*4.3. Model Performance Summary*

One of our primary tasks is to test how well the three different types of factors construction explain average excess returns on the portfolios. Table 9 (Panel A and Panel B) examines the average absolute intercept (A|*<sup>α</sup>i*|), a measure of unexplained proportion of time series return variance (1 − *R*2), and the number of portfolios with statistically significant intercept (NPSIs). Panel C of Table 9 estimates the mean, standard deviation, Sharpe ratio and cumulative wealth of size and value factors.


**Table 9.** Summary statistics for tests of CAPM, three-factor model, and size and value premiums.

Note: Author's calculation. Panel A and Panel B show the average absolute intercept <sup>A</sup>|*<sup>α</sup>i*|, the measure of unexplained proportion of time-series return variance (1 − *R*2), and the number of portfolios with statistically significant intercepts NPSIs of CAPM and the three-factor model, respectively. Panel C reports the mean, standard deviation, Sharpe ratio and cumulative wealth of size and value factors based on three different portfolio construction methodologies. FB, NB and VB represent the fixed basket, non-financial basket and variable basket, respectively. *t*-stats are in parenthesis, \*\*\* and \*\* indicate significance at 10% and 5% 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/).

Panel A of Table 9 shows that the average absolute intercepts and the average unexplained portion of the time-series returns variance of CAPM are the lowest in the variable basket. Similarly, the average values of (1 − *R*2) across the 6 LHS portfolios, measuring the unexplained portion of the time-series return variance of the three-factor model are approximately 33.29%, 32.65% and 28.26% for fixed, non-financial and variable baskets, respectively. These findings confirm that the explanatory power of the variable basket for both the three-factor model and CAPM is higher than the other two methods of factors construction. Table 9 (Panel B) further validates that the average absolute intercepts and the average values of (1 − *R*2) of the three-factor model are generally smaller than those of the CAPM. The variable basket produces only one portfolio that generates statistical significant intercept, whereas the other two baskets produce two portfolios with significantly positive intercepts. Further, Panel C of Table 9 shows that the Sharpe ratio, cumulative wealth and the significance level (5%) of SMB are higher in variable basket than non-financial and fixed baskets. The HML is significant at 5% level in all

the three baskets, however the Sharpe ratio and cumulative wealth are higher if HML is constructed by including only non-financial stocks.

Figure 1 plots the cumulated monthly value of one rupee (nPKR) invested at the start of January 2002 and compounded at the monthly returns of the two factors (SMB and HML) in the KSE, Pakistan. The solid lines represent the two factors constructed by using fixed basket (SMBf and HMLf). The round-dotted lines represent the non-financial basket (SMBn and HMLn), and the square-dotted lines represent the variable basket (SMBv and HMLv). The time period is from January 2002 to December 2015. Figure 1 shows that both factors follow the same pattern under all the three ways of constructing the factors. The cumulative wealth of SMB factor is the highest when it is constructed based on the variable basket, whereas the cumulative wealth of HML factor is the highest when it is constructed based on the non-financial basket.

**Figure 1.** Cumulative value of the size and value factors using three different methodologies. Source: Author's own plotting. The sample period is 2002:01–2015:12. 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/).

Overall, the results reveal that the three-factor model based on each of the basket of stocks explains the time-series variation in Pakistani stock returns very well. The fixed basket, used by most of the previous studies on the Pakistani stock market, performs the worst in terms of explanatory power and significance of the risk factors. The explanatory power of the three-factor model is relatively high when the portfolios include both financial and non-financial stocks (variable basket) as compared to when the portfolios include only non-financial stocks. Based on the explanatory power of the model, Sharpe ratio, cumulative wealth, and significance of the intercepts and the risk factors, we consider size and value factors constructed by using a variable basket of stocks for further analysis and robustness checks.
