An Empirical Examination of the Interrelations of Risks and the F

8/12/2019 An Empirical Examination of the Interrelations of Risks and the F

1/158


2/158

THE FLORIDA STATE UNIVERSITY

COLLEGE OF BUSINESS

AN EMPIRICAL EXAMINATION OF THE INTERRELATIONS OF RISKS AND THE

FIRMS RELATION WITH ENTERPRISE RISK MANAGEMENT

By

DAVID M. POOSER

A Dissertation submitted to theDepartment of Risk Management/Insurance, Real Estate, and Legal Studies

in partial fulfillment of therequirements for the degree of

Doctor of Philosophy

Degree Awarded:Summer Semester, 2012


3/158

ii

David M. Pooser defended this dissertation on June 27, 2012.

The members of the supervisory committee were:

Kathleen A. McCullough

Professor Directing Dissertation

Pamela CoatsUniversity Representative

Patricia Born

Committee Member

Cassandra R. Cole

Committee Member

The Graduate School has verified and approved the above-named committee members, and

certifies that the dissertation has been approved in accordance with university requirements.


4/158

iii

To my mother and father


5/158

iv

ACKNOWLEDGEMENTS

I would like to acknowledge several individuals that provided me with help and support

throughout my doctoral studies and dissertation, without whom I would not have completed my

PhD and the process would have been substantially less enjoyable. First, Kathleen McCullough

has provided me with tremendous support and assistance as a mentor and friend from the first

day of my doctoral studies through the last day of my dissertation. I still cant believe the

amount of time she has invested in developing me as a researcher and teacher. I could not have

asked for a better dissertation chair or major professor.

I am also grateful for my dissertation committee, Patricia Born, Cassandra Cole, and

Pamela Coats. My committee was supportive and helpful throughout the entire process,

provided excellent suggestions for strengthening my work, and made themselves available to meanytime I needed assistance. I would like to thank Jim Carson, my first doctoral advisor, who

approaches each project with a positive attitude that spreads to others around him, Pat Maroney

for his support through the Florida Catastrophic Storm Risk Management Center, and Richard

Corbett, who helped spark my interest in the insurance major. I would also like to thanks Laura

Waltke, who has helped me more times than I can count as a student and teacher, and who will

be missed in the department office.

I am grateful for the lasting friendships I have formed throughout my four years as a

doctoral student at FSU. I would especially like to thank Adrian Valencia, Jared Delisle, Barbara

Bliss, Brad Karl, Lucy Fier, and Steve Fier for making my time here so enjoyable. I would

especially like to thank Steve for being my sounding board for problems, ideas, revelations, and

nonsense for the last four years. Without him I would be far less optimistic about the future.

Finally, I would like to thank my family not only for their support during my time as a

doctoral student, but throughout my entire scholastic career. My mother and father never left

any doubt in my mind that I made the right choices. Because of them I always believed I could

accomplish the next task.


6/158

v

TABLE OF CONTENTS

List of Tables ................................................................................................................................ viiList of Figures ................................................................................................................................ ixAbstract ............................................................................................................................................x

1. INTRODUCTION ...................................................................................................................1

2. LITERATURE REVIEW ........................................................................................................7

2.1 Insurer Diversification ...................................................................................................72.1 Enterprise Risk Management .......................................................................................112.1 Enterprise Risk Management and Firm Value .............................................................132.1 Enterprise Risk Management Activities ......................................................................14

3. ACCOUNTING FOR LINE OF BUSINESS CORRELATION WHEN MEASURING

CONCENTRATION: EVIDENCE FROM THE INSURANCE INDUSTRY .............................16

3.1 Introduction ..................................................................................................................163.2 Literature Review.........................................................................................................19

3.2.1 Measures of Diversification that do not Consider Correlation ........................193.2.2 Measures of Diversification that Consider Correlation ...................................213.2.3 Modern Portfolio Theory .................................................................................22

3.3 Hypotheses Development ............................................................................................243.3.1 The Modified HHI Changes Concentration .....................................................243.3.2 The Modified HHI is Different from the Traditional HHI ..............................253.3.3 The Difference in Concentration Varies Across Firms ....................................263.3.4 The Modified HHI Alters the Empirical Findings of Prior Research ..............29

3.4 Methodology for Measuring Diversification ...............................................................303.4.1 Developing a Modified HHI Based on Correlation .........................................303.4.2 Data and Methodology .....................................................................................32

3.5 Results ..........................................................................................................................343.5.1 Univariate Tests for Change in Concentration.................................................343.5.2 Testing for a Change in Variable Distribution .................................................353.5.3 Firm Factors Related to the Change in Concentration .....................................383.5.4 The Impact of the Modified HHI on Prior Literature ......................................413.5.5 Robustness of the Modified HHI Measure ......................................................43

3.6 Conclusions and Future Research ................................................................................47Appendix 3.1 .........................................................................................................................49

4. ERM DETERMINANTS, USE, AND EFFECTS ON THE FIRM ......................................714.1 Introduction ..................................................................................................................714.2 Literature Review.........................................................................................................75

4.2.1 Enterprise Risk Management Overview ..........................................................754.2.2 Firm Factors Related to ERM ..........................................................................784.2.3 Enterprise Risk Management and Insurer Risk Management Techniques ......794.2.4 The Effect of ERM on Insulating the Firm from Adverse Changes ................85

4.3 Data and Hypotheses Development / Methodology ....................................................86


7/158

vi

4.3.1 Firm Factors Related to an ERM Program ......................................................874.3.2 Differences in Risk Management Techniques .................................................904.3.3 Testing the Effectiveness of an ERM Program................................................93

4.4 Results ..........................................................................................................................954.4.1 Examining Differences in Firm Characteristics Related to an ERM Rating ...95

4.4.2 Testing for Simultaneity in Risk Management Techniques .............................974.4.3 Examining the Effectiveness of ERM in Preventing Performance Shocks .....994.5 Conclusion .................................................................................................................103Appendix 4.1 .......................................................................................................................120Appendix 4.2 .......................................................................................................................126

REFERENCES ............................................................................................................................138

BIOGRAPHICAL SKETCHES ..................................................................................................147


8/158

vii

LIST OF TABLES

3.1 Determinants of Concentration Variable Description ...........................................................50

3.2 Comparison of Mean HHI Values Using Three Correlation Measures ................................51

3.3 Distribution of HHI and Modified HHI .................................................................................52

3.4 Sign Test for Equality of Distribution ...................................................................................53

3.5 Wilcoxon Sign-Rank Test for Equality of Distribution ........................................................54

3.6 Correlation Matrix of Determinants of Concentration Variables ..........................................55

3.7 Multivariate Regression Factors Related to Firm Concentration .......................................56

3.8 Summary Statistics for the Corporate Demand for Reinsurance ...........................................57

3.9 Regression Results Corporate Demand for Reinsurance ....................................................58

3.10 Differences in Mean HHI measured by-region, by-line ........................................................59

3.11 Distribution of Line-Region HHI and Modified HHI ...........................................................60

3.12 Differences in Mean HHI Using Three-Year Average Correlation for Personal andCommercial Insurers ......................................................................................................................61

3.13 Distribution of HHI by Business Mix ...................................................................................62

4.1 ERM Sample Statistics ........................................................................................................105

4.2 Descriptions of Firm Variables with Expected Relation to the Presence of an ERM Program.............................................................................................................................................106

4.3 Summary Statistics for All Firm Variables .........................................................................107

4.4 Mean Value and T-Tests of Firm Variables by ERM-Rating Type ....................................108

4.5 Logistic Regression Results: Determinants of ERM ...........................................................1094.6 Simultaneous Equations Models for Firm Risk and Risk Management Techniques ..........110

