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.
Highlights
The current study elaborates the comparison of various risk factors and signifies the sensitivity of returns towards these risk factors
This study presents the six-factor model in which the question is whether downside risk, Value at Risk (VaR), can be used as the systematic risk factor or idiosyncratic risk factor
The well-established cross-sectional analysis provided by Fama and French [18] is tested in the Pakistani stock market, and to some extent, results are different than in developed markets
Summary
The current study elaborates the comparison of various risk factors and signifies the sensitivity of returns towards these risk factors. There are two types of risk; one is the systematic risk, which cannot be avoided. The other is the idiosyncratic risk that can be avoided or reduced [1]. The Capital Asset Pricing Model (CAPM) introduced market beta as the systematic risk factor. Market beta provides the sensitivity of security returns towards well-diversified portfolio returns. Idiosyncratic risk is generated from firm-specific factors, and it can be evaded by changing the investment strategy or diversification. Value at Risk (VaR) and Expected Shortfall (ES) are the risk factors related to the worst expected losses and systematically measure risk [2,3]. This study applies VaR and ES as both systematic and idiosyncratic risk factors and signifies the optimum risk-return trade-off
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