Chapter # 01
INTRODUCTION
1.1 Introduction:
Financial crisis occurred in recent years (2007) has come up with a need for policymakers
and economists to identify those firms which are financially distressed. The most versatile
instrument for the purpose of identification is stock price because of availability and
frequency of information. Typically, financially troubled firms should have high returns
on stocks to be expected and higher risk indicators based on market, such as earnings to
price ratio and ratio of book- to- market; because wisdom based on conventional advocate
that those firms which have higher risk will have definitely lower values of market as
compared to other firms. Consequently, financial distress can also be the link to account
for the value premium, i.e., the significant positive relationship between returns on stocks
and indicators of risk based on market as frequently argued in literature. The most
confusing anomaly of asset pricing is the terrible performance of stocks of firms
approaching towards financial distress. The result contrasting to it, although yet comprise
an incongruity, but understanding of this incongruity will be simple. Distress aspect is
explained by Fama and French (1992), in their opinion it is inadequately measured by
past betas would settle the elevated returns for those firms who have high book to market,
however Capital Asset Pricing Model (1964) may be considered insufficient for the
estimation of distress risk. The literature on asset pricing evoked the financial distress
concept to explain abnormal patterns in the range of stock returns (Chan and Chen, 1991)
and Fama and French (1996). According to this phenomena certain companies have set
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elevated probability that show their failure to meet financial obligations these firms are
financially distressed and stocks of these companies move align, hence risk associated
with such stocks is not diversifiable so, investor demand premium with respect to
bearing risk on such type of stocks. Standard model of asset pricing i.e CAPM is not able
to capture the premium that is demand by investor for bearing risk on distress stocks.
Theoretical underpricing of CAPM build by Sharpe (1964) and Lintner (1965) never led
to a pragmatic success. In early empirical work, the Black (1972), extended the model,
which can hold a compliment exchange of standard return for market beta, got some
success. But in the era of late 1970’s many variables uncover by research like size, P/E
ratio and thrust that insert into the justification of average returns grant by beta. These
problems are severe enough to nullify most functions of the CAPM.
Researchers show that average return of stocks related to various variables. Such as its
size, book-to-market equity (BE/ME), “the ratio of the book value of common equity to
its market value)”, earning/price (E/P'), cash flow/price (C/P'), and growth of historical
sales. (Banz, 198l), Basu (1983), Rosenberg, Reid, and Lanstein (1985), and Lakonishok,
Shleifer andn Vishny (1994).) These are patterns regarding to which average returns of
stocks vary. CAPM doesn’t explain these patterns (Sharpe (1964) and Lintner (1965)),
these are normally called as anomalies of CAPM. Most of the anomalies of CAPM are
related to average-returns of stocks and model presented by Fama and French (FF 1993)
three factor model captured these anomalies and tested pricing of these anomalies in
equity market. The model state that three factors are sensitive to expected return on a
portfolio in surplus of risk-free rate: (i) surplus return on portfolio of extensive market (ii)
in a given portfolio difference between return on stocks of small size and large stocks
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(SMB, Small minus Big); (iii) the discrepancy between return on those portfolios having
stocks of high-book-to-market and those portfolios having stocks of low-book-to-market.
(HML, High minus Low).
Fama and French (1995) illustrate that book-to-market equity and incline on HML
substitute for relative distress. Weak firms with steadily low earnings lean to have high
BE/ME and affirmative slopes on HML; financially sound firms with steadily high
income have low BE/ME and downbeat slopes on HML. Using HML to make clear
returns is therefore in line with the support of Chan and Chen (1991) that there is co
variation in proceeds associated to relative distress that is not detained by the market
return and is compensated in average returns. Similarly, using SMB to explain returns is
in line with the evidence of Huberman and Kandel (l987) that there is co variation in the
returns on small stocks that is not captured by the market return and is compensated in
average returns. Financial distress is major risk factor that affects the stocks. Firms which
are financially distress represent unhealthy firms and healthy firms are those who meet
their financial standards. In addition to HML and SMB we can also incorporate HMU
healthy minus unhealthy. Hence the purpose of this study is to explore the relation of
financial distress and stocks returns by adding variable of HMU in typical Fama and
French three factor model and to find out does financial distress exist as a risk factor.
1.2 Rationale of the Study and Research Gap:
There is need to look at financial distress as a risk factor which can affect the expected
return on stocks in a given portfolio because when we include small and big firms, high
and low firms, there must be some firms which are meeting their financial obligations and
some which are below the standard they are facing the financial distress risk factor and
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investor demand risk premium for holding such stocks. The need of hour is to mention
such firms separately by finding the difference of their stocks returns can be known as
healthy and unhealthy firms, HMU. The relation of financial risk and returns on stocks
has been studied by many researchers in different aspects in developed countries. Models
of bankruptcy have been used by many researchers for division of firms by possibility of
failure to pay, so it is found by them again and again that the higher the failure likelihood,
the poorer the return (Dichev (1998). Regular amendment for risk makes this relation
stronger. Moreover the effect is more dominant in those companies with low ratio of
B/M, where threat of failure is implausible to play a significant role (Griffin and Lemmon
(2002). They study the distress risk with book to market equity and stocks returns. One
well known explanation for demanding high premium for high book to market equity is
that those firms are allocate a privileged risk premium because of the larger risk of
distress. Consistent with this analysis, Fama and French (1995) and Chen and Zahng
(1998) show that firms with high book to market equity (BE/ME) have determinedly low
income, higher fiscal leverage, more earnings ambiguity and are more likely to slash
dividends contrast to their low BE/ME corresponding item. In distinction, Dichev (1998)
uses procedures of bankruptcy risk projected by Ohlson (1980) and Altman (1968) to
discover firms with high possibility of financial distress and get that these firms have a
tendency to have low standard stock returns. Dichev’s consequences appear to be
conflicting with the analysis that firms with elevated BE/ME make high profits as a
premium for distress risk. Researchers tried to predict financial distress by analyzing the
performance of distress stocks (Campbell, et al, 2010). Some researcher incorporate the
financial distress risk factor with equity returns by using the variable difference between
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winning and losing stocks, UMD Gao et al (2013). Although financial distress has been
reported in many studies in foreign countries but those studies done with several
limitations. Financial distress is never studied in the context of healthy and unhealthy
stocks. And there is no evidence of such type of study in Pakistan as previously no
one has theoretically and empirically examined the full interaction among portfolio stock
returns and the difference between financially distress stocks returns and healthy stocks
returns. Hence there is need to conduct research on this topic. The proposed study tries to
discover the pricing of distress risk on stocks returns.
1.3 Theoretical Foundation:
Asset pricing theory (CAPM): This theory plays a vital role in proposed study.
The birth of theory regarding asset pricing comes from model of (CAPM) given by John
Lintner (1965) and William Sharpe (1964). The appeal of CAPM is that it intuitively and
powerfully predicts about measurement of risk and captures the relation between risk and
return to be expected. It is stated by theory of CAPM that return to be expected on a stock
endures a relationship which is linear in nature with covariance of stock with return on
portfolio of market. However, the basis of typical CAPM base on some key traditions,
which are listed below:
• The securities returns presumed to be distributing generally.
• The investor functions of utility are either normal or quadratic.
• All non-market risk, that is unsystematic, assumed to be eliminated.
• The opportunity for risky assets is determined by the existence of assets that are risk
free and market portfolio.
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• Costs and taxes on standard transactions are excluded.
Whenever the above listed assumptions are fulfilled the standard model of CAPM is
applicable, hence the main concern of investor is linked with the mean-variance of the
returns on their stocks. This typical model of single factor is also identified as standard
model of two-moment. This model lies on such tradition that is normal distribution of
returns and investor function of utility is quadratic. Basically, the fact on which the
typical model base is that if the risk is high the return will be definitely high. However,
empirically this relation has failed to persist because alone market beta is not able to
explain the variations that comes in returns of stocks and the unrealistic assumptions of
the model. The empirical evidence on asset pricing show the theme of FINANCIAL
DISTRESS to explain otherwise anomalous patterns in the cross-section of stock returns
(Chan and Chen (1991) and Fama and French (1996)). The idea is that certain companies
have an elevated probability that they will fail to meet their financial obligations; the
stocks of these financially distressed companies tend to move together, so their risk
cannot be diversified away; and investors charge a premium for bearing such risk.' The
premium for distress risk may not be captured by the standard Capital Asset Pricing
Model (CAPM) if corporation failures are correlated with
deteriorating investment
opportunities (Merton (1973)) or declines in unmeasured components of wealth such as
human capital (Fama and French (1996)) or debt securities (Ferguson and Shockley
(2003)). In this case distress risk may help to explain patterns such as the size and value
effects that are anomalies in the standard CAPM.
Fama and French (1992) Model: Joint roles of Size, market beta, Earnings/price,
book to market and leverage ratios studied by Fama and French on average returns of
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cross-section stocks for Amex, NYSE and NASDAQ for the period of 1963 to 1990.
Results suggest that market beta has no descriptive power while E/P, Size, B/M and
leverage have noteworthy descriptive power for the explanation of returns on average.
However book to market ratio and size become significant when beta is incorporated, and
in explaining the average returns on stocks they appear to absorb the effect of E/P and
leverage. FF (1992) thus, argues that risk associated with stock should be
multidimensional if pricing of stocks is rational. Fama and French (1993) used technique
of time series regression to extend the scope of their study on both bonds and stocks.
Returns on monthly basis for bonds and stocks are regressed upon five characteristics:
portfolio of market, portfolio of size factor, portfolio of BM, a premium of default and
premium of term. Results for bonds and stocks are slightly different. For stocks, three
factors come up significant these are returns on portfolio of market, portfolio of size and a
book to market portfolio and for bonds two factors are significant and these are default
and term. As an outcome, model of three factor constructed by Fama and French (1993)
also known as model of asset pricing which incorporates three factor namely factor of
market, size and value factor. Study reports that this extension of model is useful for
capturing the returns on average for the cross section of stocks. According to this model
the return to be expected on portfolio in surplus of rate which is risk free is described in
such sense that how returns of portfolio are sensitive to three factors: (i) the surplus return
on portfolio of broad market (ii) the difference between portfolio’s returns of small size
stocks and portfolio of large size stocks. (SMB) and (iii) the difference between portfolio
return having stocks of high B/M ratio and portfolio return having stocks with low B/M
(HML).
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1.4 Problem Statement: Curiosity in the pricing of financially troubled firms is
extensive. Chan and Chen (1991) depict insignificant and distressed firms as follow:
Their market value is lost, their producers are inefficient and their chances of taking
financially leverage is high and they are suffering from problems of cash flows. They are
minor in the logic their prices likely to be more responsive to changes in the market, and
the chances of their survival are less under unfavorable economic conditions. Theory of
asset pricing advocate that for holding stocks of such marginal firms investors will claim.
