A Mean‐Preserving Increase in Ambiguity and Portfolio Choices

• Author: Yi‐Chieh Huang,Larry Y. Tzeng
• Date: 01 December 2018
• DOI: http://doi.org/10.1111/jori.12188
• Published date: 01 December 2018

©2017 The Journal of Risk and Insurance. Vol.85, No. 4, 993–1012 (2018).

DOI: 10.1111/jori.12188

A Mean-Preserving Increase in Ambiguity and

Portfolio Choices

Yi-Chieh Huang

Larry Y. Tzeng

Abstract

This article investigates under what conditions an increase in ambiguity re-

duces demand for an uncertain asset (or raises demand for coinsurance). We

find that the comparative statics of ambiguity and of risks have structuralsim-

ilarities under the smooth ambiguity aversion model (Klibanoff, Marinacci,

and Mukerji, 2005). The determinant condition on ambiguity preferences

is analogous to that on risk preferences. However, the comparative statics

have fundamental differences under the ˛-maxmin model (Ghirardato, Mac-

cheroni, and Marinacci, 2004). When relative risk aversion is less than 1, only

an increase in ambiguity,which broadens support for an investor ’s belief in

the probability of the return distribution in the manner of a strong increase

in risk, can reduce demand for an uncertain asset.

Introduction

Since Ellsberg (1961) uncovered the phenomenon from the experiment that people

are generally averse to the uncertainty of probabilities, ambiguity and ambiguity

aversion have received much attention in the literature. In particular, the literature

shows the importance of ambiguity and ambiguity aversion in financial markets.1

Yi-ChiehHuang is at the Department of Risk Management and Insurance, Feng Chia University,

Taichung City 40724, Taiwan. Huang can be contacted via e-mail: huangyic@fcu.edu.tw.Larry

Y. Tzeng is at the Department and Graduate Institute of Finance, National Taiwan University,

TaipeiCity 10048, Taiwanand at Risk and Insurance Research Center (RIRC), National Chengchi

University, Taipei City 11605, Taiwan. Tzeng can be contacted via e-mail: tzeng@ntu.edu.tw.

We deeply appreciate the anonymous coeditor’s helpful and valuable suggestions. We also

would like to express our gratefulness to the three anonymous referees for their detailed and

helpful comments and suggestions. Huang and Tzeng acknowledge financial support from the

research grant of Ministry of Science and Technology(MOST) (MOST 104-2410-H-035-052 and

MOST 102-2410-H-002-028-MY3, respectively).

1In addition to financial markets, recently, research on decision making under ambiguity has

also been extended to genetics and medical science. For example, Chew, Ebstein, and Zhong

(2012) provide a better understanding of decision making under ambiguity by identifying the

genes related to ambiguity aversion. Berger,Bleichrodt, and Eeckhoudt (2013) show that under

ambiguity aversion, demand for treatmentincreases when a patient’s health status is uncertain,

but decreaseswhen the effect of treatment is uncertain. Moreover, Hoy,Peter,and Richter (2014)

find that ambiguity aversion can help explain why people are disinclined to receive a costless

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Regarding asset pricing, some papers demonstrate that ambiguity-averse investors

react asymmetrically to good and bad news in stock markets (Epstein and Schneider,

2008) and prefer trading stocks according to aggregate information rather than

separable information (Caskey, 2009). Other papers find evidence from survey data

that ambiguity aversion can help to explain several anomalies in stock markets, such

as the higher risk premiums of small firms (Olsen and Troughton, 2000) and the

equity premium puzzle (Rieger and Wang, 2012).

Regarding portfolio choices, the literature shows, theoretically and empirically, that

when considering the uncertainty of expected returnsand ambiguity aversion, the out-

of-sample performance of the optimal portfolio measured by the Sharpe ratio is better

than those of the mean-variance and Bayesian portfolios (Garlappi, Uppal, and Wang,

2007). Several papers find that ambiguity-averse investors’ holdings of risky assets

decrease with greater ambiguity in dynamic settings (e.g., Fei, 2009; Faria and Correia-

da-Silva, 2016) and with greater ambiguity aversion under certain conditions (Gollier,

2011). In a portfolio choice experiment, Ahn et al. (2014) find that about 25 percent

of subjects exhibit ambiguity aversion.2Further, increasing numbers of papers point

out the significant impact of ambiguity and/or ambiguity aversion on equilibrium

in the insurance markets (e.g., Koufopoulos and Kozhan, 2014),3insurance decisions

such as demand for self-insurance and self-protection (e.g., Snow,2011; Alary,Gollier,

and Treich, 2013),4and the pricing of insurance premiums (e.g., Cabantous, 2007;

Cabantous et al., 2011; Huang, Huang, and Tzeng, 2013).5

Although the above-mentioned papers provide insight into the influence of ambi-

guity and ambiguity aversion on portfolio choices and insurance decisions, none has

explored the impact of an increase in ambiguity in terms of a change in the probability

distribution on demand for a risky asset (or demand for coinsurance) when the return

distribution is uncertain. As in Gollier (2011), throughout this article we refer to a

risky asset with an uncertain return distribution as an uncertain asset.6Following this

line of literature, the aim of this article is to find the conditions under which there is a

genetic test, as the genetic test introduces uncertainty regarding the probability of genetic

mutation.

2However,the results also revealed that most subjects (about 65 percent) are ambiguity neutral.

3Koufopoulos and Kozhan (2014) demonstrate that an increase in ambiguity can improve the

welfare of both high- and low-risk individuals when the former face the sufficiently larger

increase in ambiguity than the latter.

4Snow (2011) shows that both the presence of ambiguity and an increasein ambiguity aversion

raise demand for self-insurance and self-protection in two states of nature. When considering

multiple states of nature, Alary,Gollier, and Treich(2013) find the conditions under which am-

biguity aversion increases demand for self-insurance but reduces demand for self-protection.

5Cabantous’s (2007) survey results suggest that uncertainty of loss probability induces actu-

aries to charge a higher premium. From experimental data, Cabantous et al. (2011) confirm

Cabantous’s finding and further found that different types of ambiguity lead to differential

premiums charged by insurers. Regarding insurance bargaining, Huang, Huang, and Tzeng

(2013) show that both more ambiguity and more ambiguity aversion cause the client to settle

with the insurer on a higher premium for a full-coverage contract.

6Gollier (2011) interchangeably uses the terms uncertain asset and ambiguous asset.