Short- And Long-Term Value-At-Risk, Skewness, Kurtosis and Coherent Risk Measure

Abstract

Standard risk management focuses on short-run risks rather than longer periods. We introduce an improved risk measure which can be used to estimate both short-and long-term structure of value at risk and the corresponding expected shortfall. The short- and long-term coherent measure of risk is specified and computed for both S&P 500, HSI and SHSZ 300. We also test long-term skewness and kurtosis from empirical analysis for S&P 500, HSI and SHSZ 300. We also show that our improved risk measure gives a better estimate of the value at risk for short horizons and never decreases to negative values like VaR for long-run horizons. Both long-term skewness and kurtosis for HSI and SHSZ 300 are analyzed empirically.