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1 July 2019 Financial Analysts Journal

Choosing and Using Utility Functions in Forming Portfolios (Summary)

  1. Keyur Patel

This In Practice piece gives a practitioner’s summary of the article “Choosing and Using Utility Functions in Forming Portfolios,” by Geoffrey J. Warren, published in the Third Quarter 2019 issue of the Financial Analysts Journal.

What’s the Investment Issue?

A common approach to constructing portfolios is to use metrics that summarise the distribution of outcomes, mean–variance analysis being the most commonly used solution.

But mean–variance analysis assesses risk and return over an often-limited horizon in a one-size-fits-all approach. The author points out that a customised utility function, although rarely used in practice, offers investors a customised approach that accommodates multiple horizons and targeted outcomes. This is of particular use with endowments, private wealth clients, retired investors, and defined benefit funds. The author sets out to provide practical guidance on how investors can build portfolios tailored to their objectives and preferences using utility functions, without the need to delve into complex mathematical or simulation techniques.

How Does the Author Tackle the Issues?

The author looks at three of the most applicable utility functions. One is power utility, which tends to be more suited to investors whose risk aversion does not change with their level of wealth. The other two are variations of reference-dependent utility, which is typically appropriate for investors with an objective that involves achieving some target. The author compiles charts to compare how power utility and reference-dependent utility evaluate outcomes (portfolios) and shows that they have differing implications for optimal asset distribution as horizons and wealth change.

Next, the author explores how investors might choose a suitable utility function. He charts and compares the results of experimental studies from prior literature to portray the dangers of picking a utility function “off the shelf.”

Third, he describes a four-step approach for identifying optimal portfolios using utility functions and then applies his approach to four representative investor types: private investors investing in a pot of wealth they want to grow, an endowment fund investing in a pool of capital to support philanthropic activities, a defined benefit fund investing to satisfy a stream of pension payments, and an individual at the point of retirement.

What Are the Implications for Investors and Investment Professionals?

The author makes the case that utility-based analysis can offer a flexible and effective approach to constructing investment portfolios in practical settings. The familiar mean–variance analysis may be less suitable over long horizons—especially when investors intend to draw on wealth over multiple periods. It can also be ineffective when investors care about a target outcome, such as delivering a real return or generating a required income stream (e.g., one required by defined benefit funds, endowments, and retirees). By contrast, a utility-based analysis can be tailored to many different types of investors with varying objectives and preferences and can be implemented in a spreadsheet.

A key takeaway of this study, says the author, is that investors should select a utility function based on their particular circumstances. Simply relying on findings from academic literature to provide validation may be counterproductive. There is no “right” utility function—investors differ, and utility functions need to be purposefully selected to reflect what really matters to any individual investor.

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