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: hamidtoru@gmail.com 2 Dr. Attaullah Shah is a Faculty Member at the Institute of Management Sciences, Peshawar Email: attaullah.shah@imsciences.edu.pk

Abstract

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.

Rm = ln(Mt+1/ Mt) ----------------------------- (C)

Mt+1 is the index value at the end of time period t and Mt is the index value at the beginning of period t.

Total risk (TR) is calculated as variance of the security and it is calculated through the following formula:

σi2 = Σ (Rit – Ri)2/ n-1

σi2 is the variance of security i (variance of market) Rit is the rate of return of stock i (rate of return of market

index) at time t. Ri is the average rate of return of security i (average market index return).

Systematic risk (SR) can be calculated either by multiplying beta square with variance of market or by

multiplying R2 with variance of individual security. In this study the later procedure is adopted to compute

SR. SR is subtracted from the TR to calculate the unsystematic risk (UR) (James and Philip, 1978). In step

two, individual securities’ and market returns are calculated for the period from June 6, 2005 to October 13,

2008 with the help of the formulae as stated above. Then 171 sets of cross-sectional regressions are run to

predict the securities returns with the help of various risk measures estimated in step one above. Individual

securities’ returns are taken as dependent variable. Finally in step three, average of the weekly slopes

(coefficients) of Beta, TR, and UR are computed and tested with the help of t-statistics.

3.2.2 Rolling Regression

Rolling regression is estimated using least-square estimation technique. It fits a linear equation for time series

data by estimating coefficients over more than one time, however a fixed length of sample is utilized each

time. In doing so first observation of the previous sample is dropped and new observation at the end of that

sample is included to estimate coefficient of the new sample. This technique is usually used to test model

stability overtime as it can capture time varying characteristics of parameters. Due to fluctuations and

variations in economic conditions, the assumption that model parameters remain constant overtime is,

however, not admissible. In estimating expected returns with the help of CAPM, the proponents of this model

argue that beta is instable and hence rolling regression technique is a preferable way to capture its time

varying nature.

Under this technique, step one (explained in section 3.2.1) is repeated. Then numbers of regressions are run by

rolling the initial regression period forward, that is each time new week is added and the first week of the

previous regression is discarded such that up to period 243 rd total 171 regressions are run and the coefficients

are averaged and reported in Table 2. Panel A of the table reports results generated with the help of stata.

In addition to the above the whole period of the study is divided in three sub sets. Then step 1 is repeated for

first 72 weeks (Jan 5, 2004 to May 30, 2005) and thirty nine equally weighted portfolios, with equal portfolio

sizes (five stocks in each) are formed on the basis of betas estimated in the first step. The portfolios were so

formed while arranging betas in descending order. Thus the last portfolio stocks’ betas were the smallest and

those for the first portfolio the stocks were holding the largest betas. Portfolios returns are regressed against

the market returns and slopes of these portfolios are estimated and SR, UR, and TR of portfolios are also

computed for the period from week 73rd to week 168th (Jan 6, 2005 to April 16, 2007). In the final stage,

returns of these 39 portfolios are matched with their corresponding portfolios’ betas and SR obtained from the

estimation period. The process is repeated in the way that each time the first week’s observation of the initial

regression is dropped and new week of the testing period is added. The process is repeated for the whole

testing period till Oct 13, 2008. The weekly returns of the portfolios are then regressed on their corresponding

estimated risk coefficients. Portfolios weekly returns are used in the regression such that we estimated one set

of set of slope coefficients for parameters.

3.3.3 Time Series Regression

The whole time period is divided in three sub-periods (almost of equal numbers of weeks). Betas, SR, UR,

and TR are estimated in the first period (January 5, 2004 to May 30, 2005). Then securities are ranked on the

basis of beta values in descending order. In the second period 39 portfolios of same sizes are formed.

Portfolios returns are calculated for the testing period. These time varying betas, SR, UR, and TR are matched

with the corresponding returns of the portfolios. Portfolio returns are used as dependent and SR, UR, and TR

are used as independent variables in the so called stacked cross-sectional regression. The slope coefficients of

the variable(s) if appears greater than zero then it can be inferred that the variable(s) is priced by the market.

