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Dissecting the Bourse:
A Cross Sectional Study on the Efficiency and Performance
Drivers of Philippine Stocks
Submitted by:
Bodollo, Ralph Christian G.
Lim, Chelsea Vanessa C.
Tupas, Fred Nyll S.
Submitted to:
Dr. Elvira P. De Lara-Tuprio
Mr. Anthony R. Zosa
Dr. Emmanuel A. Cabral
In partial fulfillment of the requirements for
AMF291: Mathematical Finance Project
Ateneo de Manila University
Quezon City, Philippines
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Dissecting the Bourse:
A Cross Sectional Study on the Efficiency and Performance
Drivers of Philippine Stocks
Is there a way to operationalize the valuation process for the
Philippine Stock Market? In this
work, we provide a firm-by-firm answer through an application of
the Efficient Market Hypothesis
and an adapted version of the Arbitrage Pricing Theory. The
Event Study methodology is
employed to give a concrete account on how stock prices evolve.
By combining the tools of
quantitative finance and practices in portfolio management, we
construct an updated picture of the
state of Philippine Stock Market that is useful for investors
and supervisors alike.
Executive Summary
Stock valuation is the vision instrument for any equity
investment journey. A valuation
methodology is truly useful if its key assumptions operate in
the market persistently. Thus, there
is a need to investigate if stocks indeed react to the factors
assumed in pricing models. One of our
main tasks is to empirically assess this by digging into the
cross section of the Philippine market.
By cross sections, we mean the various ways we can group the
stocks aside from treating them as
a whole market. We use stock returns and firms data from January
2004 to October 2014.
The discussion comprises four main sections. Opening part sets
the context by providing
exposition about the Philippine Stock Market and the present
observations regarding its equities.
This is complemented by a brief introduction on the theory of
stock returns and market efficiency.
The second part is a comprehensive account on the equilibrium
model for individual firm stock
returns. We argue that the traditional CAPM and Rational Asset
Pricing based on fundamentals
cannot be uniformly applied and thus we propose an alternative
which is closer to the practice of
portfolio management. Third part is where we carry out the Event
Study to test the information
absorption characteristic of stock returns with regards to
earnings, GDP and inflation rate
announcement. In this part, the equilibrium model derived in the
previous will be used as a
benchmark for measuring abnormal returns. Lastly, the fourth
section presents the results with
respect to various stock categories and the implications to the
process of stock selection.
Keywords
Philippine Stock Market; Cross Section of Stock Returns; Equity
Valuation; Earnings
Impact; Market Efficiency; Multifactor Analysis; Event Study;
Portfolio Management
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Table of Contents
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Introduction
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Review of Related Literature
Efficiency of the Philippine Stock Market
Several Filipino scholars have published studies on the
informational efficiency of the Philippine
stock market by applying various statistical methods on stock
market data that span across different
periods throughout the history of the bourse. One of the
earliest studies was published by Evangelista
(1978). The study focused on investigating the informational
content of stock dividends. A total of 23
securities listed in the Manila Stock Exchange (MSE) which
issued stock dividends of no less than 20%
from 1975 to mid-1976 were included in the study. To determine
the factor that is affecting the return of
each security, Evangelista (1978) used the following market
model:
= + + ,
where
is the price relative of the th security for month .
is the price relative of the market for month .
is a random error incorporating the effect of factors affecting
the th security.
where and of the above market model are further defined as
=( + )
1,
where
is the price of the th stock at the end of month .
are the cash dividends on the th security during month , where
the dividend
is taken as of the ex-dividend date rather than the payment
date.
After solving for the parameters of the model, the average and
cumulative average residuals over the
months surrounding the stock split were derived using the
following equations, respectively:
=
=1
,
where
is the sample regression for the security in month .
is the number of splits for which data are available in month
.
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and
=
=12
.
Evangelista (1978) explains that the average residual represents
the average deviation of the return of
the securities which had a stock split from the normal market
return. On the other hand, the cumulative
average residual is the cumulative deviation of the return of
the securities from the normal market
return. Basically, represents the cumulative effect of the stock
split in the deviation of the stocks
return from that of the market. Results show that securities
which had a stock split recorded higher
returns in the succeeding months compared to those securities
that didnt. However, Evangelista (1978)
was rather careful in wholly attributing the higher returns to
the declaration of stock splits alone. She
cited the possibility that other factors or events may have
contributed to the higher returns and pointed
out the need for further research to confirm the results of her
study.
On a more recent study covering the Philippine Stock Exchange,
Dumlao (2001) investigated the
degree of efficiency of the Philippine stock market from August
1998 to July 1999 through the use of two
primary statistical methods namely, the serial correlation test
and the variance ratio test. In performing
the test for serial correlation, the ordinary least squares
method (OLS) was applied amongst returns of
lag 1. The stochastic equation is expressed as
+1 = + +1,
where
represents the relationship between and +1 or the serial
correlation.
+1 represents the stochastic error term.
Three possible conclusions can be made depending on the result
of the test. First, the absence of serial
correlation implies that the efficient market hypothesis holds
and that there is a possibility that the
market follows a random walk process. Second, a weak/low serial
correlation is sufficient for the efficient
market hypothesis to hold, but rejects the random walk process.
