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Risk and utility in portfolio optimization

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  • Cohen, Morrel H.
  • Natoli, Vincent D.

Abstract

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.

Suggested Citation

  • Cohen, Morrel H. & Natoli, Vincent D., 2003. "Risk and utility in portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 81-88.
    • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:81-88
    DOI: 10.1016/S0378-4371(02)01957-X
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    References listed on IDEAS

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    1. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, University Library of Munich, Germany.
    2. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    3. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
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    Cited by:

    1. Eliazar, Iddo, 2004. "Doubling an investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 240-252.
    2. Gökgöz, Fazıl & Atmaca, Mete Emin, 2017. "Portfolio optimization under lower partial moments in emerging electricity markets: Evidence from Turkey," Renewable and Sustainable Energy Reviews, Elsevier, vol. 67(C), pages 437-449.
    3. Meryem Masmoudi & Fouad Ben Abdelaziz, 2018. "Portfolio selection problem: a review of deterministic and stochastic multiple objective programming models," Annals of Operations Research, Springer, vol. 267(1), pages 335-352, August.
    4. Bohdan Yu. Kyshakevych & Anatoliy K. Prykarpatsky & Denis Blackmore & Ivan P. Tverdokhlib, 2010. "Statistically Optimal Strategy Analysis of a Competing Portfolio Market with a Polyvariant Profit Function," Papers 1005.2661, arXiv.org.

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