4. Results and Discussion

This section contains the results obtained from the three different methods. In addition results of concurrent

regression estimation are also presented. The concurrent regressions are based on observations on securities’

returns and estimated beta values of the same period (January 5, 2004 to May 30, 2005).

Table 1 reports results of cross-sectional regression using stata software. First column contains the equations;

second column shows average value of the coefficients of independent variables along with respective average

standard errors and t values. These results indicate that beta, total risk and systematic risk could not explain

the security returns. These findings are not in line with the CAPM. However the findings are not unique

particularly in the case of a negative and insignificant beta. For example Hawawini et al., (1983) reported

negative beta for poor performing French stock market. Numbers of different studies reported such instances.

Fama and McBeth (1973) though reported positive and significant beta for the whole period but the beta was

insignificant in the sub-period regressions. There are studies those rejected the practicality of beta and

suggested that other measures can explain returns more efficiently (see e.g. Chan, Hamao, and Lakonishok,

1991; Fama and French, 1992, 1996a). However alternative reason for the evidence of insignificant and/or

negative beta in so called unconditional regression estimation is given by Pettengill et al., (1995). They

proposed an alternative, conditional framework, method to test R-R relationship. The insignificant coefficient

of TR suggests that probably there are some other factors which are valued by investors in the Pakistani stock

markets.

Table 1: Cross-Sectional Regressions – R-R Relationship

Equation Coeff. Std. Errors t-Stat Remarks

Ri = αo+α1 β+ єi -0.0010 0.0101 -0.1001 Insignificant

Ri = αo+α1SR+ єi -0.4556 0.7502 -0.61 Insignificant

Ri = αo+α1 TR+ єi -0.0089 0.0022 -0.43 Insignificant

Note: Total 171 regressions from June 6, 2005 to October 13, 2008 are run for each of the above equations

and then the average values of the coefficients of beta (β), systematic risk (SR) and total risk (TR) and

standard errors along with t statistics are reported.

It is generally argued that when testing reliability of beta on the CAPM, portfolios returns shall be preferred

due to its lower estimation errors and contained specific risks. Therefore these results are reported in Panel-B

of Table 2. Here portfolios’ returns are used as dependent variable. However results reported in Table 2 are

not different from those reported in Table 1. Systematic risk and relative measure of systematic risk (beta)

both are not used by investors when pricing assets.

Table 2: Rolling Regressions – R-R Relationship

Equation Coeff. Std. Errors t-Stat Remarks

Panel A

Rit =αo+α1SRit -1.7246 1.1843 -1.46 Insignificant

Rit =αo+α1TRit -0.2345 0.1532 -1.53 Insignificant

Rit =αo+α1βit -0.0008 0.0028 -0.31 Insignificant

Rit =αo+α1SRit+α2URit α1 α2

Coeff. -1.4401 -0.2000

Std. Errors 1.1601 0.1535

t-Stat -1.24 -1.30

Remarks Insignifican

t

Insignifican

t

Panel B Coeff. Std. Errors t-Stat Remarks

Rpit =αo+α1βpit -0.0054 0.0037 -1.45 Insignificant

Rpit

=αo+α1βpit+α2TRpit

α1 α2

Coeff. -0.0056 0.0813

Std. Errors 0.0043 1.6378

t-Stat -1.31 0.05

Remarks Insignifican

t

Insignifican

t

Note: Panel A presents average values of coefficients of 171 regressions (rolling) estimated with stata. In

panel B, using stata, average values of coefficients of beta, beta and TR from 75 regressions are reported; here

rolling regression procedure is used and portfolio returns are taken as dependent variable.

Table 3 carries test statistics of time series regression. Four different equations, with respect to independent

variable, are estimated. These equations are shown in the first column from the left. Second and third columns

present estimated values of constant terms with their associated t-statistics respectively. In all cases the

constant term is positive but insignificant. This is in line with the CAPM. Column four and five (from left to

right) shows coefficient of SR carries negative sign and is insignificant whether used separately or with TR.

Values of test statistics on TR are reported in column six and seven. Portfolios’ returns are once regressed

against TR alone and then against TR as well SR at the same time. In each case TR is negatively and

insignificantly associated. Again these findings are not different from those reported in Table 2. The last two

columns suggest that unsystematic risk is negatively but insignificantly related to portfolio returns.

