Human capital in asset pricing - A machine learning perspective on the six-factor model for Pakistan's equity market

Aug 6, 2026

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The study extends the Fama-French five-factor model by introducing human capital as a sixth factor, with emphasis on Pakistan’s frontier equity market. Three estimation approaches—OLS, ARIMAX, and LSTM-RNN—are evaluated by comparing their predictive performance. Using machine learning to assess estimation power provides insights into how market-specific and contextual conditions shape model effectiveness. Evidence indicates deep-learning complexity is not always beneficial in underdeveloped markets with limited high-frequency data. Findings also support a human-capital premium: firms investing heavily in human capital earn a positive premium, while low-investment firms earn a negative one.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

AccessFree to download

Introduction

Asset pricing and factor models

Role of estimation approaches

Research focus and contributions

Methodology

Estimation techniques: OLS, ARIMAX, and LSTM-RNN

Empirical findings

Six-factor model results in Pakistan's market

Predictive power comparisons

Discussion and implications

Article Human capital in asset pricing: A machine learning perspective on the six-factor model for Pakistan's equity market Ozair Siddiqui 1 , Naveed Khan 2,* , and Arshad Ali Bhatti 3 Citation: Siddiqui, O., Khan, N., Bhatti, A.A. (2025) . Human capital in asset pricing: A machine learning perspective on the six-factor model for Pakistan's equity market. Modern Finance, 3(4), 96-117. Accepting Editor: Adam Zaremba Received: 11 September 2025 Accepted: 20 December 2025 Published: 29 December 2025 Copyright: © 2025 by the authors. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) license ([https://creativecommons](https://creativecommons)[.org/licenses/by/4.0/](.org/licenses/by/4.0/)) . 1 International Islamic University, Islamabad; [email: ozairsiddiqui.acca@gmail.com](email: ozairsiddiqui.acca@gmail.com) 2 International Islamic University, Islamabad; [email: naveedkhan.fin@gmail.com](email: naveedkhan.fin@gmail.com) 3 International Islamic University, Islamabad; email: [arshad_bhatti@iiu.edu.pk](arshad_bhatti@iiu.edu.pk) * Correspondence: Faculty of Management Sciences, International Islamic University, Islamabad; email: [naveedkhan.fin@gmail.com](naveedkhan.fin@gmail.com) Abstract: The study aims to extend the Fama-French five-factor model by adding human capital asthe sixth factor, with a specific focus on Pakistan's frontier market. Additionally, we also test the efficacy of three estimation approaches, OLS, ARIMAX, and LSTM-RNN, by comparing their predictive power. Employing a machine learning approach to assess the predictive power of estimation techniques offers fresh insights into the importance of contextual and market-specific factors. The study provides empirical evidence that the complexity of deep learning models is not always an advantage, especially in ‘underdeveloped’ markets that lack high-frequency market data and large datasets. Additionally, our results also support the inclusion of the sixth factor (human capital) in the asset pricing model. The findings show that firms with high investment in human capital exhibit a positive premium, whereas firms with low investment in human capital exhibit a negative premium, supporting Human Resource Theory in the Pakistani market. Keywords: deep learning; machine learning; human capital; asset pricing; six-factor model 1. Introduction Understanding the mechanics of asset pricing has been a central focus of economics and finance literature for decades. Fama and French (1992, 2015); Markowitz (1952); and Sharpe (1964), all argue that investment decisions follow two key principles: efficient resource allocation and consideration of the risk-return trade-off. Therefore, for capital allocation decisions, pricing assets becomes a key focus for the investors, whether firms or individuals. Additionally, Fama (1970) links the level of market efficiency to the extent of information reflected in asset prices. Therefore, asset prices in a weak, less transparent market will not reflect all information promptly, as in developed markets (Fan et al., 2011) . However, market efficiency is not the only concern in the asset-pricing problem; one must also understand the factors that impact asset prices. For example, Sharpe (1964) argues for a single (market) factor that explains prices of individual stocks (or more precisely, stock returns) . Conversely, Khan et al. (2022) argue for a six-factor model, including human capital as the additional factor to the Fama and French five-factor model (or simply, FF5) (2015) . Similarly, with the advancement in technology, numerous other factors have been added to the asset pricing models, including management and investor sentiment and sustainability practices (or Environmental, Social and Governance (ESG) score) (Maiti, 2021; Sakariyahu et al., 2024) . Additionally, advances in technology not only complicate the i

FAQs

What does the study add to the Fama-French asset pricing framework?

It extends the Fama-French five-factor model by adding human capital as a sixth factor, tailored to Pakistan’s frontier equity market.

Which estimation methods are compared to predict asset returns?

The study compares OLS, ARIMAX (via maximum likelihood estimation), and LSTM-RNN (a deep learning approach) by evaluating their predictive power.

What relationship between human capital investment and asset pricing premium does the study find?

Firms with high human capital investment show a positive premium, whereas firms with low investment show a negative premium, supporting Human Resource Theory in the Pakistani market.

Aug 6, 2026

Upload by Maeve