Portfolio Similarity and Asset Liquidation

in the Insurance Industry∗

Mila Getmansky† Giulio Girardi‡ Kathleen W. Hanley§

Stanislava Nikolova¶ Loriana Pelizzon‖

This Draft: March 16, 2016

Abstract

The designation of insurance companies as Systemically Important Financial Institutions(SIFI) explicitly considers the potential for the interconnectedness of their portfolios to af-fect the asset liquidation channel of systemic risk transmission. In this paper, we studythe determinants and effects of interconnectedness on the selling behavior of insurers usingcosine similarity. We document that greater portfolio similarity between two insurers is sig-nificantly related to the similarity in insurers’ asset liquidation decisions. This relationshipis stronger when both insurers are capital constrained but only at the asset class level sug-gesting that correlated re-balancing to improve capital ratios occurs at a higher level thanindividual securities. We find that the relationship between the portfolio holdings of bothilliquid securities and downgraded issuers and sales similarity is greater during the financialcrisis. In addition, we show that portfolio similarity cannot be explained by easily observ-able characteristics such as return correlation, concentration or assets under management.We interpret our findings to mean that the co-investment decisions of insurers under manydifferent economic conditions are an important determinant of selling behavior. Overall, ourpaper provides an implementable mechanism to identify and monitor the interconnectednessof insurance company portfolios.

Keywords: Interconnectedness, Asset liquidation, Similarity, Systemic Risk, Financial Sta-bility, Insurance Companies, SIFI

∗We thank Mark Flannery and participants at the Temple University Workshop on Systemic Risk andthe Insurance Industry and MIT CSRA Meeting for helpful comments. We thank Max Riedel and MatteoSottocornola for excellent research support. The Securities and Exchange Commission, as a matter of policy,disclaims responsibility for any private publication or statement by any of its employees. The views expressedherein are those of the author and do not necessarily reflect the views of the Commission or of the authorscolleagues on the staff of the Commission.†Isenberg School of Management, University of Massachusetts, Amherst, MA 01003, Email: msher-

man@isenberg.umass.edu.‡Division of Economic and Risk Analysis, U.S. Securities and Exchange Commission, Washington DC

20549-9040, Email: girardig@sec.gov.§College of Business and Economics, Lehigh University, Email: kwh315@lehigh.edu.¶College of Business Administration, University of Nebraska–Lincoln, Lincoln, NE 68588, Email:

snikolova2@unl.edu.‖Goethe University Frankfurt - Center of Excellence SAFE and Ca’ Foscari University of Venice, Depart-

ment of Economics, 30100 Venice, Email: pelizzon@unive.it.

“The severity of the disruption caused by a forced liquidation of Prudentials assets couldbe amplified by the fact that the investment portfolios of many large insurance companiesare composed of similar assets, which could cause significant reductions in asset valuationsand losses for those firms. The erosion of capital and potential de-leveraging could result inasset fire sales that cause significant damage to the broader economy.” (emphasis added)

Basis for the Financial Stability Oversight Council’s Final DeterminationRegarding Prudential Financial, Inc.

1 Introduction

The recent global financial crisis of 2007-2009 exposed many vulnerabilities in the fi-

nancial system. One of these was the implicit and explicit interconnectedness of financial

institutions, which led to the collapse of Lehman Brothers, Bear Stearns, Washington Mu-

tual, Wachovia, and AIG, among others. In addition, the events of this period precipitated

huge losses in several financial markets (e.g. stocks, credit default swaps, subprime mortgage,

and money markets). Governments in the United States, United Kingdom, and several other

Western European countries were forced to intervene in order to prevent further declines.

Following the global financial crisis, the U.S. Congress passed the Dodd-Frank Wall Street

Reform and Consumer Protection Act of 2010 (Dodd-Frank Act). The Act created the Fi-

nancial Stability Oversight Council (FSOC) and endowed the Council with the authority to

designate bank and nonbank Systemically Important Financial Institutions (SIFIs). Com-

panies that are designated as SIFIs are subject to enhanced prudential standards with the

goal of limiting the effect of a SIFI’s distress on financial stability. In designating nonbank

financial institutions, such as insurance companies, asset management companies, savings

and loan holding companies, broker-dealers, and other financial firms as SIFIs, a variety

of factors have been considered by regulators with size and interconnectedness being two

criteria.1

1As noted in the final rule on the Authority to Require Supervision and Regulation of Certain NonbankFinancial Companies, “Section 113 of the Dodd-Frank Wall Street Reform and Consumer Protection Act(Pub. L. 111203, 124 Stat. 1376 (2010).) authorizes the Financial Stability Oversight Council to determinethat a nonbank financial company shall be supervised by the Board of Governors of the Federal ReserveSystem and shall be subject to prudential standards... if the Council determines that material financialdistress at the nonbank financial company, or the nature, scope, size, scale, concentration, interconnectedness,or mix of the activities of the nonbank financial company, could pose a threat to the financial stability of the

1

Although it is relatively straight-forward to measure the size of a financial institution

(global assets, or for a foreign institution, U.S. total consolidated assets), there is no consen-

sus on how to measure interconnectedness. Interconnectedness among financial institutions

can contribute to systemic risk in a variety of ways on both the asset and liability side

of the balance sheet. Prior research that has focused on the contribution of insurers to

systemic risk generally examines interconnectedness through operational risks, reinsurance,

non-traditional investments, and financing. Harrington (2009) suggests that the systemic

risk of property and casualty (P&C) insurers is low, while that of life insurers could be high

because of higher leverage and potential policyholder withdrawals during a financial crisis.

Cummins and Weiss (2014) conclude that the core activities of both life and P&C insurers

are not a source of systemic risk, but the non-core activities of life insurers could make them

systemically relevant. Reinsurance can also be a source of interconnectedness (Cummins and

Weiss (2014) and Park and Xie (2014)), as can be insurers’ increased exposure to derivatives

(Geneva Association (2010) and Grace (2010)) and increased reliance on short-term funding

(Geneva Association (2010)).

The Council defines the asset liquidation channel as occurring when a “nonbank finan-

cial company holds assets that, if liquidated quickly, would cause a fall in asset prices and

thereby significantly disrupt trading or funding in key markets or cause significant losses or

funding problems for other firms with similar holdings.”2 In this paper, we focus on the

asset side of the balance sheet and examine whether the interconnectedness among the in-

vestment portfolios of insurers could contribute to systemic risk through the asset liquidation

channel. We contribute to the literature in two ways. First, we outline a methodology that

captures interconnectedness between pairs of insurers. Second, we show how our measure of

interconnectedness is related to the asset liquidation channel.

United States.” Similar characteristics are used internationally by the Financial Stability Board to designateglobally systemically important institutions (G-SIFIs), with size and interconnectedness being two criteria((BIS (2014))).

2See Basis for the Financial Stability Oversight Council’s Final Determination Regarding PrudentialFinancial, Inc. available on the FSOC website (FSOC (2013)).

2

Sales of securities can be triggered by asset valuation shocks (Brunnermeier and Pedersen

(2005)), capital constraints (Ellul, Jotikasthira, and Lundblad (2011), Danielsson, Shin, and

Zigrand (2004) and Brunnermeier and Pedersen (2009)), and sale of collateral (Shleifer and

Vishny (2011)). The price impact of portfolio re-balancing is exacerbated when the securi-

ties sold are illiquid (Brunnermeier and Pedersen (2009) and Cont and Wagalath (2015)).

According to Kartasheva (2014), insurers do not need to fail to propagate systemic risk; it

may be sufficient for them to “fire sell” assets to produce a significant systemic impact.

The transmission of systemic risk through the asset liquidation channel is likely to occur if

the portfolios of insurance companies are similar. When faced with a financial shock to either

assets or liabilities, the assumption is that insurers will re-balance their portfolios in the same

fashion thereby transmitting systemic risk throughout the economy. For example, Ben S.

Bernanke (Monitoring the Financial System, 2013) states that “Examples of vulnerabilities

include interconnectedness, and complexity, all of which have the potential to magnify shocks

to the financial system. Absent vulnerabilities, triggers [such as losses on mortgage holdings]

would generally not lead to full-blown financial crises.” However, little research has been

conducted to examine the similarity of insurers’ portfolios and whether it affects their selling

behavior.

We propose a measure of interconnectedness among insurers based on the cosine similarity

of their portfolios and selling behavior. The National Association of Insurance Commissioners

(NAIC) requires that insurance companies disclose their portfolio holdings and transactions

at the individual security level. Therefore, we are able to determine both the yearly portfolio

composition and re-balancing through time. We demonstrate that our interconnectedness

measure can predict asset liquidation at both the security issuer and at the asset class level.

Using the sample of all insurers in Schedule D, we show that their asset allocation de-

cisions can be characterized by only a few different strategies. Cluster analysis reveals that

insurer allocation strategies can be divided into three distinct strategies based upon the pri-

mary investment by the insurer: 1) municipal bonds and equity, 2) corporate bonds, and

3

3) U.S. government debt. We find that broad asset allocation strategies among insurance

companies tend to be long-term in nature and do not vary much over the business cycle.3

Although broad asset class allocation strategies may remain similar through time, the

actual composition of the portfolios may exhibit substantial variation either because the

weights of the asset classes or the choice of individual securities within the strategy differ.

Restricting our sample to approximately 99 publicly-traded insurers that comprise around

70% of the book value of securities held by the insurance industry, we first construct a vector

of portfolio weights at the asset class or issuer (6 digit CUSIP) level for each insurer. We then

use cosine similarity to measure how similar are the portfolios of a pair of insurers in terms of

asset classes or issuers.4 One benefit of cosine similarity is that it has an easy interpretation

because it is bounded between zero and one. The more (less) similar are the portfolios of

two insurers, the closer the cosine similarity is to one (zero). Our sample consists of over

41,000 insurer pair-years from 2002 to 2014.

We examine the determinants of pairwise portfolio similarity using a multivariate ap-

proach that controls for characteristics of the two insurers and their portfolios. We show

that for both asset class and issuer level similarity, two insurance companies have generally

more similar portfolios if they are both in the same line of business (life or P&C).

Insurers are also more similar if their portfolios are less, not more, concentrated, as

measured by a Herfindahl index suggesting that diversification increases portfolio similarity.

This is consistent with a growing literature (Allen, Babus, and Carletti (2012), Castiglionesi

and Navarro (2008), Ibragimov, Jaffee, and Walden (2011), and Wagner (2010)) that argues

that diversification in the banking industry can lead to greater systemic risk because it leads

banks to invest in similar assets. In support of the adverse effects of diversification, Wagner

(2009) argues that asset allocation in banks is not efficient and proposes that the optimal

3Cluster analysis is one metric with which to examine systemic risk. Allen, Babus, and Carletti (2012)propose a model in which asset commonality and short-term debt of banks interact to generate excessivesystemic risk. They show that in a clustered structure, groups of institutions that hold similar assets defaulttogether. Blei and Ergashev (2014) use cluster analysis to construct ACRISK, a measure of systemic riskbased on commonalities in bank’s asset holdings that captures the buildup of systemic risk.

4Sias, Turtle, and Zykaj (2015) analyze hedge funds’ trading behavior also using cosine similarity.

4

regulatory treatment of banks is to encourage more correlation among bank asset holdings

at already highly correlated banks and lowering the correlation at other banks.

At the asset class level we find that both pairs of potential SIFIs (PSIFIs) and pairs

of non-PSIFIs have greater portfolio similarity although the coefficient for PSIFI pairs is

only marginally significant. (We define a PSIFI as an insurer that either has $50 billion in

consolidated assets in at least one year of our sample period.)5 At the issuer level, portfolio

similarity continues to be greater when the pair of insurers are both non-PSIFI, but we do not

have any evidence that PSIFI pairs are more likely to have higher portfolio similarities. In

addition, the average level of portfolio similarity between pairs of PSIFIs is generally lower

than the average portfolio similarity between pairs of non-PSIFIs throughout the sample

period. Thus, we do not find strong evidence for the assumption that the portfolios of

PSIFIs are more likely to be composed of similar assets than other pairs of insurers.

