Franchise Value, Competition and Insurer Risk-takingaria.org/meetings/2006papers/RenSchmit.pdf · Franchise Value, Competition and Insurer Risk-taking ... (MM) paradigm, under certain

Franchise Value Competition and Insurer Risk-taking

Yayuan RenUniversity of Wisconsin-Madison

Joan T Schmit

University of Wisconsin-Madison

July 2006

ABSTRACT

Franchise value and competition provide contrary risk-taking incentives to firms

Franchise value provides a risk-constraining incentive to firms while competition

generally induces firms to take more risk Existing empirical evidence on these

relationships however have been mixed motivating us to reexamine these issues

This study adds to the literature by considering the influence of franchise value

and competition on risk-taking simultaneously rather than separately importantly

including an interaction term between the two factors to account for their joint effect

We further add to the literature by incorporating the effect of the underwriting cycle

on these relationships

Our main findings are that the effect of franchise value and competition on

insurer risk-taking is jointly determined and conditional on the underwriting cycle

The specific relationships between the influences of franchise value competition and

the underwriting cycle vary across different business lines and ownership structures

1 Introduction

Insurer solvency is an issue of great importance to insurance regulators

consumers as well as the owners and managers of the firms themselves As a result a

large body of research has been conducted to understand factors that influence insurer

solvency In particular recent research has focused on factors that influence insurer

risk-taking behavior Increased incentives to take risks are expected to increase the

potential for insolvency

Two important results are well established in the existing literature regarding

risk-taking incentives First as reported by Marcus (1984) Keeley (1990) and

Demsetz et al (1996) (among others) franchise value1 provides a risk-constraining

incentive to firms Second as reported by Rhoades and Rutz (1982) Keeley (1990)

and Harrington and Danzon (1994) (among many others) competition induces firms

to take more risk The empirical evidence regarding the effect of franchise value and

competition however is mixed

11 Franchise value and firm risk-taking

The economic worth of a firm includes the value of both tangible and intangible

assets Franchise value represents a firms intangible assets that is the value of the

firm above and beyond the value of its tangible assets In insurance intangible assets

typically generate from an insurers goodwill growth opportunities market power

existing distribution networks and renewal rights on existing business arrangements

with reinsurers as well as specialized knowledge about the risks generating from their

current book of business

Franchise value increases the costs of financial distress (bankruptcy) because

shareholders will loose the franchise value in case of bankruptcy Franchise value

therefore provides risk-constraining incentives to firms to protect their franchise value

Marcus (1984) and Li et al (1995) develop option-pricing models that demonstrate 1 The definition and discussion of franchisecharter value is detailed in section 11

how franchise value can induce risk-averting which is known as Franchise Value

Theory (FVT) This theory predicts negative relationship between franchise value and

firm risk-taking Keeley (1990) and Demsetz et al (1996) provide empirical evidence

in favor of FVT Most notably Keeley (1990) documents declines in bank franchise

value during the 1950s 1960s and 1970s when the banking industry was

experiencing deregulation and increased competition from non-bank financial

institutions He argues that this drop in franchise value led to increased risk-taking in

the 1980s An insurance study made by Staking and Babbel (1995) reports evidence

in support of FVT Their results suggest that insurers will expend scarce resources

(leverage and interest rate risk) to control risk in order to protect franchise value They

did not however examine the relationship between franchise value and insurer

overall risk-taking

A stream of empirical literature however shows that the risk-averting

incentives attributed to franchise value may be constrained or even inverse under

certain situations Boyd and De Nicolo (2004) report a positive relationship between

bank size (generally positively correlated with franchise value) and the probability of

a banking crisis which is contrary to FVT Hughes et al (1996) Demsetz and Strahan

(1997) and Saunders and Wilson (2001) report that a banks franchise-enhancing

expansions increase systematic risk exposures which eventually may expose

high-franchise-value banks to potentially large losses during economic contractions

These studies suggest a sensitivity of the relationship between franchise value and

bank risk-taking to the business cycle

12 Competition and firm risk-taking

Competition has an important external effect on firm risk-taking decisions

Increased competition is generally hypothesized to induce more risk-taking Existing

empirical evidence on the relationship between competition and risk-taking however

is far from being conclusive While some literature2 supports a positive relationship

2 Eg Rhoades and Rutz1982 Keeley 1990 Harrington and Danzon 1994 Browne and Hoyt

between competition and insolvency some other research reports either a negative or

an inconclusive correlation between competition and bank failure For example

Jayaratne and Strahan (1998) find that deregulation was followed by sharp reductions

in loan losses contrasting Keeleys earlier results De Nicoloacute etal(2005) take a

different approach to empirically represent banking system fragility They construct a

probability of failure measure for the five largest banks in a country viewed as an

indicator of banking fragility Their measure of competition is a five-bank

concentration ratio They find that the probability of failure measure is positively and

significantly associated with bank concentration meaning that ceteris paribus a more

concentrated banking industry is more prone to banking fragility Another work is by

Beck et al (2003) who find that banking crises are less likely in more concentrated

banking system however in a banking market with less restrictions on bank entry

indicating more competition the probability of bank crisis also decreases This result

leads the authors to question if concentration ratios (which have long been a standard

measure of market structure in finance and banking literature) can be used as simple

proxy measures for competition

The mixed evidence on relations of franchise value and competition with firm

risk suggests that some important factors or pontential are missed in the prior

analysis Some literature has found that business cycle have important effect on firm

risk-taking strategies (eg Rampini 2004) therefore this study incorporates this

factor into the analysis and examine if the underwriting cycle affects the relationships

between franchise value competition and firm risk

13 Research purpose

The roles of franchise value and competition on firmsrsquo risk-taking behavior are

important issues in insurance because of their implications for regulatory policies

Theoretical studies argue that high franchise value constrains firm risk-taking while

1995 Browne Carson and Hoyt 1999

competition induces risk-taking

The motivation for this paper is two-fold First even though the theoretical

predictions are clear empirical evidence on the influence of franchise value and

competition is mixed motivating us to reexamine these relationships Second recent

research has identified other important factors related to firm risk-taking such as

business cycle (eg Rampini 2004)

Much of the research to date has considered these factors singly rather than as a

whole This study therefore adds to the literature by considering the influence of

franchise value and competition on risk simultaneously rather than separately

importantly including an interaction term between the two factors to account for their

joint effect By doing this we can test whether or not the mixed results occur because

franchise value and competition jointly influence risk-taking Furthermore we add to

the literature by considering the effect of the underwriting cycle on these

relationships

In summary the purpose of the research reported here is to examine the effect

of franchise value and competition on insurer risk-taking strategies simultaneously in

context of the underwriting cycle Due to the complicated interactive relationships

between franchise value competition and underwriting cycle the net effect of each

factor is ambiguous which may explain why the prior evidence on each effect is

mixed A true picture of the factors driving risk-taking decisions at insurers may not

emerge unless franchise value competition and underwriting cycle are all examined at

the same time

The rest of this study is organized as follows Section 2 provides a theoretical

analysis on the factors affecting insurer risk-taking and develops research hypotheses

Section 3 explains empirical methodology Section 4 describes data and variables to

be used Section 5 presents the estimation results Section 6 summarizes our

conclusions and suggests future research

2 Factors Affecting Insurer Risk-taking

The section reviews relevant literature and discuss factors affect insurer

risk-taking Research hypotheses are developed following the analysis

21 Firm Risk

Firm risk generates from numerous sources and its management is critical to a

firmrsquos success Considering only financial risk3 variability is caused by investment

risk interest rate risk credit risk exchange rate risk etc all of which have been

studied extensively Each of these sources of variability affects a firmrsquos assets

liabilities or both For instance both investment risk and credit risk influence

variability in asset values while exchange rate risk and interest rate risk may influence

both asset and liability values For purposes of this study our interest is not so much

with the sources of risk but rather with their influence on the sufficiency of assets to

pay liabilities which we define as a firmrsquos level of solvency

Much of the existing literature considers firm risk-taking strategies in terms of

asset risk and leverage neglecting liability risk For banks the subject of much of the

literature the relatively smooth nature of bank liabilities allows for such omission

But for insurers whose liabilities can fluctuate dramatically liability risk is a critical

component of solvency risk Therefore in the study reported here we consider firm

solvency risk which incorporates asset risk leverage and liability risk

22 Franchise Value and Asset-substitution Moral Hazard

According to Modigliani-Miller (MM) paradigm under certain friction-free

assumptions (including perfect information no taxes or transaction cost and efficient

market) neither capital structure choices nor corporate risk management affects the

value of the firm Shareholders will be indifferent to the level of risk-taking because

the security-specific or nonsystematic risk already has been diversified by the

individual shareholders through portfolio formation Itrsquos obvious that assumption of 3 Firms face non-financial risk as well but these are not considered here

perfect market is unrealistic but MM theorems provide a clear benchmark to help us

understand firm financing and risk management decisions through exploring the

consequences of relaxing the MM assumptions

One of the important market imperfections is information asymmetry leading to

a variety of agency problems A well-established result about the agency conflict

between shareholders and debtholders is known as ldquoasset substitution moral hazardrdquo

or ldquorisk shifting effectrdquo Shareholders who want to maximize the equity value rather

than the total of equity and debt value of the firm have an incentive to increase the

risk of investment assets at the expense of the debtholders interests Limited liability

can be considered an option held by shareholders to put losses onto the debtholders

whenever the firm is liquidated Since option value increases with asset risk and

leverage shareholders have incentives to take excessive risks to exploit this option

value This theory implies two results First for any given level of capital firms will

always seek to increase shareholder value by maximizing risk and looting the firms

assets (Jensen and Meckling 1976) Second high leveraged firms have more

incentive to increase risk-taking (Green and Talmor 1985)

The asset-substitution moral hazard is exacerbated by the existence of state

guarantee funds and deposit insurance which charge a flat premium on insurer and

bank risk-taking Merton (1977) shows that deposit insurance can be viewed as a put

option with exercise price equal to the promised value of its debt Increasing the

volatility of surplus will increase the value of the put option Thereby an equity value

maximizing bank shareholder has an incentive to take excessive risks to exploit this

option value (Dothan and Williams 1980 Kareken and Wallace 1978) Cummins

(1988) made a similar analysis on the impact of guarantee funds which provide an

incentive for insurers to increase volatility

Although asset substitution theory is an appealing explanation for excessive

risk-taking it fails to explain the moderate risk-taking by many firms A sizable

literature 4 presents different motivations for firmrsquos risk management taxes

bankruptcy costs contracting cost managerial risk aversion costly external capital 4 Mayers and Smith (1982) Stulz (1984) and Froot Scharfstein and Stein (1993) etc

and real service efficiency One of the important reasons for risk management is that

financial distress or bankruptcy is costly for firms especial when the intangible assets

(franchise value) are considered As explained in section 121 franchise value can be

understood as intangible assets for insurance companies and cannot be fully liquidated

Provided franchise value is sufficiently large then shareholders will have an incentive

to avoid liquidation by reducing asset risk or increasing capital Marcus (1984)

develops option-pricing models that demonstrate how franchise value can

counterbalance asset substitution moral hazard and constrain risk-taking

Optimal insurer risk-taking decisions involve trade-offs between risk-constraining

strategies which reduce the likelihood of losing the franchise and risk-maximizing

strategies which exploit the guarantee funds and policyholdersrsquo wealth Intuitively

when franchise value is sufficiently large the moral hazard problem of risk shifting

may be alleviated and when franchise value is small the incentive to shift risk to

debtholders may dominate This trade-off however may be affected by some other

factors The impact of competition on insurer risk-taking will be discussed in the

following part

23 Competition and Insurer Risk-taking

A traditional perception is that there is a trade-off between efficiency and financial

stability in competitive market Applying standard industrial economics to the

insurance industry in a perfectly competitive market insurers are profit-maximizing

price-takers such that costs and prices are minimized Therefore insurers are more

efficient in a competitive market than in a non-competition market On the other hand

a variety of models show firmsrsquo risk-taking increases in competition5 indicating a

negative relationship between competition and financial stability

Following these arguments insurance companies react to increased competition in

two ways to keep profitability one is to improve efficiency so as to maintain or

5 See Canoy et al (2001) and Carletti and Hartmann (2002) for excellent surveys of the literature on financial

stability and competition

increase market share6 and the other way is to increase risk for higher return The

first way will improve a firmrsquos profitability without increasing risk and ensure a firmrsquos

success in long run As competition becomes very intensive however the room for

efficiency improvement reduces and thus dropped profitability is likely resulted

Therefore the efficiency improving strategy alone may not effectively keep market

share and profitability The second choice is a strategy of higher risk for higher return

