Market Expectations Following Catastrophes:
An Examination of Insurance Broker Returns
Marc A. Ragin
Temple University
Martin Halek*
University of Wisconsin-Madison
Abstract
We investigate the effect catastrophes are expected to have on equilibrium price and quantity in the
insurance market. We conduct an event study on insurance brokers, who earn commissions on premium
revenue but do not pay losses. We find that broker stocks earn positive abnormal returns following the
43 largest recent catastrophes. These returns are positively related to loss size and negatively related
to existing insurer capital, indicating that catastrophe shocks are expected to increase net industry
revenue. This response is consistent with economic theories of a negative relationship between capital
and insurance prices and price-inelastic demand for commercial insurance.
Keywords: catastrophe, insurance, insurance demand, insurance intermediary, event study
September 2014
_______________________________________
*Contact author: [email protected]
1
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) developed 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 noted 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
paper estimating corporate insurance demand elasticities that we are aware of is a study by Michel-Kerjan
et al. (2014). The researchers used proprietary purchasing data to estimate the price elasticity of demand
for corporate property and terrorism insurance and found that firms were relatively price inelastic for both
types of coverage.2
The objective of our paper 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
1 Cummins and Danzon (1997) developed a similar model, which specifically allowed 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.
1
disaster. Prior catastrophe event studies focusing on insurers have found that insurers generally experience
negative abnormal returns as a result of their expected loss payments (Lamb, 1995; Cummins and Lewis,
2003; Doherty et al., 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 subsequent to 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 twenty events with the largest insured losses, broker stocks earned abnormal
returns of 0.38% on the day of the catastrophe and another 0.13% the day after. In the 10-day and 30-day
windows following the top twenty catastrophes, broker stocks generated 1.29% and 4.14% 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 twenty catastrophes, a 1% 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
2
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.
The remaining paper is organized as follows. In the next section we discuss related research on commercial
insurance demand, capital shocks, event studies focused on the insurance industry, and brokers. Section 3
explains our methodology, while Section 4 describes our data. Our results are presented in Section 5, and
Section 6 concludes.
2
Related Research
2.1
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 et al.
(2004) found that individuals have much more elastic demand for catastrophe insurance (P = −2.064 in
NY and −1.915 in FL) than for non-catastrophe (e.g. fire) insurance (P = −0.331 in NY and −0.404 in
FL).3 As another example, Browne and Hoyt (2000) studied the demand for flood insurance, including both
individuals and businesses in their dataset. 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 (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, risk-averse 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
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% price increase, individuals reduce their quantity demanded by 20%, 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 (
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 “Insurance in force” quantity variable is more relevant to
our research.
3
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 et al., 2003; Zou and
Adams, 2006; Aunon-Nerin and Ehling, 2008, among others). In this paper, 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 paper has
estimated the elasticity of demand for commercial insurance. Michel-Kerjan et al. (2014) used a proprietary
dataset to compare price elasticities for catastrophe and non-catastrophe commercial insurance. Contrary
to Grace et al.’s comparison for personal lines insurance, the authors found that the price elasticities were
similar between catastrophe and non-catastrophe coverage—following a 10% premium increase, corporate
purchasers are expected to decrease their quantity of coverage demanded by 2.93% (for property insurance)
and 2.42% (for terrorism insurance).
Our paper 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
sub-section 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.
