TY - JOUR
T1 - Portfolio optimization beyond utility maximization
T2 - the case of driftless markets
AU - Vecer, Jan
AU - Richard, Mark
AU - Taylor, Stephen
N1 - Publisher Copyright:
© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2025
Y1 - 2025
N2 - This paper presents a novel perspective on portfolio optimization by recognizing that prices can be expressed as a scaled likelihood ratio of state price densities. This insight leads to the immediate conclusion that the optimal portfolio has a simple representation in terms of the likelihood ratio between the agent-defined physical measure and the risk-neutral measure, eliminating the need for utility maximization. The agent only needs to specify her choice of the physical measure, and we demonstrate both frequentist and Bayesian approaches for this selection. Utility maximization can be seen as a specific method for choosing the physical measure. The resulting likelihood ratio is log-utility optimal with respect to all benchmarks, aligning our approach with finding the growth optimal portfolio described in the literature. Notably, the expected log return corresponds to the relative entropy between the physical and risk-neutral measures, establishing a fundamental link to information theory. As a proof of concept, we explore previously unexplored territory in portfolio optimization, specifically addressing perceived mean reversion in specific driftless markets, such as foreign exchange (FX) markets.
AB - This paper presents a novel perspective on portfolio optimization by recognizing that prices can be expressed as a scaled likelihood ratio of state price densities. This insight leads to the immediate conclusion that the optimal portfolio has a simple representation in terms of the likelihood ratio between the agent-defined physical measure and the risk-neutral measure, eliminating the need for utility maximization. The agent only needs to specify her choice of the physical measure, and we demonstrate both frequentist and Bayesian approaches for this selection. Utility maximization can be seen as a specific method for choosing the physical measure. The resulting likelihood ratio is log-utility optimal with respect to all benchmarks, aligning our approach with finding the growth optimal portfolio described in the literature. Notably, the expected log return corresponds to the relative entropy between the physical and risk-neutral measures, establishing a fundamental link to information theory. As a proof of concept, we explore previously unexplored territory in portfolio optimization, specifically addressing perceived mean reversion in specific driftless markets, such as foreign exchange (FX) markets.
KW - Bayesian market
KW - Likelihood ratio
KW - growth optimal portfolio
KW - relative entropy
KW - utility maximization
UR - http://www.scopus.com/inward/record.url?scp=85198726694&partnerID=8YFLogxK
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U2 - 10.1080/1351847X.2024.2375221
DO - 10.1080/1351847X.2024.2375221
M3 - Article
AN - SCOPUS:85198726694
SN - 1351-847X
VL - 31
SP - 318
EP - 347
JO - European Journal of Finance
JF - European Journal of Finance
IS - 3
ER -