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Risk Management and Financial Institutions, 4th Edition by John C. Hull

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CHAPTER 12 Value at Risk and Expected Shortfall

Chapters 8 and 9 describe how a trader responsible for a financial institution's exposure to a particular market variable (e.g., an equity index, an interest rate, or a commodity price) quantifies and manages risks by calculating measures such as delta, gamma, and vega. Often a financial institution's portfolio depends on hundreds, or even thousands, of market variables. A huge number of these types of risk measures are therefore produced each day. While very useful to traders, the risk measures do not provide senior management and the individuals that regulate financial institutions with an indication of the total risk to which a financial institution is exposed.

Value at risk (VaR) and expected shortfall (ES) are attempts to provide a single number that summarizes the total risk in a portfolio. VaR was pioneered by JPMorgan (see Business Snapshot 12.1.) and is widely used by corporate treasurers and fund managers as well as by financial institutions. As Chapter 15 and 16 show, it is the measure regulators have traditionally used for many of the calculations they carry out concerned with the setting of capital requirements for market risk, credit risk, and operational risk. As explained in Chapter 17, regulators are switching to ES for market risk.

This chapter introduces the VaR and ES measures and discusses their strengths and weaknesses. Chapters 13 and 14 discuss how they are calculated for market risk while Chapter 21 considers ...

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