Table 3: Time Series Regression – R-R Relationship

Equation α1t –

Statα2

t –

Statα3

t –

Stat

Rpit = αo+α1 SRpit-

0.0037

-

0.75- - - -

αo+α1 SRpit + α2

TRpit

-

0.0009

-

0.04

-

0.0020

-

0.11- -

αo+α2 TRpit-

0.0026

-

0.75

αo+α3 URpit-

0.0069-0.67

Note: Total numbers of observations were 5772. Coefficients of systematic (SR), unsystematic (UR), and total

risk (TR) along with their respective t-statistics are reported.

Table 4 presents average values of coefficients, standard errors, and t-statistics of the variables used in the

equations as shown in the left most column of the table. All the coefficients are insignificant and thus the

variables in the equations are unable to predict individual securities returns. Whether it is SR, UR or TR none

of them are incorporated by investors when pricing assets in Pakistan.

Table 4: Concurrent Regression – R-R Relationship

Equation Coeff. Std. Errors t-Stat Remarks

Rit = αo+α1 SRit 0.8844 2.1283 0.42 Insignificant

Rit =αo+α1 TRit -0.0041 0.1446 -0.03 Insignificant

Note: Total 72 regressions from January 5, 2004 to May 30, 2005are run for the two equations. Average

values of the coefficients of systematic risk (SR) and standard errors along with t statistics are reported.

5. Conclusion

In this study weekly returns’ data of the KSE-100 index (market return) and of 194 non-financial firms listed

on KSE-100 index for the period from January 5, 2004 to October 13, 2008 is used to investigate R-R

relationship. Different measures of risk such as beta, SR, UR, and TR are used as independent variables to

explain portfolio and individual securities returns. Fama and McBeth (1973) procedure with some variation is

adopted and different estimation methods are used. 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 R-R

relation as proposed by CAPM. Alternatively it can be inferred that Fama and McBeth (1973) approach does

not work in Pakistan stock market.

These results in Pakistani stock market are not different from those arrived at in earlier studies. Ahmed and

Zaman (1999) used GARCH-M model and observed volatility clustering in Pakistani stock market. Findings

of this study offer no support for the applicability of standard CAPM, instead this study support the predictive

power of a higher-moment conditional CAPM. Iqbal and Brook (2007) rejected the validity of unconditional

CAPM, they documented the presence of non-linear nature in the R-R relationship in Pakistani equity market.

Iqbal, Javed, Brooks and Galagedera (2008) through empirical analysis compared risk and return models and

could not found evidence in favor of CAPM. They supported conditional version of risk and return models

and conditional variables such as trading volume, dividend to price ratio were reported to have more

predictive power in R-R relationship. In this study they used monthly data from October 1992 to March 2006

and the sample included 101 stocks listed on KSE. Javid and Ahmad (2008) could not determine support for

CAPM. The results of the study showed that conditional CAPM was more appropriate. More specifically, they

documented that conditional coskewness could better explain asset pricing whereas conditional covariance

and cokurtosis had little explanatory power.Javid (2009) concluded that CAPM lack the power to explain risk

and expected return association in KSE. In this study she considered both higher moments and autoregressive

process of the returns. Hanif and Bhatti (2010) investigated 360 stocks during the period from 2003-08. They

observed evidence in support of CAPM but for 28 stocks and for limited period. Hanif (2010) investigated

tobacco stocks listed on KSE for the period 2004-07. They reported that the beta was instable and its value

was higher for weekly data relative to beta estimated with monthly data. Correlation between actual monthly

returns and expected returns from CAPM was stronger than that for weekly data. More recently, Zubair and

Farooq (2011) used CAPM and reported existence of weak correlation between actual returns and expected

returns.

It is suggested that further studies should be conducted to investigate how investors price assets in stock

market in Pakistan. Moreover in these studies other methodologies (e.g. the one proposed by Pettengill et. al.,

1995) and variables (e.g. size, book to market ratio, and macroeconomic factors) should be used to determine

what factors cause variations in the returns of both individual securities and portfolios. Studies on different

data sets (e.g. daily, monthly, semi-annually, and annually) and extended data sets may also prove beneficial.

It is suggested that investors in Pakistan shall not rely only on the results of CAPM and shall also use alternate

asset pricing model in order to make right investment decisions.

REFERENCES

Ahmad, E. and Badar-u-Zaman, (1999), “Volatility and Stock Return at Karachi Stock Exchange”, Pakistan

Economic and Social Review, 37(1), pp. 25–37.