2.2
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) developed and formalized 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 theorized that insurers whose financial capital is reduced will
increase premiums and reduce coverage rather than raise costly external capital. Winter’s initial theory of
4
“capacity constraint” was 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 modeled the effect of capital shocks on equilibrium price, with scenarios
for both inelastic and elastic demand. First specifying inelastic demand, they showed that the partial
derivative of equilibrium price with respect to capital is negative (PK < 0) . They then modeled 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 N q[P (K), K] = Q[P (K), K]. Using their models of insurer profits, differentiating
price with respect to capital gives:
PK =
P (K − ηK )
K(P + ηP )
The sign of PK depends on the relative elasticities of demand (K =
(1)
QK K
Q )
and supply (ηK =
qK K
q )
with respect to capital. The authors concluded that the lack of substitutes for insurance and insurance
regulation make it likely that K < ηK , and thus PK < 0. In addition, they noted that increased elasticity
of demand with respect to price (P =
−QP P
Q
) would temper any price increases resulting from the capital
shock. Cummins and Danzon (1997) centered a similar model around insurer insolvency risk, determining
that prices could potentially decrease following capital shocks if insurance buyers re-entered the market to
switch to different insurers with lower default risk.6 They empirically tested this model, determining that
the liability loss shocks of the 1980s did not cause insurance prices to increase substantially. Instead, the
authors attributed 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) found 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) found 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),
5 The primary difference between these theories is that Winter assumes that regulation reduces the probability of bankruptcy
to zero, while Gron 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 Their model also allowed for price increases consistent with Cagle and Harrington. They allowed 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.
5
Higgins and Thistle (2000), Choi et al. (2002), Weiss and Chung (2004), Fenn and Vencappa (2005), and
Derien (2008).
2.3
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) found 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) investigated both Hurricane Andrew and
a subsequent freeze of American International Group’s premium rates. The authors found negative stock
price effects for both events and provided evidence that expectations of higher prices may have offset the
negative effects of Hurricane Andrew until the premium freeze. Cagle (1996) identified 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 et al. (2008) found
evidence of increased short selling of insurer stocks beginning two 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) tested the effect of the 2001 World Trade Center
(WTC) terrorist attacks on insurance company stocks and found that insurer stocks were negatively affected
by the attacks, though financially strong insurers recovered their stock losses within a few weeks. The authors
found similar negative results for insurers following Hurricane Andrew and the Northridge Earthquake in
replicating Lamb’s (1995) event study. Doherty et al. (2003) also examined 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 calculated generally were consistent with the negative abnormal returns
calculated by Cummins and Lewis. The authors noted 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
7 There are two studies that found positive returns for insurers following a disaster. Shelor et al. (1992) and Aiuppa et al.
(1993) both studied the effect of the 1989 Loma Prieta earthquake in California, finding that insurance company stock prices
experienced positive returns following the event.
6
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.
2.4
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 commission rate was 10.3% and the industry paid $45.55
billion in direct commissions on $447.44 billion in net written premiums (Best’s Aggregates and Averages,
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) conducted a series of interviews with brokers and found 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
8 The average commission was 8.6% for earthquake insurance, 13.4% for fire, and 16.4% for commercial non-liability 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 Section 5.
7
insurance accounted for 52.0% of broker revenue on average. The fourth-largest broker, A.J. Gallagher,
reported that 52% of 2012 revenues came from direct brokerage commissions, 16% came from brokerage
fees, 22% came from risk management and consulting fees, and 5% 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% of total premiums billed in 2004 (Cummins and
Doherty, 2006). For commercial lines, contingent commissions comprise on average 5 to 6% 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.
3
Methodology
3.1
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, which 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
11 For robustness, we conduct the same analysis using various alternative estimation models (market model, market adjusted
returns) without significant differences in results.
8
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) examined the variance of daily
abnormal returns and found that errors followed a generalized autoregressive conditionally heteroskedastic
(GARCH) framework. Cheng et al. (2009) studied the effect of the 2004 Spitzer bid-rigging lawsuits on the
stock returns for publicly-traded brokers in the U.S. and found 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:
Rit = αi + βi Rmt + si SM Bt + hi HM Lt + it
(2)
where Rit is the actual return of the stock of firm i on day t; Rmt is the rate of return of a market index m
(we chose the CRSP equally-weighted index) on day t; SM Bt is the return on a portfolio of small marketcapitalization stocks minus the average return on three portfolios of large market-capitalization stocks; HM Lt
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; it is a random error variable with a conditional
expectation of zero given Ψt−1 (the information available at time t − 1) and conditional variance:
σ 2 (it |Ψt−1 ) = hit = ωi + δi hit−1 + γi 2it−1
(3)
where ωi > 0, γi > 0, δi ≥ 0 and γi + δi < 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:
ARit = Rit − (α̂i + β̂i Rmt + sˆi SM Bt + ĥi HM Lt )
(4)
where α̂i , β̂i , sˆi , and ĥi are the estimates of the coefficients in Equation (2) using an 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
12 One consideration for our data is that earlier catastrophe events occur during an event’s estimation window. This is not
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
9
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 T1 and ending at
day T2 to determine the cumulative effect of the event for each broker as shown in Equation (5).