However for bearing such risk whether investors are in reality rewarded or not that is an
empirical question. Researchers tried to use different models to classify firms by the
possibility of failure. Consistently they reported that firms whose chances of failure
are more their returns are respectively low, ( Dichev, 1998). The puzzle of distress
risk has got most considerable attraction, both in theoretical and empirical studies. The
basic theme regarding distressed stocks is that their returns are low, but on theoretical
basis researchers argues, against it being inferred as an abnormality. Campbell,
Hilscher,and Szilagyi (2008), advocated that stocks related to those firms which are
distressed, in reality, too stumpy to arranged in single framework. It is showed that
market betas of financially distressed stocks are higher, their standard deviations are also
high and other procedures for measuring risk yet, returns generated by them are low. Thus
it becomes important to check that “How financially distress stocks affect the expected
stock return of portfolio?”
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1.5 Research Questions: This study addresses following research questions:
 ‘’Does financial distress priced as a risk factor in equity market of Pakistan’’?
 “Does the excess returns on portfolio stocks are sensitive to distress risk or not”?
1.6 Research Objectives:

To check the impact of financial distress on stocks returns.

To check whether financial distress exists as a risk factor for affecting the
expected return on portfolio in the context of listed firms of Karachi stock
exchange.

To assess the distress risk premium.
1.7 Significance of the study:
This paper illustrates a lot of research work done on the topic under discussion and the
difference of opinions in the results of authors and it adds significantly to the growing
body of literature considering the interaction among financial distress and stocks returns.
This study was stimulated by pragmatic phenomena of typical concept of financial
distress and underwrites new intuitions to this complex and exciting pitch of research
about financial risk. This study tries to overcome the previous limitations (taking HML as
proxy for distress) and deliver such a comprehensive form of theoretical framework
which is in the form of dynamic process of corporate failure and supported empirically.
Hence this study contributes a proper mechanism for the better understanding of
procedures for financial distress in the context of practical and theoretical domain.
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1.7.1Theoritical Contribution:

This study make addition of new asset pricing anomaly in the typical Fama and
French 3 Factor Model by adding a new variable, HMU. This addition is
significant in the sense because in previous studies financial distress is measured
by bankruptcies, so for the first time financial distress is quantified in the context
of stocks returns.

The present developed model about financial distress can be useful for both
academic purposes to have the logical understanding of financial distress in
corporate sector of Pakistan and also can become as a base for the further
development of models regarding financial risk which are still absent
theoretically.
1.7.2 Practical Contribution:
The complete theoretical debate of proposed study was initiated by practitioners and their
interpretations concerning the discrepancy occurring between theory and practice. Theory
only nominate market risk this is only risk which is priced in returns of equity and
practiced. But financial risk incorporating continuously for last several years. The
requirement for theoretical explanation that why some investors, like private houses of
equity, institutional investors and hedge funds become able to outperform the market by
overlooking risk of market inspired this study to go in this direction. The results of this
empirical study can be used by practitioners to improve their level of understanding and
knowledge about distress risk and financial distress. The world of finance can take the
advantage of this study in following listed ways.
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
Study how value of company suffers in the state of financial distress and how
distress risk affects the weakening performance of bankrupt candidate.

Enhance knowledge about how to price distress stocks and become able to
progress strategy about making investment in those securities which are
financially distressed.

This study brings the community of science a bit advance in understanding what
actually happens when a company suffers from financial distress and why those
stocks which are financially distressed become attractive for an investor with
comprehensive risk appetite. This research contribute to theory of asset pricing by
categorizing the distress risk nature, and answer positively the research question
about pricing this type of risk in equity market of Pakistan.

It can also provide useful information that helps regulators to revisit their policies
and design a realistic structure in which no firm face financial distress risk factor.
1.8 Organization of the Study:
The proposed study combined in five chapters. Chapter 1 presents introduction, which
includes background, research gap, problem statement, research questions, research
objectives, and significance of study. In chapter 2 literature of (1) Capital Asset
Pricing Model; (2) Fama and French three factor Model (3) (SMB, small minus big);
(4) (HML, high minus low), (5) Financial distress and stocks returns (HMU, healthy
minus unhealthy) explained and hypothesis are developed, chapter 3 described data
and methodology and chapter 4 presents results and discussion. Finally in chapter 5
conclusion, policy implications, limitations and future directions are given.
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Chapter # 2
LITERATURE REVEW
The present study is aimed to analyze the impact of Financial Distress on stocks returns in
non-financial listed firms of Pakistan. In doing so, it is essential to delve into the literature
and historical perspectives of these variables to analyze the nature of relationships that
have been explored and supported by different studies. Major findings of these studies are
reviewed below.
2.1 Capital Asset Pricing Model
Pioneers of CAPM are Sharpe (1964) and Lintner (1965), CAPM states that rate which is
risk free and premium on expected risk both combines and become equal to expected
return. It points out that variation in cross-sectional expected returns is only explained by
market beta. In essence, according to CAPM a stock is expected to earn the rate which is
free of risk together with a compensation for tolerating extra risk as précised by the beta
of that stock.
Data of private sector in UK scrutinized, Greene (1990) initiate that CAPM is not fit for
data of UK, though Sauer and Murphy (1992) have assured that for explaining the data of
German stock market CAPM is best model. However, Hawawini (1993), have study more
thoroughly, the healthiness of CAPM in stock markets of France, Canada, Japan, UK,
Spain and the US cannot be validated. Non-normality in returns have shown in various
studies, thereby restrict the use of model of mean-variance to only pricing on theoretical
basis (Galagedera, 2004).
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Unconditional distribution of security returns is not normal stated by Chung et al. (2001)
.The extensions of standard CAPM to high co-moments models are led by ambiguous
results of it. Investors were become aware of to become worried for all moments of
returns on stocks. Subsequently, the variance and mean of returns only were inadequate
for full characterization of distribution of returns (Rubinstein, 1973). Hereafter,
nonparametric models were developed by researchers that add more moments to typical
CAPM. The two-moment model of CAPM has expanded through incorporation of the
third moment, fourth moment, skewness and kurtosis, by several authors. Moreover,
claimed by Harvey (2000) both kurtosis and skewness are not assessed in developed
markets but, they do exist in emerging markets. A noteworthy positive relationship
between returns and volatility was establish in those markets which are emerging, with
the importance of the coefficient of volatility being wrinkled by the insertion of kurtosis
and co-skewness in the model of CAPM. The “Security Market Line (SML)” illustrates
the relationship between asset beta and its expected returns. Beta shows relation of
surplus return which is expected on a stock compare to the on the whole surplus return of
market. The extent to which the asset expected returns are sensitive to the movements of
market is explained by beta. When beta is zero, it is considered to be neutral for changes
incorporated in market. For decades, unconditional single-factor of CAPM model was
accepted by financial analyst. When comparison done with multifactor models of asset
pricing it is comparatively simple to use and also regard as efficient in cost. For the
purpose of verification, that asset may be fairly priced or not, the CAPM SML can be in
use for both analysis of individual security and portfolio analysis. The main proposition
of the CAPM is emphasized by Fama (1976), Roll (1977), that when market is at
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equilibrium, the value-weighted portfolio of market, M, is “mean-variance-efficient”. The
efficiency of mean-variance of M says that: (i)𝛽, is the only risk that is needed to explain
the return which is expected; beta the incline in the regression of a return on security on
the market return, (ii) for 𝛽 risk positive premium is expected.Main point is that proof of
(ii) support for CAPM is positive relation between 𝛽 and return to be expected, only if (i)
if, 𝛽 be enough to explain expected return. On the other hand, like FF (1992), KSS find
that 𝛽 provided the explanation of size in avrage return confirming Banz
(1981).Moreover, the prime awkwardness of CAPM is no longer size. Variables that
(unlike size) do not appear to be associated with 𝛽(such as earnings/price, cash
flow/price, BE/ME, and past sales growth) add even more notably to the explanation of
average return provided by 𝛽 (Basu (1983), Chan, Hamao, and Lakonishok (1991), FF
(1992, 1993, 1996), and Lakonishok, Shleifer, and Vishny (1994)). The anomalies of the
CAPM regarding average return suggest that, if pricing of asset is rational, a multifactor
edition of Merton's (1973) intertemporal CAPM (ICAPM) or Ross' (1976) pricing theory
of arbitrage (APT) can provide an improved explanation of average returns. The excess
return on market of the CAPM is a relevant risk in many multifactor substitutes, like the
ICAPM and Connor's (1984) equilibrium side of the APT. Thus, proof of a positive
relation between, and expected return does not favor the CAPM over these alternatives.
This point has been illustrated by three-factor model of Fama and French (1993, 1994,
1995, and 1996). As compared to CAPM this model provides an improved description of
normal returns, and it captures those anomalies of average-returns that CAPM missed.
2.2 Fama and French 3 Factor Model: A different perspective of asset pricing
has been presented by models of Fama and French (1993). The aim of their study is to
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explain excess returns on portfolio related to three risk features. These risk factors are
excess return on market portfolio, the difference between the portfolio of small stocks
having excess return and portfolio containing big stocks having excess return, difference
between portfolio’s surplus returns of high B/M ratio and portfolio of low B/M. They
uncover that construction of portfolios is for imitate factors of risk that are associated to
factor of market, size and value of stocks and stocks returns are notably effected by these
factors. Their model claimed to be successful for capturing the average returns of crosssection on U.S. stocks.
Difference between returns of stocks on stock exchange of New York (NYSE) and
(NASD) have been explained by Fama et.al (1993). Returns of similar size stocks on both
NYSE and NASD vary; returns on stocks of NYSE are much higher in the duration of
testing. The difference is explained by using Fama and French model of three factors.
Reason for the variation on returns of same size stocks demonstrated by their analysis and
they come up with the following justification that risk of stocks is different, Fama and
French model of three factors captured it. It is argued by Fama et al. (1993, p.37) that
stocks having high level of sensitivity be likely to be those firms who have steadily
deprived earnings, this results in low prices of stocks and therefore their ratios of B/M is
high. On the other hand stocks having low sensitivity have a propensity determinedly
elevated earnings, it direct to low ratio of B/M. They come up with this conclusion that
ratio of B/M is the mainly central factor of risk that illuminates the difference between
returns of NYSE and returns of NASD stocks. A test has been conducted by FF (1995) to
check that discrepancies that come on prices of stocks, in relative to size effect and effect
of BE/ME reveal the deviations comes in firm’s earnings. High ratio of BE/ME reports
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poor earnings and if BE/ME is low it indicates high earnings if constant with rational
pricing reported by Fama and French (1995, p.131). Their model was tested on AMEX,
NYSE and stock market of NASDAQ. It is reported, size and factor of market in earnings
enlighten the factors of returns but no relation was found by them between value factors
and factors of returns and earnings.
