Writeup Pse

42
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

    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

  • 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

  • Table of Contents

  • Introduction

  • 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 .

  • 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.

  • 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.

  • 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

  • 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.

  • 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

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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

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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.

  • 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

  • = + , = 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()),

  • = , = , , 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 ).

  • 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

  • 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

  • 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).

  • 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.

  • 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

  • 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

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    Chelsea LimSticky NoteConsider moving this to another section

  • =/

    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.

    Chelsea LimHighlight

    Chelsea LimHighlight

    Chelsea LimHighlight

    Chelsea LimHighlight

    Chelsea LimHighlight

  • 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

    Chelsea LimHighlight

    Chelsea LimHighlight

    Chelsea LimHighlight

  • 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

    Chelsea LimHighlight

  • -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

  • Bibliography

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