1.7.4 Example: Australian Equities (Monte Carlo Transformation)

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.

Exhibit 1.06: Results of the Monte Carlo analysis
Exhibit 1.07: Histogram of realizations for the portfolio’s value at time 1

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.