Life Insurer Cost of Equity with Asymmetric Risk Factors

• DOI: http://doi.org/10.1111/fire.12073
• Date: 01 August 2015
• Published date: 01 August 2015

The Financial Review 50 (2015) 435–457

Life Insurer Cost of Equity with

Asymmetric Risk Factors

Vickie L. Bajtelsmit

Colorado State University

Sriram V. Villupuram∗

University of Texasat Arlington

Tianyang Wang

Colorado State University

Abstract

This study presents an improved model for estimating life insurer cost of capital with the

inclusion of upside and downside risk factors and controlling for life insurer characteristics.

Although various asymmetric measures of market risk havebeen shown to be priced factors for

the broader equity market, life insurer realized equity returns include a much larger premium

for bearing downside risk, even after controlling for firm characteristics and other measures

of risk. Cross-sectional regression analysis finds a positive (negative) premium for downside

(upside) betas, conditional on down and up markets, respectively. Coskewness and cokurtosis

are also priced factors.

Keywords: cost of equity, upside risk, downside risk, equity market, life insurance industry,

prospect theory

JEL Classifications: D81, G12, G22

∗Corresponding author: Department of Finance and Real Estate, Universityof Texas at Arlington, Arling-

ton, TX 76019; Phone: (817) 272-3705; Fax: (817) 272-2252; E-mail: sriramv@uta.edu.

C2015 The Eastern Finance Association 435

436 V.L. Bajtelsmit et al./ The FinancialReview 50 (2015) 435–457

1. Introduction

In the insurance industry, the cost of equity is an important factor in pricing,

performance, and reserving. Investors, regulators, and managers benefit from more

precise measurement of expected equity returns. There is literature that incorporates

unique industry factors in modeling insurer cost of equity (Cummins and Phillips,

2005; Wen, Martin, Lai and O’Brien, 2008; Nissim, 2013). Insurance regulators

are particularly concerned about underestimation of the cost of equity because it

can result in inadequate reserves and increased risk of financial distress. Although

this can be an issue for all types of insurers, it is more important for life insurers

because of the long-term nature of their liability portfolio. This paper provides an

improved model for estimating life insurer cost of equity with the inclusion of upside

and downside market risk factors and controlling for specific life insurer charac-

teristics and risk factors. We find that life insurer realized equity returns include a

much larger premium for bearing downside risk than is typical in the broader equity

market.

The traditional and most common approaches for estimating the cost of equity

capital are based on the capital-asset pricing model (CAPM) model (Sharpe, 1964;

Lintner, 1965; Mossin, 1966) and the Fama-French three-factor model (Fama and

French, 1992, 1996). Both models assume that stock returns symmetrically relate

to market movements and other factors, which implies that the cross-sectional risk-

return relationship is robust to either up or down markets. However, behavioral

finance and decision theory suggests that individual decision makers tend to be loss-

and disappointment-averse (Kahneman and Tversky, 1979). In an expected utility

framework, asymmetric attitudes toward risk cause individuals to overweight the

disutility of a potential loss relative to the positive utility from a potential gain.

Although asymmetric risk factors have been shown to be priced in the broader

cross-section of stocks (Ang, Chen and Xing, 2006), unique characteristics of the life

insurance industry imply that investorsmay weight downside risk for these companies

more heavily.

1.1. Prospect theory and downside risk for life insurers

The economics and finance literatures recognize that investors perceive and

react to gains and losses differently (Roy, 1952; Markowitz, 1959; Bawa and

Lindenberg, 1977; Maurice Tse, Uppal and White, 1993; Barberis and Huang, 2001;

You and Daigler, 2010). Many studies also find support for asymmetric preference

directions toward higher moments of investment return distributions (e.g., Rubin-

stein, 1973; Gooding, 1976; Scott and Horvath, 1980; Benishay, 1992; Lambert and

H¨

ubner, 2013). The theoretical explanation for asymmetric attitudes toward upside

and downside risk, discussed by Gul (1991), has its foundations in prospect the-

ory (Kahneman and Tversky, 1979) and is based on a rational disappointment-averse