ValueatRiskChapter 9RiskManagementandFinanciallnstitutions3e,Chapter9,CopyrightJohnC.Hull2012
Chapter 9 Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 Value at Risk 1
TheQuestionBeingAskedinVaRWhat loss level is such that we are X%confident it will not be exceededin Nbusiness days?"2RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull2012
The Question Being Asked in VaR “What loss level is such that we are X% confident it will not be exceeded in N business days?” Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 2
VaR and Regulatory CapitalRegulators base the capitalthey requirebanks to keep on VaRThe market-risk capital is k times the 10-day 99% VaR where k is at least 3.0Under Basel Il, capital for credit risk andoperational risk is based on a one-year99.9% VaR3RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull2012
VaR and Regulatory Capital ⚫ Regulators base the capital they require banks to keep on VaR ⚫ The market-risk capital is k times the 10- day 99% VaR where k is at least 3.0 ⚫ Under Basel II, capital for credit risk and operational risk is based on a one-year 99.9% VaR Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 3
AdvantagesofVaR It captures an important aspect of riskin a single numberIt is easy to understandIt asks the simple question: “How bad canthings get?"RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull20124
Advantages of VaR ⚫ It captures an important aspect of risk in a single number ⚫ It is easy to understand ⚫ It asks the simple question: “How bad can things get?” Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 4
Example 9.1 (page 185) The gain from a portfolio during six monthis normally distributed with mean $2million and standard deviation $10 million The 1% point of the distribution of gains is2-2.33x10 or - $21.3 million The VaR for the portfolio with a six monthtime horizon and a 99% confidence levelis$21.3 million.RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull20125
Example 9.1 (page 185) ⚫ The gain from a portfolio during six month is normally distributed with mean $2 million and standard deviation $10 million ⚫ The 1% point of the distribution of gains is 2−2.33×10 or − $21.3 million ⚫ The VaR for the portfolio with a six month time horizon and a 99% confidence level is $21.3 million. Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 5