On time consistency for mean-variance portfolio selection

This paper addresses a comparison between different approaches to time inconsistency for the mean-variance portfolio selection problem. We define a suitable intertemporal preferences-driven reward and use it to compare three common approaches to time inconsistency for the mean-variance portfolio selection problem over [t0,T]: precommitment approach, consistent planning or game theoretical approach, and dynamically optimal approach. We prove that, while the precommitment strategy beats the other two strategies (that is a well-known obvious result), the consistent planning strategy dominates the dynamically optimal strategy until a time point t∗∈ (t 0,T) and is dominated by the dynamically optimal strategy from t∗ onwards. Existence and uniqueness of the break even point t∗ is proven.