When we design a value-at-risk measure, we must decide what physical or financial assets to represent with mathematical assets (, ). We might measure equity positions in shares or round lots. In Exercise 1.12 we measured them as the number of USD held in a given stock at time 0. Positions in cocoa might be measured in pounds, bags, or tons. The choice of units is largely arbitrary, but it must be explicit if we are to define portfolio holdings.
A portfolio’s holdings is a row vector ω indicating the number ωi of units held by the portfolio in each asset.