[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Copenhagen Business School

Marco Rossi

Texas A&M University

Liquidity provision for corporate bonds has become significantly more expensive afte

2008 crisis. Using index exclusions as a natural experiment during which uninformed in

trackers request immediacy, we find that the cost of immediacy has more than doub

In addition, the supply of immediacy has become more elastic with respect to its p

Consistent with a stringent regulatory environment incentivizing smaller dealer invento

we also find that dealers revert deviations from their target inventory more quickly 

the crisis. Finally, we investigate the pricing impact of information, changes in owner

structure, and differences between bank and nonbank dealers. (JEL C23, G12)

Received February 22, 2017; editorial decision May 29, 2018 by Editor Itay Golds

Authors have furnished an Internet Appendix, which is available on the Oxford Univer

Press Web site next to the link to the final published paper online.

Liquidity entails transacting at a fair price and on short notice. Low b

spreads may indicate transactions take place near a fair price, but they te

about the speed of execution. Unlike brokers who simply match custo

dealers provide immediacy by using their inventories.1 Since the onset 

2008 crisis, aggregate corporate bond inventories have shrunk by mor

50% (Figure 1A), while bonds outstanding have almost doubled.2 Shr

We are grateful to Itay Goldstein (the editor) and two anonymous referees for their helpful feedb

suggestions. We also thank Jennie Bai, Jack Bao, Darrell Duffie, Peter Feldhütter, Thierry Fouca

Helwege, Charles Himmelberg, Soeren Hvidkjaer, David Krein, David Lando, Mads Stenbo Nielse

Heje Pedersen, Christophe Perignon, Jonathan Sokobin, Chester Spatt, Ilya Strebulaev, Erik Thiessen

Venkataraman, and Avi Wohl and participants of the Fixed Income Conference 2012, MFA conferen

FINRA/Columbia conference 2015, 2016 4Nations cup, Corporate bond workshop 2016, Financial Econ

and Empirical Asset Pricing Conference 2016, MIT GCFP conference 2016, Notre Dame conference on 

regulation 2016, 14th Paris December Finance Meeting 2016, AFA conference 2017, Macro Financial M

Conference 2018, and SEC, FCA, Danish CFA, CBS, SMU, Texas A&M, Notre Dame, Heriot-Watt U

and Helsinki Aalto seminars for their helpful comments. Special thanks goes to Jonathan Sokobin (FIN

providing the transaction data and Charles Himmelberg (Goldman Sachs) for providing the aggregate c

bond inventory data. This paper won second prize in the 2012 SPIVA awards and first place in the 2016 

cup. Jens Dick-Nielsen is a research fellow at the Danish Finance Institute and gratefully acknowledge

from the FRIC Center for Financial Frictions [DNRF102]. Supplementary data can be found on The R

Financial Studies Web site. Send correspondence to Jens Dick-Nielsen, Copenhagen Business School, 

Plads 3, 2000 Frederiksberg, Denmark. E-mail: jdn.fi@cbs.dk.

1 See Garman (1976), Stoll (1978), Amihud and Mendelson (1980), and Ho and Stoll (1981).

2 See, for example, the 2017 SIFMA Fact Book.

© The Author(s) 2018. Published by Oxford University Press on behalf of The Society for Financial S

All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

doi:10.1093/rfs/hhy080 Advance Access publication July 
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anticipate or experience significant changes in market structure and reg

framework during the sample period. In the spirit of the Lucas (1976) c

regulations increasing the cost of immediacy may induce market part

to optimally, albeit reluctantly, adjust their trading behavior.

The main contribution of this study is to quantify the cost of immed

corporate bonds in a trading environment that circumvents the Lucas 

critique. We identify trades in which the motive to obtain immediac

strong that liquidity seekers do not orchestrate alternative trading arrang

Furthermore, these trades reveal no information about the fundament

of the assets traded. Specifically, we compute liquidity costs around exc

from the Barclay Capital investment-grade corporate bond index. In this 

experiment, index trackers (the sellers) request immediacy from deal

buyers) in order to minimize their tracking error. Moreover, mechanic

rules, not fundamentals, dictate the decision to trade, thus ensuring 

dealer’s pricing reflects the cost of providing immediacy, rather than the 

selection problem of dealing with informed traders (Easley and O’Hara 

We show that the price of immediacy has more than doubled since be

2008 crisis. Our empirical analysis also shows that the price elasticit

supply of immediacy has increased significantly after the crisis. This i

in elasticity is indicative of higher market-making costs, which transla

higher average transaction costs, thus providing support for standard 

of market maker inventories. For safe bonds, which are quickly turn

again by dealers, the cost of immediacy has approximately doubled, w

for more risky bonds, the cost has more than tripled.

