مقاله انگلیسی رایگان در مورد انتخاب پورتفوی در تعادل شخصی – الزویر 2018

This paper finds that in portfolio choice where reference point arises endogenously in personal equilibria, investors behave as if they had a concave probability weighting function. This finding establishes a link between the reference-dependent utility and the rank-dependent utility theories.

Introduction

In a stimulating paper, Kőszegi and Rabin (2007) (KR, henceforth) explored how individuals with expectation-based referencedependent preferences make a risky choice. In their model, individuals care about consumption utility as well as gain–loss utility (i.e., utility over deviations from the reference), and the reference is the full distribution of the payoff reflecting individuals’ expectations. KR provide a solution framework for the formation of expectations-based reference, in which the individual knows exactly how he or she will behave in any future contingency and his or her reference point reflects this actual behavior. KR’s framework has inspired numerous applications. Among others, Heidhues and Kőszegi (2008) use this framework to study the Salop price competition; Herweg et al. (2010) apply it to re-design the employee compensation contracts; Karle and Peitz (2014) employ it to study the firm competition with asymmetric information regarding consumer tastes. In financial markets, Pagel (2016) explores the assetpricing implications of KR’s solution in a Lucas-tree model with dynamic asset allocations, while Pagel (2018) uses KR’s framework to solve a life-cycle portfolio choice problem in which the investor experiences loss-averse utility over news. Despite the existing applications, the implications of KR’s framework on optimal portfolio choice are not fully investigated. Pagel (2016, 2018) use KR’s framework in intermediate steps to solve the portfolio choice problems. However, she obtained the unique solution only for power and log utility functions under lognormal distributions for risky assets. It is not clear whether the solution would be unique for all concave utility functions and all continuous distributions, and how to characterize the optimal portfolio weights in KR’s framework in the more general setting. The purpose of our paper is to address these questions. Specifically, we offer an explicit characterization of the solution to the portfolio choice problem in KR’s framework under a general setting. KR introduces two specific solution concepts. One is the ‘‘unacclimating personal equilibrium’’ (UPE, henceforth), defined for the case where the choice is made based upon the reference, and equilibrium is achieved when the optimal choice coincides exactly with the reference. The other one is the ‘‘choiceacclimating personal equilibrium’’ (CPE, henceforth), defined for the case where the individual first sets the choice as the reference, and then optimizes over the choices. As KR argued, UPE arises in a context where individuals expect a choice only if they are willing to follow it through, while CPE applies in a context where individuals commit to a choice before outcomes occur. We show that investors in both UPE and CPE behave as if they had a concave probability weighting function, as axiomatized by Yaari (1987). This characterization is interesting because it establishes an equivalence between nonstandard utility under correct beliefs and standard utility under distorted beliefs. The equivalent concave probability weighting function implies that the choice in UPE is unique. Only with uniqueness, we are able to determine the UPE by virtue of the first-order condition and further translate this condition into a rank-dependent structure. This result is in contrast to the previous finding of multiple UPE choices under a discrete choice set, as shown in KR.1 The change in the property of UPE is driven by the change in the structure of the choice set: when the choice set contains only discrete strategies, the adjustment of reference in the UPE is likely to get stuck on some choice that is not globally optimal, yielding multiple UPE. In contrast, when the choice set contains the continuum of all possible strategies (as in the context of portfolio choice), the suboptimal equilibria are easily disturbed, and the UPE converges to a unique strategy. This result thus enriches our understanding on the implications of UPE.