CARik =
T2
X
ARikt
(5)
t=T1
For each window specified, we have a CARik 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 X
CARik
N
where N = i × k
(6)
i,k
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 post-event, 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:
SARikt =
ARikt
sAikt
(7)
where sAikt is the standard deviation of the abnormal returns, adjusted for any missing trading days. The
Z-score for the N broker-events measured from T1 to T2 is then:
N
1 X i
ZT1 ,T2 = √
Zk,T1 ,T2
N i,k
(8)
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% and the CAAR over all brokers increased from
-0.42% on day +66 to 3.89% on day +68.
10
where for each broker i and event k:
T2
X
1
i
q
SARikt
Zk,T
=
,T
1
2
QiT1 ,T2 t=T1
(9)
and:
QiT1 ,T2 = (T2 − T1 + 1)
Mi − 2
Mi − 4
(10)
with Mi being the number of nonmissing trading days in the estimation window. Assuming cross-sectional
i
independence of Zk,T
, ZT1 ,T2 follows a standard normal distribution.
1 ,T2
3.2
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 (IN SLOSS) 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 IN SLOSS and SHOCK.
SHOCKk =
IN SLOSSk
P HSq=−1
(11)
We use policyholder surplus (PHS) as our measure of capacity available in the market. PHS is the
14 We
attempted to collect estimated losses at the time of the event, but these were not reported consistently.
11
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 (P HSq=−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:
RELCAPk =
1
4
P HSq=−1
P−2
q=−5 P HSq
(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
(P RIORCAR). 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 (OV ERLAP ). We also include
indicator variables for catastrophe location (U S) and type (earthquake, EQ, and the World Trade Center
event, W T C). At the broker level, we include an indicator variable for company news surrounding the event
(N EW S).16 We also control for earnings announcements around the event (EARN IN GS).17 To account
for heterogeneity between brokers that is not accounted for in the N EW S and EARN IN GS 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 ordinary least squares (OLS) cross-sectional regressions
with standard errors clustered at the event level to control for intraclass correlation.
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 search 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.
12
Formally, our regression model is:
CARi,k = α + αi + qk + β1 IN SLOSSk + β2 RELCAPk + β3 P RIORCARk
+ β4 OV ERLAPk + β5 U Sk + β6 EART HQU AKEk
+ β7 N EW Si,k + β8 EARN IN GSi,k + β9 W T Ck + i,k
(13)
with i indicating the broker and k indicating the event. A positive coefficient on IN SLOSS 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,
IN SLOSS is replaced by LOG(IN SLOSS), SHOCK, or LOG(SHOCK).
4
Data
4.1
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 ten 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 Tōhoku Earthquake ($75 billion versus $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% 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% of PHS, while the median is 1.24%. Narrowing the sample of
events to the top 20 (top 10) largest, the median loss size is $12.00 ($21.14) billion. The mean loss sizes are
substantially larger due to the influence of Hurricane Katrina.
All but one of the events—the 9/11 terrorist attacks (“WTC”)—were natural disasters. The most frequent
13
Table 1: Top 10 largest catastrophes by insured loss
Rank
Event
Date
1
2
3
4
5
6
7
8
9
10
H. Katrina
Tōhoku EQ
H. Andrew
9/11 Attacks
Northridge EQ
H. Ike
H. Ivan
H. Wilma
Thailand Floods
New Zealand EQ
8/29/05
3/11/11
8/24/92
9/17/01
1/17/94
9/15/08
9/16/04
10/24/05
7/27/11
2/22/11
Insured Loss
($B, 2011)
Shock
(% of PHS)
74.7
35.0
25.6
23.8
21.2
21.1
15.4
14.5
12.0
12.0
15.65
6.20
9.90
6.66
7.90
4.23
3.49
2.94
2.23
2.13
Source: Swiss Re Sigma, 2011 and 2010
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 U.S.