4.7 Description of Shock Events and Average Number of Shocks for Firms with ERM Ratingsand Firms without ERM Ratings .................................................................................................111

4.8 Logistic Regression Results for Loss Ratio Shocks ............................................................112


9/158

viii

4.9 Logistic Regression Results for ROA Shock ......................................................................113

4.10 Distribution of the Change in Loss Ratio ............................................................................114

4.11 Distribution of the Change in ROA .....................................................................................1154.12 Regression Results for the Difference in Loss Ratio ...........................................................116

4.13 Quantile Regression Results for the Difference in Loss Ratio ............................................117

4.14 Regression Results for the Difference in ROA ...................................................................118

4.15 Quantile Regression Results for the Difference in ROA .....................................................119

4.16 Simultaneous Equations Models for Firm Risk and Risk Management Techniques (Weak

ERM Rating = No ERM Rating) .................................................................................................1294.17 Logistic Regression Results for Loss Ratio Shock (Expanded ERM Classification) .........130

4.18 Logistic Regression Results for ROA Shock (Expanded ERM Classification) ..................131

4.19 Regression Results for the Difference in Loss Ratio (Expanded ERM Classification) ......132

4.20 Regression Results for the Difference in ROA (Expanded ERM Classification) ...............133

4.21 Regression Results for the Absolute Difference in Loss Ratio ...........................................134

4.22 Quantile Regression Results for the Absolute Difference in Loss Ratio ............................135

4.23 Regression Results for the Absolute Difference in ROA ....................................................136

4.24 Quantile Regression Results for the Absolute Difference in ROA .....................................137


10/158

ix

LIST OF FIGURES

3.1 Scatter Plot of HHI and ModHHI ..........................................................................................63

3.2 Difference Between HHI and ModHHI ................................................................................64

3.3 Premium Growth and Difference in HHI ..............................................................................65

3.4 Change in Net Income and Difference in HHI ......................................................................65

3.5 Firm Size and Difference in HHI ..........................................................................................66

3.6 Kenney Ratio and Difference in HHI ....................................................................................66

3.7 BCAR and Difference in HHI ...............................................................................................67

3.8 Industry Concentration Index and Difference in HHI ...........................................................67

3.9 Geographic Concentration and Difference in HHI ................................................................68

3.10 ROA and Difference in HHI ..................................................................................................68

3.11 Public Dummy and Difference in HHI ..................................................................................69

3.12 Mutual Dummy and Difference in HHI ................................................................................69

3.13 Difference Between HHI and ModHHI Across U.S. Regions ..............................................70


11/158


12/158

1

CHAPTER ONE

INTRODUCTION

Enterprise risk management (ERM) refers to the joint management of firm risk using

multiple risk management techniques and considering the interrelations or correlation between

risk exposures. Rather than focusing on traditional risk management (insurance buying, physical

mitigation, liability reduction) or financial risk management (purchasing options and derivatives,

diversifying investments), enterprise risk management simultaneously considers all forms of firm

risk, the interrelatedness of the risks, and creates a plan to treat overall firm risk. ERM

researchers and risk management consultants typically define four sources of firm risk: financial,

operational, hazard, and strategic (e.g. Gates, 2006; Ai, Brocket, Cooper and Golden, 2011).

ERM became a popular topic amo ng academic researchers in the early 2000s, and has

continued to interest researchers through the present. Several failures of large firms, increases in

technology impacting the ability to track firm risks, and increases in regulatory scrutiny of

managers and directors has led to the progression of ERM. The growth of ERM has also led to

increased interest among academic researchers examining firm performance and firm value.

Additionally, risk managers, ratings agencies, regulators, and investors are becoming more

interested in ERM and its impact on firms.

ERM differs from traditional risk management in two main ways. First, firm risks are

viewed as potentially correlated, instead of as silos of stand -alone risk exposures. Second,

ERM treats both pure and speculative risk exposures simultaneously. Firms have historically

attempted to minimize the cost of risk through transfer, reduction, retention or avoidance of a

risk exposure while an ERM program attempts to optimize firm risk in order to maximize value.

Prior research often finds a decrease in firm value for firms that practice risk

management, leading some authors to question whether or not firms should manage risk (Amitand Linvat, 1988). Risk management is costly, and investors can diversify their own stock

holdings to eliminate idiosyncratic risk from their portfolios, theoretically eliminating the need

for firms to engage in risk management. Many firms implement risk management programs in

order to avoid disasters, or to stay in business after a catastrophe (CASACT, 2003).

Implementing an ERM program is difficult because it requires coordination and communication


13/158

2

throughout the firm, requires an investment of manpower and financial resources, and relies on

the support of managers to succeed (Gates, 2006). Nevertheless, a well implemented ERM

program may be able to increase productivity and reduce the chance of ruin through enhanced

risk identification (Harrington and Niehaus, 2002).

ERM is hypothesized to add value by enabling risk quantification and optimization

(Nocco and Stulz, 2006) and increasing efficiency (Hoyt and Liebenberg, 2011). However, the

findings on this subject are mixed. Grace, Leverty, Phillips and Shimpi (2010) and Hoyt and

Liebenberg (2011) do find increased value for ERM firms, while Lin, Wen and Yu (2010) do not

find an increase in firm value using Tobins Q as a measure of firm value.

An issue closely related to ERM is diversification. Diversification affects the firms

overall risk and return, and is an enterprise risk management consideration. Within

diversification decisions, firms must consider how one line of business is related to other lines(Robins and Wiersema, 1995). Diversification is a form of corporate risk management that has

been extensively researched in prior literature across several fields. Often, researchers have

asked the question of why firms diversify. Diversification may occur for several reasons. Firms

that are mature in one industry but still seeking growth opportunities may decide to enter new

industries (Biggadike, 1976). Firms that wish to reduce earnings volatility may diversify across

industries. Sometimes, managers may seek to raise their personal profile by entering new sectors

and growing the firm beyond shareholder expectations (Morck, Shleifer and Vishny, 1989;

Montgomery, 1994). However, some researchers have found that diversification destroys firm

value and reduces profits (e.g., Amit and Linvat, 1988; Liebenberg and Sommer, 2008). One

challenge facing diversification studies is developing a definition of diversification that accounts

for the impact of related lines of business. This is especially important in an ERM framework

where potential interrelation among risks is one of the cornerstones of an ERM perspective.

In this dissertation, I discuss and analyze the ERM decisions of property and casualty

insurance firms operating in the US. In the first essay, I focus on one of the primary ways in

which insurers can reduce risk, diversification. Specifically, I develop a measure of

diversification that accounts for the interrelatedness between lines of insurance. This

diversification measure is then incorporated into the second essay which focuses on ERM. I first

characterize the firms that are most likely to obtain an ERM rating from Standard and Poors.

Then I look at the potential differences in firm behavior of the ERM rated and non-rated firms


14/158

3

with respect to how insulated they are from performance shocks as well as potential differences

in the interrelation of the use of risk management techniques.

The first essay of this dissertation develops a method for measuring diversification that

incorporates the interrelatedness of an insurers lines of business into one concentration index,

the modified HHI. Insurers that operate in highly correlated lines of insurance do not gain the

full diversification effect compared to insurers that operate in independent lines of insurance,

because the losses between correlated lines of insurance trend simultaneously. This new index

provides a more accurate description of an insurers line of business concentration than prior

measures that do not account for the potential correlation or interrelatedness between lines of

insurance.

