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Market expectations following catastrophes: an examination of insurance broker returns.

INTRODUCTION

The commercial insurance industry relies heavily on financial capital to maintain equilibrium. Large disasters reduce available capital, creating uncertainty in the market. To recoup lost capital, insurers may raise external funds, increase prices, and/or restrict coverage, but they also must consider how policyholders, competitors, investors, and regulators may react. Insurance buyers may face rate increases, impaired insurers, and existing losses as they make decisions regarding future insurance purchases. Considering all these factors, how is the commercial insurance market equilibrium expected to change following a major disaster?

Many existing theories suggest that insurance supply will contract after a capital shock, but few explicitly consider the response of commercial demand. Following seminal work by Winter (1994) and Gron (1994), Cagle and Harrington (1995) develop a model of insurer profits, ultimately showing that a shock's effect on price depends on the elasticity of demand relative to the elasticity of supply. The authors note that insurance guaranty funds, compulsory insurance requirements, and the lack of substitutes for insurance make it likely that demand is less elastic than supply, concluding that prices will increase following a capital shock. (1) The measurement of corporate insurance demand elasticities has not been widely studied--the only empirical article estimating corporate insurance demand elasticities that we are aware of is a study by Michel-Kerjan, Raschky, and Kunreuther (Forthcoming). The researchers use proprietary purchasing data to estimate the price elasticity of demand for corporate property and terrorism insurance and find that firms were relatively price inelastic for both types of coverage. (2)

The objective of our article is to contribute to this nascent literature by examining the expected effect of a major disaster on commercial insurance market equilibrium. Our approach is innovative in several ways. First, we use an event study methodology to examine stock returns, which isolates the effect of a catastrophe from other factors that may impact the insurance market. In other words, rather than examining the realized revenue changes in the quarter following the disaster (which would be influenced by interest rates, investment returns, inflation, and other losses), we study the stock market's immediate reaction in the days following the 43 largest insured-loss catastrophes since 1970. This captures any new expected change in insurance premium revenue as a direct result of the disaster.

Second, rather than examining stock returns for insurers, we examine returns for insurance brokers. Net increases in premium revenue benefit insurers, but that benefit may be offset by claim payments following a disaster. Prior catastrophe event studies focusing on insurers find that insurers generally experience negative abnormal returns as a result of their expected loss payments (Lamb, 1995; Cummins and Lewis, 2003; Doherty, Lamm-Tennant, and Starks, 2003). Insurance brokers, on the other hand, derive a substantial portion of their revenues from commissions on premiums paid, so broker revenues may serve as a proxy for insurer revenues. Unlike insurers, however, insurance brokers have little (if any) exposure to policyholder claims. Hence, expected changes in premium revenue resulting from a catastrophe more directly affect broker profits than insurer profits. We examine broker stock returns to evaluate the expected change in broker profits. The results of these returns will thus provide information on market expectation of insurance industry revenue immediately after a catastrophe's shock to financial capital.

Finally, with the results of our event studies, we conduct a cross-sectional regression to examine factors associated with the size of the cumulative abnormal returns (CARs) for brokers. Our primary variable of interest is the shock to insurer capital as measured by the size of the insured loss. A second variable of interest captures the relative amount of capital available in the insurance market at the time of the disaster. We also include the type of disaster, location of the disaster, and broker-specific attributes as control variables.

We consistently find positive and significant CARs for insurance brokers following the largest natural disasters. On average over the 20 events with the largest insured losses, broker stocks earned abnormal returns of 0.38 percent on the day of the catastrophe and another 0.13 percent the day after. In the 10-day and 30-day windows following the top 20 catastrophes, broker stocks generated 1.29 percent and 4.14 percent cumulative average abnormal returns (CAARs), respectively. Consistent with these results, we find that the size of the loss is positively related to broker CARs following the disaster. For the top 20 catastrophes, a 1 percent increase in loss size is associated with a 0.12 percentage point increase in the CAR over days 0 to +1 relative to the event. For this same set of events, we also find that existing capital is negatively related to broker CARs--for each percentage-point decrease in available capital, the average broker return increases by 0.13 percentage points.

The event study results provide evidence that investors expect broker profits to rise following large disasters. From the regression analysis, the CARs' positive association with loss size and negative association with capital suggest that price increases are the source of this expected revenue increase. An expected positive revenue change following a price increase implies that the price increase dominates any potential decrease in quantity. We cannot be certain why investors believe in this dominance-they may anticipate positive shifts in insurance demand or assume that demand for insurance is relatively inelastic. Regardless, the net effect remains-catastrophes are expected to have a positive overall impact on revenues for commercial insurers, reinsurers, and brokers. While the revenue increase for insurers and reinsurers may be offset by claim payments, brokers are expected to profit from the change. Our results provide empirical evidence in support of prior work proposed by Cagle and Harrington (1995), Winter (1994), and Gron (1994), despite not being a direct test of their hypotheses.

RELATED RESEARCH

Commercial Insurance Demand

In this section, we discuss four areas of related research; however, our study is most closely related to the limited research done on measuring commercial insurance demand. A natural first question to ask in examining this literature is: how price sensitive are insurance buyers? Prior research has found evidence of relatively price elastic demand for personal insurance, particularly for catastrophe coverage. For example, Grace, Klein, and Kleindorfer (2004) find that individuals have much more elastic demand for catastrophe insurance ([[epsilon].sub.p] = -2.064 in New York and -1.915 in Florida) than for noncatastrophe (e.g., fire) insurance ([[epsilon].sub.p] = -0.331 in New York and -0.404 in Florida). (3) As another example, Browne and Hoyt (2000) study the demand for flood insurance, including both individuals and businesses in their data set. While they were not able to differentiate individuals from firms, they found demand to be relatively price elastic when measuring quantity as the dollar amount of insurance in force per capita ([epsilon]p = 0.997). (4) Our focus is on commercial insurance demand rather than demand for personal insurance.

Commercial insurance demand differs from personal insurance demand in that risk aversion cannot explain purchases by corporations (see Mayers and Smith, 1982). Proposed sources of demand include contractual obligations to purchase coverage, riskaverse owner-managers who are limited in diversifying their investment in the firm, potential costs of bankruptcy, service efficiencies provided by the insurance companies, and tax incentives, among many other reasons (Mayers and Smith, 1982). A number of researchers have tested the influence of these factors on demand (Yamori, 1999; Hoyt and Khang, 2000; Zou, Adams, and Buckle, 2003; Zou and Adams, 2006; Aunon-Nerin and Ehling, 2008, among others). In this article, we focus on expected shifts in equilibrium rather than the sources of demand. The literature measuring corporate demand for insurance is limited, mostly due to the lack of firm-level purchasing data--to our knowledge, only one published article has estimated the elasticity of demand for commercial insurance. Michel-Kerjan, Raschky, and Kunreuther (Forthcoming) use a proprietary data set to compare price elasticities for catastrophe and noncatastrophe commercial insurance. Contrary to Grace, Klein, and Kleindorfer's (2004) comparison for personal lines insurance, the authors find that the price elasticities were similar between catastrophe and noncatastrophe coverage--following a 10 percent premium increase, corporate purchasers are expected to decrease their quantity of coverage demanded by 2.93 percent (for property insurance) and 2.42 percent (for terrorism insurance).

