Master funds in portfolio analysis with general deviation measures

R. Tyrrell Rockafellar, Stan Uryasev, Michael Zabarankin

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

Generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, derived for example from conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors. They lead nonetheless to generalized one-fund theorems in which a more customized version of portfolio optimization is the aim, rather than the idea that a single "master fund" might arise from market equilibrium and serve the interests of all investors. The results that are obtained cover discrete distributions along with continuous distributions. They are applicable therefore to portfolios involving derivatives, which create jumps in distribution functions at specific gain or loss values, well as to financial models involving finitely many scenarios. Furthermore, they deal rigorously with issues that come up at that level of generality, but have not received adequate attention, including possible lack of differentiability to th deviation expression with respect to the portfolio weights, and the potential nonuniqueness of optimal weights.

Original languageEnglish
Pages (from-to)743-778
Number of pages36
JournalJournal of Banking and Finance
Volume30
Issue number2
DOIs
StatePublished - Feb 2006

Keywords

  • Basic fund
  • Conditional value-at-risk
  • Convex analysis
  • Deviation measures
  • Efficient frontier
  • Master fund
  • One-fund theorem
  • Portfolio optimization
  • Risk measures
  • Value-at-risk

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