Third, a high serial correlation rejects
both the efficient market hypothesis and the random walk
process. The serial correlation is deemed
significant at the 5% level if it is greater than twice the
standard error. The results of the study show that
37% of the stocks involved in the study have significant
correlation a strong indication that the efficient
hypothesis does not hold and that the market does not follow the
random walk process.
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For the variance ratio test, the variance ratio of one-day rate
of return was compared with two-
days, four-days, and eight-days returns using the following
formula:
(
)
( 1
1)
= 1,
where
is the stock price today.
is the stock price days ago.
1 is the stock price yesterday.
In addition, the homoscedastic-consistent and
heteroscedastic-consistent test statistic for Z were
calculated to provide the basis for the conclusion. The random
walk hypothesis is accepted at the 5% level
if the test statistic has a value less than the Studentized
Maximum Modulus (SMM) critical value of 2.49.
The tests statistics show that 47% of the stocks reject the
random walk hypothesis a conclusion that
echoes the result of the serial correlation test.
Dumlao (2001) further confirms the results of the aforementioned
tests by ranking the efficiency
of the Philippine stock market against those of the ASEAN
countries specifically, Malaysia, Thailand,
Singapore, and Indonesia, and that of the United States.
Theorists posit that a more developed economy
would necessarily have a more efficient stock market. The
results of the study confirm this theory as the
United States, represented by the Dow Jones Industrial Averages,
emerged as the most efficient followed
by Malaysia, Thailand, Singapore, Philippines, and
Indonesia.
Aquino (2006) used a two-pronged approach in evaluating the
efficiency of the Philippine stock
market. The initial hypothesis that the market is weak-form
efficient was confirmed through statistical
modelling where the continuously compounded daily returns from
July 1987 to May 2004 fitted into an
AR(1) process with Laplace residuals. The Laplace is
characterized by the density function
() =1
21 [
||
], < <
where
represents the residuals
represents the location parameters of the distribution, and
represents the scale parameters of the distribution.
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The second part of the study tested the hypothesis that the
market is semi-strong form efficient. An event
study was performed in order to see how the Philippine stock
market reacted to crucial political,
economic, natural, and foreign events throughout the period of
interest. Although event studies are
usually performed on normally distributed data, such a condition
does not hold in this study. Hence, the
AR(1) process from the first part of the study was used as the
model for deriving the expected price
changes, while the residuals following a Laplace distribution
represented the abnormal price changes
(Aquino 2006). Furthermore, the absolute value of the deviation
of the residuals from the Laplace location
parameter was found to have an exponential distribution and the
sum of independent and identically
distributed random variables assumed a gamma distribution. The
formula
= | |
=1
represent the sum of the absolute deviation of the residuals
from the location parameter over N days.
The significance of was contingent on meeting the criterion ( )
0.05.
The result of the event study show that although the market was
quick to react and absorb the
information on majority of the events being examined, the same
cannot be observed on days of extreme
stress and uncertainty from financial and political shocks such
as the Black Monday and 9/11 terrorist
attacks where abnormal residuals were found to linger for
several days after the actual event day.
Moreover, there were days when abnormal residuals were detected
in the absence of any significant
news. Aquino (2006) attributes this to the personal expectations
of rational investors based on how they
viewed fundamental factors. The lack of a coherent observation
prevented the author from giving a
categorical judgement on whether the Philippine stock market is
indeed semi-strong form efficient.
Rufino (2013) published the most recent study investigating the
informational efficiency of the
Philippine stock market. The dataset used consist of the weekly
log returns of the six sectoral indices and
the all-shares index from October 2006 to May 2012 a period
which covered the implementation of the
modernization programs undertaken by the Philippine Stock
Exchange to improve the speed of
disseminating public disclosures. A financial market is said to
follow a random walk when the unit root
component of the series exists and the time series follows a
martingale difference sequence (MDS). The
augmented Dickey-Fuller (ADF) unit root test and panel unit root
test was applied to each of the indices,
and the results verified that a unit root exists in each of
them. Multiple variance ratio tests were used to
verify whether each of the indices follow a martingale
difference sequence. The results confirmed the
weak-form efficiency hypothesis across the six sectoral indices
and the Philippine stock market as a whole
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as represented by the all-shares index. This means that stock
prices do reflect every available information
instantaneously such that it is futile to predict stock price
movements using historical data or technical
analysis.
Chelsea LimSticky NoteMake a general conclusion. Tie up
everything.
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Theoretical Exploration
The Role of Capital Markets
The most important decisions that an economy makes are related
to the appropriate allocation
of capital resources. Such decisions play a critical role in
responding to the needs of society and meeting
the growth targets of an economy in the long-run. Public
sovereignty is achieved when the flow of capital
goods is responsive to the desires and relevant to the goals of
every individual consumer. This allows
capital to serve as the link that brings people to their
envisioned future. Furthermore, growth in a nations
output is fuelled by the efficacy of such decisions. For
example, the decision to allocate capital resources
on factories and machineries help facilitate the growth and
expansion of an economys manufacturing
sector. (Baumol 1965)
The realization of the aforementioned economic decisions
relating to the allocation of capital
resources is made possible by financial institutions. Banks,
insurance companies, and monetary agencies
under the government among others ultimately decide on how an
economy will realize its decisions on
by providing the monetary capital.
