Estimating the Cost of Equity Capital for Insurance Firms With Multiperiod Asset Pricing Models

• Author: Alexander Barinov,Jianren Xu,Steven W. Pottier
• DOI: http://doi.org/10.1111/jori.12267
• Published date: 01 March 2020
• Date: 01 March 2020

ESTIMATING THE COST OF EQUITY CAPITAL FOR INSURANCE

FIRMS WITH MULTIPERIOD ASSET PRICING MODELS

Alexander Barinov

Jianren Xu

Steven W. Pottier

ABSTRACT

Previous research on insurer cost of equity (COE) focuses on single-period

asset pricing models. In reality, however, investment and consumption

decisions are made over multiple periods, exposing firms to time-varying

risks related to economic cycles and market volatility. We extend the

literature by examining two multiperiod models—the conditional capital

asset pricing model (CCAPM) and the intertemporal CAPM (ICAPM). Using

29 years of data, we find that macroeconomic factors significantly influence

and explain insurer stock returns. Insurers have countercyclical beta,

implying that their market risk increases during recessions. Further, insurers

are sensitive to volatility risk (the risk of losses when volatility goes up), but

not to insurance-specific risks, financial industry risks, liquidity risk, or

coskewness after controlling for other economy-wide factors.

INTRODUCTION

Prior studies on insurer cost of equity (COE) focus on single-period asset pricing

models, such as the capital asset pricing model (CAPM) and the Fama and

French (1993) three-factor model (FF3). Merton’s (1973) seminal article on multi-

period asset pricing demonstrates that when investment decisions are made at

more than one date, additional factors are required to construct a multi-period

model because of uncertain changes in future investment opportunities. More-

over, firms are exposed to business and economic cycles. Multi-period models

account for the time-varying risks (factors) that reflect these cycles.

© 2018 The Journal of Risk and Insurance

DOI: 10.1111/jori.12267

Alexander Barinov is at the Department of Finance, School of Business, University of California

Riverside, 900 University Ave., Riverside, CA 92521. Barinov can be contacted via e-mail:

alexander.barinov@ucr.edu. Jianren Xu (corresponding author) is at the Department of

Finance, Insurance, RealEstate and Law, G. Brint Ryan College of Business, University of

North Texas, 1155 Union Circle #305339, Denton, TX 76203-5017. Xu can be contacted via email:

jianren.xu@unt.edu. Steven W. Pottier is at the Department of Insurance, Legal Studies, and

Real Estate, Terry College of Business, University of Georgia, 610 South Lumpkin Street,

Athens, GA 30602. Pottier can be contacted via e-mail: spottier@uga.edu. Steven Pottier

gratefully acknowledges the support of a Terry-Sanford Research Grant.

213

. Vol. 87, No. 1, 213–245 (2020).

In this study, we extend the insurance literature by examining two multi-period

models—the conditional CAPM (CCAPM) and the intertemporal CAPM (ICAPM).

These two models are examined along with the single-period models studied in the

prior literature—the CAPM and FF3, as well as newer single-period models like the

Fama and French (2015) five-factor (FF5) model and the Adrian, Friedman, and Muir

(2016) (AFM) model with financial industry risk factors.

1,2

Our empirical analysis

consists of three major parts. First, we evaluate the four asset pricing models

mentioned earlier (CAPM, FF5, CCAPM, and ICAPM) and consider their

applicability to insurance firms by examining the relation between realized (actual)

returns on portfolios of insurer stocks and the risk factors associated with each model.

We show that insurance firms are exposed to volatility risk and have countercyclical

betas. More specifically, insurance portfolio values drop when current consumption

has to be cut in response to surprise increases in expected market volatility, and its

market beta increases in recessions when bearing risk is more costly. Therefore,

insurers are riskier and thus should have higher cost of capital than what the CAPM/

FF5 estimates.

FF3/FF5 are also often regarded as ICAPM-type models with SMB, HML, and

recently RMW and CMA acting as “placeholders” for yet unidentified risk.

3

While a

number of articles have tried to identify the risks behind these factors (Liew and

Vassalou, 2000; Petkova and Zhang, 2005; Petkova, 2006; Campbell, Polk, and

Vuolteenaho, 2010), the consensus as to which business cycle variables are behind the

factors still has not emerged. Even more, a number of articles have contested the claim

that SMB and HML are driven by risk and argued that they represent mispricing and

market sentiment swings (Daniel and Titman, 1997; Baker and Wurgler, 2006).

