Practical analysis for investment professionals
12 May 2023

Regret and Optimal Portfolio Allocations

How is risk defined in portfolio optimization objective functions? Usually with a volatility metric, and often one that places a particular emphasis on downside risk, or losing money.

But that only describes one aspect of risk. It doesn’t capture the entire distribution of outcomes investors could experience. For example, not owning an asset or investment that subsequently outperforms could trigger an emotional response in an investor — regret, say — that resembles their reaction to more traditional definitions of risk.

That’s why to understand risk for portfolio optimization purposes, we need to consider regret.

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Among different investors, the performance of speculative assets such as cryptocurrencies could potentially evoke different emotional responses. Since I don’t have very favorable return expectations around cryptocurrencies and consider myself relatively rational, if the price of bitcoin increases to $1 million, I wouldn’t sweat it.

But another investor with similarly unfavorable bitcoin return expectations could have a much more adverse response. Out of fear of missing out on future bitcoin price increases, they might even abandon a diversified portfolio in whole or in part to avoid such pain. Such divergent reactions to bitcoin price movements suggest that allocations should vary based on the investor. Yet if we apply more traditional portfolio optimization functions, the bitcoin allocation would be identical — and likely zero — for the other investor and me, assuming relatively unfavorable return expectations.

Considering regret means moving beyond the pure math of variance and other metrics. It means attempting to incorporate the potential emotional response to a given outcome. From tech to real estate to tulips, investors have succumbed to greed and regret in countless bubbles throughout the years. That’s why a small allocation to a “bad asset” could be worthwhile if it reduces the probability that an investor might abandon a prudent portfolio to invest in that bad asset should it start doing well.

I introduce an objective function that explicitly incorporates regret into a portfolio optimization routine in new research for the Journal of Portfolio Management. More specifically, the function treats regret as a parameter distinct from risk aversion, or downside risk — such as returns below 0% or some other target return — by comparing the portfolio’s return against the performance of one or more regret benchmarks, each with a potentially different regret aversion level. The model requires no assumptions around return distributions for assets, or normality, so it can incorporate lotteries and other assets with very non-normal payoffs.

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By running a series of portfolio optimizations using a portfolio of individual securities, I find that considering regret can materially influence allocation decisions. Risk levels — defined as downside risk — are likely to increase when regret is taken into account, especially for more risk-averse investors. Why? Because the assets that inspire the most regret tend to be more speculative in nature. Investors who are more risk tolerant will likely achieve lower returns, with higher downside risk, assuming the risk asset is less efficient. More risk-averse investors, however, could generate higher returns, albeit with significantly more downside risk. Additionally, allocations to the regret asset could increase in tandem with its assumed volatility, which is contrary to traditional portfolio theory.

What are the implications of this research for different investors? For one thing, assets that are only mildly less efficient within a larger portfolio but potentially more likely to cause regret could receive higher allocations depending on expected returns and covariances. These findings may also influence how multi-asset funds are structured, particularly around the potential benefits from explicitly providing investors with information around a multi-asset portfolio’s distinct exposures versus a single fund, say a target-date fund.

Of course, because some clients may experience regret does not mean that financial advisers and asset managers should start allocating to inefficient assets. Rather, we should provide an approach that helps build portfolios that can explicitly consider regret within the context of a total portfolio, given each investor’s preferences.

People are not utility maximizing robots, or “homo economicus.” We need to construct portfolios and solutions that reflect this. That way we can help investors achieve better outcomes across a variety of potential risk definitions.

For more from David Blanchett, PhD, CFA, CPA, don’t miss “Redefining the Optimal Retirement Income Strategy,” from the Financial Analysts Journal.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Image credit: ©Getty Images / jacoblund


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About the Author(s)
David Blanchett, PhD, CFA, CFP

David Blanchett, PhD, CFA, CFP®, is managing director, portfolio manager, and head of retirement research for PGIM DC Solutions. PGIM is the global investment management business of Prudential Financial, Inc. In this role, he develops solutions to help improve retirement outcomes for investors with a specific focus on defined contribution plans. Prior to joining PGIM, he was the head of retirement research for Morningstar Investment Management LLC. Blanchett has published more than 100 papers in both industry and academic journals that have received a variety of awards, including the Financial Analysts Journal Graham and Dodd Scroll Award in 2015. Blanchett is currently an adjunct professor of wealth management at The American College of Financial Services and a research fellow for the Alliance for Lifetime Income. He was formally a member of the executive committee for the Defined Contribution Institutional Investment Association (DCIIA) and the ERISA Advisory Council (2018-2020). Blanchett holds a bachelor’s degree in finance and economics from the University of Kentucky, a master’s degree in financial services from The American College of Financial Services, a master’s degree in business administration from the University of Chicago Booth School of Business, and a doctorate in personal financial planning program from Texas Tech University. When he isn’t working, Blanchett is probably out for a jog, playing with his four kids, or rooting for the Kentucky Wildcats.

2 thoughts on “Regret and Optimal Portfolio Allocations”

  1. Charles M Reilly says:

    In the paragraph that starts with “Among different investors,” and the next two paragraphs , do the terms ‘investor’ & ‘investors’ refer to investment managers or investors who invest in the portfolios of investment managers ?

    1. Dare Shola Oyewo says:

      I believe they refer to investors who have their portfolios managed by investment managers, such that the investors have an input into what assets they would like their funds to be allocated to, except in cases where the investment manager has full autonomy over the asset allocation, hence the feeling of regret will be on the part of the investment manager, if he/she failed to invest in bitcoin and it happened to perform well.

      In either case, the author advises, that regret is to be factored in as a risk while allocating assets to mitigate its effect on the fund owner.

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