Figure 1: Illustration of Networks Based on Overlapping Portfolios vs.
Investors
BR (a) Network of Overlapping Portfolios
(b) Network of Overlapping Investors
Sub-figure
(a) illustrates the conventional network of financial institutions, or
investors, constructed via their overlapping portfolios. In this
example, Investor 1 holds positive amounts of Assets 1, Investor 2 holds
positive amounts of Assets 1 and 2, and Investor 3 holds positive
amounts of all three assets. The resulting network of overlapping
portfolios has connections between all investors through their common
holdings of Asset 1 or Assets 1 and 2. Sub-figure (b) depicts our new
network of financial assets constructed via the overlapping investors.
Notice that the focus is now on assets and the arrows are flipped,
enabling the interpretation that Asset 1 is held by all investors, Asset
2 is held by Investors 2 and 3, and Asset 3 is held only by Investor 3.
In this network of overlapping investors, Assets 1 and 2 are connected
via their common exposure to Investors 2 and 3, Assets 1 and 3 are
connected through Investor 3, and Assets 2 and 3 are connected through
Investor 3.
Figure 1 has two illustrations of networks based on overlapping portfolios vs. overlapping investors. In the first sub-figure, an example of the network of overlapping portfolios is depicted. Investor 1 holds positive amounts of Assets 1, Investor 2 holds positive amounts of Assets 1 and 2, and Investor 3 holds positive amounts of all three assets. The resulting network of overlapping portfolios has connections between all investors through their common holdings of Asset 1 or Assets 1 and 2. In the second sub-figure, an example of the network of overlapping investors is depicted. Asset 1 is held by all investors (1,2, and 3), Asset 2 is held by Investors 2 and 3, and Asset 3 is held only by Investor 3. In this network of overlapping investors, Assets 1 and 2 are connected via their common exposure to Investors 2 and 3, Assets 1 and 3 are connected through Investor 3, and Assets 2 and 3 are connected through Investor 3.
Figure 2: Number of Financial Institutions and Corporate Bonds in the
Network
(a) Number of Unique Investors
(b) Number
of Unique Corporate Bonds
Sub-figure (a) plots the number of
unique investors in the network of financial investors (institutions)
and corporate bonds. Investor types were carefully verified and assigned
via a manual auditing process; see Appendix A for more details.
Sub-figure (b) plots the number of unique corporate bonds held by these
investors over time. Quarterly figures are averaged within a year.
Sources: eMAXX and authors’ calculation.
Sub-figure (a) plots the number of unique investors in the network of financial investors (institutions) over time, in line charts. The x-axis denotes year, ranging from 2000 to 2021. The y-axis denotes number of unique investors, ranging from 0 to 400. “Investment managers” and “Other” type of investors have been the largest group during the period, their respective numbers ranging between 200 and 400. However, “Investment managers” started to outnumber “Other” around 2009 and remained so afterwards. “Banks” and “Insurance companies” are relatively fewer in number; They each counted about 100 and 60 at the beginning of the sample period and gradually reduced to a little more than 50 and around 40 by the end of the sample period. Sub-figure (b) plots the number of unique corporate bonds held by these investors over time, in line charts. The time period is the same, ranging from 2000 to 2021. The y-axis denotes the number of unique corporate bonds, ranging from 500 to 2,500. All four types of investors show a rise in the number of corporate bonds they hold, with a noticeable jump from around the Great Financial Crisis. “Investment managers” hold the largest number of CUSIPs, closely followed by “Other” types of investors and “Banks”; in the most recent period, they all each held between 2,000 and 2,500 different CUSIPs. “Insurance companies” hold far fewer number of CUSIPs, around 1,700 in the most recent period.
Figure 3: Network of Corporate Bonds Based on Overlapping Investors
(a) Full network
(b) Network of bond issuers with
largest amount outstanding
This figure shows the network of
corporate bonds based on overlapping investors. Each node is a corporate
bond issuer, and the (weighted) edges between two nodes capture the
cosine similarity of the overlapping investors holding the corporate
bonds of the two issuers. Sub-figure (a) shows the entire network in
2021:Q3; sub-figure (b) shows the sub-network of the largest 20
corporate bond issuers in 2021:Q3. Sources: eMAXX and authors’
calculation.
Sub-figure (a) shows an illustration of the full network estimated from our data, consisting of dots (nodes) connected by lines of connections in between the nodes. In the center is a densely connected circular network, surrounded by another layer of a larger circular network that is quite dense but to a lesser extent than the inner circle. Outside of these two layers are sparsely laid out dots, the so-called periphery, with some dots farther out from the overall inner networks than others. Sub-figure (b) zooms in on the network of 20 bond issuers with largest amount outstanding. Again, this is an illustration of a partial network, consisting of several dots (nodes) connected by lines of connections (edges). Size of the dot indicates the amount outstanding and thickness of the line connections indicates the strength of connection between the two dots. Each dot has the acronym for each bond issuer, where some of the largest ones are “VZ” (Verizon), “PEMEX” (the Mexican petroleum company), and “ORCL” (Oracle). There are also familiar bank names such as “GS” (Goldman Sachs), “BAC” (Bank of America), and “CITI” (Citibank). On average, these top 20 issuers have strong connections with each other.
