Granularity Adjustment for Efficient Portfolios

This article considers large portfolios of assets submitted to both systematic and unsystematic (or idiosyncratic) risks. The idiosyncratic risks can be fully diversified if the portfolio size is infinite, but only partly diversified otherwise. The granularity adjustment measures the effect of partly diversifying idiosyncratic risks. We derive the granularity adjustments for a portfolio with naive diversification and for the efficient mean-variance portfolio allocation. We consider in particular the Sharpe performances, with and without short-sale restrictions and we highlight the effect of concentration risk.