Benchmark-based deviation and drawdown measures in portfolio optimization

Michael Zabarankin, Bogdan Grechuk, Dawei Hao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Understanding and modeling of agent’s risk/reward preferences is a central problem in various applications of risk management including investment science and portfolio theory in particular. One of the approaches is to axiomatically define a set of performance measures and to use a benchmark to identify a particular measure from that set by either inverse optimization or functional dominance. For example, such a benchmark could be the rate of return of an existing attractive financial instrument. This work introduces deviation and drawdown measures that incorporate rates of return of indicated financial instruments (benchmarks). For discrete distributions and discrete sample paths, portfolio problems with such measures are reduced to linear programs and solved based on historical data in cases of a single benchmark and three benchmarks used simultaneously. The optimal portfolios and corresponding benchmarks have similar expected/cumulative rates of return in sample and out of sample, but the former are considerably less volatile.

Original languageEnglish
Pages (from-to)1561-1578
Number of pages18
JournalOptimization Letters
Volume18
Issue number7
DOIs
StatePublished - Sep 2024

Keywords

  • Benchmark
  • Deviation measure
  • Drawdown measure
  • Portfolio optimization

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