Arrow, K. J. (1953) trans. (1964), "The Role of Securities in the Optimal allocation of Risk bearing", Review

of Economic Studies, 31,pp.17-78.

Attiya, Y. J. (2009), “Test of Higher Moment Capital Asset Pricing Model in Case of Pakistani Equity

Market”, European Journal of Economics, Finance and Administrative Sciences, 15, pp. 144-162.

Bachelier, L. (1900), “Theorie de la Speculation”, Annales de l’Ecole Normale Superieure de Paris.

Ball, R. (1978), “Anomalies in relations between securities’ yields and yield- surrogates”, Journal of

Financial Economics, 6, pp.103 – 126.

Banz, R. (1981), “The relationship between return and market value of common stocks”, Journal of Financial

Economics, 9, pp.3 – 18.

Basu, S. (1977), “Investment performance of common stocks in relation to their price – earnings ratio: A test

of the efficient market hypothesis”, Journal of Finance, 32, pp.663 – 682.

Black, F. (1972), “Capital Market Equilibrium with Restricted Borrowing", Journal of Business,

45(3),pp.444-455.

Black, F. (1974), “International Market Equilibrium with Investment Barriers ", Journal of Financial

Economics,1(4),pp.337-52.

Blume, M. E. (1971), "On the Assessment of Risk", The Journal of Finance, 26(1),pp. 1-10.

Brealey, R. A. (1969), "An Introduction to Risk and Return from Common Stocks", Cambridge: The MIT

Press, Massachusetts Institute of Technology.

Brennan, M. J. (1970), "Taxes, Market Valuation and Corporate Financial Policy", National Tax Journal,

23,pp.417-427.

Chan, L. Hamao, Y. Lakonishok, J. (1991), “Fundamentals and stock returns in Japan”, Journal of Finance,

46, pp.1739 – 1789.

Chen, Nai-fu, Roll, R. and Ross, S. A. (1986), " Economic Forces and The Stock Market: Testing the APT

and Alternative Asset Pricing Theories", Journal of Business, 59, pp.383-403.

Chui, A. and Wei, J. (1998), “Book-to-market, firm size, and the turn-of-the-year effect: Evidence from

Pacific-Basin emerging markets”, Pacific-Basin Finance Journal, 6, pp. 275 – 293.

Clark, F. J. (1972), "Investments: Analysis and Management", New York: McGraw-Hill Book Company.

Cohen, J. B., Edward, D. Z., and Arthur, Z. (1973), "Investment Analysis and Portfolio Management",

Homewood, Illinois: Dow Jones-Irwin Inc.

Damodaran, 1997

Evan, J. L. and Archer, S. H. (1968), "Diversification and the Reduction of Dispersion: An Empirical

Analysis", Journal of Finance, pp.761-68.

Fama, E. and French, K. (1992), “The cross-section of expected stock returns”. Journal of Finance, 47,

pp.427 – 465.

Fama, E. and French, K. (1996b), “The CAPM is wanted, dead or alive”, Journal of Finance, 54, pp.1947 –

1958.

Fama, E. French, K. (1996a), “Multifactor explanations of asset pricing anomalies”, Journal of Finance, 51,

pp.55 – 84.

Fama, E. MacBeth, J. (1973), “Risk, return, and equilibrium: Empirical tests”, Journal of Political Economy,

81, pp.607 – 636.

Hanif, M. & Bhatti, U. (2010), “Validity of Capital Assets Pricing Model: Evidence from KSE-Pakistan”

Harvey, C. R. (1995), “Predictable Risk and Return in Emerging Markets”, The Review of Financial Studies,

8, pp. 773–816.

Haugen, R.A. and Baker, N.L. (1991), “The efficient market inefficiency of capitalization-weighted stock

portfolios”, Journal of Portfolio Management, 17, pp.35 – 40.

Hawawini, G. and Michel, P.A. (1982), “ The pricing of risky assets on the Belgian stock market”, Journal of

Banking and Finance, 6, pp.161 – 178.

Hawawini, G. Michel, P.A. and Viallet, C.J. (1983), “ An assessment of the risk and return of French common

stocks”, Journal of Business Finance and Accounting, 10, pp. 333 – 350.