Capital markets are one of the financial institutions that play
an integral part in the appropriate
allocation of capital resources in an economy. According to Fama
(1970), The primary role of a capital
market is allocation of ownership of the economys capital stock.
In general terms, the ideal is a market
in which firms can make production-investment decisions, and
investors can choose among the securities
that represent ownership of firms activities under the
assumption that security prices at any time fully
reflect all available information.
The Theory of Efficient Markets
The basic definition of an efficient market is that it is a
market in which prices fully reflect every
available information. However, this definition is too general
that scholars have developed empirical
methods to test the process of price formation in the market and
use this to objectively assess its overall
efficiency. The empirical work evolved through three levels of
market efficiency.
At the first level of efficiency, studies related to methods on
testing the weak-form efficiency
hypothesis were conducted. Security prices of an efficient
market in the weak form are able to fully
incorporate information embedded on past price histories. Most
of the results that supported the weak-
form efficiency hypothesis are available in the random walk
literature.
Chelsea LimHighlight
Chelsea LimSticky Noteplace "in the long-run" here
Chelsea LimHighlight
Chelsea LimSticky Noteinsert comma
Chelsea LimHighlight
Chelsea LimSticky Notewith the aid of
Chelsea LimSticky Noteused
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Once extensive scholarly work has confirmed the efficiency of
the markets at the weak-form level,
the focus shifted to testing the semi-strong form efficiency
hypothesis. Current security prices of an
efficient market in the semi-strong form fully reflect all kinds
of publicly available information. Most of
the studies in this level used martingale models.
Lastly, studies on testing the strong form efficiency hypothesis
came out much later. In contrast
to the semi-strong form, current security prices of an efficient
market in the strong form fully reflect all
kinds of publicly and privately available information. This
means that investors/traders will not be able to
earn higher than expected profits due to an exclusive access to
certain information. Scholars have not
been successful in coming up with tests to sufficiently
investigate market efficiency at this level, and it is
widely accepted that no particular market around the world
possess this level of efficiency.
Implications of Market Efficiency
The practice of technical analysis relies on studying historical
price patterns in order to time ones
entry and exit price on a particular security. However, this
method is deemed futile as security prices an
efficient market reflects all past information. On the other
hand, the practice of fundamental analysis
relies on studying company news and fundamentals with the goal
of computing for a securitys underlying
value and determine appropriate entry and target prices.
Likewise, this method is deemed ineffective as
security prices in an efficient market immediately reflects all
available information. Thus, for the investor
or trader, an efficient market implies that no strategy will
allow him to beat the market. At best, one
could only achieve a return that is equivalent to the market
return. Under this scenario, the most viable
investment strategy that one could make is to invest in a
low-cost financial market product such as an
index fund whose returns mirror that of the market. Furthermore,
for the portfolio manager, the efficient
market hypothesis implies that it is impossible for him to
generate above-average returns regardless of
how he manages a portfolio or fund. Thus, instead, his focus
must be on mitigating risks and preserving
capital.
The Fundamental Valuation Equation
Preference-dependent valuation theories are specializations of
the following fundamental
valuation equation
= [
()
()
. |
=+1
],
Chelsea LimHighlight
Chelsea LimSticky Notebaligtad
Chelsea LimSticky Notein
Chelsea LimSticky Notedetermining
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Basically, the equation says that the price of a claim is
equivalent to the expected future payoff and the
marginal rate of substitution of the investor.
Other Statistical Models:
The Constant-Mean-Return Model
Let , the th element of , be the mean return for asset . The
constant-mean-return model is
= + ,
[] = 0 and [] = 2 ,
where is the period- return on security ,
is the disturbance term, and
2 is the (, ) element of .
The Market Model
One of the most typically used statistical model is the market
model. Essentially, the model relates the
return of a security to the return of the market portfolio
(Campbell, Lo, and MacKinlay 1997). The model
follows the form of a typical linear regression as it assumes
the normality of the security returns. For any
security , the market model is given by
= + + ,
[] = 0 and [] = 2 ,
where is the period- return on security ,
is the period- return on the market portfolio,
is the zero mean disturbance term, and
, , and 2 are the parameters of the market model.
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EMPIRICAL METHODS
The AR Model
An autoregressive model of order or () follows the form
= 11 + 22 + + + ,
where is stationary,
1, 2, , ( 0) are constants, and
~(0, 2 ).
Notice that the AR model assumes the form of a typical simple
linear regression model where is the
dependent variable and 1, 2, , are the explanatory
variables.
The ARCH Model
In his seminal work published in July 1982, Engle introduced the
autoregressive conditional
heteroscedasticity (ARCH) model as his method for estimating the
variance of inflation in the United
Kingdom. His pioneering scholarly work has inspired other
scholars to use the ARCH model as the primary
method for modelling the volatility of a given time series.
Generally, an ARCH model assumes the form
of a simple linear regression model where the value of a time
series at time is dependent on past
information. The simplest ARCH model is an autoregressive (AR)
model of order one, or simply AR(1)
model and it follows the formula:
= 0 + 11 + ,
where is the log return of the series at time ,
~(0, 2).
