A Gentle Introduction to Risk Aversion and Utility Theory

• DOI: http://doi.org/10.1111/j.1540-6296.2009.01173.x
• Date: 01 March 2010
• Published date: 01 March 2010
• Author: David A. Cather

C

Risk Management and Insurance Review, 2010, Vol.13, No. 1, 127-145

DOI: 10.1111/j.1540-6296.2009.01173.x

EDUCATIONAL INSIGHTS

AGENTLE INTRODUCTION TO RISK AVERSION

AND UTILITY THEORY

David A. Cather

ABSTRACT

While the topics of risk aversion and utility theory have been discussed exten-

sively in the academic literature on risk and insurance, this literature does not

include a pedagogical discussion that is widely accessible for classroom use.

This article provides a practical introduction to risk aversion that is designed

for readers with little prerequisite course work in economics or statistics. We

describe a simple model of insurance demand that can be applied to the prop-

erty,liability, life, and health insurance markets. We also demonstrate how risk

aversion affects a variety of real-life insurance decisions made under conditions

of uncertainty, including how much the market will bear to pay for insurance

administrative expenses and how demand varies for different types of auto in-

surance coverage. Exercises and practice problems are provided so that readers

can test their mastery of the concepts presented in the article. An instructional

note on using this article to teach risk aversion in the classroom is also provided.

INTRODUCTION

One of the largest and least understood industries in the world is the insurance industry.

Browne et al. (2000) estimate that 8 percent of the world’s GDP is spent on insurance

products. Global insurance premiums totaled $3.7 trillion in 2006, and the United States

ranked first among all countries as the largest consumer of insurance products in the

world (Swiss Re, 2007). For most noncommercial consumers in the United States, in-

surance consumption has focused on personal insurance products, such as auto, health,

homeowners, life, and retirement insurance products. But while they spend a great deal

of money on insurance, many consumers appear to have a limited understanding of the

factors that affect their demand for insurance products.1

People buy insurance for a variety of reasons. In some instances, the purchase is required

by law, as is the case for compulsory auto liability insurance. In other cases, consumers

David A. Cather is with the Department of Insurance and Real Estate, Smeal College of Business,

Pennsylvania State University, 355 Business Building, University Park, PA 16802-3603; phone:

(814) 863-5455; fax: (814) 865-6284; e-mail: cather@psu.edu. The author wishes to thank two

anonymous referees who provided helpful suggestions for improving this article. This article

was subject to double-blind peer review.

1For example, see “401(k) Plan Education Not Working, Surveys Suggest,” by Jacobius (2003);

“Workers Underestimate Health Benefits,” Employee Benefit News (2005),” or “Insurance In-

dustry Woes in the Aftermath of Hurricanes Katrina and Rita” by Rosenberg et al. (2006).

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128 RISK MANAGEMENT AND INSURANCE REVIEW

buy insurance to satisfy the requirements of other parties that they are doing business

with; e.g., mortgage lenders require that homeowners buy insurance on the homes that

the lenders are financing as a condition of obtaining loans. Many others buy insurance

due to a more abstract reason, a behavioral tendency known as risk aversion. As it

relates to the demand for insurance, risk aversion refers to the tendency to prefer to pay

a defined sum of money that is known with certainty instead of being exposed to the

risk of suffering a larger and uncertain financial loss in the future. Thus, the practice

of individuals buying insurance protection instead of bearing risk without insurance

reflects risk aversion.

Scholarly texts typically explain the concept of risk aversion using an economic model

called utility theory.Readers with previous course work in economics can find excellent

discussions on utility theory, risk aversion, and the demand for insurance in several

different books.2Readers without such course work may find it difficult to understand

utility theory, however, as discussions on the topic are usually written assuming that

readers have a fairly advanced understanding of economics. Moreover, unless they are

particularly familiar with the insurance industry, readers often find it difficult to relate

the concepts discussed in most descriptions of utility theory to practical applications in

their insurance consumption decisions.

The objective of this article is to provide a general introduction to utility theory and risk

aversion as it applies to the demand for insurance. This primer thus provides an inter-

mediate reading that covers the prerequisites assumed in more advanced discussions

on the topic. To demonstrate that utility theory is not an abstract “ivory tower” exercise

with limited relevance to the real world, the article includes several examples that show

how risk aversion relates to real-life insurance demand patterns. In the next section, we

describe how many consumers exhibit behavioral tendencies toward wealth that lend

themselves to risk-averse behavior. The middle section explains how risk aversion re-

sults in a demand for insurance protection and examines how this demand is affected by

insurance administrative loading charges. The final section of the article demonstrates

how utility theory applies to everyday insurance purchasing decisions, and describes

anecdotal evidence on how risk aversion has shaped consumer demand patterns in the

personal auto insurance markets.

THE UTILITY THEORY MODEL

The relationship between risk aversion and the demand for insurance can be introduced

by developing a simple model of consumer preferences regarding wealth. The model

is built around two assumptions. First, it is assumed that consumers always prefer

more wealth instead of less wealth. Second, it is assumed that as a person’s wealth in-

creases, the amount of additional satisfaction generated by each additional dollar in his

or her possession will decrease. It is easy to visualize these assumptions by representing

them pictorially. A graph that reflects these two assumptions is shown by the darkened

curve in Figure 1, where personal wealth is plotted along the horizontal axis, and the

2Among risk management textbooks, please see Doherty (2000), Harrington and Niehaus (2004),

or Phillips (1998). Health economics textbooks by Folland et al. (1997), Phelps (2003), and

Santerre and Neun (2007) provide more focused discussions on the topic as it applies in a health

insurance setting.