I examine this new measure of diversification with four hypotheses. First, I hypothesize

that the modified HHI significantly increases the concentration of insurers due to positivecorrelation in lines of insurance. Second, I hypothesize that the modified HHI provides new

information regarding insurer concentration, resulting in a shift in the distribution of

concentration for my sample. Third, I hypothesize that several firm characteristics

systematically relate to the change in concentration. Finally, I hypothesize that the modified

HHI will alter the results of empirical research when used, compared to the traditional HHI. I

provide an initial test of this hypothesis by examining Mayers and Smith (1990) using both

indices.

I find support for all four hypotheses. The modified HHI significantly increases the

measurement of insurer concentration. This increase is not linear across firms, but rather

represents a shift in concentration distribution. Additionally, there are several key firm

characteristics, including the insurers corporate structure , that relate to the difference between

the traditional and modified HHI measure. These differences are important because they may

indicate variables where the use of the modified HHI is likely to impact the results of studies or

influence the interpretation of financial results. For example, the results of prior research may be

altered by more completely accounting for the impact of interrelatedness among lines of business

when measuring diversification. I use the modified HHI in an extension of the Mayers and

Smith (1990) empirical model. While the coefficient estimates for the traditional HHI and

modified HHI are not statistically different, using the modified HHI causes the corporate

structure variable coefficient to lose significance in contrast to the model using the traditional


15/158

4

HHI. Taken together the results show that the new modified HHI conveys potentially important

diversification information.

The modified HHI is more powerful than prior concentration measures that considered

interrelation because it quantifies the correlation between lines of insurance. Failing to account

for correlation between lines of insurance will provide inaccurate estimates of line of business

concentration and may lead to misleading results in an empirical test that includes line of

business concentration as a variable. Additionally, the modified HHI is useful to researchers,

actuaries, and regulators in that it expresses diversification values with one single variable and is

directly comparable with the traditional HHI. The modified HHI is particularly important when

examining diversification in an ERM framework where the interrelation of firm risk is one of the

foundations. In this setting, defining diversification in such a way that incorporates correlation

between the lines of business provides a measure consistent with the focus of ERM.The second essay of this dissertation examines enterprise risk management by performing

several tests on insurers with and without ERM ratings from Standard and Poors Ratings Di rect

in an effort to understand both the types of firms utilizing ERM ratings as well as differences in

firm behavior. 1 In order to perform these tests I develop three hypotheses. First, I hypothesize

that the firm characteristics of ERM rated and non-ERM rated firms will differ based on

predictions and evidence in prior literature. Second, I hypothesize that ERM rated firms will

jointly manage their use of risk management techniques. I test for joint significance in the risk

management variables in explaining firm risk for firms with and without ERM ratings. Finding

joint significance in the risk management variables for ERM rated firms provides evidence that

these firms manage overall firm risk using multiple risk management techniques simultaneously.

Finally, I hypothesize that ERM rated firms are more insulated from adverse changes in

performance than non-ERM rated firms. I test for this by observing if ERM rated firms

experience fewer average performance shocks than non-rated firms in both univariate and

multivariate settings. I also test whether or not ERM rated firms experience more favorable

changes in the loss ratio and ROA, which are two of the variables that determine performance

shocks.

My findings support the hypotheses. First, I find that insurers with ERM program ratings

are systematically different from those without ERM ratings. The ERM rated insurers tend to be

1 Standard and Poors provides quality rating s to ERM programs for insurers.


16/158

5

larger, more often organized as publicly traded firms, and use less reinsurance than insurers

without ERM program ratings. Further, I find joint significance in the risk management

techniques determining firm risk for ERM rated firms, but find no significance for these

techniques for non-ERM rated firms. This result provides strong evidence that ERM firms

jointly manage firm risk using several interrelated techniques. This behavior is at the heart of

most definitions of ERM firms. Thus, my findings confirm a systematic difference in the

behavior of ERM and non-ERM rated firms. Additionally, this test may serve as a metric for

regulator, rating firms, and other tasked with determining whether firms are engaging in an ERM

program. Finally, the existence of an ERM program is associated with differences in the firms

potential exposure to performance shocks and changes in performance. As hypothesized, I find

that ERM rated firms, on average, experience fewer shocks to performance than non-ERM rated

firms. Additionally, ERM rated firms experience more favorable changes in the loss ratio andROA than non rated firms. This is important because the results provide evidence that ERM

improves an insurers resilience against adverse events. Several parties, including regulators,

rating agencies, consumers, and shareholders, may find this important when considering the

benefits of implementing an ERM program.

Essay two also contributes to the ERM literature because the empirical tests are

performed on an outside measure of ERM as well as a broader dataset than has been used in prior

empirical ERM research. Several prior studies that empirically examined ERM have gathered

data using surveys (e.g., Kleffner, et al., 2003, Beasley, et al., 2005, Altuntas, et al., 2010) and

news reports and press releases for publicly traded insurers (e.g., Liebenberg and Hoyt, 2003,

Hoyt and Liebenberg, 2011). This essay uses the Standard and Poors ERM Ratings dataset as

an outside, verified measure of ERM implementation combined with the NAICs U.S. property

and casualty insurance data. Since I merge the Standard and Poors measure with the NAIC

data, I am able to conduct tests based on the full sample of property and casualty insurers rather

than a sample of only ERM firms or publicly traded insurers. Additionally, to my knowledge, no

prior studies on ERM have investigated the interrelatedness of risk management techniques. I

also examine the effectiveness of ERM in reducing the effects of negative performance events,

which is beyond the scope of many prior ERM analyses. These findings will grow in importance

as ERM implementation is expected to expand due to requirements by regulators and ratings

agencies to quantify and manage firm risk. Greater scrutiny on managers and directors post-


17/158

6

SOX and financial crisis is leading many firms to pursue and ERM strategy as well. The

hypotheses developed in this essay provide a basis for further empirical tests of ERM

effectiveness and behavior of firms with ERM as more data becomes available or across other

industries.

As the visibility and importance of ERM continues to grow in industry, academic

research will also continue to define tests related to ERM, refine measurement of ERM, and

produce results based on the impact of ERM on firms. This dissertation uses available data on

ERM implementation and provides testable hypotheses and results for future research.

Additionally, as ERM research and importance continues to grow, more specific and accurate

data regarding ERM practices will become available leading to greater research potential on this

subject. The methods in this dissertation will help future researchers, as well as regulators and

ratings agencies, identify firms that do and do not practice ERM through the joint use of riskmanagement techniques. The accurate measurement of insurer diversification and methods for

measuring ERM practices are important tools for researchers, regulators, and other stakeholders

that examine the impact of financial decisions on insurer characteristics, performance, and

behavior. The findings and methods in this essay may also be applied to industries outside

insurance.

This dissertation is organized as follows. Chapter two presents prior literature on

enterprise risk management and corporate diversification. Chapter three develops a method for

measuring line of business concentration that accounts for correlation between the lines (the

modified HHI) and performs empirical tests on this measure. Chapter four empirically examines

the effect of ERM on firm characteristics, the effect obtaining an ERM program rating on the

impact of performance shocks, and the joint use of firm risk management techniques for firms

with and without ERM ratings.


18/158

7

CHAPTER TWO

LITERATURE REVIEW

This dissertation examines insurer concentration decisions by developing a method for

measuring concentration that incorporates correlation into the concentration index, providing a

control for potential interrelatedness between lines of insurance. It also examines firm

characteristics associated with an ERM program, tests whether or not firms with ERM program

ratings experience fewer performance shocks, and seeks to find joint management of firm risk

through risk management techniques. Below, I discuss how prior literature has examined insurer

diversification and how this relates to the topic of enterprise risk management.