The Markov-Switching Model
Hamilton (1989) introduced the state-dependent Markov-switching
(MS) model. In his paper published
on March 1989, Hamilton provided an empirical way of analysing
post-war U.S. real GNP. His analysis led
him to observe that periodic shifts in economic growth (i.e.
positive growth to negative growth and vice
versa) is a recurrent feature of the United States business
cycle (Hamilton, 1989). Since then,
mathematicians and econometricians have used the
Markov-switching model to capture regime shifts,
within a nonlinear time series, triggered by exogenous
variables. The model is expressed as
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= + , = 1,2, . , ,
~(0, 2 ),
= 0(1 ) + 1,
2 = 0
2(1 ) + 12,
= 0 1,
where represents the regime,
under regime 1, the parameters are given by 1 and 12,
under regime 0, the parameters are given by 2 and 22.
The Markov-Switching Autoregressive (MS-AR) Model
Hamilton and Susmel (1994) pointed out the short-comings and
inadequacies of ARCH models as a
method for modelling the volatility of stock returns. Given a
portfolio of stocks traded on the New York
Stock Exchange, they computed for the forecasting performance
and persistent statistics of different
ARCH models that characterized stock returns. Each of the
different ARCH models tested yielded poor
performance statistics; and the authors attributed this to the
presence of a structural change in the ARCH
process. They pointed out that the nonlinearity of the
volatility of stock returns makes the Markov-
switching autoregressive (MS-AR) model a better fit for the
purpose of modelling the volatility of the
stock returns series.
Moreover, Cai (1994) arrived at a similar conclusion as he
highlighted how combining the ARCH model of
Engle (1982) and the MS model of Hamilton (1989) perfectly
describes the properties and characteristics
of a time series. Whereas he Markov-switching model captures the
effects of sudden political and
economic events on a time series, the ARCH model captures all
the movements in the variance (Cai, 1994).
Hence, the MS-AR model has the unique ability to model
volatility clustering and at the same time,
capture discrete shifts among regimes in a given time series. A
Markov-switching autoregressive model
of two regimes with an AR() process is given by
= () + [ ( ())
=1
] + ,
~. . (0 , 2()),
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= , = , , 1,2
where and are unobserved regime variables that take the values
of 1 or 2 and the
transition between regimes is governed by a first-order Markov
process as follows:
( = 1 | 1 = 1) = 11
( = 1 | 1 = 2) = 12 = 1 11
( = 2 | 1 = 1) = 21 = 1 22
( = 2 | 1 = 2) = 22
with 11 + 12 = 21 + 22 = 1.
The MA Model
A moving average model of order or () follows the form
= + 11 + 22 + + + ,
where represents the number of lags in the moving average,
1, 2, , ( 0) are parameters, and
~(0, 2 ).
The ARMA Model
There are cases when lower order AR or MA models alone fail to
capture the dynamics of a financial time
series. To avoid the cumbersome practice of fitting higher order
AR or MA models, which require many
parameters, the autoregressive moving-average (ARMA) presents
itself to be a more practical alternative.
An ARMA model essentially combines the features of the AR and MA
models into a compact form so that
the number of parameters will be few and parsimony in
parameterization can be achieved. By definition,
a time series {; = 0, 1, 2, } is (, ) if it is stationary and
follows the form
= 11 + + + + 11 + + ,
where 0, 0, and 2 > 0,
and are called the autoregressive and moving average orders,
respectively,
~(0, 2 ).
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Seasonal Models
Financial time series which exhibit cyclical behaviour or
periodic fluctuations are referred to as seasonal
time series. Examples of a seasonal time series are the earnings
of companies, GDP data, and
temperature. Such seasonal times series are modelled by
incorporating autoregressive and moving
average polynomials that identify the seasonal lags into the (,
) model. The modified model now
takes the form
() = (
) ,
where () = 1 1
22
, and
() = 1 + 1
+ 22 + +
are the seasonal autoregressive operator and the seasonal moving
average operator of orders and ,
respectively, with seasonal period .
Multiple Linear Regression Model
A multiple linear regression model is a regression model that
involves more than one explanatory
variables and a dependent variable. Multiple regression fits a
model to predict a dependent variable (Y)
from two or more independent variables (X). It follows the
form
= + 11 + 22 + + + ,
where are constants and are the residuals which are independent
of each other and are normally
distributed with mean 0 and variance 2.
First, we assume that the relationship between the exogenous
variables and the endogenous variable
should be linear. We assume that there should be little to no
correlation among the independent
variables. This means that the explanatory variables must be
dependent from each other. Lastly, we
assume that there are not serial correlations (autocorrelations)
between the errors or the residuals.
However with the number of explanatory variables for this
multiple regression model, there is a
possibility that some of these variables are highly correlated
to one another. This occurrence is referred
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to as multicollinearity and Paul (2005) pointed out how high
multicollinearity may lead to misleading
results since the goal is to understand how the explanatory
variables impact the dependent variable.
To address the problem of high multicollinearity, we look into
the variance inflation factors of the
explanatory variables. It is measured as =1
, where TOL refers to tolerance which measures the
influence of one independent variable to another independent
variable. When the VIF > 5, there is an
indication for multicollinearity and so some independent
variables should be excluded from the model.
Event Study Methodology
The event study methodology uses econometrics to investigate how
certain events impact a financial
time series. A case where the event study methodology would be
particularly useful is in investigating the
effect of quarterly earnings announcements of publicly listed
companies on stock prices. A typical event
study proceeds in the following manner:
1. Event Definition
The preliminary task in conducting an event study is to define
the event that will be
considered in the study, and then identify the period or event
window over which the time series
of interest will be examined (Campbell, Lo, and MacKinlay 1997).