One more research on U.S data was provided by Fama and French (1996). The argument
they given was that when model of three-factor used anomalies missed by CAPM widely
disappear. Formation of portfolios with respect to cash flow/price, earnings/price and
sales growth is tool for explaining the well-built patterns in returns observed. For the
period of 1963-1993 model of Fama and French was tested on NASDAQ, NYSE and
AMEX by Daniel and Titman (1996). The findings of their test were not in the support of
FF typical model. Their conclusion was that there does not prevail any relation between
Fama- French three types of risk factors and expected return. For the period of 1981-1993
model was tested on listed stocks of “Italian Stock Exchange” by Aleati et.al (2000).
They find that in the returns of stocks only variables associated with interest rate changes
and market index are priced. They wrap up that ratio of price-to book is dependent on the
period of estimation. The study of Daniel and Titman’s (1997) was extended by Davis,
Fama and French (2000) they tested the model from period of 1929 to 1997. The results
of their study were contradicting from Daniel and Titman. Study done by them was in the
support of model of FF. In India Sehgal and Connor (2001) scrutinize the model of FF
empirically. Results of this study were in the support of model. They accepted this fault
that there are several unanswered questions in the study done by them. One of
unanswered question was that whether value and size factors are persistent in reporting
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the risk for a portfolio of wider range. Validity of this model was also tested by Güzeldere
and Sarıoglu (2012) on ISE-100 index from year 1999 to 2011. Panel data was used to
analyze monthly returns. Results of this study were also in the support of the FF model
considering three main factors. Hence conclusion comes out in the favor of this model as
it seems to be more powerful and best as an alternative for CAPM. In financial sector
efficacy of this model was tested by Hamid et.al (2012) by using returns of portfolio.
Stocks of “Karachi Stock exchange” held in Pakistan were used. Six portfolios were taken
for the implication of Model of FF in this study. Data on monthly basis was taken related
to 20 banks for time period of five-year from period of January 2006 to December 2010.
Results of this study showed that model is appropriate for financial sector presiding in
Pakistan’s economy.
2.3 Firm Size (SMB), Firm Value (HML) and Stocks Returns:
Relation between characteristics at firm level and returns on stocks is extensively
investigated after 1980 in developing and developed countries. A significant link between
specific factors of firm and returns on stocks suggested by findings of literature in
examined countries. The effect of size was first recognized by Reinganum and Banz
(1981) who come to know that premium is present for return on stocks of small size for
the period of 1936-1975 for the stocks which are listed on NYSE. This effect was later
also confirmed in Australia and USA by Stambaugh and Blume (1983) and Brown et al.
(1983) respectively. The effect of BM was firstly renowned in (1985) by Rosenberg et al.
Premium was found by them on returns of those stocks who have high ratios of BE/ME in
stock market of US. Such value premium or effect of BM was later established in USA by
Davis et al (1994) and outside USA by Capul et al, (1993) and Chan et al. (1991).Their
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findings reveal that size of firm and BE/ME have significant effect on expected returns on
stock, positive and negative, respectively. Developed countries were covered in study of
first group. According to FF (1992) there is no power of market beta for explanation of
variation comes in returns of stock in U.S while selecting firms from non-financial sector,
hence they find that size of firm and equity ratio of book to market can captured the
variations that come in cross – sectional returns on stock for the time of 1962 to1989. It is
reported by Fama and French (1992) that premium related to risk for size and BM
variables are simply computable, drastically with negative and positive sign. Three factor
model of FF (1993) was empirically examined by Eleni and Andreas (2004) they use data
of Japan from 1992 to 2001 time period. The conclusion reveals noteworthy relationship
among specific three factors and returns to be expected on stocks in the Japanese market.
Additionally, it undoubtedly shows that there is only factor of market which have mainly
explanatory power for explaining the variation comes on returns of stock returns. The
expressive power of the factor of size (SMB) is more dominating than the explanatory
power of value factor the BE/ME (HML) it is true for those portfolios which consist of
small size stocks and vice versa for testing portfolios of big size stocks, Bryant and
Eleswarapu (1997) from period of 1971 to 1993 and also Pinfold et al (2001) from
duration of mid- 1993 to 2001March, acknowledged a strong effect of BM but a very
weak effect of size on stocks of US. Strong effect of size and BM was described by Vos
and Pepper (1997) over the time period of 1991-1995, whereas their study was replicated
by Li and Pinfold (2000), over the time period of 1995 to June 1999, and hence they did
not find any evidence of book to market effect.
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In the market of Japan Chui and Wei (1998) and Daniel et al. (1997) find that for the
explanation of variations come in stock returns book-to market of equity plays a
considerable role. This relationship was investigated by second part of studies for mostly
developing market also includes stock market of Sri Lanka. When use approach of
multifactor model for Malaysia by Veeraraghavan and Drew (2002) evidence reported by
them for premium on factor of value and size. They account that for Malaysia, factors
recognized by FF (1993), enhanced the explanation of variations come in stock returns. In
“Shanghai stock market” size effect and less persistent BM effect was reported by Drew
et al. (2003). Regression model of Fama-Macbeth (1973) was applied by Senthilkumar
(2009) on particular industries of India for inspecting the performance of stock returns in
ratio of book to market and size. They come up with no effect of size while considering
overall markets and a noteworthy effect of book to market in all of related groups. When
test was applied on both variables, there is less significant negative relationship between
size of firm and average return; when book to market included in selected stock returns of
India it seems to take in the role of size. The two most popular factors were investigated
by Anuradha (2007) on returns of stocks listed on CSE and reports the negative relation
of size with respect to return and positive relation of BE/ME. It is also reported by
Mahawanniarachchi, (2006) that a significant negative relationship found between factor
of size and individual returns on stocks and positive relationship between BE/ME, factor
of market and single stock return. Auxiliary, it is reported that factor of size, market
factor and BE/ME factors have substantial descriptive powers for the explanation of stock
return in Sri Lanka. Chaturika Nimal and Seneviratne employed model of three factor
(FF) (1995) for investigating the size and BM factors for explaining equity returns and
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earnings for the stocks of CSE. Outcomes of the study suggest that the earnings of
corporation are linked with three factors, but reliable link doesn’t provide by it among the
performance of factors in earnings and returns on stocks on CSE. Also, they recognize
that factor of market has more capability for predicting the stock returns of future in
comparison to size and value on CSE. The size effect provides that firms having small
capitalization of market reveal high returns on average which notably exceed the returns
of big cap firms. The effect of BM indicates that if ratio of B/M is higher then returns on
average will be higher for such stocks and also vice versa. Premium on such high B/M
stocks is known as premium of value. Analyses on features of firms having high ratio of
BM and firms having stocks of low B/M is done by Fama and French (1995). Firms with
high ratio of BM found in distress persistently and other with low ratio found continual
profitable. Study reports that the higher returns of those stocks whose BE/ME is high can
be attributed to holding of less profitable and riskier stocks. Study further reveals that
HML in model of three factor is used as substitute for relative distress. Financially
unsound firms having persistently low earnings have a tendency to to have high ratio of
BM and on HML have positive slopes, financially sound firms with higher income
earnings lean to have low B/M and their slopes on HML are negative. Dennis, Perfect,
Snow, and Wiles (1995) provide support to Fama and French’s results and confirm prior
findings that for any given size category, average annual portfolio returns increase as the
BE/ME increases and, for any given BE/ME category, average returns decrease as size
increases. The BE/ME effect is found significant for different holding periods and a
trading strategy based on BE/ME and size could have been profitable. The implication of
their study is that investors can significantly outperform the market if they select small20
size-high-BE/ME securities for their portfolios during the period. Fama and French
(1998) provide additional valuable out-of-sample evidence by testing the FF three factor
models in thirteen different markets over the period 1975 - 1995. Study reports that 12 of
the 13 markets record a premium of at least 7.68% per annum to value stocks. Seven
markets show statistically significant BM/ME betas.
However, Daniel and Titman (1997) do not agree with Fama and French (1992, 1993, and
1996). Daniel and Titman (1997) investigate the impact of factor loadings on stock
returns for the period 1973 –1993 and report that expected returns are not a function of
loadings on the Fama and French risk factors. They argue that it is the covariance
between high book-to-market ratio stocks that leads to similar properties rather than a
common risk factor. Kothari (1995) MacKinlay (1995) and Loughran (1997) see the
matter in from a different perspective. It is argued by them that a considerable premium
portion is because of biasness of survivor and snooping of data. The source of data for BE
contains firms unevenly and those firms have high ratio of BE/ME and they survive in
distress so the return on average for such firms is overstated. The hypothesis regarding
snooping of data speculates that researcher’s desire of searching for variables that are
related to average return, may lead to identification of anomalies that are present
specifically in the sample and are used for identification. However, several studies
consider it a weak argument and dismiss the biasness of survivor and hypothesis about
snooping of data. Halliwel et al. (1999) tests the Fama and French (1993) model in
Australian equity market and reports the presence of some premium on small sized and
high book-to-market ratio stocks.
21
However, study reports that explanatory power of Fama and French three factor model is
not significantly higher than traditional CAPM. Halliwel et al. (1999) do not find any
evidence for the decrease in size sensitivity, given a transition from low to high book-tomarket ratio stocks. This behavior is found inconsistent with Fama and French (1993) that
reports the presence of a tendency for size sensitivity to fall when moving from lower to
higher book-to-market portfolios. Model of Fama and French was tested by Sehgal and
Connor (2001) on Indian market and they found that three factors i.e Size, factor of BM
and return of market explain more powerfully the mean returns of cross- sectional stocks
as compared to typical asset pricing model (CAPM) that lies upon only one factor that is
market returns.
When model of Fama and French was applied on Australian data by Faff (2001) for the
time period of 1991 to 1999 results strongly supported this model and accepted the high
explanatory power of three factors for average returns. Existence of significant negative
relationship was evidenced by this study which is in actual contradicts to expected
relationship that is premium should be positive for stocks of small size. Faff (2001)
therefore reported that his study results seem to be consistent with other reverse size
effect evidenced recently. Comparison of CAPM and Fama and French model of three
factors was done by Veera raghavan and Drew (2003). In this study descriptive power of
both models was challenged for markets of South East Asian and presence of value and
size premium was reported in such markets. This study reports that variations
incorporated in returns for those markets can well explained by FF model of three factor.
Premiums demand by investors are actually compensation for bearing certain type of risk
and model of asset pricing based on single factor is unable to explain this type of
22
premium argued by Drew and Veera raghavan (2003).In equity market of Australia Gaunt
(2004) execute test out of sample for the time period of 1991 to 2000 and concludes that
for small size companies having low BM ratios beta tends to be higher. So after a long
discussion on size of firm and value of firm we come up with following hypothesis.
H1: There is a negative relationship between firm size and stocks returns.
H2: There is a positive relationship between book-to-market value of equity of a
firm and stock returns.
2.4 Financial Distress and Stocks Returns:
Stocks of distressed firms perform below standards and their underperformance becomes
an anomaly that comes in the form of twist. High returns on “value stocks” that are
anomalous is explained by several researchers and Fama and French (1996) by assuming
that such firms are moving towards bankruptcy: due to incorporation of bad news in
market their prices effected and move towards down. And risk of bankruptcy is somewhat
that markets should quite dislike. Losses that may occur due to default can be in the form
of systematic risk for lot of reasons, and the collective default rate is rather volatile. For
the returns of shares bearing high risk this argument provide support for the prediction of
risk premium for default to be positive.
