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**Sample selection and data collection**

The testing of the CAPM requires selection of an index which can be used as a proxy to the market. Index construction based on free float market capitalization is regarded as the most suitable method where the level of index at any point of time reflects the free float market value of a company in relation to the base period. Several reputed index providers such as Morgan Stanley Capital International (MSCI), Financial Times Stock Exchange (FTSE) and Standard & Poor (S&P) use this method of index construction as it has become globally accepted practise. In this paper, the Karachi stock exchange (KSE-30) index launched in 2006, is used as a proxy for market portfolio since it is based on the free float market capitalization representing the thirty largest companies from diverse sectors of the economy. Additionally, the KSE-30 index is an appropriate choice as it includes all stocks of a company that are readily available to be traded on the market while closely held companies are excluded. As it is the case that the closely held corporations are controlled by few shareholders and the valuation of their share prices depends on few individuals rather than the market as a whole. Consequently, se-lection of the KSE-30 index serves the pupose of both enhancing sector and market coverage.

In this study the KSE-30 index is biannually recomposed, therefore 10 companies are selected which have been listed on the stock market during the whole sample time pe-riod between February 2009 and January 2013. Iqbal and Brooks (2007) mention the ef-fect of thin trading and argue it is often prevalent in emerging markets and to counter this probelm we opt for only those companies that have continuously traded on the mar-ket during the entire chosen time period. These companies represent sectors such as oil and gas, telecommunication, agriculture and banks which have performed remarkably well during the recent past. Moreover, the criteria for the sample companies inclusion is based upon getting the overview of the whole market to the maximum extent by select-ing stocks from different sectors of the economy.

Weekly stock returns which were collected from KSE website for all 10 companies are computed between February 2009 and January 2013. The closing price of the last trad-ing day of the week is used to calculate weekly returns. By using weekly returns rather than monthly returns, the aim is to obain more obervations for better estimation results (bartholdy & Peare, 2004).

The theory of the CAPM implies that the market index should comprise of all the assets in the world. In reality not all the assets are traded on the stock market; instead a proxy market is used for the empirical testing of CAPM and as argued we opt for KSE-30. The three month government bonds issued by the State Bank of Pakistan are used as a proxy to risk free interest rate. Since these bonds are issued by the government and trusted by people due to no risk of financial loss. Statistical formulas such as the mean, variance and standard deviations are applied to the proxy to risk free interest rate in determining beta.

**Estimation of SML. Non-linearity and Non-systematic test for entire testing period**

CAPM testing is carried out on each period from Period 2 to Period 8 for all the stocks in a pooled regression. Each stock has six months of observations in each period. As a result, we obtain 60 observations for ten stocks in one period. Since we have divided the time frame into seven testing periods, a total of 420 observations is obtained The re-sults are summarized for all individual stocks in table 4 for the entire testing period. Based on the t-test, coefficients , and are analysed to see if the CAPM hy-pothesis regarding each of these variables holds true or not. Equations 3 to 5 are respec-tively used for the estimation of SML, testing for non-linearity and testing for non-systematic risk. The critical value used at the 5% significance level is 1.96. Additionally results for each individual company in each period are found in the Appendix 7.2. Ta-ble 8-14.

**Estimation of SML**

The estimate for the intercept coefficient is significantly different from zero as its t-value in absolute terms. 8.492. is greater than 1.96 so these results are inconsistent with the CAPM. However. the coefficient is significantly positive and in accordance with the CAPM. The coefficient of the average risk premium is positive as compared to early periods where it was found to be negative.

**Non-linearity test**

The zero intercept prediction of CAPM is not accepted while the average risk premium is also not found to be greater than zero. However. the test for non-linearity reveals that there does not appear to be a linear risk and return relationship as the t-statistic for the coefficient in absolute terms, 5.849, is significant and inconsistent with CAPM. Therefore, the CAPM is clearly rejected.

**Test for non-systematic risk**

The estimate for the coefficient is significantly different from zero and is therefore inconsistent with CAPM. Expected returns are not only affected by single risk beta as shown in table 6.

The results obtained in table 6 follows the similar pattern as in table 4. The intercept, linearity and systematic risk assumptions are not in accordance as specified by the theo-ry of CAPM for the last four testing periods. However the beta risk premium coefficient is found to be positive and significantly different from zero as predicted by the model.

1 Introduction

2 Theoretical Framework

2.1 Classic theory of the CAPM

2.2 Debate surrounding the CAPM

2.3 Challenges to the validity of the Mode

2.4 Previous Research on the emerging markets

3 Research Methodology

3.1 Sample selection and data collection

3.2 Method of the CAPM testing

3.3 The CAPM hypothesis

3.4 Testing

4 Empirical Data Analysis

4.1 Beta Estimation

4.11 R-square values

4.12 Estimation of SML. Non-linearity and Non-systematic test for entire testing period

4.2 Intercept and beta risk premium coefficients graph

4.3 Results from Period 2, 3 and 4

4.4 Results from Period 5, 6, 7 and 8

4.5 Summary of results

5 Conclusion

6 References

7 Appendix

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Testing the Capital Asset Pricing Model on the Karachi Stock Exchange