In a competitive insurance market the risk-increasing strategy usually involves in

low-price market expansion strategy The insurers expect to increase or maintain their

existing market share through low-price marketing assuming their risk cannot be

fully priced due to information asymmetry between customers and insurers

Low-price marketing strategy is usually followed by negative loss development7 and

risky investment resulting in greater insolvency risk This risk-increasing strategy

might be attractive to insurance companies because the claim is not paid when

insurance policies are sold which gives insurers time to make income before

liabilities are due The uncertainty nature in the timing and the amount of insurance

claim especially for long-tail lines magnifies the incentive to take risky strategy

As competition increases itrsquos likely that insurers take both efficiency improving

strategy and risk-increasing strategy The question is which strategy dominates If

efficiency improving strategy dominates increased competition will not result in more

risk-taking On the other hand if the risk-increasing strategy dominates competition

will cause financial instability In the following we will discuss how the balancing

between the efficiency strategy and the risk-increasing strategy may depend on an

insurance companyrsquos franchise value and underwriting cycle

As we discussed before high-franchise-value firms have stronger incentive to

protect franchise value by avoiding liquidation Therefore high-franchise-value firms

should also be motivated to prevent their franchise from reduction in competition

6 Demsetz (1973) proposes the efficient-structure hypothesis which argues that efficiency is the principle

determinant of market structure 7 In insurance industry low-price marketing strategy usually reflects in loosening underwriting criteria thus

leading to negative loss development

Franchise value representing future profitability is largely generated from a firmrsquos

market power (De Jonghe and Vander Vennet 2005) As increased competition tends

to erode market power (Keeley 1990) high-franchise-value firms will react so as to

avoid loosing market power and resultant franchise value Improving efficiency is a

good choice for high-franchise-value insurers since it enhances profitability without

increasing risk and high-franchise-value insurers are usually large firms and have

advantages in economy scale8 and efficiency improvement It is however likely that

efficiency improving strategy alone cannot successfully make high-franchise-value

insurers maintain their market share and then the risk-increasing strategy may be

under consideration9 This case is likely resulted especially when severe competition

exists between large players In summary competition will encourage

high-franchise-value insurers to improve efficiency which counters risk-taking but

may also induce them to take risky strategy as efforts to maintain market power

The case is different for low-franchise-value insurance companies in an

increasingly competitive market A traditional view is that for low-franchise-value

firms the asset-substitution moral hazard dominates and as a result they have less

incentive to improve efficiency and are likely to take gambling strategy The gambling

strategy may become less attractive to low-franchise-value insurers under two

conditions First a successful low-price market expansion strategy requires high level

of capacity but low-franchise-value insurers may not have enough capacity to survive

the low-price marketing strategy especially when the competition is very intensive In

this case the gambling strategy would not be a rewarding and financially feasible

choice for low-franchise-value firms Second low-franchise-value insurers are

exposed to more monitoring by regulators and may not be able to take the gambling

strategy 10 Therefore itrsquos unclear that if low-franchise-value insurers will take 8 Existing research has not found conclusive evidence of economy scale for insurance companies 9 Hellman Mardock and Stiglitz (2000) examine bank charter value in an environment that has capital regulation

They argue that higher capital requirements decrease charter value which indicates that a negative relationship

between charter value and capital ratio Saunders and Wilson (2001) presents evidence that charter value itself may

derive from high-risk activities indicating that minimizing risk-taking also would limit the value of the charter 10 Repullo (2003) models banking competition in the deposit market where banks can invest in either a gambling

or a prudent asset He demonstrates that in an environment with capital requirement prudent equilibrium always

excessive risk as competition increases

Above discussion shows that the effect of franchise value on insurer risk-taking is

conditional on the degree of competition and vice versa We can have the following

hypothesis

Hypothesis 1 The effects of franchise value and competition on insurer risk-taking

strategies are jointly determined

This hypothesis implies that a prior expectation about the effects of franchise

value and competition on insurer risk-taking cannot be tested without also accounting

for their joint effect That is the degree of competition is not necessarily positively

related with risk-taking and neither is franchise value negatively related with

risk-taking rather the influence of franchise value (competition) is conditional on the

degree of competition (franchise value)

24 Underwriting Cycle and Insurer Risk-taking

Business cycle has encompassing influence on industry insiders Business cycle

influences franchise value market structures managerial incentives and nearly every

aspects of the industry Firms may become more (or less) risky in some stages of

business cycle than in other stages Many studies have investigated the effect of

business cycle on firms or firmsrsquo reaction to business cycle in various aspects11 which

indicates the important influence of business cycle on firm risk-taking

Underwriting cycle is an insurance industry specific business cycle that consists

of alternative periods in which insurance price is low (soft market) and periods in

which insurance price is high (hard market) There are few studies examining the

relation of underwriting cycle and insurer risk-taking Browne and Hoyt (1995) and

Browne Carson and Hoyt (1999) examine macroeconomic influence on insurer

insolvency The main contribution of these studies is to demonstrate that not only firm

internal factors but also external factors play an important role in insurer solvency

While sharing the same idea with these two studies regarding the importance of prevails 11 For instant Rampini (2004) Vennet Jonghe and Baele (2004) Philippon (2003) Angeletos and Calvet (2003)

external factors on insurer risk-taking this study assumes that outside-industry factors

usually affect insurer risk-taking in an indirect way through changing insurance

industry environment which can be represented by the underwriting cycle

The underwriting cycle is a comprehensive indicator of insurance industry

conditions that have significant influence on insurer risk-taking strategies It consists

of alternating periods of soft markets with plentiful coverage supply and flat or falling

premium rate and hard markets with restricted coverage supply and sharp premium

rate increases

Numerous theories have been developed to explain the underwriting cycle but

none has been conclusively confirmed The goal of the following review of these

theories12 is not to provide a definitive explanation of the causes of underwriting

cycle but rather to evaluate potential influence of the underwriting cycle on insurer

risk-taking behavior

Explanations of the underwriting cycle often begin with what is referred to as

the following ldquofundamentalsrdquo of insurance pricing loss and underwriting expenses

the uncertainty about the frequency and severity of those expenses the timing of

future claim payments (ie the length of the tail) interest rate and the cost of holding

capital These factors taken together constitute the cost of providing insurance

Because these fundamentals fail to explain many aspects of the underwriting cycle

however researchers have looked to additional factors to understand the cycle

The most widely cited underwriting cycle theory is the ldquocapacity constraintrdquo

theory which posits that (a) industry supply depends on the amount of available

insurer capital and (b) hard markets are triggered by periodic exogenous large

negative shocks to insurer capital because raising capital from external markets is

more costly compared with internal capital In these models13 a shock to insurer

capital due to factors such as catastrophes or unexpected increase in claim leads to a 12 Both Baker (2005) and Harrington (2004) provide a good literature reviews and analysis on the theories

regarding underwriting cycle 13 Winter (1998 1991 1994) and Gron (1994) develop the basic capacity constraint model Cummins and Danzon

(1997) Cagle and Harrington (1995) and Doherty and Garben (1995) extend the basic model on several

dimensions

contraction of capacity reflected in leftward shifting of the short-run supply curve and

increasing premium rate

The capacity constraint theory contributes substantially to the explanations for

hard markets Yet it is far from a complete explanation Capacity constraint models

fail to explain why the unpredictable capacity shocks can cause a cycle and do not

persuasively explain what causes soft markets

Harrington and Danzon (1994 2005) develop and test alternative hypotheses of

excessive competition during the soft market They hypothesize that if some insurers

undercharge due to either inexperience or moral hazard of excessive risk-taking then

other insurers will cut prices to preserve market share and avoid loss of quasi-rents

from renewal business This ldquoherd behaviorrdquo effect exacerbates the soft market The

winners in the competition for market share are the low-pricing insurers who in the

end may well find the premiums are insufficient to pay the claims which is known as

ldquoWinnerrsquos curserdquo An observation consistent with this hypothesis is that rapid

premium growth is often followed by negative loss reserve development Soft-market

periods of underpricing cannot continue indefinitely Whether the excessive price

cutting in the soft market ultimately contributes to overpricing in the followed hard

market remains an untested hypothesis

All the contributing factors discussed above are directly or indirectly related to

insurer risk-taking behavior The influence of the underwriting cycle on insurers

risk-taking behavior can be analyzed from two angles first the underwriting cycle

represents changes in the competitive conditions to which insurers are exposed and

second the underwriting cycle is likely to affect low- and high-franchise value firms

differently These effects are discussed instantly as follows

Similar to the four typical phases of an economic cycle the underwriting cycle

undergoes four stages soft market peak hard market and trough Market conditions

and the nature of competition change along the underwriting cycle At the start of the

soft market competition increases moderately price drops and then demand for

insurance increases As a result the market expands and insurers undergo positive

premium growth As the soft market deepens premium growth declines since

insurance demand is nearly saturated At this stage insurers compete intensely for

revenue and market share through price-cutting According to Harrington and

Danzonrsquos hypothesis the underpricing could be led by what they call ldquoaberrant firmsrdquo

who undertake the underpricing due to either inexperience or excessive risk-taking

and then cause a herd behavior of price-cutting around the industry As a result

significant overhang risk accumulates due to a lack of underwriting discipline These

conditions generally lead to unfavorable development of loss reserves

As the market softens to the point that profits diminish or vanish completely the

capital needed to underwrite new business is depleted A ldquohardrdquo turn in an

underwriting cycle comes when insurers collectively respond to the fact that

prevailing premiums cannot cover future claim payments As a result the supply of

coverage is restricted and price increases sharply At the beginning of the hard market

competition within the insurance industry is lessened and insurers tend to behave

conservatively At the same time the high profit of hard market attracts new players

enter the insurance industry lead to a new round of competition and underwriting

Generally speaking the intense competition in the soft market induces insurers to

take more risk and in the hard market insurers tend to reduce risk-taking The next

question is if this result is generally true for all insurers For instant we are

particularly interested in whether or not this result is compatible with the franchise

value theory which predicts that high-franchise-value firms take less risk compared

with low-franchise-value firms and whether high-franchise-value firms take less risk

moderate risk or excessive risk in soft market In another words we are interested in

whether or not the risk-constraining effect of franchise value varies with underwriting

Franchise value has two sometimes incompatible effects on firm risk-taking

decisions On one hand insurers with high franchise value have incentives to avoid

losing their franchise value through bankruptcy by taking less risk On the other hand

high franchise value indicates large quasi-rents from renewal business for insurance

companies which motivate them to compete for market share so as to preserve the

existing franchise value In this case high-franchise-value firms may take more risk