Next we examine whether public market information such as return correlation is related

to portfolio similarity. A number of papers have proposed return correlation as a measure

of interconnectedness (Billio, Getmansky, Lo, and Pelizzon (2012), Neale, Drake, Schorno,

and Semann (2012), and Brunetti, Harris, Mankad, and Michailidis (2015)). Including return

correlation in the model of pairwise determinants of portfolio similarity does not substantially

improve the model. For asset class similarity, the return correlation coefficient is insignificant

and for issuer similarity it is significantly negative with little improvement in the R2 in any

specification. These findings suggest that return correlation may not be an appropriate

metric to measure the effect of interconnectedness on the transmission of risk through the

asset liquidation channel.

In order for our measure to be useful, it must predict whether insurers are selling similar

assets. When we examine the determinants of quarterly pairwise sales similarity, we do not

find a strong association between business lines and sales similarity. Unlike the determinants

of portfolio similarity, we show that PSIFI pairs are more likely to have similar sales behavior

5The methodology for determining global systemically important insurers is also presented in (IAIS(2013))and (IAIS (2015)).

5

at both the asset class and issuer level but non-PSIFIs are not. Furthermore, the sales

similarity between two insurers is stronger if both of them have concentrated portfolios.

Despite the fact that we do not find that PSIFIs are more likely to hold similar portfolios,

our results do provide confirmation that PSIFIs are more likely to make similar selling

decisions when their portfolios are similar.

In order to examine the potential for interconnectedness in portfolio holdings to influence

the asset liquidation channel, we analyze whether portfolio similarity captures commonality

in asset re-balancing. At either the asset class or issuer levels, we find that portfolio simi-

larities at prior year-end are significantly related to quarterly sales similarity regardless of

whether both insurers are PSIFIs or non-PSIFIs. As with portfolio similarity, we present

evidence that return correlations cannot substitute for our measure of interconnectedness.

Other factors may influence selling behavior, most notably, capital regulation. The litera-

ture has shown that capital-constrained insurers attempt to improve their regulatory capital

standing primarily by re-balancing their investment portfolios (Ellul, Jotikasthira, and Lund-

blad (2011), Ambrose, Cai, and Helwege (2008), Manconi, Massa, and Yasuda (2012)), and

these activities can lead to fire sale prices (Merrill, Nadauld, Stulz, and Sherlund (2013)).

We examine whether our findings are driven by both insurers in a pair having low risk-based

capital (RBC) ratios. To do so, we interact a dummy variable, equal to one if both insurers

have low RBC ratios, with our two measures of portfolio similarity. The results indicate that

insurers with low RBC ratios and similar portfolios are more likely to sell the same asset

class. At the issuer level, however, low RBC ratios do not appear to affect sales similarity.

We interpret this finding to mean that insurers with similar portfolios re-balance within the

same asset class but not necessarily by selling the same set of issuers.

In addition, we analyze whether the relationship between portfolio similarity and sales

similarity can be captured by the similarity in holdings of illiquid or liquid securities or

the similarity of downgraded and non-downgraded bonds. Given a broad literature on the

potential for regulated entities to sell liquid securities in times of crisis and to sell downgraded

6

securities in order to avoid an increase in capital, it is possible that the relationship we

document is driven by insurers’ portfolio re-balancing in these types of securities and not

more generally (or vice versa). We decompose insurers’ portfolio similarity into liquid/illiquid

by asset classes and by whether or not an issuer was downgraded in the following year. We

find that the portfolio similarity of all of these subsets predicts sales similarity and therefore,

our results are not simply due to a specific group of securities.

Finally, we analyze whether our findings change in the period surrounding the financial

crisis. We define three dummy variables, equal to one if the time period falls within 2002-2006

(Pre-Crisis), 2007-2009 (Crisis) and 2010-2014 (Post-Crisis), zero otherwise, and interact

them with the portfolio similarities based on liquidity and downgrades. We find that the

relationship between the portfolio similarity of illiquid and downgraded issuers and sales

similarity is stronger during the financial crisis indicating that the co-investment decisions

of these assets are more likely affect selling behavior in times of market stress.

Our analysis complements recent work on corporate bond herding among insurers. Chi-

ang and Niehaus (2016) examine the herding behavior of life insurers and find that buy-side

herding is more pronounced when insurers are part of groups that have been designated as

SIFIs and the bond has been downgraded. Comparing mutual funds, pension funds and

insurers, Fang Cai and Li (2016) also find evidence of herding by insurance companies in

downgraded bonds. Our methodology provides two potential benefits over other measures of

herding. First, we can measure interconnectedness a over a wide variety of asset classes, not

just corporate bonds. This means that we allow insurers to re-balance the portfolio using

any asset class and issuer. Second, our methodology allows for insurers to make the decision

not to sell any particular securities. This is because sales similarity is based on changes in

portfolio holdings that may, in some cases, be zero.

Overall, our results indicate that the interconnectedness of insurers’ portfolios, as mea-

sured by cosine similarity, captures attributes of interconnectedness that other simple mea-

sures such as portfolio, return correlation, concentration or size do not. Our methodology can

7

be applied more broadly to assess the level of interconnectedness of specific activities among

entities that may contribute to systemic risk. For example, one could measure whether

similarity in mortgage portfolios leads to correlated losses or lending behavior. More impor-

tantly, it also captures commonality in asset liquidation across insurers making our measure

relevant to regulators who are tasked with monitoring systemic risk in the economy.

The remainder of the paper is organized as follows. In Section 2 we present how our sam-

ple and variables are constructed as well as summary statistics. In Section 3 we describe the

composition of insurers’ portfolios using cluster analysis. In Section 4 we define our pairwise

similarity measure and investigate its determinants. Section 5 presents our examination of

the relationship between portfolio similarity and sales similarity. We examine how capital

constraints, liquidity, downgrades and the financial crisis affect our findings in Section 6. We

conclude in Section 7.

2 Data

We analyze the interconnectedness of insurance companies from 2002 to 2014 using infor-

mation from their statutory filings with the NAIC as distributed by A.M. Best. Specifically,

Parts 1 and 2 of Schedule D of these filings report for each insurer the par value and book

value of each security held at calendar year-end. Our holdings data includes all non-negative

reported positions and is constructed at an annual frequency. Disposals of securities are

reported in Parts 4 and 5 of Schedule D. The data includes, for each insurer, every security

disposed of during the year along with its par value, disposal value, and date of disposal. We

exclude security disposals due to maturity, repayment, calls, or other non-trading activity,

and construct selling transactions at a quarterly frequency.

Both portfolio holdings and sale transactions are reported at the individual security (9-

digit CUSIP) level. For each insurer, we aggregate this information to the asset class or to the

security issuer level.6 In order aggregate at the asset class level, we categorize each security

6When calculating portfolio weights, we use par value for fixed-income security holdings. Since no

8

into one of the following asset classes: (1) U.S. government debt, (2) GSE debt (including

mortgage-backed securities), (3) municipal debt, (4) sovereign debt, (5) corporate debt, (6)

private-label RMBS, (7) private-label CMBS, (8) private-label ABS, (9) equity (common

and preferred stock), and (10) mutual fund shares. We do so using information from several

data sources. We identify RMBS and CMBS using the NAIC-provided list of PIMCO- and

BlackRock-modeled securities.7 We classify all remaining fixed-income securities using (1)

the sector and subsector codes in S&P RatingXpress, then (2) the type and subtype codes in

DataScope, then (3) the issue description and issuer name in NAIC Schedule D, and finally

(4) the issuer name and collateral asset type in SDC Platinum’s New Issues Module. If we

are unable to categorize a security using this algorithm, we assign it to the asset class its

holder reports in Schedule D.

We also aggregate holdings and sales at the security issuer level. We use the first 6 digits

of each CUSIP to identify securities issued by the same entity.8 We classify every security

with the same 6 digit CUSIP as having the same issuer.

We conduct most of our analysis at the holding company rather than the group or indi-

vidual insurer level. The predominant organizational model in the insurance industry is the

insurance group, with a single holding company owning several insurance groups. Although

in many ways individual companies operate independently, some aspects of their operations

are centrally managed thus creating strong connections among the members of a group and

the subsidiaries of a holding company. By focusing on holding companies rather than on

individual companies or insurer groups, we are also able to compute equity market measures

of interconnectedness used in the existing literature that are available only at the publicly

traded holding company level.

comparable number exists for equity securities, we aggregate equity using book value.7The NAIC changed its capital assessment methodology for certain asset classes by replacing credit

ratings as the measure of expected loss with expected loss estimates from PIMCO for RMBS and BlackRockfor CMBS. The NAIC publishes the list of PIMCO- and BlackRock-modeled securities annually. For moreinformation on this change, see Hanley and Nikolova (2015).

8The use of the 6-digit CUSIP only approximates the ultimate issuer of the securities as a parent companymay have different 6-digit subsidiary CUSIPs.

9

The number of individual insurance companies in the A.M.Best Schedule D data ranges

from 3,568 to 4,270 depending on the calendar year. They are organized in 1,194 to 1,727

insurance groups with an average of 2.8 individual insurers in a group. To aggregate Schedule

D data to the holding company level, we match insurer groups to firms in CRSP/Compustat

Merged manually by name. Of the groups for which we have holdings/trade data, between

73 and 99 (depending on the calendar year) have CRSP and Compustat data. For all of the

analysis except the determination of portfolio strategies using cluster analysis, we restrict

our sample to only these publicly traded insurance groups. Nonetheless, this subset accounts

for 68-76% of the book value of Schedule D holdings reported by the insurance industry. For

each of these insurers, we collect daily holding period returns from CRSP, and financial

statement information from Compustat. Appendix A provides detailed definitions of the

variables used in our analysis.

In addition, we perform some of our analysis separately for subsets of insurers. We classify

insurers as P&C, life, or other (e.g. health, fraternal, and title) by whether at least half of

the insurers’ portfolio assets are held in a given year by companies in the group that are in

that line of business. In order to examine whether systemically important insurers are more

likely to have similar portfolios, we classify insurers as Potentially Systemically Important

Institutions (or PSIFIs) if they have more than $50 billion in total assets in at least one year

of the sample. Based on this size threshold, we identify 34 insurers as potential candidates

for SIFI designation by the FSOC.

2.1 Sample Characteristics

Table 1 presents descriptive statistics on insurer portfolio composition by issuer and asset

class for our sample of publicly traded insurers. The table shows that the average insurer

in our sample holds 2,937 different securities issued by 1,475 different issuers. The median

number of securities (issuers) held is less than half of the sample average, implying that

some insurers invest in significantly more securities than others. The average total assets

10

for a given insurer is $138.6 billion. By construction, PSIFIs hold significantly more assets

($398.3 billion) compared to non-PSIFIs ($11.5 billion). We also find that life insurers are

approximately twice as large as P&C insurers.

The table also presents insurers’ portfolio composition by asset class. We average each

insurer’s holdings through time and report the cross-sectional mean, median, and standard

deviation of the time-series averages. Consistent with the common perception that insurers

are important investors in fixed-income markets, we find that fixed-income securities make

up the majority of their holdings with more than 79% on average. Corporate bonds (41%),

GSE securities (12%) and municipal bonds (9%) represent the largest proportion of insurers’

fixed-income investments in our sample. Equity holdings of insurers are primarily in the

form of common and preferred stock, and these securities account for 17% of the portfolio

on average. The median insurer tends not to hold any mutual fund shares in its portfolio.

Finally, there appears to be significant cross-sectional variation in asset class holdings as

indicated by the standard deviation of each asset class’ proportion across insurers.

Figure 1 summarizes the time-series variation of our sample of insurers’ cross-sectional

average holdings and indicates that shifts in and out of asset classes occur through time.

Over our sample period, the portfolio allocated to equity decreases while holdings of US

government securities and mutual fund shares increase. The figure also shows that insurers’

holdings of RMBS and CMBS increase in the period leading up to the financial crisis and then

gradually decrease consistent with the evidence presented in Hanley and Nikolova (2015).