Figure 4: Quantile Regressions
(a) Spread
(b)
Illiquidity (IQR)
(c) Realized Volatility
This
figure illustrates the results of quantile regressions between
interconnectedness measures and bond market quality measures (spread,
illiquidity, and realized volatility.) Source: eMAXX, TRACE, and
authors’ calculations.
Figure 4 has three sub-figures each illustrating the results of quantile regressions between interconnectedness and spread, illiquidity, and realized volatility. In sub-figure (a), the y-axis is the coefficient for spread, ranging from -1.5 to 0.5 and the x-axis is quantiles of standard deviation of interconnectedness, ranging from 0 to 100. The line graph is concave and decreasing. The confidence interval around it is very narrow. In sub-figure (b), the y-axis is the coefficient for illiquidity as measured in interquartile range of traded prices, ranging from -1 to 0 and the x-axis remains to be quantiles of standard deviation of interconnectedness, ranging from 0 to 100. The line graph is concave and decreasing. The confidence interval around it is very narrow. In sub-figure (c), the y-axis is the coefficient for realized volatility, ranging from -0.5 to around -0.05 and the x-axis is quantiles of standard deviation of interconnectedness, ranging from 0 to 100. The line graph is concave and decreasing. The confidence interval around it is very narrow.
Figure B1: Shares of Corporate Bond Holdings by Investor Type
This figure depicts how much each investor type holds out of
the total outstanding amount of bonds in our final sample of bond
holding data. Each point represents the sum of bond holdings by the
investor type—as shown in eMAXX—divided by the sum of outstanding amount
of the bonds based on FISD. Bonds in eMAXX and FISD are matched based on
CUSIPs. Quarterly statistics are averaged within each year. Sources:
eMAXX and FISD.
This figure plots shares of corporate bond holdings by investor type over time, in line charts. The x-axis denotes year, ranging from 2000 to 2021. The y-axis denotes the share of par amount held by each investor type out of total amount outstanding, ranging from 0 to 0.8. “Investment managers” line has been steadily increasing, with a noticeable jump after the Great Financial Crisis. Currently, it holds the highest share at 0.7. The share of “Insurance companies” have come down significantly from the beginning of the period and now stands at around 0.2. “Banks” and “Other” have the lowest shares, “Banks” slightly above “Other”, with both of the shares remaining at or below 0.1 as of the most recent.
Figure B2: Number of Quarters a Bond Appears in Our Sample
This figure shows the distribution of the number of quarters a bond
appears in our data (bond is aggregated at the issuer level). Sources:
eMAXX.
This figure plots a density histogram of the number of quarters a bond appears in our dataset. The x-axis is the number of quarters in sample, ranging from 0 to 80. The y-axis is density, ranging from 0 to slightly above 0.1. The highest density at above 0.1 is shown of the lowest number of quarters in sample. The histogram follows a convex, declining shape afterwards, with the bulk of higher number of quarters showing near-zero density.
Figure B3: Cross-sectional Distribution of Interconnectedness of
Corporate Bonds
This figure shows the distribution of
interconnectedness, as measured by cosine similarity, in the
cross-section of corporate bonds in our sample (aggregated at the issuer
level). Specifically, for each bond, we take the arithmetic average of
our interconnectedness measure across the time period in which that bond
appears in the sample. Source: eMAXX and authors’
calculation.
This figure plots a cross-sectional density histogram of interconnectedness of corporate bonds as estimated with cosine similarity in the paper. The x-axis is cosine similarity, ranging from 0 to 0.0008. The y-axis is fraction, ranging from 0 to 0.04. The distribution is bell-shaped with flattening at the top between cosine similarities of 0.0002 and 0.0005.
Figure B4: Cross-Sectional Distributions of Other Network Measures
This figure shows the distribution of other network measures
in the cross-section of corporate bonds in our sample (aggregated at the
issuer level). Specifically, for each bond, we take the arithmetic
average of the variables across the time period in which that bond
appears in the sample. Sources: eMAXX and authors’
calculation.
We show three sub-figures here. In sub-figure (a), we show a histogram of strength as measured at the company-level. The y-axis is fraction, ranging from 0 to 0.5. In sub-figure (b), we show a histogram of degree as measured at the company-level. The y-axis is fraction, ranging from 0 to slightly over 0.08. In sub-figure (c), we show a histogram of number of overlapping investors as measured at the company-level. The y-axis is fraction, ranging from 0 to 0.1. All of the three sub-figures have convex, declining shape of distributions.