We infer the cost of immediacy by computing a dealer-specific ab

bond return. We do this by defining an intertemporal bid-ask spread, w

based on the percentage difference between the post-exclusion ask pr

the pre-exclusion bid price. This measure captures the essence of the 

role, who uses her inventory to absorb the selling pressure generated 

index trackers unloading their positions, and then resells the bonds to 

the desired level of inventory. These dealer returns indicate that the 

providing immediacy has increased in the post-crisis, low-inventory re

Before measuring transaction costs around index exclusions, we 

that these exclusions are indeed events during which index trackers 

immediacy. Our analysis reveals that the traded volume of bonds exi

index peaks during the day of the exclusion, and it is at least 4 to 5 time

than that in the surrounding weeks. The peak in trading volume is co

3 For instance, Trebbi and Xiao (2017), Adrian et al. (2015), and Bessembinder et al. (2018) find th

trading costs have improved.

2
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Corp. sec. inventory (US

0 50 100 150 200 

Jan03 Jan07 Jan11 Jan15

Corp. bond inventory (U

10 15 20 2

Market illiquidity factor

Market illiqudity factor

−1 0 1 2 3 4 5

Jan03 Jan07 Jan11 Jan15

B

Figure 1

Corporate bond market statistics

Panel A shows the primary dealer inventories in corporate securities (investment grade more than 

maturity) and in corporate bonds. The first series can be retrieved from the New York Fed statistics on 

dealer holdings. The graph on corporate bonds can be retrieved from the same place after March 2

numbers prior to that date have been computed by Goldman Sachs using yearly SEC filings from the 

dealers. Panel B shows the market liquidity measure from Dick-Nielsen, Feldhutter, and Lando (20

measure can be downloaded from peterfeldhutter.com

with index trackers attempting to minimize their tracking errors by trading 

to the index exclusion date.4 Back-of-the-envelope calculations indeed 

that reluctance to trade away from the exclusion date results in a hidde

of indexing5 for final investors of approximately 34 bps annually.

Having established the existence of a demand for immediacy, we veri

dealers absorb the resultant selling pressure and thus provide such imme

Dividing the sample into three subperiods shows that dealer behavi

4 Blume and Edelen (2004) show that stock index trackers display a similar behavior.

5 See also Chen, Noronha, and Singal (2006), Petajisto (2011), and Pedersen (2018) about this cost.
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

for at least 100 days, after the crisis the inventories return to near pre-ex

levels within approximately 20 trading days. More formally, we estimate 

specific inventory mean reversion parameters following Madhavan an

(1993) and find that after the 2008 crisis dealers are less willing to 

deviations from their desired level of inventory. The estimated invento

life significantly decreases from before to during and from during to a

crisis. These findings suggest an increase in inventory costs of market 

We conclude our empirical analysis by exploring several potential c

leading to a higher price of immediacy. First, using institutional bond h

we document an increased role of mutual funds in the corporate bond 

We find that both insurance companies and mutual funds are net sellers 

exclusions, a change of behavior for mutual funds that used to trade in t

direction as dealers before the crisis. We control for these demand shift

multivariate analysis and find that, while important, these shifts do no

the conclusion that dealers’ supply elasticity is higher after the crisis. 

we control for contemporaneous new information potentially affectin

prices and find that it does not affect earlier conclusions. Third, we te

of predictions based on search models. The results of our test suggest 

increase in the cost of immediacy is consistent with an increase in in

holding costs and not driven by an increase in dealer market power.

In addition to contributing to the literature on corporate bond li

this paper occupies a natural place in the literature connecting reg

to financial market efficiency. The debate on the repercussions of the 

Frank act on the financial system offers positions that view the reg

changes as potentially harmful (Duffie 2012) as well as beneficial (Ric

2012). Our study cautions against drawing conclusions about liquidity b

realized aggregate transaction costs. Liquidity measures, such as the on

in Figure 1B, are the outcome of market participants’ optimization pr

and a large-scale policy change alters the optimal behavior of invest

dealers. An analogy would be new rules that significantly increased 

of air travel would induce more travelers to use the bus instead. Disco

air travel might well lower the average realized cost of transportation 

the bus is cheaper), but average utility would decline because of the 

immediacy. Traveling from Los Angeles to New York in 3 days by bu

the same as completing the trip in 5 hours by plane.