Table 1 also shows that some of this variation in holdings by asset class is related to

insurer type. Life insurers invest in more securities and issuers than P&C and their portfolios

are more heavily weighted toward corporate bonds, and less toward municipal bonds, GSE

securities and equity.

We also separately examine the portfolio composition of PSIFI and non-PSIFI insurers.

The statistics in Table 1 indicate that PSIFIs hold an average of 6,678 different securities

issued by 3,183 issuers compared to the non-PSIFI mean of 1,466 securities issued by 820

11

issuers. The size of PSIFIs’ portfolios compared to non-PSIFIs is related to the overall size

of the two groups of insurers. Both PSIFIs’ and non-PSIFI portfolios invest most heavily in

corporate bonds, PSIFIs are much more heavily weighted toward equity and mutual funds

(mainly affiliated funds).

We measure the level of portfolio concentration at both the asset class level and the issuer

level using a Herfindahl index. Specifically, asset-class portfolio concentration is:

Concentration ACi,t =N∑

n=1

w2i,n,t (1)

where wi,n,t is asset-class n weight for an insurer i and is calculated as the dollar amount

invested in asset class n relative to the total value of the insurer i portfolio at the end of

year t. Similarly, issuer-level concentration is:

Concentration Ii,t =N∑

n=1

w2i,n,t (2)

where wi,n,t is issuer n weight for an insurer i and is calculated as the dollar amount invested

in issuer n relative to the total value of the insurer i portfolio at the end of year t.

Table 1 reports the mean, median and standard deviation of insurers’ time-series averages

of the two concentration measures. The average issuer concentration in our sample is 0.06

and the average asset class concentration is 0.37. Issuer (asset class) concentration appears

to differ across types of insurers with an average of 0.06 (0.39) for Life and 0.03 (0.30)

for P&C insurers. Although life insurers invest in more issuers and securities than P&C

insurers, they hold more concentrated portfolios, as measured by either asset class or issuer

composition. Finally, PSIFIs’ portfolios do not seem more concentrated or diverse than those

of non-PSIFIs.

12

3 Portfolio Composition Using Cluster Analysis

In this section, we examine the portfolio strategies of insurers at the asset class level using

cluster analysis. We are interested in whether insurance companies differ in their portfolio

allocation strategies and whether their strategies change over time. In order to examine the

portfolio choices of our sample of insurers more carefully, we first determine whether there

exist different portfolio strategies using the entire sample of insurer groups (approximately

1,750 groups in 2014). Using all insurer groups, rather than our smaller sample of publicly

traded insurers lets us gain power in detecting different strategies.

Cluster analysis allows us to separate insurers into subgroups (clusters) that are likely

to have closer connections with each other than with those outside the cluster. As shown in

Appendix B, the cluster validation process indicates that the optimal number of clusters in

our data is three. Therefore, only a small number of portfolio strategies are being employed

by firms in the insurance industry. The average structure of the three clusters, namely the

coordinates of their centroids, is displayed in Figure 2. The figure allows one to evaluate

both the composition of the clusters (color code) and the general asset class allocation of

the sample (y-axis). Independently from the cluster and consistent with Figure 1, the most

represented asset classes are corporate bonds, equity, and U.S. government debt. ABS,

CMBS, GSE securities, mutual fund shares, sovereign bonds, and RMBS account for a

smaller portion of insurers’ portfolios. Cluster 1 of the sample is heavily tilted towards

municipal bonds and equity. Cluster 2 is mainly invested in corporate and GSE debt. Cluster

3 is dominated by U.S. government debt. In terms of the number of insurance groups in each

cluster, Cluster 1 and Cluster 2 are evenly split with approximately 45% of the sample of

all insurers in each cluster. The remaining 10% of insurance groups are in Cluster 3. If we

apply the cluster analysis separately in each year, the optimal number of clusters remains at

three and the composition of each cluster is relatively stable.

Figure 3 shows the distribution of our sample of publicly traded insurers in each cluster.

Most notably, few insurers in our sample are in Cluster 3 and the majority of insurers are in

13

Cluster 2. (In unreported results, we find that insurers infrequently move between clusters.)

A similar pattern is found for the portfolio allocation strategies of PSIFIs. Most PSIFIs are

in Cluster 2 and very few in Cluster 3 and there appears to be little difference between the

portfolio allocation strategy of PSIFIs and non-PSIFIs.

Using cluster analysis to determine portfolio strategy suggests that insurance companies

are likely to be very similar in their asset composition and therefore, potentially in their

trading strategy. Unlike the mutual fund literature in which there are a large number of

portfolio strategies, insurers appear to follow only a few. In the next section, we discuss a

methodology that captures the granularity of portfolio choices among insurers.

4 Portfolio Similarity

In order to determine whether insurers with similar portfolios are likely to trade in a

similar fashion, we construct a measure of portfolio similarity using cosine similarity. Cosine

similarity is well-suited to comparing the “distance” between two vectors and in economics,

has been more recently used in text analytics (Hanley and Hoberg (2010) and Hanley and

Hoberg (2012)) and analyzing hedge fund portfolios (Sias, Turtle, and Zykaj (2015)). An

important benefit to this methodology is that cosine similarity does not rely on self-reported

or empirically determined investment strategies in the determination of similarity and thus,

allows an objective measure of interconnectedness in portfolio allocation and security sales.

To construct this measure, we first calculate the proportional dollar value of each asset

class or issuer in an insurer’s portfolio at the end of each year. For each insurer, we create a

vector of portfolio weights using all asset classes or issuers that appear in insurers’ portfolios

in a given year. For example, the maximum vector in a given year is approximately 32,000

unique issuers and therefore, each insurer’s portfolio has a vector length of 32,000. If an

insurer does not invest in a particular issuer in a given year, the weight is set to 0.

To measure the degree of similarity between insurers i and j in year t, we calculate the

14

cosine similarity as the dot product of the pair’s portfolio weight vectors normalized by the

vectors’ lengths. We refer to this quantity as Similarityi,j,t where the portfolio weights are

measured at either asset class or issuer level.

Similarityi,j,t =wi,t · wj,t

‖wi,t‖ ‖wj,t‖(3)

Because all portfolio weight vectors have elements that are non-negative, this measure of

portfolio similarity has the property of being bounded in the interval (0,1). Intuitively, the

portfolio similarity between two insurers is closer to one when they are more similar and can

never be less than zero if they are entirely different.

Table 2 presents descriptive statistics for Similarity for the whole sample period and

three different years, 2002, 2008 and 2014. Average similarity based on asset class is high

and close to one. This finding is consistent with our cluster analysis, which finds only a

small number of portfolio strategies employed by insurers. Asset class similarity decreases

from 2002 to 2014 from a high of 0.74 in 2002 to 0.62 in 2014.

Although insurers appear to follow similar investment strategies at the asset class level,

there appears to be little overlap in the investment in individual issuers. The average cosine

similarity at the issuer level is only 0.10 in 2002 and this is only slightly lower in 2014. Overall,

issuer level similarity is fairly constant with only a small decrease during the financial crisis

of 2008. These findings point to a potential difference in interpretation of how interconnected

insurers’ portfolios are when comparing similarity at the asset class and issuer levels.

The table presents portfolio similarity by whether the insurer pairs are both PSIFI or

non-PSIFI. We find little difference between the portfolio similarity of pairs of PSIFIs and

non-PSIFIs. In each year examined, the similarity between a pair of PSIFIs is lower than

the similarity between a pair of non-PSIFIs. Although PSIFIs are assumed by the FSOC

to hold more similar securities, we do not find that this is the case. The average asset class

similarity ranges between 0.58 to 0.74 for PSIFIs, and 0.66 and 0.77 for non-PSIFI insurers

from 2002 to 2014. PSIFIs are also less similar to other PSIFIs at the issuer level.

15

Figure 5 shows the time series of the average pairwise similarity at the asset class and

issuer level for the sample of all publicly-traded insurers and for the subsamples of non-PSIFI

and PSIFI pairs. At both the asset class and issuer level, PSIFI pairs have lower portfolio

holdings similarity than non-PSIFI pairs and the level of similarity fluctuates over time.

At the asset class level, there is little difference between pairs of PSIFIs and pairs of non-

PSIFI insurers until just after the financial crisis in 2010 when the similarity between PSIFIs

begins to decline. Whether this is due to the increased regulation and scrutiny is unclear

but suggests that PSIFIs are not holding the same assets to the same degree as before the

financial crisis. At the issuer level, PSIFI pairs are also less similar than non-PSIFI pairs

but we do not see the same time trend. In fact, the level of similarity in portfolio holdings

measured at the issuer level rises until 2012 when both PSIFI and non-PSIFI pairs have the

same issuer similarity, and then begins to decline afterward.

Table 2 also presents the return correlation between issuer pairs. We measure the an-

nual return correlation for a pair of insurers RetCorr Pair at year-end using daily returns

throughout the year. This measure is commonly used in the systemic risk literature to

capture the potential for two entities to be interconnected. The average return correlation

between insurer pairs is 0.32 and follows a concave pattern over the three years in the table

with the highest return correlation in 2008 during the financial crisis. However, even though

PSIFIs are less similar in their portfolio construction compared to non-PSIFIs, the average

return correlation between pairs of PSIFIs is higher than the average return correlation be-

tween non-PSIFIs, and both subsamples follow a similar pattern as the sample as a whole.

PSIFIs, being large financial institutions by construction, are more likely to be affected by

common market factors, which is consistent with their return correlation being larger than

that of other insurers. This result indicates that portfolio similarity and return correlation

measures may capture different characteristics of insurers interconnectedness.

16

4.1 Determinants of Portfolio Similarity

To gain a better understanding of the determinants of pairwise portfolio similarity, we

examine the relationship between pairwise similarity and insurer pair characteristics. Be-

cause our dependent variable Similarity is a pairwise variable, we construct our independent

variables in a similar fashion. In order to control for firm characteristics, we use indicator

variables equal to one if both insurers are life (Life Pair) or P&C (PC Pair) and if both

insurers are PSIFI (PSIFI Pair) or non-PSIFI (Non-PSIFI Pair). We define a large insurer

as one with portfolio assets above the median and create indicator variables equal to one if

both insurers are large (Big Pair) or small (Small Pair). We also consider the asset class or

issuer concentration of an insurer’s portfolio and define it as high (low) if it is above (below)

the median for the sample. We then construct two pairwise indicator variables at both the

asset class (AC) and issuer (I) level that equal one if both insurers in the pair have portfolios

with high (Conc Pair) or low (NonConc Pair) concentration.

We estimate OLS regressions where the dependent variable, Similarityi,j,t, is the pairwise

similarity measure in a given year defined at either the asset class (Models (1) - (3)) or

issuer level (Models (4) - (6)). Table 3 presents the regression results. When we use asset

class similarity, we find that the similarity between two insurers is greater if they are in the

same line of business. When both insurers are either PSIFIs or non-PSIFIs, they have greater

asset class and issuer similarity but the relationship between being a PSIFI pair and portfolio

similarity is only marginally significant. We find similar relationships when examining the

determinants of portfolio similarity at the issuer level. However, insurers pairs who both are

life insurers and insurers pairs who are both PSIFIs are not more likely to be similar to each

other.

We split the sample of insurers into PSIFI pairs and non-PSIFI pairs (all pairs of firms

that include one PSIFI and one non-PSIFI are not included) to examine whether the determi-

nants of greater similarity within these categories differ. At the asset class level, non-PSIFI

pairs in the same line of business are more similar but only PSIFIs who are life insurers

17

are more similar to each other when they are in the same line of business. Non-PSIFIs are

more similar if they are both large insurers and less similar if they are both small. When we

consider the issuer level of portfolio similarity, we find that non-PSIFIs are not more similar

to each other if they are in the same line of business but PSIFIs are. The relationship on

size for non-PSIFIs flips for issuer level similarity.