2.1 Insurer Diversification

Diversification is an insurer risk management technique that has received substantial

attention in prior literature. Prior research related to insurer diversification often examines the

impact of diversification on firm value or firm risk. The strategic focus hypothesis predicts that

insurers that focus on one line of business, or on one industry, will earn better returns than

diversified insurers due to specialization in that field. This hypothesis has been tested several

times by prior literature. Hoyt and Trieschmann (1991) find that focused insurers, defined as

insurers that operate in either the life-health or property-liability industry, yielded better stock

returns than diversified insurers. Liebenberg and Sommer (2008) find that diversified insurers

have lower firm risk as measured by the standard deviation of ROA. However, they find strong

support that focused insurers have higher ROA and ROE than diversified insurers. Elango, Ma

and Pope (2008) find a non-linear relationship between product diversification and return. At

low levels, diversification is negatively related to return, but as diversification increases (and

concentration decreases) firm returns begin to increase, which may be caused by different

geographic concentration strategies. Very high levels of both geographic and line of businessconcentration are associated with lower returns. While most research regarding diversification

finds lower returns for diversified firms, Elango, et al. (2008) shows that this finding depends on

the way diversification is measured.

Berry-Stlzle, et al. (2011) examine insurer diversification and account for the

relatedness of lines of business by how commonly these lines are written together. They


19/158

8

investigate firm characteristics related to total diversification and unrelated diversification. The

authors find that stock insurers are more likely to participate in unrelated diversification, which

supports the managerial discretion hypothesis. My first essay also examines insurer

diversification using a measure of relatedness between lines of insurance. However, instead of

measuring relatedness as a propensity for two lines to be written together, I measure relatedness

as the correlation of income streams between insurer lines of business.

I develop a measure diversification using a method that accounts for potential

interrelatedness between lines of business and incorporates this into a single value. Prior

literature has measured diversification using methods that consider all lines of business as

independent and using methods that account for interrelatedness between lines. While this topic

is explored more completely in the first essay, below I discuss some diversification measures

common to business and economics literature.Equation (1) is the Hirschman-Herfindahl Index (HHI), one of the most commonly used

measures of diversification or concentration in insurance research. The HHI is often used to

measure line of business, geographic, or industry concentration.

(1)

where s i is the proportion of the firms premiums in a particular line of business. A s the number

of lines of business (diversification) increases, the Herfindahl index decreases. We see a similar

result in portfolio theory. In that case, as uncorrelated securities are added to a portfolio, the portfolio variance decreases.

Another diversification measure often seen in the literature is the entropy measure.

(2)

where s i is the proportion of the firms premiums in a particular line of business. Jacquemin and

Berry (1979) note that the entropy measure is more sensitive to subtle differences in line of

business diversification than the Herfindahl index. The entropy measure lends more weight to

small proportions of a line of business, and thus accounts for the number of lines of business,even when the revenue from that line is small.

The previous measures of diversification are appropriate for measuring line of business

concentration when correlation between lines of business is very low or does not exist.

However, when correlation exists between different lines of business a different diversification

measure may be necessary. There are a variety of approaches to incorporate correlation across


20/158

9

lines. For example, some entropy measures also attempt to treat potential correlation by dividing

the proportion of business into related and unrelated lines. Robins and Wiersema (1995), in a

study of diversification interrelations, present the modified entropy measure in equation (3),

which divides the sample of business lines into 4-digit (D T) and 2-digit (D U) SIC indices, using

the logic that the four-digit SIC is far more granular than the two-digit. Here, and are the

proportion of revenue in each SIC category. The entropy index is increasing with diversification,

so a more granular SIC code should lead to a greater value of D. Therefore, D R will be a positive

value, and the related measure of diversification, present in the 2-digit SIC code, is removed

from the equation.

(3)Because the entropy measure increases with diversification, correlation among the lines would

normally inflate this measure. By subtracting the 2-digit SIC entropy measure from the 4-digit

measure, equation (3) attempts to remove any potential correlation that occurs as a result of

operating in largely similar lines.

Rob ins and Wiersema (1995)s also use a diversification measure for correlated lines of

business by estimating correlation. This method observes the actual correlation between two

lines, and estimates diversification based on the proportion of business written in each line.

Following Robins and Wiersema (1995), in equation (4), si is the proportion of business written

in a given line, and ij is the correlation between the lines i and j.

(4)This measure has one primary drawback, if it is to be related to the Herfindahl index and modern

portfolio theory it is additive instead of multiplicative. As the authors discuss, the value can

range outside of -1 and 1 with more than one line of business, and is scaled by (n-1), where n is

the number of lines, to bring the range between -1 and 1. Additionally, there is no direct

comparison of this concentration measure another concentration measure that does not account

for correlation, or to portfolio variance because the business proportions are added instead ofmultiplied. This approach to measuring concentration helps motivate the first essay

methodology by accounting for measured correlation between lines of business. When

correlation is positive firms are measured as more concentrated. When correlation is negative

firms are measured as more diversified.


21/158

10

Modern Portfolio Theory. As Markowitz (1952)s modern portfolio theory shows, the

covariance between returns on securities will affect the overall portfolio variance. Portfolio

variance is a method for quantifying the riskiness of a portfolio of securities which controls for

correlation between individual securities and accounts for the riskiness of each security.

Similarly for measuring line of business concentration, the correlation between lines of business

will affect the true value of diversification for a firm. For example, an insurer that operates in

two highly correlated lines is less diversified with respect to earnings than an insurer that

operates in two lines with little correlation. Markowitz (1952)s portfolio variance equation is

measured as:

= (5)

In the portfolio context, s i indicates the proportion of total assets invested in an individual

security, i is the standard deviation of the security return, and ij is the correlation between

returns of securities i and j. The portfolio variance is the sum of the variance of each security

times its respective weight squared, plus the sum of the additional portfolio covariances, for

securities that are correlated. When all securities are independent, ij will equal zero, and only

the individual security variance will matter. Comparing equation (1) to equation (5), the HHI is

a measurement of the weights across lines of business without a value of standard deviation or

variance.

This methodology can be extended to the insurer framework where the lines of businesswritten can be viewed as securities in a portfolio, allocated share s i, and have a return based on

the loss ratio the insurer experiences. Previous research has used a portfolio approach for

assessing insurers. For example, Kahane (1977) views insurer operations as a portfolio of

policies when measuring the optimal insurer business strategy based on risk and return of the

available lines. 2 In essay one, I estimate the correlation between lines of business and construct a

modified version of the HHI that accounts for this correlation. This approach is similar to the

Markowitz (1952) methodology, but does not measure the standard deviation of each line. If

correlation between lines of insurance is mostly positive, the value of concentration should

increase for insurers. If correlation between insurers is mostly negative, the value of

2 Kahane (1977) states that, ... the activity of an insurance company may be viewed as the management of a

portfolio of insurance policies,, that the decision to write in different lines is a concern that cannot be madeindependently, and that correlation in the portfolio (they discuss this in terms of underwriting and investment) must

be considered in deciding the optimal product mix.


22/158

11

concentration should decrease. If correlation is mostly measured as insignificant, the modified

HHI should not alter the HHI in a distinguishable fashion.

2.2 Enterprise Risk Management

While diversification is one method of insurer risk management, enterprise risk

management is the simultaneous consideration and treatment of all firm risks using multiple risk

management techniques (CASACT, 2003). Empirical research ERM research has grown more

complex since its inception. Early studies on ERM performed analyses on the determinants of

implementing an ERM program or summary statistics for ERM firms (e.g., Liebenberg and

Hoyt, 2003; Kleffner, Lee and McGannon, 2003). Recently, researchers have asked more

complex questions in ERM research, including how ERM impacts the marginal cost of risk

(Eckles, Hoyt and Miller, 2010) and how ERM affects firm value (Hoyt and Liebenberg, 2011),

Below, I discuss the progression of literature on ERM. I discuss how ERM relates to firm valueand what methods researchers have used to measure ERM implementation and ERM activity.