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 Tōhoku Earthquake in 2011, which struck at 12:45am
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% in the five trading days following, and 23.34% 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 runup 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
18 To test if investors anticipate weather events we conducted a t-test for different average abnormal returns (AARs) between
weather events and non-weather events. We found that weather event AARs are 0.7% higher on day -7 and 0.2% higher on day
-5 (significant at the 1% and 10% levels respectively). No other prior-event days between -10 and 0 had significantly different
abnormal returns between weather and non-weather 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.
14
Table 2: Summary statistics of insured loss, by catastrophe type
Cat Type
Mean
Median
Min
Max
SD
N
Hurricane
Winter Storm
Earthquake
Storms
Floods
Typhoon
Terrorist
Tropical Storm
Fires
Hail
12.77
5.29
14.22
6.10
5.86
7.39
23.85
4.58
2.81
2.80
6.13
5.49
10.12
6.59
2.89
7.39
-
2.61
2.57
3.65
3.92
2.70
5.45
-
74.69
8.04
35.00
7.30
12.00
9.32
-
17.34
2.30
11.96
1.54
5.32
2.74
-
17
7
6
4
2
2
1
1
1
1
Total
10.01
6.13
2.57
74.69
12.41
43
Top 20 Catastrophes
Top 10 Catastrophes
17.67
26.66
12.00
21.14
6.61
12.00
74.69
74.69
16.56
19.51
20
10
Values in billions of 2011 U.S. dollars.
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 3/1/2010, Winter Storm Lothar
(#17) with Winter Storm Martin (#36) on 12/27/1999, and Hurricane Frances with Typhoon Songda (#30)
on 9/7/2004. This provides a final dataset of 43 events for our event study.
4.2
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
15
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 dataset 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.
Table 3: Commercial P&C brokers traded on U.S. exchanges, 1987-2011
Firm
Ticker
Start Date
End Date
Acordia
Alexander & Alexander
Aon Corp.
Brown & Brown
Arthur J. Gallagher
Hilb, Rogal & Hobbs
Hub International
Marsh & McLennan
USI Holdings
Willis Group Holdings
ACO
AAL
AON
BRO
AJG
HRH
HBG
MMC
USIH
WSH
10/21/1992
12/14/1972
4/24/1987
4/29/1999
6/20/1984
7/15/1987
6/18/2002
2/16/1968
10/22/2002
6/12/2001
7/9/1997
2/21/1997
12/31/2011
12/31/2011
12/31/2011
10/1/2008
6/13/2007
12/31/2011
5/4/2007
12/31/2011
Currently
Wells Fargo
Aon
Same
Same
Same
Willis
Apax
Same
Goldman
Same
We use stock return data from The Center for Research in Security Prices (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.
4.3
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
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.
16
loss amount is highly skewed. Taking the natural log tempers this skewness. The shock variable is expressed
as a percent of policyholder surplus, ranging from 0.49% (which appears as 0 in the table due to rounding) to
15.65%. We take the log of SHOCK × 100 to make most of the values positive, though the eleven smallest
still have negative values as they were less than 1% 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.
Table 4: Summary statistics for explanatory variables of interest
Variable
Insured Loss ($B)
Log(Insured Loss)
Shock (% of PHS)
Log(Shock×100)
Relative Capacity
Mean
Median
Min
Max
SD
N
10.43
1.94
0.03
0.56
1.03
6.13
1.81
0.01
0.24
1.05
2.57
0.95
0.00
-0.71
0.89
74.69
4.31
0.16
2.75
1.11
13.32
0.81
0.03
0.83
0.06
264
264
264
264
259
Data was not available to calculate relative capacity for the earliest event (“Storms and Floods in Europe,”
the #21 largest event, on 10/15/1987), 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.