When examining both asset class and issuer level similarity as well as subsamples of

insurers, we consistently find that non-concentrated (more diversified) insurers are more

similar than concentrated insurer pairs. Diversification is an important risk management

tool to reduce individual insurance risk. However, recent theoretical works have shown that

full diversification is not optimal because it can increase systemic risk through various forms

of financial contagion (Allen, Babus, and Carletti (2012), Castiglionesi and Navarro (2008),

Ibragimov, Jaffee, and Walden (2011), Wagner (2010)). Ibragimov, Jaffee, and Walden

(2011), Wagner (2010), and Beale, Rand, Battey, Croxson, May, and Nowak (2011) show

that even though diversification of assets reduces each institution’s individual probability of

failure, it makes systemic crises more likely.

4.2 Return Correlation and Portfolio Similarity

The previous section documents that portfolio similarity is generally related to insurer

characteristics. In this section, we examine whether portfolio similarity is captured by pub-

lic market information such as return correlation. For example, Billio, Getmansky, Lo, and

Pelizzon (2012), Neale, Drake, Schorno, and Semann (2012), and Brunetti, Harris, Mankad,

and Michailidis (2015) use return correlation as a measure of interconnectedness for insur-

ance and interbank markets. This analysis is important because market-based measures of

interconnectedness for other types of nonbank financial companies that may contribute to

systemic risk, such as hedge funds, is not readily available but portfolio similarity may be

(Sias, Turtle, and Zykaj (2015)).9

9See Ben Bernanke, in his speech to the Federal Reserve Bank of Atlanta in 2006 discussing the systemicrisk of hedge funds http://www.federalreserve.gov/newsevents/speech/bernanke20060516a.htm.

18

The advantage of using a market-based measure of interconnectedness like return corre-

lation is that it is easy to compute. However, return correlation may not capture the full

extent to which insurers are connected through their portfolio strategies. Table 2 presents the

average return correlation between a pair of insurers for the sample as a whole and by PSIFI

category in 2002, 2008 and 2014. Return correlation increases during 2008 at the height of

the financial crisis from 0.26 to 0.45 and then declines during the last year of sample period

to 0.36. As can be seen in each year, PSIFI pairs have higher average return correlation

when compared to non-PSIFI pairs although the difference between the two narrows during

the financial crisis.

In order to determine whether the pairwise correlation of stock returns (RetCorr Pair)

is a good proxy for a pair of insurers’ portfolio similarity, we re-estimate the specifications

in Table 3 and include the return correlation between two pairs of insurers as an indepen-

dent variable. Table 4 presents the estimation results. We generally find no relationship

between RetCorr Pair and asset class portfolio similarity after adjusting for the pair’s port-

folio concentration, size, and line of business. The exception are PSIFI pairs, where we

find a positive relationship between asset class similarity and return correlation. Looking at

the issuer similarity, the relationship between return correlation and similarity for PSIFIs is

negative.

Overall, the findings in Table 4 indicate that a market-based measure of interconnected-

ness such as the correlation of insurers’ equity returns does not capture portfolio similarity

well. This is likely due to the fact that equity returns reflect many different aspects of

an insurer’s a balance sheet and operations of which portfolio allocation is one character-

istic. Using return correlation alone to predict asset liquidation for insurers and possibly

other portfolio managers may be problematic. Below we investigate whether our portfolio

similarity measures contain information about future asset liquidation.

19

5 Portfolio Similarity and Asset Liquidation

We begin our analysis of the link between portfolio similarity and asset liquidation with

the descriptive statics presented in Table 5. The table reports insurers’ sales of each asset

class as a percentage of all sales from 2002 to 2014. The table shows that the majority of

sales are of corporate bonds, equity, GSE securities, mutual fund shares, and U.S. government

bonds. The proportion of corporate bonds and equity sold has decreased over time while the

proportion of mutual fund shares sold has increased. During the financial crisis of 2008 the

sale of equity decreased while the sale of GSE securities increased.

In order to examine whether insurers that are more similar are more likely to trade either

the same asset class or issuer, we construct a measure of sales similarity, Sales Similarityi,j,q

between insurers i and j in quarter q using the cosine similarity methodology described

earlier. For each insurer, we create a vector of sales weights for every possible asset class or

security issuer in a given quarter. If an insurer does not sale assets in a particular asset class

or issuer, the weight is set to 0.10

Figure 6 presents the times series of quarterly sales similarity for the sample of insurers

as well as for PSIFIs and non-PSIFIs. There is a great deal of variation in the similarity

in portfolio sales over the sample time period. At the asset class level, PSIFIs have greater

sales similarity, in general, with a slight decline over the sample period from around 0.6 to

0.45. When we define sales at the issuer level, PSIFIs always have greater sales similarity

than non-PSIFIs even though their portfolio similarity is lower. We do not see any evidence

that the sales similarity of insurers increased during the financial crisis. The figure provides

preliminary evidence to support regulators’ concerns about correlated trading behavior.

In Table 6, we investigate the determinants of sales similarity. At the asset class level, life

insurer pairs but not P&C insurer pairs tend to have greater sales similarity. Both more and

less concentrated pairs of insurers tend to sell the same asset classes. The results are different

10If an insurer does not sell anything during the quarter, we cannot compute the cosine similarity withother insurers and therefore, these pairs are not included in our tests.

20

at the issuer level. At the issuer level, insurers in the same business line are less likely to

sell the same issuers. If both insurers have high (low)concentration of issuers, they have

greater (lower) sales similarity. Therefore, diversification, while important for the similarity

in portfolio holdings, is less so when determining asset liquidation.

When examining whether PSIFI pairs have greater similarity, we find that regardless of

the type of sales similarity examined, PSIFI Pair is positively significant and non-PSIFI Pair

is negative. However, we find that if both non-PSIFIs are large, they have greater sales sim-

ilarity. This means that both potentially systemic insurers and relatively large insurers tend

to sell similar issuers but smaller non-systemic insurers do not.

Next we investigate whether our measure of portfolio similarity is able to predict sales

similarity as suggested by the theoretical work of Allen, Babus, and Carletti (2012). Specif-

ically, we estimate OLS regressions of quarterly sales similarity on the prior year portfolio

holdings similarity constructed at the issuer or asset class levels. We control for other pair

characteristics and include year-quarter fixed effects. Table 7 presents the results from these

estimations.

At both the asset class and issuer level, we find a significant relationship between the

similarity in portfolio holdings and the similarity in asset sales. Insurers with more similar

holdings have more similar sales and this relationship is stronger at the issuer level than at

the asset class level. The R2 for the models using asset class is around 10% compared to

the R2 of 15% when using issuer similarity. With the exception of life insurer pairs at the

asset class level, insurers in the same line of business have lower, not higher, sales similarity.

When we split the sample into PSIFI and non-PSIFI pairs, we continue to find a significant

relationship between portfolio and sales similarity.

We also document that two insurers that both hold concentrated portfolios have greater

sales similarity than two insurers that both hold non-concentrated portfolios. Although

concentration and size have been proposed as potential metrics to identify systemically im-

portant financial institutions (Haldane and May (2011) Gai, Haldane, and Kapadia (2011)

21

and Allen, Babus, and Carletti (2012)), our results suggest that portfolio similarity adds

significantly in determining the potential for similar asset liquidation.

All of the relationships for the full sample hold generally for the subsamples of PSIFI

pairs and non-PSIFI pairs. It should be noted that for non-PSIFIs, the similarity in sales is

greater for larger insurers and smaller for smaller insurers. Overall our findings confirm that

size and concentration are important determinants of sales similarity and that our measure

of portfolio similarity is significantly related to the decision as to whether or not to sell

the same asset classes and issuers. Thus, our portfolio interconnectedness measure appears

to capture information about future sales that could be used to monitor insurers who may

contribute more to the transmission of systemic risk through the asset liquidation channel.

5.1 Return Correlation and Sales Similarity

As noted previously, a number of studies, most notable Billio, Getmansky, Lo, and Peliz-

zon (2012) use return correlations as a proxy for interconnectedness among financial institu-

tions. In this section, we examine whether our findings on the sales similarity between two

issuers can be characterized by the pairwise return correlation.

In Table 8, we include the return correlation between a pair of issuers in the quarter

before sales similarity is measured. At the asset class level, the return correlation is pos-

itively related to sales similarity. Including portfolio similarity in the set of independent

variables results in the coefficients of both return correlation and similarity being positive

and significant. We find that the the return correlation is only significant for PSIFI pairs.

For non-PSIFI pairs, return correlation does not add additional information.

When we measure portfolio similarity at the issuer level, we document that by itself, the

return correlation does not have any marginal contribution in predicting issuer level sales

similarity for the sample as a whole. However, when coupled with portfolio similarity, the

return correlation is significantly and positively related to sales similarity but is a significant

predictor of sales similarity only for the subsample of non-PSIFI pairs. For PSIFI pairs,

22

adding return correlation to the specification does not add any additional power. Comparing

models (5) and (6) in Table 6 to models (7) and (8) in Table 8, we see that adding return

correlation does not increase the R2 of the regressions for either subsample.

6 Effect of Capital Regulation and the Financial Crisis

on Sales Similarity

Entities subject to capital regulation have an incentive to engage in asset sales when

capital is depleted. The literature has documented that insurers replenish capital by selling

downgraded assets (Ellul, Jotikasthira, and Lundblad (2011)) and/or selling liquid assets

(Ellul, Jotikasthira, Lundblad, and Wang (2015)). In this section, we examine whether

our findings on the relationship between portfolio similarity and sales similarity are due to

capital constrained insurers. In addition, we analyze whether the relationship is due to the

similarity in downgraded securities and liquid securities. Since the need to replenish capital

is greatest in the period surrounding the financial crisis, we explore whether our results only

hold during the financial crisis period.

6.1 Risk-Based Capital Ratios

We assess the extent to which an insurer is regulatory-capital constrained through its ratio

of statutory to risk-based capital (RBC ratio). A low RBC ratio may provide an incentive for

an insurer to engage in asset sales to rebalance their portfolio in order to replenish capital.

Therefore, pairs of insurers who both have low RBC ratios and who hold similar assets, may

be more likely to re-balance their portfolios in similar ways.

We consider an insurer under-capitalized if its RBC ratio is below the median and well-

capitalized if the RBC ratio is above the median for the sample. We then construct two

pairwise indicator variables, (RBC High Pair) and (RBC Low Pair), equal to one if both

insurers are well-capitalized or under-capitalized, respectively. In our specifications in Table

23

9, we include RBC High Pair and RBC Low Pair and the interaction terms between these

indicator variables and portfolio similarity at both the asset class and issuer level. As in

prior tables, we also examine PSIFI pairs and non-PSIFI pairs separately.

The results in Table 9 captures the interaction effect of regulatory capital constraints

and portfolio similarity on sales similarity. At the asset-class level, we find that pairs of

insurers with greater portfolio similarity and who both have low RBC ratios, have greater

sales similarity. This finding is consistent with the literature on the effects of regulation on

asset liquidation. Capital constrained insurers who have similar portfolios are more likely to

sell the same types of assets. The interaction term of similarity and low RBC ratio remains

significant and positive for both the samples of PSIFI pairs and non-PSIFI pairs. There is

no relationship between sales similarity of insurer pairs who have high asset class similarity

and high RBC ratios.

When considering the interaction between portfolio similarity at the issuer level and low

RBC ratio, we do not find any evidence that insurer pairs that are more similar in their

portfolio holdings but capital constrained have greater sales similarity. This suggests that

any asset liquidation that occurs when insurers are capital constrained occur within the

same asset class but not necessarily the same issuer. Interestingly, when we examine the

subsample of PSIFI pairs, capital constrained PSIFIs are less likely to make the same selling

decision at the issuer level.

Overall, this subsection suggests a stronger relationship between portfolio similarity and

sales similarity when both pairs of insurers are constrained and is only apparent for simi-

larity at the asset class level. Next we examine whether our findings are driven by either

downgraded securities or the liquidity of the assets.

