Loss Reserve Error Volatility and Internal Capital Markets
James M. Carson
Daniel P. Amos Distinguished Professor of Insurance
Terry College of Business
The University of Georgia
Athens, GA 30602
Phone: 706-542-3803
Email: [email protected]
David Eckles
Associate Professor of Risk Management and Insurance
Terry College of Business
The University of Georgia
Athens, GA 30602
Phone: 706-542-3578
Email: [email protected]
In Jung Song (contact author)
Terry College of Business
The University of Georgia
Athens, GA 30602
Phone: 706-583-0465
Email: [email protected]
July 1, 2015
Working Paper
Do not cite or circulate without permission
1
Loss Reserve Error Volatility and Internal Capital Markets
Abstract
The property-liability insurance business is inherently risky and the estimation process of reserves
is imperfect, making variability in loss reserves inevitable. This paper investigates the relation
between loss reserve error volatility and internal capital markets (ICMs). High loss reserve error
volatility suggests inconsistency of error and thus high information risk. We first look at certain
firm characteristics that are associated with high loss reserve error volatility such as group
membership. Then we further inspect the relation between group loss reserve error volatility with
ICMs activities. We find that affiliated insurers have lower individual firm-level loss reserve error
volatility than single unaffiliated insurers. We hypothesize that unaffiliated single insurers have
their own authority to manage reserves whereas affiliated insurers can transfer capital internally
to other insurers in the group via internal capital markets. We show that affiliated firms with more
ICMs tend to have more consistent loss reserve errors which result in low loss reserve error
volatility and correspondingly low information risk.
Keywords: Earnings Management, Information Risk, Loss Reserve Error Volatility, Information
Risk, Accounting Discretion, Insurance
JEL classification: G34, G32; G22
1. Introduction
Loss reserves, the insurer’s estimated liability for unpaid claims, generally are the largest
and most important liability on a property-liability insurer’s balance sheet. Insurance companies
need to estimate the proper amount of reserves to meet future liabilities from losses. However, the
insurance business is inherently risky and the estimation process is imperfect; thus, some
variability in loss reserves is unavoidable.
Estimation of loss reserves is not a formulaic process. Rather it requires quantitative
methods and subjective consideration and managerial judgment. Frequently, an insurer’s loss
reserve errors are used as a measure of managerial discretion (Weiss, 1985; Petroni, 1992; Beaver,
McNichols, and Nelson, 2003; Eckles and Halek, 2010; Grace and Leverty, 2010, 2012). Whether
loss reserves are properly estimated can only be determined over time. Comparing previous loss
2
reserves for certain claims with the actual dollars paid for those claims shows the degree to which
the reserves were correctly set. Each year, insurers reestimate prior years’ loss estimates to reflect
actual payments made and changes in estimates. Estimations must be made in advance of ultimate
settlement and thus the accuracy of an insurer at setting loss reserve levels is important.
The accuracy of an insurer can be calculated by loss reserve error volatility. This volatility
can be considered information risk according to Eckles, Halek and Zhang (2014).1 Information
risk refers to the potential for inaccurate or incomplete firm information. High loss reserve error
volatility suggests inconsistency of error and uncertainty of firm information and thus relatively
high information risk. On the other hand, low loss reserve error volatility suggests consistency of
error and more certainty of firm information therefore relatively low information risk.
Accounting measures such as loss reserves are widely used for a firm’s information
dissemination to managers, shareholders, regulators and rating agencies. These parties all have an
interest in knowing the magnitude and variability of these potential deviations in loss reserves
over the time period. Managers often alter loss reserve estimates for many reasons including
income smoothing, tax avoidance, regulatory scrutiny avoidance, and executive compensation
incentives. Shareholders and regulators may care about loss reserves in terms of financial
weakness and solvency. Insurers may make sure to keep their values in line with expectations
because variability can be seen as an indicator of a firm’s risk. Also, rating agencies consider
information risk as uncertainty of the firm when they rate the firm (Carson, Eastman and Eckles,
2015).
The insurance industry is a perfect laboratory to study the loss reserves not only because
it provides a homogeneous sample of firms but also insurer-specific accruals, loss reserves, can
be used to measure the actual error in accruals unlike other measures used in many accounting and
1
Eckles, Halek and Zhang (2014) utilize standard deviation of insurer loss reserve error as well as conventional
accruals measures to measure accruals quality, also known as information risk.
3
finance studies examining non-insurance firms. In addition to the unique ability to witness the loss
reserve errors, the insurance industry is also comprised of two distinct structures; group affiliated
and single unaffiliated firms.2 The group structure allows for a potentially active internal capital
market (ICM) with corporate headquarters allocating capital among the group members in the
form of reinsurance ceded to affiliates (William, 1975; Stein, 1997; Houston, James, and Marcus,
1997). In this paper, we investigate insurers’ loss reserve error volatility both at an individual
single unaffiliated and aggregate group affiliated level.
This paper will extend the existing literature in three ways. First, we look at the
characteristics of insurers as they relate to loss reserve error volatility, in particular whether or not
the insurer is affiliated with an insurer group. Second, we compare the loss reserve error volatility
both at the individual firm level and aggregate group level. Here we also derive a new unique
measure of group level loss reserve error and its volatility. Third, we further inspect the relation
between group loss reserve error volatility and internal capital market transactions. Prior literature
provides support for the existence of ICMs within group insurers but has not incorporated loss
reserve error nor its volatility. We find evidence that affiliated insurance companies have lower
individual firm-level loss reserve error volatility than single unaffiliated insurers and that internal
capital market activities are associated with lower aggregate group-level loss reserve error
volatility.
The remainder of this paper proceeds as follows. The second section summarizes prior
literature on loss reserve errors and internal capital markets. The third section discusses conceptual
background and hypotheses. The following section presents the model and data followed by the
2
Insurance regulation has focused on the operations and financial strength of insurers on a legal entity basis. Propertyliability insurers have the ability to operate in groups and they are required to prepare statutory filings at the group
level. Additionally, model laws specifically states as insurance holding companies and regulate transactions within
the insurance group. Single unaffiliated firms are defined if no other firms on the National Association of Insurance
Commissioner (NAIC) property-liability database shares the same group code and group affiliated firms are the
opposite.
4
empirical results. The last section concludes.
2. Literature Review
There is a large body of literature devoted to evaluating earnings management via loss reserves
in the property-liability insurance industry. Prior studies in this area have examined loss reserve
practices based exclusively on individual insurance company data. Prior studies have not focused
on the characteristics or conditions of the groups with which affiliated insurers are associated. In
this paper, we investigate insurers’ loss reserve error volatility both at the single unaffiliated, the
single affiliated and aggregate group affiliated levels.
2.1 Loss Reserve Error
Property-liability insurer reserve errors have been discussed extensively in the existing
literature. However insurer reserve error volatility has been largely ignored. Most previous studies
examine earnings management via loss reserve manipulation and have shown that the
manipulation is driven by a number of incentives. First, financial weakness of a firm is examined as
an inducement to manipulate loss reserves. Petroni (1992) shows evidence that financially weak
insurers tend to underestimate loss reserves to improve Insurance Regulatory Information System
(IRIS) ratios.3 Petroni (1992) shows not only that financially weak firms understate their reserve
estimates to avoid regulatory attention but also that managers of insurers close to receiving
regulatory attention understate reserve estimates. Studies also find that financially weak firms
tend to under-reserve to a greater extent than financially strong firms (Petroni, 1992; Petroni and
Beasley, 1996; Penalva, 1998; Gaver and Paterson, 2000 2004).
3
Insurance Regulatory Information System (IRIS) ratio is a typical industry-specific ratios which are designed by
regulators to identify financially weak insurers (Petroni 1992, Harrington and Danzon 1994, Nelson 2000, Beaver,
McNichols, and Nelson 2003, Gaver and Paterson 2004, Grave and Leverty 2012)
5
Building upon Petroni (1992), Gaver and Patterson (2004) also study whether insurers
manage loss reserves to avoid regulatory intervention. Along with Petroni (1992), they assert that
financially strong firms and tend to over-reserve and financially weaker firms tend to underreserve. Moreover, insurers manage loss reserves to reduce the number of IRIS ratio violations.
Regulatory scrutiny is a crucial motivation of insurers to manipulate their reserves.
