Reinsurance Networks and Their Impact on Reinsurance Decisions: Theory and Empirical Evidence

• Published date: 01 September 2015
• DOI: http://doi.org/10.1111/jori.12032
• Date: 01 September 2015

©2014 The Journal of Risk and Insurance. Vol.82, No. 3, 531–569 (2015).

DOI: 10.1111/jori.12032

Reinsurance Networks and Their Impact on

Reinsurance Decisions: Theory and Empirical

Evidence

Yijia Lin

Jifeng Yu

Manferd O. Peterson

Abstract

This article investigates the role of reinsurance networks in an insurer’s

reinsurance purchase decision. Drawing on network theory, we develop a

framework that delineates how the pattern of linkages among reinsurers de-

termines three reinsurance costs (loadings, contagion costs, and search and

monitoring costs) and characterizes an insurer’s optimal network structure.

Consistent with empirical evidence based on longitudinal data from the U.S.

property and casualty insurance industry, our model predicts an inverted

U-shaped relationship between the insurer’s optimal percentage of reinsur-

ance ceded and the number of its reinsurers. Moreover,we find that a linked

network may be optimal ex ante even though linkages among reinsurers may

spread financial contagion, supporting the model’s prediction regarding so-

cial capital benefits associated with network cohesion. Our theoretical model

and empirical results have implications for other networks such as loan sale

market networks and over-the-counter dealer networks.

Introduction

The real-world prominence of reinsurance as a risk transfer method in the insurance

industry raises questions about its benefits and costs. While there exists a rich liter-

ature that explains why insurers should purchase reinsurance (Mayers and Smith,

1982; Cole and McCullough, 2006; Cole et al., 2011), little is known about how and the

extent to which varied reinsurance costs affect such organizational activities. Much of

the prior research makes the implicit but extreme assumption that reinsurance costs

Yijia Lin is in the Department of Finance, College of Business Administration, University of

Nebraska–Lincoln, P.O.Box 880488, Lincoln, NE 68588. Jifeng Yu is in the Department of Man-

agement, College of Business Administration, University of Nebraska–Lincoln. Manferd O.

Peterson is in the Department of Finance, College of Business Administration, University of

Nebraska–Lincoln. Lin can be contacted via e-mail: yijialin@unl.edu. This article was presented

at the American Risk and Insurance Association Annual Meeting in Washington,DC in August

2013. We appreciatehelpful comments from Charles Nyce and the participants at the meeting.

The authors also thank the two anonymous referees for their very helpful suggestions and

comments during the revision process.

531

532 The Journal of Risk and Insurance

are exogenous or independent of risk characteristics and ignores costs associated with

the distinct risk exchange relations between insurers and reinsurers. Studies have so

far linked reinsurance demand to firm characteristics, such as firm size, group affili-

ation, and organizational form (Cole and McCullough, 2006; Cole et al., 2011). While

researchers have also looked at how reinsurance demand relates to exogenous rein-

surance costs, many of them ignore determinants of those costs due to the lack of a

promising venue in which to quantify reinsurance costs, which severely limits pre-

vious studies in this area. To fill the gap, this article brings a network perspective

to the study of reinsurance costs, motivated by the proliferation of reinsurance net-

works. Building on a well-known optimizing model of costly external financing, we

directly link various reinsurance costs to an insurer’s network structure. Our evi-

dence confirms the conjecture that an insurer’s network relationships are significant

determinants of its level of reinsurance purchase.

Networks are a common market phenomenon (Hochberg, Ljungqvist, and Lu, 2007;

Yu, Gilbert, and Oviatt, 2011). Among assorted networks, reinsurance networks are

not entirely new, but have been evolving rapidly in number, form, and complexity

in the relatively short period of a half century. In the insurance industry, insurers

tend to be closely tied to multiple reinsurers to transfer business risk (Garven and

Grace, 2007). This indicates that insurers are bound by their current and past risk

management practices into webs of relationships with those partners. Hence, their

use of reinsurance is influenced by direct and indirect ties among firms embedded in

networks.

