Performance of factor models in explaining anomalous return patterns: Evidence from Pakistan

ABSTRACT

We compared classic and contemporary asset pricing factor models in explaining anomalous returns in the Pakistani stock market using a sample of 290 companies listed on the Pakistan Stock Exchange. We replicated 54 anomalies with a successful replication rate of 31.5%. We also replicated the factors of chosen factor models, including Fama and French's three-, five-, and six-factor models and an alternate six-factor model; Hou, Xue, and Zhang's q-factor model and an alternate q-factor model; and Stambaugh and Yuan's mispricing factor model and an alternate mispricing factor model. The performance of the factor models is tested using various time-series tests. We found that there is no clear winner in explaining anomalous returns, and we require other approaches to test the models’ abilities in explaining anomalies in Pakistan.

KEYWORDS:

• asset pricing
• factor models
• anomalous returns
• emerging markets
• Pakistan stock market

JEL CLASSIFICATIONS:

• G11
• G12
• G15

Data availability statement

The data that support the findings of this study are available from the corresponding author, MY, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The supplementary file is available upon request.

2 T-bills are issued in 3, 6, and 12 months frequencies in Pakistan, we converted a 6-month T-bill rate into monthly rate and the calculated monthly rate is taken as a one-month risk-free rate.

3 The details about the construction of anomalies and portfolios are in the supplementary file.

4 The average distance metric is calculated as $AD=\sqrt{MSE\left(\tilde{\alpha }\right)+MSE\left(\widetilde{{\sigma }_{\alpha }}\right)}$. MSE is the mean squared error. $\tilde{\alpha }$ is the alpha of test assets. $\widetilde{{\sigma }_{\alpha }}$ is the standard error of alphas.

5 The positive profitability factors in M4 models might be due to its construction based on a set of anomalies related to profitability, whereas other profitability factors are calculated using a single measure of profitability.

6 The negative profitability factors of Fama-French in our study are justifiable as Guo et al. (2017) also reported these factors negative using OP and CP. However, using ROE as a measure of profitability has been reported positive. Profitability using ROE in our study is negative. This might be due to the firms and timeframe chosen in the sample which are 290, whereas other studies used 400+ firms. Moreover, the firms in the weak leg of profitability factor in those studies might have underperformed during the period but in our study, small-weak profitable and big-weak profitable firms outperformed.