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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. 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.
    3. 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.
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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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