In light of the above observations, we present a simple model of an insurer’s reinsur-

ance demand in the context of a networked market following Froot, Scharfstein, and

Stein. Froot, Scharfstein, and Stein’s framework is built on the pecking order theory of

financing and the correlation between investment opportunities and risk factors being

hedged, both of which are satisfied in our insurance setting. First, the pecking order

theory of financing has been applied to an intermediated market such as an insurance

market in the existing literature because “intermediaries have limited capital and face

costs of adding more, as in Froot and Stein (1998). Intermediary costs of external fi-

nance would seem natural since intermediaries are themselves corporations, subject

to the same kinds of frictions that make corporate hedging desirable in the first place”

(Froot and O’Connell, 2008). Second, property and casualty insurers have valuable

opportunities to write more policies or purchase policies from other insurers during

catastrophic periods when claims by insured are high. Prices are usually high in the

aftermath of major catastrophes driven by decreases in the supply of insurance as

well as increases in demand. This provides profitable opportunities to those property

and casualty insurers that have internal funds to write more business, which makes

hedging desirable.

In our model, because of costly external financing (Froot, Scharfstein, and Stein, 1993),

reinsurance is meaningful and can assist in maximizing the insurer’s value, the mech-

anism of which, however,is subject to various reinsurance costs—loadings, contagion

costs, and search and monitoring costs. Given this setup, we solve for the insurer’s op-

timal reinsurance ratio. The approach of this study is unique in that whereas research

Reinsurance Networks and Their Impact on Reinsurance Decisions 533

on reinsurance often rests on a neglect of network and community structures with

an assumption of independent, atomistic market players, this article goes deeper and

describes how factors related to an insurer’s reinsurance network affect the magni-

tude of its reinsurance costs, which in turn determine its reinsurance ratio. We provide

economic intuition about what generates differences in insurers’ network structures

and how their endogenous network planning relates to their levels of reinsurance

activities.

Our arguments about various reinsurance costs are built on two properties of an

insurer’s network, network centrality and network cohesion. In this study, network

centrality refers to the number of reinsurers in the insurer’s network, and network co-

hesion denotes the strength and cohesiveness of linkages among the reinsurers. Two

testable predictions emerge from our theory. First, other things equal, there exists an

inverted U-shaped relationship between the optimal reinsurance level and the net-

work centrality.This nonlinear relationship reflects the trade-off between two effects:

(1) transferring risk to more reinsurers decreasesthe total loadings for the insurer, and

(2) transferring risk to more reinsurers increases the insurer’s search and monitoring

costs. As the number of reinsurers increases, we show the cost reduction fromthe first

effect exceeds the cost increment from the second effect, but only up to a point. The

model thus predicts that the insurer’s optimal reinsurance level first increases with

the number of its reinsurers but there is a cutoff point above which ceding risk to

more reinsurers decreases the optimal reinsurance level. Second, the model predicts

that the insurer’s reinsurance level has an inverted U-shaped relationship with the

network cohesion. This is because network cohesion has two opposite effects on the

percentage of reinsuranceceded. On the one hand, an increase in the network cohesion

coincides with an enlarged contagion cost, which reduces the reinsurance ratio. On

the other hand, an increase in the network cohesion among reinsurers lowers search

and monitoring costs because of the benefit of social capital.

We test these predictions based on reinsurance demand from a sample of U.S. prop-

erty and casualty primary insurers. Weconstruct measures of network centrality and

test our first hypothesis on an insurer’s reinsurance levels and the number of reinsur-

ers. We calculate measures of network cohesion and test our second hypothesis on

an insurer’s reinsurance level and the linkages among reinsurers. Using a sample of

1,262 primary insurers between 1993 and 2005, in addition to the results consistent

with the existing reinsurance literature, we present new evidence on how network re-

sources determine reinsurance levels, which is strongly supportive of the model’s two

main predictions. Importantly, the magnitude of the network effect on the reinsurance

decision is statistically and economically significant. Weshow that, on average, trans-

ferring risk to one more reinsurer increases an insurer’s risk ceding level by 2 percent.

Moreover,in this market, the benefit of social capital in most cases dominates the cost

of contagion among reinsurers. For an average firm, a one standard deviation increase

in network cohesion is associated with an 18.8 percent increase in risk transfer,all else

equal.

Our article contributes to the growing body of researchon corporate risk management

in general and reinsurance specifically in three ways. First, it complements previous