How are risks identified in the Portfolio Optimization Objectives functions? Usually with a measure of volatility, often with a particular focus on downside risk, or losing money.
But this describes only one aspect of the risks. It does not include a full breakdown of the results that investors can experience. For example, not owning an asset or investment that will subsequently outperform may cause an investor’s emotional reaction—with regret, for example—much like it does to traditional definitions of risk.
That’s why to understand risk for portfolio optimization purposes, we need to consider regret.
Among different investors, the performance of speculative assets such as cryptocurrencies can trigger different emotional reactions. Since I don’t have very favorable return expectations around cryptocurrencies and consider myself relatively rational, if the bitcoin price goes up to $1 million, I wouldn’t sweat it.
But another investor with unfavorable expectations of Bitcoin’s return may have a more negative reaction. For fear of missing out on future bitcoin price increases, they may give up a diversified portfolio in whole or in part to avoid such pain. This mixed reaction to bitcoin price movements suggests that the allocation should vary based on the investor. However, if we apply more traditional portfolio optimization functions, the bitcoin allocation will be identical – and potentially zero – to the other investor and me, assuming relatively unfavorable return expectations.
Thinking about regret means going beyond the pure mathematics of variance and other measures. It means trying to integrate the possible emotional response to a particular outcome. From technology to real estate to tulips, investors have succumbed to greed and regret in countless bubbles over the years. This is why a small allocation to “bad assets” can be beneficial if it reduces the likelihood that an investor will abandon a prudent portfolio to invest in those bad assets if they start to do well.
I presented an objective post explicitly incorporating regret into a portfolio optimization routine in new research for Portfolio Management Journal. More specifically, the function treats regret as a separate parameter from risk aversion, or downside risk – such as returns below 0% or some other target return – by comparing the return of the portfolio against the performance of one or more regret criteria, each with a probability Different level of regret aversion. The model requires no assumptions about the distributions of asset returns, or normality, so it can integrate lotteries and other assets with an unusual return.
By running a series of portfolio improvements using a portfolio of individual securities, I find that reflection on regret can materially influence allocation decisions. Risk levels — defined as downside risk — are likely to increase when regret is factored in, especially for risk-averse investors. Why? Because the assets that inspire the most regret tend to be more speculative in nature. More risk-tolerant investors are likely to achieve lower returns, with higher downside risks, assuming the risk asset is less efficient. However, more risk-averse investors could generate higher returns, albeit with significantly greater downside risk. In addition, provisions for the unfortunate asset can increase in parallel with 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 moderately less efficient within a larger portfolio but have the potential to cause regret may receive higher allowances depending on expected returns and variances. These findings may also influence how multi-asset funds are structured, particularly about the potential benefits of explicitly providing investors with information about the distinct exposures of a multi-asset portfolio versus a single fund, for example the Target Date Fund.
Of course, just because some clients may feel remorse doesn’t mean financial advisors and asset managers should start allocating inefficient assets. Instead, we should offer an approach that helps build portfolios that can explicitly consider regret in the context of an aggregate portfolio, given each investor’s preferences.
People are not utility-maximizing robots, or “human economics”. We need to create portfolios and solutions that reflect this. In this way we can help investors achieve better results across a variety of potential risk definitions.
For more information from David Blanchett, PhD, CFA, CPA, don’t miss “Redefining Optimal Retirement Income Strategy” from Financial Analysts Journal.
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All posts are the opinion of the author. As such, it should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of the CFA Institute or the author’s employer.
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David Blanchett, Ph.D., CFA, CFP