An event window covers a
certain number of days/weeks before and after the event
occurs.
2. Derive the Normal and Abnormal Returns
The event study methodology measures an events impact on the
financial time series
based on the abnormal return of say, a particular stock. The
abnormal return is the return of the
stock after the event subtracted by the normal return of the
stock over the event window. The
normal return refers to the expected stock return in the absence
of the event. This is derived
from the model of the financial time series. For a particular
firm and event date , the abnormal
return is given by the formula
= [|],
where is the actual return of stock for time period , and
() is the normal return of stock for time period .
3. Aggregation of Abnormal Returns
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To be able to draw meaningful conclusions about the event of
interest, the abnormal
returns of different stocks derived from the previous step must
be aggregated. Aggregation is
done in two ways through time and across securities (Campbell,
Lo, and MacKinlay 1997).
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Data Description
A pool of dataset was gathered from various sources. First, a
list of the stocks of publicly-listed
companies which traded on the Philippine Stock Exchange (PSE)
from January 2004 to October 2014,
accompanied by a historical data on the daily closing prices of
each stock, was provided by the PSE
management. Second, data on firm-specific financial ratios,
earnings, and earnings announcements were
found and downloaded individually from the Technistock software
in the PSE library. Third, historical data
on the daily closing value of the All-Shares Index from January
2004 to October 2014 was given by the
PSE management. Fourth, the Bangko Sentral ng Pilipinas (BSP)
website was accessed to find the
historical PDST-R2 rates. Lastly, the monthly PSE report which
contains data on Philippine Treasury rates
and information on the monthly volume traded of each stock was
requested from the PSE management.
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Methodology
A total of 207 publicly-listed companies were obtained, however
after scrutinizing each of their
stock prices, only 183 of them are considered for the model
development to avoid outliers from
influencing the results. In the historical data provided by the
PSE management, no entry for the closing
price would mean that the stock has not been traded for the day.
We set a selection criteria that a stock
must be traded at least once a month and if the company changed
into a new name, the collated stock
prices must still be generally complete during January 2004 to
October 2014. For each stock, the simple
monthly return is computed by subtracting from the closing price
on the last trading day of the month
the closing price on the first trading day of the month and
dividing the said difference with the closing
price on the first trading day of the month. For the simple
weekly return, the same process is used but
for the weekly timeframe. To illustrate, let be the stock price
at time T and so the simple monthly
return for the stock TEL for January 2004 is given by:
2004 = 30 2004 9 2004
9 2004
There are 130 observations for the monthly returns while 523
observations for the weekly returns.
Factor Returns
Factor Selection
One of the objectives of this study is to design financial
factor models that would determine the
sensitivity of stock returns as a function of various factors
which investors consider in the investment
decision-making process. A factor used in a financial factor
model serves as a signal that shows a certain
level of correlation with the asset return. Stone, He, and White
(2014) found out on their factor analysis
regarding which factors drive performance that Valuation (ratios
commonly used to measure companys
financial health), Growth (earnings growth), Price Momentum
(Mean reversion and Price Returns),
Risk/Size (Market sensitivity and Market Capitalization), and
Payout (Dividend Payout measurements)
factors are helpful in explaining asset returns. In this study,
15 factors are used and are subdivided into
three: Fundamentals (Earnings per share (EPS), Price-To-Book
Value (PTB), Dividend Payout Ratio (DPR),
Free cash flow per share (FCFPS), Market Capitalization (MC),
Price/Earnings to Growth (PEG)), Market
(Index Beta (IB), Premium Beta(PB)), Technicals (Trend Signal
(TS), 9-Month RSI (9MRSI), 12-Month RSI
(12MRSI), 1-Month Mean Reversion (1MMR), 1-Month Price Momentum
(1MRET), 3-Month Price
Momentum (3MRET), 12-Month Price Momentum (12MRET). These
factors all belong to the pool of
Chelsea LimHighlight
Chelsea LimSticky NoteNo need, just present a general
formula
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factors that Stone, He, and White (2014) were able to determine
in their study and to accommodate the
abnormal effects of the 2008 financial crisis, a binary variable
Global Financial Crisis factor (F) is
introduced. The resulting financial factor models would provide
insights to which investment strategies
are possible in yielding desired asset returns in the Philippine
setting.
Definition
Earnings per Share
It serves as an indicator of a companys profitability as it is
the portion of the allocation of the net
income to each outstanding share of common stock as defined by
Investopedia.
=
Higher EPS means higher profitability while lower EPS implies
low profitability for a company.
Price-to-Book or P/B
It is the ratio between the stocks market value to its book
value. This is determined by taking the
book value per share and dividing it from the current closing
stock price.
=
Free Cash Flow per Share
It is measured by dividing the companys free cash flow by the
number of outstanding shares. It
suggests the ability of a company to pay debt, dividends, buy
back stocks and facilitate the growth of
business as explained by Investopedia.
=
Price/Earnings to Growth (PEG)
It is the ratio of a companys price-to-earnings ratio and the
growth rate of its earnings for a time
period. Although price-to-earnings ratio is commonly used by
analysts in determining the stocks value,
PEG ratio is believed to provide a wider picture since it takes
into account the growth of the earnings of
a company. The lower the PEG ratio, the more the stock tends to
be undervalued because of the earnings
performance as suggested by Investopedia.
