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.