Earnings management by property-liability insurers via loss reserve manipulation has been
discussed frequently in the context of insurers manipulating their loss reserves to smooth their
income. Weiss (1985) supports the hypothesis that loss reserves are used as a tool in smoothing
underwriting results. Theoretical analysis with respect to income smoothing is also introduced by
Grace (1990). Aiuppa and Trieschmann (1987) empirically incorporate size, organizational
structure, and product mix of the firm. They show evidence that small insurers experience
relatively more reserve error and stock insurers experience relatively more accurate reserves.
Insurers also have an incentive to smooth earnings in order to minimize their associated
tax liability. By overestimating losses relative to current premiums, the insurer reduces its current
tax liability and can also postpone the tax payments until future periods. Grace (1990)
hypothesizes that overestimating reserves gives insurers an opportunity to shelter their earnings
and finds evidence that insurers over-reserve as taxable income increases. However, Petroni (1992)
finds no evidence of earnings management to minimize taxes and Grace and Leverty (2012) shows
mixed results.
Also, Beaver, McNichols, and Nelson (2003) examine the effect of reserve bias on firm’s
earnings and find that less profitable firms understate reserves relative to more profitable firms.
Specifically for public and mutual firms, small firms with positive earnings understate loss
reserves relative to insurers with small negative earnings. They conclude that insurers manage
reserves across the distribution of earnings.
When it comes to managerial discretion, executive compensation can be another reason why
6
insurers manipulate loss reserve. Eckles and Halek (2010) find that larger proportions of
managerial compensation from bonus payments and restricted stock have a positive relationship
with earnings management. Along with this, Eckles, Halek and Zhang (2011) combine the effect
of managerial compensation with corporate governance board structure on firm’s earnings
management with a group level data.
Grace and Leverty (2012) consider the income smoothing, financial weakness, tax, and
rate regulation motives together. They conclude that a firm’s incentive to over-reserve is higher
when there is potential tax savings from reserving. Firms smooth earnings to follow the
expectations of stakeholders and regulators. Further, firms with more than four IRIS ratios outside
acceptable ranges under-reserve to avoid regulatory attention.
Although earnings management via loss reserve manipulation in property-liability
insurers is thoroughly examined in the existing literature, loss reserve error volatility is less so.
Recently, Eckles, Halek, and Zhang (2014) use loss reserve error volatility to measure the accruals
quality (AQ), also called information risk, which refers to the potential for inaccurate or
incomplete firm information. They find a negative relation between the quality of accruals and the
cost of debt. In this paper, we follow a similar technique to compute the volatility of loss reserve
error. We further examine the characteristics of insurers experiencing high loss reserve error
volatility with respect to group membership and integrate loss reserve error volatility with internal
capital markets activities among the group subsidiaries.
2.2 Internal Capital Markets (ICMs)
The property-liability insurance industry also provides the ability for insurers to operate
in groups which allows for ICM transactions. A substantial theoretical and empirical literature on
ICM activities and efficiencies has developed. The literature generally shows that conglomerates
have the benefit of ICMs since the insurers within the group structure can allocate internal capital
7
across the group members (Gertner, Scharfstein and Stein, 1994; Stein, 1997; Houston and James,
1998; Maksimovic and Phillips, 2002,2006; Powell and Sommer, 2007; Powell, Sommer, and
Eckles, 2008; Fier, McCullough, and Carson, 2012) though empirical results for ICM efficiency
are mixed (Shin and Stulz, 1998; Rajan, Servaes, and Zingales, 2000; Powell and Sommer, 2007).
Stein (1997) develops a model in which headquarters creates value by engaging in
“winner picking” and allocating capital to projects having the highest expected returns.4 On one
hand, headquarters could raise more than stand-alone firms because of fewer credit constraints.
On the other hand, there involves high expense in monitoring headquarters.
A number of studies find internal capital markets play a significant role in the operations
of financial intermediaries (Houston, James, and Marcus, 1997; Shin and Stulz, 1998), the
nonfinancial industry (Khanna and Tice 2001), and the property-liability insurance industry
(Powell and Sommer, 2007; Powell, Sommer and Eckles, 2008; Fier, McCullough and Carson,
2012; Niehaus 2014). In Powell, Sommer, Eckles (2008), the authors model a change in an
affiliated insurer’s capitalization through ICM transactions by transferring capital to another
affiliated insurer through reinsurance. They distinguish between affiliate and non-affiliate uses of
capital and reinsurance and find that ICM transactions in group insurers stimulate growth in
affiliate’s investment. The common proxy for ICMs used in many studies is reinsurance which can
be measured as the changes in net reinsurance ceded or the difference in the ratio of net reinsurance
premiums ceded to total premiums written. Both measures affect the internal capital structure since
increasing the premium ceded to reinsurers allows an insurer to write more insurance.
Recently, Niehaus (2014) shows that a profit maximizing group may want to recapitalize
subsidiaries after negative capital shocks. Recapitalizing weak subsidiaries allows the group to
continue to earn rents from previous investments in the subsidiary’s reputation. He examines
4
“Winner picking” represents headquarters having the ability to reallocate capitals from divisions where returns are
low (losers) to divisions where returns are high (winners) (Stein, 1997; and Gertner, Scharfstein and Stein, 1994)
8
insurers receiving internal capital contributions as well as insurers paying internal shareholder
dividends as proxies for internal capital markets. He finds evidence that insurance groups manage
capital with respect to insolvency risk and concludes that ICMs play a crucial role within groups
for life and health insurers.
In contrast, other studies indicate that internal capital market activities are not a significant
factor in the investment strategy of conglomerate firms and are associated with less efficiency
(Shin and Stulz, 1998; Scharfstein and Stein, 2000; Rajan, Servaes, and Zingales, 2000).
Scharfstein and Stein (2000) introduce the agency problems among division managers and
conclude the hierarchies lead to misallocation of internal capital. Further, Rajan, Servaes, and
Zingales (2000) argue diversified firms may invest inefficiently since ICMs might in fact hinder
investment efficiency by allocating resources more poorly than would external capital markets.
Theory indicates that diversification via ICMs is associated with both costs and benefits.
In general, benefits associated with diversification include economies of scope (Teece, 1980),
internal capital markets without information asymmetries (Stein, 1997), as well as risk pooling
(Cummins, Phillips, and Smith, 2001). Gertner, Scharfstein and Stein (1994) compare internal
capital markets with external capital markets via bank lending and find that ICMs are less costly
and more efficient than external capital markets since they reduce agency costs as well as
information asymmetries. Gertner, Scharfstein and Stein (1994) and Stein (1997) both find that
ICMs play a significant role as conglomerates allocate capital to the divisions with the best
expected returns. Corporate headquarters creates value in a way that headquarters has the ability
to reallocate capital from divisions where expected returns are low to divisions where expected
returns are high.
On the other hand, transferring capital among affiliates can create an information
asymmetry between insurance groups and other parties such as shareholders, policyholders, and
regulators. Diversification via internal capital markets may magnify agency costs (Harris, Kriebel,
9
and Raviv, 1982; Rotemberg and Saloner, 1994) and agency problems can increase among division
managers which may lead to misallocation of internal capital according to Scharfstein and Stein
(2000). Likewise, it may allow inefficient cross-subsidization of poorly performing business units
(Rajan, Servaes, and Zingales, 2000).
As discussed above, the prior literature provides support for the existence of internal
capital markets within group insurers and various incentives for earnings’ management by insurers
via loss reserve error but has not incorporated loss reserve error volatility with internal capital
markets. Some potential benefits associated with ICMs include lower monitoring costs, reduced
agency problems, greater efficiency of capital allocation and lower cost of internal capital
compared to external capital. The lower cost of capital drives the reduced information asymmetries
and lower agency costs within the internal capital markets.
3. Theoretical Background and Hypotheses Development
3.1. Loss Reserve Error Volatility at the Firm-level
Theoretically, under the assumption that all firms and managers are profit maximizers, we
would expect unaffiliated single firms and affiliated group firms to behave the same. However,
the argument that these two types of firms differ in their ability to exploit market opportunities is
not new (Maksimovic and Phillips, 2002 2007).5
In our first analysis, we investigate insurers’ loss reserve error volatility at the firm-level.
We look at the characteristics of insurers as they relate to loss reserve error volatility, in particular
whether or not the insurer is affiliated with a group of insurers.
