MarketRiskVaR:ModelBuildingApproachChapter 15RiskManagementandFinanciallnstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 Chapter 15 Market Risk VaR: ModelBuilding Approach 1
The Model-Building ApproachThe main alternative to historical simulation is tomake assumptions about the probabilitydistributions of the returns on the marketvariablesThis is known as the model building approach(or sometimes the variance-covarianceapproach)2RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 The Model-Building Approach ⚫ The main alternative to historical simulation is to make assumptions about the probability distributions of the returns on the market variables ⚫ This is known as the model building approach (or sometimes the variance-covariance approach) 2
Microsoft Example (page 323-324)We have aposition worth $10 million inMicrosoft shares The volatility of Microsoft is 2% per day(about 32% per year)We use N=10 and X=993RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 Microsoft Example (page 323-324) ⚫ We have a position worth $10 million in Microsoft shares ⚫ The volatility of Microsoft is 2% per day (about 32% per year) ⚫ We use N=10 and X=99 3
Microsoft Example continued The standard deviation of the change inthe p0rtfolio in 1 day is $200,000 The standard deviation of the change in 10days is200,000/10 = $632,456RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull20124
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 Microsoft Example continued ⚫ The standard deviation of the change in the portfolio in 1 day is $200,000 ⚫ The standard deviation of the change in 10 days is 200,000 10 = $632,456 4
Microsoft Examplecontinued.We assume that the expected change inthe value of the portfolio is zero (This isOK for short time periods) We assume that the change in the value ofthe portfolio is normally distributed Since N(-2.33)=0.01, the VaR is2.33 x 632,456 = $1,473,621RiskManagementandFinancialInstitutions3e,Chapter15,CopyrightJohnC.Hull20125
Risk Management and Financial Institutions 3e, Chapter 15, Copyright © John C. Hull 2012 Microsoft Example continued ⚫ We assume that the expected change in the value of the portfolio is zero (This is OK for short time periods) ⚫ We assume that the change in the value of the portfolio is normally distributed ⚫ Since N(–2.33)=0.01, the VaR is 2.33 632,456 = $1,473,621 5