Our article adds to this particular strand of literature by providing an examination of the expected shift in equilibrium price and quantity reflected in premium revenue. While the theory discussed in the next subsection indicates that insurers will respond to a financial shock with a price increase, few researchers have examined how demand for coverage is expected to change. The estimates for price elasticity imply that commercial buyers facing a price increase will decrease their quantity demanded, but not by enough to counter the positive effect of the price increase on industry revenue. The results of our study are consistent with this elasticity measure and subsequent effect, suggesting that net insurance industry revenue will be expected to rise following a capital shock.

Capital Shocks in the Insurance Industry

With perfect competition and capital markets, insurance premiums would be based only on the present discounted value of expected claims and other expenses, without regard for fluctuations in capital (Myers and Cohn, 1987). In reality, the property-casualty (P&C) insurance industry has experienced what is known as the "insurance cycle" or "underwriting cycle"--an ebb and flow of premiums and profitability while increasing or reducing the amount of insurance available to customers. Capital shocks are one explanation for this cycle.

Winter (1988,1994) develops and formalizes the idea that shocks to financial capacity are the primary cause of the insurance cycle. Inflation, increases in interest rates, poor investment performance, or claims may shock insurer financial capital. Winter theorizes that insurers whose financial capital is reduced will increase premiums and reduce coverage rather than raise costly external capital. Winter's initial theory of "capacity constraint" is supported, refined, and tested by Gron (1994). (5) When capacity is reduced, the insurance supply curve shifts to the left, increasing premiums and decreasing the "quantity" of insurance in the market.

Cagle and Harrington (1995) also model the effect of capital shocks on equilibrium price, with scenarios for both inelastic and elastic demand. First specifying inelastic demand, they show that the partial derivative of equilibrium price with respect to capital is negative ([P.sub.k] < 0). They then model the case of elastic demand, where N insurers each supply quantity q of insurance, and insurance buyers demand total quantity Q. Both supply and demand depend on capital K and price (itself a function of capital, P(K)). The equilibrium model is Nq[P(K), K] = Q[P(K), K]. Using their models of insurer profits, differentiating price with respect to capital gives:

[P.sub.K] = p([[epsilon].sub.K] - [[eta].sub.K])/K([[epsilon].sub.p] + [[eta].sub.p]) (1)

The sign of PK depends on the relative elasticities of demand ([[epsilon].sub.K] = [Q.sub.K]K/Q) and supply ([[eta].sub.K] = [q.sub.K]K/q) with respect to capital. Cagle and Harrington conclude that the lack of substitutes for insurance and insurance regulation make it likely that [[epsilon].sub.K] < [[eta].sub.K], and thus [P.sub.K] < 0. In addition, they note that increased elasticity of demand with respect to price ([[epsilon].sub.p] = -[Q.sub.p]P/Q) would temper any price increases resulting from the capital shock. Cummins and Danzon (1997) center a similar model around insurer insolvency risk, determining that prices could potentially decrease following capital shocks if insurance buyers reentered the market to switch to different insurers with lower default risk. (6) They empirically test this model, determining that the liability loss shocks of the 1980s did not cause insurance prices to increase substantially. Instead, Cummins and Danzon attribute price increases to interest rate decreases and increased expected losses.

Capacity constraint theory has been tested empirically many times over the past 20 years. Winter (1994) finds empirical support for his theory, estimating a positive and significant relationship between industry relative surplus and the economic loss ratio (the reciprocal of price). Gron (1994) finds a negative relationship between insurer net worth and underwriting margins. Other research finding evidence of capacity constraint includes Niehaus and Terry (1993), Cagle and Harrington (1995), Doherty and Garven (1995), Higgins and Thistle (2000), Choi, Hardigree, and Thistle (2002), Weiss and Chung (2004), Fenn and Vencappa (2005), and Derien (2008).

Catastrophe Event Studies

A number of event studies have examined the effect of specific catastrophes on the insurance industry. Most have focused on insurers and have found negative insurer returns subsequent to the catastrophe. In many of these studies, the authors describe the possibility of offsetting effects--insurers must pay claims in the short term but may be able to raise rates in the long term to recoup their losses. Lamb (1995) finds that insurers with significant operations in Florida or Louisiana experienced negative abnormal returns following Hurricane Andrew in 1992, while stock returns for insurers not writing business in those states were not affected. Following Lamb's work, Angbazo and Narayanan (1996) investigate both Hurricane Andrew and a subsequent freeze of American International Group's premium rates. The authors find negative stock price effects for both events and provide evidence that expectations of higher prices may have offset the negative effects of Hurricane Andrew until the premium freeze. Cagle (1996) identifies negative abnormal returns for insurers following Hurricane Hugo in 1989. The 1995 Hanshin earthquake in Japan created similar negative returns for Japanese insurers according to Yamori and Kobayashi (2002). Blau, Van Ness, and Wade (2008) find evidence of increased short selling of insurer stocks beginning 2 days after Hurricane Katrina made landfall and several days before Hurricane Rita hit 28 days later. (7)

The 9/11 terrorist attacks were a unique event--virtually unpredictable, economically significant across the globe, and man-made. Cummins and Lewis (2003) test the effect of the 2001 World Trade Center (WTC) terrorist attacks on insurance company stocks and find that insurer stocks were negatively affected by the attacks, though financially strong insurers recovered their stock losses within a few weeks. The authors find similar negative results for insurers following Hurricane Andrew and the Northridge Earthquake in replicating Lamb's (1995) event study. Doherty, Lamm-Tennant, and Starks (2003) also examine the effect of the WTC attacks on insurer stock returns, using the capacity constraint model to predict the impact of the attacks on insurers. The raw insurer stock returns they calculate generally were consistent with the negative abnormal returns calculated by Cummins and Lewis. Doherty, Lamm-Tennant, and Starks note that insurance brokers fared well following the attacks, as exposure to the risk is limited and revenue is directly related to premium levels.

In the context of insurer event studies, expectations about claim payments appear to dominate anticipated price increases. To examine the expected effect of catastrophes on equilibrium price and quantity in the commercial insurance market, we look instead to insurance brokers, who are compensated based on premium revenue but who do not pay claims.

Brokers

The final area of related research focuses on brokers, as we utilize broker returns to examine expected insurance market responses to catastrophes. The primary role of a commercial insurance broker is to purchase insurance coverage from retail insurers on behalf of their commercial clients. Brokers also may engage in benefits brokerage and consulting, wholesale or reinsurance brokerage, alternative risk financing, risk analysis, and human resources consulting, among other activities. These brokers are primarily compensated one of two ways. Most often, brokers are paid a percentage of the premium paid for each policy they manage, called a "direct commission." In 2011, the average direct commission rate was 10.3 percent and the industry paid $45.55 billion in direct commissions on $447.44 billion in net written premiums (A.M. Best Company, 2012). (8) Broker direct commission revenue immediately reflects insurer premium revenue (and thus market equilibrium price and quantity). Commission rates do vary across business lines and over time, but do not change as frequently as price and quantity. Brokers also may be paid a flat fee for placing coverage, which is often negotiated annually with the client and generally does not vary directly with the amount of coverage placed.