The literature on ERM has developed significantly over the last 10 years. The earliest

studies provided very general definitions of ERM and how an ERM program would likely impact

a firm (e.g. Lam, 2000; D Arcy, 2000; Harrington and Niehaus, 2002). Early studies typically

predict better risk identification and risk quantification for ERM firms. DArcy (2000) describes

a general ERM process and recommendations for measuring the effectiveness of ERM in the

future. The author notes that one reason ERM is becoming more common is that advances in

technology make it possible for firms to simultaneously track different risk exposures (i.e.

computers became more advanced in the 1990s). Dickinson (2001) argues that the establishment

of ERM was a natural process after several avoidable and high profile company failures that

could have been prevented firm risks were properly managed. Risk financing decisions, for

example, must not be considered alone. The entities in a corporation that purchase and trade

options and derivatives, as well as the the entities that manage insurance contracts, must be

aware of the financial decisions of the other. The lack of communication between risk

management entities within a firm is a form of inefficiency that may lead to increased costs and

reduced value. Additionally, according to Dickinson (2001), ERM implementation is being

further motivated by increasingly stringent government regulations on managers and directors.

Compliance with these regulations becomes part of the ERM process. Managers facing greater


23/158

12

personal liability from firm performance benefit from risk management of the risks that affect

them personally.

Two early empirical studies of ERM are Liebenberg and Hoyt (2003) and Kleffner, Lee

and McGannon (2003). Liebenberg and Hoyt analyze the determinants of ERM implementation

by observing the appointment of a chief risk officer (CRO) for firms in news outlets and press

releases. The findings show that smaller firms and more leveraged firms more frequently

appoint a CRO, which can signal the implementation of an ERM program. Kleffner, Lee, and

McGannon (2003) report survey data from corporations on their usage of ERM. The survey

responses show that ERM requires management buy-in and is limited by the difficulty of risk

identification, budget constraints (especially when risk management is not a firm priority), and

the uncertainty of the value it adds to a corporation. Many risk managers, however, view ERM

as beneficial because it tends improve communication processes regarding firm risk. Insummarizing the firms that implement ERM, both Kleffner, et al. (2003) and Liebenberg and

Hoyt (2003) find that firms implementing ERM programs are spread evenly by revenue and firm

size. These studies provided initial findings regarding ERM use which future studies expanded

upon.

Beasley, Clune and Hermanson (2005) examine the determinants of ERM

implementation and the extent of use. The study uses 2004 survey data from IIAs Glo bal Audit

Information Network. This study finds that larger firms will be more likely to implement an

ERM program in contrast to Liebenberg and Hoyt (2003). Using an ordinal logit model to

measure the extent of ERM implementation (this is self reported in the survey), the authors find

that firms with CROs, higher revenue, and firms in the banking and insurance sectors will utilize

ERM at a more developed stage. Additionally, U.S. based firms are less likely than international

firms to implement an ERM program or be advanced in plan implementation. Given these

findings, the insurance sector provides a good environment for testing hypotheses related to

ERM, since it is found to be associated with greater ERM implementation.

Gates (2006) conducted a survey to identify reasons that ERM is becoming a corporate

priority. The majority of respondents were either implementing, or preparing to implement an

ERM program. Development of an ERM program is generally most important to the CFO and

financial auditing division of the firm, rather than other managers and directors. Many risk

managers face limitations establishing an ERM program because they have difficulty obtaining


24/158

13

technology and manpower resources (their funding priority is low) and convincing management

of the importance of ERM. Firms that implement ERM often cite improved informational

efficiency, better strategic positions and strengthened corporate governance as major benefits.

Eckles, Hoyt and Miller (2010) use a Heckman two step model controlling for the

likelihood a firm will adopt ERM to determine how ERM will affect firm risk (measured as stock

volatility). Additionally, they measure firm performance (as ROA per unit of risk) based on

ERM usage. They find that less diversified firms, larger firms, and firms with higher prior stock

return volatility are more likely to implement an ERM program. Once a program is instituted,

firms realize a reduction in stock return volatility and increased performance per unit of risk.

This empirical study provides evidence on the firm characteristics related to ERM

implementation, and find that ERM improves firm performance.

2.3 Enterprise Risk Management and Firm ValueFollowing several discussion papers on ERM and empirical studies that examine firm

characteristics related to ERM, researchers began asking how ERM affects firm value. Although

the findings are mixed for this question, many authors hypothesize that ERM adds value through

increased efficiency in the risk management process, better communication across departments

related to risk decisions, and improved risk quantification.

Nocco and Stultz (2006) argue that ERM adds value to firms because it enables risk

quantification and optimization by managers so that the firm can choose the best operating

strategy and that ERM should integrate with a firms culture and incentivize workers to make

decisions that align with firm objectives. Additionally, because ERM considers all risks

simultaneously, it can be a useful tool in determining the optimal level of default risk (Nocco and

Stulz, 2006).

Mackay and Moeller (2007) test the value of firms that use corporate risk management.

They find that corporate risk management leads to an increase in value for a corporation when

risk factors are not linearly related to revenues and costs. This finding differs from some prior

studies, which show a weak or negative relationship between risk management and firm value

(e.g., Tufano, 1996). Mackay and Moeller (2007)s finding of a positive relation between risk

management and value may be due to greater efficiency in risk management and firm

communication regarding risk practices (Hoyt and Liebenberg, 2011).


25/158

14

Lin, Wen and Yu (2010) find that ERM for insurers is positively related to reinsurance

purchases and derivatives use and is associated with lower firm value. Grace, et al. (2010) use

survey data from insurers that have ERM programs to perform an efficiency analysis on firm

performance. They find evidence that ERM leads to cost savings that result in an increase in

ROA.

Hoyt and Liebenberg (2011) tests whether ERM is associated with greater firm value

using a sample of publicly traded insurance firms. Hoyt and Liebenberg (2011) argue that ERM

should be value enhancing because it minimizes the inefficiencies inherent in traditional (silo)

risk management techniques, and enriches the information available to firms on their own

operations. Their findings contradict Lin, Wen, and Yu (2010). The authors find that ERM

implementation is positively related to Tobins Q, a measure of firm value and growth

opportunities. In addition, they find that ERM usage is negatively related to financial leverageand reinsurance, but positively related to firm size. The inverse relationship between ERM and

reinsurance may indicate a substitution, because some insurers may find it more efficient to

manage risk internally and avoid costly contracting costs. These findings contradict the findings

of Liebenberg and Hoyt (2003) that higher leverage firms are more likely to use ERM.

2.4 Enterprise Risk Management Activities

Prior literature has measured ERM implementation and ERM activities in several ways.

Liebenberg and Hoyt (2003) use the appointment of a CRO as a proxy for the implementation of

an ERM program. Other studies employ surveys to gather data on ERM usage (e.g. Kleffner, et

al., 2003; Beasley, et al., 2005; Gates, 2006; Altuntas, Berry-Stoelzle and Hoyt, 2010). Eckles,

Hoyt and Miller (2010) and Hoyt and Liebenberg (2011) measure implementation of ERM by

performing searches for key words in news outlets and press releases for publicly traded insurers.

Essay two of this dissertation uses Standard and Poors ERM Ratings Direct data to measure

which insurers have obtained ERM program ratings. I combine this data with the NAIC annual

statements in order to observer the full sample of U.S. property and casualty insurers. McShane,

et al. (2011) also uses Standard and Poors ERM data, but does not expand the sample to include

non-ERM rated firms.

