《金融风险管理》课程PPT教学课件（Risk Management and Financial Institutions）Chapter 09 Value at Risk

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

Example 9.2 (page 186)All outcomes between a loss of s50 millionand a gain of $50 million are equally likelyfor a one-year projectThe VaR for a one-year time horizon and a99% confidence level is $49 million6RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull2012

Example 9.2 (page 186) ⚫ All outcomes between a loss of $50 million and a gain of $50 million are equally likely for a one-year project ⚫ The VaR for a one-year time horizon and a 99% confidence level is $49 million Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 6

Examples 9.3 and 9.4 (page 186). A one-year project has a 98% chance ofleading to a gain of $2 million, a 1.5%chance of a loss of $4 million, and a 0.5%chance of a loss of $10 millionThe VaR with a 99% confidence levelis $4millionWhat if the confidence levelis 99.9%?What if it is 99.5%?RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull 20127

Examples 9.3 and 9.4 (page 186) ⚫ A one-year project has a 98% chance of leading to a gain of $2 million, a 1.5% chance of a loss of $4 million, and a 0.5% chance of a loss of $10 million ⚫ The VaR with a 99% confidence level is $4 million ⚫ What if the confidence level is 99.9%? ⚫ What if it is 99.5%? Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 7

Cumulative Loss Distribution forExamples 9.3 and 9.4 (Figure 9.3, page 186)1Cumulative0.995Probability0.990.9850.980.9750.970.965Loss ($million)0.960.9550.9508-224610RiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull20128

Cumulative Loss Distribution for Examples 9.3 and 9.4 (Figure 9.3, page 186) Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 8

VaR vs.Expected ShortfallVaR is the loss level that will not beexceeded with a specified probabilityExpectedshortfallis the expected lossgiven that the loss is greater than the VaRlevel (also called C-VaR and Tail Loss)Two portfolios with the same VaR canhave very different expected shortfallsRiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull 20129

VaR vs. Expected Shortfall ⚫ VaR is the loss level that will not be exceeded with a specified probability ⚫ Expected shortfall is the expected loss given that the loss is greater than the VaR level (also called C-VaR and Tail Loss) ⚫ Two portfolios with the same VaR can have very different expected shortfalls Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 9

DistributionswiththeSameVaRbutDifferentExpectedShortfallsVaRVaRRiskManagementandFinancialInstitutions3e,Chapter9,CopyrightJohnC.Hull201210

Distributions with the Same VaR but Different Expected Shortfalls Risk Management and Financial Institutions 3e, Chapter 9, Copyright © John C. Hull 2012 VaR VaR 10