Whether either of these two effects dominates in a particular stage of underwriting

cycle remains unknown A few factors discussed below may magnify

high-franchise-value insurersrsquo incentive to take more risk to preserve market share in

soft market

First customers tend to shop for lower price and choose low-pricing

underwriters over high-pricing underwriters In a soft market especially the deepened

soft market the demand for insurance is nearly saturated The insurers offering a

lower price could steal market share from high-pricing insurers Watching premiums

flow to other high-franchise-value insurers would revise their prices so that they are

more in line with those being offered elsewhere in the market so that they can keep

the existing business and the quasi-rent from renewal business Second the

expectation of the regular alternating of soft market and hard market creates moral

hazard of increasing risk-taking in the soft market When insurance companies

compete for market share through low-pricing marketing at expense of their

profitability in soft market they expect to be able to recoup their loss from the

following hard market where price rises This moral hazard may become more severe

for high-franchise-value firms compared to low-franchise-value firms because the

former group has stronger incentive to prevent market share (and resultant franchise

value) from reduction These factors may attribute to a weaker risk-constraining effect

of franchise value in a soft market than in a hard market

The above analysis shows that the underwriting cycle implies a varying nature of

competition and influence on the effect of franchise value on insurer risk-taking

incentives A hypothesis regarding the interactive relationships between franchise

value competition and underwriting cycle can be stated as follows

strategies are influenced by the underwriting cycle

3 Methodology

31 Multilevel Analysis

Multilevel analysis is a conditional modeling framework taking account of the

nested relationships (interactions) across different levels Multilevel models are

specified through conditional relationships where the effects described at one level

are conditional on the variables of the level above it Multilevel analysis has been

used increasingly in the fields of education demography and sociology to

simultaneously examine the effects of group- or macro-level and individual-level

variables on individual-level outcomes Multilevel method has many advantages over

single-level approaches in that it contains rich information and is less biased and more

robust A detailed discussion of advantages and limitations of the multilevel methods

can be found in Diez-Roux (2000)

The idea that individual firms may be influenced by both the market and

industry context makes the multilevel approach appealing to our analysis To

investigate the effect of market competition and the underwriting cycle on individual

firm risk-taking we specify two-level longitudinal models where individual firms are

level-1 units of observations and industry variables are level-2 variables

32 Regression Models

Hypotheses 1 described above suggests an interactive effect of franchise value

and competition on firm risk-taking Considering franchise value as firm-level effect

and competition as industry-level effect the nested relationship of franchise value in

the context of industry can be specified by the following two-level model The level-1

model can be written as

Ln(Risk) it = a0 i + a 1t + a2t (franchise value)it-1 + a3 (control variables)it + eit

Where there are i = 1 hellip n firms and t = 1hellipTi years

Prior empirical studies (Calem and Rob 1996 Staking and Babbel 1995 and

Bigg 2003) indicate a non-linear relationship between risk and franchise value

Therefore the measure of risk is logged to capture the potential nonlinearities14 We

use one-period lagged franchise value to investigate its effect on ex post firm risk

In equation (1) the intercept a0i is random among individual firms and a3 is

constant over all observations a1t and a2t are time-specific intercept and slope which

will be modeled by level-two variables One feature of multilevel model is that the

parameters in level-1 model themselves are also models

Our interest is to examine how the time-varying parameter a1t and a 2t vary over

market competition Then the level-2 model to specify a1t and a 2t can be written as

a1t = a11 (competition)t + e1t (11)

a2t = a20 + a21 (competition)t + e2 t (12)

Equation (11) represents the main effect of competition on dependent variable

and equation (12) represents the interaction effect of competition and franchise value

Substituting the level-2 models (11) and (12) into the level-1 model (1) yields the

combined equation

Ln(Risk)it = a0i + a11 (competition)t + [ a20 + a21 (competition)t ] (franchise

value)it-1 + a3 (control variables)it-1 + variance (13)

= a0i + [a11 + a1 (franchise value)it-1 ] (competition)t + a20 (franchise

value)it-1 + a3 (control variables)it + variance (14)

Where variance = [(franchise value)it-1 e2t+ e1t + eit] is mean-zero random

variables

From equation (13) itrsquos easy to see that the effect of franchise value on firm risk

which is represented by [ a20 + a21 (competition)t ] is conditional on competition A

positive coefficient a21 indicates that as competition increases the effect of franchise

value on risk tends to be positive Similarly by rearranging equation (13) to equation

(14) we see that the effect of competition on risk is also conditional on franchise

14 Another method to account for the non-linear relationship is to include a squared term of franchise value Our

samples show an ambiguous effect of the squared term of franchise value on the dependent variable Therefore a

logarithm relationship between franchise value and the dependent variable is employed

Equations (13) and (14) can be expressed in the following equation (15) which

is the model we need to fit A significant interaction term a21 (Competition)t (franchise

value)it-1 would indicate a support to Hypothesis 1

Ln(Risk)it = a0i + a11 (competition)t + a20 (franchise value)it-1 + a21 (competition)t

(franchise value)it-1 + a3 (control variables)it + variance (15)

Hypothesis 2 posits that the influence of competition and franchise value on firm

risk is conditional on the underwriting cycle To examine these conditional

relationships we incorporate the underwriting cycle effect into the model

In order to make interpretations easier we substitute equation (11) into to

equation (1) and rewrite the level-1 model as follows

Ln(Risk)it = b0i + b1t (franchise value)it-1 + b2t (competition)t + b3 (control

variables)it +ζit (2)

Now the variables of franchise value and competition all appear in the level-one

model Please note that b0i is a random effect for each firm b2t and b3t are

time-varying slopes To test Hypothesis 2 we specify coefficients b2t and b3t as

functions of underwriting cycle The level-2 model can be written as

b1t = b11 (competition)t + b12 (underwriting cycle)t +ζ1t (21)

b2t = b20 + b21 (underwriting cycle)t + ζ 2t (22)

Note that b1t depends on both competition and the underwriting cycle and b2t

depends on the underwriting cycle Substituting the level-2 models (21) and (22) into

level-1 model (2) we have

Ln(Risk)it = b0i + b10 (franchise value)it-1 + b11 (competition)t (franchise value)it-1

+ b12 (underwriting cycle)t (franchise value)it-1 + b20 (competition)t + b21

(underwriting cycle)t (Competition) + b3 (control variables)it-1 + variance

where variance = [(franchise value)it-1ζ2t + (competition)tζ3t +ζ3 it ]

To fit model (23) we need to estimate both six fixed effect b10 b10 b11 b12 b20

b21 and the parameters for control variables The measurement of all variables is

described later in section 35

4 Data and Variables

41 The CRSP sample and the NAIC sample

The empirical work is based on two panel datasets one obtained from The Center

for Research in Security Prices (CRSP) database and the other from National

Association of Insurance Commissioners (NAIC) database over the period of

1994-2003 CRSP database includes around 100 publicly-traded PampC insurance

companies and NAIC database provide historical financial information for about

3000 PampC (mutual and stock) insurers

The CRSP and NAIC databases employ different accounting practice rules and

provide different financial information The CRSP (merged with COMPUSTAT)

database using the Generally Accepted Accounting Principles (GAAP) provides

general information of balance sheet income statement cash flows as well as stock

price return and volume data for publicly-traded stock companies The NAIC

database using Statutory Accounting Principles (SAP) 15 contains detailed

information of annual financial statements including balance sheet income cash

flows detailed underwriting and investment exhibit and loss reserve development etc

for all types of insurance companies but does not collect stock price return and

volume data because most of the insurers are not publicly traded

We test the hypotheses on two samples for several reasons One is that if we

relied solely on the CRSP data base we would be limited in the number of insurers

observed Furthermore CRSP allows us to observe only publicly traded stock insurers

Using the NAIC data base allows us to rectify these two limitations however the

NAIC data base does not permit measurement of Tobins q which is the commonly

employed measure of franchise value Tobins q is based on stock values Undertaking

the analysis on both data sets allows us to succeed in achieving objectives across our

spectrum of purposes Neither data set is perfect yet with the combination we will

15 A set of accounting regulations prescribed by the NAIC for the preparation of an insuring firms financial statements SAP is regarded as more regulatory and conservative than the GAAP method of preparing financial statements

obtain the best information currently feasible

42 By-line Analysis

An important aspect of this study is to examine the influence of industry factors

(competition and underwriting cycle) on firm risk The insurance industry however is

segmented by different lines each with its own market and characteristics For

example the firms specializing in auto insurance may face different market conditions

compared to the firms specializing in commercial liability lines To control for the

differences across lines a by-line analysis is needed Particularly for this study we

examine four major lines separately personal auto liability insurance homeowner

insurance general liability insurance and commercial multiple peril insurance The

first two are personal lines and the other are commercial lines which in sum account

for more than 50 of total premium written by the property and casualty industry In

addition to their importance another reason to select these four lines is the different

risk nature of these lines

Since by-line data is only available in NAIC database the by-line analysis is only

conducted for the NAIC sample As for the CRSP sample the industry variables are

calculated based on the overall property and casualty industry This will not be an

issue for the CRSP sample because most of the publicly-traded insurance companies

included in our sample are group companies focusing on multiple lines

As many firms are engaged in more than one business line in order to reduce

overlaps across the samples the sample for each line is collected to include firms with

more than 30 premium written in a particular line

43 Measuring Firm Risk

Four measures of the level of firm risk-taking are employed in this study (i) the

volatility of stock return a market-base measure of equity risk (ii) Value at risk (VaR)

a downside risk measure (iii) Risk-Based Capital ratio a comprehensive measure of

insurance companiesrsquo insolvency risk used for regulation purpose and (iv) Leverage

an indicator of a firmrsquos financial strength We describe them in turn as follows

Standard deviation of stock returns

The first measure of risk we consider is standard deviation in stock return which

is the most commonly used market-based measure of risk16 Specifically we look at

the annualized standard deviation of a firmrsquos daily stock returns Given the

assumption of efficient market this would give a good measure of firm risk because

all the information about profitability and risk should be reflected in the stock price

This measure is unavailable for the most of the insurance companies however

because most insurers are not publicly traded stock companies

Value-at-Risk

Volatility is the most popular measure of risk The main problem with volatility

however is that it does not account for the direction of a stock returns movement a

stock can be volatile because it suddenly jumps higher17 But both investors and firms

care more about the odds of a big loss A few studies (Roy 1952 Baumol 1963 Levy

and Sarnat 1972 Arzac and Bawarsquos 1997) indicate that most investors are principally

concerned with avoiding a possible disaster and that the principle of safety plays a

crucial role in the decision-making process Some authors (Post and Vliet 2004 Baili

Demirtas and Levy 2006 Bali Nusret Yan and Zhang 2005 ) have used

Value-at-Risk (VaR) as a measure of downside risk and examined the relationship

between downside risk and stock return

VaR measures the maximum likely loss over a given time period at a given

confidence level In this study we use 1 VaR and 5 VaR to measure a firmrsquos

downside risk The estimation is based on the lower tail of the actual empirical

distribution We use the empirical distribution of daily returns during the past 12

months to estimate the level of 1 VaR or 5 VaR At 12-month horizon 1 VaR

and 5 VaR are defined as the daily return at the 1 percentile and 5 percentile of the

left tail of a firmrsquos stock return distribution It should be noted that the original VaR

16 For example Hamada (1972) Galai and Masulis (1976) French Schwert and Stambaugh (1987) Ghysels

Santa-Clara and Valkanov (2004) Galloway Winson and Roden (1997) among many others 17 See The Uses and Limits of Volatility by David Harper 2004

measures are multiplied by -1 before running our regressions The original maximum

likely loss values are negative stock returns since they are obtained from the left tail

of the distribution The downside risk measure 1 VaR and 5 VaR used in our

regression is defined as -1 times the maximum likely loss Therefore downside risk is

positively related with the value of VaR

The information needed (such as stock price) to calculate variance of stock return

and VaR is only available for publicly-traded stock companies which is provided by

the CRSP database Most of insurance companies however are non-publicly-traded

Therefore we need another measure of risk-taking for the non-publicly-traded

insurance companies contained by NAIC database

Risk-Based Capital Ratios

Risk-Based capital (RBC) is a method developed by the NAIC used to set capital

requirements for an insurance company considering the degree of risk taken by the

insurer The components of the RBC formula for PampC insurance companies include

asset risk underwriting risk credit risk and off-balance sheet risk As RBC contains

comprehensive information about an insurance companyrsquos financial strength it is used

as an important regulatory solvency prediction method by regulators in

property-liability insurance The higher the ratio of an insurerrsquos RBC to its actual

capital the lower possibility of insolvency The RBC system requires regulators to

take specified actions if an insurerrsquos actual capital falls below certain thresholds A

few studies (Grace Harrington and Klein 1995 1998 Cummins Grace and Philips

1998 Pottier and Sommer 2000) examine the performance of RBC ratio in predicting

insurer insolvency and show that when used in isolation RBC is not very successful in

predicting a firmrsquos failure 18 In spite of this limitation RBC ratio is still an

informative comprehensive measure of firm risk available for all insurance companies

