An empirical study of Pakistani Equity Market. This study investigates the validity of Capital Asset Pricing Model in Pakistani equity market by employing traditional as well as conditional approaches proposed by Black, Jensen and Scholes (1972), Fama and Macbeth(1973)and Pettengil et. al(1995) for the period 1/ 2002 to 31/2007. Test have been performed on 10 portfolios consisting of 15 beta sorted securities during each analysis period. KSE-100 index and T bill rates have been used as proxy of market portfolio and risk free rates respectively
Results of Black, Jensen and Scholes methodology indicates that no significant relationship exists between systematic risk (beta) and portfolio risk premiums and explanatory power of Model is extremely weak. Fama and Macbeth approach also confirms the results and indicates that no meaningful relationship exists between conventional beta coefficients and risk premiums of the portfolios. Thus traditional approaches do not support the validity of CAPM in Pakistani equity market. However Pettengill et al. methodology provides evidence about existence of significant relationships between beta and risk premium of portfolios. It is documented that there exists a negative relationship between risk premium and beta in down markets and there exist a positive relationship between risk and return in up markets. However only 24% variations in portfolio risk premium can be explained with the help of beta of market and it opens the door for active identification of factors that can enhance the explanatory power of model. Further, this study provides that existing relationship between systematic risk(Beta) and portfolio risk premium is linear in nature.
Key words: Beta, Capital Asset Pricing Model, Pakistan, risk premium
JEL Classification: G11, G12, G14.
1. Introduction
Asset pricing is one of the central themes in modern finance. Markowitz Mean Variance Theory lays down the foundations of modern asset pricing theory on which Sharpe (1964), Lintner (1965), Mossin (1966) and Black (1972) develop the Capital Asset Pricing Model separately .CAPM assumes that equity return is a linear function of its systematic risk and its covariance with the returns of market portfolio. It also postulates that equity returns are independent of company specific factors. Capital Asset Pricing Model is one of the most debated topics in modern finance and it has been extensively tested during last 35 years. But evidence is mixed. Earlier studies of Black, Jensen and Scholes(1972) and Fama and MacBeth(1973) , Blume and Friend (1973), Ross (1978), Gibbons and Ferson (1985), Terregrossa (2001), Feldman and Riesman (2003) support the capital asset pricing model. But simultaneously there are number of studies that report anomalies in CAPM. These studies include Basu(1977), Roll (1977), Francis and Fabozzi (1979),Roll and Ross (1980), Banz(1981) ,Stambaugh(1982), Reinganum (1981), Elton and Gruber (1984), De Bondt and Thaler(1985), Merton (1987), Lee (1990), Chan (1997), and Maximiliano (2001). These empirical studies reveal that beta of Capital Asset Pricing Model can not fully explain the expected returns of securities or portfolios and conditional CAPM is better descriptor of expected returns. However, Black (1993), Kothari and Shanken (1995) and Daniel and Titman (1997) argue that these anomalies are result of data dredging. Therefore, considerable controversy surrounds standard capital asset pricing model.
Large volume of empirical literature is available for developed markets but Pakistani capital market is still unexplored in the field of asset pricing. Therefore it is necessary to test the applicability and validity of CAPM in Pakistani context. Pakistan is an emerging equity market of south Asia and has shown phenomenal growth during last few years. It has attracted considerable foreign investment in recent past. Strategic decisions like Investment, valuation and capital generation are based on correct estimation of risk and return relationship. These decisions lead to optimal allocation of resources in the capital market as well as economy. So, it becomes more important to investigate the determinants of required rate of return for emerging economies like Pakistan. Therefore, this study has been conducted to investigate the relationship between equity returns and market returns. Secondly it will ascertain validity of the standard Capital Asset Pricing Model in the Pakistani capital market which is still unexplored.
The paper is organized in V Sections. Section II provides an overview of empirical work done with reference to testing of CAPM in unconditional and conditional setting. Section III explains model specification and methodology adopted to test the Capital Asset Pricing Model in Karachi Stock Exchange. Section IV discusses the empirical results and finally Section concludes the results and sheds light on policy implications of study.
