Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

Appendix 10.1: Various Formulae for Marginal Contribution and Volatilities

Marginal Contribution for Subportfolios—Partitioning

The marginal contribution can be calculated not just for single assets but also for groups of assets or for subportfolios. (See also Marrison 2002, 142.) For the full portfolio, the weights are the column vector:

with

These vectors can be formed into a matrix (which will have n rows and as many columns as partitions):

The partition might take the form of grouping assets together, for example, grouping assets 1 and 2 in partition a and all other assets on their own:

or it may take the form of subportfolios, so that the components ω_1a,...ω_na represent subportfolio ...