Company stakeholders might want to know not only the COE of their firm or projects,

but also the reasons behind a certain rate, namely, what risks result in a high or low

COE. Without risk-based explanations, stakeholders might feel uncomfortable

accepting a COE estimate. The additional alternative that the factors can be picking up

market-wide mispricing makes the decision even more complicated. For example, the

“Model Performance and Applicability and Insurer Risk Sensitivities” section reveals

that insurers tend to be value (positive HML beta) firms. If we believe that HML picks

up high returns of value firms as their underpricing is corrected, should we

benchmark insurers’ COE against other value firms, thus asking them to deliver a

higher return than their risk warrants and abandoning some positive NPV projects?

1

In the “Asset Pricing Models and Literature” section, we review the related literature on

insurer cost of equity capital and argue that since the models used are single-period models,

they do not account for the time-varying risks that insurers face.

2

As discussed in the “Asset Pricing Models and Literature” section, while reestimating beta(s)

in CAPM/FF5 allows for the COE to vary over time, these approaches do not incorporate the

covariance of factor beta(s) with economic conditions. In COE estimation, the CAPM and FF5

implicitly assume, by using long-term averages of the factor risk premiums, that the amount of

risk in the economy is constant. Thus, in the CAPM and FF5, there is no possible covariance

between the betas and the business cycle “by construction.”

3

For example, this is the view Fama and French took in their original article, Fama and French

(1993), as well in subsequent articles like Fama and French (1995) and Fama and French (1996).

2 THE JOURNAL OF RISK AND INSURANCE

(This is what using FF5 in COE estimation suggests.) Alternatively, should we

exercise all positive NPV projects, effectively ignoring the positive HML beta if we

think HML is mispricing?

Theory-based multiperiod models, such as the CCAPM and ICAPM, considered in

our article, are immune to both problems. First, they identify the risks they are talking

about (“insurance companies lose more than average when market volatility

increases,” “the market beta of insurance companies increases when deflation

occurs”). Second, they are only picking up risk-based effects in expected returns/

COE, and one does not have to worry about mispricing.

In the second major part of our empirical analysis, we also consider for potential

inclusion in the CCAPM and ICAPM the underwriting cycle variables, in

addition to the standard business cycle variables from the finance literature.

Further, we add the insurance factors and financial industry factors (the AFM

factors) to FF5. While changes to underwriting cycle variables and insurance/

financial industry factors clearly affect the value of insurers, it is not clear a priori

that they will be related to expected returns because all their effects can be on the

cash-flow side.

The finance theory suggests (e.g., Cochrane, 2007) that only the variables that are

related to expected market risk premium and thus to marginal utility of

consumption should be included in any asset pricing models (either CCAPM or

ICAPM in this study). We check the existence of such a relation between several

underwriting cycle variables (including average combined ratio, total cata-

strophic losses, etc. in a quarter) and find none. Consequently, we find that

inclusion of these variables in either the CCAPM or ICAPM does not materially

affect our COE estimates. That happens even though some underwriting cycle

variables seem to be related to the beta/realized returns of insurers: the

underwriting cycle variables earn zero risk premium (controlling for other risk

factors) because their effects can be diversified away by investing in multiple

industries. Similarly, we find adding the insurance factors or financial industry

factors neither improves the model goodness of fit of FF5 nor contributes to

estimating COE (controlling for market-wide factors) due to their diversifiable

nature.

The irrelevance of underwriting cycle (or any other insurance/financial industry

specific) variables as candidate CCAPM/ICAPM factors goes beyond the application

at hand. Even if such factors are correlated with insurance companies’ realized

returns, they will not contribute to expected returns due to being unrelated to the

economy as a whole.

In the third major part of our empirical analysis, we apply four models (CAPM, FF5,

CCAPM, and ICAPM) to estimate COE for all U.S. publicly traded insurers, and the

two subgroups, P/L insurers and life insurers, over an 18-year period (1997–2014).

4

Since additional time-varying risks demand greater rewards, we find that on average

4

In COE estimation, we lose 10 years as the initial estimation period for CCAPM, for which we

need 120 months to estimate six parameters with enough precision.

ESTIMATING INSURER COE WITH MULTIPERIOD MODELS 3