2. Literature Review
Black, Jensen and Scholes (1972) examine the relationship between equity returns and beta for US equity market by employing cross sectional regression analysis on monthly data for the period 1931 to 1965. Two step Procedure is adopted for investigation of relationship. In first step, Beta coefficients are estimated for all stocks for five year periods and ten portfolios are structured on basis of beta ranking. In second step, Average returns of these portfolios are regressed against beta of portfolios. Results of cross sectional regression analysis support CAPM and provide that there exist a significant positive relationship between equity returns and beta coefficients.
Fama and MacBeth (1973) investigate the relationship between equity returns and beta for US equity market by analyzing all common stocks listed at New York stock exchange for the period 1926 to 1968 by employing three step approach. This approach involves following steps
Portfolio formation on the basis of beta ranking
Estimation of portfolio beta
Testing of relationship between portfolio returns and beta of portfolio unconditionally.
Fama and MacBeth (1973) divide the whole time frame into nine periods for investigation. Each investigation period is further divided into portfolio formation period, beta estimation period and testing period. Betas are calculated for each portfolio formation period consisting of four years and on the basis of ranking of beta of securities twenty portfolios are formed. In second step, Portfolio betas are worked out for the subsequent beta estimation period consisting of five years. Finally, Portfolio returns are calculated for the testing period and these are regressed against the betas calculated in estimation period. Results provide evidence about existence of significant positive relationship between betas and equity returns in general.
Roll (1977) questions the testability of Capital Asset Pricing Model. Main problem lies in market portfolio which is indescribable. It is not theoretically clear which assets can justifiably be disqualified from the market portfolio and availability of data also considerably restricts the assets that are included. Therefore proxies for the market portfolio are used to test of the CAPM. Roll states that as tests use proxies, not the true market portfolio, so we learn nothing about the CAPM. The relation between expected return and market beta of the CAPM is just the minimum variance condition that holds in any efficient portfolio, applied to the market portfolio. Thus, if we can find a market proxy that is on the minimum variance frontier, it can be used to describe differences in expected returns, and we would be happy to use it for this purpose. The strong rejections of the CAPM described above, however, say that researchers have not uncovered a reasonable market proxy that is close to the minimum variance frontier
Pettengill, Sundaram and Mathur (1995) test the CAPM in the presence of positive and negative market and portfolio risk premiums separately. He argues that if up market premiums and down market premiums are simultaneously drawn on scatter diagram. The slope of regression line will be approximately zero indicating that no significant relationship exists between risk premium and beta. This situation weakens the ex-post relationship between betas and risk premiums. However, when regression lines up market and down market are drawn separately the results reveal a different scenario. Here regression lines with up markets and down markets offer estimates which are consistent with SML estimates. Pettengill et al(1995) investigates 660 observations and identifies 280 negative market risk premiums and 380 positive market risk premium. The modified Fama and Macbeth model is employed to investigate the relationship in up market and down market independently. The sample period is divided into sub periods (i) portfolio formation period;(ii) portfolio beta estimation period; and(iii) testing period. Beta sorted portfolios are created for portfolio formation period. In step two portfolio betas are calculated for portfolio beta estimation period. Finally, returns of beta sorted portfolios are regressed against the portfolio betas for up market and down markets. Results of unconditional CAPM test indicate the existence of systematic relationship between portfolio beta and risk premiums in whole period but these results are found insignificant for the sub periods. However, significant positive association is observed between risk and return in up market and significant negative association is documented for down markets.
Jagannathan and Wang (1996) examine the static relationship between risks and return for the securities listed at American equity markets for the period 1962 and 1990 under the assumption of time varying beta. In first step ten portfolios are formed on the basis of size. Market value of firm is used as proxy of size. Then beta is calculated for each firm and ten beta sorted portfolios are identified in each size decile. Thus 100 Portfolios are formed. Study also uses human capital to capture the effect of return on wealth. Results support conditional Capital Asset Pricing Model in time varying betas assumption.
