Risk and utility in portfolio optimization

Morrel H. Cohen, Vincent D. Natoli

Research output: Contribution to journalConference articlepeer-review

12 Scopus citations


Modern portfolio theory (MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to alleviate that weakness which, typically, combine utility and risk. We present here a modification of MPT based on the inclusion of separate risk and utility criteria. We define risk as the probability of failure to meet a pre-established investment goal. We define utility as the expectation of a utility function with positive and decreasing marginal value as a function of yield. The emphasis throughout is on long investment horizons for which risk-free assets do not exist. Analytic results are presented for a Gaussian probability distribution. Risk-utility relations are explored via empirical stock-price data, and an illustrative portfolio is optimized using the empirical data.

Original languageEnglish (US)
Pages (from-to)81-88
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - Jun 1 2003
Externally publishedYes
EventProceedings of the International Econophysics Conference - Bali, Indonesia
Duration: Aug 29 2002Aug 31 2002

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics


  • Finance
  • Mean-variance
  • Portfolio
  • Risk utility


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