By focusing on a homogenous, information-free event in which ag

not arrange alternative trading strategies before and after the suggested 

change, our analysis is able to uncover the potential adverse effect 

new regulatory, low-inventory regime has had on corporate bond li

Separating dealers into banks and nonbanks, we show that the post-crisis 

4
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immediacy closely linked to dealers’ inventory costs. Using a more 

sample that covers the implementation of the Volcker rule, Bao, O

and Zhou (2018) confirm its adverse impact on liquidity provision. Sim

Bessembinder et al. (2018) provide evidence that dealers are less will

commit overnight capital after the crisis.

Our paper also contributes to the literature on index revisions and t

around predictable events (see, e.g., Admanti and Pfleiderer, 1991).6 

index revisions have been recently studied by Newman and Rierson (200

Chen et al. (2014), but these authors focus on special one-time announc

effects, months before the actual index revision date. Newman and R

(2004) look at a large and unique issuance event for European te

companies. Chen et al. (2014) look at the effect of a unique rating rule c

for the Lehman index. Unlike these studies, our paper looks at the tradin

close to the actual index revision dates.

1. Corporate Bond Index Tracking

We consider exclusions from the Barclay Capital corporate bond Index, 

was previously known as the Lehman corporate bond Index and is cur

called the Bloomberg-Barclay corporate bond Index. These exclusions p

an ideal natural experiment for studying the cost of immediacy over time

month corporate bond index trackers demand immediacy from dealers 

they seek to sell bonds exiting the index.

That the rules for bonds entering or exiting the index are both trans

and mechanical makes the monthly exclusion events information-fre

homogeneous over time. As of July 2005, the index contains all U.S. cor

bond issues with an investment-grade rating by at least two of the three 

rating agencies (Standard and Poor’s, Moody’s, and Fitch). Furthermo

issuance size must be at least $250 million and time to maturity must be 

than 1 year.7 Bonds exit the index for three main reasons: time to m

becomes less than 1 year; issuers call their bonds; their median rating 

from investment grade to speculative grade, so if for instance only two r

are available, the lower and more conservative rating is used. Bonds en

index for two main reasons: if they are newly issued and index eligible o

6 See, for example, Chen, Noronha, and Singal (2004) for studies on equity index revisions and Lou, 

Zhang (2013) for anticipated trading in the Treasury market.

7 Index eligibility requires more qualitative rules. See the index rules at https://ecom

barcap.com/indices/index.dxml
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Maturity<1 3,102 645,374 0.92 5.7

Called 392 461,354 0.52 7.

Downgrade 1,078 484,269 5.1 6.8

Other 2,119 358,501 6.0 6.5

B. Bond presence in TRACE

Reason Total excluded In TRACE Traded Sol

at exclusion at excl

Maturity<1 3,102 2,732 2,532 2,45

Downgrade 1,078 893 804 79

The statistics are accumulated from July 2002 to November 2013 for the Barclay Corporate Bond Inde

Lehman). Panel A shows characteristics for the excluded bonds. Market value represented in $1,00

average market value at the time of the index revision. The table shows four reasons for being exc

maturity of the bonds can fall less than 1 year during the month. The bond can be called. The b

downgraded from investment grade to speculative grade during the month. Additionally, the bond can b

for various other reasons. Most of these exclusions are due to revisions of the general index rules, 

the size requirement has been increased twice over the period. In all cases, the bonds are excluded 

of the month (last trading day). Panel B shows the number of excluded bonds with transactions in T

number of bonds traded at exclusion (event day -2 to 0), and the number of bonds sold (bought) by 

(dealers) at exclusion.

rating goes from speculative grade to investment grade.8 These rules r

an index that covers a large fraction of the market. The index is rebalanc

a month on the last trading day of the month at 3:00 pm EST and all bo

are no longer index eligible are excluded at this point in time. We note 

actual downgrade date of a bond takes place before the bond is exclud

the index, so in principle it represents a separate event from exclusio

(We explore actual downgrades in Section 5.3.)