18 Grace Harrington and Klein (1995 1998) and Cummins Grace and Philips (1998) find that Financial Analysis

and Surveillance Tracking (FAST) audit ratio system outperforms RBC ratios in predicting insurer insolvency

Pottier and Sommer (2000) find that the capital adequacy ratio used by AM Best outperforms RBC ratios but the

predictive ability of NAIC RBC improves dramatically when ranks of the RBC ratios are used rather than the

ratios themselves

Pottier and Sommer (2000) find that the rank of RBC compared to the absolute level

of RBC ratio is a better indicator of solvency risk Hence we use the rank of RBC

ratio as a measure of risk for the insurance companies contained by NAIC database

Higher rank of RBC ratio represents for higher risk

Leverage

Carson and Hoyt (1995) Grace Harrington and Klein (1998) find leverage and

surplus are strong indicators of insurer financial strength and insolvency risk We

employ leverage as one of measures of firm risk Particularly for this study using

leverage as a measure of firm risk has an advantage in that it provides the same risk

measure for the CRSP and NAIC samples We use the ratio of (total assets-total

surplus) total surplus as a measure of leverage To account for the different

accounting rules used by CRSP and NAIC we add GAAP adjustments to the statutory

capital (See Sommer 1996) Statutory capital is adjusted for pre-paid acquisition costs

by adding the product of expense ratio (the ratio of underwriting expenses to net

premiums written) and the unearned premium reserve to statutory surplus Also the

reserve for unauthorized reinsurance and the excess of statutory over statement

reserves are added to surplus These are standard GAAP adjustments

44 Measuring Franchise Value

Our purpose in measuring franchise value is to consider the true value of what is

lost if a firm becomes insolvent Tangible assets are only a portion of what is lost

franchise value represents the remainder of firm value above and beyond the value of

tangible assets Intangible assets typically generate from a firmrsquos (insurerrsquos in this case)

goodwill growth opportunities market power existing distribution networks and

renewal rights on existing business arrangements with reinsurers as well as

specialized knowledge about the risks generating from their existing book of business

These are not monetary assets yet nonetheless have great value to the firm as a going

concern

Tobinrsquos q

A commonly used measure for franchise value is Tobinrsquos q which is a ratio of the

market value of a firm to the replacement cost of its assets The higher a firmrsquos

franchise value the higher its q ratio Keeley (1990) argues that q is a useful proxy for

franchise value and presents evidence of a negative relationship between franchise

value and risk Smirlock (1984) argues that because q relates the market value of

firmsrsquo assets to their current cost it is an ideal ldquoall-inrdquo measure of the economic rents

Any pricing power irrespective of its source would be reflected in the market value

of a companyrsquos equity and thus assets but not in the cost of acquired assets

Furthermore Tobinrsquos q as a measure for franchise value has the advantage of allowing

comparability across different firm sizes

Determining the market value of a firm and the replacement cost of its assets is a

difficult task We need estimators to approximate the true value of q The most

commonly used estimator which is also employed in this study is defined as

following

q = (Market value of equity + book value of liabilities) book value of tangible

assets

The market value is set to equal the market value of equity plus the book value of

insurersrsquo liabilities This is reasonable since the value of a going concern is reflected

in the market value of the equity as the equity holders would be the beneficiaries not

the debt holders Previous studies have lacked a market value estimator of the

replacement cost of assets They generally use the book value of tangible assets For

the sample of publicly traded insurers (the CRSP sample) we will conduct the

analyses using this standard measure of franchise value

Ratings

Although Tobinrsquos q is a well-established measure of franchise value the majority

of insurers are not publicly traded and therefore the sample available when Tobinrsquos q

is used is very limited To develop a proxy for franchise value for both publicly and

non-publicly traded insurers in the NAIC database we consider using a firmrsquos rating

as a proxy of its franchise value

To find an appropriate proxy for franchise value of a non-publicly traded stock

company is difficult Financial ratings of a firm can be used as an instrument variable

for franchise value Yu et al (2003) employ AM Best ratings as a measure of

intangible assets and find a negative relationship between an insurerrsquos intangible asset

and asset risk In this research we also use transformed A M Bests financial rating to

measure a firmrsquos franchise value Instead of using the level of rating directly we

transfer the alphabetic rating levels A++ to F into percentile ranks of each rating level

according to the distribution of ratings in a year For example if 90 of all insurersrsquo

ratings are lower than A++ then the revalued number for A++ is 090 Therefore the

value of rating rank ranges from 0 to 1 Using percentile rank as a measure of

franchise has two advantages compared to absolute (number) level of ratings (1)

percentile rank better reflects the relative standing of a firmrsquos franchise value within

the industry than the number level (2) A firmrsquos rating may not change for a long time

but the rank of its rating thereby the value of a firmrsquos franchise relative to its peers

changes over years

45 Measuring Competition

We employ two measures for degree of competition each of which captures a

certain characteristic of market competition

Herfindahl Index

A commonly used measure of competition in the insurance literature is

HerfindahlndashHirschman index (HHI) (eg Joskow 1973 Grace and Klein 1999)

which measures the degree of market concentration As market concentration

increases economic theory suggests that competition decreases This line of

discussion derives from the economics of increased market power with a larger share

of the market concentrated in one or a few firms As a result HHI inversely related

with the degree of competition In this study HHI is equal to the sum square of each

firmrsquos market share at group level A transformed HHI (-1HHI + N)19 is employed

so that it positively correlated with the degree of competition

19 N is a positive number equal to the sum of maximum and minimum of HHI HHI is transformed in this way such that it positively relates with competition and keeps the original value range

Efficiency

While the Herfindahl index is often used and represents easily obtained measures

of competition an alternative representation may be found in measures of efficiency

Increased competition should force firms to operate more efficiently so that high

efficiency would indicate the existence of competition and vice versa Furthermore

increasing concentration actually could represent higher levels of competition if the

concentration occurs because more efficient insurers are purchasing less efficient

insurers and benefiting from the opportunity to earn profits through improved

efficiency (Fenn et al 2006)

Among various types of efficiency X-efficiency is generally expected to relate

closely to competition Leibenstein (1966) introduced the theory of X-inefficiency

generated from non-competition As a concept it may be summarized as follows for

a variety of reasons people and organizations normally work neither as hard nor as

effectively as they could In situations where competitive pressure is light many

people will trade the disutility of greater effort or search for the utility of feeling less

pressure and of better interpersonal relations (See Leibenstein 1966) Economic

theory suggests that increased competition forces insurance companies to drive down

their X-inefficiency Therefore X-efficiency increases in competition X-efficiency of

a firm is defined as the difference in costs between that firm and the best practice

firms of similar size and input prices Errors lags between the adoption of the

production plan and its implementation human inertia distorted communications and

uncertainty cause deviations between firms and the efficient frontier formed by the

best-practice life insurers with the lowest costs controlled for output volumes and

input price levels (Leibenstein 1966)

Various approaches (Non-parametric approaches or parametric approaches) are

available to estimate X-inefficiency (see for example Lozano-Vivas 1998) All

methods involve determining an efficient frontier on the basis of observed minimal

values rather than presupposing certain technologically determined minima Each

method using different assumptions and has advantages and limitations20

We use the data envelopment analysis (DEA) a non-parametric approach to

estimate firmsrsquo cost efficiency DEA is a nonparametric approach that has been used

extensively in a variety of industries (eg Cooper Seiford and Tone 2000) A few

insurance studies (eg Cummins and Weiss 2000 Cummins and Xie 2006) also use

DEA to estimate efficiency and productivity of insurance companies The descriptions

of DEA estimation methodology are presented in Cooper Seiford and Tone (2000)

The details of DEA cost efficiency estimation is explained in Appendix I After

calculating X-efficiency score for each firm industry X-efficiency is computed by the

average of all firmsrsquo X-efficiency score weighted by market share

45 Measuring the Underwriting Cycle

The underwriting cycle is generally demonstrated by the fluctuation of the

industry combined ratio which is equal to (Incurred Claims + Expenses) Premiums

earned Each line of insurance may well be subject to its own cycle21 The combined

ratio for each of the selected line is calculated separately

46 Control Variables

We also include a number of control variables that may be systematically related

to insurer risk-taking behavior These control variables are mainly firm characteristics

The industry factors like the shocks due to interest rate and stock market are

considered to be absorbed by the industry combined ratio which is used as a proxy of

industry performance

Firm Size

Firm size is a critical factor in insurer risk analysis Grace Harrington and Klein

(1995) and Cummins Grace and Phillips (1998) find that small firms are more

vulnerable to insolvency than large firms For our study the firm size is measured by 20 See Bikker et al (2006) and Cummins and Weiss (2000)rsquos discussion on the pros and cons of various estimation method of X-efficiency 21 See Sean M Fitzpatrick Fear is the Key A Behavioral Guide to Underwriting Cycle 10 CONN Ins L J 255 257 (2004)

logarithm of total assets

Ownership structure

A firms risk-taking behavior is highly influenced by its ownership structure First

due to the limited access to capital in the presence of financial stress mutual insurers

usually operate more conservatively than stock companies Regan and Tzeng (1999)

report that stock insurers are involved in more risk than mutual insurers Second

Ownership structure implies different managerial incentives As the literature on

agency theory demonstrates managers and owners of firms do not automatically have

consistent objectives leading to potential moral hazard problems Managers who are

not closely monitored andor whose objectives are not closely aligned with those of

the owners may take actions inconsistent with shareholder objectives With regard to

risk-taking behavior managers may take a more conservative strategy or a over

aggressive strategy than shareholders desire Prior research shows that ownership

structure serves as an internal mechanism to control managerial incentives The stock

form of ownership provides a superior mechanism (such as equity-based

compensation or stockholders monitoring incentives) for owners to monitor and

control managers Mutual ownership form eliminates the conflict between

policyholders and owners by merging the policyholder and ownership functions but is

less effective in monitoring and controlling managers (Mayers and Smith 1981) due

to the lack of interest conflict aligning mechanism between managers and owners

Born Gentry Viscusi and Zeckhauser (1995) assesses the responses by stock and

mutual insurers to changes in the underwriting environment from 1984 to 1991 and

find that stock companies are much quicker to exit unprofitable markets and expand

business in profitable markets This result implies that stock insurers are more flexible

in adjusting their strategies than mutual insurers To account for the effect of

ownership structure on insurer risk we use a dummy equal to 1 for mutual companies

and zero for stock companies

Group Affiliation

As noted in prior studies (eg Baranoff and Sager 2003) membership in a group

of affiliated companies can be an important factor for corporate operations Insurance

companies that belong to a group can benefit more from internal capital support and

risk diversification among the affiliated members of the group An affiliated firm is

expected to tend to take more risk than an unaffiliated firm A dummy variable equal

to 1 for companies in a group and equal to zero for unaffiliated companies is included

to control for difference due to corporate affiliation membership

Business Diversification

An insurance firm can reduce risk through internal diversification among different

product lines Therefore a more business diversified firm faces less risk than a less

diversified firm To control for the effect of business diversification we employ a

firmrsquos product line Herfindahl index based on the proportion of net premium written

by product lines The product line Herfindahl index is inversely related to business

diversification

Interest Rate

Interest rate is an important affecting factor for insurance industry Interest rate is

used to discount expected future claim and claim cost and directly affect the

investment profit Therefore interest rate affects not only the value of insurersrsquo

liabilities but also the value of insurersrsquo assets The higher the interest rate the fewer

assets needed to pay a future claim We use the return of one-year return of US

treasury as a measure of interest rate

Stock Index

Stock index is directly related to insurersrsquo investment income and consequent

operation profitability We use SampP 500 index as a reprehensive of stock index

Descriptions of the variables used in the regression model are summarized in

Table 41

Variable Description Variable Description

Dependent Variable

Risk Return_Std Annualized standard deviation of daily stock returns

Leverage Adjusted Leverage= log[ 10 +(total assets ndash adjusted surplus)adjusted surplus]