Altuntas, Berry-Stlzle and Hoyt (2010) survey German firms on their implementation of

ERM programs. This study identifies several of the most important risks targeted by an ERM

program and describes methods insurers use in order to manage risk under and ERM program.


26/158

15

The majority of insurers in the sample of Altuntas, et al. (2010) identify underwriting and

investment risks as important operating factors that must be evaluated quantitatively. According

to survey results, 91 percent of insurers in 2007 consider the interdependencies of the risks when

making decisions, up from 8 percent in 1999. According to the survey results, 45 percent of

companies allocate risk capital, up from zero before 2002. For regulators, capital allocation is an

important tool in solvency monitoring. For insurers, capital allocation can affect expected

returns. For the companies that do allocate capital, nearly all allocate capital based on risk in

their underwriting and investments operations.

Ai, Brockett, Cooper and Golden (2011) theoretically examine ERM. They model four

enterprise risk types: hazard, project, financial and operational. Project risk in this study is also

referred to as strategic risk in other ERM studies (e.g., Gates, 2006). Ai, et al. (2011) model

financial and operational risk as co-dependent for an insurer. Examples of financial andoperational risk include underwriting activities and asset management. Underwriting activities

are one of the key operations of an insurer and can be managed through diversification and

hedging activities. Asset management may include investment strategies and diversification

decisions. In essay two, I provide a more detailed discussion of ERM techniques in order to

provide a basis for measuring the risk management techniques of insurers with ERM ratings.

Based on predictions in prior literature, I should observe joint significance in the risk

management techniques of ERM rated firms.


27/158

16

CHAPTER THREE

ACCOUNTING FOR LINE OF BUSINESS CORRELATION

WHEN MEASURING CONCENTRATION:

EVIDENCE FROM THE INSURANCE INDUSTRY

Section 3.1 - Introduction

Business and economics researchers often seek justification for the presence of

diversified firms i.e., why do firms diversify? Are diversified firms more valuable? Is the risk

lower for these firms? Or are there other reasons for firms to diversify, such as improved access

to capital or increased borrowing capacity (Lewellen, 1971)? Most authors agree thatdiversification reduces volatility in earnings when different lines of business are not perfectly

correlated (Lewellen, 1971; Lee, 1977). However, investors can diversify their personal

holdings by purchasing securities of different firms whose earnings are not perfectly correlated,

reducing any need for firms to diversify directly. Still, firms merge with other firms, acquire

smaller firms, and diversify their operations.

Numerous studies have investigated the reasons that firms diversify most typically

testing whether or not diversification adds value. Results are mixed for this question. For

example, the findings of Amit and Linvat (1988) and Liebenberg and Sommer (2008) suggest

that corporate diversification reduces firm value, while other authors find that diversification can

be value enhancing (e.g Hadlock, et al., 2001; Villalonga, 2004; Berger, Cummins, Weiss and Zi,

2000).

There have been several proposed reasons for why researchers observe these different

findings. One potentially overlooked factor which may influence the findings in an empirical

study is the differences in how diversification is measured. In some cases, simple dummy

variables are used. For example, in a recent analysis of diversification and focus in the Journal

of Risk and Insurance , Liebenberg and Sommer (2008) use a dummy variable to capture whether

firms operate in multiple lines. 3 Using a binary variable is useful for measuring diversification in

3 Hoyt and Trieschmann (1990); Berger, Cummins, Weiss and Zi (2000) measure diversification as an insurer that

operates in both the property and casualty and life and health industries. Choi and Weiss (2005) include reinsurancevariables as controls, in part because reinsurance may add a dimension of forced diversification to an insurers


28/158

17

an empirical study because it allows the researcher to easily interpret the economic impact of the

decision to diversify. However, continuous measures of diversification contain more

information regarding the firms line of business portfolio, and a continuous measure can

communicate economic significance on the extent of firm diversification.

One potential flaw with measures of diversification is that they fail to account for the

potential correlation between lines of business. For example, perhaps the most commonly used

diversification measure in financial research is the line of business (LOB) Hirschman-Herfindahl

index (HHI) (e.g. Mayers and Smith, 1990; Sommer, 1996; Meador, Ryan, and Schellhorn, 2000;

and Elango, Ma and Pope, 2008). 4 The traditional HHI does not make any adjustments if two

business lines are highly correlated. Similar criticisms can be made for a numerical count of

lines of business, or a dummy variable for diversification. 5 While the correlation issue has been

addressed in different ways in the strategic management literature as well as in portfolio theory,to my knowledge, it has not been adequately addressed in the financial services literature.

Failure to incorporate line of business correlation in a diversification measure is likely to

misstate the firm's actual level of concentration. This is, if two lines of business are highly

correlated (i.e., the profit and loss from these lines move simultaneously), the firm does not gain

the full diversification effect as if it operated in two completely independent business lines. 6

This dissertation develops a measure for line of business concentration a modified HHI that

incorporates the correlation between the earnings of individual business lines into a single

measure. This single measure provides a control for diversification within related lines of

insurance.

Given the detailed level of data, the insurance industry provides a natural area to test for

the potential impact of correlated earnings streams on the HHI. Four hypotheses are proposed in

books. Berger, Cummins and Tennyson (1992) also include reinsurance ceded as a variable to measurediversification, as well as the firms concentration in general liability lines as a partial diversification (orconcentration) measure. 4

Additionally, geographic measures of concentration are important because the measure may convey information

about the relative size or number of businesses in a particular area, or, at the firm level, how focused a firm is in a particular region (e.g. Kim, Mayers and Smith, 1996; Maurel and Sedillot, 1999). More detailed description on theconstruction of Herfindahl indices follows. 5 Two recent exceptions in the insurance literature that account for correlations are Liebenberg and Sommer (2008)and Berry-Stlzle, Liebenberg, Ruhland and Sommer (2011). In addition to their simple measure of diversification,Liebengerg and Sommer (2008) also employ a more complex measure as a robustness test. Berry-Stlzle,Liebenberg, Ruhland and Sommer (2011) use a distinct measure of line of business interrelation. They consider twolines of business related if they have similar production processes, which may be a result of scope economies. 6 In good years, the business lines may be profitable, and in bad years the lines may suffer losses simultaneously.With independent lines of business, profit and loss years do not trend simultaneously.


29/158

18

order to test for potential differences between the traditional and modified concentration indices.

First, I hypothesize that the modified HHI will be, on average, significantly higher than the

traditional HHI due to the relatedness of some lines of insurance. In other words, firms may not

be as diversified as previously thought when one accounts for potential interrelatedness of lines

of business. In my primary analysis, I test if the modified HHI is statistically different than the

traditional HHI. Second, I hypothesize that this difference is not simply a mean shift, but that

the two HHI measures have significantly different distributions. This hypothesis is tested using

graphical and univariate statistical methods. Third, I hypothesize that several firm characteristics

affect the firms decision to operate in statistically dependent or independent lines which

determines the difference in concentration between the HHI and modified HHI. Firms may

choose to concentrate in related lines of insurance for a number of reasons, including access to a

homogenous customer base, similarities in production factors (Berry-Stlzle, Liebenberg,Ruhland and Sommer, 2011), or due to certain scope or scale economies. This essay provides an

empirical test of the determinants of the difference between the two concentration indices.

Finally, I hypothesize that the new measure will have a significant impact on a prior empirical

analysis that utilizes the standard HHI, due to different information contained in the modified

HHI.

