The examples we have just considered are simple illustrations of the use of the linear model for calculating VaR or ES. Suppose that we have a portfolio worth P consisting of n assets with an amount αi being invested in asset . Define Δxi as the return on asset i in one day. The dollar change in the value of the investment in asset i in one day is αi Δxi and
where ΔP is the dollar change in the value of the whole portfolio in one day.
In the example considered in the previous section, $10 million was invested in the first asset (Microsoft) and $5 million was invested in the second asset (AT&T), so that (in millions of dollars) , , and
If we assume that the Δxi in ...