Value at Risk

Philippe Jorion wrote the standard reference on value at risk, the measure that summarises a portfolio's potential loss as a single number: the loss that will not be exceeded over a specified horizon with a specified probability.

The book covers the measure's construction. The three principal methods are the variance-covariance approach, which assumes normally distributed returns and computes the loss analytically from the portfolio's volatility; historical simulation, which revalues the current portfolio using historical price movements; and Monte Carlo simulation, which generates scenarios from an assumed distribution. Jorion sets out the assumptions each requires, the computational demands, and where each fails.

He is careful about the limitations, and later editions are more so. Value at risk says nothing about losses beyond the threshold, which is the region that matters in a crisis. It depends on estimated volatilities and correlations that change, and that change most when they matter most. It can be gamed by positions that concentrate risk beyond the confidence level, which is why option selling strategies report low value at risk. Jorion covers backtesting to detect model failure, stress testing as a complement, and the regulatory use of the measure under the Basel framework, which he notes creates incentives that pure risk management would not. The book also covers the applications to credit and operational risk. It is technical and assumes statistics.