Our bond sample consists of all bonds exiting the index between Ju

and November 2013. Exclusions are fairly equally scattered over time 

in Figure 2. Table 1, panel A, gives characteristics of the excluded b

large number of bonds have been excluded from the index for other r

These exclusions are mainly due to an increase in the lower size limit fo

eligibility, which is why the average issuance size of these bonds is far l

for the rest of the sample.

The objective of index trackers is to minimize tracking error betw

return on their portfolio and that of the index. Blume and Edelen (200

that index trackers following the S&P 500 index are transacting on the ex

that the index is rebalanced, even though they sacrifice potential profit b

so (Beneish and Whaley 1996). Low tracking error is a signal to invest

the index tracker is in fact committed to tracking the index and thus r

an agency problem.

8 We do not report results for index inclusions, because there is little price pressure at inclusion ev

trackers sample the index, so they can select which bonds to buy and thus have a selection of maybe 10

but only need to buy 3–10 bonds. This freedom in selection alleviates most of the price pressure.

6
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0 10 20 30 40 50 

Jan03 Jan05 Jan07 Jan09 Jan11 Jan13

Rating less than investment grade

0 10 20 30 40 50 60 70

Jan03 Jan05 Jan07 Jan09 Jan11 Jan13

Number of bonds

Number of firms

B

Figure 2

Index exclusions over time

This figure plots the number of bond (triangle) and firm (square) exclusions from the Barclay’s Investme

Index. The top panel presents exclusions due to maturity; the bottom panel presents exclusions due 

deterioration. The shaded area represents the subprime crisis.

Bond index trackers are different from stock index trackers in the wa

track the target index. Stock index trackers use an exact-replication st

(Blume and Edelen 2004), whereas bond index trackers use a sampling st

(Schwab 2009; Vanguard 2009). Exact-replication implies that the in

holds a position in each asset member of the index. For corporate bonds

a strategy would generate large transaction costs because the index is lar

market is illiquid, and the index is rebalanced every month. Instead, bond 

trackers sample the index by holding only a fraction of the bonds curre

the index. This portfolio is designed to match the index with respect to du

cash flows, quality and callability. As an example, the Vanguard Total 

Market Index Fund held 3,731 out of 9,168 bonds in the Barclay Capita
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

the index. The outside investments are usually in more liquid instrumen

as futures, options, and interest rate swaps, but also could be in nonpubli

or lower-rated bonds.

The criteria for how to invest the last 20% outside the index are rath

(Schwab 2009; Vanguard 2009), so it is not possible to know exactly 

assets the funds have on their balance sheets. The lack of transparency m

even more important for the funds to keep a low tracking error as a way t

sane investments (Blume and Edelen 2004). Looking again at the V

Total Bond Market Index Fund, we see that the annual average trackin

has been -20 bps over 1993–2017. This track record can be compared to 

Barclays Global Investors fund that tracks the S&P 500 index with a t

error of only 2.7 bps per year (Blume and Edelen 2004).

Index funds do not seek to outperform the index, because investors 

the index funds to express a view on a certain credit or asset class (see 

2016). Some investors may want to capture a specific set of factors f

exposure to these factors. Some investors might even want to have n

exposure to such factors through short positions. Second, conversatio

the leading bond funds also support that these funds demand immediacy 

when the index is rebalanced. (We verify this empirically in Section 3.1 

cuss the potential gain/loss from changing the tracking strategy in Secti

For most bonds, the fund will spread their selling activity within the ex

date, and, for larger bonds, or in a more illiquid market, they might star

1–2 days in advance. This would be the case when, for example, large c

are excluded from sovereign bond indices in which they had a large 

weight in the index, but this is less often the case for corporate bonds.

2. Data

This study uses a unique dataset of U.S. corporate bond transactions p

to us by FINRA. The dataset is identical to the Enhanced TRACE 

available on the Wharton Research Data Services (WRDS), except that 

have anonymized counterparty identifiers for each transaction. This allo

track the changes in individual dealer inventories around the exclusion 

We look at all bonds excluded from the Barclay Capital corporate bon

because of a downgrade to speculative grade or because of time to m

becoming less than 1 year. Table 1 panel B shows that not all the exclude

are actually traded in the market and therefore not present with transac

TRACE.

