Application to 4 index portfolio ? 0995 table 135

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

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

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

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