Historical simulation approach, Risk Management

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

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