The Risk and Return Relations: Evidence from Pakistani Stock Market Syed Hamid Ali Shah 1 and Dr. Attaullah Shah 2 1 Syed Hamid Ali Shah is a Faculty Member at Quaid-e-Azam College of Commerce, University of Peshawar Email: [email protected]2 Dr. Attaullah Shah is a Faculty Member at the Institute of Management Sciences, Peshawar Email: [email protected]
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The Risk and Return Relations: Evidence from Pakistani Stock
Market
Syed Hamid Ali Shah1
and
Dr. Attaullah Shah2
1 Syed Hamid Ali Shah is a Faculty Member at Quaid-e-Azam College of Commerce, University of Peshawar Email: [email protected] 2 Dr. Attaullah Shah is a Faculty Member at the Institute of Management Sciences, Peshawar Email: [email protected]
It is generally argued that risk and stocks returns relationship in emerging markets around the globe is
different from that observed in developed stocks markets. Moreover, in Pakistan investors are not well-
diversified due to large family ownership, group ownership, shallow market, and thin trading volume etc. This
gives us fair justification to believe that both systematic and unsystematic risks are relevant, and hence beta
(measure of systematic risk) under-estimates the risk premium. Different measures of risk such as beta,
systematic risk, unsystematic risk, and total risk are used as independent variables to investigate risk and
return relationship. The data set covers span of period from January 5, 2004 to October 13, 2008 and the
sample consists of 194 non-financial firms listed on KSE. It is concluded that investors in the Pakistani stock
markets do not base their assets’ pricing decisions on these risk measures. The results could not confirm beta
and returns relation as proposed by CAPM. It is suggested that investors shall not rely only on the results of
CAPM and shall also use alternate asset pricing model in order to make right investment decisions.
Key Words: CAPM, returns, risk, rolling regression, time series regression, cross-section regression,
The Risk and Return Relations: Evidence from Pakistani Stock Market
1. Introduction
Given today’s competitive and dynamic business environment corporate risk management is important due to
its potential implications on stock prices and investors’ returns cannot be denied. As accepted at large, the
prime objective of any business firm is the share value maximization (Damodaran, 1997); in the long run this
is line with the interests of almost all the stakeholders of the firm.
Pakistani stock market is one of the emerging markets of the world. It is generally argued that risk and stocks
returns relationship in emerging markets around the globe is different from that observed in developed stocks
markets. Harvey (1995) in the case of emerging markets reported the presence of stock prices volatility,
unexpected high returns and serial autocorrelation in returns. Harvey also documented presence of
leptokurtosis, skewness and volatility clustering in these markets. The later characteristics were reported in the
case of Pakistan in the Karachi Stock Exchange (KSE) (see e.g., Hussain and Uppal, 1998). Javid (2009)
indicated to the issue of determination of expected risk and return for investors in Pakistani stock market. On
the basis of unconditional and conditional higher-moment capital asset pricing model (CAPM), she concluded
that three-moment CAPM could explain the risk-return relation relatively better; however both the systematic
covariance and cokurtosis contribution to explain asset prices in KSE was marginal. Moreover, in Pakistan
investors are not well-diversified for several reasons such as family ownership, group ownership, shallow
market, and thin trading volume etc. This gives us fair justification to believe that both systematic and
unsystematic risks are relevant, and hence beta (measure of systematic risk) under-estimates the risk premium.
The results of this study shall determine the degree of receptiveness of stocks’ returns of Pakistani listed
companies to market-wide factors and to factors unique to a firm or industry. Indeed variety of stakeholders
for example, financial analysts, investors and business managers etc. might have interest in such analysis for
variety of reasons.
The main purpose of this study is to investigate, in the peculiar Pakistani Stock Market; that whether only the
systematic risk factor is relevant or the specific risk component is also of matter of concern for investors. In
this study Sharpe (1965) Lintner (1966) market equilibrium model is estimated using different approaches to
determine how well it can explain the stock price behavior in the Pakistan largest stock market i.e. KSE.
In the simplest and perfect environment discounted value of future cash flows (however never certain) can be
considered the appropriate value of a firm (returns to investors). Thus increasing these cash flows will mean
increasing returns but not without increasing risk as argued by Shimko and Humphreys (1998). They argued
that increasing cash flows by grabbing growth opportunities to increase value and returns, usually call for
taking more risk. On the other hand financial literature narrates that investor’s act such that to maximize their
returns for certain level of risk or reduce their risks given certain level of returns (Clark, 1972). This
relationship between return and risk has been the focus of the literature about asset pricing in financial capital
markets. Blume (1971) said that this risk dimension in investment decision is so important that there is no
need to convince people to include it in their analysis.
