Downside risk optimization with random targets and portfolio amplitude

Zinoviy Landsman, Udi Makov, Jing Yao, Ming Zhou

Research output: Contribution to journalArticlepeer-review


In this paper, we discuss downside risk optimization in the context of portfolio selection. We derive explicit solutions to the optimal portfolios that minimize the downside risk with respect to constant targets and random targets. In doing so, we propose using portfolio amplitude, a new measure in the literature, to characterize the portfolio selection under the downside risk optimization. Particularly, we demonstrate a mechanism by which the random target inputs its impact into the system and alters the optimal solution. Our results underpin why investors prefer holding some specific assets in following random targets and provide explanations for some special investment strategies, such as constructing a stock portfolio following a bond index. We present numerical examples of stock portfolio management to support our theoretical results.

Original languageEnglish
Pages (from-to)1642-1663
Number of pages22
JournalEuropean Journal of Finance
Issue number16
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.


  • Portfolio management
  • downside risk
  • investment behavior
  • portfolio amplitude

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)


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