Multi Cumulative Prospect Theory and the Demand for Cliquet‐Style Guarantees

• Date: 01 December 2018
• Published date: 01 December 2018
• DOI: http://doi.org/10.1111/jori.12195

©2017 The Journal of Risk and Insurance. Vol.85, No. 4, 1103–1125 (2018).

DOI: 10.1111/jori.12195

Multi Cumulative Prospect Theory and the Demand

for Cliquet-Style Guarantees

Jochen Ruß

Stefan Schelling

Abstract

Expected Utility Theory (EUT) and Cumulative Prospect Theory (CPT) face

problems explaining preferences of long-term investors. Previous research

motivates that the subjective utility of a long-term investment also depends

on interim value changes. Therefore, we propose an approach that we call

Multi Cumulative Prospect Theory.It is based on CPT and considers annual

changes in the contract values. As a first application, we can show that in

contrast to EUT and CPT, this approach is able to explain the demand for

guaranteed products with lock-in features,which in this framework generate

a higher subjective utility than products without or with simpler guarantees.

Introduction

Cumulative Prospect Theory (CPT), introduced by Tversky and Kahneman (1992),

has become one of the most prominent behavioral theories in finance, especially as a

behavioral counterpart to Expected Utility Theory (EUT). This is due to the fact that

CPT can explain behavior that can not be explained by EUT, but is still frequently ob-

served in real life. While complex financial products and long-term investments are

well studied under EUT, an analysis of such products under CPT has only recently

been in the focus of academic literature. Døskeland and Nordahl (2008) consider dif-

ferent participating life insurance contracts under CPT to explain the demand for

guaranteed products. In an empirical work, Dierkes, Erner, and Zeisberger (2010) in-

vestigate the preferences of a CPT investor considering differentinvestment strategies

and time horizons. Historical and Monte Carlo simulations are used by Dichtl and

Drobetz (2011) to analyze portfolio insurance strategies based on simple Constant

Proportional Portfolio Insurance (CPPI) strategies. Ebert, Koos, and Schneider (2012)

determine the “optimal” specification of differentguarantee types, where optimality is

defined as creating the maximum subjective utility for a CPT investor.A main result of

Jochen Ruß is at the Institut f¨

ur Finanz- und Aktuarwissenschaften and Ulm University, Lise-

Meitner-Str.14, 89081 Ulm, Germany. Ruß can be contacted via e-mail: j.russ@ifa-ulm.de. Stefan

Schelling is at the Department of Mathematics and Economics, Ulm University, Helmholtzstr.

20, 89081 Ulm, Germany.Schelling can be contacted via e-mail: stefan.schelling@uni-ulm.de.

1103

1104 The Journal of Risk and Insurance

these articles is that, in contrast to EUT, CPT can explain the demand for guarantees.1

Nevertheless, even CPT is not able to explain the popularity of more complex guaran-

teed products, such as ratchet or cliquet guarantees, as a CPT investor should prefer

a simple guarantee at maturity over more complex guarantees with lock-in features.

In both EUT and CPT,the preferences of the investor only depend on the distribution of

the terminal value. In reality, however,investors tend to reevaluate a financial product

regularly, for example, annually when they receive a financial statement. Information

about a good performance in the past year might increase the investors, reference

point against which losses are evaluated. A subsequent drop of in the product’s value

might then be perceived as a loss, even if the overall performance since the start of the

product is still positive. This is related to the concept of mental accounting introduced

by Thaler (1985). This concept describes how investors categorize investments in or-

der to monitor the future performance. In a later work, Thaler and Johnson (1990)

study how prior gains and losses affect decision makers and how they frame such

problems under Prospect Theory. Arkes et al. (2008) provide additional evidence that

investors mentally account for previous price changes and therefore regularly adapt

their reference point. Benartzi and Thaler (1995) propose the theory of myopic loss

aversion, a combination of loss aversion and frequent investment evaluation, and

show that an annual evaluation can solve the equity premium puzzle. They argue

that mental accounting implies that investors tend to evaluate their investment deci-

sion on short evaluation periods and, therefore, prefer to invest only small fractions

of their wealth in risky assets. Benartzi and Thaler (1999) give evidence that investors

make less risky choices if they are shown 1-year rather than long-term rates of re-

turn. Barberis, Huang, and Santos (2001) propose a model in terms of asset pricing,

in which investors derive utility from annual changes of the value of their financial

wealth and Barberis and Xiong (2012) are able to shed light on the disposition effect

and other puzzles by introducing the realization utility, which suggest that investors

derive utility from interim gains and losses.

If interim changes of the value influence the utility of investors during the investment

horizon, it seems only natural that when making the investment decision investors

are also affected by potential future interim changes of the value.

Based on these insights, we propose a modification of CPT, which assumes that long-

term investors tend to take into account the subjective utility of interim changes of the

value of the contract when making an investment decision. We denote this approach

Multi Cumulative Prospect Theory (MCPT).

As a first application example of MCPT, we investigate the demand for different

guaranteed products. For the sake of comparability, we apply this approach to the

guaranteed contracts presented by Ebert, Koos, and Schneider (2012); that is, we con-

sider three different types of guarantees (roll-up, ratch-up, and cliquet) and a product

without guarantee. The roll-up guarantee provides a minimal terminal payoff, which

1It is worth noting that certain results can also be achieved under EUT if the underlying as-

sumptions are more realistic. For example, Chen, Hentschel, Klein (2015) recently show that

the consideration of mortality can explain the preferences for simple guarantees at maturity

also in an EUT framework.