Financial distress can be defined in several contexts but in simple words it is defined as
“the firm’s inability to pay financially obliged liabilities as they mature”. Different
perspectives of financial distress were pointed out by Beaver (1966) for the very first
time. Every form of financial distress depend on the kind of event occurring just like
bankruptcy, default of bonds, an account of bank which is overdrawn or failure to pay
dividend on preferred stock all these characterize the operational type of financial
23
distress. Financial distress is also reported by Baldwin and Mason (1983), Andrade and
Kaplan (1998). Interpretation of financial distress is described by these authors as critical
event which occur and it occurrence let company financial soundness in trouble and to get
rid of this situation certain strategies are required. Another definition was given by
Hendel (1996) according to which chances of firm going bankrupt depends on the extent
of liquid assets it have and how much credit is available. Dichev (1998) was the first to
show that prediction does not bear out and that the performance of high risk shares is
actually very bad. He make groups for CRSP such sample which is Compustat matched
including time period from 1981 to 1991 then grouped this sample into portfolios on the
basis of degree of bankruptcy for this purpose he use ratings of ohlson (1980) and Altman
(1968). Mean returns for high risky firms are calculated and then did comparison with
average and less risky firms. Firms’ performance with high level of risk of bankruptcy is
obviously worst when comparison done with both indicators. A strategy of trade that goes
for long time in portfolio of equally weighted firms where the bankruptcy risk is low and
for short time in those firms where risk of bankruptcy is high earns almost on monthly
basis 1.17% and on annual basis 22.4%. By busing regression confirmation of results are
made. Another evidence of negative relationship between distress risk and returns is find
by Griffin and Lemmon (2002). For distress proxy is used by Ohlson's (1980) O-score,
relationship is still negative even non stationary structure of regular returns is corrected
by means of 3 factor model of Fama-French. In addition, this relationship is determined
by those firms which have low ratio of book to market (BE/ME). When firms with low
BE/ME are placed in highest quintile of Ohlson’s O score average return for such firms is
only 6.36%, and if we talk about other portfolio around half of mean return and for that
24
period to some extent lower than rate which is risk. Firms which are in subset having high
ratio of BE/ME, as these firms are consider as distressed firms their returns are not as
lower as expected from their BE/ME. While those firms which are most distressed in
given quintile, the difference between estimated return when considering high and low
BE/ME firms it is approximately 14.44%. For using the Z score as indicator of Altman
(1968) results are strong. On the other hand contrary to above argued literature Vassalou
and Xing (2004) presented an evidence which is based on measure of distance-to-default.
After the formation of portfolio authors depicts positive correlation between the measure
of risk of default and monthly returns for the small size firms as well as those having
highest ratio of BE/ME. These estimations are interpreted and repeated by Da and Gao
(2005). All the results which are important can be drawn to reversals of first month,
showed by them mostly due to problems of data problems with currency stocks, such as
bounces of bid-ask and illiquidity. Complete picture showed by two papers which are
working papers. Cumulative returns of six months are formed by Garlappi, Shu and Yan
(2005) from portfolios which are sorted conferring to risk of default. An unrestricted
returns’ negative dependence on defaulting risk has been found by them by using credit
rating of standard and poor. Firms in the sub sample having low BE/ME predict negative
relationship when they use EDF measures which are generated by data of Moody's KMV.
Indicators of default risk present in real world has been used by this study and those
indicators were vended to thousands of participants exist in market.
New grounds break by Campbell, Hilscher and Szilagyi (2005) when they construct their
own indicator of default risk in reduced form which is based on model of logit for
bankruptcy and develop concept in broader form for company failure. When firms are
25
sorted into ten diverse portfolios on the basis of their expected default risk, they illustrate
that firms which are financially distressed strongly underperform those firms which are
financially healthy. If three factor model of Fama- French and CAPM used to correct
returns the difference can be magnified. The alpha of three factor for highest percentile of
the default risk distribution relates to return of approximately -25% at yearly rate. -15%
still exists annually for highest 5%. The portfolio which is long-short and contains 10%
stocks having lowest risk of failure and take short 10% stocks having highest risk of
failure would earn an enormous 23% annually, and it is almost exactly the similar figure
set up by Dichev (1998). Stocks of financially distressed firms bear excess negative
premium for this purpose three justifications have been advocated. One possibility can be
malfunctioning of markets. Mispricing is described by Griffin and Lemmon (2002) and
difference in size is related by them to signs of informational asymmetry. However, such
deviation is unexplained that why systematic overpricing lead by informational
asymmetry?
Two versions advanced by Campbell et al. (2005). One point is this that, markets might
be irrational. Specially, financial institutions could have had a prominent an earlier
dislike of shares of distressed firms whose return characteristics does not justified them.
The shares of financially distressed firms underperform as institution’s market shares go
up. Second, inefficiency of markets may exists. The information set they possess may not
include the default indicator created by authors, though the authors carefully make sure
about availability of its components at time and bias of look-ahead was eliminated by
using rolling procedure of estimation. When default indicators of real world are used as
they can be used by anyone, effect still exist this is not explained by latter argument. A
26
fundamental explanation centered on risk reported by Livdan, Sapriza and Zhang (2005).
Investment of firms reduced by financial constraints. This reduction lowers the level of
risk they have to bear risk and therefore their anticipated returns.
One important
shortcoming of this explanation is: it is unable to explain why distressed firm’s portfolio
returns are still small even after making corrections for risk by using CAPM or a three
factor model of Fama-French, and why anomaly become more worsen after this
correction. Stock returns which are expected for distressed firms should higher and higher
risk indicators based on market, such as ratio of earnings to price and ratio of book-tomarket, because conventional insight recommend for these firms risk should high and low
values of market values as compared to other firms. So after long discussion following
hypothesis can be form
H4: There is a positive relationship between distress risk premium and stocks
returns.
27
Chapter # 3
DATA and METHODOLOGY
3.1 Modeling Framework
Market Based
Factors:
 Market
Premium
Markey Premium
Firm Specific Factors:
Market
 Size Premium
 Book-to-Market
Ratio
 Value Premium
 Distress Premium
Stock Returns
3.2 Data Sources:
The sample consists of 100 companies from different sectors for the period 2005-2012.
Data is collected from annual reports published on stock exchange website and BSA
(Balance Sheet Analysis) available on state bank of Pakistan website. Availability of data
is key concern here so sample excludes the companies for which data is not available and
financial companies such as banks and insurance companies because of difference in their
capital structure and profits from other non-financial companies. Method of data
28
collection is secondary. This study used secondary data to accomplish research because
the data on firm capitalization, firm value, and stocks returns and financial distress is
calculated from annual reports.
Single factor has been used by CAPM for the purpose of comparison of portfolio with
equity market. It has been observed by Fama and French that assets which are categorize
in certain classes perform better as compared to others. Hence two factors have been
added by Fama and French in CAPM namely value premium and size premium in order
to capture the effect of size and market to book ratio, In order to capture these factors,
portfolio approach proposed by Fama and French (1993) has been adopted by this study.
3.2 Model Specification. To check the validity of given hypothesis and to find out
the relationship between financial distress, firm size and firm value and stock returns the
following regression model is proposed
𝑅𝑖𝑡 − 𝑅𝑓𝑡 = 𝛽0 + 𝛽1 (𝑅𝑚𝑡 − 𝑅𝑓𝑡 ) + 𝛽2 𝑆𝑀𝐵𝑡 + 𝛽3 𝐻𝑀𝐿𝑡 + 𝛽4 𝐻𝑀𝑈𝑡 + 𝜖𝑖𝑡
3.3 Variable Description:
The above mentioned formula captures the succeeding dimensions:
1. The return which incorporates zero risk.
2. The premium on market beta.
3. Premium on Size effect.
4. Value premium
5. Financial Distress
7. The management impact (𝛽0)
8. Random error
29
𝑅𝑓𝑡 is rate of treasury bill in the start of Month t.
𝑅𝑚𝑡 Basically the market return or the return which is value weighted during Month t for
all those non-financial stocks which are listed on stock exchange of Karachi.
SMBt = in a given portfolio difference between return on stocks of small size and large
stocks.
HMLt = the difference between the return on a portfolio of high-book-to-market stocks
and the return on a portfolio of low-book-to- market stocks
HMUt= The difference between return on a portfolio of healthy stocks and the return on
a portfolio of unhealthy stocks.
∈𝑖𝑡 = Error term
3.4 Portfolio Formation: 1. First of all market capitalization of main portfolio is
calculated for the end of year June t-1 and then stocks are sorted in ascending order. Now
two portfolios are formed first 50 companies moved to small portfolio because they have
low market capitalization next 50 are placed in big portfolio as they have high market
capitalization. First portfolio named as Small other portfolio named as “Big”.
2. Now Small portfolio is sorted on the basis of book to market equity in descending
order. It subdivided into two portfolios one contains first 25 stocks as their median point
is 25 and 50 firms are equally subdivided into two portfolio one which have high book to
market named as S/H other contains remaining 25 stocks which have low book to market
named as S/L. Big portfolio is also subdivided into two portfolios in same manner named
as B/H and B/L.
3. In order to incorporate distress effect we use coding those firms which have Z score
higher than cutoff are coded as 1 and those firms which have z-score lower than specific
30
cutoff are coded as 0. Then sub portfolios that are S/H, S/L, B/H, B/L are sorted in
ascending order on the basis of Z score. From 25 stocks in each portfolio some stocks
categorize in small high distress portfolio S/H/D and some moved to small high un distess
S/H/UD same happen with B/H and B/L. As there is no median point one portfolio may
have 7 distress stocks other may have 12 un distress stocks so we consider only first
seven from both portfolios that is lowest number and miss other stocks. Cutoff point set
by Altman (2002) is 1.81 its accuracy rate is 84%. According to Altman when a firm have
Z-score less than 1.81 its chances of default is high. Finally. Size, B/M and z-score
portfolios are then formed at the intersections of the two z-score. P, S, B, S/H, S/L, B/H,
B/L, S/H/D, S/H/UD, S/L/D, S/L/UD, B/H/D, B/H/UD, B/L/D, B/L/UD.
3.5 Variable Construction:
SMB = 1/4 * [(S/H/D – B/H/D) + (S/L/D – B/L/D) + (S/H/UD- B/H/UD) + (S/L/UD _
B/L/UD)]
HML =1/4 * [(S/HD – S/L/D) + (B/H/D – B/L/D) + (S/H/UD – S/L/UD) + (B/H/UD –
B/L/UD)]
HMU = 1/4 * [(S/H/D – S/H//UD) + (S/L/D – S/L//UD) + (B/H/D – B/H/UD) + (B/LD –
B/L/U)]. D stands for distress firms UD stands for un distress firms.
