Naive Markowitz Policies

TL;DR

This paper analyzes naive, continuously reoptimized Markowitz policies in a Black-Scholes market, showing they are inefficient and riskier than equilibrium policies, with explicit analytical derivations.

Contribution

It introduces a novel explicit analytical characterization of naive policies in continuous-time mean-variance optimization, contrasting them with optimal and equilibrium strategies.

Findings

Naive policies are mean-variance inefficient from any starting point.

Naive policies consistently take on higher risk than equilibrium policies.

Explicit formulas for naive policies are derived and analyzed.

Abstract

We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit of discretely naive policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naive policies with pre-committed optimal policies and with consistent planners' equilibrium policies in a Black-Scholes market, and find that the former are mean-variance inefficient starting from any given time and wealth, and always take riskier exposure than equilibrium policies.