Tail Risk of Equity Market Indices: An Extreme Value Theory Approach

Both VaR and CVaR are examples of measures of tail risk, or downside risk, because they are designed to exhibit a degree of sensitivity to large portfolio losses whose frequency of occurrence is described by what is known as the tail of the distribution: a part of the loss distribution away from the central region geometrically resembling a tail. In practice, VaR provides a loss threshold exceeded with some small predefined probability, usually 1% or 5%, while CVaR measures the average loss higher than VaR and is, therefore, more informative about extreme losses. An interesting practical question is to compare tail risk as measured by VaR and/or CVaR across different markets. There are at least two reasons for that. First, understanding the sources of tail risk is the first step towards designing methods for its management and, second, understanding differences across markets is important for risk management for international portfolios.