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Investment decisions when utility depends on wealth and other attributes

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  • Andrew Grant
  • Steve Satchell

Abstract

The problem of optimal investment under a multivariate utility function allows for an investor to obtain utility not only from wealth, but other (possibly correlated) attributes. In this paper we implement multivariate mixtures of exponential (mixex) utility to address this problem. These utility functions allow for stochastic risk aversions to differing states of the world. We derive some new results for certainty equivalence in this context. By specifying different distributions for stochastic risk aversions, we are able to derive many known, plus several new utility functions, including models of conditional certainty equivalence and multivariate generalisations of HARA utility, which we call dependent HARA utility. Focusing on the case of asset returns and attributes being multivariate normal, we optimise the asset portfolio, and find that the optimal portfolio consists of the Markowitz portfolio and hedging portfolios. We provide an empirical illustration for an investor with a mixex utility function of wealth and sentiment.

Suggested Citation

  • Andrew Grant & Steve Satchell, 2020. "Investment decisions when utility depends on wealth and other attributes," Quantitative Finance, Taylor & Francis Journals, vol. 20(3), pages 499-513, March.
    • Handle: RePEc:taf:quantf:v:20:y:2020:i:3:p:499-513
    DOI: 10.1080/14697688.2019.1663903
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    Cited by:

    1. Alexander, Carol & Han, Yang & Meng, Xiaochun, 2023. "Static and dynamic models for multivariate distribution forecasts: Proper scoring rule tests of factor-quantile versus multivariate GARCH models," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1078-1096.
    2. Oleg S. Sukharev, 2020. "Portfolio Theory in Solving the Problem Structural Choice," JRFM, MDPI, vol. 13(9), pages 1-21, September.
    3. Julian Amon & Margarethe Rammerstorfer & Karl Weinmayer, 2021. "Passive ESG Portfolio Management—The Benchmark Strategy for Socially Responsible Investors," Sustainability, MDPI, vol. 13(16), pages 1-21, August.

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