Choosing CRRA or Quadratic Utility to Evaluate Portfolios

Summary

The document asks which utility function is appropriate for evaluating multi-asset funds using historical return distributions across different levels of risk aversion. It compares constant relative risk aversion (CRRA) utility with quadratic utility and asks whether conclusions about their suitability for asset allocation also apply when utility is used to rate existing portfolios.

The author characterizes CRRA as more behaviorally plausible and applicable to a wider range of return distributions, while noting that its calculation is more involved. Quadratic utility is described as most suitable when returns are normal, a condition that may not hold for many funds. The document asks when departures from normality make quadratic utility problematic and what use cases remain for it. It provides no responses, empirical comparison, or recommendation, so it raises a choice of evaluation framework without resolving it. The suitability of either measure depends on distributional assumptions and the purpose of the portfolio rating.

Key ideas

• The question compares CRRA and quadratic utility for rating multi-asset funds from historical returns.
• CRRA is presented as behaviorally more plausible and applicable to a wider range of return distributions.
• Quadratic utility is associated with normally distributed returns, an assumption the author doubts for many funds.
• The document does not determine when quadratic utility becomes problematic or recommend a preferred standard.

Tags

# The evaluation of a portfolio using quadratic utility or CRRA?


# The evaluation of a portfolio using quadratic utility or CRRA?












Given a (selection of) multi-asset fund I am finding the expected utility using the historical returns distribution for a range of risk aversion parameters, in order to yield some form of rating, and I’d like to know if there’s a preferred utility function to use. The decision, at the moment, is between CRRA and quadratic utility.

It’s become apparent that CRRA is a more sound choice behaviourally than quadratic utility along with more flexibility over the returns distributions it’s applicable to, but of course comes with a slightly more involved calculation. To my understanding quadratic utility is best when combined with normal returns which most funds don’t have. But the majority of conversations on this were in reference to the asset allocation problem, is the superiority only relevant here or do the same drawbacks manifest in the evaluation of expected utilities too?

The real question is does anyone use quadratic utility; if so which use cases? Or is CRRA just the standard nowadays? How far from the normal case do you need to stray before the issues with quadratic utility actually start to be problematic?

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