How is risk defined in goal functions of portfolio optimization? Typically with a volatility measure and infrequently with a measure that places particular emphasis on downside risk or loss of cash.
But that only describes one aspect of the danger. It doesn’t capture the complete distribution of outcomes that investors could achieve. For example, not owning an asset or investment that subsequently outperforms could trigger an emotional response—say, regret—in an investor that is analogous to their response to more traditional definitions of risk.
Therefore, we want to contemplate regret to know risk for portfolio optimization purposes.
The performance of speculative assets comparable to cryptocurrencies could potentially elicit different emotional reactions from different investors. Since I do not have particularly positive return expectations for cryptocurrencies and consider myself relatively rational, I would not worry if the worth of Bitcoin rises to $1 million.
But one other investor with similarly unfavorable Bitcoin return expectations may need a way more negative response. Fearful of missing out on future Bitcoin price increases, they may even forego a diversified portfolio in whole or partially to avoid such pain. Such varied reactions to Bitcoin price movements suggest that allocations should vary depending on investors. However, if we apply more traditional portfolio optimization functions, the Bitcoin allocation for the opposite investor and me can be similar – and possibly zero – assuming return expectations are relatively unfavorable.
Taking regret under consideration means going beyond the pure mathematics of variance and other metrics. It means trying to include the potential emotional response to a selected final result. From technology to real estate to tulips, investors have succumbed to greed and regret in countless bubbles through the years. For this reason, a small allocation to a “bad asset” may be worthwhile if it reduces the likelihood that an investor will abandon a prudent portfolio and put money into that bad asset when it performs well.
I’ll introduce one Objective function that explicitly incorporates regret right into a portfolio optimization routine in recent research for the . More specifically, the function treats regret as a parameter distinct from risk aversion or downside risk—for instance, returns below 0% or another goal return—by comparing the portfolio’s return to the performance of a number of regret benchmarks, respectively with a possible value various degrees of regret aversion. The model doesn’t require any assumptions about asset return distribution or normality, so it could actually incorporate lotteries and other assets with very unusual payouts.
By performing a series of portfolio optimizations on a portfolio of individual securities, I find that accounting for regret can significantly influence allocation decisions. The level of risk – defined as downside risk – is more likely to increase when regret is taken under consideration, particularly for more risk-averse investors. Why? Because the assets that cause probably the most regret are inclined to be more speculative in nature. Investors who’re more risk tolerant are more likely to achieve lower returns with higher downside risk if the danger investment is less efficient. However, more risk-averse investors could achieve higher returns, albeit with significantly higher downside risk. Furthermore, allocations to the regret asset could increase in parallel with its assumed volatility, contradicting traditional portfolio theory.
What implications does this research have for various investors? First, assets which are only barely less efficient inside a bigger portfolio, but perhaps more more likely to generate regret, could receive higher allocations depending on their expected returns and covariances. These findings may additionally have implications for the structuring of multi-asset funds, particularly given the potential advantages of explicitly providing details about the various exposures of a multi-asset portfolio in comparison with a single fund, for instance a goal fund for investors.
Of course, the incontrovertible fact that some clients may feel remorse doesn’t mean that financial advisors and wealth managers should start investing in inefficient assets. Rather, we must always provide an approach that helps construct portfolios that may explicitly account for regret within the context of an overall portfolio, making an allowance for each investor’s preferences.
Humans aren’t utility-maximizing robots or “homo economicus”. We have to construct portfolios and solutions that reflect this. In this fashion, we may also help investors achieve higher results across a wide selection of potential risk definitions.
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