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When do two- or three-fund separation theorems hold?

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  • Carole Bernard
  • Corrado De Vecchi
  • Steven Vanduffel

Abstract

We show that when asset returns satisfy a location-scale property (possibly conditionally as e.g. for a multivariate generalized hyperbolic distribution) and the investor has law-invariant and increasing preferences, the optimal investment portfolio always exhibits two-fund or three-fund separation. As a consequence, we recover many of the three-fund (and two-fund) separation theorems that have been derived in the literature under very specific assumptions on preferences or distributions. These are thus merely special cases of the general characterization result for optimal portfolios that we provide.

Suggested Citation

  • Carole Bernard & Corrado De Vecchi & Steven Vanduffel, 2021. "When do two- or three-fund separation theorems hold?," Quantitative Finance, Taylor & Francis Journals, vol. 21(11), pages 1869-1883, November.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:11:p:1869-1883
    DOI: 10.1080/14697688.2021.1905172
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    Cited by:

    1. Ignas Gasparaviv{c}ius & Andrius Grigutis, 2024. "The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory," Papers 2402.10253, arXiv.org.

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