Application to 4 Index Portfolio � 0995 Table 135 page 302 Risk Management and

Application to 4 index portfolio ? 0995 table 135

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Application to 4-Index Portfolio λ =0.995 (Table 13.5, page 302) Risk Management and Financial Institutions 5e, Chapter 13, Copyright © John C. Hull 2018 12 Scenario Number Loss ($000s) Weight Cumulative Weight 494 477.841 0.00528 0.00528 339 345.435 0.00243 0.00771 349 282.204 0.00255 0.01027 329 277.041 0.00231 0.01258 487 253.385 0.00510 0.01768 227 217.974 0.00139 0.01906 One-day 99% VaR=$282,204 One day 99% ES is [0.00528×477,841+0.00243×345,435+(0.01-0.00528 - 0.00243)×282,204]/0.01 = $400,914
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Volatility Scaling ° Hull and White (1998) suggest a way of incorporating estimates of volatility into the historical simulation approach ° Use a volatility updating scheme to monitor volatilities of all market variables ° If the current volatility for a market variable σ n+1 is β times the volatility σ i on Day i , multiply the percentage change observed on day i by β= σ n+1 / σ i ° Value of market variable under i th scenario becomes Risk Management and Financial Institutions 5e, Chapter 13, Copyright © John C. Hull 2018 13 1 1 1 1 / ) ( - + - - σ σ - + i i n i i i n v v v v v
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Volatility Scaling – Why? ° This approach takes account of volatility changes in a natural and intuitive way and produces VaR estimates that incorporate more current information. ° The VaR estimates can be greater than any of the historical losses that would have occurred for the current portfolio during the historical period considered. ° Hull and White produce evidence using exchange rates and stock indices to show that this approach is superior to traditional historical simulation and to the exponential weighting scheme described earlier. Risk Management and Financial Institutions 5e, Chapter 13, Copyright © John C. Hull 2018 14
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Volatility Adjusted Losses (Table 13.7, page 304) Risk Management and Financial Institutions 5e, Chapter 13, Copyright © John C. Hull 2018 15 Scenario Number Loss ($000s) 131 1,082.969 494 715.512 227 687.720 98 661.221 329 602.968 339 546.540 74 492.764 One-day 99% VaR = $602,968 One-day 99% ES = (1,082,969+715,512+687,720+661,221)/4 = $786,855
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