Unaffiliated single firms have their own authority to manage their reserves to meet
5
Maksimovic and Phillips (2002) develop a neoclassical model of profit maximizing firms with heterogeneous
industry-specific productivity. In equilibrium, the goal is to maximize firm profit for both unaffiliated single firms
and affiliated group firms. However, since they have different market opportunities, firms produce in industries in
which they have a comparative advantage and firms with lower industry-specific productivity diversify more.
10
corporate goals such as income smoothing (Weiss, 1985; Grace, 1990; Beaver, McNichols, and
Nelson, 2003), regulatory scrutiny aviodance (Petroni, 1992; Harrington and Danzon, 1994; Gaver
and Paterson, 1994; Grace and Leverty, 2012), tax minimization (Grace, 1990; Petroni, 1992;
Nelson, 2000; Grace and Leverty, 2012), executive compensation (Eckles and Halek, 2010; Eckles
et al, 2011) and external monitoring (Gaver and Patterson 2001). Therefore unaffiliated firms may
exhibit more inconsistency of error and uncertainty of firm information which corresponds with
relatively high information risk. In other words, unaffiliated firms are formed by themselves and
are not part of a group with other subsidiaries. Thus, it is completely up to the unaffiliated insurer
to manage their loss reserve to achieve corporate objectives as discussed above. Further, single
unaffiliated firms do not have the ability to transfer capital to affiliates.
On the other hand, group affiliated insurers are less likely to need to overstate or
understate the loss reserve than single unaffiliated because an affiliated insurer is a member of a
group comprised of one or more subsidiaries where group members can transfer capital internally
to the rest of the group. Consequently, we hypothesize that affiliated firms will tend to have more
consistent loss reserve errors which result in low loss reserve error volatility and more certainty
of firm information therefore correspondingly low information risk. As in Eckles, Halek and
Zhang (2014), information risk in this paper refers to the potential for inaccurate or incomplete
firm information. With this theoretical background, we inspect the characteristics of insurers
experiencing high or low loss reserve error volatility with respect to group insurer. Thus we
propose the following hypothesis:
Hypothesis 1: Loss reserve error volatility for affiliated insurers is lower than that for
unaffiliated insurers
Ultimately unaffiliated insurers are largely constrained to manage capital by managing
11
their reserves which results in high loss reserve error volatility. However, affiliated insurers have
ICM opportunities among the group members which results in less need to manage capital via
their reserves. Hence, we anticipate that the insurers that are part of a group have less volatility
than unaffiliated insurers.
3.2. Loss Reserve Error Volatility at the Group-level
The NAIC notes that “…that analysis of an individual company may not be complete
without understanding the context of the group and the markets in which the company operates”
(NAIC, 2002, p.2). Thus it is important to investigate loss reserve error volatility not only at the
individual firm level but in the context of insurers groups.
In our second analysis, we investigate an insurer’s loss reserve error volatility at the
aggregate affiliated level. The first hypothesis tested in this paper is that certain firm characteristics
are associated with high loss reserve error volatility, such as whether the insurer is part of a group
or not. Now we focus on the loss reserve error volatility at group level. With a new unique measure
of group level loss reserve error and its volatility, we further analyze the relation between group
loss reserve error volatility with internal capital markets. In this context, we only consider grouplevel data.6
Insurance regulation has focused on the operations and financial strength of insurers on a
legal entity basis. Property-liability insurers have the ability to operate in groups and are required
to prepare statutory filings at the group level. Certain model laws specifically relate to insurance
holding companies and regulate transactions within the insurance group. 7 The majority of
Under National Association of Insurance Commissioner’s (NAIC) consolidation, all assets and liabilities of a
subsidiary are brought into the parent’s financial statements.
6
7
For example, model Law (ML) 440, Insurance Holding Company System Regulatory Act, and ML 450, Insurance
Holding Company System Model Regulation with Reporting Forms and Instructions. A new proposed model law
with implications for group supervision, the Risk Management and Own Risk and Solvency Assessment
(RMORSA) Model Law is also under consideration.
12
property-liability insurers are affiliated with one or more other insurers in an insurer group.
A number of studies examine group level information since characteristics or conditions
of the groups with which affiliated insurers are associated would influence firms’ decisions
(Harrington 1981; Houston, James and Marcus, 1997; Gaver and Potter 2005). Harrington (1981),
in particular, looks at holding company’s insolvency risk and claims that holding companies may
have a lower insolvency risk than one of its subsidiary insurers would have as a stand-alone firm
since group members can transfer capital to the other members of the group. The group structure
creates ICMs which allows diversified firms to fund projects in one unit of the firm by reallocating
capital from other units. That is, corporate headquarters are able to distribute capital among the
group members (William, 1975; Stein, 1997; Houston, James, and Marcus, 1997).
To measure ICMs, we use two proxies: ICM transactions and ICM participants. First, the
most commonly used proxy for ICM transactions is internal reinsurance (Powell and Sommer,
2007; Powell, Sommer and Eckles, 2008; Fier, McCullough and Carson, 2012). The amount of
reinsurance is calculated as premiums ceded to reinsurers scaled by total premiums written. A
primary insurer may cede business to a reinsurer with which it is affiliated under the same parent
company and/or to reinsurers with which they are not affiliated. For internal reinsurers, we
calculate the net reinsurance ceded to affiliates.
Next, as a second proxy for ICMs, we utilize the number of subsidiaries in a group that
participate in ICMs. In general, the more lines of business of firms, the more diversified the firm
is with more ICMs participants (Laeven and Levine, 2007; Liebenberg and Sommer, 2008; Schmid
and Walter, 2009). Therefore, the more subsidiaries in a group, the more ICM participants. For
example, a group insurer with ten insurance ICM participants has more Internal Capital Markets
opportunities than a group with just two ICM participants. As a result, our second hypothesis on
group loss reserve error volatility is as follows:
13
Hypothesis 2: Loss reserve error volatility is negatively related to Internal Capital Market
activity
We expect that as ICM activity increases, group-level loss reserve error volatility declines.
Previous studies on property-liability insurers loss reserve do not distinguish between single
unaffiliated and group affiliated companies, aside from the inclusion of a group dummy variable.
4. Model and Data
4.1 Hypotheses
In order to calculate a property-liability insurer’s loss reserve error, we follow the same
measure of reserve error that has been widely used in the literature (Kazenski, Feldhaus, and
Schneider, 1992; Petroni, 1992; Beaver, McNichols, and Nelson, 2003; Gaver and Paterson,
2004).8 An excerpt from Schedule P can be found in Table 1. Specifically, we calculate the error
to be the difference between the initial reserve plus the reserve set sometime in the future.
Equation (1) formally shows our measure below:
Reserve Error (RE) i,t=Incurred Losses i,t– Incurred Losses i,t+n
(1)
As shown in Table1, equation (1) utilizes the difference between total incurred losses for
a firm i as of a given year t and a revised estimate of incurred losses in the future year t+n where
8
Another way to measure the reserve is discussed in Weiss (1985) and Grace (1990). They use the difference between
total incurred losses for a firm i as of a given year t and cumulative developed losses paid in future year t+j where j
also equals to five years. Unlike KFS (1992), reserve error is determined by comparing the initial estimate of reserves
with claims paid. These claims paid are not ultimate claims paid since it is limited to just five years. It cannot guarantee
all the claims are paid and thus very likely to overstate the reserve error. Thus we follow the measure used in KFS
(1992) because it does not depend on the development of losses when losses are paid. This is the same measures of
reserve error that has been widely used in the existing literature (Petroni 1992, Beaver, McNichols, and Nelson 2003,
Gaver and Paterson 2004 and Grace and Leverty 2010).
14
we set n equal to five years. This loss reserve measure requires five years of data to calculate. The
reserve Error is positive if the insurer over-reserved and negative if the insurer under-reserved.9
The insurance literature has primarily used two loss reserve error scaling factors: total
assets and developed reserves. Petroni (1992) and Beaver, McNichols, and Nelson (2003) scale
by assets but report that their results are not sensitive to the scaling variable. Gaver and Paterson
(2004) primarily scale by the developed reserve and some studies use both and find consistent
results (Grace and Leverty 2010, 2012). Thus we use both scaling factors in this paper. RE1
represents reserve error scaled by total assets and RE2 represents reserve error scaled by developed
reserve.
