Simple Formulas for Portfolio Rebalancing Rules

Abstract

Portfolio rebalancing rules are used by large scale asset managers to manage a trade-off between frequent rebalancing on one hand, and a cost of deviating from the portfolio benchmark on the other. This note contributes to the design of such policies in two ways. First, it clarifies the analytical framework, by showing how the rebalancing problem can be formulated in a standard model for asset management. Although this step is straightforward, it is important as it makes a clear distinction between a risk factor and a risk factor exposure. Keeping this distinction facilitates the design of the optimal policy.

Second, for a given policy the note provides closed form expressions for certain statistical quantities relevant for the policy design. These include average rebalancing frequency, average annual transaction amount, mean square deviation from benchmark, and mean absolute deviation from benchmark. The resulting formulas are simple arithmetic expressions, easy to interpret and straightforward to implement.