Chelsea LimHighlight
Chelsea LimHighlight
Chelsea LimHighlight
Chelsea LimSticky NoteConsider moving this to another
section
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=/
Dividend Payout Ratio
It is the portion of the profit paid to the shareholders. It is
calculated as
=
The higher the DPR, the more lucrative it is for the investors.
Thus, it is more favorable to have a
high DPR value.
Market Capitalization
It refers to the size of a company as it is measured by taking
the product of the current market
price of a stock and the total number of shares outstanding.
Companies are classified into Large Cap,
Middle Cap, and Small Cap.
Index and Equity Premium
The monthly return of PSEi or the Philippine market index is
used in this study for the index factor
while for the equity premium factor, the difference between the
monthly return of the All-Shares index,
provided by the PSE management, and the monthly return for
PDST-R2 (for risk-free rate) was in
accordance to the Capital Asset Pricing Model. For each stock,
their sensitivities to the market index and
the equity premium were computed using simple regression model
given by:
= +
= + ( )
RSI
From Investopedia, Relative strength index (RSI) is a technical
momentum indicator that
determines the overbought and oversold conditions of a stock
through the magnitude of gains and losses.
It is calculated by the formula
= 100 100
1 +
Mean Reversion
Chelsea LimHighlight
-
In finance, stock prices and returns are believed to revert back
to the average or mean. When
mean reversion is incorporated in the analysis of stock price
movements, the investors look at the
tendency of the stock to move from its current market price to
the average of the historical prices. When
the current market price deviates below the average price, the
stock will tend to be pulled-back due to
the mean reversion and the same is considered to be true when
the current market price is above the
average price. In this study, the 1-Month Mean Reversion
computation is given by
1 =1 12
12
Trend Signal
Huan and Zhou (2013) pointed out in their study that when stock
price information is very
uncertain or the stocks noise-to-signal ratio is high,
fundamental signals such as earnings and economic
outlook can prove to be ineffective in stock price analysis
therefore investors tend to rely more heavily
on technical signals, hence trend signals can be used for
uncertain stocks to determine which ones are
more profitable. For this study, moving averages are used for
the trend signal factor. The L-month moving
averages is computed by the formula
, = + +1 +
,
where L is the lag and is the stock price L months ago and , is
the average for time t. The moving
averages are then normalized by the closing price at time t.
Price Momentum
It is the rate at which the price changes. In technical
analysis, the idea of momentum is the
tendency of the prices to keep moving in the same direction that
to change directions as described in
Investopedia. Using the methodology practiced in the study of
Stone, He, and White (2014), the 1-Month,
3-Month, and 12-Month Price Momentum are computed using the
formula
=1
,
where n = 1, 3, and 12 while 1= the stock price one month prior
the rebalancing date of the portfolio
and similarly = the stock price n-months prior to the
rebalancing date. This means that they are
based on a stocks return over the interval from n months before
to one month before the portfolio
formation.
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Constructing the Factor Mimicking Portfolios
The simple monthly returns calculated are used in calculating
sensitivity with the market and in
determining the various technical momentum indicators to be used
for this study such as Trend Signal,
Relative Strength Index, Mean Reversion, and Price Momentum. The
data on earnings, financial ratios,
and necessary corporate disclosures are sorted for each stock
and prepared for a ranking process. The
stocks are ranked from least favorable to most favorable based
on the factors that were mentioned in
the theoretical framework (Fundamentals, Market,
Technicals).
For the Fundamental factors, the stocks are ranked yearly from
2004 to 2013. We assume that
the information on the financial ratios and corporate
disclosures for the year is released during April each
year. There are cases that the values for some companies are
either missing or not plausible for some
periods and so to address this problem, we set the values to the
median of the values of all the companies
for that year for the computation of the factor spreads to be
discussed below. The following table shows
how the stocks are ranked for each factor:
Fundamental Factor Low Value High Value
Earnings per Share Less favorable More favorable
Price-to-Book Value More favorable Less favorable
Free Cash Flow per Share Less favorable More favorable
Price/Earnings to Growth More favorable Less favorable
Dividend Payout Ratio Less favorable More favorable
Market Capitalization Less Favorable More favorable
For the resulting rankings in each fundamental factor, refer to
the Appendix. These rankings will be used
as basis for the rebalancing of portfolio for the next period.
This is due to the fact that as an investor, the
portfolio is built based on the available information in the
period and the rebalancing occurs right after
the next periods information is publicly disclosed.
For the Market factors, a simple moving linear regression was
first used to determine the for
each stock in each year from 2004 to 2013. In the index beta
factor, the values used for the explanatory
variable are the monthly returns of the PSEi or the Philippine
market index. In the premium beta factor,
the monthly market premium is computed by using the All-shares
index and the monthly risk-free rate of
return is determined using the PDST-R2 rates. Then the
independent variable is formulated by taking the
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-
difference of the two and used it in accordance to the Capital
Asset Pricing Model (CAPM). The yearly
period stretches from April of the current year until March of
the succeeding year. This is to synchronize
the availability of information with the release of corporate
disclosures used for the Fundamental factors.
