Gianluca Fusai (Università del Piemonte Orientale e CASS)

joint with Domenico Mignacca

Diversification is a core concept in Asset Management. Yet, this term can mean different things to different people and there is no general consensus on how it is measured nor there is a broadly accepted metric for its reporting. In this paper, we propose a new index to quantify the diversification of a portfolio. Specifically, using the Euler's formula, we outline a new risk decomposition of the portfolio volatility that it is the basis to calculate our new diversification index (DIV). The appealing feature of our measure is its computational simplicity, given that  it only requires the covariance matrix of asset returns and the portfolio allocation. The main insight beneath the DIV index is that diversification is related not to the covariance among asset returns, but to their partial covariances once we control for the portfolio return. Motivating examples supporting the use of the new measure are discussed in detail. In particular, we motivate the construction of portfolios diversifying the DIV index across assets, exploiting the entropy principle.   We also provide a mathematical rationale for our  index, so that it can be easily extended to homogeneous risk measures not strictly related to the portfolio volatility.  Finally, our formula is able to measure diversification at asset, sub-portfolio and factor level.