On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability

Taras Bodnar, Nestor Parolya, Wolfgang Schmid

Research output: Contribution to journalArticleScientificpeer-review

20 Citations (Scopus)

Abstract

In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns and the predictable variables follow a vector autoregressive process. We prove that the optimal portfolio weights depend on the covariance matrices of the next two periods and the conditional mean vector of the next period. The case without predictable variables and the case of independent asset returns are partial cases of our solution. Furthermore, we provide an exhaustive empirical study where the cumulative empirical distribution function of the investor's wealth is calculated using the exact solution. It is compared with the investment strategy obtained under the additional assumption that the asset returns are independently distributed.

Original languageEnglish
Pages (from-to)528-542
Number of pages15
JournalEuropean Journal of Operational Research
Volume246
Issue number2
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes

Keywords

  • Expected utility optimization
  • Exponential utility function
  • Multi-period asset allocation
  • Return predictability

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