1 VaR -1 (1 percentile of the daily stock return of a year)

Rank_RBC Rank of RBC ratio

Leverage Log[10+(total assetsndashsurplus)surplus]

Independent Variable

Franchise value Q (market value of equity + book value of liabilities) book value of tangible assets

Rank_rate Percentile rank of rating levels A++ to F

Competition COMP -1HerfindahlndashHirschman Index +N

Efficiency Industry weighted average score of cost efficiency

Underwriting cycle UWC Combined ratio =(Incurred Claims + Expenses) Premiums earned

Control variables Size Log (market value of equity ) Size Log (total assets)

Mutual =1 if mutual =0 if stock

Group Group=1 if affiliated =0 if unaffiliated

Bus_Div Herfindahl index of a firms product line concetration

Interest Return of 1-year US treasury

Stock index SampP 500 stock index

The NAIC SampleThe CRSP Sample

Table 41 Descriptions of Variables

47 Summary Statistics

In this section summary statistics for the CRSP sample and the NAIC sample are

presented respectively

The CRSP Sample

The CRSP sample is obtained from CRSP database The final sample size is 987

observations and sample period is 1994-2003 All the firms in this sample are

publicly-traded stock companies and most of which are group companies They are

influenced by both the insurance industry conditions and the stock market changes

Table 42 gives the summary statistics of the industry-level variables over year used

for the CRSP sample Table 43 provides the summary statistics of the firm-level

variables in the CRSP sample

Table 42 Industry variables by year (the CRSP sample)

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Herfindahl index () 232 234 240 245 239 241 227 237 238 247

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

Table 43 Summary statistics of firm-level variables (the

CRSP sample N=987)

Variable Mean Std Dev Minimum Maximum

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Table 44 gives the correlations between each pair of firm-level variables It shows

that three stock risk measures Return_Std 1VaR and 5VaR are highly positively

correlated Leverage is inversely correlated with all these three measures indicating

that higher levered firms tend to have lower stock risk In addition stock risk

(measured by Return_Std 1VaR and 5VaR) reduces in firm size while leverage

increases in firm size The correlations between Q and all risk measures are

significantly negative indicating a relationship of higher franchise value with lower

level of risk without control of other factors

Table 44 Correlation of major variables (the CRSP sample)

Return_Std 1VaR 5VaR Leverage Q Size

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

Of particular interest is to examine if the relationship between franchise value and

firm risk-taking is influenced by competition and the underwriting cycle both of

which changes over time Table 45 provides the correlations of Q and various risk

measures over years which shows a significant variation The variations are reflected

in three aspects (1) the level of correlations fluctuates over time The correlations are

positive in some years and are negative in other years (2) the significance of the

correlations also changes over year (3) the correlation of leverage and Q is inverse to

other correlations of risk and Q This is consistent with the negative relationship

between leverage and stock risk shown in Table 44

Table 45 Correlations between risk and Q over years (the CRSP sample)

Return_Std Q 5VaR Q 1VaR Q Leverage QYEAR

Corr p-value Corr p-value Corr p-value Corr p-value

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

Figure 41 and Figure 42 displays the changing pattern of the correlations

between Leverage and Q as well as Return_Std and Q The significant values are

labeled differently from the insignificant values We see that the correlations are

particularly significant at two stages 1995-1996 and 2000-2002 Now we put the

graphs of Herfindahl index (Figure 43) and industry combine ratio (Figure 44) here

together to see what is special with these two periods Interestingly we find that

1995-1996 and 2000-2002 are around the turning points industry underwriting cycle

and represent for a soft market and a hard market respectively We find that the

correlations between leverage and Q are significantly negative during 1995-1996 and

positive during period 2000-2001 while the correlations between stock risk and Q are

the opposite

Figure 41 Correlation between Q and Leverge by year

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

-o- significant at 15 level -- insignificant

Figure 42 Correlation between Q and Return_Std by year

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Figure 43 HHI () for PampC industry

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Figure 44 Combined ratio () for PampC industry

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

In summary the descriptive statistics of the CRSP sample shows that (1) The

relationship between franchise value and risk varies with industry conditions

although it is generally negative during 10-year sample period (2) Two sub periods

1995-1996 and 2000-2002 need special attention because these periods are through

the turning points of the underwriting cycle and the franchise-value vs risk

relationship is substantially different between these two stages indicating an influence

of underwriting cycle on firm risk (3) leverage and firm stock risk are negatively

The NAIC sample contains in total 14429 firms for period 1995-200322 In this

sample only stock and mutual companies are included for the purpose of comparing

between them The firms with other types of ownership structure are dropped

Table 46 gives the summary statistics of the industry-level variables over year

used for the NAIC sample As we explained before since different lines may be

subject to their own market competition and the underwriting cycle we conduct a

by-line research for the NAIC sample and fortunately the information contained by

NAIC database allows this work To visualize the changing trend of the underwriting

cycle and competition measures Figure 45 -47 presents the graphs of combined ratio

Herfindahl index of market concentration and the industry weighted average

X-efficiency over years

22 Our original data is from 1994-2003 Since we use one-year lagged ratings as one of the explanatory variables the sample is available for years 1995-2003

Table 46 Industry variables by year (the NAIC sample)

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Auto personal liability 10738 10472 10183 10249 10825 11243 11338 11021 10324

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Commercial multiple peril 10078 10369 10046 10720 10753 10765 11147 9814 8937

General liability 12015 10990 10122 10107 9739 10256 11770 13098 11017

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Cost efficiency (weighted mean)

Homeowner 043 038 050 044 043 045 044 043 050

Figure 45 shows that auto personal liability homeowner and commercial multiple

perils have similar underwriting pattern with tough at year 1997 and peak point at

2001 General liability line undergoes a longer and deeper concave through 1996 to

2000 and then rise to the peak point 2002 This is consistent to the statement that

long-tail lines are subject to a longer cycle than short-tail lines due to the greater

uncertainty involved in the claim estimation and payment (Danzon et al 2004)

In Figure 46 we see that homeowner insurance market is the most concentrated

market among the four lines and commercial multiple peril market is the least

concentrated Itrsquos noticed that the market concentration of general liability line

undergoes quite a lot fluctuation over time compared to other lines

Figure 47 displays the cost efficiency of the four lines General liability stands out

as the least efficient line Commercial multiple peril line demonstrates highest

efficiency combined with its low concentration indicating the most competitive line

among the four The auto personal liability and homeowner insurance market are

shown to be more efficient than general liability market although less concentrated

than general liability Figure 46 and Figure 47 show that a less concentrated market

is not necessarily a more efficient or competitive market For this reason we used

both concentration and efficiency to measure degree of competition

Figure 45 Combined ratio by lines

1995 1996 1997 1998 1999 2000 2001 2002 2003

Auto personal liability

Homeowner

Commercial multiple peril

General liability

Figure 46 HHI () by lines

1995 1996 1997 1998 1999 2000 2001 2002 2003

Auto personal liabilityHomeowner Commercial multiple perilGeneral liability

Figure 47 Cost efficiency by lines

1995 1996 1997 1998 1999 2000 2001 2002 2003

Table 47 provides the summary statistics of the firm-level variables in the NAIC

sample

Table 47 Summary statistics of firm-level variables (the NAIC sample N=14429)

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Table 48 gives the correlations between each pair of firm-level variables The

alternative risk measures Rank_RBC and Leverage are positively correlated The

measure of franchise value and Rank_rate are negatively correlated with risk

measures In addition both firm rating and risk increase in firm size

Table 48 Correlation of variables (the NAIC sample)

Rank_RBC Leverage Rank_rate Size

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

Table 49 provides the correlations of ratings and risk measures over years With

sufficiently large sample size most of the correlations are shown significant

Although all the correlations are negative the value of correlations changes over time

Particularly we see that the negative relationship between leverage and ratings

become less significant and even insignificant in year 2000 and 2001 which is similar

to the descriptive statistics of the CRSP sample

Table 49 Correlations between risk and franchise value over years (the NAIC sample)

YEAR Leverage Rank_rate Rank_RBC Rank_rate

Corr p-value Corr p-value

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

In summary the descriptive statistics of NAIC sample shows that (1) General

liability insurance market shows different competition and underwriting cycle pattern

than the other three lines (2) The relationship between franchise value measures and

risk measures is generally negative but both the degree of correlation and significance

vary over time Particularly the relationship turns to less significant around year 2000

In the next section the regression results for the model with more control

variables will be presented to analysis how franchise value competition and the

underwriting cycle affect firm risk-taking simultaneously

5 Regression Results

This section presents the regression results for the CRSP sample and the NAIC

sample respectively Section 51 reports the results of the CRSP sample Section 52

presents the results of NAIC sample A summary and discussion of the results for both

the CRSP and the NAIC samples is provided in Section 53

51 Regression Results for the CRSP Sample

Table 511 presents the regression results of Model 1 with four alternative

dependent variables for the CRSP sample To interpret the results we fit the

parameters into the Model 1 For example when the dependent variable is Leverage

Model 1 is fitted as follows

Leverage it = a0i + (-103 + 028 COMPt ) Qit-1 + 064 COMPt + a3 (control

variables)it + eit (51)

We see that the slope of Q is composite of a negative intercept -284 and a

positive effect of competition 136 COMPt Note that the value of COMP ranges from

247 to 267 which makes the overall value of (-103 + 028 COMPt ) negative It

can be interpreted that for publicly-traded stock insurers franchise value and leverage

are generally negatively correlated but this relationship is weaken as competition

increases

Rearranging (41) gives the expression to easily see the effect of competition

Leverage it = a0i + -103 Qit-1 + (028 Qit-1 + 064 )COMPt + a3 (control

We see that the slope of competition on leverage (028 Qit-1 + 064 ) is positive

and increases in Q indicating a stronger positive relationship between competition

and leverage for a firm high-franchise-value firm These results are significant after

control of firm size stock index and interest rate

When the dependent variable becomes Return_Std 1VaR or 5VaR we also

find a positive interaction term of QCOMP but with low significance

Hypothesis 2 is tested by Model 2 the results of which are displayed in Table

512 In Model 2 the effect of franchise value and competition is made to condition

on underwriting cycle Before go into interpreting Model 2 note that in Table 512

the effect of Q COMP and QCOMP become insignificant after controlling with

underwriting cycle indicating an ambiguous interaction effect between underwriting

cycle franchise value and competition In both Table 511 and Table 512 we see

that firm risk is significantly influenced by stock index and interest rate

Table 511 Regression Results of Model 1 (The CRSP Sample N=984)Dependent variable

= LeverageDependent variable

=Return_StdDependent variable

= 1Var Dependent variable

= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ -103 00524 -587 04470 -446 00971 -518 02573COMP 064 00000 -120 00000 -088 00000 -103 00000QCOMP 028 00016 242 02938 187 01300 215 01503Size 018 00000 -021 00000 -022 00000 -022 00000Stock index 006 00000 007 00000 008 00000 007 00000Interest -065 06012 -191 00000 -194 00004 -231 00000-2log 2002 502 617 482AIC 2007 508 622 486

= 5VaRParameter Estimate P value Estimate P value Estimate P value Estimate P valueQ 662 02997 -291 05760 -050 09138 -280 05815COMP 006 06479 -283 00021 -306 00002 -243 00025QCOMP -634 01704 189 02735 112 00642 157 02268QUWC 729 02300 -154 08011 -198 04667 -089 08274COMPUWC 033 00912 151 02663 203 00137 130 01882Size 020 00000 -020 00000 -021 00000 -020 00000Stock Index 005 00008 007 00000 008 00000 006 00000Interest -081 08161 -231 00000 -264 00000 -278 00000-2log 1996 453 591 441AIC 2002 458 595 446