Although the flat fee approach is becoming more common, commissions continue to drive broker revenue. Maas (2010) conducts a series of interviews with brokers and finds that the role of an insurance broker in the past has been primarily transactional, implying that brokers were compensated with direct commissions for placing coverage. Only in recent years have brokers migrated to more of a "consultant" role. (9) It is possible that positive abnormal returns for brokers following catastrophes are due to investors' expectations of an increased demand for loss control services or consulting, rather than increases in price. This effect is difficult to disentangle, as brokers rarely report consulting revenue separate from insurer commission revenue. (10) One aggregate estimate, the 2011 Business Insurance Market Sourcebook, found that placing commercial retail insurance accounted for 52.0 percent of broker revenue on average. The fourth-largest broker, A.J. Gallagher, reported that 52 percent of 2012 revenues came from direct brokerage commissions, 16 percent came from brokerage fees, 22 percent came from risk management and consulting fees, and 5 percent came from supplemental and contingent commissions.

In addition to regular compensation, brokers also may receive contingent commissions. These commissions are most often based on profitability, but also can be based on revenues, growth, or other metrics. While contingent commissions are a source of revenue for brokers, they do not comprise a major portion of revenue--overall, they amounted to only about 1.1 percent of total premiums billed in 2004 (Cummins and Doherty, 2006). For commercial lines, contingent commissions comprise on average 5-6 percent of brokerage revenue. Because contingent commission revenue makes up such a small portion of overall revenue and contingent commissions usually are paid quarterly or annually, we believe that changes in premiums paid (and thus direct commissions) are the primary driver of broker revenue changes. In our study, we proxy anticipated broker revenue changes subsequent to catastrophes by examining the abnormal stock returns for publicly traded insurance brokers.

METHODOLOGY

Event Study

We first conduct an event study to test whether stocks of U.S.-traded brokers consistently experience positive abnormal returns following catastrophes. Event studies examine the difference between a security's expected return and its observed return over a specified window of time. The expected return is most often calculated by using return data from an "estimation window" prior to the event of interest to estimate parameters to predict returns in the future. The abnormal return is the deviation from these predictions during an "event window" surrounding the event of interest. This is the common formulation in Brown and Warner (1985) and Scholes and Williams (1977), among others, who normally estimate parameters using the capital asset pricing model (CAPM). To predict returns as accurately as possible, we use the Fama-French (1993) three-factor model outlined in Equation (2) below. (11)

Our standard benchmark estimation period for estimating a broker's expected return ends 46 trading days before the event date. The estimation period is set at 255 trading days long if possible, with a minimum of 60 days. We test windows 10 days prior to the event through 90 days following the event.

In many cases, shocks cause abnormal returns to become more volatile. In order to improve the fit of event studies with induced volatility, Lamoureux and Lastrapes (1990) examine the variance of daily abnormal returns and find that errors followed a generalized autoregressive conditionally heteroskedastic (GARCH) framework. Cheng, Elyasiani, and Lin (2009) study the effect of the 2004 Spitzer bid-rigging lawsuits on the stock returns for publicly traded brokers in the United States and find that daily abnormal returns for insurance brokers also follow a GARCH (1,1) framework. We specify the same GARCH errors in our analysis.

To calculate expected returns, we estimate coefficients in the following model using benchmark data from the estimation period:

[R.sub.it] = [a.sub.i] + [[beta].sub.i][R.sub.mt] + [s.sub.i][SMB.sub.t] + [h.sub.i][HML.sub.t] + [[epsilon].sub.it], (2)

where [R.sub.it] is the actual return of the stock of firm i on day t; [R.sub.mt] is the rate of return of a market index m (we chose the Center for Research in Security Prices [CRSP] equally weighted index) on day t; [SMB.sub.t] is the return on a portfolio of small market-capitalization stocks minus the average return on three portfolios of large marketcapitalization stocks; [HML.sub.t] is the average return on two portfolios of stocks with high book-to-market ratios minus the average return of two portfolios of stocks with low book-to-market ratios; [[epsilon].sub.it] is a random error variable with a conditional expectation of zero given (the information available at time t - 1) and conditional variance:

[[sigma].sup.2]([[epsilon].sub.it]|[[THETA].sub.t-1]) = [h.sub.it] = [[omega].sub.i] + [[delta].sub.i][h.sub.it-1] + [[gamma].sub.i][[epsilon].sup.2.sub.it-1], (3)

where [[omega].sub.i] > 0, [[gamma].sub.i] > 0, [[delta].sub.i] [greater than or equal to] 0 and [[gamma].sub.i] + [[delta].sub.i] < 1. We use maximum likelihood to estimate these coefficients.

The abnormal return of stock i on day t is the empirical difference between the observed return and the expected return during the event window:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (4)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the estimates of the coefficients in Equation (2) using an ordinary least squares (OLS) regression on data from the estimation window. We chose to use this multifactor model to reduce the variance of the abnormal return as much as possible. As MacKinlay (1997) states, the marginal explanatory power (and thus variance reduction) of using such a model over a standard market model will be greatest with similar firms. (12)

This provides us with an estimate of the abnormal return for a particular broker stock each day during the event window. We then sum abnormal returns over a specified window starting at day [T.sub.1] and ending

at day [T.sub.2] to determine the cumulative effect of the event for each broker as shown in Equation (5).

[CAR.sub.ik] = [[T.sub.2].summation over (t = [T.sub.1])] [AR.sub.ikt]. (5)

For each window specified, we have a [CAR.sub.ik] for each broker i traded during catastrophe k. This provides a single observation per broker, per event, and consolidates each broker stock's reaction to each catastrophe. We can then summarize the CARs by calculating the cumulative average abnormal return (CAAR) for the entire set or subset of events.

CAAR = 1/N [summation over (i,k)] [CAR.sub.ik] where N = i x k. (6)

We use the Patell (1976) test for statistical significance. This test assumes abnormal returns are serially uncorrelated, which may not be a correct assumption. However, the bias resulting from this assumption is generally small when the event window is shorter than 60 days (Karafiath and Spencer, 1991; Cowan, 1993). While we report CAARs up to 90 days postevent, our primary interest is on CAARs in the first few days following the event as longer CAARs may be confounded by other factors or events that influence broker returns. (13) The Patell Z-scores are calculated using a standardized abnormal return (SAR) for each insurance broker, i:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the standard deviation of the abnormal returns, adjusted for any missing trading days. The Z-score for the N broker-events measured from [T.sub.1] to [T.sub.2] is then:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (8)

where for each broker i and event k:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

and:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (10)

with [M.sub.i] being the number of nonmissing trading days in the estimation window. Assuming cross-sectional independence of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] follows a standard normal distribution.

Regression

Once the CARs are calculated for each of the 264 broker-events, we use them as the dependent variable in our cross-sectional regression models. Since the reason we use the event study methodology is to isolate the effect of the catastrophe, we use a short CAR window (0,+1) as our dependent variable. This should capture the response on the day of the event as well as any slightly delayed responses, while minimizing the amount of time other factors may influence results. CARs appear to differ by broker, but not by time (in other words, the CARs estimated for events in the 1990s do not appear to differ from those estimated for events in the 2000s). There is some intraclass correlation of CAR within events, so we cluster standard errors by event in our regressions.

