Optimisation of Time-Varying Asset Pricing Models with Penetration of Value at Risk and Expected Shortfall

Adeel Nasir, Kanwal Iqbal Khan, Mário Nuno Mata, Pedro Neves Mata and Jéssica Nunes Martins
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Adeel Nasir: Department of Management Sciences, Lahore College for Women University, Lahore 54000, Pakistan
Kanwal Iqbal Khan: Institute of Business & Management, University of Engineering and Technology, Lahore 54000, Pakistan
Mário Nuno Mata: Lisbon Accounting and Business School Lisbon Polytechnic Institute, Avenida Miguel Bombarda 20, 1069-035 Lisbon, Portugal
Pedro Neves Mata: ESCS—Escola Superior de Comunicação Social, Lisbon Polytechnic Institute, 1549-014 Lisbon, Portugal
Jéssica Nunes Martins: NOVA Information Management School, Universidade Nova de Lisboa Campus de Campolide, 1070-312 Lisboa, Portugal

Mathematics, 2021, vol. 9, issue 4, 1-38

Abstract: This study aims to apply value at risk (VaR) and expected shortfall (ES) as time-varying systematic and idiosyncratic risk factors to address the downside risk anomaly of various asset pricing models currently existing in the Pakistan stock exchange. The study analyses the significance of high minus low VaR and ES portfolios as a systematic risk factor in one factor, three-factor, and five-factor asset pricing model. Furthermore, the study introduced the six-factor model, deploying VaR and ES as the idiosyncratic risk factor. The theoretical and empirical alteration of traditional asset pricing models is the study’s contributions. This study reported a strong positive relationship of traditional market beta, value at risk, and expected shortfall. Market beta pertains its superiority in estimating the time-varying stock returns. Furthermore, value at risk and expected shortfall strengthen the effects of traditional beta impact on stock returns, signifying the proposed six-factor asset pricing model. Investment and profitability factors are redundant in conventional asset pricing models.

Keywords: value at risk; expected shortfall; CAPM; Fama and French; VaR; asset pricing; risk and return; risk management; mathematical modelling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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