6.2 Liquidity and Downgrades

In examining the impact of liquidity, we are trying to determine whether the similarity

in portfolio holdings has the potential to be disruptive to markets. If the similarity of the

24

sales among insurers is due to the similarity in the portfolio of liquid assets, regulators may

be less concern about forced selling and price impact. On the other hand, if the similarity

of sales is a function of the similarity in the portfolio of illiquid assets, then systemic risk

regulators might be worried that having interconnected insurers will have a larger impact

on prices and increase the probability of a downward spiral in valuation (Brunnermeier and

Pedersen (2009) and Cont and Wagalath (2015)). We classify an issuer as liquid if it falls

within the following asset classes: equity, mutual fund shares, US government securities,

GSE securities, and sovereign bonds. Issuers in the remaining asset classes are considered

illiquid: corporate bonds, municipal bonds, RMBS, CMBS and ABS.

A similar logic to the one discussed above regarding liquidity prevails with respect to the

effect of downgraded assets. A number of studies document that asset sales of distressed

securities by capital constrained insurers tend to depress prices (Ellul, Jotikasthira, and

Lundblad (2011) and Merrill, Nadauld, Stulz, and Sherlund (2013)) and is one of the reasons

why some insurers have been designated as systemically important. Thus, it could be the

case that the relationship between portfolio similarity and sales similarity is simply due to

the similarity in downgraded assets. Using credit ratings information from DataScope, we

identify the year in which a security is first downgraded from investment grade (IG) to non-

investment grade (NIG) by S&P, Moodys or Fitch. This information is aggregated to the

security’s issuer level and we define a downgraded issuer as one that has at least one of its

securities downgraded from IG to NIG in a given year. For portfolio holdings, we define a

variable Downgraded as an indicator variable equal to 1 if an issuer, held by a given insurer

at the end of a given year is downgraded in the following year, and 0 otherwise. All holdings

that are not downgraded are classified as NotDowngraded.

Figure 7 shows the proportion of portfolio holdings and sales that are comprised of illiquid

issuers and downgraded issuers. In Panel (a), approximately 50% of insurers holdings are

composed of issuers in asset classes that we consider illiquid and this is relatively constant

over the time period. In contrast, insurers are selling fewer illiquid assets during and after

25

the financial crisis than before. Panel (b) shows a significant time trend in the percentage

of insurers holdings that are downgraded and a sharp increase in 2009 in the sale of these

securities. Thus, it could be the case that the liquidity or credit quality of the securities

affects the relationship between portfolio similarity and sales similarity.

We decompose the portfolio of an insurer into two pares: one that is composed of issuers

that are classified as liquid and another that is composed of issuers classified as illiquid.

In the same fashion, we decompose the portfolio of an insurer into issuers that are down-

graded in a year and issuers that are not downgraded. We compute four different portfolio

similarities between firms i and firms j in year t: Similarity Illiquid, Similarity Liquid, Simi-

larity Downgraded, and Similarity NotDowngraded. Each of these portfolio similarities mea-

sures the extent to which a pair of insurers are exposed to illiquid (liquid) and downgraded

(not downgraded) issuers.11

Table 10 presents the analysis of the relationship of the decomposed portfolio similarities

and the sales similarities between a pair of insurers. As can be seen from the table, our

results are not driven specifically by the liquidity of the asset or by downgraded issuers.

The coefficient on each of the portfolio similarity interactions with liquidity and downgrade

status is highly significant and positive. The sales similarity of a pair of issuers is affected

by the portfolio similarity of all securities in the portfolio and not just those that have lower

liquidity or lower credit ratings. Next, we examine whether the financial crisis exacerbates

any of these relationships.

6.3 The Financial Crisis

Given the concern about the selling behavior of regulated entities during the financial

crisis, it is natural to examine whether our findings are due only to the time period of the

crisis. We consider three different time periods and create indicator variables equal to 1 if

the time period is: (1) Pre-Crisis from 2002-2006, (2) Crisis from 2007 to 2009, and (3)

11Note that we do not include asset class in this table because the downgrade variable requires issuerinformation.

26

Post-Crisis from 2010 to 2014. We interact two of these indicators, Crisis and Post-Crisis

with portfolio similarity using liquid/illiquid assets and issuers that are downgraded/not

downgraded.

In Table 10, for the sample as a whole, we find that the relationship between the portfolio

similarity of both illiquid and downgraded portfolios with sales similarity is stronger during

the crisis. We do not find any change in the relationship for the portfolios composed of

liquid or non-downgraded issuers. In other words, during the financial crisis, correlated

selling decisions of pairs of insurers are more greatly influenced by the holdings of similar

securities that are either hard to trade or have experience credit deterioration.

For downgraded issuer, PSIFI pairs have a stronger relationship between the portfolio

similarity of these issuers and sales similarity but a decline in the relationship for the portfolio

of non-downgraded issuers. We interpret these findings to mean that, during the financial

crisis, PSIFIs’ selling decisions were more heavily weighted toward their joint holdings of

downgraded assets at the expense of their joint holdings of non-downgraded issuers. The

greater relationship between the portfolio holdings of downgraded issuers and sales similarity

continues to hold after the financial crisis as well indicating that investment in downgraded

issuers has a greater impact on the re-balancing decisions of insurers during and after the

financial crisis.

The greater influence of the portfolio similarity of downgraded issuers in predicting sales

similarity is likely due to the fact that a greater proportion of both the portfolio holdings and

sales of insurers are now composed of downgraded assets. Thus, the influence of downgraded

issuers in predicting selling behavior may be attributed to its increase importance of these

securities in insurers’ portfolios. It seems worth also pointing out that, even though the crisis

dummy is highly statistically significant when interacted with the downgraded variable, the

beta is still quite small in magnitude (0.076). As a consequence, the overall beta during the

financial crisis for the downgraded holdings similarities (0.157+0.076) it is still smaller than

the beta during the financial crisis for the non-downgraded holdings similarities (0.464-0.049).

27

This result points to one of the main finding of our paper, i.e. that the co-investment decision

of insurers are an important determinant of selling behavior in all economic condition and

across all type of securities.

7 Conclusion

In this paper, we develop a novel measure of pairwise insurance interconnectedness that

focuses on insurance portfolio similarities. The Financial Stability Oversight Council (FSOC)

has an authority to designate nonbank Systemically Important Financial Institutions (SIFIs).

Size and interconnectedness between financial companies are two factors FSOC currently

considers in the designation. However, there are no specific guidelines about calculating

interconnectedness. We attempt to add to the academic literature and to the important

policy discussion by explicitly measuring pairwise insurance interconnectedness using the

cosine similarity of insurers’ portfolio holdings and measuring its effect on selling behavior.

Our findings show that pairs of insurers that have greater portfolio similarity will have

greater sales similarity at both the asset class and issuer level and this result holds when

both pairs are potential SIFIs (PSIFIs) and non-PSIFIs. Portfolio re-balancing at the asset

class but not issuer level is more likely when both insurers are capital constrained indicating

that insurers sell the same type of security but not the same issuer of the security. We find

that both the portfolio similarity of liquid and illiquid securities as well as downgraded and

non-downgraded issuers predict liquidation decisions. However, the relationship between

the portfolio similarity of illiquid and downgraded issuers and sales similarity is stronger

during the financial crisis meaning that the co-investment decisions of these assets are more

likely to affect selling behavior in times of market stress. Finally, we show that our measure

of interconnectedness and its relationship to selling behavior is not captured by market

observable characteristics such as stock return correlation.

Overall, our results support the use of our measure to capture the important mechanics

28

of the asset liquidation channel of systemic risk transmission in the insurance industry.

Specifically, it can predict the sales of similar assets and issuers. The measure can be used by

insurance companies and regulators to assess the level of interconnectedness in the industry

and the possible impact of interconnectedness on asset liquidation.

29

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32

Appendix A: Variable Definitions

Variable Definition

Big An indicator variable equal to 1 if a non-PSIFI insurer’s portfolio assets are above the samplemedian at calendar year end, 0 otherwise.

Big Pair An indicator variable equal to 1 if Big=1 for both insurers in a pair, 0 otherwise.

Concentration Issuer/asset class Herfindahl index of an insurer’s portfolio at calendar year end:

Concentrationi,t =N∑

n=1w2

i,n,t where wi,n,t is issuer/asset class n’s proportion in insurer

i’s portfolio at the end of year t. Issuer/asset class proportions are calculated as the dollaramount invested in each issuer/asset class relative to the total value of the insurer portfolio

Conc AC An indicator variable equal to 1 if an insurer’s asset class concentration is above the samplemedian at calendar year end, 0 otherwise.

Conc Pair AC An indicator variable equal to 1 if Conc AC=1 for both insurers in a pair, 0 otherwise.

Conc I An indicator variable equal to 1 if an insurer’s issuer concentration is above the samplemedian at calendar year end, 0 otherwise.

Conc Pair I An indicator variable equal to 1 if Conc I=1 for both insurers in a pair, 0 otherwise.

CRISIS An indicator variable equal to 1 for the years 2007, 2008, and 2009 and 0 otherwise.

Life An indicator variable equal to 1 if more than 50% of portfolio assets are held by insurancecompanies in the group that are categorized by A.M. Best as providing life insurance, 0otherwise.

Life Pair An indicator variable equal to 1 if Life=1 for both insurers in a pair, 0 otherwise.

Non-PSIFI An indicator variable equal to 1 if an insurance company does not meet the $50 billion inassets SIFI designation threshold in any year during our sample period.

NonConc Pair An indicator variable equal to 1 if Conc=0 (either Conc AC or Conc I) for both insurers ina pair, 0 otherwise.

Other Pair An indicator variable equal to 1 if Life=0 and P&C=0 for both insurers in a pair, 0 otherwise.

P&C An indicator variable equal to 1 if more than 50% of portfolio assets are held by insurancecompanies in the group that are categorized by A.M. Best as providing property and casualtyinsurance, 0 otherwise.

P&C Pair An indicator variable equal to 1 if P&C=1 for both insurers in a pair, 0 otherwise.

PSIFI An indicator variable equal to 1 if an insurer could potentially be designated as a SIFI becauseit meets the $50 billion in assets threshold in at least one year during our sample period.

RBC A measure of capital adequacy calculated as the ratio of total adjusted capital to authorizedcontrol level risk-based capital.

RBC Pair High An indicator variable equal to 1 if RBC is above the sample median in a given year for bothinsurers in a pair, 0 otherwise.

RBC Pair Low An indicator variable equal to 1 if RBC is below the sample median in a given year for bothinsurers in a pair, 0 otherwise.

RetCorr Pair For a pair of insurers, the annual correlation of daily holding-period returns calculated atyear end for each pair of insurers.

RetCorr Qtr Pair For a pair of insurers, the annual correlation of daily holding-period returns calculated at athree month lag for each pair of insurers.

Similarity Similarity measure based on the cosign similarity between a pair of insurers’ issuer portfolioweights (Similarity I) or between a pair of insurers’ asset class portfolio weights (Similar-ity AC).

Small An indicator variable equal to 1 if a non-PSIFI insurer’s portfolio assets are below the samplemedian at calendar year end, 0 otherwise.

Small Pair An indicator variable equal to 1 if Small=1 for both insurers in a pair, 0 otherwise.

TA Total assets at calendar year end (ATY in Compustat).

ln(TA Pair) Natural logarithm of the sum of total assets for a pair of insurers at a calendar year end.

33

Appendix B: Cluster Analysis

Cluster Algorithm

Cluster analysis could be performed using several algorithms that differ significantly in

their notion of what constitutes a cluster and how to efficiently find clusters. The approach

used in our paper is largely based on the concept that clusters include groups with small

distances among the cluster members with particular statistical distributions. As described

in more detail below, we apply internal validation measures, namely Dunn Index (Dunn,

1974), Silhouette Width (Rousseeuw, 1987) and Connectivity (Handl, Knowles, and Kell,

2005), on the most utilized unsupervised clustering algorithms (Self Organizing Maps, Self

Organizing Tree Maps, K-means, hierarchical).

