Regulator's Determination of Return on Equity in the Absence of Public Firms: The Case of Automobile Insurance in Ontario

• Author: Fred Lazar,Eliezer Z. Prisman
• DOI: http://doi.org/10.1111/rmir.12039
• Date: 01 September 2015
• Published date: 01 September 2015

Risk Management and Insurance Review

C

Risk Management and Insurance Review, 2015, Vol.18, No. 2, 199-216

DOI: 10.1111/rmir.12039

REGULATOR’SDETERMINATION OF RETURN ON EQUITY

IN THE ABSENCE OF PUBLIC FIRMS:THE CASE

OF AUTOMOBILE INSURANCE IN ONTARIO

Fred Lazar

Eliezer Z. Prisman

ABSTRACT

In a regulated market, such as automobile insurance (AI), regulators set the

return on equity that insurers are allowed to achieve. Most insurersare engaged

in a variety of insurance lines of business, and thus the full information beta

methodology (FIB) is commonly employed to estimate the AI beta. The FIB uses

two steps: first, the beta of each insurer is estimated, and then the beta of each

line of business is estimated, as the beta of an insurer is a weighted average of

the betas of the lines of business. When there are a sufficient number of public

companies, company and market returns are used. Otherwise, researchers have

resorted to using accounting data in the FIB. Theoretically, the two steps are not

separable and the estimation should be done with one step. We introduce the

one-step methodology in our article. The one-step and two-step methodologies

are compared empirically for the Ontario market of AI. Insurers in Ontario are

predominantly private companies; thus, accounting data are used to estimate

the AI beta. We show that a significant bias is introduced by the traditional,

two-step FIB methodology in estimating the betas for different lines of business,

while insurers’ betas are very similar under both methods. This has a significant

application to the estimation of betas of “pure players” in classic corporate

finance. It implies that their betas and hence the resulting, required rates of

return used in the net present value calculations should be estimated based on

the one-step method that we develop in this article.

INTRODUCTION

In a regulated market, such as automobile insurance, a regulator sets the return on

equity (ROE) that market players are allowed to achieve. Since the ROE is random and

not an assured rate, its average must be above the risk-free rate in the market in order

to provide a sustainable financial environment for the insurers. Insurers must make a

Both authors are at the Schulich School of Business, YorkUniversity; e-mail: flazar@yorku.ca and

eprisman@yorku.ca. The authors would like to thank Dennis Chan, Darlene Hall, Nick Polsoni,

and Richard Tillmann from the Financial Services Commission of Ontario (FSCO) for insightful

conversations. The ideas presented here, as well as any remaining errors,are those of the authors

and do not necessarily represent FSCO’s ideas.

199

200 RISK MANAGEMENT AND INSURANCE REVIEW

profit; otherwise, they will not survive in the market. The ROE must be such that it

compensates for the risk taken in order to attract the required investments. On the other

hand, for political reasons, it must not provide insurers with above-average profits that

result in “excessive” premiums for consumers. Thus, the allowed ROE must be a rate

that would prevail in a competitive market in the absence of regulators. Therefore, there

is a need to assess the risk profile of insurers to determine the allowed ROE for insurers

so they are adequately compensated.

When the insurers are public companies, determining their risk profiles, for example,

their betas utilizing the capital asset model (CAPM), and estimating an adequate ROE are

straightforward tasks.1However, if there are only a handful of publicly listed insurers,

an alternative method must be used to estimate their risk profiles and the resulting

recommended ROE. Moreover, most insurers are engaged in a variety of insurance

lines of business, and thus there are very few pure players. This presents an obstacle

to estimating the beta of the automobile insurance line of business, or any specific

line of business. Classical corporate finance offers a solution, the full information beta

methodology (FIB) in the absence of pure public players, pioneered by Ehrhardt and

Bhagwat (1991) and expanded on by Kaplan and Peterson (1998).

The essence of the FIB is a property of beta. The beta of a portfolio or a firm is a weighted

average of stocks in the portfolio, or of the lines of business of the firm. Hence, having

an estimate of the beta of a firm that is engaged in automobile insurance and other lines

of business, and the percentage of the firm’s revenues in each line of business, the beta

can be solved for each line of business. Specifically, a system of equations stipulating

each firm’s beta as a weighted average of the betas of each of the firm’s lines of business

can be set. The weight of each line of business is the percentage of the firm’s revenues

in each line, and the system of equations can be solved using a second-best solution, for

example, minimum least squares, as empirically the system is not consistent.

Thus, the beta of each line of business is recovered using a two-step method. In the first

step, the beta of each firm is estimated, and the second step solves for the betas for each

line of business. However, theoreticallyif the betas for each line of business are the same

and independent of the firm in which this line of business resides, the two steps are not

separable. Employing the two-step method causes a loss of information, and so the two

steps should be combined. The beta of each firm should be replaced by the weighted

average of the betas of each line of business, and the estimation problems for the beta of

each firm should be combined into one estimation problem.

1For an insurance company,the premiums obtained from writing insurance are in fact borrowing

at a risky rate of return (depending on the unknown magnitude of the claim). Hence, it can be

interpreted as a short position. For early applications of the CAPM in this area, see Quirin

and William (1975), Biger and Kahane (1978), Fairley (1979), Hill (1979), and Cummins and

Harrington (1985). Thus, to be more precise, beta should be defined as beta equity or beta assets

(unlevered beta) as in classical corporate finance. However, for the purpose of this article, it is

sufficient to address the beta equity, as all the Ontario insurers are required by the regulator

to hold the same minimum ratio of reserves. Competitive market forces motivate all insurers

to hold the minimum ratio. Hence, the reality is that they all have the same debt–equity ratio.

Consequently, their risk profilecould be judged by the beta equity, and we use the term “beta”

henceforth for beta equity.