Reserve Error (RE1) i,t=
Reserve Error (RE2) i,t=
(𝐼𝑛𝑐𝑢𝑟𝑟𝑒𝑑 𝐿𝑜𝑠𝑠𝑒𝑠 𝑖,𝑡 – 𝐼𝑛𝑐𝑢𝑟𝑟𝑒𝑑 𝐿𝑜𝑠𝑠𝑒𝑠 𝑖,𝑡+5)
𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 𝑖,𝑡
(𝐼𝑛𝑐𝑢𝑟𝑟𝑒𝑑 𝐿𝑜𝑠𝑠𝑒𝑠 𝑖,𝑡 – 𝐼𝑛𝑐𝑢𝑟𝑟𝑒𝑑 𝐿𝑜𝑠𝑠𝑒𝑠 𝑖,𝑡+5)
𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑅𝑒𝑠𝑒𝑟𝑣𝑒 𝑖,𝑡
(2.1)
(2.2)
This paper also utilizes a unique measure of loss reserve error volatility both at the firm
and a group level. As discussed in previous sections, loss reserves are insurer-specific accruals
and reserve errors measure the actual error in accruals unlike the accruals used in many accounting
and finance studies. Insurers need to re-estimate prior years’ loss estimates to reflect actual
payments made and changes in estimates. Because reserve estimations must be made in advance
of ultimate settlement, the accuracy of an insurer setting loss reserve levels is important.
According to Eckles, Halek and Zhang (2014), we can calculate loss reserve error volatility which
can be considered as information showing the potential for inaccurate or incomplete firm
information.
9
In contrast, Petroni 1992, Beaver, McNicholas and Nelson (2003), Eckles and Halek (2010) switch the elements in the
equation, Reserve Error (RE) i,t=Incurred Losses i,t+j – Incurred Losses i,t which only flips the sign of error.
15
We calculate the standard deviation of the reserve error to compute the volatility of the
loss reserve error at individual firm-level by using both three-year and five-year volatilities based
on the prior 3 (or 5) years, j , reserve errors.
Firm Vol (RE1),j,i,t= 𝜎 𝑖, 𝑡 =
Firm Vol (RE2) ,j,i,t= 𝜎 𝑖, 𝑡 =
√
2
∑𝑡𝑡−(𝑗−1) 𝑅𝐸1𝑖,𝑡
𝑡
∑𝑡−(𝑗−1)(𝑅𝐸1𝑖,𝑡−
)
𝑗
𝑗−1
√
(3.1)
2
∑𝑡𝑡−(𝑗−1) 𝑅𝐸2𝑖,𝑡
𝑡
∑𝑡−(𝑗−1)(𝑅𝐸2𝑖,𝑡−
)
𝑗
𝑗−1
(3.2)
If a firm has high loss reserve error volatility, it suggests there is inconsistency of loss
reserve error, thus relatively high uncertainty of firm information, which can be considered as high
information risk. On the other hand, if a firm has low loss reserve error volatility, it indicates there
is consistency of loss reserve error, and thus relatively low uncertainty of firm information, and
low information risk.10
Next, we further investigate a new and unique measure of group loss reserve error
volatility to examine the relation between group loss reserve error volatility and internal capital
markets. Group loss reserve error volatility can be calculated as a weighted average of each
company’s standard deviation of loss reserve error from equation (3.1) and (3.2). Equation (4.1)
and (4.2) formally show our measures.
Group Vol (RE1) j,t= 𝜎 𝑗, 𝑡 = ∑𝑛𝑖,𝑡 Firm Vol (RE1)i, t ∗ % of NPW within a group (4.1)
10
We note that a firm can consistently be a “poor reserve” and have low information risk. That is, if a firm is
always wrong, then decision makers will know to discount their reported reserves.
16
Group Vol (RE2) j,t= 𝜎 𝑗, 𝑡 = ∑𝑛𝑖,𝑡 Firm Vol (RE2)i, t ∗ % of NPW within a group (4.2)
This unique measure is designed to examine the relation between group loss reserve error
volatility and internal capital markets. Just like firm level loss reserve error volatility, group level
loss reserve error volatility has a similar meaning. High group level loss reserve error volatility
suggests inconsistency of group members’ reserve errors after consideration of their net premium
written relative to other members ultimately high uncertainty of firm information can be
considered as high information risk. By the same token, low group level loss reserve error
volatility suggests more consistency of group members’ reserve errors after consideration of their
net premium written relative to other members ultimately low uncertainty of firm information can
be considered as low information risk.
4.2 Model
We use two parallel sets of variables. The first set is based on individual company-specific
data. We include common variables used in the existing loss reserve literature. The second set,
applicable to group-affiliated insurers only, is based on consolidated data for the group with which
the insurer is affiliated. Two models and variables used in each are discussed below, along with
the hypothesized association with loss reserve volatility.
In order to test our first hypothesis, we employ the following Ordinary Least Square (OLS)
regressions based on individual company-specific data. The regression includes firm and year
fixed effects and standard errors are adjusted for heteroskedasticity.
Firm Vol (REi,t) = β0 + β1 Groupi,t+ β2 Agei,t+ β3 Sizei,t+ β4 Netincomei,t +
β5 Mutuali,t+ 𝛽6Reinsurancei,t + β7Growthi,t+ β8Geo-Herfi,t + β9 Product-Herfi,t+
β10 Longtaili,t + εi,t
(5)
17
where i represents each individual insurer and t represents year. REi,t is insurer reserve error
calculated from equation (1) divided by two scaling factors: total assets and developed reserve.
Firm Vol (REi,t) is the firm level loss reserve error volatility which is shown in equation (3.1) and
equation (3.2).
Our main variable of interest is Groupi,t which is an indicator variable equal to one if firm
i is a member of an insurer group and zero otherwise. This itests our first hypothesis on affiliation
of firms to investigate the impact of group membership on the loss reserve error volatility at the
firm level. We expect that reserve error volatility for affiliated vs. unaffiliated insurers is
significantly different because of the group mechanism.
We also include common variables used in the existing loss reserve literature. Agei,t
represents the years a firm i operating businesses since established. Sizei,t is the natural logarithm
of total assets in billions. Netincomei,t is firm i’s net income in billions. Mutuali,t is a binary
variable equal to one if the organizational structure form is a mutual and zero if stock.
Reinsurancei,t represents reinsurance ceded divided by reinsurance assumed plus direct
premiums.11 Growthi,t is the one year percentage change in net premiums written. Geo-Herfi,t is a
geographic Herfindahl index, which is the sum of the squared percentage of business written in
each of the 50 states and the District of Columbia. Product-Herfi,t is a product Herfindahl index
which is the sum of the squared percentage of premiums earned in each of the lines of propertyliability insurance. Longtaili,t is the proportion of a firm i’s business written in “long-tailed”
insurance lines. 12 ε i,t is an error term. All of the above variables are defined in Table 2 and
11
This variable refers only to business with reinsurers with which they are not affiliated since group dummy variables
already considers affiliates reinsurers. However, we will use ceded business to a reinsurer with which it is affiliated
under the same parent company as one proxy for Internal Capital Markets in the next analysis.
Prior literature defines longtail lines as farm multi peril, homewoner’s multi peril, commercial multi peril, medical
malpractice, workers’ compensation, products liability, automobile liability, and other liability (Berger et al, 2000;
Grace and Leverty, 2012; Eckles, Halek and Zhang, 2014).
12
18
consistent with existing literature.
To test our second hypothesis, we estimate a second Ordinary Least Square (OLS)
regression for group level loss reserve error volatility. This second model, applicable to groupaffiliated insurers only, is based on consolidated data for the group with which the insurer is
affiliated. The regression includes group and year fixed effects, and standard errors are adjusted
for heteroskedasticity.
Group Vol (REj,t) = β0 + β1 ICMsj,t+ β2 Agej,t+ β3 Sizej,t+ β4 Netincomej,t+
β4 Growthj,t+ β6 Geo-Herfi,t+ β7 Product-Herfj,t+ β8 Longtailj,t + εj,t
(6)
where j represents each group insurer and t represents year. REi,t is an insurer’s reserve error
calculated from equation (1) divided by two scaling factors: total assets and developed reserve.
Group Vol (REj,t) is the group insurer loss reserve error volatility calculated from equation (4.1)
and equation (4.2). All variables in the second regression are identical to the variables from the
first regression except they are aggregated at the group level instead of individual firm level.
Our variable of interest, ICMsj,t, has two proxies: ICM transactions and ICM participants.