.8
.9
Relative Capacity
1
1.1
1.2
Figure 1: Quarterly Relative Capacity over Time
1990
1995
2000
Year
17
2005
2010
More than half of the catastrophes (26) occurred in the United States. Many happened soon after an
earlier event—seventeen occurred within 90 days of an earlier event. There were twelve instances where the
broker announced earnings within ten 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% 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 five days of an event.
5
Results
5.1
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 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%, 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
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 non-catastrophe event—the large dip in CAARs around day +20
was the market reaction to Eliot Spitzer’s bid-rigging lawsuit against Marsh, which had contagion effects on other brokers as
documented in Cheng et al. (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).
18
Table 5: Cumulative average abnormal returns (CAAR), including overlap
and WTC, by 2011 rank
(a)
All Events
CAAR (%)
(b)
Top 20
CAAR (%)
(c)
Top 10
CAAR (%)
(-11,-1)
0.17
(139:125)
0.60
(70:55)
0.26
(34:29)
(0,0)
0.34***
(145:119)
0.71***
(78:47)
1.65***
(51:12)
(0,+1)
0.12
(131:133)
0.82***
(73:52)
2.02***
(49:14)
(0,+5)
0.20
(124:140)
1.02***
(67:58)
2.75***
(44:19)
(0,+10)
0.67**
(137:127)
1.99***
(77:48)
3.91***
(46:17)
(0,+30)
0.24
(134:130)
3.25***
(78:47)
4.38***
(40:23)
(0,+90)
-1.84**
(127:137)
2.17**
(72:53)
4.80**
(41:22)
Events
Obs.
43
264
20
125
10
63
Window
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.
19
Cum Avg Abnormal Return (CAAR)
−.05 0
.05
.1
.15
.2
.25
Figure 2: Unique Market Response to 9/11 Terrorist Attacks (“WTC”)
0
10
20
30
40
50
60
70
80
90
Day
WTC only
Mean CAAR, All Events Excl. WTC
Mean CAAR, Top 20 Events Excl. WTC
Mean CAAR, Top 10 Events Excl. WTC
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% 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.
20
Table 6: Cumulative average abnormal returns (CAAR), dropping ARs during
subsequent events and WTC, by 2011 rank
(a)
All Events
CAAR (%)
(b)
Top 20
CAAR (%)
(c)
Top 10
CAAR (%)
(-11,-1)
0.26
(139:120)
0.90**
(73:52)
1.36**
(42:24)
(0,0)
0.17***
(140:119)
0.38***
(75:50)
0.79***
(48:18)
(0,+1)
-0.03
(126:133)
0.51***
(71:54)
1.24***
(46:20)
(0,+5)
0.00
(119:135)
0.53**
(65:60)
1.50***
(40:26)
(0,+10)
0.16
(114:118)
1.29***
(68:49)
2.74***
(39:19)
(0,+30)
-0.08
(83:88)
4.14***
(41:20)
5.95***
(20:7)
(0,+90)
-2.59**
(68:77)
6.85***
(37:13)
8.28***
(21:6)
Window
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 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.
21
Cum Avg Abnormal Return (CAAR)
−.1
−.05
0
.05
.1
.15
Figure 3: WTC Event Following Tropical Storm Allison
−.15
9/17/2001
0
10
20
30
40
50
60
70
80
90
Day
5.2
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, with (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 two-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% 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.
24 In
this part of the analysis, CAR is in decimal notation, where a 100% CAR would be equal to 1.
22
Table 7: OLS Regression Analysis of Factors Influencing CAR (0,+1)
All Events
Dependent var: CAR (0,+1)
Insured Loss ($B)
(1)
Top 20 Events
(2)
0.0005
(3)
∗∗∗
(4)
∗∗∗
0.0004
(0.0001)
(0.00006)
0.008∗∗∗
Log(Insured Loss)
0.012∗∗∗
(0.002)
Relative Capacity
CAR(-2,-1)
Overlap Ind
0.005
-0.154∗∗∗
-0.127∗∗
(0.039)
(0.039)
(0.048)
(0.055)
Earthquake Ind
News Ind (-5,+5)
EPS Results (-10,+10)
WTC Ind
Broker FE
Quarter FE
Obs.
