**6. Conclusions**

Using monthly data from Pakistan's Karachi stock exchange (KSE) between 2002 and 2016, the article conducts an empirical investigation of the Fama-French's three-factor model. Specifically, this article inspects three different ways (fixed basket, non-financial basket, and variable basket) of constructing size and value factors in order to gauge the effects of the special features in Pakistani stock market. Our main findings are as follows.

First, the findings demonstrate that the formation of the Fama-French factors can have a significant impact in empirical studies that apply the Fama-French models to Pakistani stock returns. We recommend that the risk factors be constructed by including both financial and non-financial companies, where the model explains about 71.23% of the variations in the stock returns on Pakistani market. It is noticed that the average *R*<sup>2</sup> values of the three-factor model are meaningfully higher than those of the CAPM. Since our sample includes financial firms, an augmented four-factor model that includes term structure premium (TSP) is tested. Although the loadings on TSP are mostly significantly positive, but the relevance of size (SMB), value (HML) and market factors is not deteriorated. The four-factor model does not improve the explanatory power of the model, whilst it increases the significance and the magnitude of the average intercept.

Second, the study explores the ability of the SMB, HML and market factors to predict future growth of the Pakistani economy (GDP). The paper provides evidence of statistically significant and positive relation between future growth of the Pakistani economy and the market factor, which is robust in the presence of SMB, HML and the business cycle variables in the models. Further evidence shows negative and statistically significant relationship between future growth of the Pakistani economy and SMB, whilst the loadings on the HML, T-bill and term structure premium are negative, but statistically insignificant. The market and size factors are robust to the inclusion of the business cycle variables in the model. The negative relation of SMB with future economic growth, presumably, indicate that the investors would rather hold the big capitalization stocks when they notice that the economy is in a bad state (low or instable growth).

Third, the robustness test confirms that the three-factor model captures the time-series variations in stock returns across the three sub-periods (pre-, during-, and post-crises), six risk regimes (portfolios' risk profile), and across three different portfolio construction methodologies (baskets of stocks). However, the significance and coefficients vary over time, across risk-profile of the portfolio, and across portfolio construction methodology. The three-factor model performs better in the post-crises period (2010–2015): (1) the average value for *R*<sup>2</sup> is the highest, approximately 81.82%; (2) intercepts are statistically insignificant for all the six LHS portfolios; and (3) loadings on the market, SMB and HML factors are mostly significant at 1% level.

By and large, considering the empirical evidence, across the different estimation techniques and methodologies, we find that the size and book-to-market (value) are the factors significantly and consistently exist in the Pakistani equity returns; however, the significance and magnitude of these factors and the three-factor model vary. Most importantly, these factors, except for HML, have relevance with the future growth of the Pakistani economy. Being a small open economy, factors such as foreign investors trading (Ceylan et al. 2015) may have influence on the stock prices and future

economic growth of Pakistan. The study of these factors will be worth doing in the future to further understand special characteristics of KSE, Pakistan.

**Author Contributions:** Fahad Ali and RongRong He contributed to data collection and management, and interpreted the results; YueXiang Jiang contributed to the analysis of the estimation results; Fahad Ali and YueXiang Jiang provided analytical materials and methodological tools; Fahad Ali, RongRong He and YueXiang Jiang wrote the manuscript. All authors read and approved the final manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
