Attributes and their Characteristic Portfolios
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 =(a1,…,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
KeywordsInternal Model Optimal Portfolio Risky Asset Excess Return Sharpe Ratio
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