I find support for all four hypotheses. For hypotheses one, the results indicate that the

modified HHI yields significantly higher values of insurer concentration due to correlation

among lines insurance. This finding is robust for different measures of correlation, and for

different samples of insurers (I test whether the propensity to write in a particular type of

business affects the results). With respect to hypothesis two, I find that the modified HHI

changes non-linearly from the traditional HHI, indicating a different distribution than the

traditional HHI and new information rather than a simple mean shift.

For hypothesis three, an empirical tests on the determinants of the difference in

concentration (between the traditional HHI and modified HHI) show that premium growth, firm

size, organizational structure, firm exposures to industry concentration, and the insurers

geographic concentration significantly affect the decision to operate in related lines of insurance.

For hypothesis four, I use the modified HHI measure to test the findings of Mayers and Smith

(1990). My findings indicate that the modified HHI leads to different results than the traditional


30/158

19

HHI. Specifically, using the modified HHI causes the corporate structure variable to lose

significance in testing the demand for reinsurance.

For robustness, I test whether including a geographic dimension in the HHI that accounts

for correlation between lines of business and regions of the country alters the primary results. I

also differentiate the sample of insurers by testing whether or not insurers that specialize in

commercial and personal lines of business show similar results to the full sample.

The modified HHI adds a dimension of correlation to the standard diversification

measure. This correlation is based on observed data and the new index is more powerful than

previous methods of measuring diversification that are based on assumptions of independence

between lines of business. The development of a concentration index that controls for line of

business correlation is important to researchers and insurers. The failure to account for

significant correlation between lines of business will provide a misstated value of concentration,and may result is misleading or inaccurate results in an empirical analysis. Additionally, insurers

and regulators that observe and determine diversification behavior must accurately measure the

relatedness of lines of insurance, because correlation among lines will affect one dimension of

the insurers revenue diversification. This methodology provides one framework for this

purpose based on easily observable insurer statutory data.

This essay is organized as follows. Section two contains a literature review that discusses

historical and current measures of diversification. Section three provides the hypotheses

development for testing the impact of the new HHI measure. Section four outlines the

methodology that I employ in the empirical tests of modified insurer diversification. Section five

presents empirical results from my model, and section six concludes.

Section 3.2 Literature Review

Researchers in business, economics, and other fields are often interested in measuring the

concentration of firms in an industry, a firms geographic operations, and a firms lines of

business. This paper focuses on the firms line of business concentration (or diversification).

Numerous previous studies on the topic have explored how corporate diversification affects the

performance of firms.

3.2.1 Measures of Diversification that do not Consider Correlation


31/158

20

I can look to the literature for a number of measures of diversification. As mentioned

earlier, the product mix, line of business concentration, or number of lines of business an insurer

participates in are often included as independent or dependent variables to account for the

concentration or diversification of a firm.

Jacquemin and Berry (1979) provide some analysis of measures of diversification or

concentration, which I will summarize below. Equation (1) is an historic simple measure of

concentration that is the sum of product share multiplied by a weight for each product.

(1),

where C is the measure of concentration, s i is the proportion of business written in one line

compared to the whole, and w i is some defined weight for each line. This does not account for

any interrelatedness or correlation of industries or products.

Equation (2) is the Herfindahl index that is commonly used as a measure ofdiversification across many disciplines, including insurance.

(2)The Herfindahl index is essentially a measurement of the weighting factors of variance

from Markowitz (1952)s portfolio variance measure . As with the prior measure, there is no

correction made for correlation across lines. As the number of lines of business (diversification)

increases, the Herfindahl index simply decreases. I see a similar result in portfolio theory. In

that case, as uncorrelated securities are added to a portfolio, the portfolio variance decreases.For simplicity in interpreting results, authors may modify the Herfindahl index as in

Equation (3) so that the value will increase as diversification increases. Here, I denote

diversification as D, which is simply 1 C.

(3)

The practical result of this modification is that the measure for diversification is increasing,

rather than decreasing, with the addition of more lines of business. Elango, Ma and Pope (2008)

use this modified measure so that the increasing term will match their other measure of

diversification, which also increases as lines are added.

Equation (4) is the entropy measure of diversification. As with the modified Herfindahl

measure above, it also increases with diversification.

(4)


32/158

21

Jacquemin and Berry note that the entropy measure is more sensitive to subtle differences in line

of business diversification than the Herfindahl index, which is generally preferred in industry or

geographic diversification. The entropy measure lends more weight to small proportions of an

index, and thus accounts for the number of lines of business, even when the business written in

that line is small.

Elango, Ma and Pope (2008) use another measure of the entropy measure, in Equation

(5), which adds a dimension of diversification for writing in different segments of the insurance

industry, as well as multiple lines within each segment.

(5)As in the previous equations, s denotes product share. In this case, s i is the proportion of

business in each line of business, and s l is the proportion of business written in a particularmarket segment (i.e. life or property). As explained by Elango, et al. (2008), the entropy

measure controls for the number of market segments, and considers the number of lines of

business and the weights in each line within each segment. In this sense, this measure may be

more robust than the traditional Herfindahl index in measuring product line diversification,

which only measures the weights of each line, and does not account for market segments.

3.2.2 Measures of Diversification that Consider Correlation

The measures of diversification in the previous section are appropriate for measuring line

of business concentration when correlation between two lines of business or two firms is very

low, or does not exist. However, when correlations exist between different lines of business a

different diversification measure may be necessary in order to account for any dependencies or

interrelatedness between the lines. There are a variety of approaches to incorporate correlation

across lines. These approaches include the concentric index, several modified versions of the

entropy index that account for related business (I explain one version in greater detail below),

and portfolio measures of correlation using line of business weights (Vachani, 1991; Robins and

Wiersema, 1995). Robins and Wiersema (1995) approach the correlation problem with different

measures of diversification. The first, in equation (6), is the concentric index, which was

brought to the strategic management literature by Montgomery and Wernerfelt (1988).

(6),


33/158

22

where si and s j are the proportion of business written in two lines of business to the whole, and r ij

is a measure of correlated diversification that equals zero if the lines are in the same segment and

industry, one if the lines are in different segments of an industry, and two if the lines are in

different industries. This equation adds another dimension to the Herfindahl index by

considering the proportion (weight) of two lines of business.

Some entropy measures also attempt to deal with potential correlation by dividing the

proportion of business into related and unrelated lines. For example, Robins and Wiersema

(1995) also present the modified entropy measure in eq. (7). This measure divides the sample of

lines into 4-digit (D T) and 2-digit (D U) SIC indices, using the logic that the four -digit SIC is far

more granular than the two-digit. The entropy index is increasing with diversification, so a more

granular SIC code should lead to a greater value of D. Therefore, D R will be a positive value,

and the related measure of diversification, present in the 2-digit SIC code, is removed from theequation.

(7)Because the entropy measure, here D, increases with diversification, correlation among the lines

would normally inflate this measure. By subtracting the 2-digit SIC entropy measure from the 4-

digit measure, equation (7) attempts to remove any potential correlation that occurs as a result of

operating in largely similar lines.

I directly extend Robins and Wiersema (1995)s last measure of diversification for

potentially correlated lines of business. This method captures the actual correlation between two

lines, and estimates diversification based on the proportion of business written in each line.

Following Robins and Wiersema (1995), in equation (8), si is the proportion of business written

in a given line, and ij is the correlation between the lines i and j.

(8)This measure has one primary drawback, if it is to be related to the Herfindahl index and modern

portfolio theory it is additive instead of multiplicative. As the authors discuss in appendix twoof their work, the value can range outside of -1 and 1 with more than one line of business, and is

thus not directly comparable between firms when observing an industry. Additionally, using a

diversification measure comparable to portfolio variance is beneficial because a value closer to

zero implies a less risky portfolio.