How to assess distress risk premium?
To measure distress risk or to check which firms are financially distressed and which are
financially healthy Z-score has been used as proxy. Accounting ratios which are predefined, Z score can be derived from the weighted sum of such ratios. Altman (1968).
Those firms whose Z score lie above specified cut off seldom fail, although the rate of
failure is much high in those firms having z-scores lower the cut off. When we use this
31
model of bankruptcy a firm which have calculated z score <1.81 its financial profile will
be closer to formerly bankrupt firms, therefore taking itself at an obvious risk of
bankruptcy, on the other hand if z>1.81it indicates that firm’s financial position is not at
the risk of bankruptcy.
Z = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 +0.999X5
X1 = working capital which includes current assets- current liabilities/total assets,
X2 =earnings which are retained for future/ total assets,
X3 = EBIT/ total assets,
X4 = market capitalization/total liabilities reported in balance sheet.
X5 = sales/total assets.
32
Chapter # 4
RESULTS and DISCUSSION:
Table 1: Average Return Difference
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Time Period
2005-2012
Average Return
Small
-0.010119734
Average Return
Big
-0.006754473
Difference
t-stat
-0.003365261
0.735952368
Average Return
Small
-0.010119734
Average Return
of Market
-0.001836818
Difference
t-stat
-0.008282916
0.476493392
Average Return
Big
-0.006754473
Average Return
of Market
-0.001836818
Difference
t-stat
-0.004917655
0.669249667
Average
Return High
-0.015290237
Average Return
Low
-0.014467349
Difference
t-stat
-0.000822888
0.940470546
Average Return
High
-0.015290237
Average Return
of Market
-0.001836818
Difference
t-stat
-0.013453419
0.270333776
Average Return
Low
-0.014467349
Average Return
of Market
-0.001836818
Difference
t-stat
-0.012630531
0.288369636
Average Return
Distress
-0.020893596
Average Return
Un Distress
-0.006954652
Difference
t-stat
-0.013938944
0.316368304
Average Return
Distress
-0.020893596
Average Return
of Market
-0.001836818
Difference
t-stat
-0.019056778
0.160323032
Average Return
Un Distress
-0.006954652
Average Return
of Market
-0.001836818
Difference
t-stat
-0.005117834
0.701221971
33
4.1 Average Return Difference: Table 1 reports mean excess returns of small and
big capitalization portfolios and difference between their average excess returns. Theory
is supported by results, as results reported in this table clearly indicated outperformance
of big firms over portfolios of small firms for the time period during which sample is
taken. Hence, small capitalization firms are supposed as being more risky than big firms
and consequently investors of small firms will claim higher returns for adjusting risk they
are bearing. Though, t-stat directs that there is no noteworthy difference between mean
returns of small and big portfolio. When comparison of returns of small firms portfolio is
done with portfolio of market, value of t-stat shows that there is no considerable
difference between small portfolio returns and market portfolio. Results reported in table
also specify that portfolio of big firm’s stocks underperforms portfolio of market for the
period of sample. Again of t stat indicates that there occurs no significant variance
between mean returns of market portfolio and big portfolio. When portfolio of high book
to market is compared with low, premium for high portfolios are certainly higher as they
are risky enough for investor to demand high returns. Whereas t value is still insignificant
which depicts no markedly difference between returns of high and low portfolios. When
returns of high portfolio is compared with market return, t stat specifies no marginal
difference between both portfolios. For the taken sample time period low book to market
portfolio is also compared with portfolio of market here also low portfolio underperforms
the market portfolio and t value suggests that there does not exist a significant difference
between both portfolios under consideration.
In the last distress factor is reported first mean returns of portfolios of distress firms are
compared with the average return of un distress portfolio just like small capitalization
34
firms distress firms also perceived as risky and it is clear from the average returns that un
distress firms outperforms distress firms and high returns for distress stocks is the
justification of their being risky. Finally distress and un distress portfolios are separately
compared with returns of market portfolio and results are same as described above for
size and value factors.
Table 2: Descriptive Statistics
Portfolio
Mean
Standard Deviation
Minimum
Maximum
P
-0.012680429
0.060162568
-0.185728024
0.088813473
S
-0.010119734
0.065433168
-0.192427327
0.113098157
B
-0.006754473
0.06368697
-0.205346709
0.113406614
S/H
-0.015290237
0.073435844
-0.252247357
0.139149166
S/L
-0.014467349
0.069105902
-0.227496535
0.14428767
B/H
-0.010352684
0.078293815
-0.209243955
0.243654158
B/L
-0.010611446
0.071083701
-0.281598087
0.2277578
S/H/D
-0.020893596
0.091110373
-0.257222916
0.20028863
S/H/UD
-0.006954652
0.088646514
-0.284559387
0.265752981
S/L/D
-0.012599765
0.101227933
-0.31496036
0.233344752
S/L/UD
-0.015110556
0.076966943
-0.31483471
0.147430614
B/H/D
-0.002502499
0.048723493
-0.171767239
0.136208142
B/H/UD
-0.025789328
0.122645933
-0.777155174
0.187015258
B/L/D
-0.016500738
0.046364576
-0.240863962
0.093523727
B/LUD
-0.012891691
0.056609822
-0.277490037
0.252666432
4.2 Descriptive Statistics: In table 2 descriptive statistics are reported for all of
sample companies, size and book-to- market and distress premium sorted portfolios.
Mean return of sample companies taken in this study for time period 2005-2012 is 0.012% and average standard deviation of all returns is 0.07%. Mean of all portfolios
35
come negative this is may be due to abnormal behavior of market for the time period of
sample taken. Another reason can be overlapping of time period returns of one year effect
the all returns when mean calculated. When comparison of small portfolios and big
portfolios is did for the purpose of descriptive statistics it is obvious that average return of
big market capitalization firms is high as compare to small capitalization firms. One
reason may be this that big firms are represented in value-weighted index of KSE, whose
performance was well during the period of study except for few years when period of
crisis came. Hence, on average companies of small capitalization stocks pay low and their
returns adjusted for risk should be high as their profile is perceived as high risky.
Statistics of standard deviation indicate that average risk for both small firms and big
firms portfolio is nonetheless same, even though the average return of big firms is high in
contrast to small stocks. When measures of descriptive statistics for high and low bookto-market firms portfolios is compared, it is showed that portfolios of low book-to-market
outperform portfolios of high book-to-market in terms of high mean return. Again, high
risk is associated with portfolios of high book-to-market.
The regression model has been applied at the confidence interval of 95% to test the
validity of the 4 factor model.
Table 3: Sensitivity of Four Factors for Main Portfolio ‘P’, Small ‘S’, Big ‘B’
Dependent
Variable/Subportfolios
P
t-Statistics
p-Value
P
t-Statistics
Intercept
MKT
-0.01176
-2.48624
0.01494
-0.01284
-2.92956
0.500
8.826
0.000**
0.436
7.921
SMB
0.2944
3.8548
HML
HMU
Adj. R2 F-Stat. F Sig
0.480
77.90
0.000
0.555
52.96
0.000
36
p-Value
P
t-Statistics
p-Value
P
t-Statistics
p-Value
S
t-Statistics
p-Value
S
t-Statistics
p-Value
S
t-Statistics
p-Value
S
t-Statistics
p-Value
B
t-Statistics
p-Value
B
t-Statistics
p-Value
B
t-Statistics
p-Value
B
t-Statistics
p-Value
0.004408**
-0.01193
-3.18604
0.002057**
-0.01205
-3.22933
0.001809
-0.00941
-1.50717
0.135611
-0.01093
-1.91196
0.059417
-0.00962
-2.05908
0.04274
-0.00978
-2.10405
0.038555
-0.00568
-1.27819
0.20479
-0.00581
-1.2981
0.197938
-0.00524
-1.22916
0.222614
-0.00525
-1.22355
0.224759
0.000**
0.406
8.5957
0.000**
0.4273
8.5970
0.000**
0.3858
5.1531
0.000**
0.2952
4.1124
0.000**
0.2527
4.2828
0.000**
0.2808
4.5360
0.000**
0.5863
11.010
0.000**
0.5787
10.302
0.000**
0.5603
10.406
0.000**
0.5622
9.8294
0.0000**
0.0002**
0.3321
5.0677
0.000**
0.3250
4.9645
0.000**
0.4133
4.1499
0.000**
0.4676
5.7183
0.000**
0.4580
5.6172
0.000**
0.0349
0.4490
0.6546
0.0584
0.7830
0.4359
0.0577
7.6709
0.0044**
0.434
5.581
0.0000**
0.3942 -0.1085
4.7364 -1.306
0.0000** 0.1952
0.6246
6.4366
0.000**
0.5708