We have two primary explanatory variables of interest: the size of the catastrophe's insured loss and the capacity available in the insurance market. The size of the insured loss (INSLOSS) is the amount (in billions of 2011 dollars) reported in the Swiss Re Sigma reports of the largest insured losses since 1970. While this amount is obviously not known on the day of the loss, it serves as a proxy for the relative impact of each loss. (14) For robustness, we develop another set of regression models using a "shock" variable rather than the estimated raw insured loss (Equation (11)). Because these loss amounts are highly skewed, we also conduct analysis using natural logarithms of INSLOSS and SHOCK:

SHOCKk = [INSLOSS.sub.k]/[PHS.sub.q=-1]. (11)

We use policyholder surplus (PHS) as our measure of capacity available in the market. PHS is the difference between insurer assets and insurer liabilities, which serves as a proxy for the industry's ability to pay claims and write new business. It is not appropriate to use PHS from the same quarter as the event, since that value has not yet been aggregated and reported, so we use PHS from the prior quarter ([PHS.sub.q=-1] in Equation (11)). (15) Following Winter (1994), we divide PHS known at the time of the event by its recent historical average for a measure of relative capacity (RELCAP). Since we collect PHS on a quarterly basis, we compare PHS in the immediate prior quarter to the average of the prior four quarters to establish a proxy for our second explanatory variable of interest, the capacity available in the insurance market:

[RELCAP.sub.k] = [PHS.sub.q=-1]/1/4 [-2.summation over (q = -5)][PHS.sub.q]. (12)

We include a number of controls in our model. To account for the general state of broker abnormal returns immediately prior to the event, we include a prior window of returns CAR (--2, --1) as an explanatory variable (PRIORCAR). Returns for events that occur within 90 days of a prior event may have been affected by the prior event's returns, so we include an indicator variable for such events (OVERLAP).We also include indicator variables for catastrophe location (US) and type (earthquake [EQ], and the World Trade Center event [WTC]). At the broker level, we include an indicator variable for company news surrounding the event (NEWS). (16) We also control for earnings announcements around the event (EARNINGS). (17) To account for heterogeneity between brokers that is not accounted for in the NEWS and EARNINGS variables (e.g., larger brokers may benefit more from price increases, as their negotiating power draws new customers), we include a fixed effect for each broker in our regression models. We also include a fixed effect for each quarter to control for seasonal effects. Our analysis uses OLS cross-sectional regressions with standard errors clustered at the event level to control for intraclass correlation.

Formally, our regression model is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (13)

with i indicating the broker and k indicating the event. A positive coefficient on INSLOSS would indicate that larger insured catastrophe losses are positive news for brokers. This idea is consistent with the idea that investors expect brokers to benefit from increased revenues of insurers. A negative coefficient for RELCAP would indicate decreases in insurer surplus are associated with larger (positive) abnormal returns. This is consistent with capacity constraint leading to increased prices. Finally, in our alternative specifications, INSLOSS is replaced by LOG(INSLOSS), SHOCK, or LOG(SHOCK).

DATA

Catastrophes

Information on the largest catastrophes since 1970 comes from the 2010 and 2011 Swiss Re Sigma lists of the most costly insurance losses during that time. Table 1 describes the 10 largest losses. It is clear that the size of losses is highly skewed--the largest catastrophe loss, Hurricane Katrina, is more than double the size of the next-largest loss, the Tohoku Earthquake ($75 billion vs. $35 billion). As a measure of market capacity, we collect PHS for the P&C insurance industry in aggregate on a quarterly basis and convert to 2011 dollars. Shock is measured as the size of the loss relative to the prior quarter's PHS (see fifth column of Table 1). Hurricane Katrina is also the largest insured loss relative to market capacity, comprising over 15 percent of the existing PHS.

Table 2 provides summary statistics on insured loss size for the different catastrophe types. Overall, the mean insured loss is $10.01 billion with a standard deviation of $12.41 billion, while the median insured loss is $6.13 billion. The average loss size is 2.41 percent of PHS, while the median is 1.24 percent. Narrowing the sample of events to the top 20 (top 10) largest, the median loss size is $12.00 ($21.14) billion. The mean loss sizes are substantially larger due to the influence of Hurricane Katrina.

All but one of the events--the 9/11 terrorist attacks (WTC)--were natural disasters. The most frequent catastrophes were hurricanes, though earthquakes had the largest average insured loss when considering disaster types that occurred more than once. Earthquakes also possess the clearest "event date," since the onset of an earthquake is essentially unpredictable. The weather-related events, on the other hand, may be predicted several days prior to their onset. (18) We specified the "event date" as the first full trading day after the event began causing widespread destruction. In most cases, this was the date of landfall in the United States for hurricanes, the date of landfall in Japan for typhoons, and the date of widespread damage and business closures for flooding or winter storms. We also considered the time of day, so if an earthquake struck in the early morning hours of a trading day (such as the Tohoku Earthquake in 2011, which struck at 12:45 am New York time) we would consider that same day the "event date."

WTC was unique in several ways. First, this event had the highest cumulative average abnormal return (12.96 percent in the 5 trading days following, and 23.34 percent in the 30 trading days following). Second, the stock markets did not open on September 11, 2001 (a Tuesday) and remained closed until September 17 (the following Monday). This may have led to pent-up demand for investment in certain stocks and thus a run-up in prices once the markets reopened. Finally, this is the only intentionally man-made catastrophe on the list, (19) creating a question about whether stock market effects related to the WTC attacks are representative of the rest of the sample. We conduct our event studies both with and without WTC and include a corresponding control variable in our regressions.

The earliest event was in 1987. The year with the most catastrophes was 2011, which had two earthquakes, one major flood, two storm systems with tornadoes, and one major hurricane. However, 2005 contained the highest aggregate damage due to Hurricanes Katrina, Rita, and Wilma, which together caused over $100 billion in insured losses. From an original set of 46 events, there were three incidences of events that had the same or nearly the same event date. To avoid double-counting of abnormal returns, we collapsed the data for both catastrophes into the observation for the event causing more damage. We merged data for the Chilean earthquake (ranked #15) with Winter Storm Xynthia (#39) on March 1, 2010, Winter Storm Lothar (#17) with Winter Storm Martin (#36) on December 27, 1999, and Hurricane Frances with Typhoon Songda (#30) on September 7, 2004. This provides a final data set of 43 events for our event study.

Brokers

We compile a list of commercial P&C brokers who were publicly traded on U.S. exchanges during the period surrounding the disaster. We limit our search to commercial P&C brokers because these brokers are highly commission driven, and the P&C insurance market has direct exposure to the catastrophic events. To get a comprehensive list of the brokers, we search the SEC EDGAR database under SIC code 6411 (Insurance Agents, Brokers, and Service) and examine each firm's annual 10-K filings to verify that each derived a substantial amount of revenue from retail commercial P&C brokerage. (20) We also consider similar SIC codes and several editions of the annual Business Insurance Market Sourcebook, which lists the top 100 brokers each year. We eliminate brokers with a very small amount of revenue, brokers primarily traded on foreign exchanges, brokers who operate as insurance companies, and specialty or wholesale brokers. Due to IPOs and acquisitions, brokers come in and out of the data set throughout the period from 1987 to 2011. There was one broker (Acordia) who was only traded during four events, while four brokers (Aon, Brown & Brown, A.J. Gallagher, and Marsh & McLennan) were traded during all events. Table 3 provides the list of brokers that comprise our 264 broker-events.

