Estimating the Cost of Equity for Property‐Liability Insurance Companies

Abstract

Due to the highly skewed and heavy-tailed distributions associated with the insurance claims process, we evaluate the Rubinstein-Leland (RL) model for its ability to improve the cost of equity estimates of insurance companies because of its distribution-free feature. Our analyses show that there is as large as a 94-basis-point difference in the estimated cost of insurance equity between the RL model and the capital asset pricing model (CAPM) for the sample of property-liability insurers with more severe departures from normality. In addition, consistent with our hypotheses, significant differences in the market risk estimates are found for insurers with return distributions that are asymmetrically distributed, and for small insurers. Third, we find significant performance improvements from using the RL model by showing smaller values of excess return of the expected return of the portfolio to the model return for a portfolio of insurers with returns that are more skewed and for a portfolio of small insurers. Finally, our panel data analysis shows the differences in the market risk estimates are significantly influenced by firm size, degree of leverage, and degree of asymmetry. The implication is that insurers should use the RL model rather than the CAPM to estimate its cost of capital if the insurer is small (assets size is less than $2,291 million), and/or its returns are not symmetrical (the value of skewness is greater than 0.509 or less than - 0.509). Copyright The Journal of Risk and Insurance, 2008.

Life Insurer Cost of Equity with Asymmetric Risk Factors

“…Because the upside and downside betas are decompositions of the traditional beta, we do not include all three measures in any of our model specifications. Based on economic justification of the pricing factors and consistency with prior research, Model III, the preferred model, is specified in Equation Wen, Martin, Lai and O'Brien () find that insurer cost of equity is better estimated using industry‐specific measures of firm characteristics. Therefore, we re‐estimate the models substituting life insurance‐specific measures in place of ln(size) and book‐to‐market.…”

“…This estimation method is different from that of other studies such asWen, Martin, Lai and O'Brien (2008) in that the studies that employFama and French (1993) factors use a time series of returns as factors, which are themselves risk premiums for each unit of risk.…”

Skewed distributions in finance and actuarial science: a review

“…More recent studies by Harvey and Siddique (2000), which is discussed in Section 3, and Chung, Johnson, and Schill (2006) empirically examine the effects of co-skewness and higher-order co-moments on determination of the cost of equity. According to Wen et al (2008), adoption of the n-moment insurance CAPM could possibly capture the non-normal characteristics of the insurance claims process, but the determination of the optimal moment and its finite nature limits the application of this model. Froot (2007) develops a new pricing model that explicitly considers the asymmetry in insurance risk.…”

“…A second study using an alternative modeling approach is Wen et al (2008). Using a sample of publicly traded property-liability insurers, they compare the equity betas generated from the Rubinstein/Leland (Leland 1999) model to those generated by the CAPM.…”

Econometric Tests of the CAPM Model for a Portfolio Composed of Companies Listed on Nasdaq and Dow Jones Components

“…These are adverse to standard deviation, skewness and kurtosis. Wen et al (2008) have investigated whether the CAPM model used constantly by insurance companies is effective for them. Returns achieved in this sector follow a nonnormal distribution so they considered that it is more effective to estimate expected returns using the model Rubinstein-Leland (RL) when estimating the cost of capital for a small insurance company.…”