A GOALS-BASED THEORY OF UTILITY

PUBLISHER: Journal of Behavioral Finance, forthcoming
DATE: February 6, 2020 (online)
DOI: https://doi.org/10.1080/15427560.2020.1716359

IN-ENGLISH SUMMARY
In this article, I am primarily concerned with building a cohesive theory for two basic things.

First, how can you divvy wealth between multiple goals that are mutually-exclusive? For example, suppose you want to buy a vacation home in five years and retire in 25 years. Funding a vacation home necessarily reduces your probability of retirement. Given the framework of this paper, we can now know how much of your wealth you should dedicate to the vacation home and how much you should dedicate to retirement.

Second, I find that mean-variance optimization (modern portfolio theory, or MPT) is not ideal for goals-based investors. Rather, goals-based investors should be using a probability maximization framework. For most applications they are the same, but for aspirational goals MPT delivers lower probabilities of goal achievement.

I also spend some time analyzing a few utility paradoxes and probability weighting functions showing that they can be solved if individuals are goals-based.

FORMAL ABSTRACT
Theoretical frameworks to date have prescribed how an investor should allocate wealth within mental accounts. However, there is no fully cohesive solution to prescribe how an investor should rationally allocate resources across mental accounts. It is the aim of this discussion to fill that theoretical gap. We present a framework which can be used to rationally allocate resources both within and across mental accounts or goals. We then compare and contrast this method with mean-variance optimization and behavioral portfolio theory, showing that both are stochastically dominated by the goals-based utility framework. In further analysis of empirical validity, we discuss the Samuelson Paradox, Friedman-Savage puzzle, and probability weighting functions.

KEYWORDS
Mental accounting, Goals-based investing, Portfolio theory, Utility theory