Stressed Expected Shortfall (ES) and Stressed Analytic VaR for Emerging Markets and Illiquid Assets Complying with new Basel Committee Standards

Abstract

This paper introduces Stressed Expected Shortfall (ES) and mathematically correct analytic VaR applied to portfolios of emerging markets and illiquid assets with large liquidation horizons and/or high volatilities. The new metrics are explicitly derived for the normal distribution of price returns; thus, remaining an indispensable risk management tool more versatile than historic or MC Simulation VaR and ES. The formulas can be used to calculate market and liquidity risk and the empirical evidence on whether to use option implied volatility to take into account “tail” risk gave mixed results . The stressed ES and VaR is arrived by compiling data for the most volatile periods in recent history – patching different stressed periods together is one form of stress testing. Preliminary results show the minimum stressed multiplier for the data analyzed for ES and VaR lies in the range 1.8 to 2.2, and the most extreme, passing from calm period Jan-02 – Dec-06 to stressed Lehman demise aftermath, Sep-08 – Mar-09 is 3.65. Both numbers are useful in the decision making process to determine capital adequacy. Appendices A and B propose further research regarding the use of option implied volatility and asset classification based on realistically required days for asset liquidation, respectively.