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Utility Functions and Taylor Expansions in Portfolio Optimization

Article Quant Q&A · Author: Gcube
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Summary

The document raises a conceptual question about utility-based portfolio optimization. The author is unsure how to choose among common utility functions, including exponential and isoelastic utility, and questions how an expression involving exponential utility and a risk-aversion parameter should be interpreted in a maximization problem. They also ask whether utility should be approximated with a Taylor series, perhaps retaining terms through the fourth moment of the profit distribution.

The focus is on understanding the role of utility functions and the connection between utility maximization and distribution moments, with particular interest in isoelastic utility. The text gives no proposed solution, worked derivation, portfolio example, or empirical evidence. It is therefore a statement of questions rather than an explanation of an optimization method, and it leaves unresolved how utility choice should depend on investor preferences or portfolio constraints.

Key ideas

  • The author asks how to select a utility function for portfolio optimization.
  • Exponential and isoelastic utilities are mentioned as candidate forms.
  • The document questions how risk aversion affects the objective being maximized.
  • A Taylor expansion through the fourth moment is proposed as a possible approximation, but no answer is supplied.

Tags

Portfolio constructionRisk managementStatistics
Full text
# Utility-based portfolio optimization


# Utility-based portfolio optimization












I think I can't get the idea of optimization based on utility. For some reasons, I should choose one of several common utility functions (exponential, isoelastic function and some others). Obviously, in it's formal representation as 1-exp(-a*Profit)- a (risk-aversion) doesn't make any sense in maximization. So, should any function be expanded by Taylor series, for example until 4th moment of distribution? Like this:

Would be glad if you could help me with this. I'm especially interested in isoelastic function. Thank you in advance!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.