We use stock return data from CRSP to estimate abnormal returns for the brokers traded surrounding the catastrophe. We examine events between 1987 and 2011, which is why five of the brokers in Table 3 have "end dates" of December 31, 2011. All brokers who left the sample early did so due to an acquisition--Acordia, Alexander, and HRH were acquired by competitors, while Hub and USI were taken private by equity firms.

Other Variables

For our regression models, our primary explanatory variables of interest are the size of the insured loss (raw dollars and relative to PHS) and the relative capacity in the insurance market known at the time of the event. Summary statistics for these variables are provided in Table 4. As described earlier, the raw insured loss amount is highly skewed. Taking the natural log tempers this skewness. The shock variable is expressed as a percent of PHS, ranging from 0.49 percent (which appears as 0 in the table due to rounding) to 15.65 percent. We take the log of SHOCK x 100 to make most of the values positive, though the 11 smallest still have negative values as they were less than 1 percent of PHS. Relative capacity ranges from 0.89 (constrained capacity) to 1.11 (excess capacity). A graph of relative capacity over time is provided in Figure 1.

Data were not available to calculate relative capacity for the earliest event ("storms and floods in Europe, the #21 largest event, on October 16,1987), which is why this variable has only 259 observations. This early event is ultimately dropped from our regressions due to the missing variable of interest.

More than half of the catastrophes (26) occurred in the United States. Many happened soon after an earlier event--17 occurred within 90 days of an earlier event. There were 12 instances where the broker announced earnings within 10 days of an event and, on average, the broker fell short of expectations by $0.04. In one case, Aon missed earnings by $0.37, causing their stock to drop 32 percent in a day. There were 41 cases (out of the 264 broker-event observations) where the Wall Street Journal reported on a particular broker within 5 days of an event.

RESULTS

Positive Broker CAARs Following Catastrophes

The results of the event study are outlined in Table 5. The results are reported as the difference in percentage return for all broker-event combinations. For example, the CAAR of 2.75 in the (0,+5) window for the top 10 events (in column (c)) means that, on average, broker returns were 2.75 percentage points higher than would be expected based on how broker stocks normally perform with the rest of the market. When considering all 43 events in the sample (column (a)), CAARs are positive and significant for the day of the event, and they appear to remain positive for the first month following the event. (21) When we restrict the sample to the 20 largest events (with insured losses of at least $6.6 billion), we find a large, significant, and more persistent positive return (column (b)). (22) The (0,0) window is twice as large as for the full sample, with a CAAR of 0.71 percent, while the (0,+1) window also reflects positive and significant returns. Longer windows continue the positive returns, indicating that the 20 largest catastrophes had a lasting positive effect on expectations for broker profits. The positive and significant results in column (c) for the 10 largest catastrophes (with insured losses of at least $12 billion) reinforce this idea. The larger CAARs as we restrict the sample (moving from column (a) to column (c)) also suggest that loss size influences the magnitude of the abnormal returns.

These results are subject to two potential problems. One is that the WTC event is included, and as previously discussed, this event appears to be distinct from the other catastrophes. Figure 2 illustrates the broker return response to the WTC event relative to the other events--it is clear that WTC was an outlier and that the CARs for this event influence the CAAR calculation for all other events. (23)

The second potential problem is that some of the event windows overlap with a subsequent event, which may artificially boost calculated returns in the earlier event window(s). For example, Tropical Storm Allison (ranked #28) had a CAAR of 8.59 percent in the (0,+90) day window following, but the WTC event (ranked #4) occurred on day +68. WTC certainly impacts abnormal returns associated with the Tropical Storm Allison event for day +68 and later, as illustrated by Figure 3. To account for these overlapping events, we conduct a subsequent event study dropping abnormal returns for days on or after a subsequent event. For example, we dropped the Tropical Storm Allison abnormal returns from day +68 to day +90. For events with dropped ARs in a particular window, the CAR for that window is not calculated. In the Tropical Storm Allison example, the CARs are calculated and reported for the (0,0), (0,+5), (0,+10), and (0,+30) windows, but not for the (0,+90) window since the ARs are missing for days 68-90.

Table 6 displays updated event study results using this methodology for overlapping events, and dropping the WTC event. These results continue to reflect positive and significant CAARs for the top 20 and top 10 event subsamples. Overall, these event study results show that insurance broker stocks earn positive abnormal returns following major catastrophes, and provide an initial indication that the size of the event plays a role.

Effects of Loss Size and Financial Capital on Broker CARs

We report the results of our regression models in Table 7. This analysis utilizes the days (0,+1) event window CARs as the dependent variable. (24) Columns (1) and (2) contain the regression results for the full sample of 42 events, (1) using Insured Loss as the variable of interest and (2) using log(Insured Loss). Columns (3) and (4) replicate the models in columns (1) and (2), restricting our sample to the top 20 largest events. WTC is included in this sample, but the extreme response is controlled for with an indicator for the event. These models use fixed effects for broker and quarter, and cluster standard errors by event.

In all cases, the coefficient for loss size is positive and significant. Columns (1) and (3) show that each additional billion dollars in losses is associated with an increase in the average 2-day CAR of approximately 0.04 percentage points. While statistically significant, this effect is very small and likely affected by the large skew in the distribution of insured losses. A better measure of the effect of loss size may be log(Insured Loss). The coefficient on log(Insured Loss) indicates that a 1 percent increase in insured losses is associated with an 0.8 percentage point increase in the expected broker CAR (if considering all losses). That relationship increases to 1.2 percentage points if the loss is already large enough to be in the Top 20.

The coefficient on relative capacity in columns (3) and (4) shows that broker CARs are negatively associated with financial capital. (25) With lower levels of relative capacity, additional catastrophe shocks to insurer financial capital are expected to raise prices, ultimately benefiting brokers. The coefficient estimate on relative capacity in column (4) shows that capital 1 percent lower than the past year's average is associated with postcatastrophe broker CARs 0.13 percentage points higher, all else equal.

Our control variables appear to be appropriate, though they often are not consistently significant. The return in the prior CAR window is negatively associated with postevent CARs, perhaps indicating that brokers currently under duress are expected to benefit disproportionately from a potential price increase. Events that occur during a prior event's window have relatively larger CARs. We also include controls for catastrophe type and location, news items about the broker in the days surrounding the catastrophe, and whether the broker announced earnings in the days before and after the event. None of these controls is significant across specifications. (26) The [R.sup.2] statistics indicate that our models fit the data well. While only a few of the control variables included in the analysis were consistent and significant, the inclusion of broker/quarter fixed effects and clustered standard errors likely improved the overall fit of the model.

We conduct an alternative analysis using a relative measure of loss size, SHOCK, which is the size of the loss as a percent of PHS. The regression results for this specification are reported in Table 8. The shock variable is positive and significant, supporting the results reported in Table 7. The coefficient on shock in column (3) can be interpreted to mean that a 1 percentage point increase in the relative shock is associated with a 0.18 percentage point increase in broker CAR in the 2 days following the catastrophe. The coefficient on log(Shock) is not significant in column (4), possibly because the relative capacity variable already accounts for the current level of capital. The high significance for all other measures of loss size gives us confidence that CARs are positively related to the size of the loss. Similar to the analysis reported in Table 7, the relative capacity variable is not significant for the full sample, but is negative and significant when examining only the 20 largest events.

