May 2012
Beginner
558 pages
15h 47m
English
book
Quantitative Risk Management: A Practical Guide to Financial Risk, + Website
by Thomas S. Coleman, Bob Litterman
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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 ω1a,...ωna represent subportfolio ...
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