Value-at-risk: historical simulation.

QT A series designed to introduce readers to the quantitative tools used in today's financial services industry.

Market risk-potential loss in market value of a trading position-is determined by two factors: market risk exposure and volatility of the markets.

* The exposure ("Greeks") demonstrates a vulnerability of trading positions to the market changes. It is expressed as the market value change for a small change in relevant market factors. There exist a large number of these measures that describe the market value sensitivity to various market factors, such as interest rates, foreign exchange rates, volatilities, and so on, and their combinations. Most of the tools in market risk management are exposure-based.

* With all their usefulness for hedging and scenario-based risk analysis, these measures describe only trading positions and do not reflect how risk of the same position changes with changes in the markets volatility. VAR, on the other hand, is the only risk tool that combines exposure of trading positions with measurement of volatility of current market conditions into a single risk measure-potential loss.

The significance of VAR as a market risk tool makes accuracy essential. If we do not know whether our risk measure parallels reality, none of the other issues, including VAR implementation challenges or its computational efficiency, are of any importance. The only valid criterion of accuracy is that VAR realistically measures what it is supposed to measure-maximum market loss for a given holding period and confidence level. A backtesting procedure performs this analysis by comparing each day's VAR to actual losses. From a statistical point of view, the backtesting procedure evaluates accuracy of our P&L distribution forecast (at the selected point corresponding to the required confidence level) by comparing it with a "real" distribution of profits and …