After obtaining the yearly for each of the stocks in the
respective periods, they are ranked according to
the sensitivity with the factors which is through the values of
the s. These rankings will be used as basis
for the rebalancing of portfolio for the next period and
rebalancing happens every month since it is a
moving regression. Refer to the appendix for the rankings for
the Market factors.
For the Technical factors, each has a different way of
determining the rank. For the RSI factors,
the 9-month and 12-month RSIs of each stock are computed
periodically starting from April 2005. For 9-
month RSI, the period is every 9 months and there are 13 periods
from March 2005 to October 2014 while
12-month RSI has 12 months every period with 10 periods from
March 2005 to 2014. Then for each
period, the stocks are ranked according to the RSI values with
the lowest RSI being the top in the rank
and the highest RSI being the bottom in the rank. This is
because low RSI implies that the stock may be
getting oversold and so it is likely to become undervalued so if
you enter into a long position for this stock,
you will likely to gain from the spread while the high RSI would
suggest that the stock may be getting
overbought and so it is likely to become overvalued so it is
more favorable if the RSI is low. These rankings
will be used as basis for the rebalancing of portfolio starting
April 2004 and every period thereafter. For
the Mean Reversion factor, the monthly mean reversion measure
was calculated starting from March
2004 and there are 115 periods. The stocks are ranked according
to the mean reversion measure values
with the most negative being the top in the rank and the most
positive being the bottom in the rank. This
is due to the fact that as the magnitude of the mean reversion
increases, the pull-back tendency of the
return to revert to the mean is higher therefore when the
magnitude is high and the sign is negative, the
return tends to move towards the mean in an increasing manner
and so it is favorable to enter in a long
position. On the other hand, when the magnitude is high and the
sign is positive, the return tends to
move towards the mean in a decreasing manner and so it is
unfavorable to enter in a long position. These
rankings will be used as basis for the rebalancing of portfolio
starting April 2005 and every month
thereafter. For the Price Momentum factors, the 1-month,
3-month, and 12-month Price Momentum
values are computed starting March 2005 to synchronize the
rebalancing of portfolio for the other factors
which will start on April 2005. The computation is periodic so
the rebalancing is monthly, quarterly, and
yearly for 1-Month, 3-Month, and 12-Month Price Momentum
respectively. The rankings will be used as
basis for the rebalancing of portfolio for the next period.
Lastly for the Trend Signal, the 3-Month, 6-
Month, and 12-Month moving averages are computed. We run a
cross-section regression each month
regressing monthly stock returns on the three moving averages to
obtain time-series of the coefficients
on the trend signals as performed by Huan and Zhou (2013).
Chelsea LimSticky NoteRephrase this sentence
-
= 0, + 1,1,3 + 2,1,6 + 3,1,12 + ,
where =rate of return of the stock
,= trend signals at the end of month t-1 with lag L
0, = intercept in month t
,= coefficient of moving average signal with lag in month t
Then the expected return for month t is then estimated using the
averages of the coefficients in the
moving averages
1[] = 1[1,]1,3 + 1[2,]1,6 + 1[3,]1,12
Then the expected return for each stock are ranked monthly with
low returns being the less favorable
stocks while high returns are the more favorable stocks. Refer
to the appendix for the rankings for the
Technical factors.
Factor Spread
Next step is to divide the rankings into three equal-weighted
portfolios that consists of 61 stocks
for each. Since the rankings are already sorted from least
favorable to most favorable in each factors, the
division results in having the 1st portfolio, which we will call
1st or Bottom Tercile, consisting of the least
favorable 61 stocks while the 3rd portfolio, which we will call
3rd or Top Tercile, will consist the most
favorable 61 stocks. This was the most appropriate division of
stocks for the rankings instead of quintiles
and quartiles, which are more popularly used in studies of stock
returns, due to the number of stocks in
this study. The portfolio must be diverse enough so that the
effect of the outliers in the monthly stock
returns will be lessened if not avoided. The average of the
monthly returns are then computed and this
becomes the monthly return of the portfolio. There is also the
problem of some stocks greatly influencing
the monthly return of the portfolio so in order to address it,
an upper fence and lower fence were
constructed. Among the stocks in the Terciles, they are
sub-divided into quartiles based on their monthly
returns and the interquartile range (IQR) is computed by taking
the difference of the return in the 75th
and 25th percentile as pointed out by Elizabeth (2014) in her
study on interquartile ranges and outliers.
Then the upper fence is constructed by taking the monthly return
in the 75th percentile and adding 1.5
times the IQR while the lower fence is constructed by taking the
monthly return in the 25th percentile and
subtracting 1.5 times the IQR. To illustrate the upper and lower
fence are given by
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-
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Jul-
07
Oct
-07
Jan
-08
Ap
r-0
8
Jul-
08
Oct
-08
Jan
-09
Ap
r-0
9
Jul-
09
Factor Investing Buy-and-Hold Return, Aug 2007 -Jul 2009
= 3 1.5
= 1 1.5
This means that the stocks falling outside the fences are
excluded in the computation of the monthly
returns of the Terciles. This is to avoid the outliers from
greatly influencing the spreads between the 3rd
and 1st Tercile (Top and Bottom Tercile). The factor spreads are
then calculated by subtracting the
monthly return of the Top Tercile with the monthly return of the
Bottom Tercile. Since some of the stocks
had values for financial ratios that are missing or not valid
for some of the Fundamental factors, it is
important that these stocks that were forced to the 2nd Tercile
or the Middle portfolio so that they will
not influence the calculation of the factor spreads. The factor
spreads tell us the potential return that an
investor can earn if he or she had invested in the stock
belonging to the 3rd Tercile in comparison to the
case if he or she had invested on the lesser favorable stocks
based on the factor.
