Event Studies for Publicly Traded Insurers: An Investigation of the Bad-Model Problem

Abstract

The potential that abnormal returns are due to a misspecified expected (normal) return model is well known in the event study literature. Prior research shows that this “bad-model problem” is serious in long-run studies, and can also be problematic in short-run studies for firms grouped by certain characteristics. We investigate the bad-model problem for a large sample of insurance firms over an 18-year period, based on nine different expected return models and short- and long-run event windows. Using 1000 samples of randomly selected firms and dates, we find that the different normal return models make little difference in the statistical or economic significance of abnormal returns for short event windows (up to 3 days). However, for longer event windows, such as 1 month and 13 months, statistically and economically significant abnormal returns are more common. Further, we find that characteristic-based benchmark models generally perform better than models that require an estimation period. We also examine a sample of insurers that experienced a financial strength rating downgrade, and find significant differences between characteristic-based benchmark models and other normal return models for the 13-month event window. We recommend that abnormal returns from actual events be evaluated for their qualitative significance in relation to random samples with random event dates. Our results support the need to exercise caution in interpreting the findings of event studies.

Notes

1 To describe the residual term from an estimate of normal returns as an abnormal return is a misnomer, as Frankfurter and McGoun (1993) discuss. There is nothing inherently abnormal about residual terms, as they result from the normal statistical processes by which expected or normal returns are generated for a sample of firms. And even if the model used to estimate normal returns is the “true” or “equilibrium” model, random deviations are not necessarily “abnormal” but are part of an underlying chance process. A rebuttal to saying residuals are not abnormal is when residuals exhibit a statistically significant deviation from zero for firms that experience an event and not a significant difference from zero for firms that do not experience the event. As the terminology “abnormal return” has become standard in event studies, we continue to use it with the understanding that what is an abnormal return is ultimately subjective.

2 In Fama (1970), three forms of market efficiency are described: strong form, semi-strong form, and weak form. Strong form states is when security prices fully reflect private information, public information, and past security prices. Semi-strong form is when security prices fully reflect public information and past security prices. Weak form is when security prices reflect past security prices. Event studies are tests of semi-strong market efficiency (Fama 1991).

3 Ahern (2009) draws samples from the highest and lowest deciles of market equity, prior returns, book-to-market, and earnings-to-price ratios.

4 Benchmark or reference portfolio models match event firms to a portfolio of similar nonevent firms to estimate abnormal returns. Equilibrium asset pricing models estimate normal returns based on market-wide, systematic risk factors based on statistical and empirical conditions that must hold in equilibrium. See Section 2 for further discussion.

5 Using the pattern of disagreement between bond rating agencies, Morgan (2002) finds that insurance is the opaquest industry. In addition, the sensitivity to different market and economy-wide risks varies across industries and across time (see Barinov, Xu, and Pottier 2020).

6 Harvey et al. (2016) identifies 316 anomalies proposed as potential factors in asset pricing models.

7 High BE/ME signals sustained low earnings on book equity (less profitable firms, low average returns on book equity). Size is also related to profitability after controlling for BE/ME. Small stocks tend to have lower earnings on book equity than do large stocks.

8 These studies are summarized in the appendix. See Ragin and Xu (2019) for a review of studies on the stock market response to catastrophes.

9 See Harvey et al. (2016) for an extensive list of variables that have been used to estimate expected returns. Fama and French (1997) find that sensitivities to the market model and three-factor Fama–French model size and book-to-market factors are very volatile for many industries.

10 Fama and French (1992; 1997) use 60 months to estimate expected factor risk loadings. Short horizon event studies usually use estimation periods of up to 1 year. Long horizon event studies usually use estimation periods up to 3 years.

11 Such aggregation leads to what is known as the “clustering” problem in event studies when event firms share a common event date. The clustering problem is essentially one of highly correlated residual terms that may bias statistical inferences. There are well-established tests and remedies to the clustering problem. In our study, firms do not share a common event date. For our main analysis, as explained in Section 4, event dates are randomly generated. For our secondary analysis, as explained in Section 5, event dates are the date an event firm experiences a rating downgrade. See Hilliard et al. (2018) and Ghosh and Hilliard (2012) on clustering events in the insurance industry.

12 Brockett et al. (1999) use a time-series autoregressive regression approach to obtain expected returns and consider certain known characteristics of financial time series, including autocorrelation.

13 Kothari and Warner (2007) state that in “short-horizon tests … risk adjustment is straightforward and typically unimportant.” Based on several studies, Kothari and Warner suggest that in long horizon event studies expected returns should be based on “post-event, not historical risk estimates.” These authors identify the two main methods for post-event risk-adjusted performance as the characteristic-based matching approach and the calendar-time portfolio approach.

14 Barber and Lyon (1997) and Lyon et al. (1999) provide a thorough discussion of the inference problems in tests on long-term returns.