According to the modern portfolio theory of Markovitz (1952), expected rate of return can be maximized for
given level of risk by pooling different assets (however with lesser covariance) together or putting in other
words for a given expected rate of return its accompanying risk can be minimized through diversification. One
of the important assumptions of this theory is that investors evaluate risk as a whole rather than considering
the risk associated with an individual security. However diversification does not remove all types of risks3,
though diversification helps to reduce total risk of an investor. Brealey (1969) stated that variations in market-
wide conditions cause fluctuations in financial assets’ prices and this variability of prices cannot be
completely diversified. The part of risk which can be diversified is termed as unsystematic risk. This
unsystematic risk is also called specific risk being specific to the firm or industry in which the firm operates.
The non-diversifiable risk component is called systematic risk. This market-wide risk causes variation in
assets’ prices in the whole range of a market and results due to changes in broad economic environment
(Cohen, Edward, and Arthur, 1973). Moreover, it is generally believed that investment markets do not
compensate for specific risk (firm/ business type associated risk) and only reward the systematic risk or
market-wide risk for example as modeled by Sharpe (1964). Further, Brealey (1969) stated that most plausible
3Risk here is defined as the degree of uncertainty of an outcome that can be assigned with some objective or subjective probability and thus can be quantified; more specifically here it is the variance of past rates of return.
addition to a portfolio is the asset that shows the minimum covariance with the market but if otherwise desired
by an investor; say for example opting for a security that varies exactly with the market.
Fama and McBeth (1973) supported the traditional CAPM in their empirical study. However other studies
have shown that beta is not the only relevant factors and other factors such as size, earnings/price ratio, cash-
flow/price ratio, book-to-market equity ratio, and past sales growth significantly explain variation in average
stock returns (see for example, Ball, 1978; Banz, 1981; Basu, 1977; Chan, Hamao, and Lakonishok, 1991;
Fama and French, 1992, 1996a; Lakonishok and Shapiro, 1984).
To judge the reliability of beta, Pettengill, Sundaram, and Mathur (1995) proposed following procedure. They
argued that there is the probability that realized return can be lower than the risk-free return. In fact, if
investors are certain that realized return would be greater than the risk-free rate then they would not hold risk-
free assets. Given beta as risk measure postulates that relatively high beta assets will have high risk and vice
versa. And when the realized market returns are greater than risk-free return (so called up market condition)
then beta shall be positively related to the realized returns. And if the realized market returns are negative (so
called down market condition) then beta shall be negatively related to realized returns. Consistent with this
conditional framework in US stock market, they showed strong support for beta. More recently Tang and
Shum (2004) investigated data of Singapore stock market from April 1986 to December 1998 and reported
that beta is significantly related to ex-post returns but have little explanatory power. Addition of stocks
skewness and kurtosis provided however little incremental benefits. But when they applied the conditional
framework (up and down markets) the explanatory power increased more than 100 times. Moreover their
results indicated positive (negative) relation between beta and realized returns when market excess returns
were positive (negative). The results hold when other stock characteristics such as unsystematic risk, total risk
and kurtosis are added separately to the beta and return relation during up and down markets with increased
explanatory power. They also reported that unsystematic risk has an impact in pricing risky assets. They
concluded that when pricing risk, assets beta as well as other stock characteristics shall also be considered as
investors do not necessarily hold diversified portfolios.
Section 1 introduces the study. Section 2 describes the relevant and brief literature review of the topic. Section
3 introduces the methodology and Section 4 discusses the results and concludes.
2. Literature Review
Bachelier (1900) stated that past, present and future discounted events are related to financial assets prices
however do not explain changes in prices of these assets. Later, building on the idea of the Bachelier,
Markowitz (1952) proposed his famous theory of portfolio diversification. Markpwitz (1991) narrated that the
idea of portfolio theory blinked in his mind while he was reading “the theory of investment value” 4 by
Williams (1938). According to the modern portfolio theory of Markovitz, the expected rate of return can be
maximized for given level of risk by pooling different assets (however with lesser covariance) together or
putting in other words for a given expected rate of return its accompanying risk can be minimized through
diversification. One of the important assumptions of this theory is that investors evaluate risk as a whole
rather than considering the risk associated with an individual security. He stated that by adding securities that
have lesser covariance will reduce risk of the portfolio in more noticeable form. He explained that individuals
can identify set of portfolios, for a given level of risk with the highest expected returns such that this given
risk will be the lowest for these returns. The resultant curve of these portfolios is termed as efficient frontier
and these are the most economical set of portfolios for individuals who care about the tradeoff between risk
and expected return.