R2
Adj. R2
∗
-0.123
-0.134
-0.262
(0.082)
(0.085)
(0.148)
0.007
∗∗
0.004
(0.004)
US Ind
(0.002)
0.013
0.010
∗∗
-0.250∗
(0.147)
0.007∗
(0.004)
(0.004)
0.004
0.004
∗
(0.004)
0.008
0.005
(0.004)
(0.004)
(0.004)
(0.005)
0.007
0.005
0.001
-0.003
(0.007)
(0.007)
(0.013)
(0.014)
0.001
0.0003
-0.007
-0.007
(0.004)
(0.004)
(0.008)
(0.008)
∗∗∗
0.786
0.782
∗∗∗
0.250
0.253
(0.1)
(0.102)
(0.191)
(0.193)
0.075∗∗∗
0.069∗∗∗
0.056∗∗∗
0.055∗∗∗
(0.007)
(0.007)
(0.008)
(0.009)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
259
0.587
0.550
259
0.584
0.547
125
0.524
0.427
125
0.522
0.425
Note: Standard errors clustered by event in parentheses. Stars *, **, and *** indicate significance at
the 0.10, 0.05, and 0.01 levels, respectively.
23
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% lower than the past year’s average is associated
with post-catastrophe 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 post-event 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 R2 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 policyholder surplus. 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 one percentage point increase in the relative shock is
associated with a 0.18 percentage point increase in broker CAR in the two 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 Section 2.4, the proportion
of broker revenue attributed to consulting and other fees has risen in recent years. Assuming this is true for
25 Relative
capacity is measured in percentage terms, comparing the prior quarter’s policyholder surplus to the historical
average.
26 The positive and significant coefficient 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% 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% for that event in the (0,+1) day window.
24
Table 8: OLS Regression Analysis of Factors Influencing CAR (0,+1)
All Events
Dependent var: CAR (0,+1)
Shock
(1)
0.208
Top 20 Events
(2)
(3)
∗∗∗
0.178
(0.035)
(0.047)
Log(Shock)
Relative Capacity
CAR(-2,-1)
Overlap Ind
Earthquake Ind
News Ind (-5,+5)
EPS Results (-10,+10)
Broker FE
Quarter FE
Obs.
R2
Adj. R2
0.007
(0.002)
(0.005)
0.004
-0.137∗∗
-0.149∗∗
(0.04)
(0.04)
(0.064)
(0.065)
∗
-0.123
-0.129
-0.253
(0.083)
(0.085)
(0.147)
0.008
∗∗
0.006
(0.004)
∗∗∗
0.012
(0.005)
-0.253∗
(0.148)
0.009∗
(0.005)
0.004
0.004
0.007
0.008
(0.004)
(0.005)
(0.005)
(0.006)
0.008
0.008
0.001
0.001
(0.007)
(0.007)
(0.014)
(0.015)
0.001
0.001
-0.007
-0.007
(0.004)
(0.004)
(0.008)
(0.008)
0.275
0.282
(0.205)
(0.21)
∗∗∗
0.789
0.790
(0.098)
WTC Ind
0.007∗∗∗
0.012
(0.004)
US Ind
(4)
∗∗∗
0.073
∗∗∗
(0.098)
∗∗∗
0.070
∗∗∗
0.059
∗∗∗
0.055∗∗∗
(0.006)
(0.007)
(0.011)
(0.009)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
259
0.585
0.548
259
0.576
0.538
125
0.513
0.413
125
0.495
0.392
Note: Standard errors clustered by event in parentheses. Stars *, **, and *** indicate significance at
the 0.10, 0.05, and 0.01 levels, respectively.
25
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.
−.1
−.05
Model residuals
0
.05
.1
Figure 4: Model Residuals over Time
1990
1995
2000
Year
95% CI
6
2005
Fitted values
2010
Residuals
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
26
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 due 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 cumulative abnormal returns
(CARs) following catastrophes. Using our most restrictive event study specification, we find that brokers
earn a 0.17% 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% average abnormal returns for the twenty
largest events and 0.79% returns for the ten 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.
27
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