1.7.4 Example: Australian Equities (Monte Carlo Transformation)
We discuss the Monte Carlo method formally in Chapter 5. For now, an intuitive treatment will suffice. We assume is joint-normal with conditional mean vector 1|0μ =
and conditional covariance matrix 1|0Σ given by [1.35] Based upon these assumptions, we “randomly” generate 10,000 realizations,
,
, … ,
, of
. We set
[1.36]

for each k, constructing 10,000 realizations, ,
, … ,
, of
. Results are indicated in Exhibit 1.6.
Realizations of
are summarized with a histogram in Exhibit 1.7. We may approximate any parameter of
with the corresponding sample parameter of the realizations.


The sample .05-quantile of our realizations is GBP 191,614. We use this as an approximation of the .05-quantile,
(.05), of
. The .95-quantile of portfolio loss is:
[1.37]

[1.38]

[1.39]

The portfolio’s 1-day 95% GBPvalue-at-risk is approximately GBP 5925.