3.2.3 Modern Portfolio Theory


34/158

23

The method I develop to measure the correlation for insurer line of business

diversification is based, in large part, on modern portfolio theory. Markowitz (1952)s modern

portfolio theory shows that the covariance between returns on securities will affect the overall

portfolio variance. The principle of the theory is that an investor who wishes to hold a

diversified portfolio must consider the interrelatedness of the stocks he or she purchases. 7

Similarly, an insurer that operates in two or more correlated lines of business should consider the

potential interrelatedness of those lines when making capital adequacy decisions.

By combining the principles of portfolio theory with work in papers such as Robins and

Wiersema (1995), I hope to create a more robust diversification measure that captures reductions

in actual diversification due to the existence of correlated earnings patterns. Markowitz (1952)

measures the total variance of a portfolio of securities as:

= (9)

In the portfolio context, s i indicates the proportion of total assets invested in an individual

security, i is the standard deviation of the security return, and ij is the correlation between

returns of securities i and j. The portfolio variance is the sum of the variance of each security

times its respective weight squared, plus the sum of the additional portfolio covariances, for

securities that are correlated. When all securities are independent, ij will equal zero, and only

the individual security variance will matter.

This methodology can be extended to the insurer framework where the lines of businesswritten can be viewed as securities in a portfolio, allocated share si, which have a return based on

the loss ratio the insurer experiences. Lines of insurance are similar to securities in a portfolio.

An insurer collects premiums and pays out losses for a line, and can measure profitability using a

loss ratio, which indicates the percentage return on that line. Previous research has also used a

portfolio approach for assessing insurers operations. For example, Kahane (1977) views insurer

operations as a portfolio of policies when measuring the optimal insurer business strategy based

on risk and return of the available lines. 8

7 For example, an investor that purchases two bank stocks may realize a large drop in portfolio value when thefinancial sector enters a period of losses. However, an investor that diversifies into bank and energy securities may

be less negatively affected by a downturn in the financial sector, since the earnings patterns of these industries arenot perfectly correlated.8

Kahane (1977) states that, .. the activity of an insurance company may be viewed as the management of a portfolio of insurance policies,, that the decision to write in different lines is a concern that cannot be made


35/158

24

Section 3.3 Hypotheses Development

In this section I develop the hypotheses needed to test if the modified HHI measure is

different than the traditional HHI measures. Additionally, I develop tests to examine whether the

difference between the modified and traditional HHI vary across firms, and if the difference has

a meaningful impact on research, as well as the use of those results for regulators and insurers.

3.3.1 The Modified HHI Changes Concentration

In general, adding a correlation component to the traditional HHI measure will only

change the value of the HHI if correlation between lines of insurance is found to be significant.

It is possible that, on average, correlation between lines of insurance is very low or non-existent,

in which case there will be no measurable difference between the HHI and the modified HHI.

However, if firms diversify into related lines of insurance, I expect to see a positivecorrelation between these lines. This would indicate that certain lines of insurance are

simultaneously experiencing periods of profit or loss with other lines. A positive correlation

between lines of insurance would cause the modified concentration index to increase. Thus, if

significant correlation exists between lines of insurance written by firms, I expect the modified

HHI to be higher than the traditional HHI. 9

Hypothesis 1 The value of the modified HHI will be, on average, significantly different

from the traditional HHI. Specifically, the modified HHI should be significantly higher

than the traditional HHI.

In order to test hypothesis 1, a t-test is performed between the HHI and modified HHI to

determine whether or not the two indices have significantly different mean values. I create three

versions of the modified HHI, based on differences in measuring correlation and described in

section 4. I also test whether or not the three versions of the modified HHI are similar and

discuss their merits to establish which version is the best to use in testing the subsequent

independently, and that correlation in the portfolio (they discuss this in terms of underwriting and investment) must be considered in deciding the optimal product mix. 9 It is possible that the modified HHI could also be significantly lower than the traditional HHI. For this to occur,one or more lines of insurance would have to be negatively correlated with other lines of insurance. This wouldindicate that a certain line of insurance would experience periods of profitability, while simultaneously another lineof insurance would experience periods of loss.


36/158

25

hypotheses. In each case, it is expected that the modified HHI will be significantly higher than

the traditional HHI measure.

3.3.2 The Modified HHI Is Different from the Traditional HHI

The value of creating a modified HHI is in the information conveyed through the

measure. By including correlation components between the lines of insurance, I am able to

quantify the financial relatedness of these lines into one index. However, even if hypothesis 1 is

supported and the mean value of the modified HHI is significantly different from the traditional

HHI, there may be no new information conveyed. For instance, a small positive correlation

between all lines of insurance would simply cause the value of the modified HHI to increase by a

few percentage points, but would not affect the distribution of insurer concentration. That is, the

ranking of insurers by concentration pre- and post-correlation would be roughly identical.

However, if insurers vary in the degree to which they write business in correlated lines ofinsurance, or if some types of insurers systematically operate within related or unrelated lines of

insurance, the shift between the traditional and modified HHI is likely to vary. This variation

may convey new information on diversification patterns across insurers. Thus, the value of

developing a modified HHI stems in part from whether or not I observe a shift in the distribution

of insurer concentration.

Hypothesis 2 The distribution of insurer concentration will be significantly different

when measured using the modified HHI compared to the traditional HHI.

Hypothesis two is tested using several methods including graphical and statistical

examinations of the modified and traditional HHI variables. Further, by observing the summary

statistics of each HHI variable, I can compare the dispersion in the variables distributions.

Because the HHI and the modified HHI are expressed numerically on the same scale (this

is discussed in greater detail in section 4), an XY scatterplot graph allows one to observe the

linear dispersion of one HHI variable compared with the other. Greater dispersion in the

scatterplot would indicate that the observations are not shifting completely linearly they move

both up and down, or not at all. Additionally, a histogram of the difference between the

modified and traditional HHIs provides visual insight into where the difference clusters. If the

differences are observed all across the axis, there are many shifts in concentration. If the


37/158

26

differences all cluster at one point, the shift does not greatly affect the distribution of

concentration.

I also perform the univariate sign and Wilcoxon sign-rank tests on the two values (these

tests provide non-parametric approaches to determining whether or not the variable distribution

is equivalent). Essentially, this is a test to see whether or not the ranking of firms in terms of

diversification shifts between the two measures. These tests provide statistical evidence of a

change in the variables equality, but do not require a normal distribution as in the t -test, and

consider both positive and negative differences.

The expectation is that given potent ial differences in insurers strategies and business

mixes, I will see a difference in the concentration ranking of insurers based on the modified HHI

as compared to the traditional measure.

3.3.3 The Difference in Concentration Varies Across FirmsIn addition to testing for the potential change in concentration for insurers, an important

question is what affects an insurers decision to participate in lines of insurance that are related

or independent? Hypothesis 3 explores the extent to which potential differences in the modified

HHI and traditional HHI are related to firm characteristics. Due to the fact that decisions to

diversify or not diversify into related lines are likely related to key firm characteristics, I expect

that there are systematic differences in firm characteristics that relate to the difference in the

traditional and modified HHI.

Hypothesis 3 The difference between the traditional HHI and the modified HHI is

related to key firm operational, financial, and organizational characteristics.

The operational, financial and organizational firm characteristics are related to corporate

diversification decisions. These characteristics are widely discussed in prior literature related to

diversification and focus decisions. When a firm participates in lines of business that are

positively correlated, it effectively increases its concentration. In this case the

Documents

An Empirical Examination of the Interrelations of Risks and the F