The TRACE data are cleaned up before usage following the gu

in Dick-Nielsen (2009). We then remove residual price outliers 

8
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specific buying price for each bond. The dealer specific buying price 

volume-weighted average buying price over days -2, -1, and 0 for a 

bond and a given dealer. Here, day 0 is the index exclusion day, and d

and -1 are the 2 days leading up to the event date. Second, to circumve

problem that many dealers may not transact the purchased bonds for man

following the event, we calculate a market-wide average selling price o

day following the event date. The selling price is the volume-weighted av

selling price over all sell-side transactions across all active dealers i

bond. Because this calculated selling price can be seen as a market-wide 

it is likely the price that the individual dealer would use to mark-to-mark

acquired inventory position.

The intertemporal bid-ask spread is the return calculated as the logar

difference between these two prices, and adjusted for accrued interest. I

are no transactions on a given day following the event date the ret

calculated using the first available price after that date. To limit any inform

bias caused by the nontrading days, the sample is restricted to bonds 

the prices are observed within 3 days of the nontrading date. Further

an abnormal return is formed by subtracting the return of a benchmark 

(Barber and Lyon 1997). The benchmark is a portfolio of bonds match

rating and time to maturity. When matching on time to maturity the bo

the benchmark bracket the maturity of the excluded bonds.

We define the cost of immediacy as the return on the transaction a

from the dealer’s viewpoint, which is why the bid-ask spread is included 

returns as explained above. Put differently, the cost (or price) of immed

the return that dealers must expect to earn in order to provide liquidity pro

and sufficiently. We note that these returns are not replicable by other inv

in the economy, who would face a possibly large bid-ask spread to impl

the strategy of buying at the exclusion date and selling afterward. The rest 

study uses the following terminology. When the benchmark return is subt

from the raw return, it is called an abnormal return; when the benchmark 

is not subtracted, it is called an intertemporal bid-ask spread. The latter m

is also used as the event return in Goldstein and Hotchkiss (2008), where

former method is used as the event return in Cai, Helwege, and Warga (

and Ambrose, Cai, and Helwege (2012).

3. Volume and Inventory Dynamics

Costly provision of immediacy has both inventory and pricing implicatio

this section, we explore the first implication; we deal with pricing in th

section.
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

gg 

the index because of low maturity. Day 0, the event day, is the last trad

of the month in which the bond is excluded. Trading volume is agg

across all the bonds excluded during a given event and then averaged 

all event dates. Panel B replicates panel A for bonds excluded becau

recent downgrade to speculative grade. Table 2 shows the same data 

the figure as well as the standard error of the mean volume estimate 

trading volume fraction relative to the day 0 volume. For both types of 

trading activity spikes on the exclusion date. Table 2 shows that the vol

days before and after the event is only 19% to 25% of that at the eve

The peak in trading activity is thus 4 to 5 times that of the normal le

similar trading pattern can be seen around revisions of the S&P 500 

Noronha, and Singal 2004; Harris and Gurel 1986; Shleifer 1986), the 

225 (Greenwood 2005), and the FTSE 100 (Mase 2007).

Because corporate bonds trade over-the-counter, index trackers ca

certain to transact at the desired point in time which is why activity is a

right before and after the exclusion date. Figure 3 and Table 2 show th

investors are tracking the index and that they seek to minimize their t

error, which leads to a spike in the demand for immediacy.

3.2 Dealer inventory around index exclusions

Let’s turn our attention to the supply of immediacy. Figure 4 show

inventories for the bonds excluded from the index. The inventor

cumulative, aggregated over all dealers, and with a chosen benchmar

100 trading days before the event. The daily change in inventory is calcu

the total volume in dealer buys minus the sales. For the low-maturity bo

see the increase starting around 3 days prior to the exclusion date, whe

buildup for the downgraded bonds starts earlier but also increases in ma

approximately 3 days prior to the event. The buildup in the downgrade

from day -23 to day -4 is in part caused by a buy up from the dealer

actual downgrade date. On the downgrade date itself other investors, d

from index trackers, demand liquidity because many firms have an inv

policy that discourages holding speculative-grade assets. This sell ou

downgrade date happens despite a grace period of up to 2 months in w

institutional investors are allowed to hold these bonds (see, e.g., Ambro

and Helwege, 2012, Ellul, Jotikasthira, and Lundblad, 2011). As we w

later, in terms of immediacy, the downgrade date is a smaller event t

exclusion date.

9 Tables A1 and A2 in the Internet Appendix show that the findings are robust to considering abnorm

volume.

10
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Event day

Av. daily volume (U

50 100 15

−100 −50 0 50 100

Rating less than investment grade

Event day

Av. daily volume (USD mill.)