Fletcher (1997) examines the relationship between portfolio returns and beta for stocks listed at FTSE for the period 1975 to 1994 by employing Pettengill methodology. The conditional relationship is examined by using cross sectional regression analysis that includes size as conditional variable. Results provide evidence about existence of significant positive relationship between portfolio returns and beta in periods of up-market. However, in a period of down market, a significantly negative relationship has been observed. Size is not found affecting returns in equity market of UK as evident from insignificant relationship between returns and beta.
Hodoshima, Garza and Kunimura (2000) examine the relationship between monthly equity return and beta of stocks listed at first section of Japanese equity market by employing cross sectional regression analysis. Results reveal that no significant relationship is observed between equity retunes and beta when regression analysis is performed on excess returns of all months. However when regression analysis is performed on positive excess market returns and negative excess market returns separately, a significant conditional relationship is observed between equity returns and beta. This conditional association between equity return and beta are better fit for the period when the market excess return is negative as evident from higher R2 and S.E of estimate.
Pedro and Ocampo (2003) tests capital asset pricing model in traditional and conditional setting by employing modified Fama and Macbeth approach for equity market of Philippine. Cross Sectional regression analysis provides evidence about the existence of significant relationship between portfolio returns and beta in case of conditional CAPM. However, weak relationship is observed between equity returns and beta under unconditional CAPM test
Zhang and Wihlborg (2004) investigate the relationship between equity return and risk for emerging equity markets of Russia, Hungary, Czech Republic, Turkey, Poland, Greece and Cyprus by employing conditional as well as unconditional approach proposed by Fama and McBeth (1973) and Pettengill(1995) respectively . Results reveal that there exist a significant relationship between risk and return in domestic market under conditional framework. Results also show that unconditional positive relationship is observed between risk in return in equity markets of Russia and Czech Republic. A comparison between DCAPM and ICAPM is also made to investigate the comparative explanatory potential of CAPM.
Sandoval and Saens (2004) test conditional and unconditional Capital Asset Pricing Model for equity markets of Latin American countries i.e Argentine, Brazil, Chile and Mexico for the period 1995 to 2002 by using Black (1972) approach and Pettengill (1995) Model. Control variable include book to market ratio , size and the momentum. Betas of securities are worked out by regressing equity returns against lagging, matching and leading market returns of LASMI and S&P 500. In step 2, Portfolios are formed on the basis of beta ranking of securities. Then, portfolio betas are calculated ed for estimation periods. These portfolio beta are used as independent variables in subsequent period. Finally, cross sectional Regression analysis is performed as proposed by Black (1972). Results reveal that there exists significant positive relationship between beta and equity premium during up- markets. However the direction of relationship is reversed in down markets. It is worth mentioning that no significant relationship is observed between size, book to market ratio and momentum and equity risk premium. Level of integration is also investigated and it is found that degree of integration decrease in down markets.
Ang and Chen (2005) examine the relationship between risk premium and beta for all securities listed at NYSE, NASDAQ and AMEX for the period 1926 to 2001 by using conditional single factor model. The conditional variable investigated is book to market ratio. A brief overview of previous studies show that when portfolios are sorted on the basis of book to market then betas of portfolios may fluctuate over time and regression analysis may lead to inconsistent estimates of conditional alphas and betas. This study employs conditional Capital Asset Pricing Model that uses portfolios structured by considering time varying betas, market risk premium and stochastic systematic volatility to capture the role of book to market ratio in explaining the equity returns in the long run. Results show that proposed model significantly explains the relationship between risk and return. Similarly, proposed model does not provide evidence that conditional alpha for a BMR trading strategy is statistically different from zero.