Might investors be responding to potential for increased consulting business rather than expecting prices to increase? This is plausible, but changes in price immediately affects broker commission revenue, while increased consulting revenue might not be realized for some time. As discussed in the "Brokers" section of "Related Research," the proportion of broker revenue attributed to consulting and other fees has risen in recent years. Assuming this is true for our set of brokers, the power of our model would decrease as brokers generate more revenue from consulting and fees. In Figure 4, we plot the residuals from our model (Table 7, column (2)) over time, showing that there is no obvious trend in the fit of our model as consulting fees possibly become a larger part of broker revenue.

CONCLUSION

How is the insurance market equilibrium expected to change following a large catastrophe? Considering prior research on (1) the relationship between insurance prices and financial capital and (2) the elasticity of demand for corporate insurance with respect to price, we propose that catastrophes will be expected to increase insurance prices without a fully offsetting decrease in demand. The expected price increases outpace any expected decrease in equilibrium quantity, either due to a perception of inelastic demand or an expected shift in the demand curve to the right. This dynamic will increase net revenue for insurers and reinsurers, and insurance brokers will benefit by earning commissions on this increased revenue.

To isolate the effect of the catastrophe from other factors that may influence price and quantity, we examine stock returns in the days following the event. Prior research has shown that stocks for insurers and reinsurers generally experience negative returns due to the large claim payments made to policyholders. Insurance brokers, on the other hand, earn commissions on the total premium for each policy but are not exposed to loss payments. We conduct our event study on publicly traded insurance brokers, expecting that brokers will earn positive abnormal returns as investors consider the effect of the catastrophe on equilibrium price and quantity.

We find evidence that insurance broker stocks earn positive and significant CARs following catastrophes. Using our most restrictive event study specification, we find that brokers earn a 0.17 percent average abnormal return on the day of the 43 largest catastrophes since 1970. This effect is particularly striking for large catastrophes-brokers earned 0.38 percent average abnormal returns for the 20 largest events and 0.79 percent returns for the 10 largest. For these large event subsets, CARs continued to increase at least 90 days post-event.

We find that the relative size of the catastrophe is positively related to broker abnormal returns, and that returns are larger when insurance prices have been decreasing. Specifically, we find a positive relationship between the insured loss size and the broker CARs following the catastrophe. A proposed explanation for this relationship is that large losses have greater impact on financial capital. Consistent with theoretical work on the relationship between insurer capital and insurance prices, lower levels of capital at the time of a shock are associated with higher CARs for brokers. In other words, strained financial capital preceding a loss is expected to benefit insurance brokers, and our best explanation for this relationship is that investors expect price increases to dominate any potential decrease in the equilibrium quantity of insurance.

Future research might examine the extent to which investors are correct in buying broker stocks following catastrophes. While our research shows that investors expect broker revenues to increase as a result of the catastrophe, it does not determine whether revenues actually increase as a result of the disaster. A comparison of broker CARs to insurer CARs following catastrophes also may be an interesting avenue for future research.

DOI: 10.1111/jori.12069

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Marc A. Ragin is in the Department of Risk, Insurance, and Healthcare Management in the Fox School of Business at Temple University. Ragin can be contacted via e-mail: mragin@temple.edu. Martin Halek is in the Department of Actuarial Science, Risk Management, and Insurance in the Wisconsin School of Business at the University of Wisconsin-Madison. Halek can be contacted via e-mail: mhalek@bus.wisc.edu. We would like to thank the two anonymous referees for their insights and suggestions. Thanks also are due to Joan Schmit, Jed Frees, Mark Browne, Justin Sydnor, Morris Davis, and seminar participants at the American Risk and Insurance Association and Western Risk and Insurance Association annual meetings, Florida State University, Temple University, and the Federal Reserve Bank of Chicago.

(1) Cummins and Danzon (1997) develop a similar model, which specifically allows for potential price decreases following capital shocks under certain conditions that may affect elasticity of demand.

(2) Our use of the term "elastic" versus "inelastic" is somewhat arbitrary. We generally describe an elasticity absolute value less than 0.5 as "inelastic" and greater than 1.0 as "elastic." This is intended to capture the effect of these elasticities on total revenue, as a demand elasticity greater than 1.0 indicates a price increase would cause total revenue to decrease.

(3) These elasticities for catastrophe insurance are large enough to imply a net negative impact on total revenue following a price increase. For a 10 percent price increase, individuals reduce their quantity demanded by 20 percent, and thus the net change in total premium revenue is negative.

(4) Using a different measure of quantity (the number of policies per capita), demand was relatively price inelastic ([epsilon]p = -0.109). We believe price-elastic firms facing a price change after a major catastrophe would first choose to change limits rather than add or cancel coverage, so we believe Browne and Hoyt's (2000) "Insurance in force" quantity variable is more relevant to our research.

(5) The primary difference between these theories is that Winter (1988, 1994) assumes that regulation reduces the probability of bankruptcy to zero, while Gron (1994) does not make such an assumption. Gron assumes that insurers hold net worth to comply with regulatory requirements rather than to reduce the probability of insolvency (though that is the intent of the regulatory requirements). Both generate an upward-sloping short-run supply curve that shifts left following shocks to capital.

(6) Cummins and Danzon's (1997) model also allows for price increases consistent with Cagle and Harrington (1995). They allow for price increases if external capital becomes more expensive, demand increases following a shift in the loss distribution, policyholders renew coverage to decrease the probability of insolvency, or industry-wide shocks create informational barriers to entry for new insurers and switching costs for policyholders.

(7) There are two studies that find positive returns for insurers following a disaster. Shelor, Anderson, and Cross (1992) and Aiuppa, Carney, and Krueger (1993) both study the effect of the 1989 Loma Prieta earthquake in California, finding that insurance company stock prices experienced positive returns following the event.

(8) The average direct commission was 8.6 percent for earthquake insurance, 13.4 percent for fire, and 16.4 percent for commercial nonliability multiperil. These commissions are averaged over both independent agents (such as brokers) and captive agents, so they may not accurately reflect the commissions earned by the brokers in this study.

(9) Acquisition activity by brokers provides some anecdotal support for this. Aon's largest acquisition was Hewitt Associates, a human resources consulting firm, in 2010 for $5 billion. Marsh purchased Kroll Inc. (a security and risk consulting firm) for $2.25 billion in 2004. Marsh's largest acquisition was the $2.75 billion purchase of Sedgwick Group (an insurance broker and claims consulting firm) in 1998. Sedgwick's claims management group was spun off as an independently owned company. All amounts adjusted to 2011 dollars.

(10) Given the gradual increase in consulting activity, one might expect investor response to capital shocks to decrease over time as direct commission revenue becomes diluted. We examine this possibility in the "Results" section.

(11) For robustness, we conduct the same analysis using various alternative estimation models (market model, market-adjusted returns) without significant differences in results.

(12) One consideration for our data is that earlier catastrophe events occur during an event's estimation window. This is not a particular cause for concern, however, as this would bias down our abnormal return estimates for the specified event. We calculate "normal" returns using a period where returns are higher than they otherwise would be (due to the prior event), so our calculated abnormal returns are relative to a higher baseline.

