The Reinsurance Network Among U.S. Property–Casualty Insurers: Microstructure, Insolvency Risk, and Contagion

• Author: Mary A. Weiss,Tao Sun,J. David Cummins,Hua Chen
• DOI: http://doi.org/10.1111/jori.12269
• Date: 01 June 2020
• Published date: 01 June 2020

THE REINSURANCE NETWORK AMONG U.S.

PROPERTY–CASUALTY INSURERS:MICROSTRUCTURE,

INSOLVENCY RISK,AND CONTAGION

Hua Chen

J. David Cummins

Tao Sun

Mary A. Weiss

ABSTRACT

Reinsurance is the primary source of interconnectedness in the insurance

industry. As such, reinsurance connectivity provides a transmission

mechanism for financial shocks and potentially exposes insurers to

contagion and systemic risk. In this article, connectivity within the U.S.

property–casualty (P/C) reinsurance market is modeled as a network. We

model the network of all primary insurers and reinsurers in the market. We

analyze all bilateral reinsurance counterparty relationships (domestic and

foreign) of U.S. P/C insurers, and we model both intra- and intergroup

transactions. We extend the prior literature by providing a detailed

examination of the reinsurance network structure, including network

density, network components, centrality of individual insurers, and sub-

network analysis for top insurers. Our analysis of contagion and insolvency

risk reveals that even the failure of the top 10 in-degree or in-strength

insurers with 100 percent loss given default would not lead to widespread

insolvencies in the U.S. P/C insurance industry.

INTRODUCTION

Economic agents do not exist in isolation, but rather are connected by various

economic relationships. One common driver of interconnectedness is economic

transactions among financial institutions that comprise the so-called “financial

network” (Upper, 2011). A growing body of evidence shows that characteristics of the

financial network have important economic implications for contagion risk and

the stability of particular financial markets (e.g., Billio et al., 2012; Hasman, 2013;

Hua Chen is at Temple University, Philadelphia, Pennsylvania. Chen can be contacted via

e-mail: hchen@temple.edu. J. David Cummins is at Temple University, Philadelphia,

Pennsylvania. Cummins can be contacted via e-mail: cummins@temple.edu. Tao Sun is at

Lingnan University, Hong Kong. Sun can be contacted via e-mail: taosun@ln.edu.hk. Mary A.

Weiss is at Temple University, Philadelphia, Pennsylvania. Weiss can be contacted via e-mail:

mweiss@temple.edu.

©2018 The Journal of Risk and Insurance (2018).

DOI: 10.1111/jori.12269

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. Vol. 87, No. 2, 253–284 (2020).

Acemoglu, Ozdaglar, and Tahbaz-Salehi, 2015). Financial network characteristics

also can affect individual economic agents’ decisions and performance (e.g., Li and

Schurhoff, forthcoming).

Reinsurance plays a fundamental role in the insurance industry, allowing insurers to

transfer risk among each other, thereby enhancing risk sharing and diversification.

Reinsurance transactions connect insurers in a complex network where insurers

hold bilateral exposures to each other, leading to potential contagion risk. Therefore,

reinsurance has been recognized as the primary source of interconnectedness

in the property–casualty (P/C) insurance industry (Cummins and Weiss, 2014).

Reinsurance interconnectedness can serve as a transmission mechanism for financial

shocks and may exacerbate insurers’ exposure to contagion and/or systemic risk.

1

The objective of the present article is to utilize network theory to provide a

sophisticated analysis of the microstructure and topology of the reinsurance network

of U.S. P/C insurers. Network theory is a mathematical approach to the study of

graphs, representing relations among discrete objects. A network describes a

collection of nodes and the links between them. In the insurance market context,

nodes are insurers and links are reinsurance transactions. We utilize network theory

to analyze all inter- and intragroup bilateral reinsurance counterparty relationships

(domestic and foreign) of U.S. P/C insurers for the sample period 2000–2015.

The prior literature on reinsurance relationships among U.S. P/C insurers is rather

limited. Cummins and Weiss (2014) provide summary statistics on bilateral

relationships but do not further analyze the data.

2

Park and Xie (2014) study

reinsurance counterparty risk for U.S. P/C insurers from 2003 to 2009, and provide

evidence that selected reinsurer insolvencies would not lead to widespread failures of

U.S. P/C insurers. Our article goes beyond Park and Xie in several important ways.