In summary the empirical results of the CRSP sample provide strong support to

Hypothesis 1 which positing that firm risk is jointly determined by franchise value

and competition but show little evidence for Hypothesis 2 Particularly for the

publicly-traded stock insurers firms with higher franchise value tend to have higher

leverage and stock risk especially when competition increases In addition we find

the stock risk (measured by Return_Std 1VaR 5VaR) decreases in firm size but

leverage increases in firm size

52 Regression Results for the NAIC Sample

As explained previously in Section 42 for the NAIC sample we conduct a

by-line analysis to account for the substantial difference between various lines

Particularly we examine four lines auto personal liability insurance homeowner

insurance commercial multiple perils insurance and general liability insurance

Section 521 to Section 524 presents regression results for each of the four lines in

order A comparison of the results across lines is provided in Section 525

521 Auto Personal Liability Insurance

The regression results of Model 1 for auto personal liability insurance is

presented in Table 5211 and Table 5212 Competition is measured by

concentration in Table 5211 and by efficiency in Table 5212

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -112 00000 -026 01674 Rank_rate 194 00000 021 00065COMP 032 00000 007 00000 Efficiency 427 00000 086 00000Rank_rateCOMP 016 00015 004 02283 Rank_rateEfficiency -430 00000 -109 00000Size 004 00000 005 00000 Size 004 00000 006 00000Bus_Div 000 00414 000 01566 Bus_Div 000 00005 000 02311Group 000 08905 -007 00000 Group 004 00001 -005 00002Mutual -002 00162 000 08121 Mutual -002 00882 002 03332Stock Index 000 01136 000 00004 Stock Index 000 01278 000 03968Interest 050 00000 051 00000 Interest 439 00000 120 00000-2log -6638 -3933 -2log -4096 -2762AIC -6635 -3928 AIC -4092 -2758

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -096 00000 -008 08229 Rank_rate 204 00000 004 00961COMP 046 00000 007 00000 Efficiency 571 00000 136 00526Rank_rateCOMP 018 00000 004 02468 Rank_rateEfficiency -360 00000 -013 00000Rank_rateUWC 015 01783 003 08976 Rank_rateUWC -040 00115 -002 04448COMPUWC -005 00000 001 07231 EfficiencyUWC -146 00000 025 07084Size 004 00000 005 00000 Size 004 00000 005 00000Bus_Div 000 00067 000 01540 Bus_Div 000 00008 000 01578Group -002 00257 -007 00000 Group 003 00013 -006 00000Mutual -002 01235 000 08208 Mutual 001 03981 002 03947Stock Index 000 00000 000 00005 Stock Index 000 02272 000 01946Interest -045 00000 053 00000 Interest 528 00000 086 00001-2log -6226 -2194 -2log -6826 -3394AIC -6218 -2186 AIC -6818 -3386

Dependent variable = Leverage

Dependent variable = Rank_RBC

Table 5211 Regression Results of Model 1 (NAIC Sample Auto personal liability N=3089)

When dependent variable is Leverage Table 5211 shows similar results as in

the CRSP sample The slope of Rank_rate is given by (-112+ 016 COMP) which is

generally negative and increases in COMP It indicates that the negative effect of

Rank_rate on Leverage decreases as market become less concentrated The slope for

COMP (032 +016 Rank_rate) is positive and increases in Rank_rate

Shown by Table 5212 when dependent variable is the rank of RBC ratio the

results are similar but with lower significance Table 5212 reports the results for

Model 1 when the competition is measured by Efficiency the industry weighted

average of X-efficiency Higher efficiency indicates higher degree of competition

Since the value of Efficiency for auto liability insurance is less than 05 the

overall relationship between ratings and firm leverage (194 + -43 Efficiency ) is

negative especial when industry efficiency increases As for the influence of

efficiency on leverage given by the slope (427 + -43 Rank_Ratet-1 ) we see that

firm with lower ratings tends to increase its leverage as the industry efficiency

improves These relationships are about the same when the dependent variable is

Rank_RBC

Note that the results regarding the effect of franchise value and competition on

firm risk are different between Table 5211 where competition is measured by

concentration and Table 5212 where competition is measured by efficiency This

leads to a question that which one concentration or efficiency is a better proxy of the

degree of competition But in either case the interaction term of franchise value and

competition is significant indicating a support to Hypothesis 1

The results of Model 2 for auto personal liability insurance are shown in Table

5213 and Table 5214 When the dependent variable is Leverage and competition is

measured by concentration as in Table 5213 Model 2 is fitted as follows

Leverageit = b1 i + b2t Rank_rate it-1 + b3t COMPt + b4 (control variables)it +ζit

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

We see that the slope of Rank_rate increases in UWC indicating that when the

industry is less profitable (higher industry combined ratio) the relationship of

franchise value and leverage tends to be positive The negative interaction term (-005

UWCCOMP) indicates an increasing negative effect of competition on leverage as

industry becomes less profitable

When dependent variable is Rank_RBC the major explanatory variables become

insignificant suggesting an ambiguous influence of underwriting cycle on the

relationships between franchise value competition and risk

In Table 5214 the measure of competition is Efficiency instead of COMP

Similar to the results of Model 1 the sign for parameters of Rank_rate Efficiency and

Rank_rate Efficiency reserves compared to those in Table 5213 The interaction

terms with UWC are significantly negative when the dependent variable is leverage

but are less significant when dependent variable becomes Rank_RBC which is as

same as in Table 5213

As for the effect of control variables firm risk increases in firm size Insurers

with more diversified business have a significant lower leverage Firms belong to a

group tend to have higher leverage but lower insolvency risk measured by RBC ratio

Mutual companies are shown to have lower leverage Firm risk is found sensitive to

the interest rate but not to stock index

In summary for the sample of auto personal liability insurance the interaction

effect between competition and franchise value is significant which is consistent to

the Hypothesis 1 The different measures of competition concentration and efficiency

lead to opposite sign of the interaction term of competition and franchise value The

risk-constraining effect of franchise value decreases in competition as if the degree of

competition is measured by concentration but increases in competition if degree of

competition is measured by efficiency The effect of franchise value and competition

on firm leverage is significantly influenced by industry combined ratio providing a

support to Hypothesis 2 When the market is less profitable (combined ratio is higher)

the risk-constraining effect of franchise value and the risk-increasing effect of

competition tends to be dampened However this result is not significant when the

risk is measured by the rank of RBC ratio

522 Homeowner Insurance

Homeowner insurance is a personal line with combined property and liability risk

Compared to auto personal liability homeowner insurance is a shorter tailed line with

less uncertainty of loss expenses Many mutual insurance companies focus on

homeowner insurance Particularly in our sample of homeowner insurance 62 of

the firms are mutual companies As we discussed before different ownership structure

has different implications for corporate management and risk decisions The test

results of the homeowner insurance sample largely exhibit risk-taking behavior of

mutual insurers

Table 5221-Table 5224 presents the test results for the sample of homeowner

insurance

Compared with the sample of auto personal liability the results of the homeowner

insurance sample has two major differences (1) we see a negative interaction term of

franchise value and competition which indicates that risk-constraining effect of

franchise value is magnified as competition increases (2) The signs of the major

variables are consistent between the two competition measures COMP and Efficiency

This suggests that industry efficiency improves as the market becomes less

concentrated and therefore either efficiency or concentration is a good measure of

competition for homeowner insurance market

With respect to the effect of underwriting cycle the interaction terms related with

UWC are found significant in both Table 5223 and Table 5224 The negative

interaction term of Rank_rate UWC and the positive interaction term CompUWC

indicates that when industry is less profitable the risk constraining effect of franchise

value and the risk-increasing effect of competition tend to be strengthened

Table 5221 Regression Results of Model 1(NAIC Sample Homeowner N=1329)

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 469 00000 209 00000 Rank_rate 456 00000 040 00005COMP 032 00000 006 00000 Efficiency 475 00000 073 00000Rank_rateCOMP -064 00000 -033 00000 Rank_rateEfficiency -1026 00000 -163 00000Size 003 00000 006 00000 Size 003 00000 008 00000Bus_Div 001 00844 000 08966 Bus_Div 002 00187 000 08275Group 001 02072 -002 01813 Group 001 03152 -002 02095Mutual 001 03328 000 08761 Mutual 002 00497 004 00839Stock Index 000 00000 000 00071 Stock Index 000 01261 000 00097Interest 026 00009 010 06019 Interest 164 00000 015 03765-2log -3386 -1340 -2log -990 -1270AIC -3382 -1335 AIC -983 -1266

Table 5223 Regression Results of Model 2 (NAIC Sample Homeowner N=1329)

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 439 00000 218 00004 Rank_rate 1056 00000 178 00000COMP 030 00000 004 00007 Efficiency -151 00000 -063 00009Rank_rateCOMP -058 00000 -030 00000 Rank_rateEfficiency -1036 00000 -186 00000Rank_rateUWC -016 00709 -026 00052 Rank_rateUWC -546 00000 -120 00000COMPUWC 003 00000 002 00721 EfficiencyUWC 649 00000 160 00000Size 003 00000 006 00000 Size 004 00000 007 00000Bus_Div 001 00982 000 08984 Bus_Div 002 00054 000 09991Group 001 03407 -002 02033 Group 001 03551 -002 02017Mutual 001 03730 000 08675 Mutual 002 02407 001 06905Stock Index 000 00000 000 00077 Stock Index 000 00000 000 00000Interest 045 00000 007 07583 Interest -112 00000 -057 00061-2log -3390 -1332 -2log -2031 -1327AIC -3386 -1328 AIC -2027 -1322

523 General Liability Insurance

General liability insurance (including product liability) is commercial liability

insurance long-tail insurance with great uncertainty and complexity Most companies

with high volume of business in general liability are organized in form of stock

ownership rather than mutual ownership Particularly in our sample 93 of these

firms are stock companies Hence the results regarding this sample provide

information about the risk-taking behavior of stock companies most of which are

non-publicly traded stock firms The test results for general liability insurance are

presented in Table 5231 ndash Table 5234

The results with respect to the interaction effect between franchise value and

competition shown by Table 5231 and Table 5232 are similar as in the sample of

auto personal liability insurance A positive Rank_rateCOMP and a negative

Rank_rateEfficiency are found

The effect of underwriting cycle is given by Table 5233 and Table 5234 In

both tables we see a negative interaction term of Rank_rate UWC which means the

slope of Rank_rate decreases in UWC and a positive interaction term CompUWC

indicates the slope of Comp decreases in UWC These results indicate that other

things being equal when industry is less profitable the risk constraining effect of

franchise value and the risk-increasing effect of competition tend to be strengthened

This is the same as what we observe in the sample of homeowner insurance but with

greater significance It indicates that for insurers focusing on general liability

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -113 00000 014 00255 Rank_rate 285 00000 -008 02949COMP -026 00000 -002 00031 Efficiency 650 00000 032 00035Rank_rateCOMP 024 00000 002 00815 Rank_rateEfficiency -1016 00000 -053 00238Size 006 00000 012 00000 Size 006 00000 012 00000Bus_Div 000 01662 000 00011 Bus_Div 000 04625 000 00019Group 006 00098 -005 00326 Group 005 00248 -004 00395Mutual 010 00051 009 00233 Mutual 006 00555 008 00452Stock Index 000 00000 000 00009 Stock Index 000 00000 000 00087Interest 702 00000 025 01699 Interest 192 00000 009 06030-2log -4220 -3187 -2log -4226 -3194AIC -4212 -3181 AIC -4218 -3186

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -016 04782 003 08017 Rank_rate 391 00000 021 02112COMP -040 00000 000 09065 Efficiency 037 03705 -023 03947Rank_rateCOMP 029 00000 001 02782 Rank_rateEfficiency -831 00000 -060 00197Rank_rateUWC -110 00000 -012 00865 Rank_rateUWC -146 00000 -024 00367COMPUWC 011 00000 001 01102 EfficiencyUWC 534 00000 055 00219Size 006 00000 012 00000 Size 005 00000 012 00000

Bus_Div 000 02410 000 00010 Bus_Div 000 09240 000 00017Group 005 00167 -005 00361 Group 003 00974 -005 00236Mutual 009 00092 009 00206 Mutual 003 02272 008 00439Stock Index 000 00000 000 00040 Stock Index 000 00000 000 00115Interest 647 00000 031 01127 Interest 185 00000 003 08609-2log -4226 -3194 -2log -4226 -3194AIC -4218 -3186 AIC -4218 -3186