Hussain, F. and Uppal, J. (1998), “The Distribution of Stock Return in Emerging Market: The Pakistani

Market. Pakistan Economic and Social Review, 36(1), pp.47–52.

Iqbal, J. Brooks, R. and Galagedera, D. A. U. (2008), “Testing Conditional Asset Pricing Model: An

Emerging Market Perspective”, Working Paper 3/08. Monash University, Australia.

Iqbal, J. Brooks, R., and Galagedera, D. A. U. (2007), “Asset Pricing with Higher Co- movement and

Alternate Factor models: The Case of Emerging Markets”, Working Paper, Monash University.

Isakov, D. (1999), “Is beta still alive? Conclusive evidence from the Swiss stock market”, European Journal

of Finance, 5, pp. 202 – 212.

James, E. H. and Philip, L. T. (1978), “Systematic and Unsystematic Risk of Rates of Returns Associated with

Selected Forest Products Companies”, Southern Journal of Agricultural Economics, pp. 135-138.

Javid, A.Y. and Ahmad, E. (2008), “The Conditional Capital Asset Pricing Model: Evidence from Karachi

Stock Exchange”

Javid, Y. and Ahmad, E. (2008), “Multi-Moment Asset Pricing Behavior of the Listed firms at Karachi Stock

Exchange”, PIDE Working Paper 47.

King, B. F. (1966), “Market and Industry factors in Stock Price Behavior", Journal of Business, 39(1), pp.139-

190.

Lakonishok, J. and Shapiro, A.C. (1986), “Systematic risk, total risk and size as determinants of stock market

returns”, Journal of Banking and Finance, 10, pp.11 5 – 132.

Lakonishok, J. Shapiro, A.C. (1984), “Stock returns, beta, variance and size: An empirical analysis”,

Financial Analysts Journal, 40, pp.36 – 41.

Lintner, J. (1965), “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios

and Capital Budgets”, Review of Economics and Statistics, 47(1), pp. 13–37.

Lintner, J. (1966), “The Valuation of Risk Assets and Selection of Risky Investments in Stock Portfolio and

Capital Budgets”, Review of Economics and Statistics, 47(1), pp. 13–47.

Markowitz, H. M. (1991), "Foundations of Portfolio Theory", The Journal of Finance, 46(2), pp. 469-477.

Mayers, D. (1972), “Non-marketable Assets and Capital Market Equilibrium under Uncertainty”, im Jensen,

M. (1972)

Mossin, J. (1966), “Equilibrium in a Capital Asset Market”, Econometrica, 34, pp.768–783.

Pettengill, G.N., Sundaram, S. and Mathur, I. (1995), “The conditional relation between beta and returns”,

Journal of Financial and Quantitative Analysis, 30, pp.101 – 116.

Reinganum, M. (1981), “A new empirical perspective on the CAPM”, Journal of Financial and Quantitative

Analysis, 16, pp. 439 – 462.

Roll, R. and Ross, S. A. (1980), “An Empirical Investigation of the Arbitrage Pricing Theory", Journal of

Finance, 35, pp.1073-1103.

Schwert, G. (1983),”Size and stock returns, and other empirical regularities”, Journal of Financial

Economics, 12, pp.3 – 12.

Sharpe, W. F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”,

Journal of Finance, 19(3), pp. 425- 442.

Sharpe, W. F. (1965), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”,

Journal of Finance, 19(3), pp. 425-442.

Solnic, B. H. (1974), “An Equilibrium Model of International Capital Market", Journal of Economic Theory,

8(4), pp.500-524.

Tinic, S. and West, R. (1984), “Risk and return: January vs. the rest of the year”, Journal of Financial

Economics, 13, pp.561 – 574.

Tobin, J. (1958), “Liquidity Preference as Behavior towards Risk”, Review of Economic Studies, 67, p.22.

Williams, J. B. (1938), "The Theory of Investment Value", (Harvard University Press, Cambridge).

Williams, J. T. (1977), "Capital Asset Prices with Heterogeneous Beliefs", Journal of Financial Economics,5,

pp.219-39.

Zubairi, H. J. and Shazia, F. (2011), “ Testing the Validity of CAPM and APT in the Oil, Gas and Fertilizer

Companies Listed on the Karachi Stock Exchange, Pakistan Business Review, pp. 439- 458.