50 100 150 200

−100 −50 0 50 100

B

Figure 3

Trading activity around the event

These graphs show the average trading volume around the monthly exclusions. Panel A shows the tradin

for the bonds excluded due to low maturity. Panel B shows those bonds excluded because of a down

speculative grade. Trading volume is aggregated across all the bonds excluded at a given event date 

averaged across all event dates.

After the exclusion event, Figure 4 shows that the dealers sell all or p

their newly acquired inventory. After 2 weeks most of the acquired inv

of the low-maturity bonds has been sold off. For downgraded exclusion

around two-thirds of the bonds have been sold after 100 days. The two 

thus differ in the way dealers use their inventory. Because dealers on av

do not sell one-third of the buildup again within 100 days, the decrease 

general willingness to hold inventory is expected to have affected the trans

cost of the downgraded bonds the most.

3.3 Dealer behavior before and after the 2008 crisis

Figures 5A and 5B show the change in dealer inventories around the 

before, during, and after the crisis. Tables 3 and 4 show statistics 
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

−100 40.2 17.1 0.18 42.9 4.1 

−50 51.5 22.6 0.23 43.5 5.2 

−40 35.5 9.8 0.16 39.2 3.7 

−30 37.5 14.6 0.17 39.6 4.0 

−20 46.3 9.5 0.21 55.4 8.4 

−10 77.9 21.4 0.35 58.2 8.0 

−9 72.3 21.2 0.32 52.2 6.2 

−8 83.0 28.9 0.37 57.5 5.4 

−7 86.4 25.0 0.39 56.0 5.0 

−6 66.3 13.8 0.30 62.8 6.5 

−5 63.8 15.3 0.29 66.0 8.2 

−4 97.4 33.0 0.44 123.2 24.0 

−3 107.2 27.8 0.48 164.1 20.9 

−2 107.8 26.7 0.48 155.7 15.5 

−1 125.7 25.1 0.56 131.7 12.5 

0 222.8 50.2 1.00 221.9 18.1 

1 88.9 27.1 0.40 99.2 8.4 

2 101.3 29.1 0.45 93.5 8.5 

3 95.8 21.8 0.43 85.5 7.6 

4 79.8 16.7 0.36 79.1 7.8 

5 74.0 16.7 0.33 73.2 6.9 

6 69.2 17.5 0.31 72.4 7.6 

7 61.2 14.4 0.27 54.8 5.7 

8 64.0 15.7 0.29 65.1 5.4 

9 49.2 10.7 0.22 65.4 5.6 

10 64.7 18.7 0.29 52.2 4.8 

20 53.5 14.7 0.24 41.1 3.7 

30 47.4 11.6 0.21 43.4 4.4 

40 49.4 15.4 0.22 47.0 5.2 

50 50.3 13.0 0.23 40.8 4.7 

100 56.8 27.7 0.25 34.8 4.7 

This table shows the average transaction volume around the monthly exclusions. The average is acro

dates. Day 0 is the exclusion date. SE is the standard error of the mean transaction volume. Frac

transaction volume relative to the volume at the exclusion date. Volume is measured in $millions.

corresponding inventory positions.10 The precrisis period is from 200

2007Q2, the crisis period is from 2007Q3 to 2009Q4, and the post-crisi

is from 2010Q1 to 2013Q4. Dealers’ behavior for the short maturity bo

changed from before to after the crisis in that dealers on average provid

as much immediacy after the crisis than before. But they decrease the in

to 0 over roughly the same time interval. Hence, the speed with which t

off again has approximately doubled (we model this pattern more rigor

the next section).

For the downgraded bonds there is a clear shift in dealer behavior from 

and during the crisis to after the crisis. Before and during the crisis deale

a large fraction of the inventory increase on their books. However, after th

they only have 16% of the inventory left after 30 days compared to 58% 

the crisis and 38% during the crisis. Because the shift in behavior happe

10 Results are similar when looking at normalized inventory positions (see Tables A3 to A8 of the Internet 

12
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Event day

Cum. dealer inventory (

0 50 100 

−100 −50 0 50 100

Rating less than investment grade

Event day

Cum. dealer inventory (USD mill.)

