The second step is to sort the 250 changes in portfolio value in ascending order to
arrive at an observed distribution of changes in portfolio value. The histogram of
these changes is shown in Figure 3. The VaR number will be equal to that percentile
associated with the specified level of confidence. For a 95 per cent level of
confidence, the VaR number is 68.17 AUD and equals the 5th percentile of the
distribution of changes in portfolio value. The kth percentile means that the lowest
k per cent of the sample of changes in portfolio value will exceed the VaR measure.
Since there are 250 observations, essentially this means that 12.5 losses (or 5 per
cent of the sample) will be larger than the VaR measure (the VaR measure is
essentially the 13.5 lowest observation). Similarly, for a 99 per cent level of
confidence the VaR number is 102.11 and equals the first percentile. These results
are summarised in Table 5.