Diversification Return and Leveraged Portfolios

Abstract

It is widely accepted that portfolio rebalancing adds diversification return to fixed-weight portfolios, but this is only true for long-only unleveraged portfolios. Qian provides analytical results regarding portfolio rebalancing and the associated diversification returns for different kinds of portfolios including long-only, long-short, and leveraged. He shows that portfolio rebalancing is linked to underlying portfolio dynamics. For long-only unleveraged portfolios, rebalancing amounts to a mean-reverting strategy, and the diversification return is always non-negative. But for short (or inverse) and leveraged portfolios, portfolio rebalancing on the top-down level amounts to a trend-following strategy that detracts from diversification return. Qian analyzes diversification returns of risk parity portfolios and shows that the diversification return of a leveraged long-only portfolio can generally be decomposed into two parts, both of which are related to a scaled unleveraged portfolio. The first part is the positive diversification return from rebalancing among individual assets at the bottom- up level, which is amplified by leverage. The second part is the negative diversification return caused by the leverage of the overall portfolio. His numerical examples show that diversification return is, in general, positive for leveraged risk parity portfolios when the leverage ratio is not too high. In addition, he shows that low correlations between different assets are crucial in achieving positive diversification return and reducing portfolio turnover for risk parity portfolios.