0 20 40 60 80 100

−100 −50 0 50 100

B

Figure 4

Cumulative dealer inventory around the event date

These graphs show the average cumulative dealer inventory around the monthly exclusions. Panel A s

inventory for the bonds excluded due to low maturity. Panel B is for the bonds excluded due to a down

speculative grade. Cumulative inventory is determined by subtracting dealer sells from dealer buys and cu

the imbalance over time. The dealer inventory is relative to the arbitrarily chosen starting point of event 

Inventory is aggregated across all the bonds excluded at a given date and then averaged across all the ev

the crisis, and not only during the crisis, it is reasonable to infer that th

is not driven solely by limited risk-bearing capacity of the dealers. Me

of dealer risk-bearing capacity, such as dealer leverage, or the VIX inde

improved since the crisis.

This change in behavior after the crisis is consistent with the new regu

environment successfully discouraging market makers from keeping a 

inventory. Downgraded bonds are no longer kept on inventory but are i

unloaded rather quickly. Note that, although new regulations are no

implemented during our sample period, the change in behavior ha

before the actual implementation date. For instance, starting in 20

major investment banks close or sell off their proprietary trading acti
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Event day

Cum. dealer inventory (

−100 0 50 15

−20 0 20 40 60 80 100

Rating less than investment grade

Event day

Cum. dealer inventory (USD mill.)

0 50 100 150

−20 0 20 40 60 80 100

Precrisis

Crisis

Post−crisis

B

Figure 5

Cumulative dealer inventory by subperiod

This graph shows the cumulative dealer inventories for three periods. Precrisis: 2002Q2 to 2007Q2; cris

to 2009Q4; and post-crisis: 2010Q1 to 2013Q4. The cumulative inventory and the two panels are calc

in Figure 4, except that the referencing point is now event day -30.

motivating this action with reference to regulatory compliance. The re

of proprietary trading has two effects on the market. First, it redu

desired portfolio position of the dealers. Second, it potentially reduced 

for the bonds by eliminating a natural counterparty unless the sold o

maintained the same level of activity (which they did not, because m

them closed down later). Both of these effects would increase inventory 

costs thereby increasing the cost of obtaining immediacy (Madhavan an

1993).

3.4 Speed of inventory adjustment

To provide liquidity, market makers often have to deviate from their desir

of inventory. Provided that inventories are costly and pose risks comme

to the volatility of the assets traded, dealer inventories will displa

14
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

−30 −2.1 1.5 −0.02 0.5 1.8 0.01 −0.3 1.9 

−20 8.9 10.3 0.07 2.4 10.5 0.05 21.3 15.3 

−10 −10.1 12.0 −0.08 1.6 12.7 0.03 13.4 14.1 

−5 −18.7 12.8 −0.15 −1.2 10.7 −0.03 19.4 14.5 

−4 23.7 38.2 0.18 7.0 13.0 0.15 65.0 21.5 

−3 25.4 24.1 0.20 36.8 14.0 0.78 117.4 21.5 

−2 48.6 24.2 0.38 37.6 15.2 0.79 140.0 21.6 

−1 65.2 24.6 0.51 33.7 14.4 0.71 153.9 20.6 

0 128.4 26.0 1.00 47.3 17.5 1.00 244.0 26.3 

1 131.1 26.6 1.02 43.7 18.2 0.92 219.6 24.8 

2 126.5 26.2 0.99 32.3 18.4 0.68 201.6 23.9 

3 113.9 26.2 0.89 22.1 17.7 0.47 179.9 23.9 

4 104.9 25.6 0.82 12.5 16.4 0.26 152.1 20.9 

5 99.4 25.6 0.77 5.3 16.9 0.11 134.7 20.5 

10 57.2 26.3 0.45 −14.9 16.2 −0.31 76.5 18.6 

20 28.1 26.3 0.22 −21.2 18.3 −0.45 28.4 18.4 

30 5.8 25.8 0.04 −30.3 18.1 −0.64 −1.9 19.3 

40 −1.9 29.4 −0.01 −40.4 16.6 −0.85 −31.3 19.9 

50 −19.4 32.1 −0.15 −52.2 15.8 −1.10 −44.6 21.2 

100 −46.2 42.3 −0.36 −72.1 15.3 −1.52 −82.9 21.5 

This table shows the average cumulative dealer inventory around the monthly exclusions because of low 

Cumulative inventory is found by subtracting dealer sells from dealer buys and cumulating the imbal

time. The dealer inventory is relative to the arbitrarily chosen starting point at event day -100. Inve

$millions) is aggregated across all the bonds excluded at a given date and then averaged across all the ev

