Evolution of Equity Market Risk During the Crisis

Financial equity risk of a country may be measured in terms of Value at Risk (VaR) or Conditional Value at Risk (CVaR) of a representative financial stock index. In case of financial market instability, the risk measure suitable to capture tail risk is the CVaR. Here the Johnson transformations have been adopted in the valuation of equity VaR and CVaR. Applying the Johnson systems it is possible to obtain closed formulas for VaR and quasi-closed formulas for CVaR calculation, starting from the estimation of the first four moments of the distribution. These formulas have been applied to historical data of six important stock indices relative to Europe, U.S., China, India, Brazil and Russia. With the aim to analyse for any index the evolution of countries’ equity riskiness over the years 2008-2012 and to show the relevance of tail risk, we have used a rollover mechanism obtaining about one thousand of values of VaR and CVaR for each index. A comparison of the results obtained in the Johnson framework with those obtained in the simpler normality assumptions together with historical estimations of VaR and CVaR has been made for different levels of probability.