the 8 indexes with respect to the results for the mean, median and
standard deviation (SD). It appears natural that the sector indexes show similar
results in comparison to the IPC as this main index of the Mexican stock market
reflects the overall behavior of the entire market. The average returns of the
indexes for the analyzed period are only just above 0. For instance, the IPC
shows a mean return of 0.0115 %. This return level appears to be marginal.
However, one has to consider that the database is formed by daily index prices
and, thus, returns are expressed on a daily basis as well.
As shown in Table 1 and
Figure 2 the highest mean return corresponds to the Consumer Discretionary
Sector Index (SE4) and the lowest to Telecommunication Services Sector Index
(SE9). The Financial Sector Index (SE7) represents the highest risk expressed
by the standard deviation and the Consumer Staples Sector Index (SE5) the
lowest one.
Moreover, it can be observed that
the analyzed indexes show leptokurtic distributions what implies a higher
concentration of the return data around their mean. The values for kurtosis of
the analyzed indexes are all above 3 what is according to DeCarlo (1997) the
reference value for a normal distribution.
In fact, the assumption of a normal
distribution is rejected because the Jarque-Bera
statistics reach very high values. Furthermore, the skewness coefficients are
slightly below 0, suggesting that the data is skewed to the left, which means
that the probability of having negative returns is slightly higher.
Figure 2
Media and standard deviation of
analyzed indexes
Source: own elaboration.
ARCH Effects and GARCH (1,1) Model
After running the regression of
Equation 2, the Lagrange Multiplier (LM) test proposed by Engle (1982) is
performed in order to detect heteroscedasticity. The results of this test are
shown in Table 2.
Table 2
ARCH LM test
Source:
own elaboration.
Note: All values are significant at the 1 %
level.
The null hypothesis states that no
ARCH effects exist. Analyzing the probabilities obtained for each index, the
null hypothesis is rejected. Thus, further results of the outlined
Equation 2 will not be shown. Instead, Equation 2 will be adjusted to
a GARCH (1,1) model in order to take into account heteroscedasticity.
The GARCH models are composed of two
equations that are solved simultaneously – one for the conditional mean and the
other for the conditional variance. Table 3 presents the results of
Equation 2 adjusted to a GARCH (1,1) model. Results were obtained using Eviews 10.
Table 3
GARCH (1,1) model results for
Equation 2
Source: own elaboration.
Note: The values in
brackets are p-values.
*** Significant at the
1 % level.
** Significant at the
5 % level.
* Significant at the
10 % level.
Table 3 shows that neither the
IPC nor the sector indexes show any statistically significant abnormal returns
in the month of January with respect to the rest of the year.
The months with most seasonal
effects are March, October and December. In March there are calendar effects
for the IPC, SE5 (Consumer Staples Sector), SE6 (Health Care Sector) and SE7
(Financial Sector), in October for SE5 (Consumer Staples Sector), SE7
(Financial Sector) and SE9 (Telecommunication Services Sector), and December for
SE2 (Materials Sector), SE5 (Consumer Staples Sector) and SE7 (Financial
Sector). On the other hand, months like January, April, May, August and
September do not present significant abnormal returns.
The most relevant calendar effects –
with a level of significance of 1 % – can be found for SE5 (Consumer
Staples Sector) in March and December and for SE6 (Health Care Sector) in
February. Unlike the rest of the indexes, the Industrial Sector (SE3) and the
Consumer Discretionary Sector (SE4) do not present seasonal effect.
In addition, the Consumer Staples
Sector (SE5) appears to be most relevant, not only because it shows the most
calendar effects (6), but also because half of the coefficients are significant
at the 5 % level and even at the 1 % level for the months of March
and December. The second most important sector index is the Financial Sector
(SE7) with a total of 4 calendar effects, including three significant ones at
the 5 % level (July, October and December).
With reference to the question if
the identified calendar effects are either positive (positive abnormal return)
or negative (negative abnormal return) one can see in Table 3 that the
vast majority of the total of 16 effects with statistical significance on
the 10 %, 5 % and 1 % level are positive. Hence,
15 identified calendar anomalies imply an abnormal positive return for a
specific index in a specific month in comparison to other months. Just one
calendar anomaly shows negative abnormal returns – Health Care Sector (SE6) in
February. In addition, the sum of the coefficients (α + β) is close
to one in all cases what implies that volatile shocks are persistent.
The present article had the research
objective to search for empirical evidence of the January effect within the
time series of the IPC and the sector indexes of the Mexican stock market using
econometric GARCH analysis.
The IPC as the main index does not
present a January effect. However, abnormal returns can be detected for the
month of March. These results coincide with the study of Rojo
(2013) who also does not find a January effect for the time series (1992-2013)
of the Mexican IPC, but abnormal returns in March.
Within the analysis of the different
sector indexes none of them show statistical evidence of a January effect.
However, evidence of other calendar effects can be found for several sector
indexes. Especially the months of March, October and December seem to be
important as a total of 9 statistically significant calendar effects
distributed between the following sector indexes can be identified: Materials
Sector Index (SE2), Consumer Staples Sector Index (SE5), Health Care Sector
Index (SE6) and Financial Sector Index (SE7) and SE9 (Telecommunication
Services Sector).
In general, the hypothesis that the
January effect is present in the IPC and the sector indexes of the Mexican
stock market is rejected since no statistical evidence for a January effect is
found.
This, however, is by far not enough
to reject the EMH in its weak form sense for the Mexican stock market in
general which in fact, on the one side, appears to be an efficient market with
respect to the general non-existence of the January effect. Nevertheless, the
identification of other calendar anomalies for the IPC and several sector
indexes questions again this assumed weak form efficiency of the Mexican stock
market.
From the perspective of an investor
the results of the present study could be used in order to better time short
and medium-term investments in certain indexes and like this realize abnormal
financial profits. For example, one can recommend investments in general
throughout the whole year in the Consumer Staples Sector Index (SE5) as this
index shows a total of 6 statistical significant calendar effects
(February, March, June, October, November, December) and all of them imply
positive abnormal returns. Furthermore, the Consumer Staples Sector Index (SE5)
is the less risky one according to the calculated standard deviation.
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