Derivatives and Internal Models pp 535-551 | Cite as

# Attributes and their Characteristic Portfolios

## Abstract

The financial instruments, or in general the assets, of a portfolio have many *characteristics* or *attributes* such as expected return, market capitalization, beta with respect to an index, membership in a certain economic sector, etc. If we denote a certain attribute by *a*_{ i } for asset *i* (having value *V*_{ i }) then the *exposure* of a portfolio *V* (with weights *w*_{ k } for *k* = 1,..., *M*) to this particular attribute is defined as

where we have used the obvious notation **a**^{ T } =(*a*_{1},…,*a*_{ M })- If, for instance the characteristics *a*_{ i } are measures of how strongly the assets *i* = 1,…, *M* belong to the automotive industry then *a*_{ V } is the exposure of the portfolio to the automotive industry. Another example: If the characteristics *a*_{ i } are the asset returns *R*_{ i } then the exposure *a*_{ V } is simply the portfolio return *R*_{ V }. From these examples one can already guess that characteristics (or attributes) are a very general and rather abstract concept with broad applications.^{1}

## Keywords

Internal Model Optimal Portfolio Risky Asset Excess Return Sharpe Ratio## Preview

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