3. Data Description and Methodology
3.1 Data Description
This study examines monthly equity prices for 150 stocks listed at Karachi Stock Exchange for the period January 2000 to December 2007. Sample is selected on the basis of market capitalization and represents approximately 85% of total market capitalization. Sample has a history is of continuous listing at KSE for the above stated period. Month end prices of stocks are not adjusted for dividends and stock splits as said data was not available. However, it does not affect the results as there is no stock split during this period and tendency to pay dividends is also low. Equity returns have been calculated as under
Rt = ln (Pt / Pt-1)
Where Rt is return on stock "i" and Pt and Pt-1 is price of stock "i" at the end of the month t and t-1 respectively.
Three Treasury Bill rate is used as a proxy for the risk-free rate and KSE -100 index is used as proxy of market portfolio and market return is calculated as
Rm = ln (It / It-1)
Where Rm is market rate of and It and It-1 is KSE 100 index at the end of the month t and t-1 respectively.
A careful review of empirical literature provide that three different approaches are used to test the CAPM. These include
Black, Jensen and Scholes Approach
Fama and MacBeth Approach
Pettengill Approach
These models can be applied on individual securities as well as portfolios. The literature on the subject argues that creating portfolios reduces idiosyncratic volatility and enables more precise estimation of factor loadings and risk premium so this study uses portfolios for testing capital asset pricing models. These tests estimate a series of monthly cross-section regressions of portfolio returns on beta and then test whether the average slope coefficient in these regressions is statistically different from zero. It is hypothesized that the intercept equals to zero and the slope of SML equals the average risk premium. It is also hypothesized that there exist a linear relationship between portfolio returns and portfolio betas. Detailed Procedure followed under each approach is explained below.
3.2 Black, Jensen and Scholes Approach
Black, Jensen and Scholes Approach is based on two step procedure. In first step, Beta coefficients are estimated for all stocks are calculated by regressing excess actual returns against the excess market returns.
E (Ri) = RF + ï¢i (RM - RF)
Where E (Ri) are expected returns of individual securities and ï¢I is beta of individual securities or it can be calculated by using
ï¢i= Cov(Ri,Rm) / Var(Rm)
In this study beta is calculated by using above formula. Stocks are arranged in descending order and ten portfolios are created on the basis of beta ranking. In second step, Average returns of these portfolios are calculated and regressed against beta of portfolios.
Rit = λ ot + λ 1t ï¢ i + ï¥ it
Where R it is the return on portfolio "i" in month t, ï¢ i is the beta of portfolio "i" and ï¥ it is error term. It is worth mentioning that beta of portfolio is adjusted each month to new information about securities prices. Therefore this study uses time varying beta for analysis.
Results of cross sectional regression analysis provide evidence about the relationship between equity risk premium and beta. A significant positive relationship exhibits applicability of Capital Asset Pricing Model in equity market. This study investigates two analysis periods
Analysis Periods I
Analysis Periods II
Beta Estimation period
2002-2003
2004-2005
Testing period
2004-2005
2006-2007
3.3 Fama and MacBeth Approach
Fama and MacBeth Approach is based on three step procedure. In the first step, beta for each individual security is calculated for portfolio formation period. Beta can be calculated by regressing the excess returns of individual securities against excess returns of market as shown below.
RS- RF = ï¢i (RM - RF)+ï¥
Beta can also be calculated by using following relationship.
ï¢i= Cov(Ri,Rm) / Var(Rm)
This study follows the second approach which is also adopted by Fama and MacBeth. Securities are then grouped into ten portfolios on the basis of ranking of the estimated betas. In the second step, betas of ten portfolios are calculated for initial estimation period consisting of next two years. These betas can either be calculated by taking average of betas of the securities assigned to each portfolio or by regressing the excess returns of each portfolio against excess market returns for initial estimation period. This study uses second approach. In third step, realized returns of each portfolio are regressed against time varying betas of portfolios in testing period. Realized returns of portfolios are taken as dependent variable and time varying beta is taken as explanatory variable.
Rit = λ ot + λ 1t ï¢ i + ï¥ it
Where R it is the return on portfolio "i" in month t, ï¢ i is the beta of portfolio "i" and ï¥ it
is error term.
