Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-12-09
Physics
Condensed Matter
Statistical Mechanics
10 pages, 1 figure, presented at 2002 Conference on Econophysics in Bali Indonesia
Scientific paper
10.1016/S0378-4371(02)01957-X
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.
Cohen Morrel H.
Natoli Vincent D.
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