The Five-Factor Asset Pricing Model Tests and Profitability and Investment Premiums: Evidence from Pakistan

ABSTRACT

Using an extensive sample of the Pakistani stock market over the 2003–2016 period, this paper is the first to evaluate and compare the performance of four most popular factor pricing models: the Fama and French three-factor model, Carhart’s four-factor model, the five-factor model proposed by Fama and French, and the six-factor model that adds momentum to the five-factor model. We also test different nested models and find that the five-factor model best explains the returns of anomaly portfolios and outperforms the other models. We note that the profitability factor significantly improves the description of average returns, whereas factor spanning tests show that the value and momentum factors are redundant for the Pakistani stock market. Our results are robust to alternative factor definitions, formation of test assets, and across sub-periods.

KEY WORDS:

• asset pricing
• factor models
• profitability and investment
• momentum
• emerging markets
• Pakistani stock market

Acknowledgments

We thank the editor and anonymous referees for their helpful comments. We also thank He RongRong (Hong Kong Baptist University) for the enormous help. All remaining errors are our own.

Supplementary material

Supplemental data for this article can be accessed on the publisher’s website.

Notes

1. The profitability and investment patterns in the average returns for the U.S. stock market are previously discussed by several articles, such as Fairfield, Whisenant, and Yohn (2003), Titman, Wei, and Xie (2004), Fama and French (2008), and Aharoni, Grundy, and Zeng (2013).

2. Similar findings are reported by Ali and Ülkü (Forthcoming) that mispricing also varies with the varying performance of the profitability factor across different regions.

3. See Khwaja and Mian (2005) and Bruner et al. (2002) for the characteristics that are different between developed and emerging markets.

4. There are three stock markets in Pakistan, namely Karachi stock exchange, Lahore stock exchange, and Islamabad stock exchange. Karachi stock exchange is the most liquid and the biggest of the three stock markets in terms of market capitalization and trading volume. However, all these three markets merged on January 11, 2016 and renamed as the Pakistan stock exchange.

5. These factors include: political uncertainty, army takeover, and Asian Crisis.

6. The official website of the Pakistan Stock Exchange is: (https://www.psx.com.pk/).

7. The official website of the State Bank of Pakistan is: (http://sbp.org.pk/).

8. Ali, He, and Jiang (2018) examine different types of variable construction methodologies that could affect the significance and existence of the size and value premiums. They conclude that size factor performs the best when it includes both financial and nonfinancial stocks, whereas HML performs the best when it includes only nonfinancial stocks.

9. See Section 5 of this article and Xie and Qu (2016) for detailed factor construction methodologies.

10. The way we calculate four factors (SMB, HML, RMW, and CMA) is closely related to the factor construction methodology developed by Xie and Qu (2016). For momentum (UMD) factor, we followed the guidelines provided by Fama and French (2018).

11. Momentum factor has performed very poorly, but we do not exclude it from the factor spanning tests and other parts of this article (suggested by the reviewer). However, excluding UMD does not change the factor redundancy results.

12. Racicot and Theoret (2016) applied principal component analysis (PCA) to examine the uniqueness of the risk factors. We also perform PCA and results using orthonormal returns in Figure S1 (Panel C) indicate that HML contains unique information (see the Supplementary Material, available online). In short, we have not excluded HML in the following parts of this article.

13. We also check the performance of the 20% threshold ratio version of factors (results will be provided upon request). However, the choice between 25% and 20% seems inconsequential.

14. Our approach for robustness check differs from Racicot (2015) who developed an extension of the GMM model. This approach is further applied by Racicot and Rentz (2016, 2017) and Roy and Shijin (2018) to examine the robustness of the five-factor model from the perspective of measurement errors in the explanatory variables. Given that it is the first comprehensive study for the Pakistani stock market, following Chiah et al. (2016), Guo et al. (2017) and Huynh (2018), we prefer to use well-documented anomaly variables, multiple subsets of factor models, and alternative factor definitions to examine the robustness.