5.5062
0.000**
-0.1465
-1.4157
0.1607
0.2695
3.0436
0.0031**
0.2659 -0.0097
2.7767 -0.101
0.0068** 0.9194
0.676
58.84
0.000
0.6792 44.948
0.0000
0.2354 26.555
0.000
0.3616 24.515
0.0000
0.5742 38.311
0.0000
0.579
29.595
0.0000
0.5916 121.23
0.0000
0.5875 60.129
0.0000
0.6257 47.263
0.0000
0.6210 35.011
0.0000
* denotes significance at 5% level, ** denotes significance at 1% level
37
Table 4: Sensitivity of Four Factors for Small High, ‘S/H’, Small Low, ‘S/L’, Small High
Distress, ‘S/H/D’, Small High Unditress, ‘S/H/UD’, Small Low Distress, ‘S/L/D’ and Small
Low Undistress, ‘S/L/UD’
S/H
t-Statistics
p-Value
S/H
t-Statistics
p-Value
S/H
t-Statistics
p-Value
S/H
t-Statistics
p-Value
S/L
t-Statistics
p-Value
S/L
t-Statistics
p-Value
S/L
t-Statistics
p-Value
S/L
t-Statistics
p-Value
S/H/D
t-Statistics
p-Value
S/H/D
t-Statistics
p-Value
S/H/D
t-Statistics
p-Value
S/H/D
t-Statistics
p-Value
S/H/UD
t-Statistics
-0.01437
-2.17354
0.032624
-0.01653
-3.00119
0.003574
-0.01493
-4.01311
0.000134
-0.01506
-4.07436
0.00010
-0.01393
-1.96327
0.05300
-0.01561
-2.38672
0.01933
-0.01475
-2.37591
0.01989
-0.01504
-2.46602
-2.46602
-0.01996
-2.25905
0.02653
-0.02186
-2.64301
0.00986
-0.01987
-3.02743
0.003318
-0.01931
-3.20821
0.00193
-0.00618
-0.69226
0.5011
6.3224
0.0000**
0.3722
5.3811
0.0000**
0.3202
6.8158
0.0000**
0.3433
6.9716
0.0000**
0.2917
3.4289
0.0009**
0.1920
2.3382
0.0218*
0.1642
2.0951
0.0393*
0.2164
2.6647
0.0093**
0.5095
4.8106
0.000**
0.3961
3.8129
0.0002**
0.3312
3.9970
0.0001**
0.2279
2.8419
0.0057**
0.4197
3.9193
0.5883
6.1309
0.0000**
0.6548
10.057
0.0000**
0.6469
9.9730
0.0000**
0.4553
3.9972
0.0001**
0.4907
4.5166
0.000**
0.4729
4.4194
0.0000**
0.5180
3.5948
0.0005**
0.6009
5.2332
0.0000**
0.6360
6.0204
0.0000**
0.7643
9.8920
0.0000**
0.7200 -0.1205
8.7311 -1.4640
0.0000** 0.147
0.4073
3.1594
0.0022**
0.3072 -0.272
2.2583 -2.006
0.0266* 0.048*
0.9532
6.9951
0.0000**
1.1512 0.538
8.5713 4.019
0.0000** 0.000**
0.3195 39.973
0.0000
0.5294 47.698
0.0000
0.7857 102.44
0.0000
0.7887 78.464
0.000
0.1147 11.757
0.000
0.2514 14.941
0.000
0.3261 14.392
0.000
0.3507 12.209
0.000
0.2105 23.142
0.000
0.310
0.000
19.715
0.5670 37.231
0.0000
0.6359 37.251
0.000
0.1475 15.361
0.000
38
p-Value
S/H/UD
t-Statistics
p-Value
S/H/UD
t-Statistics
p-Value
S/H/UD
t-Statistics
p-Value
S/L/D
t-Statistics
p-Value
S/L/D
t-Statistics
p-Value
S/L/D
t-Statistics
p-Value
S/L/D
t-Statistics
p-Value
S/L/UD
t-Statistics
p-Value
S/L/UD
t-Statistics
p-Value
S/L/UD
t-Statistics
p-Value
S/L/UD
t-Statistics
p-Value
0.49072
-0.00856
-1.06872
0.28836
-0.00661
-1.04697
0.298267
-0.00738
-1.44376
0.15276
-0.01153
-1.18396
0.23985
-0.0146
-1.76846
0.08075
-0.01508
-1.83519
0.07019
-0.01503
-1.81714
0.07298
-0.01482
-1.7806
0.07868
-0.01737
-2.43953
0.01689
-0.01686
-2.39136
0.01913
-0.01785
-3.43413
0.00095
0.0001**
0.2782
2.7668
0.0070**
0.2147
2.6954
0.0085**
0.3577
5.2541
0.0000**
0.5812
4.9774
0.0000**
0.3986
3.845
0.0002**
0.4144
3.9932
0.0001**
0.4034
3.6616
0.0004**
0.1604
1.6079
0.1116
0.0081
0.0909
0.9277
-0.0084
-0.0944
0.9249
0.1749
2.5254
0.0135*
0.6459
4.6301
0.0000**
0.7271
6.5862
0.0000**
0.6784
7.5630
0.0000**
0.8339
5.7993
0.0000**
0.8137
5.6582
0.0000**
0.8175
5.6326
0.0000**
0.6952
5.6046
0.0000**
0.7164
5.8059
0.0000**
0.6540
7.1665
0.0000**
0.9332
7.1234
0.0000**
0.6589 -0.746
5.7784 -6.558
0.0000** 0.000**
-0.2322
-1.3609
0.1773
-0.2112
-1.1447
0.2557
0.2429
1.6590
0.1010
-0.1086
-0.9365
0.3518
0.057
0.3112
0.756
0.3175 20.313
0.000
0.5772 38.773
0.000
0.7227 55.101
0.000
0.2226 24.775
0.000
0.4439 34.133
0.0000
0.4497 23.612
0.000
0.4434 17.533
0.000
0.0187 2.5856
0.111
0.2842 17.478
0.000
0.2993 12.821
0.000
-0.956
-8.262
0.6194 34.769
**
0.0000
0.0000
* denotes significance at 5% level, ** denotes significance at 1% level
Table 5: Sensitivity of four factor for Big High ‘B/H’, Big Low ‘B/L’, Big High Distress
‘B/H/D’, Big High Undistress ‘B/H/UD’, Big Low Distress ‘B/L/D’, Big Low Undistress
‘B/L/UD’
B/H
t-Statistics
p-value
B/H
-0.00915
-1.48886
0.14035
-0.00929
0.6523
8.8480
0.0000**
0.6443 0.0364
0.4821 78.288
0.000
39
t-Statistics
p-Value
B/H
t-Statistics
p-Value
B/H
t-Statistics
p-Value
B/L
t-Statistics
p-Value
B/L
t-Statistics
p-Value
B/L
t-Statistics
p-Value
B/L
t-Statistics
p-Value
B/H/D
t-Statistics
p-Value
B/H/D
t-Statistics
p-Value
B/H/D
t-Statistics
p-Value
B/H/D
t-Statistics
p-Value
B/H/UD
t-Statistics
p-Value
B/H/UD
t-Statistics
p-Value
B/H/UD
t-Statistics
p-Value
B/H/UD
t-Statistics
p-Value
-1.49937
0.13766
-0.0086
-1.43755
0.15446
-0.00859
-1.42778
0.15729
-0.00959
-1.6306
0.10680
-0.00995
-1.68712
0.09542
-0.00946
-1.62973
0.10709
-0.0095
-1.62792
0.10752
-0.01296
-1.99433
0.04943
-0.0114
-1.91037
0.05962
-0.01045
-1.90368
0.06054
-0.01009
-1.92655
0.05763
-0.02557
-1.90512
0.06027
-0.02475
-1.83954
0.0695
-0.0215
-2.01755
0.04699
-0.02279
-2.62668
0.01035
8.2816
0.0000**
0.6217
8.2357
0.0000**
0.6213
7.747
0.0000**
0.5572
7.9043
0.0000**
0.5358
7.2376
0.0000**
0.5199
7.0965
0.0000**
0.5282
6.7920
0.0000**
0.2806
3.6023
0.0005**
0.3734
4.9826
0.0000**
0.3424
4.9416
0.0000**
0.2756
3.9499
0.0001**
0.1210
0.7524
0.4539
0.1694
1.0027
0.3189
0.0635
0.4722
0.6380
0.3028
2.6189
0.0105*
0.3373
0.7367
0.0652
0.6232
0.5348
0.0653
0.6186
0.5379
0.0975
0.9497
0.3450
0.1178
1.1609
0.2491
0.1150
1.1229
0.2648
-0.4237
-4.0754
0.0001**
-0.3841
-3.9997
0.0001**
-0.3613
-3.9317
0.0001**
-0.2209
-0.9425
0.3487
-0.0856
-0.4593
0.6471
-0.1670
-1.0970
0.2759
0.3311
2.6667
0.0092**
0.3319 0.002
2.4714 0.0166
0.0156* 0.986
0.2338
1.9407
0.0558
0.2179
1.6729
0.0982
-0.043
-0.333
0.739
0.4551
3.9932
0.0001**
0.5833 0.348
4.9925 2.991
0.0000** 0.003**
1.5555
7.0297
0.0000**
1.0967 -1.248
5.6644 -6.459
0.0000** 0.000**
0.4765 38.778
0.000
0.5132 30.173
0.000
0.5070 22.347
0.000
0.4255 62.478
0.000
0.4248 31.652
0.000
0.4438 23.078
0.000
0.4375 17.144
0.000
0.1261 12.976
0.000
0.2658 16.028
0.000
0.3802 17.972
0.000
0.4362 17.056
0.000
-0.0052 0.5661
0.453
-0.0066 0.7268
0.486
0.3699 17.246
0.000
0.5825 29.95
0.000
40
B/L/D
t-Statistics
p-Value
B/L/D
t-Statistics
p-Value
B/L/D
t-Statistics
p-Value
B/L/D
t-Statistics
p-Value
B/L/UD
t-Statistics
p-Value
B/L/UD
t-Statistics
p-Value
B/L/UD
t-Statistics
p-Value
B/L/UD
t-Statistics
p-Value
-0.01617
-3.3597
0.00118
-0.01506
-3.38071
0.00111
-0.01509
-3.3635
0.001183
-0.01514
-3.35931
0.00120
-0.0125
-2.1195
0.03707
-0.01117
-2.03782
0.044832
-0.01138
-2.07087
0.041595
-0.01154
-2.10766
0.03823
0.1801
3.1212
0.0024**
0.2461
4.3997
0.0000**
0.2471
4.3621
0.0000**
0.2571
4.2806
0.0000**
0.2130
3.0131
0.0034**
0.2920
4.2405
0.0000**
0.2988
4.3054
0.0000**
0.3285
4.5020
0.0000**
-0.3015
-3.8856
0.0002**
-0.3027
-3.8567
0.0002**
-0.3061
-3.8691
0.0002**
-0.013
-0.148
0.882
-0.033
-0.328
0.743
-0.3605
-3.77413
0.00030**
-0.36921 -0.0997
-3.83863 -0.8734
0.00024** 0.3850
-0.37933 -0.1567
-3.94558 -1.2825
0.00017** 0.2034
-0.052
-0.521
0.603
-0.1552
-1.2726
0.2068
0.0952 9.742
0.002
0.228
13.25
0.000
0.218
8.738
0.000
0.211
6.562
0.000
0.088
9.078
0.003
0.2154 12.394
0.0000
0.2131 8.4932
0.0000
0.2191 6.8242
0.0000
* denotes significance at 5% level, ** denotes significance at 1% level
4.3 Multivariate Regression: The regression model has been applied at the
confidence interval of 95% to test the validity of the 4 factor model. The results of four
factor model have been summarized in the table. Regression results support the presence
of traditional CAPM in the equity market of Pakistan and it is positive and significant for
all the portfolios and except one.
The existence of market risk premium along with size and value has been supported in P
portfolio with R2 of 0.67. The MKT, SMB and HML have positive and significant
relationship with t-stat values of 8.59703, 4.964506 and 4.736407 respectively whereas
41
HMU have insignificant impact with t stat value of -1.306 for dependent variable P and
therefore does not explain returns of portfolio P.
In portfolio S result support the existence of MKT, SMB, and HML, MKT, SMB and
HML have positive and significant relationship with dependent variable S and have the t
stat values of 4.53601, 5.61725 and 5.506205 respectively. However HMU have been
found to have insignificant relationship with stock returns with t value of -1.4157and
therefore do not explain dependent variable S. The value of R2 in this regression is 0.57
For dependent variable B the relationship of explanatory variables MKT and HML is
positive and significant with t values of 9.82946 and 2.776726 respectively whereas SMB
and HMU have been found to have an insignificant relationship with stock returns their
reported t values are 0.767091 and -0.101 thus no impact on B with value of R2 equals to
0.62.
