Measures of Contribution for Portfolio Risk

Chapter 1 Introduction This dissertation is intended to an analysis of the methods presented in literature which aim to quantify the impact of a single investment opportu- nity, an asset, a business line or a little portfolio to the total risk. We will see in fact that, as we have different investments constructing a portfolio, the sum of stand alone risks will not equal the aggregate risk, but it will be less (or at most equal). This due to the well-known effect of diversification. Before delving more specifically, it is better to introduce the basis of risk management, moving from some definition, a little bit of history and regulation. In the last years this field of finance has vastly developed and has been strongly revised in a mathematical basis. This thanks to the intro- duction of risk measures add to classical variance, rooted into the portfolio selection theory of Markowitz in the early mid-century. So risk contribution starts from the study of portfolio risk; in particular we will examine impor- tant properties that risk measures should satisfy. Afterwards, once these concepts are clear, we will proceed with the portfolio risk decomposition through various methods, each with different objective but this not means that are totally perfects. 1