Above equation is derived by using pooled regression analysis and provides estimates of the average values of monthly coefficients λ ot and λ 1t .These values of monthly coefficients are finally then examined to see the significance of relationship. It is hypothesized that ï¢ i should be the only variable that explains the relationship between risk and returns. If any other variable is included in model than it should have insignificant relationship with portfolio returns.
This study uses two years portfolio formation period, two years portfolio betas estimation period and two years testing period.
Analysis Periods
Portfolio Formation Period
2002-2003
Initial estimation Period
2004-2005
Testing Period
2006-2007
3.4 Pettengill Approach
Pettengill approach is modification and extension of Fama and MacBeth approach that investigates the relationship between risk premium and beta in up market and down market separately. An up market is period with positive risk premium and a down market is period with negative risk premium. The sample period is divided into sub periods (i) portfolio formation period ;(ii) portfolio beta estimation period; and(iii) testing period. In step one, Beta sorted portfolios are created for portfolio formation period. In step two portfolio betas are calculated for portfolio beta estimation period. Finally, returns of beta sorted portfolios are regressed against the portfolio betas. Dummy variables are used for up market and down markets. Thus the traditional regression equation is modified as
R pt = λ0t + λ 1t Dï¢ i + λ 2t (1- D) ï¢ i + ï¥ it
where D = 1 if R mt - R ft is positive , and D = 0 if R mt - R ft is negative. Where R mt is the market portfolio return and R ft is the risk-free rate. The null and alternative hypothesis are :
Ho : λ 1t = 0
H1 : λ 1t > 0
And
Ho : λ 2t = 0
H1 : λ 2t < 0 .
In nutshell, it is hypothesized that there exist a negative relationship between risk premium and beta in down-markets and there exist a positive relationship between risk and return in up markets.
Finally two more aspects are analyzed by incorporating additional variables in the traditional regression equation. Linearity assumption has been tested for Capital Asset Pricing Model by using the following equation. If λ 2t is not significant at ï¡= .05 then we can say that there exist a linear relationship exists between beta and portfolio risk premium.
Rp,t - Rf = λ ot + λ 1t ï¢p ,t-1 + λ 2t ï¢2 p ,t-1 + ï¥ it
4. Empirical Results
Table 1 shows the annualized monthly returns for each portfolio and beta. Results provide that portfolios with high betas generally have high returns and portfolios with small beta have small returns. These results are consistent with established theory and empirical literature on the subject. However certain anomalies have also been observed in certain years like 2002. These anomalies can be result of high volatility in the year 2002.
Table 1 Annualized Monthly Returns and Beta
Port 1
Port 2
Port 3
Port 4
Port 5
Port 6
Port 7
Port 8
Port 9
Port 10
2002
Return
0.916
1.231
0.556
0.782
0.582
0.460
0.213
0.417
0.430
0.325
Beta
1.446
1.195
0.855
0.753
0.436
0.337
-0.317
0.032
-0.054
0.045
2003
Return
0.896
0.575
0.791
0.527
0.574
0.690
0.692
0.345
0.578
0.504
Beta
1.844
1.570
1.205
1.019
0.794
0.795
0.608
0.472
0.347
-0.076
2004
Return
0.910
0.375
0.365
0.207
0.339
0.416
0.517
0.237
0.649
0.500
Beta
1.626
1.549
1.219
0.789
1.007
0.785
0.455
0.830
0.627
0.479
2005
Return
0.214
0.162
0.317
0.199
0.101
-0.023
0.191
0.009
-0.095
0.193
Beta
1.131
0.921
0.702
0.764
0.549
0.510
0.323
0.224
0.071
-0.168
2006
Return
-0.219
-0.172
-0.289
-0.137
-0.165
-0.237
-0.097
-0.396
-0.148
-0.108
Beta
0.611
0.345
0.679
0.556
0.181
0.387
0.476
0.183
0.301
0.486
2007
Return
0.277
0.323
0.302
0.324
0.265
0.403
0.366
0.300
0.237
0.143
Beta
0.756
0.327
0.844
0.769
0.451
0.621
0.708
0.973
0.264
0.356
Avg
Return
0.499
0.416
0.340
0.317
0.283
0.285
0.313
0.152
0.275
0.260
Beta
1.362
1.103
0.972
0.858
0.591
0.597
0.329
0.430
0.389
0.137
Figure I below represents the relationship between average returns of portfolio and beta of the portfolio for the period 2002-2007 and result are in broad agreement with the hypothesis that portfolio with high beta have high returns. However, in low beta portfolio these results inconsistent. This may be due to inefficiency of market. Hasan et al (2007) in a recent study also provides evidence about inefficiency of Pakistani equity market.