First, the most commonly used proxy for ICM transaction is internal reinsurance (Powell and
Sommer, 2007; Powell, Sommer and Eckles, 2008; Fier, McCullough and Carson, 2012). In order
to measure internal reinsurance, we only focus on ceded business to a reinsurer with which it is
affiliated under the same parent company. This is calculated as affiliated reinsurance ceded minus
affiliate reinsurance assumed divided by total premiums written. Next, we use the number of
subsidiaries in a group that participate in ICM as a second proxy for internal capital markets. From
equation (9), we examine the relation between group loss reserve volatility with internal capital
markets activities. We expect to see as ICMs transactions and ICMs participants increase, grouplevel loss reserve volatility declines.
19
4.3 Data
Under Statutory Accounting Principles (SAP), Schedule P of the National Association of
Insurance Commissioner’s (NAIC) annual statement requires property-liability insurers to
disclose the gradual settlement of claims over time and record all changes of the loss reserve
estimate. Those changes indicate whether the originally reported reserve was reported with error
at the firm level.
Our data is from all property-liability insurers in the United States. Insurer characteristics
are from insurers’ annual statutory filings with the NAIC from 1996 to 2011.13 Our first analysis
includes affiliated and unaffiliated single insurers whereas the second model is applicable to groupaffiliated insurers only which is based on consolidated data. In total there are 3,456 unique insurers
and 294 groups. There are 15,483 firm-year observations and 4,912 group-year observations. Table
3 and 4 demonstrate the descriptive statistics for analysis one and two respectively.14
Table 3 panel A shows summary statistics for affiliated insurers and panel B reflects
summary statistics for unaffiliated firms only in accord with our first analysis. The majority of
firms in the first sample over-reserve. The average magnitude of reserve error scaled by total assets
(RE1) is 0.08% while reserve error scaled by developed reserve (RE2) is 2.81% for affiliated
insurers. The average magnitude of RE1 is 2.50% while RE2 is 9.85% for unaffiliated firms. This
indicates all firms overestimate their reserves but single unaffiliated generally over-reserve more
than the affiliated insurers based on univariate comparison.15
13
Since the reserve error calculation requires five year data, our final sample ranges from 1996 to 2006 for insurer
reserve error. For volatility, we use three year (five year) standard deviations. Thus we further lose the first three (five)
years in the beginning.
14
First analysis refers to Equation (5) where we examine the characteristics of high firm reserve error volatility
insurers and the second analysis refers to Equation (6) where we incorporate ICMs with group insurer reserve error
volatility.
15
We conduct difference in mean test as well as Wilcoxon rank sum test and find they are significantly different.
Further, we conduct a permutation test on affiliation of firms (with other firm characteristics hold constant) to
investigate the impact of group membership on the loss reserving practice. The null hypothesis, H0, is framed as
group membership having no effect on loss reserve volatility. We reject the null with a signoficance level at 1%.
20
When it comes to the loss reserve volatility, for example, the average magnitude of three
year volatility of reserve error scaled by developed reserve, Firm Vol(RE2_3), is 7.90% while the
average magnitude of five year volatility of reserve scaled by developed reserve, Firm Vol(RE2_5),
is 14.05% for affiliated insurers. However, for unaffiliated single, the average magnitude of three
year volatility of reserve error scaled by developed reserve, Firm Vol(RE2_3), is 11.22% while the
average magnitude of five year volatility of reserve scaled by developed reserve, Firm Vol(RE2_5),
is 19.59% for unaffiliated frims. Consequently, the univariate comparison tells us that affiliated
insurers have lower reserve error and lower volatility than unaffiliated single insurers regardless of
scaling factors.
Table 4 displays the descriptive statistics at the aggregated group level for our second
analysis. Again, groups in the sample over-reserve on average. The average magnitude of group
reserve error scaled by total assets, Group RE1, is 0.069% while the group reserve error scaled by
developed reserve, Group RE2, is 1.59%. With respect to the loss reserve volatility, all four
measures of group reserve error volatility, Group Vol(RE1_3), Group Vol(RE1_3), Group
Vol(RE2_3), Group Vol(RE2_3), range from 3.85% to 8.69% which are relatively lower than the
reserve volatility at the firm level.
For data screening, we implement a screen similar to existing studies. We remove all
insurers with negative total assets, and negative surplus. We also remove professional reinsurers
defined as any insurer whose reinsurance assumed from unaffiliated firms is greater than 75% of
the direct premiums written less reinsurance assumed from affiliated insurers. Also we only include
either stock or mutual firms and exclude firms with values of Geo-Herfi,t, Product-Herfj,t, and
Longtailj,t greater than one or less than zero. Finally, we eliminate firms which cede all premiums
to reinsurers and write most of their premiums in workers compensation.
21
5. Empirical Results
The regression result for the first analysis corresponding to equation (5) is reported in
Table 5. The dependent variables are firm level loss reserve volatility. In the first column (1), the
dependent variable is (Firm Vol (RE1_3)) firm level loss reserve volatility which is a three year
standard deviation of reserve error scaled by total assets. In the second column, (2) displays the
result for Firm Vol (RE1_5) which is the same as (1) except it is measured by a five year standard
deviation. Likewise in (3), the response variable is (Firm Vol (RE2_3)) firm level loss reserve
volatility calculated as a three year standard deviation of reserve error scaled by developed reserve
and (4) indicates the result for Firm Vol (RE2_5) which is the same as (3) except it is computed as
a five year standard deviation. Other explanatory variables are defined and explained in previous
sections and Table 2.
In all of the regressions in Table 5, the estimated coefficient of our variable of interest,
Group, is strongly significant and negative with values ranges from -0.05% to -2.28%. This result
illustrates evidence that firm level loss reserve error volatility for affiliated and unaffiliated
insurers is significantly different. In fact, affiliated insurer loss reserve volatility is lower than that
of unaffiliated insurers.
As discussed earlier, unaffiliated single firms have more control over reserves and do not
have access to internal capital markets. Therefore unaffiliated firms tend to have more inconsistent
errors and uncertainty of firm information which leads to relatively high information risk.
On the other hand, group affiliated insurers have less individual control and have access
to internal capital markets. Our regression results support our first hypothesis and suggest that
insurers that are part of group have less loss reserve error volatility than unaffiliated single insurers.
Affiliated firms are more consistent with loss reserves and therefore have correspondingly low
information risk.
Additionally, we find that control variables such as Age, Size, Netincome, Mutual, and
22
Geo-Herf are associated with lower firm-level loss reserve error volatility as well. The estimated
coefficients for Size and Netincome are negative and significant meaning that the bigger and
financially stronger firms have lower volatility of reserve error. Sommer (1996) shows that smaller
companies that write a few small lines of business have less ability to diversify variability than
larger companies that write many lines of business which is consistent with the result in this paper.
Moreover, stock firms engage in higher risk than mutual firms (Mayers and Smith, 1988; He and
Sommer, 2010; Lamm-Tennant and Starks, 1993). Our result also demonstrates that volatility of
loss reserves of stock firms is higher than mutual. Geographical diversification variable shows
significant and negative relation with insurers reserve error volatility although product
diversification and longtail lines seem to be associated with higher volatility.
In our second analysis we examine the association between insurer group loss reserve
volatility and internal capital markets. These results are presented in the next two tables. In this
analysis, we only include group level data for affiliated insurers from our sample. To measure
internal capital markets (ICMs), we use two proxies; ICM transactions and ICM participants.
Table 6 shows the results for the first proxy while Table 7 represents the results for the second
proxy.
In both Table 6, and Table 7, dependent variables from (1) to (4) are group level loss
reserve error volatility which is a sum of each insurer’s standard deviation of loss reserve error
divided by scaling factors multiplies weighted by the percentage of net premium written for a firm
within a group as shown in equation (4.1) and (4.2). Colums (1)-(4) represent the same volatility
measures as Table 5. All of other variables also have the same meaning as in Table 5 except they
are now aggregated at the group level.
Our first proxy for the ICMs is an internal reinsurance variable calculated as reinsurance
ceded to affiliates minus reinsurance assumed from affiliates divided by total premiums written
(Powell and Sommer, 2007; Powell, Sommer and Eckles, 2008; Fier, McCullough and Carson,
23
2012). The more internal reinsurance transactions, the more active their internal capital market is.
In all of the regressions in Table 6, the estimated coefficient of our variable of interests,
ICM transactions, is strongly significant and negative with values ranged from -0.08% to -0.34%.
