By the mid-1990s, every major bank needed a single number to summarise the market risk of its trading book — something a board member with no derivatives training could read and interpret. J.P. Morgan's RiskMetrics (1994) supplied the answer: the Value-at-Risk. VaR tells you the loss level that your portfolio will not exceed in of trading days. Its simplicity drove its adoption across global capital markets, and Basel II enshrined it as the regulatory capital measure for market risk in the trading book.
This note gives VaR a precise definition, derives closed-form expressions for normal and Student loss distributions (the two most common models in practice), explains the regulatory horizon and confidence-level choices, and describes how VaR enters the Basel trading-book capital charge. It also states clearly what VaR does not tell you — setting up the need for Expected Shortfall and the coherence axioms of the next lessons.
Learning objectives. By the end of this note you should be able to:
- state the formal definition of VaR as the -quantile of the loss distribution;
- compute VaR analytically for normal and Student loss distributions;
- explain why different confidence levels and horizons are chosen for market risk vs credit risk capital;
- write down the Basel market-risk capital charge formula and explain the role of the multiplier ;
- identify three structural limitations of VaR (tail blindness, non-coherence, procyclicality).
In this lesson
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- Three approaches to risk measurement
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- Value-at-Risk: definition
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- VaR in closed form
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- Choosing VaR parameters
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- VaR in regulatory capital calculations
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- Limitations of VaR
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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