Equally Diversified or Equally Weighted?

The aim of this paper is to shed new light on the concept of diversification showing that it is not necessarily related to the reduction of the volatility of a portfolio, as it is commonly perceived. We introduce a diversification index that exploits the decomposition of portfolio volatility into undiversified volatility and a diversification component. The diversification component offsets the undiversified part leaving as a final result the portfolio volatility itself. Our decomposition has a clear statistical interpretation because it relates the diversification component to the so-called partial covariances, i.e. the covariances between the residuals of the regressions of the weighted asset returns with respect to the portfolio return. On this basis, we advocate the construction of an equally diversified portfolio versus an equally weighted portfolio. An empirical analysis illustrates the superior performance of the equally diversified portfolios with respect to the equally weighted portfolio.