Fig. 1 Portfolio Returns and Beta
The Sharpe-Lintner-Black capital asset pricing model (CAPM) proposes that security returns are a positive linear function of their market betas and that these betas are sufficient to describe the cross-section of expected security returns. Table 2 exhibits the results of Black, Jensen and Scholes Approach that tests the validitiy of capital asset pricing Model.
Table 2 Results for the Black, Jensen and Scholes Test
2002-2005
2004-2007
λ ot
0.0128
-0.0082
λ 1t
0.0029
0.0041
t ( λ ot)
1.2716
-0.7859
t ( λ 1t)
0.2546
0.2487
P value (λot)
0.2048
0.4326
P value (λ1t)
0.7992
0.8037
R2
0.0003
0.0003
F Statistics
0.0648
0.0619
Results indicate that no significant relationship exist between beta of portfolio and excess return of portfolio as λ 1t is not significantly different from zero during sub period 2004-2005 and 2006-2007 . The Positive value of λ 1t may be a result of consistent positive monthly equity risk premiums during the period studied.. This result is in contravention with CAPM hypothesis. Moreover R 2 indicates the presence of extremely weak explanatory power of ordinary least square method. Therefore Black, Jensen and Scholes Approach exhibits no ex-post relationship between systematic risk (beta)and portfolio risk premiums. This situation requires that additional factors should be identified to explain the portfolio return in the context of arbitrage pricing theory.
Table 3 displays the results of Fama and Macbeth Approach that explores the validity of capital asset pricing Model by testing that λ ot = 0 and λ 1t ≠0. This model uses three step procedures to avoid the problems associated with errors in variable.
Table 3 Results for Fama and Macbeth Test
2002-2007
λ o
-0.0055
λ 1t
0.0003
t ( λ ot)
-0.3887
t ( λ 1t)
0.0131
P value (λ ot)
0.6978
P value (λ 1t)
0.9895
R2
7.19E-07
F Statistics
0.0002
A careful examination of findings reveals that no significant relationship is observed between portfolio risk premium and beta during testing period 2006-2007. The coefficient λ 1t is not significantly different from zero as the absolute t-value (0.0131) is less than tabulated value (1.96) at 95% confidence level. According to CAPM λ1t should be equal to the average risk premium and it should be positively correlated to portfolio return so result is inconsistent with the CAPM hypothesis. However market risk premium is found positive as evident from λ 1t and it may be a result of consistent positive monthly equity risk premiums during the period studied. R 2 also confirms the results that explanatory power of model is weak and no relationship exists between portfolio risk premium and beta. Therefore we can conclude that Fama and Macbeth Approach does not provide any evidence about existence of ex-post relationship between systematic risk (beta)and portfolio risk premiums. Therefore multifactor models like Fama and French three factor model or Carhart four factor model may be explored to explain the portfolio returns in Pakistani equity market.
Table 4 displays the results of Pettengill approach which is an extension of Fama and Macbeth approach and examines the relationship between risk premium and beta in up market and down market separately.
