9.4.1 Example: Coffee Spreads
Consider our coffee wholesaler from Section 8.7. Based upon the primary mapping we constructed, the portfolio has exposures to a vector of coffee spreads:
[9.52]
Many of these coffees trade inactively, so historical data is unavailable for their spreads. We address the problem by identifying eight coffees that are actively traded, and consider a vector of spreads for these
[9.53]
We cannot directly approximate 1R Spreads with 
. The former has 30 components, whereas the latter has only 8. offers among its components no reasonable proxy for many of the components of 1R Spreads. We solve the problem by approximating 1R Spreads with a 30-dimensional vector 1Q comprising “blends” of the components of . Blends are specified by a knowledgeable coffee trader. The remapping has form
[9.54]
The mapping function 
is a linear function that can be represented with a matrix:
[9.55]
For each row of the matrix, components sum to 1. This is a practical requirement, but it is not logically necessary. The remapping provides us with key vector for which historical data is available.