### 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.

Original language | English (US) |
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Pages (from-to) | 81-88 |

Number of pages | 8 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 324 |

Issue number | 1-2 |

DOIs | |

State | Published - Jun 1 2003 |

Externally published | Yes |

Event | Proceedings of the International Econophysics Conference - Bali, Indonesia Duration: Aug 29 2002 → Aug 31 2002 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

### Keywords

- Finance
- Mean-variance
- Portfolio
- Risk utility

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## Cite this

*Physica A: Statistical Mechanics and its Applications*,

*324*(1-2), 81-88. https://doi.org/10.1016/S0378-4371(02)01957-X