1) What difference does it make to the Var calculated in Example if the exponentially weighted moving average model is used to assign weights to scenarios as described in Section 12.3?
Suppose that Five stressed scenarios are considered. They lead to losses($000s) of 235, 300, 450, 750, and 850. The subjective probabilities assigned to the scenarios are 0.5%, 0.2%, 0.2%, .05% and.05% respectively. The total probability of the stressed scenarios is, therefore, 1%, This means that the probability assigned to the scenarios generated by historical simulation if 99%, Assuming the equal weighting is used, each historical simulation scenario is assigned a probability of .99/500 =.00198. The probabilities assigned to scenarios are accumulated from the worst scenario to the best. The Var level when the confidence level is 99% is the first loss for which the cumulative probability is greater than.01. in the our example this is $300,000
Investment portfolio used for VaR Calculations.
Index Portfolio Value ($000s)
DJIA $4,000
FTSE 100 $3,000
CAC 40 $1,000
Nikkei 225 $2,000
Total $10,000
Table
Scenarios generated for September 26, 2008
Scenario Number DJIA FTSE100 CAC 40 Nikkei 224 Portfolio Value (000s) Loss ( $000s)
1 10,977.08 5,187.46 4,236.71 12,252.62 10,021.502 -21.502
2 10,925.97 5,234.87 4,275.48 12,155.54 10,023.327 -23.327
3 11,070.01 5,164.10 4,186.01 11,986.84 9,985,478 14.522
.
.
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499 10,831.43 5,057.36 4,117.75 12,030.80 9828.450 171.550
500 11,222.53 5,300.42 4,342.14 11,899.00 10,141.826 -141.82