Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management

TL;DR

This paper develops a unified dynamic asset allocation framework that balances active outperformance with passive tracking, providing explicit strategies and analyzing their risk-reward trade-offs.

Contribution

It introduces a novel stochastic control approach to combine active and passive objectives in portfolio management with explicit solutions.

Findings

Explicit closed-form optimal allocation strategies.

Optimal strategies relate to growth optimal portfolios.

Numerical results illustrate favorable risk-reward profiles.

Abstract

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investor's portfolio and that of a performance benchmark while penalizing risk-weighted deviations from a given tracking portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the optimal allocation and we show how the optimal strategy can be related to the growth optimal portfolio. The admissible benchmarks encompass the class of functionally generated portfolios (FGPs), which include the market portfolio, as the only requirement is that they depend only on the prevailing asset values. Finally, some numerical experiments are presented to illustrate the risk-reward profile of the optimal allocation.