The idea of diversification by the investors was also coined by Arrow (1953). In the context of his theory of
general equilibrium with incomplete asset markets, Arrow contended that in a complete asset market
individuals can cover any loss. He added that individual may willingly opt for risk if an economy exhibits
such characteristics. In a manner he suggested to hold diversified portfolios. On the basis of their empirical
investigation Evans and Archer (1968) showed that by adding just ten or more securities the effect of
diversification is achieved thus concluded that diversification process takes place quickly.
4 William (1938) stated that value of stock shall equal to discounted value of future dividend streams. And due to the inherent uncertainty in it; Markowitz took this value as expected value.
Tobin (1958) explained in the light of separation theorem (assuming that investors can borrow or lend at risk
free rate) that which efficient portfolio is the optimal one, for investors’ given level of risk propensity. He
stated that individuals would allocate funds to cash or risk free assets subject to his/her risk preferences
(degree of their risk propensity). Tobin added that the single optimal risky portfolio is the market portfolio
which is portfolio with the maximum expected return and minimum associated risk, and all other portfolios on
the efficient frontier will have relatively higher risk or lower expected return.
Although Tobin did simplify the process of portfolio selection but Morkovitz model was still not fully
utilized. Soon after, Sharpe (1964), Mossin (1966), and Litner (1965) made their historic contributions that
produced the capital asset pricing model (CAPM). The simple CAPM equation can be stated as:
Ri = Rf + β (Rm-Rf)
Where Ri is return on stock I; Rf is the risk free rate; Rm is the return on market portfolio; and β is the
systematic risk (beta) of stock i. Note that (Rm – Rf) is the market risk premium.
CAPM signifies relationship between financial assets’ risk and return. According to this model, security
required rate of return is independent of specific risk for it can be diversified and eliminated by investors.
These investors are rational and hold the efficient portfolios. Under the CAPM, systematic or market risk is
the relevant risk that relates return of individual and/or portfolio of risky securities to that of market portfolio
in linear fashion. The CAPM model assumes that (i) investors are risk averse, (ii) have homogeneous
expectations of maximizing expected utility, (iii) they may borrow or lend unlimited amounts of risk free asset
at a constant rate, (iv) all assets are divisible and priced efficiently, and (v) markets are perfect and frictionless
for all investors. King (1966) investigated the returns of 63 shares from about six different industries for the
period 1927-1960 and reported that share prices co-varied with the overall market return.
Other financial management scientists tried to relax these assumptions and thus resulted in producing
modified versions of CAPM. Brennan (1970) showed in the presence of taxes that the original CAPM is valid.
Mayers (1972) reported that the model structure is the same is that of the CAPM when non-traded stocks are
incorporated in the market portfolio. Black (1972) introduced his most cited zero-beta CAPM while relaxing
the assumption of riskless borrowing availability. Black (1974) and Solnik (1974) conducted their studies
while encompassing international investments in their studies and concluded that CAPM is reliable. The
model is reported to be robust even if the assumption pertaining to investors’ homogenous return expectations
are relaxed (William, 1977). The practical outcome of these studies now is that people hold pool of versions
of risk free, risky assets and assets that move with the market to insure their expected returns.
Many other studies however examined the stock returns co-movement with one another with the view of their
sensitivity to the overall market, for example Roll and Ross (1980) and Chen, Roll and Ross (1986). These
studies introduced multi factors models rather than using single factor model of Sharpe (1964). Similarly
CAPM cannot explain expected return and risk relationship in a dynamic setting and will ask for more betas.
In this context Merton (1973) devised an intertemporal CAPM. He elaborated that an investor who is
currently exposed to one interest rate and in future he/ she expects some other interest rate will have different
portfolios demands and cannot rely upon a single horizon expectations.
The discussion though very briefly, however, describes that there are methodological deficiencies to express
correctly the relationship between expected returns and the market risk factor. The various interested parties
will have to make use of one or the other form of CAPM or APT till one more valid and reliable model
introduces. More relevant to this study; from the above review one thing becomes very clear and it is the
convergence of understanding that there is one component of total risk which is diversifiable and there is
another component known as systematic risk which in non-diversifiable. It is this systematic risk which is
priced by the market.
Fama and MacBeth (1973) investigated US stock market data from 1935 to 1968 and concluded that on
average, there is a positive tradeoff between risk and return which is systematically affected only by beta.
Therefore they contended that these results support CAPM. However as the risk and return was not
significant across sub-periods so this was the case of weak support; as was so argued by Schwert (1983).
Reinganum (1981) against the efficacy of CAPM found that the cross-sectional differences in estimated
portfolio betas based on common market indices and the differences in returns of these portfolios are not
reliably related. They observed that the returns are not significantly higher for high-beta portfolios relative to
low-beta portfolios.
