22.4 THE LINEAR MODEL

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 i(1in). 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

ΔP=i=1nαiΔxi(22.2)

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) α1=10, α2=5, and

ΔP=10Δx1+5Δx2

If we assume that the Δxi in ...

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