Table 5231 Regression Results of Model 1(NAIC Sample General Liability N=1531)

Table 5233 Regression Results of Model 2 (NAIC Sample General Liability N=1531)

insurance the effect of franchise value and competition on risk-taking is more

influenced by the industry profitability

524 Commercial Multiple Perils Insurance

Commercial multiple perils insurance is a commercial insurance with combined

property and liability risk Itrsquos a shorter tailed insurance compared to general liability

insurance The test results for the sample of commercial multiple perils insurance are

provided in Table 5241 ndash Table 5244

Table 5241 and Table 5242 present the test results for Model 1 Similar to the

sample of homeowner insurance a negative interaction term of franchise value and

competition is found

With regard to the effect of underwriting cycle the interaction term of

(Rank_rateUWC) is somewhat insignificant indicating an ambiguous influence of

underwriting cycle on the relationship of franchise value and firm risk In Table

5244 the interaction term (EFFICENCYUWC) is found significantly negative

indicating a decreasing risk-increasing effect of competition as industry efficiency

increases

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate -013 01942 -003 07161 Rank_rate 389 00000 004 07105COMP 090 00000 018 00000 Efficiency 471 00000 046 00000Rank_rateCOMP -001 08823 -024 00380 Rank_rateEfficiency -821 00000 -065 00050Size 007 00000 010 00000 Size 006 00000 010 00000Bus_Div 000 09090 000 01725 Bus_Div 000 08621 000 01651Group 004 00158 003 01229 Group 003 00630 003 01390Mutual 002 03002 -001 07656 Mutual 000 08174 000 08845Stock Index 000 00000 000 00053 Stock Index 000 00012 000 06968Interest 584 00000 078 00003 Interest 069 00050 002 09195-2log -718 -952 -2log -738 -955AIC -714 -948 AIC -732 -950

Parameter Estimate P value Estimate P value Parameter Estimate P value Estimate P valueRank_rate 075 00715 -018 00003 Rank_rate 076 00091 -075 00043COMP 033 00000 018 00037 Efficiency 883 00000 157 00000Rank_rateCOMP -054 00000 024 04958 Rank_rateEfficiency -622 00000 -032 02588Rank_rateUWC 016 05517 034 01775 Rank_rateUWC 211 01934 060 00985COMPUWC 078 00150 -009 02843 EfficiencyUWC -461 00000 -116 00632Size 005 00000 009 00000 Size 005 00000 009 00000Bus_Div 000 02381 000 01080 Bus_Div 000 04489 000 01229Group 003 00460 003 01945 Group 002 01361 003 02108Mutual -001 06367 -002 04308 Mutual 000 09888 -001 06910Stock Index 000 00000 000 00428 Stock Index 000 01092 000 03731Interest 1158 00000 215 00000 Interest 424 00000 081 00069-2log -1192 -990 -2log -984 -974AIC -1186 -986 AIC -980 -970

Table 5244 Regression Results of Model 2 (NAIC Sample Commerical Multiple Perils N=1085)

Table 5241 Regression Results of Model 1(NAIC Sample Commerical Multiple Perils N=1085)

525 Summary of the By-line Analysis

As we are primarily interested in the interaction effect between franchise value

competition and underwriting cycle on insurer risk-taking the following Table 5251

gives a summary of the signs of the interaction terms for each of the selected lines

Since we have two measures of risk and two measures of competition the results are

reported for each combination of them

Table 5251 Sign of interaction terms by lines

Sample Rank_rate

Rank_rate

(Leverage COMP) (Rank_RBC COMP)

Auto personal liability + + - - NS NS

Homeowner - - + - - +

General Liability + - + + - +

Commerical Multiple

Peril - NS + - NS NS

(Leverage Efficiency) (Rank_RBC Efficiency)

Auto personal liability - - - - NS NS

General Liability - - + - - +

Commerical Multiple

Peril - NS - - + -

NS = insignificant

When competition is measured by concentration the samples of auto personal

liability and general liability shows a positive interaction term of franchise value and

competition suggesting a decreasing risk-constraining effect of franchise value as

competition increases For the samples of homeowner and commercial multiple perils

the interaction term of franchise value and competition is negative indicating

increasing risk-constraining effect of franchise value as market become more

competitive When the competition is measured by efficiency all lines show a

negative interaction term of franchise value and competition

With regard to the underwriting cycle homeowner insurance and general

liability insurance are shown to be more significantly influenced by underwriting

cycle than the other two lines Risk-constraining effect of franchise value and

risk-increasing effect of competition tend to be strengthened in less profitable market

In summary the by-line test results for the NAIC sample show that the effect of

franchise value on firm risk is significantly conditional on the degree of competition

and vice versa providing strong support to Hypothesis One The specific relationship

regarding the interaction effect between franchise value and competition varies across

lines and different measures of competition We also find support for Hypothesis two

especially for the samples of homeowner insurance and general liability insurance

53 Discussion of Results

In previous sections the two research hypotheses are empirically tested

respectively for the CRSP Sample and each of the selected lines for the NAIC sample

This section provides a comparison between different samples and a discussion of the

relationship between ownership structure and insurer risk-taking

531 The CRSP Sample vs the NAIC Sample

The CRSP sample contains publicly-traded stock insurance companies most of

which are group companies The NAIC sample contains mutual and stock companies

at individual firm level The regression results for the CRSP sample are similar to the

results for the samples of general liability and auto personal liability which are largely

composed of non-publicly-traded stock companies in that a positive interaction term

of franchise value and competition is found when the risk is measured by leverage and

competition is measured by concentration This indicates a reduced risk-constraining

effect of franchise value as competition increases The results also suggest that the

effect of franchise value and competition on firm risk is less influenced by the

underwriting cycle for publicly-traded stock insurers than for non-publicly-traded

stock insurers

532 Stock Company vs Mutual Company

Insurance studies (eg Mayer and Smith 1981) find evidence for the relationship

between the ownership structure and choice of business lines stock insurers tend to

involved in more complex lines and mutual insurer usually focus on less complex

lines This is due to that mutual companies have less control on managerial behavior

than stock companies Table 5321 shows percentages of the number of and premium

written by mutual firms in our sample for each line and confirms this claim The

sample of homeowner insurance mainly consists of small-size mutual companies

while the firms in the sample of general liability insurance are nearly all stock

companies

Table 5321 Mutual firms in the NAIC sample

Sample of number of premium written

Auto personal liability 17 43

Homeowner 62 11

General Liability 7 07

Commercial Multiple Peril 30 26

The comparison between the sample of homeowner insurance and the sample of

general liability insurance sheds light on the difference between mutual and stock

companies in terms of risk-taking behavior with a control of the endogenous variance

across business lines First in Table 5251 we see a negative interaction term of

franchise value and competition for homeowner insurance when competition is

measured by concentration but a positive interaction for general liability insurance It

indicates that mutual insurers have stronger incentive to protect their franchise value

by reducing risk than stock insurers when market becomes more competitive Second

comparing Table 5223 and Table 5224 (the sample of homeowner insurance) with

Table 5233 and Table 5234 (the sample of general liability insurance) we see that

although the signs of the interaction terms related with UWC are same but the sample

of general liability insurance show larger magnitude of the slope and higher

significance with the interaction terms of underwriting cycle This suggests that stock

insurers reacts more to the industry profitability than mutual insurers This is to some

extent consistent with the evidence reported by (Born et al 1995) who find that stock

insurers respond to the industry changes more efficiently than mutual insurers

6 Conclusions

This section consists of two parts Section 61 provides a summary of the main

findings of this research Section 62 contains a discussion of potential limitations

underlying this study and suggestions for future research

61 Summary of the Study

The purpose of this study is to examine the influence of franchise value and

competition on insurer risk-taking behavior Franchise value and competition provide

two important and contrary incentives of corporate risk-taking Franchise value is

believed to have a risk-constraining effect on firm risk because of the inability to

capture it in the case of bankruptcy On the other hand competition generally induces

firms to take more risk in order to maintain and even improve their position whether

high franchise value or not Prior empirical studies however show ambiguous

evidence regarding the effects of franchise value and competition on risk which

motivates the current study

The main contributions of this research can be summarized as follows First this

study examines the effect of franchise value and competition on risk-taking behavior

simultaneously Although franchise value provides an incentive for firms to reduce

risk firms with high franchise value are also motivated to protect franchise value

from reduction in competition and may consequently increase risk as an effort to

maintain their existing market position Therefore the risk-constraining effect of

franchise value should be examined in the context of market competition Second this

paper incorporates the influence of the underwriting cycle to examine if the effect of

franchise value and competition on firm risk-taking is influenced by this macro effect

Third we conduct a by-line analysis which not only allows a comparison across lines

but also better controls the endogenous variation in insurer risk-taking across lines

Lastly we employ both concentration and efficiency as a measure of competition

Different measures of competition provide more information about the role of

competition in insurer risk-taking

Two hypotheses are empirically tested The first hypothesis is that franchise value

and competition jointly affect insurer risk-taking The second hypothesis is that the

effect of franchise value and competition on insurer risk-taking is influenced by the

underwriting cycle

The empirical analysis provides strong support to the first hypothesis Our results

show that the risk-constraining effect of franchise value is conditional on the degree

of competition and vice versa When competition becomes intense firms with high

franchise value appear to increase risk in order to maintain their existing market

position We find evidence of this tendency for stock insurers but not for mutual

insurers When market becomes more competitive the risk-constraining effect of

franchise value tends to be strengthened for mutual insurers It indicates that as

competition increases mutual insurers have stronger incentive to protect their

franchise value by reducing risk than stock insurers

We also find support for the second hypothesis and for differences across lines

For homeowner insurance and general liability insurance the evidence shows that

when the market become less profitable both the risk-constraining effect of franchise

value and risk-increasing effect of competition tend to be stronger For auto personal

liability insurance and commercial multiple perils insurance the influence of the

underwriting cycle is ambiguous

62 Limitations and Further Research

There are several potential limitations in the study These limitations should be

kept in mind when interpreting our results they also lead to potential for future

research

First the measurement of franchise value still has room to improve especially for

non-publicly traded insurance companies It is particularly important for the insurance

industry to find a better measure of franchise value because the majority of insurance

companies are non-publicly traded firms Existing literature has made little effort in

this area

Second due to data limitation our 9-year study period contains only one soft and

one hard market period If this particular cycle was unusual the results will be

unrepresentative We generalize therefore with caution

Third our two measures of competition concentration and efficiency lead to

different results regarding the sign of interaction effect between franchise value and

competition Recent work (Fenn et al 2006) may offer some indication for the

reasons for the opposite results of these two measures yet further study is needed

Appendix I Compute Cost efficiency Using DEA Method

This study estimate a firmrsquos cost efficiency using a Data Envelopment Analysis

(DEA) approach DEA is a linear programming method for assessing the efficiency

and productivity We use input-oriented distance function to estimate a firmrsquos cost

efficiency The input-oriented model of DEA to for cost efficiency can be defined as

follows

kkikix

xwMini 1

St sumge i kiiki xx λ kforall

sumge i niini yy λ nforall

0geiλ iforall

Where X denotes the input vector W denotes the input price vector and Y

denotes the output factor K is the number of inputs N is the number of output and i is

the number of firms The X-efficiency score is given by the ratio of frontier cost to

actual cost where X is the solution of the above minimizing

problem A score of 1 indicates that the firm is fully cost efficient

i XWXW =φ

Defining inputs and outputs and their prices is an important step in efficiency

analysis There has been an extensive and unresolved debate in the literature about the

appropriate measure of insurance firmsrsquo inputs and outputs (for a survey see

Cummins and Weiss 2000) The product provided by insurers to their policyholders

can best be viewed as the expected present value of the future claims that might be

paid on those policies Follow the method of Fenn et al (2006) we use net loss

incurred as a proxy for an insurance companyrsquos output

Two types of inputs are employed in our study capital and labor The input

quantity of capital is defined as the shareholderrsquos capital and reserves plus total

borrowing from outsiders reported in the balance sheet The input price for capital is

measured by the one-year interest rate of US treasury The input of labor

(wagesquantity of labor) is measured by the total expenses on the administration

agent and brokers claim service and employee wages and benefit SAS procedures

are employed to implement the model

Reference

Baker Tom 2005 Medical Malpractice and the Insurance Underwriting Cycle Depaul Law Review 54