This suggests that affiliated insurers with access to more internal capital markets activities have
lower group-level loss reserve error volatility than affiliated insurers with less active internal
capital markets, supporting our second hypothesis.
Next, we use our second proxy for internal capital market: ICM participants. More
subsidiaries in a group represents more ICMs participants. In all of the regressions in Table 7, the
estimated coefficient of our variable of interests, ICM transactions, is strongly significant and
negative with values ranged from -0.02% to -0.04%. This also supports our second hypothesis that
affiliated insurers with access to more internal capital markets activities have lower loss reserve
error volatility than affiliated insurers with less active internal capital markets.
From our second analysis, we also find some control variables such as Age, Size,
Netincome, Geo-Herf, Prod-Herf, and Longtail are associated with lower group-level loss reserve
error volatility as well. The bigger and financially stronger groups may have lower volatility of
reserve error and the more geographically or product diversified groups experience lower group
level loss reserve error volatility. One explanation is that more diversified firms have more ability
to spread variability and larger risk pools exhibit lower volatility in underwriting results in
property-liability insurers.
Ultimately, we find evidence that as ICM transactions and participants increases, grouplevel loss reserve error volatility declines. No previous studies on property-liability insurers loss
reserve have made any distinctions between single unaffiliated and group affiliated companies
aside from the inclusion of a group dummy variable. Further, existing literature provides support
for the existence of ICMs within group insurers but has not incorporated with loss reserve
volatility (Houston, James, and Marcus 1997, Khanna and Tice 2001, Powell and Sommer 2007,
24
Powell, Sommer and Eckles 2008, Niehaus 2014).
In this paper, we examine loss reserve error volatility also known as information risk both
at the individual firm-level and aggregate group-level. We first look at the characteristics of
insurers experiencing high loss reserve volatility with respect to group membership and show
evidence that affiliated insurance companies have lower individual firm-level loss reserve
volatility than single unaffiliated firms. We also show that internal capital market activity results
in lower aggregate group-level loss reserve volatility.
6. Conclusion
The property-liability insurance business is inherently risky and the estimation process of
reserves is imperfect with variability in loss reserves is inevitable. Loss reserve variability is also
known as loss reserve error volatility and can be considered as information risk according to
Eckles, Halek and Zhang (2014). Information risk refers to the potential for inaccurate or
incomplete firm information. High loss reserve error volatility suggests inconsistency of error and
uncertainty of firm information, thus high information risk. In contrast, low loss reserve volatility
suggests consistency of error and certainty of firm information, and therefore low information risk.
In this paper, we look at the characteristics of insurers as they relate to loss reserve error
volatility and compare the loss reserve error volatility both at the individual firm level and
aggregate group level. With an unique measure of group level loss reserve error volatility, we
further inspect the relation between group loss reserve error volatility and internal capital markets.
We find evidence that affiliated insurance companies have lower individual firm-level loss reserve
error volatility than single unaffiliated insurers and that internal capital market activitiy is
associated with lower aggregate group-level loss reserve error volatility.
Our findings support our theory that unaffiliated single firms are, by definition, not formed
as a group with other subsidiaries, and are limited in managing their loss reserve to achieve
25
corporate objectives. On the other hand, group affiliated insurers are less likely to manipulate loss
reserve than single unaffiliated insures since group membership allows an affiliated insurers to
transfer capital internally to other group members through ICMs. Consequently, affiliated firms
tend to have higher consistency in their loss reserve errors which results in lower loss reserve error
volatility and more certainty of firm information, therefore correspondingly lower information risk.
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30
31
11
2011
10,507
27,003
47,249
59,972
73,086
123,011
148,487
168,396
169,724
182,811
397,577
Note: This table is an excerpt from 2011 Annual National Association of Insurance Commissioners’ (NAIC) annual statutory filing for GEICO Co. Schedule P-Part 2. Data are
used to calculate loss reserve errors. A firm’s reserve error is calculated by incurred losses in year t minus incurred losses in year t+5, scaled by total assets (RE1) and scaled by
developed reserve (RE2). For example, we sum all the values in column 6 for year 2006 (264,516) and subtract it from the sum of all the values in column 11 (340,828). Then
loss reserve error equals to 76,312. Positive error represents over-reserving whereas negative error indicates under-reserving. Thus it means GEICO Co. over-reserved by
around $76 million.
1
Accident year
Prior
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
Excerpt from the 2011 Annual Statement of GEICO Co.
NAIC Property-Liability Annual Statement: Schedule P- Part 2- Summary
Incurred Net Losses and Defense and Cost Containment Expenses Reported at Year End ($000 omitted)
2
3
4
5
6
7
8
9
10
2002
2003
2004
2005
2006
2007
2008
2009
2010
14,270
12,332
12,409
11,862
11,450
10,699
11,565
11,655
10,803
25,935
29,067
27,005
26,173
25,102
24,862
27,232
26,481
27,128
40,952
38,783
36,863
35,189
36,153
45,696
44,786
47,436
50,991
45,372
43,303
45,077
58,668
60,607
60,529
63,841
59,571
56,435
76,458
73,427
74,208
89,901
89,254
121,568
119,920
123,154
99,596
147,998
147,561
156,010
166,207
164,978
173,253
148,450
164,460
172,428
Table 1. Excerpt from Schedule P-Part 2
Table 2. Variable Definitions
Variable
RE
Firm Vol (RE)
Group Vol (RE)
Group
ICMs
Age
Size
Net Income
Growth
Reinsurance
Mutual
Product Herf
Geo Heft
Longtail
Definition
Dependent Variable
A firm’s reserve error calculated by incurred losses in year t minus incurred losses
in year t+5, scaled by total assets (RE1) and scaled by developed reserve (RE2).
A firm’s volatility of reserve error calculated by standard deviation of firm’s
incurred losses in year t minus incurred losses in year t+5, scaled by total assets
(RE1) and scaled by developed reserve (RE2) for three years (Firm Vol (RE_3))
and for five years (Firm Vol (RE_5)).
A group’s volatility of reserve error calculated by a sum of each subsidiaries’ three
year (Group Vol (RE_3)) and five year (Group Vol (RE_5)) volatility of reserve
error multiplies with the percentage of net premium written for a firm as of a given
year t within a group.
Independent Variable
An indicator variable equal to 1 if a firm is a member of group, 0 otherwise.
(1) ICMs transactions : Reinsurance ceded to affiliates minus reinsurance assumed
from affiliates divided by total premiums written
(2) ICMs participants : Number of subsidiaries that participates in ICMs
Control Variable
Number of years a firm is doing business since established.
The natural log of firm’s total assets.
A firm’s net income measured in billions in year t.
The one year percentage change in net premiums written from year t-1 to year t.
Reinsurance ceded minus reinsurance assumed divided by net premiums written
A indicator variable equal to 1 if a firm is organized as a mutual in year t, 0 if a firm
is organized as a stock in year t.
Herfindahl index of a firm’s net premiums written across lines of business in year t.
Herfindahl index of a firm’s direct premiums written in each of the 50 United States
and Washington D.C. in year t.
The proportion of a firm’s net premiums written in long-tailed lines of business in
year t. Long-tailed lines are farm multi peril, homeowners’ multi peril, commercial
multi peril, medical malpractice, workers’ compensation, products liability,
automobile liability, and “other” liability.
Note: We use all these variables at the individual firm level and aggregated group level. For the first analysis of this paper, we
examine the characteristics of high firm reserve error volatility insurer particularly with group indicator and all the variables are
used at the firm level. Thus our first sample includes affiliated and unaffiliated single insurers only. For the second analysis of this
paper, we examine the relation between group insurer loss reserve error volatility with Internal Capital Markets (ICMs) and all the
variables are aggregated at the group level. Our second sample therefore contains group insurers only.
