Attributes and their Characteristic Portfolios

Abstract

The financial instruments, or in general the assets, of a portfolio have many kind of 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

$${a_V} \equiv \sum\limits_{k = 1}^M {{w_k}{a_k}} = {w^T}a$$

((28.1))

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, …s 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 applications¹.