In small cap high book to market portfolio, results validate the presence of market
premium, SMB and HML, with positive and significant coefficients for MKT, SMB and
HML whereas negative and insignificant coefficient for HMU. The t stat value for MKT
is 6.971673, SMB is 9.973006 and HML is 8.731173. It means they explain returns of
S/H stocks. However HMU has no relationship with dependent variable with an
insignificant t stat value of -1.46404. The value of R2 is 0.78
In small cap low book to market portfolio, dependent variable S/L has been found to be
positively and significantly related with independent variables MKT, SMB and HML
negatively and significant related with HMU. The t values for MKT, SMB, HML and
42
HMU are 2.664707, 4.419461, 2.258335 and -2.00644 respectively. The reported value of
R2 is 0.35.
The existence of market risk premium along with size, value, and distress risk factor has
been supported in small cap high book to market distress S/H/D portfolio with R2 of 0.63
The MKT, SMB, HML and HMU have positive and significant relationship with t-stat
values of 2.841918, 6.020444, 8.571328, 4.01907 respectively. Hence MKT, SMB, HML,
and HMU explain the stock returns for S/H/D portfolio.
In portfolio small cap high book to market un distress risk factor S/H/UD results support
the existence of MKT, SMB, HML, and HMU. MKT, SMB and HML have positive and
significant relationship with dependent variable S/H/UD and have the t stat values of
5.25414, 7.563034 and 5.778484 respectively whereas HMU has negative and significant
relationship and the reported t stat values is -6.5580. The value of R2 in this regression is
0.722.
For dependent variable S/L/D the relationship of explanatory variables MKT and SMB is
positive and significant with t values of 3.661682, 5.632639 respectively whereas HML
have negative and insignificant relationship with t stat value, -1.14472 and HMU also
have been found to have an insignificant relationship with stock returns thus no impact on
S/L/D with value R2 equals to 0.44.
In small cap low book to market un distress portfolio S/L/UD, results validate the
presence of market premium, SMB and HMU with positive and significant coefficients
for MKT, SMB and negative and significant coefficients for HMU. The t stat value for
43
MKT is 2.525488, SMB is 7.166555 and HMU is -8.26249. It mean they explain returns
of S/L/UD stocks. However HML has no relationship with dependent variable with an
insignificant t stat value of, -0.93652.The value of R2 is 0.61.
In small cap high book to market portfolio, dependent variable B/H has been found to be
positively and significantly related with independent variables MKT and HML, whereas
no relationship with SMB and HMU have been found. The t values for MKT, SMB, HML
and HMU are 7.747, 0.618605, 2.471419 and 0.0166 respectively. The reported value of
R2 is 0.50.
The existence of market premium has been supported in B/L portfolio with R2 of 0.43.
The MKT has positive and significant relationship with t-stat values of 6.792076. SMB,
HML and HMU have insignificant impact with t stat value of 1.122912, 1.672985, 0.3338 for dependent variable B/L and therefore does not explain returns of portfolio
B/L.
In portfolio B/H/D results support the existence of MKT, SMB, HML, and HMU
premium. MKT, HML and HMU have positive and significant relationship with
dependent variable B/H/D and have the t stat values of 3.949912, 4.992542 and 2.991722
respectively whereas SMB has negative and significant relationship and the reported t stat
values is -3.93177 . The value of R2 in this regression is 0.43
For dependent variable B/H/UD the relationship of explanatory variables MKT and HML
is positive and significant with t values of 2.6189 and5.664462 respectively whereas
HMU has negative and significant relationship with t stat value, -6.4596 respectively.
44
The SMB has been found to have an insignificant relationship with stock returns thus no
impact on B/H/UD with value R2 equals to 0.58.
In high cap low book to market distress portfolio B/L/D, results validate the presence of
market premium and SMB, with positive and negative significant coefficients for MKT
and SMB. The t stat value for MKT is 4.2806, and SMB is -3.86919. It mean they explain
returns of B/L/D stocks. However HML and HMU have no relationship with dependent
variable with an insignificant t stat values of, -0.32861, -0.5219. The value of R2 is 0.21.
In high cap low book to market un distress portfolio, dependent variable B/L/UD has
been found to be positively and significantly related with independent variable MKT,
negatively and significantly related with SMB, whereas has no relationship with HML
and HMU. The t values for MKT, SMB, HML, and HMU are 4.5020, -3.94558, -1.28254
and -1.2726 respectively. The reported value of R2 is 0.21.
Table 6: Premiums of Four Factors
Portfolios
P
S
B
S/H
S/L
B/H
B/L
t-values
Β
t-values
Β
t-values
Β
t-values
Β
t-values
Β
t-values
Β
t-values
Β
Intercept
MKT
-1.09761 0.952888
-0.18515
0.21939
-1.48003
1.46357
-0.17452 0.250912
-3.05001 2.747365
-0.49161 0.563653
-1.32749 1.130185
-0.27292 0.385848
-3.01745 0.295097
-0.11008 0.048236
-1.84227 1.421954
-0.40461 0.364398
-1.44905 0.895373
-0.15581 0.125705
SMB
-0.11912
-0.00883
0.593935
0.032742
0.789674
0.082972
0.788044
0.113056
1.058856
0.103591
0.578952
0.107507
-0.32087
-0.02969
HML
HMU
0.91623
-1.1765
0.180697 -0.12901
0.602749
-0.8373
0.103046 -0.06981
4.139521 -1.96814
0.560497 -0.11014
0.121548 -0.87915
0.027855 -0.22609
-0.13862 -1.03704
-0.02281 -0.14355
3.536106 -1.79898
0.539341 -0.30156
2.931904
-5.1583
0.344395 -0.25865
Adj. R2
0.29
0.18
0.43
0.13
0.12
0.32
0.34
45
S/H/D
S/H/UD
S/L/D
S/L/UD
B/H/D
B/H/UD
B/L/D
B/L/UD
t-values
Β
t-values
Β
t-values
Β
t-values
Β
t-values
Β
t-values
Β
t-values
B
t-values
Β
-1.01323
-0.371
-1.55434
-0.1749
-3.10428
-0.27879
-0.40005
-0.08464
1.398108
0.20271
-1.579
-0.20825
-0.19132
-0.0034
-0.18104
-0.00284
0.689436
0.224718
0.900049
0.156142
1.414421
0.165244
1.275677
0.213079
-0.34231
-0.03769
1.253448
0.226166
-0.48704
-0.0378
-0.41211
-0.0316
0.188181
0.031422
-0.44393
-0.05498
2.80035
0.249438
0.49525
0.139922
0.131631
0.039159
1.861916
0.184536
-0.2163
-0.00674
0.428375
0.025224
1.025069
0.217723
0.528852
0.08412
-0.44348
-0.05694
1.449149
0.1803
-1.74895
-0.13179
-0.17714
-0.0231
-0.48589
-0.03633
-0.52707
-0.03163
0.270367
0.065802
-1.65492
-0.13978
-1.3903
-0.18889
0.247445
0.03939
-2.1201
-0.29709
-0.95679
-0.13402
-0.34306
-0.0122
-0.10046
-0.00761
-0.01
0.07
0.16
0.052
0.06
-0.00
-0.08
-0.04
4.4 Second Pass Regression: Table 4 shows two pass regression results of four
factor model for all size, book to market and distress risk sorted portfolios. Results
reported in this table hence proved that current returns of portfolios sorted on the basis of
four factors are unable to explain the future portfolio return. Rolling beta method is failed
in equity market of Pakistan.
For two pass regression procedure given by Fama and Macbeth (1973) has been used,
where time series linear regression estimate the factor betas are estimated by time series
linear regression of portfolio return on a set of common factors. Then, regression which is
cross sectional of average return on coefficients or betas estimated prices of risk factor.
Main purpose is to assess the significance level of firm specific factors in the second
phase ordinary least square (OLS). However, results reveal model of four factor fails to
illuminate relationship between MKT, Size, Value and Distress premiums and future
46
returns of stocks returns during the time period of testing. Value of R2 show insubstantial
explanatory power of the build model. Hence, insignificant relationship prevails between
betas of portfolio and premiums of systematic risk for factor model. As, all of the
coefficients for model of four factors are empirically insignificant except few one’s which
show substantial value premiums. Hence, value effect to a little extent is useful in
forecasting of future returns.
The existence of market risk premium along with size, value and distress premium has
not supported in P portfolio with R2 of 0.29. The MKT, SMB, HML and HMU have
insignificant relationship with t-stat values of 0.952888, -0.11912, 0.916234 and 1.1765
respectively therefore does not explain returns of portfolio P.
In portfolio S results does not support the existence of MKT, SMB, HML, and
HMU.MKT, SMB, HML and HMU have insignificant relationship with dependent
variable S and have the t stat values of 1.463576, 0.593935, 0.602749, -0.8373
respectively. The value of R2 in this regression is 0.18.
For dependent variable B the relationship of explanatory variables MKT and HML is
positive and significant with t values of 2.747365 and 4.139521 respectively whereas
SMB and HMU have been found to have an insignificant relationship with stock returns
their reported t values are 0.789674 and -1.96814 thus no impact on B with value of R2
equals to 0.43.
In small cap high book to market portfolio, results do not validate the presence of market
premium, SMB, HML and HMU with insignificant coefficients for MKT, SMB, HML
and HMU The t stat value for MKT is 1.130185, SMB is , 0.788044, HML is 0.121548
47
and HMU is , -0.87915. It means they don’t explain returns of S/H stocks. The value of
R2 is 0.13
In small cap low book to market portfolio, dependent variable S/L has been found to be
insignificantly related with independent variables MKT, SMB, HML and HMU. The t
values for MKT, SMB, HML and HMU are 0.295097, 1.058856, -0.13862 and -1.03704
respectively. The reported value of R2 is 0.12.
The existence of market risk premium along with size and distress risk factor has been not
supported in big cap high book to market B/H portfolio with R2 of 0.32 The MKT, SMB
and HMU have insignificant relationship with t-stat values of 1.421954, 0.578952 and 1.79898 respectively whereas HML has positive and significant relationship with stocks
returns and its reported t value is 3.536106.
In portfolio big cap low book to market B/L results don’t support the existence of MKT
and SMB. HML and HMU have positive and negative significant relationship with
dependent variable B/L and have the t stat values of 2.931904, -5.1583 respectively.
However MKT and SMB have been found to have insignificant relationship with stock
returns with t value of 0.895373, -0.32087. The value of R2 in this regression is 0.34.
For dependent variable small cap high book to market distress S/H/D portfolio the
relationship of explanatory variables MKT, SMB, HML and HMU is insignificant with t
values of 0.689436, 0.188181, 1.025069, 0.270367 respectively thus no impact on S/H/D
with value of R2 equals to -0.01.
48
In small cap high book to market un distress S/H/UD portfolio, results does not validate
the presence of market premium, SMB, HML and HMU. The t stat value for MKT
is0.900049, SMB is -0.44393, HML is 0.528852 and HMU is -1.65492. It means they
don’t explain returns of S/H/UD stocks. The value of R2 is 0.07.
In small cap low book to market distress portfolio, dependent variable S/L/D has been
found to be positively and significantly related with SMB with t value , 2.80035 and
insignificantly related with independent variables MKT, HML and HMU. The t values for
MKT, HML and HMU are 1.414421, -0.44348 and -1.3903 respectively. The reported
value of R2 is 0.16.
