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

• Main Authors: Adeel Nasir, Kanwal Iqbal Khan, Mário Nuno Mata, Pedro Neves Mata, Jéssica Nunes Martins
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Mathematics
• Subjects: value at risk; expected shortfall; CAPM; Fama and French; VaR; asset pricing
• Online Access: https://www.mdpi.com/2227-7390/9/4/394

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.