The optimal number of clusters (Nopt) is finally obtained computing the mode of the

optimal number of clusters in each of the 12 years (Nt).

Nopt = Mo(Nt) (4)

Coherently, the optimal algorithm (Copt) is derived by counting the number of times an

algorithm appears as locally optimal over the 12 years (Ct) and selecting the maximum

value.

Copt = Max(12∑i=1

Ct) (5)

We run the unsupervised K-means algorithm (MacQueen, 1967), yearly, with the follow-

ing setting:12

i) for the first year (Yt with t = 1) the number of clusters (3);

ii) for the following year (Yt with t = [2 : 12]) the centroids obtained by the cluster of the

12The algorithm is based a finite number of cycle aimed at defining the optimal cluster centroids accordingto the minimization of the distance of the n data points from their respective cluster centers, represented bythe following objective function: J =

∑kj=1

∑ni=1 ‖x

ji − cj‖2 where xj

i is a data point and cj is the clustercenter.

34

previous year (Yt−1).

The constraint for the cluster number in the first year comes from the outcome of the

validation step. The constraint for the centroids’ structure of the other years is set to

introduce a short-time memory effect in the evolution of the clusters over time. The link of

the cluster structures over time allows us to observe the transitions of the insurers among

clusters year by year.

We then analyze the clusters looking at:

i) size both in term of number of companies and volumes (amount of assets);

ii) centroids’ structure;

iii) transitions of companies among clusters over time.

The average structure of the 3 cluster’s centroids (xi) is computed as the average over

time of the centroids’ components (xit).

xi =1

12

12∑t=1

(xit) (6)

Finally the yearly net flow (NetF lowi) for cluster i is computed as follows:

Flowi,t =∑j 6=i

Ij,tIn−∑j=i

Ij,tOut (7)

The cluster validation process applied to the yearly dataset provides the best fitting

algorithm for the number of clusters. Each validation methodology is applied yearly kmeans.

A clear indication emerges for the optimal number of clusters being 3 clusters as this appears

21 times over 33 possible outcomes. 13

13Details on the validation are provided upon request.

35

Cluster Validation

To validate the cluster approach we selected a set of measures that reflect the degree of

compactness, connectedness, and separation of the cluster partitions,tested respectively with

Connectivity, Dunn index and Silhouette width.

Connectivity (Handl, Knowles, and Kell, 2005) Connectivity measures estimates to

what extent the nearest observations (in our case insurers) are placed in the same cluster.

We define N as the number of observations in the sample, M the number of attributes of

each observation (namely the coordinate of the observation in an M-dimensional space) and

nni(j) the jth nearest neighbor of observation i. Let xi,nni(j)be

xi,nni(j)=

0, if i and i are in the same cluster

1

j, otherwise (8)

Stated that, for a specific cluster partition C = {C1, ...Ck} of the N observations, connectivity

is defined as:

Conn(C) =N∑i=1

L∑j=1

xi,nni(j)(9)

where L defines the number of neighbor to use.

The connectivity has values between 0 and ∞ and should be minimized.

Silhouette Width (Rousseeuw, 1987) The Silhouette Width is the average of each ob-

servation’s Silhouette Value. The Silhouette Value is defined as:

S(i) =bi − ai

max(bi, ai), (10)

where ai is the average distance between observation i and the other observations belonging

to the same cluster and bi is the average distance between i and the observations in the

36

”nearest neighboring” cluster defined as:

bi = minCk∈C C(i)

∑j∈Ck

dist(i, j)

n(Ck), (11)

where C(i) is the cluster containing observation i, dist(i, j) is the distance between observa-

tion i and j and n(C) is the cardinality of cluster C.

Silhouette Width values lies in [−1, 1] and it should be maximized.

Dunn Index (Dunn, 1974) Dunn Index is the ratio of the smallest distance between

observations not in the same cluster and the largest intra-cluster distance

D(C) =minCk,Cl∈C,C(k) 6=Cl

(mini∈Ck,j∈Cjdist(i, j))

maxCm∈C diam(Cm), (12)

where diam(Cm) is the maximum distance between observations in cluster Cm.

Dunn Index lies between [0,∞] and should be maximized.

37

Figure 1: Portfolio Composition Through Time

This figure presents the cross-sectional average composition of insurer portfolios over 2002-2014 by assetclass.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

ABS CMBS Debt Equity GSE Muni Mutual Funds RMBS Sovereign US Govt

38

Figure 2: Clusters Structure for Holdings by Asset Class

This figure presents the average asset class dollar composition for the three clusters based on the holdingsfor all insurer groups over 2002-2014.

0%

25%

50%

75%

100%

Cluster(1 Cluster(2 Cluster(3

ABS CMBS Debt Equity GSE Municipal;bonds Mutual;funds RMBS Sovereign;bonds US;Govt

39

Figure 3: Cluster Distribution of Publicly Traded Insurers Using Asset Class Holdings

The figure shows the distribution among the three clusters from 2002 to 2014 for the sample of publiclytraded insurance companies used in this analysis.

0102030405060708090100

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Cluster21 Cluster22 Cluster23

40

Figure 4: Cluster Distribution of Asset Classes for PSIFIs and Non-PSIFIs

The figure shows the distribution among the three clusters from 2002 to 2014 for insurers in the sampleclassified as PSIFIs and non-PSIFIs We identify PSIFIs as any insurer who has assets of at least $50 billionat any time during the sample period.

0

5

10

15

20

25

30

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Cluster21 Cluster22 Cluster23

(a) PSIFI

0

10

20

30

40

50

60

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Cluster21 Cluster22 Cluster23

(b) Non-PSIFI

41

Figure 5: Pairwise Portfolio Similarity

The figure shows average pairwise portfolio similarity computed at the (a) asset class and (b) issuer levelover 2002-2014. The red line represents the average for the sample of all publicly traded insurers. The violetline represents the average for PSIFI insurers. The green line represents the average for non-PSIFI insurers.

0.50

0.55

0.60

0.65

0.70

0.75

0.80

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

All Non-­‐‑PSIFI_Pair PSIFI_Pair

(a) Asset Class Similarity

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

All Non-­‐‑PSIFI_Pair PSIFI_Pair

(b) Issuer Similarity

42

Figure 6: Quarterly Pairwise Sales Similarity

The figure shows average quarterly pairwise sales similarity computed at the (a) asset class and (b) issuerlevel from 2002-2014. The red line represents the average for the sample of all publicly traded insurers. Theviolet line represents the average for the subsample of PSIFI insurers. The green line represents the averagefor the subsample of non-PSIFI insurers.

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

All Non-­‐‑PSIFI_Pair PSIFI_Pair

(a) Asset Class Similarity

0

0.05

0.1

0.15

0.2

0.25

0.3

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

All Non-­‐‑PSIFI_Pair PSIFI_Pair

(b) Issuer Similarity

43

Figure 7: Proportion of Holdings and Sales of Illiquid and Downgraded Securities

This figure presents the proportion of holdings and sales that are composed of illiquid and downgradedissuers.

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

% Illiquid Holdings % Illiquid Sales

(a) Illiquid Issuers

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

% Downgraded Holdings % Downgraded Sales

(b) Downgraded Issuers

44

Tab

le1:

Por

tfol

ioC

omp

osit

ion

Sta

tist

ics

Th

eta

ble

pre

sents

por

tfol

ioco

mp

osit

ion

stat

isti

csfo

rth

esa

mp

leof

pu

bli

cly

trad

edin

sure

rsfr

om

2002

to2014.

Lif

ein

sure

rsop

erate

pri

mari

lyin

life

and

hea

lth

lin

esof

bu

sin

ess.

P&

Cin

sure

rsop

erate

pre

dom

inantl

yin

pro

per

tyan

dca

sualt

yli

nes

of

bu

sin

ess.

PS

IFI

ind

icate

sp

ote

nti

all

ysy

stem

icall

yim

por

tant

insu

rers

defi

ned

asth

ose

wit

hto

tal

asse

tsab

ove

$50B

inat

least

on

eyea

rd

uri

ng

ou

tsa

mp

lep

erio

d.

TA

isto

tal

ass

ets

at

cale

ndar

yea

ren

d(A

TY

inC

omp

ust

at).

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por

ate

bon

ds,

GS

Ese

curi

ties

,M

un

icip

al

bon

ds,

US

gov

tse

curi

ties

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MB

S,

CM

BS

,A

BS

,Sov

erei

gn

bon

ds,

Equ

ity,

and

Mu

tual

fund

shar

esar

eth

ed

olla

r-va

lue

per

centa

ges

of

an

insu

rer’

sp

ort

foli

oin

vest

edin

thes

eass

etcl

ass

es.N

um

ber

of

secu

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the

nu

mb

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un

iqu

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dig

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US

IPs

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rer’

sp

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olio

ina

giv

enye

ar.

Num

ber

of

issu

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isth

enu

mb

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un

iqu

eis

suer

s,id

enti

fied

usi

ng

6-d

igit

CU

SIP

s,in

anin

sure

r’s

por

tfol

ioin

agi

ven

year

.Is

suer

con

centr

ati

on

isa

Her

fin

dah

lin

dex

con

stru

cted

for

each

insu

rer

inea

chye

ar

as

the

sum

of

the

square

dw

eigh

tsof

issu

ers

init

sp

ortf

olio

.A

sset

clas

sco

nce

ntr

ati

on

isa

Her

fin

dah

lin

dex

con

stru

cted

for

each

insu

rer

inea

chye

ar

as

the

sum

of

the

squ

are

dw

eigh

tsof

asse

tcl

asse

sin

its

por

tfol

io.

Issu

er/a

sset

class

wei

ghts

are

calc

ula

ted

as

the

doll

ar

am

ou

nt

inves

ted

inea

chis

suer

/ass

etcl

ass

rela

tive

toth

eto

tal

valu

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anin

sure

r’s

por

tfol

io.

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n,

med

ian

san

dst

an

dard

dev

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on

sare

base

don

the

cross

-sec

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al

vari

ati

on

of

insu

rers

’ti

me

seri

esav

erage.

All

Lif

eP

&C

PS

IFI

Non

-PS

IFI

Mea

nM

edia

nS

DM

ean

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ian

SD

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nM

edia

nS

DM

ean

Med

ian

SD

Mea

nM

edia

nS

D

Insu

rer

Ch

ara

cter

isti

csT

A($

B)