The existence of market risk premium along with size, value and distress risk factor does
not supported in small cap low book to market un distress S/L/UD portfolio with R2 of
0.05 The MKT, SMB, HML and HMU have insignificant relationship with t-stat values
of 1.275677, 0.49525, 1.449149, 0.247445 respectively.
In portfolio big cap high book to market distress portfolio B/H/D results do not support
the existence of MKT, SMB and HML. HMU has negative significant relationship with
dependent variable B/H/D and have the t stat values of -2.1201. However MKT, SMB
and HML have insignificant relationship with stock returns with t value of -0.34231,
0.131631 and 1.74895 respectively. R2 is 0.06.
For dependent variable big cap high book to market un distress B/H/UD portfolio the
explanatory variables MKT, SMB, HML and HMU are insignificant with t values of
49
1.253448, 1.861916, -0.17714, -0.95679 respectively thus no impact on stock returns. R2
equals to -0.00.
In big cap low book to market distress B/L/D portfolio, results does not validate the
presence of market premium, SMB, HML and HMU. The t stat value for MKT is 0.48704, SMB is -0.21631, HML is -0.48589 and HMU is -0.34306. It means they don’t
explain returns of B/L/D stocks. The value of R2 is -0.08.
In big cap low book to market un distress portfolio, dependent variable B/L/UD has been
found insignificantly related with MKT, SMB, HML and HMU. The t values for MKT,
SMB, HML and HMU are -0.41211, 0.428375, -0.52707, -0.10046 respectively. The
reported value of R2 is -0.04.
4.5 Discussion:
The existing literature postulates that distressed firms are small firms, and those having
high B/M and these factors are enough to capture the risk of distress factor that is
overlooked by market factor. Though, the pricing of default risk in equity returns of
Pakistan, which is explicitly focused by this paper, has been inefficiently addressed to
date. We use method of z-score, a measure which is accounting-based and it is known to
be a strong indicator of financial distress from which firms suffer, it can be used as proxy
for bankruptcy risk.
Results we find opposing to the factor of distress hypothesis, stocks of distressed
portfolios make lower returns as compared to portfolios of non-distressed firms. Same
results concluded by Dichev (1998) on data of sample taken by him. It is argued by Fama
50
& French (1995) that only a small share of financially distressed stocks in reality go
bankrupt, while vast majority still surviving, this can be a strategy that investors invest in
distressed stocks to earn greater returns. However, proposed study empirically find that
on average proportion of firm is 18 which are reported as distressed firms for the period
of sample and these firms go bankrupt as share of default firms is sufficient enough for
driving the realized return down to implement the strategy of making investment in stocks
of distressed portfolios.
Vassalou & Xing (2002) and Griffin & Lemmon (2002) predicted that effects of size and
B/M are determined by stocks of high risk of bankruptcy. However, they make sorting in
sequence and results might be sensitive to the procedure of sorting. Further, Vassalou &
Xing’s model of contingent-claims for assessing likelihood of bankruptcy has variable of
key interest size, the proposed study also apply sorting but to identify distressed firms
stocks are sorted on the basis of Z score and its evident from results of our model of zthat for small cap firms having high book to market and financially distress portfolio
S/H/D size premium, value premium and distress premium is note ably significant which
relate our results with previous literature that small firms are risky and they are more
vulnerable to financial shocks they don’t have stable financial structure and due to their
riskiness investor claim high risk adjusted returns. It also indicate that distress premium is
priced in equity Market of Pakistan.
Table 1 reports Statistical properties of the variables of four factor model. Table 1
indicates that average return on market portfolio is high as compared to other portfolio
but negative it may be due to one reason that equity market of Pakistan perform below
51
standard for the time period of 2005 to 2012. Average return of big portfolio is high in
comparison to low portfolio which means value stocks (having high B/M) outperformed
growth stocks. On average stock returns of big portfolio are high than stocks of small size
which mean negative SMB.
In Table 2 it is indicated that portfolios of B/H and S/H have high returns and are high
risky. However, B/H found to be efficient as it offers greater returns at low risk level. In
segments of small and big stocks high B/M outperformed low B/M stocks. Returns of B/L
are low then B/H, though it is supported as empirically evidence on subject is that stocks
of high cap firm earn low returns and stocks having low ratio of book to market
underperform in relate to stocks having high ratio of book to market. (Stattman, 1980).
Standard Deviation is supporting justification of risk based on higher returns for all
portfolios.
If we make analysis of multivariate regression results it is worth to mention here that size
premium is find significant for portfolios of all stocks except B/H, B/L and S/H/D.
Therefore, factor of SMB cannot ignored whenever to make decisions at economic level.
Though market premium is significantly positively related to returns of all portfolio and
this is constant with conventional model of asset pricing. Therefore, it is perceived that
factor of market return can expressively explain returns of equity but it is unable to fully
explain the returns. So size, value and distress premium captures the returns which are
ignored by market factor.
52
Chapter 5
CONCLUSION
5. Conclusion:
The basic motive behind that study is to find out the working mechanism of asset pricing
keeping in view the relationship between size, value and stocks return in the capital
market of Pakistan. For this two broader categories of factors are used named as Market
specific Factors and Firm specific factors.In market specific factor Market Premium is
taken under consideration for the Firm specific Factors Size Premium, value Premium,
Profitability Premium, Investment and free cash flow Premium are taken under
consideration.After the deep study the best suited model for this study was Fama and
French model.Various tests were performed on the collected data, as it was five factor
model. There were four objectives of this study. First was to investigate persistence of
already tested size and value anomalies in emerging market of Pakistan. Second was to
investigate the impact of profitability premium (RMW) on excess portfolio returns. Third was to
examine the impact of investment premium (CMA) on excess portfolio returns. Fourth was to
study whether the free cash flow anomaly exists as a risk effecting the excess portfolio returns in
the context of Karachi stock exchange
53
This study explores the mechanism of asset pricing by examining the relationship
between size, value, distress and stocks returns in equity market of Pakistan for time
period of June 2005 to June 2012. For this purpose monthly prices of stocks are used. To
discover the combined effect of four factors namely market premium, size premium,
value premium and distress premium a new factor HMU has been added to three factor
model of Fama and French. Testation of this new four factor model has been done in this
study. The main objective of this study was to check whether distress risk priced in equity
market of Pakistan or not. In this study, we show that the distress risk-return relation is
dynamic. In the cross section of stocks, recent innovations in distress risk are negatively
related to subsequent return. We explore the relation between distress risk and the size
and book-to-market anomalies. We find that distress risk is a plausible explanation of the
anomalous returns of the SMB portfolio. However, we find no evidence that distress risk
can explain the anomalous returns of the HML portfolio. Distress sensitivity is came out
significant and positive for small cap firms and stocks have high book to market. Thus we
conclude that there is a financial constraint factor, an identifiable independent common
source of economic shocks to firm value. The evidence suggests that financial constraints
do affect firm value and that the severity of constraints varies over time. Second, our
investigation of the role of financial constraints in asset pricing reveals the surprising
result that constrained firms earn lower returns than un constrained firms, a result not
explainable using existing asset-pricing models. Third, financially constrained firms do
not have returns that are significantly more cyclical than average. Consider the following
explanation of the size effect in asset pricing, the fact that small firms have high returns
and have common return variation. Small firms have more precarious access to external
54
finance and are more exposed to variations in credit conditions and to macroeconomic
fluctuations generally. Therefore, investors need to be compensated for holding small
stocks. This explanation is attractive because it provides an economically meaningful
story that is consistent with the following different pieces of evidence: Small firms have
high returns, are more cyclical, have higher loadings on monetary policy, and tend to be
more financial constrained than other firms. Unfortunately, the results in this article
suggest that this explanation is wrong. Unlike small firms, financially distress stocks do
not earn high returns and are not particularly exposed to macroeconomic risk or credit
conditions. Distress stocks outperform un distress stocks. Distress factor include credit
worthiness analysis of firms for financial and non-financial institutions, identification of
undesirable investment risk for portfolio managers and individual investors and to aid in
more effective internal and external audits of firms with respect to going-concern
considerations, among others. Size premium is found significant for all portfolios except
big high, big low and big high distress. So size premium also hold in Pakistani market.
However, value premium show inconsistency. Average returns of portfolios sorted on the
base of Size indicate small portfolios have high risk as well as high returns but average of
small and big portfolios returns reports contradictory results. It can be result of anomalous
behavior of market in period of 2005 to 2006. The main findings of the study reveal that
four factor model markedly explains the returns of portfolios. Premiums for distress come
negative, so we cannot get the accurate results of second pass regression are contradictory
to our hypothesis. Griffin and Lemmon (2002) also find a negative relationship between
financial distress as proxied by Ohlson's (1980) O-score and subsequent returns, even
after correcting for the stochastic structure of returns by means of a Fama-French 3
55
factors model. In addition, they show that this relationship is driven by firms with a low
book to market (BE/ME) ratio. Garlappi et al. (2005) find that the negative relationship
between probability of default and returns is restricted to the firms with low BE/ME ratio.
Campbell et al. (2005) also observe a maximum underperformance for low BE/ME firms,
although underperformance is also high in the subset of the firms with the very highest
BE/ME ratios. There-fore, decision makers should wisely account for these factors in
making any decisions about investment or from which sources financing is possible and
about valuation. However results of second pass regression are substantially insignificant
for Pakistani market which depicts that current coefficients of four factors that are market,
size, value and distress are unable to explain the future returns, though four factor model
and conventional CAPM is significant as they explain the current stock returns of equity
market of Pakistan.
5.1 Research Limitations:
This study has some limitations just like other empirical studies which can consider as
point of start for future research.
 The availability of data is key concern here and this accessibility designed this
study for only Pakistani market.
 Unfortunately this study did not have opportunity to take under consideration
other markets in order to assess that interpretations drawn from this empirical
study can also applicable on different markets and samples.
 Limitation of time period is also noteworthy.
 In this study only model of three factor is taken now five factor has also come.
56
5.2 Future Directions: One way to extend this study is to examine the relationship
between risk of financial distress and returns on stocks in an economy under two different
states one is in good state and other is bad. This study assume that non-diversifiable risk
specifies only sensitivity of single stock or stocks in the form of portfolios to the
movements of broad market. However systematic risk can be define in form of whole
economy and its sensitivity towards shocks which are macroeconomic in nature to check
whether this new model apply provisionally on the economy’s state. Another expansion
can be to build a model in which interrelation between risk of financial distress and
recovery from this situation can be investigated. The most exciting challenge for
researchers in the area of valuation of corporations can be integration of individual
volatility with discount rate for the purpose of valuation of those stocks which are
distressed. This field of financial distress in corporations is still underdeveloped area of
empirical and academic research and it call practitioners and scholars to keep
investigating this new interesting and encouraging arena of modern finance.
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