Market RiskVaR:HistoricalSimulationApproachChapter 14RiskManagementandFinanciallnstitutions3e,Chapter14,CopyrightJohnC.Hull2012
Chapter 14 Risk Management and Financial Institutions 3e, Chapter 14, Copyright © John C. Hull 2012 1 Market Risk VaR: Historical Simulation Approach
Historical Simulation Collect data on the daily movements in allmarket variables.The first simulation trial assumes that thepercentage changes in all market variables areas on the first dayThe second simulation trial assumes that thepercentage changes in all market variables areas on the second dayand so on2RiskManagementandFinancial Institutions3e,Chapter14,CopyrightJohnC.Hull2012
Historical Simulation ⚫ Collect data on the daily movements in all market variables. ⚫ The first simulation trial assumes that the percentage changes in all market variables are as on the first day ⚫ The second simulation trial assumes that the percentage changes in all market variables are as on the second day ⚫ and so on Risk Management and Financial Institutions 3e, Chapter 14, Copyright © John C. Hull 2012 2
Historical Simulation continuedSupposeweusendaysofhistorical datawithtoday being day nLet y, be the value of a variable on day iThere are n-1 simulation trialsThe ith trial assumes that the yalue of themarket variable tomorrow (i.e., on day n+1) isV3RiskManagementandFinancialInstitutions3e,Chapter14,CopyrightJohnC.Hull2012
Historical Simulation continued ⚫ Suppose we use n days of historical data with today being day n ⚫ Let vi be the value of a variable on day i ⚫ There are n-1 simulation trials ⚫ The ith trial assumes that the value of the market variable tomorrow (i.e., on day n+1) is Risk Management and Financial Institutions 3e, Chapter 14, Copyright © John C. Hull 2012 3 i−1 i n v v v
Example:Portfolio on Sept252008(Table14.1,page304)IndexAmountInvested ($ooos)DJIA4,000FTSE1003,000CAC 401,000Nikkei2252,000Total10,000RiskManagementandFinancialInstitutions3e,Chapter14,CopyrightJohnC.Hull20124
Example: Portfolio on Sept 25, 2008 (Table 14.1, page 304) Risk Management and Financial Institutions 3e, Chapter 14, Copyright © John C. Hull 2012 4 Index Amount Invested ($000s) DJIA 4,000 FTSE 100 3,000 CAC 40 1,000 Nikkei 225 2,000 Total 10,000
U.S.DollarEquivalent of StockIndices (Table14.2,page305)DayDJIAFTSENikkeiDateCAC 40011,219.3811,131.846,373.89131.77Aug 7, 200616,378.16134.38Aug 8, 200611,173.5911,096.28211,185.356,474.04135.94Aug 9, 200611.076.183Aug 10, 200611,124.3711,016.716,357.49135.44499Sep 24,200810,825.179,438.586,033.93114.26500112.82Sep 25, 200811,022.069,599.906,200.40RiskManagementandFinancialInstitutions3e,Chapter14,CopyrightJohnC.Hull20125
U.S. Dollar Equivalent of Stock Indices (Table 14.2, page 305) Risk Management and Financial Institutions 3e, Chapter 14, Copyright © John C. Hull 2012 5 Day Date DJIA FTSE CAC 40 Nikkei 0 Aug 7, 2006 11,219.38 11,131.84 6,373.89 131.77 1 Aug 8, 2006 11,173.59 11,096.28 6,378.16 134.38 2 Aug 9, 2006 11,076.18 11,185.35 6,474.04 135.94 3 Aug 10, 2006 11,124.37 11,016.71 6,357.49 135.44 . . . . . . 499 Sep 24, 2008 10,825.17 9,438.58 6,033.93 114.26 500 Sep 25, 2008 11,022.06 9,599.90 6,200.40 112.82