138.6

13.5

316.7

160.6

19.2

343.2

85.6

8.8

268.1

398.3

175.1

446.4

11.5

4.4

13.6

Ass

etC

lass

Com

posi

tion

Corp

ora

teb

on

ds

41.2

39.5

17.8

48.4

48.4

17.5

32.7

32.9

13.9

36.4

33.5

17.0

44.3

46.4

17.3

GS

Ese

curi

ties

12.0

10.1

9.8

12.3

9.6

10.9

11.2

10.9

6.7

7.9

6.7

6.0

13.3

10.9

10.8

Mu

nic

ipal

bon

ds

9.1

2.8

12.1

5.3

2.2

8.0

16.0

13.8

13.7

5.1

2.0

7.9

11.3

5.0

14.0

US

govt

secu

riti

es7.1

3.7

9.9

7.8

3.7

13.7

6.5

5.0

5.7

7.0

3.1

12.3

6.5

4.6

7.4

RM

BS

3.3

2.1

4.0

3.8

2.2

5.0

2.9

2.3

2.8

3.1

2.3

3.0

3.5

2.1

4.4

CM

BS

2.7

2.0

2.5

2.9

2.3

2.6

2.8

1.9

3.3

4.1

4.0

3.0

2.5

1.6

2.6

AB

S2.7

2.4

2.2

2.8

2.6

2.3

4.0

3.1

4.5

3.3

3.2

2.2

2.7

2.2

2.6

Sover

eign

bon

ds

1.0

0.2

3.6

1.1

0.2

4.0

2.0

0.2

6.2

2.0

0.8

4.8

0.9

0.1

3.8

Equ

ity

17.4

11.6

17.4

12.9

9.7

11.8

21.1

17.7

17.3

25.5

18.0

21.1

13.2

9.1

14.1

Mu

tual

fun

dsh

are

s3.4

0.0

9.0

2.7

0.0

7.5

0.8

0.0

2.0

5.7

0.1

10.0

1.7

0.0

5.8

Ass

etcl

ass

con

centr

ati

on

0.3

70.3

60.1

40.3

90.3

70.1

60.3

00.2

70.1

00.3

70.3

40.1

60.3

60.3

20.1

4Is

sue/

Issu

erC

om

posi

tion

Nu

mb

erof

issu

es2,9

37

1,1

99

4,9

95

2,8

19

1,2

52

4,7

31

2,1

19

816

3,6

44

6,6

78

4,5

75

7,0

55

1,4

66

727

2,5

40

Nu

mb

erof

issu

ers

1,4

75

790

2,0

65

1,4

79

822

2,0

67

995

646

1,0

79

3,1

83

2,3

09

2,9

34

820

526

876

Issu

erco

nce

ntr

ati

on

0.0

60.0

20.1

50.0

60.0

20.1

70.0

30.0

20.0

30.0

60.0

20.1

30.0

50.0

20.1

4

45

Table 2: Insurer Pair Statistics

The table presents descriptive statistics for our sample of insurer pairs during 2002 to 2014. PSIFI indicatespotentially systemically important insurers defined as those with total assets above $50B in at least one yearduring our sample period. Similarity AC is a similarity measure based on the cosign similarity between apair of insurers’ asset class portfolio weights. Similarity AC (Similarity I) is a similarity measure based onthe cosign similarity between a pair of insurers’ asset class (issuer) portfolio weights. An issuer/asset classweight is calculated as the dollar amount invested in that issuer/asset class relative to the total value of aninsurer’s portfolio. Ret Corr Pair is the annual correlation of daily holding-period returns calculated at yearend for each pair of insurers. TA Pair is the sum of total assets for a pair of insurers at a calendar year end.

YEARS 2002 - 2014

Whole Sample Non-PSIFI PSIFI

Mean Median SD Mean Median SD Mean Median SD

Similarity AC 0.68 0.74 0.23 0.70 0.76 0.22 0.67 0.73 0.24Similarity I 0.09 0.05 0.13 0.11 0.06 0.14 0.09 0.05 0.11Ret Corr Pair 0.32 0.31 0.22 0.25 0.22 0.21 0.49 0.50 0.18ln(TA Pair) 11.37 11.36 1.90 9.34 9.60 1.07 13.21 13.3 0.95

YEAR 2002

Whole Sample Non-PSIFI PSIFI

Mean Median SD Mean Median SD Mean Median SD

Similarity AC 0.74 0.79 0.19 0.77 0.82 0.17 0.71 0.76 0.22Similarity I 0.10 0.06 0.12 0.11 0.07 0.13 0.10 0.05 0.12Ret Corr Pair 0.26 0.23 0.21 0.17 0.14 0.18 0.47 0.51 0.17ln(TA Pair) 10.99 11.03 1.78 9.19 9.31 1.02 12.81 12.81 0.86

YEAR 2008

Whole Sample Non-PSIFI PSIFI

Mean Median SD Mean Median SD Mean Median SD

Similarity AC 0.67 0.74 0.24 0.69 0.75 0.23 0.67 0.74 0.24Similarity I 0.08 0.05 0.10 0.09 0.05 0.11 0.08 0.05 0.09Ret Corr Pair 0.45 0.46 0.17 0.39 0.42 0.19 0.54 0.55 0.12ln(TA Pair) 11.51 11.44 1.86 9.35 9.60 0.99 13.19 13.21 0.99

YEAR 2014

Whole Sample Non-PSIFI PSIFI

Mean Median SD Mean Median SD Mean Median SD

Similarity AC 0.62 0.68 0.27 0.66 0.73 0.26 0.58 0.58 0.27Similarity I 0.09 0.05 0.13 0.10 0.06 0.13 0.08 0.05 0.12Ret Corr Pair 0.36 0.36 0.19 0.30 0.34 0.19 0.48 0.49 0.14ln(TA Pair) 11.81 11.71 1.75 9.77 10.05 1.01 13.40 13.56 0.86

46

Table 3: Determinants of Portfolio Holdings Similarity

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The dependentvariable is the portfolio similarity of a pair of insurers measured at the asset class or issuer level. All inde-pendent variables are defined in Appendix A. Robust t-statistics are in parentheses. Statistical significanceis denoted by ***, **, and * at the 1%, 5%, and 10% level respectively.

Asset Class Portfolio Similarity Issuer Level Portfolio SimilarityAll Non-PSIFI PSIFI All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6)

Life Pair 0.180*** 0.149*** 0.171*** 0.004 -0.016* 0.035***(17.36) (10.54) (16.01) (1.17) (-1.96) (3.98)

PC Pair 0.069*** 0.077*** -0.023 0.019*** 0.000 0.059***(11.48) (10.70) (-1.15) (6.33) (0.07) (4.67)

PSIFI Pair 0.013* -0.000(1.91) (-0.22)

Non-PSIFI Pair 0.026*** 0.016***(5.26) (9.17)

Large Pair 0.051*** -0.018***(9.15) (-8.76)

Small Pair -0.034*** 0.041***(-4.54) (8.23)

Conc Pair AC -0.035*** 0.005 -0.061***(-7.05) (0.41) (-5.10)

NonConc Pair AC 0.092*** 0.080*** 0.119***(20.88) (13.41) (11.14)

Conc I Pair -0.001 0.004 -0.013***(-0.23) (0.70) (-3.10)

NonConc I Pair 0.032*** 0.029*** 0.046***(15.28) (8.47) (10.21)

Constant 0.644*** 0.676*** 0.657*** 0.085*** 0.106*** 0.076***(199.55) (116.73) (135.82) (58.64) (35.87) (25.97)

Year FE Y Y Y Y Y Y

N 41,011 16,046 5,579 41,011 16,046 5,579R2 0.171 0.156 0.200 0.030 0.044 0.093

47

Table 4: Pairwise Return Correlation and Portfolio Holdings Similarity

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The depen-dent variable is the portfolio similarity of a pair of insurers measured at the asset class or issuer level.Ret Corr Pair is the annual correlation between a pair of insurers’ daily holding-period returns during theyear. All independent variables are defined in Appendix A. Robust t-statistics are in parentheses. Statisticalsignificance is denoted by ***, **, and * at the 1%, 5%, and 10% level respectively.

Asset Class Portfolio Similarity Issuer Level Portfolio SimilarityAll All Non-PSIFI PSIFI All All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6) (7) (8)

Ret Corr Pair -0.021 0.031 0.006 0.095** -0.050*** -0.079*** -0.027** -0.121***(-0.98) (1.51) (0.25) (2.74) (-4.09) (-7.32) (-2.29) (-3.84)

Life Pair 0.172*** 0.143*** 0.144*** 0.006* -0.009 0.033***(16.88) (9.65) (13.20) (1.83) (-1.22) (3.91)

PC Pair 0.055*** 0.072*** -0.025 0.004 -0.021*** 0.052***(9.56) (8.30) (-1.31) (1.42) (-6.08) (4.09)

PSIFI Pair 0.002 0.014***(0.23) (5.87)

Non-PSIFI Pair 0.051*** 0.008***(8.13) (3.74)

Large Pair 0.018** -0.020***(2.74) (-6.11)

Small Pair -0.000 0.057***(-0.05) (10.24)

Conc Pair AC -0.021*** 0.042*** -0.052**(-5.44) (3.88) (-2.94)

NonConc Pair AC 0.083*** 0.059*** 0.131***(18.49) (11.04) (10.30)

Conc Pair I -0.003 0.007 -0.014**(-0.89) (1.42) (-2.65)

NonConc Pair I 0.029*** 0.024*** 0.042***(16.92) (7.47) (7.86)

Constant 0.701*** 0.639*** 0.688*** 0.619*** 0.110*** 0.110*** 0.110*** 0.141***(57.88) (105.64) (117.68) (33.24) (17.05) (34.05) (38.07) (11.13)

Year FE Y Y Y Y Y Y Y Y

N 28,491 28,491 9,950 4,633 28,491 28,491 9,950 4,633R2 0.000 0.172 0.156 0.182 0.008 0.041 0.070 0.104

48

Table 5: Sales Statistics

The table presents the composition of insurers’ sales as percentage of total sales from 2002 to 2014.

Asset Class 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Corporate Bonds 22.3 22.2 20.0 21.3 21.6 17.0 16.5 19.1 16.7 16.8 19.2 18.5 17.2ABS 1.3 1.4 1.8 1.9 2.0 1.6 0.9 1.1 1.3 1.1 1.4 1.3 1.8CMBS 1.1 1.0 1.6 1.7 2.1 1.9 1.4 1.8 2.0 1.2 1.7 1.3 1.1RMBS 1.5 1.4 1.5 1.7 1.8 1.6 1.2 1.9 1.3 0.8 1.8 1.1 0.8US Govt Securities 13.8 15.3 14.0 18.1 16.8 16.6 13.8 17.1 17.9 16.7 14.9 17.4 19.0GSE Securities 26.7 31.4 28.3 23.7 21.9 24.4 30.9 27.1 28.0 30.9 32.2 31.2 28.2Sovereign bonds 1.5 2.6 1.9 2.6 1.4 1.5 1.0 1.1 2.1 1.1 2.5 2.2 1.7Equity 28.1 20.5 22.5 20.9 22.4 24.2 19.4 19.0 18.0 17.0 13.0 13.6 14.1Municipal Bonds 3.8 4.3 5.6 5.1 5.1 5.7 5.1 3.8 3.8 3.1 1.9 2.4 2.6Mutual Funds 0.0 0.0 2.8 3.1 4.9 5.4 9.7 8.0 8.8 11.3 11.4 11.0 13.5

49

Table 6: Determinants of Sales Similarity

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The dependentvariable sales similarity of a pair of insurers measured at the asset class or issuer level. All independentvariables are defined in Appendix A. Robust t-statistics are in parentheses. Statistical significance is denotedby ***, **, and * at the 1%, 5%, and 10% level respectively.

Asset Class Sales Similarity Issuer Level Sales SimilarityAll Non-PSIFI PSIFI All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6)

Life Pair 0.118*** 0.127*** 0.101*** -0.016*** -0.012*** -0.011*(19.12) (13.02) (10.17) (-4.76) (-4.01) (-1.73)

PC Pair 0.015 0.042*** -0.058*** -0.010*** -0.014*** -0.010(1.67) (3.54) (-3.42) (-3.07) (-5.37) (-0.71)

PSIFI Pair 0.063*** 0.083***(13.21) (15.77)

Non-PSIFI Pair -0.009 -0.029***(-1.67) (-20.09)

Big Pair 0.047*** 0.004**(6.25) (2.65)

Small Pair -0.033*** -0.004**(-5.31) (-2.11)

Conc Pair AC 0.022*** 0.017* 0.010(3.04) (1.79) (1.23)

NonConc Pair AC 0.022*** 0.016** 0.057***(4.75) (2.56) (6.31)

Conc Pair I 0.017*** 0.012*** 0.040***(5.01) (4.51) (5.19)

NonConc Pair I -0.007*** -0.009*** -0.013**(-4.36) (-5.04) (-2.31)

Constant 0.532*** 0.564*** 0.535*** 0.065*** 0.052*** 0.094***(160.64) (141.84) (121.56) (57.05) (40.33) (42.95)

Year-Quarter FE Y Y Y Y Y Y

N 148,951 58,035 20,403 149,098 58,075 20,432R2 0.067 0.086 0.074 0.059 0.015 0.046

50

Table 7: Predicting Sales Similarity with Portfolio Similarity

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The dependentvariable is insurers’ quarterly pairwise sales similarity at the asset class and issuer level. All independentvariables are defined in Appendix A and are measured as of the year-end prior to the sales quarter. Robustt-statistics are in parentheses. Statistical significance is denoted by ***, **, and * at the 1%, 5%, and 10%level respectively.