15 Code 6311, life insurance; 6321, accident and health insurance; 6324, hospital and medical service plans; 6331, fire, marine and casualty insurance; 6351, surety insurance; 6361, title insurance; 6399, insurance carriers; 6411, insurance agents, brokers, and services. Note that SIC codes are an initial filter for our final sample. To assure that SIC reliably indicates that an entity is an insurer, we rely on the insurer obtaining either a property-liability or life-health insurer financial strength rating from A.M. Best Company. Among the 203 firms in the final sample, only five had an SIC of 6411 in one or more years. We further examined the business mix of these five firms to confirm that each firm is primarily engaged in underwriting insurance risk.

16 Fama and French (1992, 436) use two to five years of monthly returns to estimate betas.

17 Hilliard et al. (2018) use 240 days; Halek and Eckles (2010) use 255 days; Brown and Warner (1985) and Ahern (2009) use 239 days.

18 A minimum of a 12-month drawing period has the benefit that the random dates drawn for the same firm in different samples are likely not concentrated in the same short or medium period (e.g., same month or same quarter). Requiring a longer minimum drawing period reduces the sample size (see note 28).

19 In the finance and insurance literature on event studies, the one-factor market model, or capital asset pricing model (CAPM), is typically used to test for short-run abnormal returns. A pre-event estimation period is much more common, as noted in Ahern (2009). Among the insurance studies listed in the appendix, only Halek and Eckles (2010) use a post-event estimation period in the one-factor market model. Brown and Warner (1985) use a pre-event estimation period, while Ahern (2009) use both pre-event and post-event, but present full results only for pre-event.

20 An insurance-specific event study, Ghosh and Hilliard (2012), uses the FF3F model. We are unable to identify any event studies on insurers that use any other multifactor models.

21 Womack (1996) uses industry-adjusted benchmark to calculate 12-month CAR.

22 Womack (1996) also uses the size-adjusted approach to calculate 12-month CAR.

23 Dichev and Piotroski (2001) use size, market-to-book matched portfolios to calculate 12-month CAR after the bond rating changes. Our characteristic-based benchmark portfolios include only other sample insurers. Lai et al. (2008) and Chen et al. (2018) use market capitalization (size) and market-to-book matched portfolios.

24 Often researchers do not perform any industry adjustment in the CBBM. In the general finance literature, Daniel et al. (1997) perform an industry adjustment to the BE/ME factor, but not ME. Neither Ahern (2009) nor Dichev and Piotroski (2001) perform any industry adjustment in the CBBM.

25 A 4 × 4 portfolio matching increases the number of firms in each benchmark portfolio by approximately 56 percent. Our results are qualitatively similar using a 5 × 5 portfolio matching to form the benchmark portfolios. We chose the 4 × 4 matching to be consistent with Chen, Gaver, and Pottier (2018).

26 Since an event occurring on Saturday or Sunday will automatically be counted as Monday or next trading day when return data are available, a random drawing of all dates within the drawing period will likely result in an uneven distribution of weekdays (i.e., more Mondays than other weekdays). Therefore, before drawing a random date, we discard all Saturdays and Sundays within each firm’s drawing period.

27 We do not intentionally introduce sample selection, and focusing on a single industry is not sample selection in the sense of Ahern (2009). Our sample, like almost all empirical studies of insurance company stock returns, especially event studies, is limited to insurance firms.

28 Among the 203 sample firms, 171 have at least 72 consecutive months of returns, and 145 have at least 96 consecutive months of returns. Therefore, for 145 firms, the drawing period is 60 or more consecutive months. Similarly, for these 145 firms for models that require an estimation period, the estimation (pre-event plus post-event) will be 72 months, rather than the 24-month minimum sample requirement.

29 Ahern (2009) provides abnormal returns and rejection frequencies for a three-day window around the randomly selected event date (–1,+1) for samples from the top decile of prior returns. The mean bias (i.e., abnormal returns) is “virtually unchanged” whether the sample size is 25, 100, or 250 stocks. In contrast, the rejection frequencies change substantially as the sample size increases because the statistics are becoming more precise, though they are centered about a biased mean.

30 Ahern (2009) finds that the deviations from expected value for CBBM are much smaller than for the other models in his samples of high and lower prior return firms. These two samples (i.e., high and low prior return firms) are nonrandom and more than one-third of the rejection frequencies reported in Ahern (see Table 6, p. 475) exceed 0.10. Recall that Ahern’s results are for the event day (day 0). We do not find any rejection frequencies above 0.10 for the event day or three-day (–1, +1) windows. Also, in our event month or 13-month event window, rejection frequencies in excess of 0.10 are relatively uncommon across the 14 models and four test statistics (for 3.1 percent of the event month rejection frequencies and 12.5 percent of the 13-month event window rejection frequencies).

Additional information

Funding

Steven W. Pottier gratefully acknowledges the financial support of a Terry-Sanford Research Grant.