*4.1. Regression Results*

In this section, we analyze the standard CAPM and the Fama-French three-factor model by employing time-series regression for each of the six size-B/M portfolios (SL, SM, SH, BL, BM, BH). The objective of this approach is to identify the role of size and value factors to capture variation in stock returns during the period from January 2002 to December 2015. We start from the traditional single factor CAPM in Table 6, in order to make a comparison with the three-factor model later.

**Table 6.** Capital Asset Pricing Model (CAPM) regressions on monthly excess returns of portfolios formed on size and B/M ratio (variable basket).


Note: Author's calculation. The table reports the estimation results of the single factor CAPM. Stocks are sorted into six size-B/M portfolios (SL, SM, SH, BL, BM, BH). *t*-stats are in parenthesis, \*\*\* and \* indicate significance at 10% and 1% level, respectively. The sample period is 2002:01–2015:12 (168 monthly observations). Source: the official website of the Pakistan stock exchange (https://www.psx.com.pk/) and the official website of the State Bank of Pakistan (http://sbp.org.pk/).

The results reported in Table 6 show that the average adjusted *R*<sup>2</sup> value of the CAPM is approximately 48%, suggesting that the CAPM does not explain most of the time-series variations in stock returns. The intercept of the CAPM is statistically significant for two out of six portfolios, i.e., small stocks with medium B/M ratio (SM) and small value stocks (SH). The portfolios containing small stocks generate higher average intercept and lower *R*2. Thus, the results of the CAPM regressions provide some preliminary indication for a size premium.

Next, we include size and book-to-market factors into the model. Table 7 reports the results of the Fama-French three-factor model based on variable basket. The *R*<sup>2</sup> of the six regressions, with an average of approximately 71.74%, are much higher than those of the CAPM regressions. Usually, adding an independent factor into regression increases *R*2. If the change is meaningfully higher, it is considered to be an improvement in the model. The average value of *R*<sup>2</sup> for small size group increases from approximately 30.88% to 71.08%, signifying that the three-factor model provides a massive improvement in the explanatory power over the CAPM. Therefore, our regression results support the argumen<sup>t</sup> that the three-factor model is a much better fit for KSE, Pakistan.


**Table 7.** Three factor regression on monthly excess returns of portfolios formed on size and B/M ratio (variable basket).

Note: Author's calculation. The table reports the estimation results of the three-factor model (variable basket). Stocks are sorted into six size-B/M portfolios (SL, SM, SH, BL, BM, BH). *t*-Stats are in parenthesis, \*\*\* and \* indicate significance at 10% and 1% level, respectively. The sample period is 2002:01–2015:12 (168 monthly observations). Source: the official website of the Pakistan stock exchange (https://www.psx.com.pk/) and the official website of the State Bank of Pakistan (http://sbp.org.pk/).

Theoretically, if a model satisfactorily explains the changes in the expected returns, then the intercept produced by regression results will tend towards zero. Table 7 reports that the six size-B/M portfolios produce intercepts, ranging from −0.0072 to 0.0037, are close to zero. Only the portfolio containing stocks with a high market capitalization and a high book-to-market value (BH) shows a significant (negative) intercept. The significant intercept for portfolio BH indicates that the big value firms have something not predicted by the model.

The loadings on the market factor are all significant at 1% level and thus reflect a positive sensitivity to market risk. HML has significantly positive coefficients for high B/M firms and significantly negative for low B/M firms. The coefficients of value stocks have both a large and positive sensitivity to HML, whereas growth stocks have a low and negative sensitivity to HML. Our results support the existence of value premium. Similarly, the coefficients of small firms have both a large and positive sensitivity to SMB, whereas the big firms have insignificant sensitivity. The coefficients of big firms are very small, ranging from approximately 0.019 to 0.061, whereas the coefficients of small firms range from approximately 0.737 to 1.187. Although the insignificant sensitivity of big firms to SMB is different from Fama-French's findings, the coefficient of small firms

are highly significant both in the economic and statistically sense. This finding also indicates adequate evidence to support the existence of a size premium.

*4.2. Comparative Analysis of the Three-Factor Model*

In this section, we examine the three-factor model based on 'fixed' and 'non-financial' baskets. For comparison, Table 8 represents the three factor model regression results.

**Table 8.** Three factor regression on monthly excess returns of portfolios formed on size and B/M ratio (fixed basket and non-financial basket).


Note: Author's calculation. The table reports the estimation results of the three-factor model (fixed and non-financial basket). Stocks are sorted into six size-B/M portfolios (SL, SM, SH, BL, BM, BH). *t*-stats are in parenthesis, \*\*\*, \*\* and \* indicate significance at 10%, 5% and 1% level, respectively. The sample period is 2002:01–2015:12 (168 monthly observations). Source: the official website of the Pakistan stock exchange (https://www.psx.com.pk/) and the official website of the State Bank of Pakistan (http://sbp.org.pk/).

The average *R*<sup>2</sup> value of fixed basket and non-financial basket is 66.71% and 67.72%, respectively. Two portfolios, namely SH and BL, represent statistically significant intercepts for both of the baskets. The intercepts of SH and BL range from −0.0016 to 0.0065 and −0.0027 to 0.0079, respectively. The coefficients of the market factor are all positive and significant at 1% level. The coefficients of small portfolios have a large and positive sensitivity to SMB, whereas big portfolios have a smaller and positive sensitivity to SMB. Finally, the coefficients of high B/M portfolios have a large and positive sensitivity to HML factor, while the low B/M portfolios have a smaller and negative sensitivity to HML. Our regression results are mostly similar to the variable basket. Similarly, we analyze CAPM based on fixed and non-financial baskets, in order to make a reasonable comparison with the CAPM-variable

basket. However, the primary interest in the CAPM regression is the *R*<sup>2</sup> values and the intercept term. The results reported in Table A1 (Panel A and Panel B) in the appendix demonstrate that the fixed and non-financial baskets exhibit similar patterns as the variable basket. That is, the portfolios containing small stocks generate higher average intercept and lower *R*2.