Table 4 Results for Pettengill Test
2002-2007
λ ot
-0.0048
λ 1t
0.0501
λ 2t
-0.0611
t ( λ ot)
-0.3973
t ( λ 1t)
2.4406
t ( λ 2t)
-2.9238
P value (λ ot)
0.6915
P value (λ 1t)
0.0154
P value (λ 2t)
0.0038
R2
0.2431
F Statistics
38.0515
Results indicate that there exist a significant positive relationship between risk and return in up markets as calculated value of t statistics is greater than tabulated value. Similarly significant negative relationship has also been observed between risk premium and beta in down-markets. However only 24% variations in portfolio risk premium can be explained with the help of beta of market and it opens the door for active identification of factors that can enhance the explanatory power of model.
Table 5 shows the results of linearity tests and confirms that there exists a linear relationship between beta and portfolio risk premium.
Table 5 Results for Linearity of Relationship Test
2002-2007
λ ot
0.0004
λ 1t
-0.0227
λ 2t
0.0199
t ( λ ot)
0.0134
t ( λ 1t)
-0.2139
t ( λ 2t)
0.2194
P value (λ ot)
0.9894
P value (λ 1t)
0.8308
P value (λ 2t)
0.8265
R2
0.0002
These results reveal that
The intercept, λ ot is not significantly different from zero as absolute t-value (0.0134) is less than tabulated value (1.96) at 95% confidence level. This result is in line with CAPM.
The coefficient λ 1t is not statistically significant as the absolute t-value (0.2139) is less than tabulated value (1.96) at 95% confidence level. According to CAPM λ1t should be equal to the average risk premium and it should be positively correlated to portfolio return so result is inconsistent with the CAPM hypothesis.
Finally value of ï¬ 2t is not significantly different from zero as evident from results t statistics. This indicates that the expected rate of returns and betas are linearly related with each other..
These results indicate that market risk premium is not significantly different zero which is in contravention to assumptions of CAPM. Coefficient of determination indicates that explanatory power of model is negligible. Under present conditions single index CAPM model appears as weak model as Blacks model and Fama and Macbeth Model fails to explain the excess return of portfolio in Pakistani equity market. Pettengill Model provides evidence of significant relationship but it still explains only a quarter of variations in portfolio risk premium.
In financial world, many strategic financial decisions like investment decision, financing decision, merger and acquisition decision and valuation of equity are based on correct determination of cost of equity /required rate of return of investor. Cost of equity (Ke )is calculated by employing CAPM based on beta . But beta is unable to estimate equity prices /equity returns so it is need of time to identify the factors and design an a multi factor model to explain the portfolio returns in Pakistani capital market.
5. Conclusion
The Capital Asset Pricing Model lies in the heart of one of the core theories in finance. Debate about asset pricing and valuation is revolving around this key model that provides foundations for major decisions like investment decision, financing decisions, mergers and acquisition etc. Evidence about validity of CAPM is mix. Recent studies do not support the model and find that that beta is not significantly related to returns. This paper examines the validity of CAPM in the Pakistani equity market for the period 1/ 2002 -12/2007. Monthly returns for 150 companies are used to create 10 beta sorted portfolios consisting of 15 securities. Black, Jensen and Scholes approach for testing validity of CAPM indicate that beta is unable to explain the realized returns in Karachi equity market. Fama and Macbeth model that controls the issue of errors in variables also confirms the above result and provides that no significant relationship exists between beta and portfolio returns. Pettengills methodology is also employed to test the relationship in up market and down market independently. When tests are performed under this conditional framework, beta is found significantly positively related to realized portfolio returns in up market. Beta is also viewed as significantly negatively related to realized portfolio returns in down markets. The explanatory power of model is also observed substantially high in comparison to results obtained by using traditional approach proposed by Black et al and Fama &Macbeth. However, it is still very low i.e 0.24. Therefore coefficient of determination as exhibited by the cross sectional regressions suggest that the model might be either misspecified or additional risk factors other than beta might be required to explain the tradeoff between systematic risk (beta) and portfolio risk premium. Therefore, applicability of CAPM is as asset pricing tool is questionable. Therefore it is suggested that applicability of multifactor model like Fama and French three factor model, Carhart four factor models should be explored which investigate the role of size premium, value premium and momentum premium in explaining the equity returns.