32
Table 3. Descriptive Statistics for Affiliated vs Unaffiliated Single only
N=10,648
RE1
RE2
Firm Vol (RE1_3)
Firm Vol (RE1_5)
Firm Vol (RE2_3)
Firm Vol (RE2_5)
Age
Size
Netincome
Reinsurance
Growth
Mutual
Product Herf
Geo Heft
Longtail
N=4,835
RE1
RE2
Firm Vol (RE1_3)
Firm Vol (RE1_5)
Firm Vol (RE2_3)
Firm Vol (RE2_5)
Age
Size
Netincome
Reinsurance
Growth
Mutual
Product Herf
Geo Heft
Longtail
Mean
Std.Dev
Min
Panel A: Descriptive Statistics: Affiliated insurers
Max
.0008026
.1213764
-1.676915
.0281816
.2303433
-2.617978
.0564923
.0975398
3.68e-06
.1056871
.1413851
.0025408
.0790749
.2148815
3.24e-06
.140572
.3115568
.002947
46.80875
37.70291
0
18.07385
1.983709
9.364691
.0151185
.1365804
-4.034666
.4546064
.3587919
0
.0772016
.5672489
-.8555238
.1946615
.3959435
0
.5136796
.3258122
0
.6094103
.3845471
.0302969
.4333946
.3714757
0
Panel B: Descriptive Statistics: Unaffiliated Single insurers
1.382405
4.046832
1.709714
2.411862
3.82479
5.802324
260
25.58469
6.770286
1
1.156491
1
1
1
1
.0250464
.0985342
.0608971
.111851
.1122772
.1959025
46.99193
16.44569
.0012246
.2759219
.0798539
.3958534
.6479136
.7863328
.4478587
.1392866
.3210907
.0981848
.1637507
.2380499
.4158544
44.73116
1.694338
.040315
.2639984
.5505081
.48905
.317535
.3273496
.4163153
-1.443309
-2.604938
.0000513
.0015714
.0003118
.0044743
0
8.817298
-4.815623
0
-.8555238
0
0
.0348241
4.61e-08
.8984513
4.857143
1.50232
2.42799
3.159192
5.656376
218
23.71614
1.066459
1
1.156491
1
1
1
1
Note: Our data is from all property-liability insurers in the United States. Insurer characteristics are from insurers’ annual statutory
filings of NAIC from 1996 to 2011. For the first analysis, we examine the characteristics of high firm reserve error volatility insurer.
Our first sample includes affiliated and unaffiliated single insurers. In total there are 3,456 unique insurer. There are 15,483 firmyear observations where 10,648 observations are for affiliated insurers and 4,835 observations for unaffiliated single insurers. RE1
represents insurer reserve error scaled by total assets and RE2 represents insurer reserve error scaled by developed reserve. Firm
Vol (RE1_3) is firm level loss reserve volatility which can be calculated with a three year standard deviation of reserve error. Firm
Vol (RE1_5) is the same except it is used by five year standard deviation. Our main interesting variable is Groupi,t which is an
indicator variable equal to one if a firm i is a member of an insurer group and zero otherwise. Agei,t is how many years a firm i
operating businesses since established. Sizei,t is the natural logarithm of total assets. Netincomei,t is firm i’s net income in billions.
Reinsurance is reinsurance ceded divided by reinsurance assumed plus direct premiums. Mutuali,t is a binary variable equal to one
if organizational structure form is a mutual and zero if stock. Growthi,t is the one year percentage change in net premiums written.
Geo-Herfi,t is a geographic Herfindahl index based on premiums written in 50 states in United States. Product-Herfi,t is a product
Herfindahl index via a line of business. Longtaili,t is the proportion of a firm i’s business written in “long-tailed” insurance lines.
33
Table 4. Descriptive Statistics for Group only
Mean
Std.Dev
Min
Panel A: Descriptive Statistics: Group only
N=4,921
Group RE1
Group RE2
Group Vol (RE1_3)
Group Vol (RE1_5)
Group Vol (RE2_3)
Group Vol (RE2_5)
ICMs participants
ICMs transactions
Size
Netincome
Growth
Product Herf
Geo Heft
Longtail
.0006921
.0159707
.0504093
.0869637
.0385064
.0651970
9.800184
.0638448
20.2504
.2487984
.0445389
.3746107
.3563032
.4506800
.1228623
.1085562
.1003331
.1331991
.0551222
.0830862
12.38902
.1398225
1.753466
.9109987
.4205737
.267378
.3363112
.3116116
-1.505537
-.6668418
.000283
.0037674
.0005098
.0026959
2
0
14.64725
-5.142708
-10.75383
0
.0333543
0
Max
.7835506
1.727199
1.508502
1.507302
.5477656
.8431973
67
.9237356
25.99979
12.38084
7.265815
1
1
1
Note: Our data is from all property-liability insurers in the United States. Insurer characteristics are from insurers’ annual statutory
filings of NAIC from 1996 to 2011. For the second analysis, we examine the relation between insurer loss reserve error volatility
with Internal Capital Markets (ICMs). Our second sample includes groups only. In total there are 294 unique groups. There are
4,921 group-year observations. All variables have the same meaning as in Table (2) except group loss reserve error volatility. It is
unique and can be calculated as a sum of each company’s standard deviation of loss reserve error divided by scaling factors
multiplies with the percentage of net premium written for a firm i as of a given year t within a group j. Group Vol (RE1_3) is group
level loss reserve volatility which can be calculated with a three year standard deviation of reserve error. Group Vol (RE1_5) is the
same except it is used by five year standard deviation. Our main interesting variable is ICM participants and ICM transactions.
ICM participants indicates the number of subsidiaries within a group and ICM transactions represents Reinsurance ceded to
affiliates minus reinsurance assumed from affiliates divided by total premiums written. Sizei,t is the natural logarithm of total group
assets. Netincomei,t is group j’s net income in billions. Growthi,t is the one year percentage change in group net premiums written.
Geo-Herfi,t is a group geographic Herfindahl index based on premiums written in 50 states in United States. Product-Herfi,t is a
group product Herfindahl index via a line of business. Longtaili,t is the proportion of a group j’s business written in “long-tailed”
insurance lines.
34
Table 5. Firm-level Vol (RE) Regression Result
Variable
(1)
Firm Vol (RE1_3)
-0.0055***
(-7.53)
(2)
Firm Vol (RE1_5)
-0.0203***
(-3.82)
(3)
Firm Vol (RE2_3)
-0.0152***
(-2.71)
(4)
Firm Vol (RE2_5)
-0.0228**
(-2.26)
Age
-0.0001***
(-4.06)
-0.0002***
(-4.63)
-0.0002***
(-3.36)
-0.0003***
(-3.14)
Size
0.0003
(0.71)
-0.0008
(-0.50)
-0.0047***
(-2.68)
-0.0175***
(-3.64)
Netincome
-0.0264***
(-5.36)
-0.0282***
(-3.26)
-0.0203***
(-4.01)
-0.0198***
(-4.98)
Mutual
-0.0169***
(-7.06)
-0.0301**
(-5.17)
-0.0186***
(-4.77)
-0.0350***
(-4.04)
Reinsurance
-0.0005
(-0.10)
-0.0051
(-0.48)
0.0026
(0.29)
-0.0122
(-0.60)
Growth
-0.0012
(-0.59)
-0.0014
(-0.24)
0.0039
(1.05)
0.0143
(1.50)
-0.0083***
(-3.92)
-0.0222***
(-2.66)
-0.0254***
(-3.92)
-0.0418***
(-3.13)
Product Herf
0.0072
(1.65)
0.0213**
(2.12)
0.0548***
(6.12)
0.1191***
(5.74)
Longtail
0.0040
(0.96)
0.0029
(0.29)
0.0145***
(3.21)
0.0186***
(3.02)
Intercept
0.0567***
(3.94)
0.1560***
(3.78)
0.1532***
(3.57)
0.4750***
(4.50)
Group
Geo Herf
Year fixed effect
Yes
Yes
Yes
Yes
Firm fixed effect
Yes
Yes
Yes
Yes
Clustered Std. Error
Yes
Yes
Yes
Yes
0.0563
0.0733
0.0740
0.0597
R-squared
Note: Our data is from all property-liability insurers in the United States. Insurer characteristics are from insurers’ annual statutory
filings of NAIC from 1996 to 2011. In total there are 3,456 unique insurer. There are 15,483 firm-year observations where 10,648
observations are for affiliated insurers and 4,835 observations for unaffiliated single insurers. For the first analysis, we examine
the characteristics of high firm reserve error volatility insurer. Our first sample includes affiliated and unaffiliated single insurers.
