Life Insurer Cost of Equity with Asymmetric Risk Factors

Date01 August 2015
Published date01 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
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:
C2015 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
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
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

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