(13) For example, the acquisition of Alexander & Alexander by Aon was announced on day +67 following Hurricane Fran. Alexander's abnormal return on the day of the announcement was +22.3 percent and the CAAR over all brokers increased from -0.42 percent on day +66 to 3.89 percent on day +68.

(14) We attempted to collect estimated losses at the time of the event, but these were not reported consistently.

(15) In collecting our data, we found that PHS was generally reported 3-4 months after quarter's close. Generally, we found that Q1 results were reported in mid-June, Q2 results were reported in late September, Q3 results were reported in late December, and Q4 results were reported in early April.

(16) We searched the Wall Street Journal with a 10-day window surrounding each event for any news item related to a particular broker. We found few overlaps, mostly related to bond issues, hiring or firing executives, or upcoming acquisitions or divestitures. We include a binary (0/1) indicator variable when there is a news item, as it is difficult to ascertain whether the news would have been received well or poorly by the markets.

(17) We calculate earnings announcements relative to average analyst expectations of earnings per share (EPS). The value of this variable is the difference between actual EPS and the mean expected EPS. We expect this control to be positively related to CAR.

(18) To test if investors anticipate weather events we conducted a t-test for different average abnormal returns (AARs) between weather events and nonweather events. We found that weather event AARs are 0.7 percent higher on day -7 and 0.2 percent higher on day -5 (significant at the 1 percent and 10 percent levels, respectively). No other prior-event days between -10 and 0 had significantly different abnormal returns between weather and nonweather events. This may indicate that investors react when an upcoming weather catastrophe is first forecast, but do not make any further investment in brokers until the damage begins. We do not believe this response will affect the CARs.

(19) The California East Bay Hills Fire of October 1991 (ranked #40 by insured loss) was started by a small grass fire that was not completely extinguished by firefighters. The cause of the original grass fire is unknown.

(20) This was not always available in the most current filing, so we based our criteria on the latest filing with that information. We would have liked to include in our analysis some measure of the proportion of revenue derived from P&C brokerage, but reporting was inconsistent among brokers. Often, that information was reported as an aside in management's discussion of financials, and the measurement basis was not exactly the same for each broker. Because of this inconsistency, we felt that it was not appropriate to use this information as a control in our later regression models.

(21) The positive CAARs for the prior window are likely due to weather events being anticipated by the market. In our later regressions, we control for existing positive abnormal returns by including the CAR (-2, -1) return as an explanatory variable.

(22) Columns are denoted with letters rather than numbers to illustrate the same event study model was used with a different subset of data in each column.

(23) These graphs also show the disproportionate influence of a noncatastrophe event--the large dip in CAARs around day +20 was the market reaction to Eliot Spitzer's bidrigging lawsuit against Marsh, which had contagion effects on other brokers as documented in Cheng, Elyasiani, and Lin (2009). The lawsuit was announced on October 14, 2004, which affected CARs following Hurricane Charley (day +43), Hurricane Frances (day +27), Hurricane Ivan (day +20), and Hurricane Jeanne (day +13).

(24) In this part of the analysis, CAR is in decimal notation, where a 100 percent CAR would be equal to 1.

(25) Relative capacity is measured in percentage terms, comparing the prior quarter's PHS to the historical average.

(26) The positive and significant coefficients on the EPS indicator in columns (1) and (2) are likely the result of one event. In 2002, analysts expected Aon to announce Q2 earnings per share of $0.50. Instead, Aon announced earnings per share of $0.13, which generated a CAR of -32.4 percent for the firm. This announcement coincided with major flooding in Europe (the #38 largest insured loss). The other brokers earned positive CAARs of 0.14 percent for that event in the (0,+1) day window.

Caption: Figure 1 Quarterly Relative Capacity Over Time

Caption: Figure 2 Unique Market Response to 9/11 Terrorist Attacks (WTC)

Caption: Figure 3 WTC Event Following Tropical Storm Allison

Caption: Figure 4 Model Residuals Over Time
Table 1
Top 10 Largest Catastrophes by Insured Loss

                                    Insured Loss   Shock
Rank   Event             Date       ($B, 2011)     (% of PHS)

1      H. Katrina        8/29/05    74.7           15.65
2      Tohoku EQ         3/11/11    35.0           6.20
3      H. Andrew         8/24/92    25.6           9.90
4      9/11 Attacks      9/17/01    23.8           6.66
5      Northridge EQ     1/17/94    21.2           7.90
6      H. Ike            9/15/08    21.1           4.23
7      H. Ivan           9/16/04    15.4           3.49
8      H. Wilma          10/24/05   14.5           2.94
9      Thailand Floods   7/27/11    12.0           2.23
10     New Zealand EQ    2/22/11    12.0           2.13

Source: Swiss Re Sigma, 2011 and 2010.

Table 2
Summary Statistics of Insured Loss, by Catastrophe Type

Cat Type              Mean    Median   Min     Max     SD      N

Hurricane             12.77   6.13     2.61    74.69   17.34   17
Winter storm          5.29    5.49     2.57    8.04    2.30    7
Earthquake            14.22   10.12    3.65    35.00   11.96   6
Storms                6.10    6.59     3.92    7.30    1.54    4
Floods                5.86    2.89     2.70    12.00   5.32    2
Typhoon               7.39    7.39     5.45    9.32    2.74    2
Terrorist             23.85   --       --      --      --      1
Tropical storm        4.58    --       --      --      --      1
Fires                 2.81    --       --      --      --      1
Hail                  2.80    --       --      --      --      1
Total                 10.01   6.13     2.57    74.69   12.41   43
Top 20 catastrophes   17.67   12.00    6.61    74.69   16.56   20
Top 10 catastrophes   26.66   21.14    12.00   74.69   19.51   10

Note: Values in billions of 2011 U.S. dollars.

Table 3
Commercial P&C Brokers Traded on U.S. Exchanges, 1987-2011

Firm                    Ticker   Start Date   End Date     Currently

Acordia                 ACO      10/21/1992   7/9/1997     Wells Fargo
Alexander & Alexander   AAL      12/14/1972   2/21/1997    Aon
Aon Corp.               AON      4/24/1987    12/31/2011   Same
Brown & Brown           BRO      4/29/1999    12/31/2011   Same
Arthur J. Gallagher     AJG      6/20/1984    12/31/2011   Same
Hilb, Rogal & Hobbs     HRH      7/15/1987    10/1/2008    Willis
Hub International       HBG      6/18/2002    6/13/2007    Apax
Marsh & McLennan        MMC      2/16/1968    12/31/2011   Same
USI Holdings            USIH     10/22/2002   5/4/2007     Goldman
Willis Group Holdings   WSH      6/12/2001    12/31/2011   Same

Table 4
Summary Statistics for Explanatory Variables of Interest

Variable             Mean    Median   Min     Max     SD      N

Insured loss ($B)    10.43   6.13     2.57    74.69   13.32   264
Log (insured loss)   1.94    1.81     0.95    4.31    0.81    264
Shock (% of PHS)     0.03    0.01     0.00    0.16    0.03    264
Log (shock X 100)    0.56    0.24     -0.71   2.75    0.83    264
Relative capacity    1.03    1.05     0.89    1.11    0.06    259

