Is Value-at-Risk (VaR) a Fair Proxy for Market Risk Under Conditions of Market Leverage?

Abstract

Ex-post intraday market-risk extrema are compared with ex-ante standard RiskMetrics parametric Value-at-Risk (VaR) limits for three foreign currency futures markets (British Pound, Japanese Yen, Swiss Frank) to determine whether forecasted volatility of market returns based on settlement price data provides a valid proxy for short-term market risk independent of market leverage.

Intraday violations of ex-ante one-day VaR limits at the 95% confidence level should occur for less than 5% of market days. Violation frequencies for each of the markets tested are shown to occur well in excess of this 5% tolerance level: 9.54% for the British Pound, 7.09% for the Japanese Yen, and 7.79% for the Swiss Franc futures markets.

Thus, it is empirically demonstrated that VaR is a poor proxy for short-term market risk under conditions of market leverage.

Implications for managing (measuring, monitoring, controlling), reporting, and regulating financial market risk are discussed.