If You Have Said A, You Must Also Say B: Calculating Diversified Asset Returns

Abstract

The bottom-up route to portfolio diversification is clear: Combining individual assets into a portfolio will lower portfolio risk (especially when correlations are low). The top-down route of evaluating individual assets from the perspective of the diversified portfolio is widely applied in risk budgeting but is neglected in return attributions. Consequently, many investors evaluate individual assets on the basis of their undiversified returns instead of including the diversification benefits they offer. This perspective biases the evaluation of high-volatility/low-correlation assets in the portfolio. In this note, we highlight the importance of evaluating diversified returns and show how we can calculate these returns. We illustrate the method for a U.S. asset portfolio.