ARBITRAGE PRICING THEORY
From Miachael McMillan, excess return is the difference between
a portfolios return and its benchmarks
return. In this case, the benchmark is the PDST-R2
Results and Discussion
The line charts to the left show the historical return
path, within different time periods, for the
different factor investing strategies. This
assumes a buy-and-hold strategy
-1
-0.5
0
0.5
1
1.5
2
Mar
-05
Mar
-06
Mar
-07
Mar
-08
Mar
-09
Mar
-10
Mar
-11
Mar
-12
Mar
-13
Mar
-14
Factor Investing Buy-and-Hold Return, 2005-2014 EPS
DPR
1M Ret
-
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Jul-
09
Feb
-10
Sep
-10
Ap
r-1
1
No
v-1
1
Jun
-12
Jan
-13
Au
g-1
3
Mar
-14
Oct
-14
Factor Investing Buy-and-Hold Return, Aug 2009 -Oct 2014
CAGR
2004-
2014
Aug 2007 to
Jul 2009
Aug 2009 to
Oct 2014
EPS 11.4% -0.4% 16.1%
PTB 1.5% 3.3% 2.7%
FCFPS 4.9% -3.8% 13.7%
PEG -3.8% -9.1% -1.4%
DPR 10.2% 5.1% 12.8%
MC 3.2% -2.7% 2.3%
IB 0.9% 5.8% -2.6%
PB 0.7% 5.5% -2.3%
TS 4.8% 8.7% 2.7%
9MRSI -0.3% 12.5% -1.5%
-
12MRSI -1.0% 16.6% -5.4%
1MMR -0.2% -3.5% -4.6%
RET1 -16.9% -27.6% -7.9%
RET3 2.2% -3.8% 3.7%
RET12 -1.5% -20.5% 5.8%
Market Capitalization
Dividend Payout Ration
Price-per-Earnings-per-
Growth
Free cash Flow-per-
Share
Price-to-Book
Earnings-per-Share
EPS PTB FCFPS PEG DPR MC
Equity Premium
Beta
Index Return
Beta
-
Serial Correlation among the Factors
After the factor spreads are determined, serial correlations or
autocorrelations are removed
before proceeding to the regression model building. Using the
statistical software R, each factor spread
is initially tested for serial correlation through the Box.test
command which computes for the Ljung-Box
test statistic for examining the independence for a time series.
If the p-value is less than 0.1, the null
hypothesis that there is no serial correlation present is
rejected and the alternative hypothesis that serial
correlation is present is accepted. For a given factor, if the
spread exhibits no serial correlation, then the
factor spread remains as it is. However if serial correlation is
present, an ARIMA model is fitted to the
time series to address the problem of serial correlation.
Regression Model Building
In this study, we derive a model that would explain the
relationship between the excess return
( ,) of each stock, and the factor spreads () obtained from the
construction of a portfolio
based on the rankings of the stocks for the Fundamental, Market,
and Technical factors. Using Multiple
Linear Regression, we can attempt to create a linear
relationship between the excess returns and the
factor spreads and identify which factors explain the excess
return. The regression model for stock is
given by:
= + ,, + ,, + ,, + ,,+ ,, + ,, + ,, + ,, + ,,+ 9,9, + 1,1,+,, +
1,1,+ 3,3, + 12,12, + ,+
Index Return Beta Equity Premium Beta
12M return momentum
3M return momentum
1M return momentum
1M mean reversion
12M RSI
9M RSI
Trend Signal
Indicator
TS 9M
RSI 12MRSI
1M MR
1M Ret
3M Ret
12MRet
-
where are constants and are the residuals which are independent
of each other and are
normally distributed with mean 0 and variance 2.
For each stock, the excess return is regressed against the
factors using a statistical software SAS. The
command proc reg is used and the selection method is stepwise.
From SAS support, the stepwise method
is a modification of the forward-selection technique and differs
in that variables already in the model do
not necessarily stay there. Variables are added one by one to
the model but only if the F-statistic for a
variable is significant, meaning that the p-value is less than
0.1. After the addition of the variable, the
stepwise method assesses the variables currently included in the
model and removes the variable that
does not produce an F-statistic that is significant, meaning
that the p-value is greater than 0.1. The
stepwise process therefore selects only the factors that
significantly explains the excess returns for each
stock. This means that the 16 factors mentioned above will serve
as the pool for which the factors will be
selected for the regression model. Moreover, each stock may have
different explanatory factors.
-
1Q
20
13
2Q
20
13
3Q
20
13
4Q
20
13
1Q
20
14
2Q
20
14
(5)
-
5
10
15
20
25
30
35
40
TELBPI
AGI
MEG
RCB
PX
Top Firms Earnings Actual Historical
-
Event Study
Results & Discussion
BAD NEWS NEUTRAL GOOD NEWS
-
Stock Universe Average Equal Weighted
Stock Universe Average Market Value Weighted
-
Sample Firms
-
Statistical Tests
Results and Discussion
-
Conclusion and Recommendations
-
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