Baranoff Etti and Sager Thomas 2003 the Relations Among Organizational and

Distribution Forms and Capital and Asset Risk Structures in the Life Insurance Industry Journal of Risk and Insurance 70 (3)375-400

BarNiv R and J McDonald 1992 Identifying Financial Distress in The Insurance

Industry A Synthesis of Methodological and Empirical Issues Journal of Risk and Insurance 59 543-574

Beck Thorsten Asli Demirguc-Kunt and Ross Levine 2003 Bank Concentration and

Crisis Working paper University of Minnesota from SSRNcom BoltWilko and Alexander F Tieman Banking Competition Risk and Regulation

Scandinanvia Journal of Economics 106(4) 783-804 Boyd John H and Gianni De Nicolo 2004 the Theory of Bank Risk Taking and

Competition Revisited working paper from SSRNcom Boyd John H De Nicoloacute Gianni 2005 The Theory of Bank Risk Taking and

Competition Revisited Journal of Finance 60(3) 1329-1343Bottom of Form Browne Mark J and Robert A Hoyt 1994 Economic and Market Predictors of

Insolvencies in the Property-Liability Insurance Industry Journal of Risk and Insurance 62 309-327

Browne Mark J James M Carson and Robert A Hoyt 1991 Economic and Market Predictors of Insolvencies in the Life-Health Insurance Industry Journal of Risk and Insurance 66 643-659

Carletti Elena and Philipp Hartmann 2002 Competition and Stability Whats Special

About Banking working paper available at SSRN Choi byeongyong paulMary A Weiss 2005 An Empirical Investigation of Market

Structure Efficiency and Performance in Property-Liability Insurance Journal of Risk and Insurance 72(4) 635-673

Cummins David and Neil Doherty 2002 Capitalization of the Property-Liability

Insurance Industry Overview Journal of Financial Services Research 2112 5-14

Cummins J David and David Sommer1996 Capital and Risk in Property-Liability Insurance Markets Journal of Banking and Finance 20 1069-1092

Cummins J David and Xiaoying Xie 2006 Mergers and acquisitions in the

USProperty-Liability Insurance Industry productivity and efficiency effects working paper University of Pennsylvania Philadelphia

Cummins J David 1988 Risk-Based Premiums for Insurance Guaranty Funds Journal

of Finance 43(4) 823-839 Cummins J David and Mary A Weiss 2000 Analyzing Firm Performance in the

Insurance Industry Using Frontier Efficiency and Productivity methods in Georges Dionne ed Handbook of Insurance (Norwell MA Kluwer Academic Publishers)

Cummins J David Scott E Harrington and Robert Klein 1999 Insolvency

Experience Risk-Based Capital and Prompt Corrective Action in Property-Liability Insurance working paper Wharton Research Center Financial Institutions Center

De Jonghe Olivier and Rudi Vander Vennet 2005 Competition Efficiency and Agency

Costs An Analysis of Franchise Values in European Banking working paper available at SSRN

De Leeuw J amp Kreft IGG 2001 Software for multilevel analysis 2 A H Leyland amp

H Goldstein (Eds) Multilevel modelling of health statistics187-204

Demsetz Rebecca S Philip E Strahan 1997 Diversification Size and Risk at Bank

Holding Companies Journal of Money Credit amp Banking9(3) 300-313 Diez-Roux Ana V 2000 Multilevel Analysis in Public Health Research Annual

Reviews of Public Health 21171-192 Emrouznejad Ali 2000 An Extension to SASOR for Decision System Support

Statistics and Data Analysis Paper 274-25 Fenn Paul Dev Vencappa Stephen Diacon Paul Klumpes and Chris OrsquoBrien 2006

Market structure and the efficiency of European insurance companies a stochastic frontier analysis working paper available at SSRN

Frees Edward W 2004 Longitudinal and Panel Data Analysis and Applications for the

Social Sciences Cambridge University Press

Fung Hung-Gay Gene C LaiGary A Patterson Robert Witt 1998Underwriting Cycles in Property and Liability Insurance An Empirical Analysis of Industry and By-Line Data Journal of Risk amp Insurance 65(4) p539-561

Green Richard C and Eli Talmor 1985 The Structure and Incentive Effects of

Corporate Tax Liabilities The Journal of Finance 40 (4)1095-1114 Harrington Scott 2004 Tort Liability Insurance Rates and the Insurance Cycle

Brookings-Wharton Papers on Financial Services Jayaratne Jith and Philip E Strahan 1998 Entry restrictions industry evolution and

dynamic efficiency evidence from commercial banking Journal of Law amp Economics 41(1) 239-273

John Kose Lubomir P Litov and Bernard Yin Yeung 2004 Corporate Governance

and Managerial Risk-Taking Theory and Evidence available at SSRN Keeley MC 1990 Deposit Insurance Risk and Market Power in Banking American

Economic Review 80 1183-1200 Kim Jee-Seon and Edvard W Frees 2005 Fixed effects estimation in multilevel

models working paper available at SSRN MaksimovicVojislav and Josef Zechner 1991 Debt Agency Cost and Industry

Equilibrium Journal of Finance 5 1619-1643 Marcus Alan J 1984 Deregulation and bank financial policy Journal of Banking amp

Finance 8 (4) 557-565 Merton H Miller 1977 The Wealth Transfers of Bankruptcy Some Illustrative

Examples Law and Contemporary Problems 41 (4) 39-46 Niinimaki Juha-Pekka 2004The effects of competition on banks risk taking Journal

of Economics Vol81 199-222 Rampini Adriano A 2004 Entrepreneurial Activity Risk and the Business

CycleJournal of Monetary Economics 51 555-573 Rice Nigel and Andrew Jones 1997 Multilevel Models and Heath Economics Health

Economics 6 561-575 Saunders Anthony and Berry Wilson 2001 An Analysis of Bank Charter and Its

Risk-Constraining Incentives Journal of Financial Services Research 1923 185-195

SingerJudith D1998 Using SAS PROC MIXED to fit multilevel models hierarchical models and individual growth models Journal of Educational and Behavioral Statistics 24 (4) 323-355

Staking Kim B and David FBabbel 1995 the Relationship between Capital Structure

Interest Rate Sensitivity and Market Value in the Property-liability Insurance Industry Journal of Risk and Insurance 62 (4) 690-718

Vlaar Peter JG 2003 On the Influence of Capital Requirements on Competition and

Risk Taking in Banking EFA 2003 Annual Conference Paper No 136 available at SSRN

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

ABSTRACT

Franchise value provides a risk-constraining incentive to firms while competition

generally induces firms to take more risk Existing empirical evidence on these

relationships however have been mixed motivating us to reexamine these issues

This study adds to the literature by considering the influence of franchise value

and competition on risk-taking simultaneously rather than separately importantly

including an interaction term between the two factors to account for their joint effect

We further add to the literature by incorporating the effect of the underwriting cycle

on these relationships

Our main findings are that the effect of franchise value and competition on

insurer risk-taking is jointly determined and conditional on the underwriting cycle

The specific relationships between the influences of franchise value competition and

the underwriting cycle vary across different business lines and ownership structures

1 Introduction

overall risk-taking

13 Research purpose

relationships

the same time

21 Firm Risk

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

1 Introduction

overall risk-taking

13 Research purpose

relationships

the same time

21 Firm Risk

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

overall risk-taking

13 Research purpose

relationships

the same time

21 Firm Risk

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

13 Research purpose

relationships

the same time

21 Firm Risk

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

relationships

the same time

21 Firm Risk

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

21 Firm Risk

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

following part

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

hypothesis

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

rate increases

dimensions

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

soft market

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

3 Methodology

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

combined equation

variables

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

42 By-line Analysis

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Value-at-Risk

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

ratios themselves

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Leverage

concern

Tobinrsquos q

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

following

assets

Ratings

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

changes over years

Herfindahl Index

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Efficiency

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Firm Size

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Ownership structure

Group Affiliation

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

diversification

Interest Rate

Stock Index

Table 41

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Dependent Variable

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

The CRSP Sample

Variable 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio () 1085 1065 1058 1016 1056 1078 1101 1157 1072 1001

Stock index 461 547 675 876 1088 1331 1420 1186 989 968

Interest rate () 232 840 551 624 614 431 699 744 341 147

CRSP sample N=987)

Return_Std 003 002 001 025

1VaR 007 005 000 073

5VaR 004 003 000 030

Leverage 240 164 -344 910

Q 109 023 049 506

Size 598 211 -142 1143

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Return_Std 1 092 095 -011 -010 -061

lt0001 lt0001 00023 00021 lt0001

1VaR 1 092 -011 -007 -061

lt0001 00021 00275 lt0001

5VaR 1 -010 -009 -063

00067 00048 lt0001

Leverage 1 -011 028

00013 lt0001

Q 1 015

lt0001

Size 1

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

1994 001 08900 002 08763 004 06617 -022 00249

1995 012 01969 017 00732 026 00054 -039 00002

1996 014 01481 013 01955 019 00479 -024 00211

1997 -012 02220 -012 01893 -012 02241 -011 03280

1998 -008 04414 -015 01439 -001 03588 -011 03086

1999 -016 01133 -016 01192 -014 01791 002 08860

2000 -016 01526 -018 01058 -016 01407 022 00691

2001 -021 00644 -024 00391 -023 00439 028 00227

2002 -022 00577 -023 00569 -020 00844 018 01507

2003 -038 00011 -028 00187 -033 00056 001 09527

the opposite

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Variable 1995 1996 1997 1998 1999 2000 2001 2002 2003

Combined ratio ()

Homeowner 11018 11882 9802 10717 10753 10990 12048 10871 9910

Herfindahl Index ()

Homeowner 855 846 830 833 855 844 856 877 867

Homeowner 043 038 050 044 043 045 044 043 050

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

1995 1996 1997 1998 1999 2000 2001 2002 2003

Homeowner

General liability

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

1995 1996 1997 1998 1999 2000 2001 2002 2003

sample

RBC 301 059 074 893

Rank_RBC 056 056 000 1

Leverage 246 013 -245 626

Rate 1231 185 100 1500

Rank_rate 040 027 000 094

Size 448 176 -494 1129

Bus_Div 123 3960 007 10000

Mutual 021 041 0 1

Group 076 043 0 1

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Rank_RBC 1 016 -012 031

lt0001 lt0001 lt0001

Leverage 1 -004 009

lt0001 lt0001

Rank_rate 1 042

lt0001

Size 1

1995 -008 00024 -027 00000

1996 -012 00000 -023 00000

1997 -010 00001 -023 00000

1998 -004 00662 -018 00000

1999 -006 00289 -016 00000

2000 -005 00347 -011 00007

2001 -004 01377 -011 00007

2002 -007 00032 -019 00000

2003 -003 01679 -019 00002

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

increases

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Rank_RBC

b2t = -096 + 018 COMPt + 015 UWCt +ζ2t

b3t = 046 + -005 UWCt + ζ 3t (52)

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

mutual insurers

insurance

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

increases

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Sample Rank_rate

Rank_rate

Commerical Multiple

Peril - NS - - + -

NS = insignificant

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

stock insurers

companies

Homeowner 62 11

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

6 Conclusions

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

underwriting cycle

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

research

this area

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

follows

kkikix

xwMini 1

0geiλ iforall

i XWXW =φ

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Reference

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

ABSTRACT

1 Introduction



13 Research purpose


21 Firm Risk




3 Methodology





42 By-line Analysis







The CRSP Sample

The NAIC Sample












6 Conclusions




Reference

table511-12pdf

crspmodel

table522pdf

home

Documents

Franchise Value, Competition and Insurer Risk-takingaria.org/meetings/2006papers/RenSchmit.pdf · Franchise Value, Competition and Insurer Risk-taking ... (MM) paradigm, under certain