A Near Optimal Portfolio Rule for the Life Cycle Merton Problem

Lorenzo Reus, Pablo Castañeda

Research output: Contribution to journalArticlepeer-review

Abstract

This work presents a novel method for finding near-optimal solutions to the life cycle problem à la Merton with a time-varying investment opportunity set and portfolio constraints. The method produces consumption-investment rules which are easier to compute and implement than current alternatives, at least for the investment opportunity set defined in Munk and Sørensen (2010). The first step uses the martingale approach to obtain a portfolio rule in a complete artificial market. The second step determines analytical approximations accounting for the hedging demand components, delivering a closed-form portfolio rule, even for incomplete markets. The third step finds a near-optimal solution when additional portfolio constraints are present. This is done by determining the Lagrangian processes that satisfy the primal-dual optimality conditions between the true and artificial markets. This work provides simple optimization problems for determining the multipliers in environments with multiple assets and common portfolio constraints. Simulation results in a two-asset case environment show that the solution obtained is, in many cases, similar to the solutions presented in previous studies. When differences emerge, the solution of the proposed method outperforms in most cases, both in certainty-equivalent levels and execution times. A 15-year empirical backtest applied to a portfolio of six different asset-class exchange-traded funds (ETFs) show that the method outperforms its benchmarks in terms of return/risk measures.

Original languageEnglish
JournalComputational Economics
DOIs
StateAccepted/In press - 2024
Externally publishedYes

Keywords

  • Artificial markets
  • Convex duality
  • Life-cycle investing
  • Merton solution
  • Portfolio selection

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