Dependent variable is from (1) to (4). (1) is Firm Vol (RE1_3), firm level loss reserve volatility which can be calculated with a
three year standard deviation of reserve error scaled by total assets. (2) is Firm Vol (RE1_5), same as (1) except it is used by five
year standard deviation. (3) is Firm Vol (RE2_3), firm level loss reserve volatility which can be calculated with a three year
standard deviation of reserve error scaled by developed reserve. (4) is Firm Vol (RE2_5), same as (3) except it is used by five year
standard deviation. Our main interesting variable is Groupi,t which is an indicator variable equal to one if a firm i is a member of
an insurer group and zero otherwise. Agei,t is how many years a firm i operating businesses since established. Sizei,t is the natural
logarithm of total assets. Netincomei,t is firm i’s net income in billions. Mutuali,t is a binary variable equal to one if organizational
structure form is a mutual and zero if stock. Growthi,t is the one year percentage change in net premiums written. Geo-Herfi,t is
a geographic Herfindahl index based on premiums written in 50 states in United States. Product-Herfi,t is a product Herfindahl
index via a line of business. Longtaili,t is the proportion of a firm i’s business written in “long-tailed” insurance lines. . All models
control for year and firm effects and have clustered standard errors. Standard errors account for heteroskedasticity and t statistics
in parentheses * p<0.05, ** p<0.01, *** p<0.001
35
Table 6. Group-level Vol (RE) Regression Result with ICM transactions
(1)
Group Vol (RE1_3)
(2)
Group Vol (RE1_5)
(3)
Group Vol (RE2_3)
(4)
Group Vol (RE2_5)
-0.00082***
(-3.71)
-0.00138***
(-4.26)
-0.00160***
(-3.14)
-0.00342***
(-3.39)
Age
-0.00043*
(-1.75)
-0.00053
(-1.26)
-0.00012**
(2.01)
-0.00001
(-0.95)
Size
0.00012*
(-1.82)
0.00035***
(3.00)
-0.00063***
(-3.57)
-0.00103***
(3.14)
-0.00101***
(-3.94)
-0.00102**
(-1.89)
-0.00237***
(-3.82)
-0.00121*
(-1.72)
0.00014
(0.77)
0.00036
(1.17)
0.00065
(1.41)
0.00239
(0.89)
Geo Herf
-0.00082***
(-3.55)
-0.00174***
(-3.30)
0.00032
(0.41)
0.00038
(0.30)
Product Herf
-0.00223***
(-5.24)
-0.00334***
(-4.85)
-0.00812***
(-7.64)
-0.01358***
(-6.91)
Longtail
-0.00049
(-1.05)
-0.00104
(-1.38)
-0.00249***
(-3.08)
-0.00611***
(3.71)
Intercept
-0.00205
(-1.38)
-0.00580
(-1.01)
0.0137***
(3.74)
0.0225***
(3.34)
Year fixed effect
Yes
Yes
Yes
Yes
Group fixed effect
Yes
Yes
Yes
Yes
Clustered Std. Error
Yes
Yes
Yes
Yes
0.0343
0.0425
0.0615
0.0830
Variable
ICMs
transactions
Netincome
Growth
R-squared
Note: Our data is from all property-liability insurers in the United States. Insurer characteristics are from insurers’ annual statutory
filings of NAIC from 1996 to 2011. Our second sample includes groups only. In total there are 294 unique groups. There are 4,921
group-year observations. For the second analysis, we examine the relation between insurer loss reserve error volatility with
Internal Capital Markets (ICMs). Group reserve volatility is unique and can be calculated as a sum of each company’s standard
deviation of loss reserve error divided by scaling factors multiplies with the percentage of net premium written for a firm i as of
a given year t within a group j. Dependent variable is from (1) to (4). (1) is Group Vol (RE1_3), group level loss reserve volatility
which can be calculated with a three year standard deviation of reserve error scaled by total assets. (2) is Group Vol (RE1_5),
same as (1) except it is used by five year standard deviation. (3) is Group Vol (RE2_3), group level loss reserve volatility which
can be calculated with a three year standard deviation of reserve error scaled by developed reserve. (4) is Group Vol (RE2_5),
same as (3) except it is used by five year standard deviation. All variables have the same meaning as in Table 5 except it is
aggregated at the group level. Our main interesting variable is ICM participants and ICM transactions. ICM participants indicates
the number of subsidiaries within a group and ICM transactions represents Reinsurance ceded to affiliates minus reinsurance
assumed from affiliates divided by total premiums written. Sizei,t is the natural logarithm of total group assets. Netincomei,t is
group j’s net income in billions. Growthi,t is the one year percentage change in group net premiums written. Geo-Herfi,t is a
group geographic Herfindahl index based on premiums written in 50 states in United States. Product-Herfi,t is a group product
Herfindahl index via a line of business. Longtaili,t is the proportion of a group j’s business written in “long-tailed” insurance
lines. All models control for year and firm effects and have clustered standard errors. Standard errors account for
heteroskedasticity and t statistics in parentheses * p<0.05, ** p<0.01, *** p<0.001
36
Table 7. Group-level Vol (RE) Regression Result with ICM participants
(1)
Group Vol (RE1_3)
(2)
Group Vol (RE1_5)
(3)
Group Vol (RE2_3)
(4)
Group Vol (RE2_5)
ICMs
participants
-0.00023***
(-8.82)
-0.00037***
(-8.04)
-0.00031***
(-8.70)
-0.00049***
(-9.49)
Age
-0.00001**
(-2.80)
-0.00002***
(-3.43)
-0.00002***
(-3.24)
-0.00003***
(-3.39)
Size
0.000024
(0.18)
0.00046*
(1.78)
-0.00036**
(-1.95)
-0.00029**
(2.14)
-0.00150***
(-3.30)
-0.00348***
(-3.65)
-0.00140
(-1.61)
-0.00123
(-0.75)
-0.00014
(-0.41)
0.00035
(0.52)
-0.00004
(-0.08)
0.00203
(2.39)
Geo Herf
-0.00103**
(-2.79)
-0.00109
(-0.99)
-0.00168**
(2.04)
0.00105
(0.76)
Product Herf
-0.00405***
(-5.01)
-0.00492***
(-4.22)
-0.00756***
(-6.78)
-0.0126***
(-6.61)
Longtail
-0.00119***
(-2.31)
-0.00290*
(-1.85)
-0.00225*
(-1.78)
-0.00638***
(-3.88)
Intercept
0.00049
(0.18)
-0.00057
(-0.11)
0.0128***
(3.45)
0.013**
(2.01)
Year indicator
Yes
Yes
Yes
Yes
Group indicator
Yes
Yes
Yes
Yes
Clustered Std. Error
Yes
Yes
Yes
Yes
0.0626
0.0709
0.0712
0.1261
Variable
Netincome
Growth
R-squared
Note: Our data is from all property-liability insurers in the United States. Insurer characteristics are from insurers’ annual statutory
filings of NAIC from 1996 to 2011. Our second sample includes groups only. In total there are 294 unique groups. There are 4,921
group-year observations. For the second analysis, we examine the relation between insurer loss reserve error volatility with
Internal Capital Markets (ICMs). Group reserve volatility is unique and can be calculated as a sum of each company’s standard
deviation of loss reserve error divided by scaling factors multiplies with the percentage of net premium written for a firm i as of
a given year t within a group j. Dependent variable is from (1) to (4). (1) is Group Vol (RE1_3), group level loss reserve volatility
which can be calculated with a three year standard deviation of reserve error scaled by total assets. (2) is Group Vol (RE1_5),
same as (1) except it is used by five year standard deviation. (3) is Group Vol (RE2_3), group level loss reserve volatility which
can be calculated with a three year standard deviation of reserve error scaled by developed reserve. (4) is Group Vol (RE2_5),
same as (3) except it is used by five year standard deviation. All variables have the same meaning as in Table 5 except it is
aggregated at the group level. Our main interesting variable is ICM participants and ICM transactions. ICM participants indicates
the number of subsidiaries within a group and ICM transactions represents Reinsurance ceded to affiliates minus reinsurance
assumed from affiliates divided by total premiums written. Sizei,t is the natural logarithm of total group assets. Netincomei,t is
group j’s net income in billions. Growthi,t is the one year percentage change in group net premiums written. Geo-Herfi,t is a
group geographic Herfindahl index based on premiums written in 50 states in United States. Product-Herfi,t is a group product
Herfindahl index via a line of business. Longtaili,t is the proportion of a group j’s business written in “long-tailed” insurance
lines. All models control for year and firm effects and have clustered standard errors. Standard errors account for
heteroskedasticity and t statistics in parentheses * p<0.05, ** p<0.01, *** p<0.001
37