Value at Risk
The standard technical reference for the measure and its limits.
Summary
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.
Key takeaways 7
- Value at risk states the loss that will not be exceeded over a horizon at a confidence level and says nothing about losses beyond it.
- The variance-covariance method assumes normally distributed returns, which understates tail risk in every real portfolio.
- Historical simulation avoids distributional assumptions and assumes instead that the future resembles the sampled past.
- Estimated volatilities and correlations change most in exactly the conditions where the measure is relied upon.
- Strategies that concentrate risk beyond the confidence level, including option selling, report low value at risk while carrying large exposure.
- Backtesting breach frequency against the stated confidence level is how model failure is detected.
- Regulatory use of the measure under Basel creates incentives that pure risk management would not produce.
Who should read it
Risk managers and quantitative practitioners who need the standard reference on value at risk construction and, more importantly, on its failure modes.
Where it sits in the reference 2
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