An Application of Value at Risk and Expected Shortfall to Controlling Mechanism of Systematic and Idiosyncratic Risk

Abstract

Risk is an asymmetric position that is related to an adverse situation or loss. It can be measured through severity of loss, not deviation from a well-diversified average. The global financial system faces risk from two dimensions, change in nature due to time (temporal effect) and how different characteristics of quality change (cross-sectional effect). The objective of this research is to find the best-fitting risk and return model in the Pakistani stock market by deploying the Capital Asset Pricing Model (CAPM), Value at Risk (VaR), expected shortfall (ES), size, value, investment and profitability. The study proposes that VaR and ES are relevant risk and return measures as they measure the downside risk, which is relevant to the negative bias and risk-averse behaviour of investors in the market. One hundred-and-twenty-four regression models are analyzed to elaborate the significance of various systematic and idiosyncratic risk factors. The study observes the comparison of systematic risk factors i.e. CAPM, VaR, and ES for both cross-sectional and time-series stock returns. VaR and ES estimate the worst losses at some confidence level. Different confidence levels have different effects and implications. This study uses 95% and 99% levels of confidence to estimate VaR and ES relationship with stock excess returns. The significance of ideosyncratic risk factors i.e. size, value, investment and profitability is tested in an emerging market like Pakistan. The study further checks the investor behaviour by analyzing the impact of risk factors on lower end (20th quantile), median (50th quantile) and high end (80th quantile) stocks excess returns using a quantile regression model. Results suggest that ES completely dominated the systematic risk-control mechanism when estimating the cross-sections of stock excess returns. It is also significant in time-series regression analysis. Market beta has mixed effect on stock returns. It has a negative effect on cross-sections of stock returns but has a strong positive time varying effect. The empirical findings elaborate that VaR and ES are the alternate controlling mechanisms of systematic risk. The quantile regression findings are robust to least square regression results but the key finding is the predictability of VaR and ES for low-end stock returns. The CAPM model performs significantly in median and high-return stocks but insignificantly for stocks with low returns. Among idiosyncratic risk factors, value stocks and growth stocks are most relevant in both time-series and cross-sectional stock excess returns in Pakistan. The size factor has a temporal effect but no cross-sectional effect. Investment and profitability factors are not recognized as the diversifiable risk factor in the Pakistani stock market.