Asset Class Sales Similarity Issuer Level Sales SimilarityAll Non-PSIFI PSIFI All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6)

Similarity AC 0.296*** 0.275*** 0.299***(17.81) (13.81) (10.12)

Similarity I 0.438*** 0.340*** 0.686***(23.20) (14.58) (18.14)

Life Pair 0.061*** 0.077*** 0.043*** -0.016*** -0.008*** -0.019**(7.51) (6.50) (3.84) (-5.40) (-4.03) (-2.46)

PC Pair 0.003 0.022* -0.050*** -0.018*** -0.011*** -0.060***(0.34) (1.85) (-2.72) (-4.72) (-4.28) (-4.26)

PSIFI Pair 0.057*** 0.085***(11.94) (15.12)

Non-PSIFI Pair -0.018*** -0.037***(-3.51) (-24.13)

Big Pair 0.036*** 0.010***(4.67) (5.06)

Small Pair -0.023*** -0.015***(-3.33) (-7.05)

Conc Pair AC 0.042*** 0.036*** 0.026***(6.44) (3.73) (3.26)

NonConc Pair AC -0.010** -0.018*** 0.023**(-2.63) (-3.54) (2.29)

Conc Pair I 0.019*** 0.009*** 0.055***(5.49) (3.49) (7.58)

NonConc Pair I -0.021*** -0.016*** -0.054***(-7.80) (-7.04) (-8.47)

Constant 0.280*** 0.312*** 0.315*** 0.041*** 0.024*** 0.061***(26.93) (21.15) (15.22) (21.23) (8.39) (18.95)

Year-Quarter FE Y Y Y Y Y Y

N 129,944 49,635 18,352 130,008 49,674 18,352R2 0.097 0.104 0.110 0.156 0.127 0.134

51

Table 8: Sales Similarity and Return Correlation

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The dependentvariable is insurers’ sales similarity at asset class and issuer level for quarters Q1 to Q4 in year t+ 1. Returncorrelation is measured in the quarter prior to the sales. All independent variables are defined in AppendixA and are measured as of the year-end prior to the sales quarter. Robust t-statistics are in parentheses.Statistical significance is denoted by ***, **, and * at the 1%, 5%, and 10% level respectively.

Asset Class Sales Similarity Issuer Level Sales SimilarityAll All Non-PSIFI PSIFI All All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6) (7) (8)

Similarity AC 0.309*** 0.327*** 0.261***(14.81) (12.54) (7.81)

Similarity I 0.438*** 0.325*** 0.702***(19.96) (10.25) (17.74)

Ret Corr Pair 0.057*** 0.041** -0.015 0.087** -0.008 0.022** 0.022*** -0.020(3.11) (2.13) (-0.66) (2.42) (-0.99) (2.62) (2.93) (-0.72)

Life Pair 0.116*** 0.063*** 0.086*** 0.036*** -0.002 -0.005 0.002 -0.015*(16.04) (7.21) (6.48) (2.99) (-0.64) (-1.63) (0.74) (-1.70)

PC Pair 0.037*** 0.021** 0.066*** -0.052*** -0.018*** -0.020*** -0.009*** -0.070***(3.60) (2.16) (3.92) (-2.99) (-4.42) (-5.05) (-4.18) (-5.06)

PSIFI Pair 0.061*** 0.058*** 0.103*** 0.098***(10.33) (9.68) (15.93) (14.57)

Non-PSIFI Pair -0.002 -0.014** -0.030*** -0.034***(-0.43) (-2.49) (-21.76) (-24.88)

Big Pair 0.037*** 0.005**(3.78) (2.03)

Small Pair -0.020** -0.015***(-2.10) (-4.77)

Conc Pair AC 0.035*** 0.040*** 0.022* 0.016(4.68) (5.50) (2.01) (1.52)

NonConc Pair AC 0.018*** -0.005 -0.016*** 0.031***(4.25) (-1.21) (-3.14) (2.72)

Conc Pair I 0.020*** 0.023*** 0.011*** 0.052***(4.89) (5.74) (3.60) (6.85)

NonConc Pair I -0.010*** -0.022*** -0.015*** -0.052***(-4.33) (-8.43) (-6.23) (-8.03)

Constant 0.453*** 0.254*** 0.260*** 0.297*** 0.077*** 0.032*** 0.020*** 0.077***(83.34) (17.40) (13.51) (15.07) (38.98) (11.15) (4.48) (5.58)

Year-Quarter FE Y Y Y Y Y Y Y Y

N 91,984 91,984 32,038 14,983 92,035 92,035 32,067 14,983R2 0.103 0.066 0.127 0.092 0.168 0.080 0.123 0.138

52

Table 9: Sales Similarity and RBC Ratios

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The dependentvariable is insurers’ quarterly pairwise sales similarity at the asset class and issuer level. The two pairwiseindicator variables, (RBC High Pair) and (RBC Low Pair) are equal to one if both insurers are above themedian RBC ratio for the sample or under the median RBC ratio, respectively. All independent variablesare defined in Appendix A and are measured as of the year-end prior to the sales quarter.Robust t-statisticsare in parentheses. Statistical significance is denoted by ***, **, and * at the 1%, 5%, and 10% levelrespectively.

Asset Class Sales Similarity Issuer Level Sales SimilarityAll Non-PSIFI PSIFI All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6)

Similarity AC 0.233*** 0.214*** 0.218***(12.44) (9.06) (6.69)

Similarity AC*RBC High Pair -0.012 -0.033 -0.027(-0.78) (-1.43) (-0.84)

Similarity AC*RBC Low Pair 0.099*** 0.153*** 0.094***(4.16) (4.79) (2.86)

Similarity I 0.444*** 0.366*** 0.721***(22.13) (14.84) (16.67)

Similarity I*RBC High Pair 0.055 0.000 0.063(1.59) (0.01) (1.05)

Similarity I*RBC Low Pair -0.014 0.005 -0.223***(-0.54) (0.13) (-4.66)

RBC High Pair 0.003 0.031* -0.010 -0.007*** 0.000 -0.001(0.21) (1.72) (-0.45) (-3.30) (0.25) (-0.18)

RBC Low Pair -0.065*** -0.126*** -0.045* 0.002 0.002 0.007(-3.91) (-5.80) (-1.72) (0.74) (1.00) (0.82)

Life Pair 0.065*** 0.076*** 0.043*** -0.019*** -0.010*** -0.020**(6.83) (5.88) (3.13) (-5.78) (-3.77) (-2.30)

PC Pair 0.019* 0.026* -0.077*** -0.019*** -0.008** -0.092***(1.73) (1.96) (-3.64) (-5.17) (-2.52) (-4.25)

PSIFI Pair 0.053*** 0.075***(10.74) (14.12)

Non-PSIFI Pair -0.018*** -0.034***(-3.31) (-20.91)

Big Pair 0.035*** 0.009***(4.80) (4.20)

Small Pair -0.030*** -0.016***(-4.29) (-6.67)

Conc Pair AC 0.042*** 0.043*** 0.014(5.77) (4.26) (1.49)

NonConc Pair AC -0.012*** -0.021*** 0.019(-2.88) (-3.62) (1.64)

Conc Pair I 0.017*** 0.008*** 0.048***(5.12) (2.89) (6.21)

NonConc Pair I -0.021*** -0.017*** -0.051***(-7.58) (-6.91) (-8.08)

Constant 0.333*** 0.369*** 0.362*** 0.044*** 0.023*** 0.071***(27.44) (21.66) (16.35) (20.78) (7.03) (17.55)

Year-Quarter FE Y Y Y Y Y Y

N 100,115 39,271 13,496 100,167 39,303 13,496R2 0.094 0.107 0.107 0.151 0.136 0.126

53

Table 10: Sales Similarity, Liquidity, Downgrades and the Crisis

The table presents OLS estimation results for the sample of insurer pairs from 2002 to 2014. The dependentvariable is insurers’ quarterly pairwise sales similarity at the asset class and issuer level. Similarity I Liquid isthe portfolio similarity of issuers that fall within the following asset classes that are considered liquid: equity,mutual fund shares, US government securities, GSE securities, and sovereign bonds. Similarity I Illiquidis theportfolio similarity of issuers that fall within the following asset classes that are considered illiquid: corporatebonds, municipal bonds, RMBS, CMBS and ABS. Similarity Downgraded is the portfolio similarity of issuersthat are downgraded in the following year. Similarity NotDowngraded is the portfolio similarity of issuersthat are not downgraded in the following year. Crisis is a dummy variable equal to 1 for the years 2007 to2009 and Post-Crisis is a dummy variable equal to 1 for the years 2010 to 2014. All independent variables aredefined in Appendix A and are measured as of the year-end prior to the sales quarter. Robust t-statistics arein parentheses. Statistical significance is denoted by ***, **, and * at the 1%, 5%, and 10% level respectively.

Issuer Level Sales SimilarityAll Non-PSIFI PSIFI All Non-PSIFI PSIFI(1) (2) (3) (4) (5) (6)

Similarity I Illiquid 0.235*** 0.077** 0.443***(9.47) (5.14) (7.60)

Similarity I Illiquid*Crisis 0.064** 0.010 0.014(4.97) (0.40) (0.79)

Similarity I Illiquid*Post-Crisis 0.012 0.034 -0.114(0.34) (1.19) (-1.60)

Similarity I Liquid 0.316*** 0.286*** 0.484***(13.91) (12.52) (23.40)

Similarity I Liquid*Crisis -0.037 -0.035 -0.204**(-1.07) (-0.97) (-5.62)

Similarity I Liquid*Post-Crisis -0.029 -0.067* 0.063(-1.44) (-2.62) (0.83)

Similarity I Downgraded 0.157*** 0.068*** 0.262***(11.42) (17.53) (7.10)

Similarity I Downgraded*Crisis 0.076*** 0.010 0.076**(12.70) (0.65) (3.60)

Similarity I Downgraded*Post-Crisis 0.082*** 0.018* 0.136***(6.93) (2.78) (7.19)

Similarity I NotDowngraded 0.464*** 0.378*** 0.643***(30.68) (19.64) (26.99)

Similarity I NotDowngraded*Crisis -0.049 -0.023 -0.232***(-1.30) (-0.46) (-13.95)

Similarity I NotDowngraded*Post-Crisis -0.103** -0.088* -0.062(-4.46) (-3.17) (-0.74)

Crisis -0.005 -0.002 0.026* -0.006* -0.002 0.014(-1.51) (-0.59) (3.16) (-2.55) (-0.45) (1.07)

Post-Crisis -0.004 -0.004 0.011 -0.004 0.001 -0.029**(-0.62) (-0.61) (1.09) (-1.07) (0.35) (-5.13)

Life Pair -0.018** -0.008*** -0.017 -0.018*** -0.009*** -0.013(-5.36) (-6.30) (-1.32) (-6.19) (-10.19) (-1.09)

PC Pair -0.005 -0.007* -0.011 -0.007 -0.010** 0.025**(-1.52) (-2.75) (-1.01) (-2.11) (-4.48) (3.31)

PSIFI Pair 0.070*** 0.055**(6.51) (5.71)

Non-PSIFI Pair -0.032*** -0.027***(-18.56) (-20.19)

Big Pair 0.008** 0.007**(4.89) (5.31)

Small Pair -0.016*** -0.014***(-8.88) (-8.57)

Conc Pair I 0.023*** 0.012*** 0.053** 0.022*** 0.012*** 0.045**(6.46) (7.96) (4.43) (6.80) (7.53) (4.18)

NonConc Pair I -0.024*** -0.017*** -0.046*** -0.025*** -0.018*** -0.043***(-9.28) (-9.87) (-8.24) (-10.56) (-8.99) (-12.23)

Constant 0.014** 0.008** 0.016 0.006 0.003 -0.003(4.59) (4.19) (1.58) (1.71) (1.21) (-0.21)

Quarter FE Y Y Y Y Y Y

N 129,771 49,674 18,267 125,179 47,254 18,043R2 0.165 0.113 0.156 0.195 0.131 0.20754