Table 5
Cumulative Average Abnormal Returns (CAARs), Including Overlap and
WTC, by 2011 Rank

            (a)           (b)         (c)
            All Events    Top 20      Top 10
Window      CAAR (%)      CAAR (%)    CAAR (%)

(-11, -1)   0.17          0.60        0.26
            (139:125)     (70:55)     (34:29)
(0,0)       0.34 ***      0.71 ***    1.65 ***
            (145:119)     (78:47)     (51:12)
(0,+1)      0.12          0.82 ***    2.02 ***
            (131:133)     (73:52)     (49:14)
(0,+5)      0.20          1.02 ***    2.75 ***
            (124:140)     (67:58)     (44:19)
(0,+10)     0.67 **       1 99 ***    3.91 ***
            (137:127)     (77:48)     (46:17)
(0,+30)     0.24          3.25 ***    4.38 ***
            (134:130)     (78:47)     (40:23)
(0,+90)     -1.84 **      2 17 **     4.80 **
            (127:137)     (72:53)     (41:22)
Events      43            20          10
Obs.        264           125         63

Note: The symbols *, **, ***, and *** denote statistical significance
at the 0.10, 0.05, and 0.01 levels, respectively. Significance was
tested using Patell's standardized abnormal return z-test. Figures in
parentheses are the number of securities with (positive:negative) CARs
within that event window.

Table 6
Cumulative Average Abnormal Returns (CAARs), Dropping ARs During
Subsequent Events and WTC, by 2011 Rank

            (a)           (b)         (c)
            All Events    Top 20      Top 10
Window      CAAR (%)      CAAR (%)    CAAR (%)

(-11, -1)   0.26          0.90 **     1.36 **
            (139:120)     (73:52)     (42:24)
(0,0)       0.17 ***      0.38 ***    0.79 ***
            (140:119)     (75:50)     (48:18)
(0,+1)      -0.03         0.51 ***    1.24 ***
            (126:133)     (71:54)     (46:20)
(0,+5)      0.00          0.53 **     1.50 ***
            (119:135)     (65:60)     (40:26)
(0,+10)     0.16          1.29 ***    2.74 ***
            (114:118)     (68:49)     (39:19)
(0,+30)     -0.08         4.14 ***    5.95 ***
            (83:88)       (41:20)     (20:7)
(0,+90)     -2.59 **      6.85 ***     8.28 ***
            (68:77)       (37:13)     (21:6)

Note: The symbols *, **, and *** denote statistical significance at
the 0.10, 0.05, and 0.01 levels, respectively. Significance was tested
using Patell's standardized abnormal return Z-test. Figures in
parentheses are the number of securities with (positive:negative) CARs
within that event window. The "Top 20" and "Top 10" are the top
remaining events after dropping the WTC event (i.e., Top 20 is #1-21
excluding #4, Top 10 is #1-11 excluding #4). Because we drop ARs (and
thus do not calculate CARs) beginning on the day a subsequent event
occurs, longer windows contain fewer CAR observations. The number of
broker-event observations included in each CAAR estimation can be
calculated by adding the values inside the parentheses.

Table 7
OLS Regression Analysis of Factors Influencing CAR (0,+ 1)

                         All Events             Top 20 Events

Dependent Var: CAR       (1)         (2)        (3)         (4)
(0, +1)

Insured loss ($B)        0.0005 ***             0.0004 ***
                         (0.0001)               (0.00006)
Log (insured loss)                   0.008 ***               0.012 ***
                                     (0.002)                (0.002)
Relative capacity        0.013       0.005      -0.154 ***  -0.127 **
                         (0.039)     (0.039)    (0.048)     (0.055)
CAR(-2, -1)              -0.123      -0.134     -0.262 *    -0.250 *
                         (0.082)     (0.085)    (0.148)     (0.147)
Overlap ind              0.007 **    0.004      0.010 **    0.007 *
                         (0.004)     (0.004)    (0.004)     (0.004)
US ind                   0.004       0.004      0.008 *      0.005
                         (0.004)     (0.004)    (0.004)     (0.005)
Earthquake ind           0.007       0.005      0.001       -0.003
                         (0.007)     (0.007)    (0.013)     (0.014)
News Ind (--5, +5)        0.001       0.0003     -0.007      -0.007
                         (0.004)     (0.004)    (0.008)     (0.008)
EPS results (--10, +10)   0.786 ***   0.782 ***  0.250       0.253
                         (0.1)       (0.102)    (0.191)     (0.193)
WTC ind                  0.075 ***   0.069 ***  0.056 ***   0.055 ***
                         (0.007)     (0.007)    (0.008)     (0.009)
Broker FE                Yes         Yes        Yes         Yes
Quarter FE               Yes         Yes        Yes         Yes
Obs.                     259         259        125         125
[R.sup.2]                0.587       0.584      0.524       0.522
Adj. [R.sup.2]           0.550       0.547      0.427       0.425

Note: Standard errors clustered by event are in parentheses. Stars *,
significance at the 0.10, 0.05, and 0.01 levels, respectively. **, and
*** denote statistical

Table 8
OLS Regression Analysis of Factors Influencing CAR (0,+ 1)

                         All Events            Top 20 Events
Dependent Var: CAR       (1)        (2)        (3)        (4)
(0, +1)

Shock                    0.208 ***             0.178 ***
                         (0.035)               (0.047)
Log (shock)                         0.007 ***              0.007
                                    (0.002)               (0.005)
Relative capacity        0.012      0.004      -0.137 **  -0.149 **
                         (0.04)     (0.04)     (0.064)    (0.065)
CAR(-2, -1)              -0.123     -0.129     -0.253 *   -0.253 *
                         (0.083)    (0.085)    (0.147)    (0.148)
Overlap ind              0.008 **   0.006      0.012 ***   0.009 *
                         (0.004)    (0.004)    (0.005)    (0.005)
US ind                   0.004      0.004      0.007      0.008
                         (0.004)    (0.005)    (0.005)    (0.006)
Earthquake ind           0.008      0.008      0.001      0.001
                         (0.007)    (0.007)    (0.014)    (0.015)
News ind (--5, +5)        0.001      0.001      -0.007     -0.007
                         (0.004)    (0.004)    (0.008)    (0.008)
EPS results (--10, +10)   0.789 ***  0.790 ***  0.275      0.282
                         (0.098)    (0.098)    (0.205)    (0.21)
WTC ind                  0.073 ***  0.070 ***  0.059 ***   0.055 ***
                         (0.006)    (0.007)    (0.011)    (0.009)
Broker FE                Yes        Yes        Yes        Yes
Quarter FE               Yes        Yes        Yes        Yes
Obs.                     259        259        125        125
[R.sup.2]                0.585      0.576      0.513      0.495
Adj. [R.sup.2]           0.548      0.538      0.413      0.392

Note: Standard errors clustered by event are in parentheses. The
symbols *, **, and *** denote statistical significance at the 0.10,
0.05, and 0.01 levels, respectively.
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Author:Ragin, Marc A.; Halek, Martin
Publication:Journal of Risk and Insurance
Article Type:Report
Geographic Code:1USA
Date:Dec 1, 2016
Words:11926
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