As you like it: Explaining the popularity of life‐cycle funds with multi cumulative prospect theory

• DOI: http://doi.org/10.1111/rmir.12122
• Author: Stefan Graf,Stefan Schelling,Jochen Ruß
• Published date: 01 July 2019
• Date: 01 July 2019

© 2019 The American Risk and Insurance Association

Risk Manag Insur Rev. 2019;22:221–238. wileyonlinelibrary.com/journal/rmir

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Received: 14 November 2018

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Revised: 3 April 2019

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Accepted: 23 April 2019

DOI: 10.1111/rmir.12122

FEATURE ARTICLE

As you like it: Explaining the popularity of

life‐cycle funds with multi cumulative

prospect theory

Stefan Graf

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Jochen Ruß

1,2

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Stefan Schelling

2

1

Institute for Finance and Actuarial

Sciences, Ulm, Germany

2

Institute of Insurance Science, Ulm

University, Ulm, Germany

Correspondence

Stefan Schelling, Institute of Insurance

Science, Ulm University,

Helmholtzstrasse 20, 89081 Ulm,

Germany.

Email: stefan.schelling@uni-ulm.de

Abstract

Life‐cycle (or target‐date) funds are funds, which

typically decrease their risk exposure over time. They

have been very successful in many countries, particu-

larly in the segment of old age provision. However,

ExpectedUtilityTheory(EUT)cannotexplaintheir

popularity. Moreover, recent results of Graf (2016),

imply that not only EUT but also its behavioral

counterpart Cumulative Prospect Theory (CPT) is

often not able to explain the popularity of these

products, since for each life‐cycle fund a correspond-

ing balanced fund can be constructed, which is

preferable from the investor’s perspective in most

circumstances. In a recent paper, Ruß and Schelling

(2018), have argued that potential future changes in

an investment’s value already impact the decision of

long‐term investors at outset. Based on this, they have

introduced Multi Cumulative Prospect Theory

(MCPT), which is based on CPT and considers the

subjective utility generated by annual value changes.

This paper shows that for MCPT‐investors, life‐cycle

funds are typically more attractive than their corre-

sponding balanced funds since they reduce the

potential losses toward the end of the investment

horizon. Hence, our findings provide an explanation

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for inferior decisions in old age provision. This can

serve as a basis to improve such decisions.

KEYWORDS

Cumulative Prospect Theory, life‐cycle funds, mental accounting, old

age provision, retirement saving

JEL CLASSIFICATION

D14; D81; G11; G22; G41; J26; J32

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INTRODUCTION

Results in Graf (2016), who has analyzed life‐cyclefundsforsingleandregularcontributionsand

under different asset models, imply that for any given life‐cycle fund, a rational investor

(maximizing expected utility) can find a corresponding superior balanced fund. Nevertheless, life‐

cycle funds have been and continue to be extremely successful. A study by Yang et al. (2015) shows

that assets under management of life‐cycle funds in the United States have steadily increased from

roughly$100bnin2006to$700bnin2014.Oneofthereasonsforthissuccessisthatalarge

number of pension plans allocate their contributions to these life‐cycle funds, since—according to

Charlson et al. (2010)—96% of the large

1

pension plans in the US selected life‐cycle funds as their

default asset allocation and most of the money allocated in these funds is left in the same fund until

retirement. However, Mitchell et al. (2009) show that default options alone cannot explain the

demand since life‐cycle funds are also frequently chosen when no default option exists.

The results of Graf (2016)

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imply that in most cases, the sharp contrast between optimal

utility maximizing behavior (in terms of terminal wealth)—that is, not invest in life‐cycle

funds—and observed actual behavior—that is, invest in life‐cycle funds—can also not be

explained by Cumulative Prospect Theory (CPT), the most popular behavioral counterpart to

Expected Utility Theory (EUT) that was introduced by Tversky and Kahneman (1992).

Several authors pointed out that investors tend to re‐evaluate their investment regularly, cf.,

for example, Benartzi and Thaler (1995)or Gneezy and Potters (1997). In a recent paper, Ruß and

Schelling (2018) have argued that—particularly for rather long investment horizons—investors

also get subjective utility and disutility from interim value gains and losses. They argue that this

already impacts the investment decision at outset and develop a modification of CPT that

considers potential future value fluctuations already in the decision making. They show thattheir

so‐called Multi Cumulative Prospect Theory (MCPT) is able to explain the demand for certain

complex guaranteed products thatare very popular in many markets but should not be desired by

either rational investors or CPT‐investors. Since life‐cycle funds and balanced funds—even if they

were designed to have a similar probability distribution of terminal wealth—significantly differ

with respect to the distributions of the potential value changes over time, they would create

significantly different subjective utility for an MCPT‐investor. The present paper therefore

analyzes how such an investor’s choice differs from a rational investor or a CPT‐investor.

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Defined as including more than 5,000 employees.

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Graf (2016) finds stochastic dominance for a single premium investment in a Black–Scholes economy and “practical”

stochastic dominance for regular premium investments when (far) upper and lower tails of the distribution are ignored

(cf. Figure 1 for a comparison of the resulting cumulated distribution functions).

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