Among other differences, Park and Xie’s analysis does not utilize network theory.

Their solvency analysis is based on the defaults of at most three professional

reinsurers, whereas we study the defaults of up to 10 top firms. Park and Xie also do

not simulate the potential defaults of group-affiliated insurers. Thus, our article is the

first to utilize network analysis to examine the U.S. reinsurance market and also

provides evidence that the failures of group affiliated insurers could cause more

severe surplus losses than the defaults of professional reinsurers.

3

The only prior article to use network theory in analyzing U.S. P/C reinsurance is Lin,

Yu, and Peterson (2015). They focus on testing the relationship between an insurer’s

1

In this article, we follow Cummins and Weiss (2014) and the related financial literature in

distinguishing between systemic risk and industry-focused contagion. In order to be systemic,

contagion must spill over into other sectors of the economy (e.g., banking), cause a significant

reduction in real economic activity, and satisfy certain other criteria.

2

Several priormacroeconomic studieshave concluded that reinsurers are not subjectto systemic

risk (e.g., Geneva Association, 2010; International Association of Insurance Supervisors [IAIS],

2012). However,these studies do not consider bilateral reinsurance transactions.

3

For more details about the differences between our article and both Park and Xie (2014) and

Lin, Yu, and Peterson (2015), see the working paper version of this article available on the

SSRN website.

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network position and its reinsurance utilization, while our article studies insolvency

and contagion risk to U.S. insurers resulting from failures of reinsurance counter-

parties. Lin, Yu, and Peterson also confine their analysis exclusively to binary

networks, whereas we estimate both binary and value-weighted networks.

4

Value-

weighted networks provide important additional information about the strength of

connectivity in the reinsurance network and hence its vulnerability to default.

We estimate our weighted networks using two alternative weighting variables—

premium transactions and net reinsurance payable. Net reinsurance payable

represents the net amount owed by a reinsurer to its reinsurance counterparties.

5

Reinsurance payable appears on the balance sheets of counterparties as net

reinsurance recoverable. Defaults on reinsurance payable increase the liabilities of

the reinsurer’s counterparties and thereby damage their financial condition.

By way of preview, we find that the U.S. P/C reinsurance network can be considered

sparse with a core-periphery market structure, where core firms serve as hubs

connecting periphery firms that otherwise would not be connected. Core insurers

usually are highly connected or have dominant market shares, and their rankings

remain important over our sample years. These core nodes make the market

susceptible to a too-interconnected-to-fail problem. On average, the largest strongly

connected component (SCC) accounts for 60 percent of total reinsurance premiums

ceded, suggesting that shocks to insurers within an SCC can potentially spread to

other insurers within and connected to the SCC. Therefore, we simulate the effects of

shocks to the network to determine the susceptibility of the network to contagion and

insolvency risk. The U.S. reinsurance network is found to be quite resilient—even the

failure of the top 10 in-degree or in-strength reinsurers would not lead to widespread

insolvencies in the U.S. P/C insurance industry.

The results presented in this article are important because detailed analysis of the

reinsurance network can help provide a better understanding of the interconnected-

ness created by reinsurance transactions. Moreover, network measures can have

important implications for regulation by identifying and monitoring key players and

in formulating timely macroprudential policies. Lastly, our comprehensive stress

tests shed light on whether reinsurance is a significant source of contagion or systemic

risk and/or identify insurers that are too interconnected to fail.

4

A binary network is based on indicator variables set equal to 1 if a relationship exists between

two firms and 0 otherwise, whereas a value-weighted network uses weights representing the

strength or magnitude of the relationship.

5

Reinsurance recoverable represents the portion of an insurer’s losses that can be recovered from

reinsurers. Nonpayment of recoverables is a significant threat to solvency for reinsured firms

(Cummins and Weiss, 2014; Park and Xie, 2014). Recoverables include (1) reinsured losses on

claims already paid by the ceding company, (2) reinsured losses that have occurred and been

reported but have not yet been paid by the ceding insurer, (3) incurred but not reported

reinsured losses, and (4) unearned premiums held by the reinsurer. Net reinsurance recoverable

is obtained by subtracting “ceded reinsurance balances payable” and “other amounts due to

reinsurers” from total “reinsurance recoverable.” The quoted text gives the exact wording of

these items from Schedule F, Part 3.

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