In line with the CAPM, Hawawini and Michel (1982) in the Brussels stock market observed that investors’
returns are explained by systematic risk but not by unsystematic risk. Hawawini, Michel, and Viallet (1983)
reported that average returns are related to systematic risk of the portfolio; however they also observed
negative relation between beta and returns due to the poor performance of the French stock market.
In Their study, Tinic and West (1984) showed that in the month of January risk premium is higher and when
they excluded January data reported that risk premiums are statistically insignificant. Lakonis hok and Shapiro
(1986) included firm size in the risk and return analysis and concluded that size significantly explain the
relationship but systematic or alternative (residual standard deviation) risk measure cannot explain the cross -
sectional variation in returns. Haugen and Baker (1991) investigated R-R relationship of the largest 1000 US
stocks for the period of 1972 – 1989 and reported that low-risk stocks have abnormally high returns. These
results contradict what the CAPM elucidates. Fama and French (1992) showed that beta is insignificantly
related to average monthly returns of NYSE stocks and concluded that CAPM is no more reliable and that
market capitalization and the ratio of book value to market value are the more appropriate factors. Fama and
French (1996b) rejected beta to sufficiently explain returns.
Chui and Wei (1998) used data of Hong Kong, Korea, Malaysia, Taiwan and Thailand stock markets to
analyze the risk and return link and found that stock returns are more related to size effect and book-to-market
ratio. Using the conditional framework procedure of Pttengill et al. (1995); Isakov (1999) investigated the
Swiss stock market and reported that beta is statistically significant and carried the expected sign and
therefore concluded that beta is still reliable.
The above stated studies generally show that beta is reliable under conditional CAPM but under unconditional
CAPM beta lacks in power to explain variation in realized stock returns. This study is an effort to explore this
R-R relationship under both situations.
As stated in the introduction that the purpose of this article is to measure systematic, unsystematic, and total
risk of the rates of return of the sample securities and investigate if risks other than beta are involved in
pricing securities in the Pakistani stock market? The unsystematic securities’ risk measure shall suggest about
the relative volatility whereas the systematic risk measure shall unfold the tendency of covariance of these
securities with the market. Whereas the total risk shall explain if the individual investors are not diversified
then this risk measure shall have more explanatory power in the world of CAPM.
3. Methodology
3.1 Sample and Data Sources
Weekly Data for the study on the variables of interest is downloaded from the website of Karachi Stock
Exchange (KSE). Data of 194 non-financial firms listed on KSE were acquired for a period of 244 weeks from
January 05, 2004 to October 13, 2008.
3.2 The Model
This study uses multiple methods to investigate risk and return (R-R) relation. In the first method the Fama
and McBeth (1973) procedure is adopted. The procedure is termed as cross-sectional regression. The second
method is based on the rolling regression (RRG) estimation. Time series regression is also used to predict R-R
relationship. The methods are briefly explained in the following text.
3.2.1 Cross-sectional Regression
In step one the entire length of sample, 244 weeks, is divided into two sub-periods and individual securities’
betas, total risk (TR), systematic risk (SR), and unsystematic risk (UR) for the first 72 weeks of the total
weeks are calculated from January 5, 2004 to May 30, 2005. The procedures and formulae used to compute
these values are described in the following text. Moreover, the rate of return of stocks and the market rate of
returns’ calculated through formulae are also stated.
Sharpe (1964) market model is used to measure risk component. As per this model expected return of a
security is a linear function of a constant rate (risk free rate) and the expected return on a market factor. The
proxy KSE100-Index is used to represent the theoretical market portfolio. The model is:
Rit = α + β Rmt + єit ------------------------ (A)
Rit is the rate of return of stock i at time t. α is the y- intercept. β is the slope of the regression line and
represent relative systematic risk component of the total risk of a security. Rm is the market rate of return at
time t and єit is the error term of the regression at time t.
Equation (A) produces a regression line. This line is called characteristic line and shows relationship between
individual asset’s return and market return for the particular nature of systematic and unsystematic risks of
that security. Holding Rm equal to zero, the y-intercept α is then the security rate of return. β measures
security’s rate of return volatility with respect to the change in overall market rate of return. β, thus is an index
of systematic risk of the security. β if equals one then a security required rate of return will be equal to the
market rate of return. β greater than one mean that the security is riskier than market portfolio and its required
rate of return shall be higher than the market rate of return and vice versa. Єit, the error term represents the
component risk attributable to characteristics unique to the firm or industry. In the regression results the
coefficient of determination (R2) shows percentage changes in the security returns explained by changes in the
market index. Thus it is used to measures the percentage of total risk accounted for by systematic risk (Clark,
1972).
Returns on securities and markets are computed as explained below.
Rit = ln(Pt+1/ Pt) ------------------------------ (B)
Here Pt+1 and Pt represent end of period t, and beginning of period t stock prices respectively.