SE is the standard error of the volume mean estimate. Fraction is the inventory position relative to the p

the exclusion date. The three time periods are 2002Q3–2007Q2, 2007Q3–2009Q4, and 2010Q1–2013Q

reversion. To estimate the speed of mean reversion for each dealer and 

event, we follow Madhavan and Smidt (1993), who derive the foll

equation relating inventory changes to the dealer desired level of invent

It −It−1 =β×(It−1−I 

)+εt, 

where It is inventory at time t, I  is the desired level of inventor

εt is a mean-zero unanticipated liquidity-driven volume, which is po

autocorrelated and heteroscedastic. In Equation (1), β ∈(−1,0), and is 

negative when either inventory costs or the assets’ volatilities are higher

Madhavan and Smidt (1993) show that failure to account for the 

varying nature of I  over long time periods affects the estimation of β. 

we consider a relatively short window around the exclusion event, we 

conditioned the sample on an event that could potentially change the d

inventory level. Figures 4B and 5B and Tables 3 and 4 reveal that on av

inventories do not revert to zero within 100 days, suggesting that they 

settle at a higher level after the exclusion. For this reason, we propo

following specification for the desired level of inventory

I  =α0+α11[t>−3], 

where α0 represents the desired level of inventory before the exclusion 

and α1 represents the change in desired inventory after exclusion. Note t
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

−30 −1.8 1.3 −0.02 −2.8 3.7 −0.02 0.3 1.8 

−20 −8.3 6.9 −0.08 0.8 8.3 0.01 −7.5 7.1 

−10 0.3 8.6 0.00 40.9 39.0 0.30 6.1 8.8 

−5 2.3 9.8 0.02 52.6 44.9 0.38 17.0 7.6 

−4 45.8 39.4 0.46 57.9 50.3 0.42 18.5 8.9 

−3 36.3 23.5 0.36 59.3 51.1 0.43 21.5 8.8 

−2 39.6 24.9 0.40 73.2 56.1 0.53 26.2 9.9 

−1 56.4 25.5 0.56 87.8 60.7 0.64 38.0 10.0 

0 99.9 35.0 1.00 137.2 83.6 1.00 72.2 16.5 

1 92.5 31.0 0.93 127.1 77.9 0.93 64.4 14.0 

2 89.9 31.0 0.90 119.6 74.9 0.87 55.8 11.9 

3 85.7 30.0 0.86 119.2 75.5 0.87 53.5 11.5 

4 85.5 30.3 0.86 109.6 69.4 0.80 48.8 11.0 

5 84.8 30.1 0.85 103.5 67.2 0.75 49.6 11.0 

10 84.8 29.0 0.85 112.7 77.9 0.82 40.3 10.1 

20 71.6 28.1 0.72 64.9 45.7 0.47 21.7 10.0 

30 57.6 24.1 0.58 52.8 33.5 0.38 11.4 11.1 

40 70.5 31.7 0.71 53.8 35.5 0.39 9.0 9.6 

50 51.1 28.4 0.51 38.0 30.3 0.28 13.1 10.9 

100 53.7 36.6 0.54 29.9 46.1 0.22 −11.2 12.8 

This table shows the average cumulative dealer inventory around the monthly exclusions because of a d

Cumulative inventory is found by subtracting dealer sells from dealer buys and cumulating the imb

time. The dealer inventory is relative to the arbitrarily chosen starting point at event day -100. In

$millions) is aggregated across all the bonds excluded at a given date and then averaged across all the e

SE is the standard error of the volume mean estimate. Fraction is the inventory position relative to t

at the exclusion date. The three time periods are 2002Q3–2007Q2, 2007Q3–2009Q4, and 2010Q1–2

activate the indicator variable in Equation (2) at t −3 to account for the 

the increase in inventory happening right before the event is not neces

deviation from an old desired level of inventory, but rather a migration t

new desired level of inventory. We point out that activating the dummy 

at t ={−1,−2,0} makes almost no difference on estimates of β.

Our objective is to investigate whether dealers have sped up their in

mean reversion after the 2008 crisis. To answer this question, for each ev

and for each top-five dealer, we first estimate Equation (1) with iterated 

using a Bartlett kernel with three lags (see Madhavan and Smidt (199

determine top dealers we focus on the dealers that take on the most in

in t ∈[−2,0] in a given event date. Note that the composition of the top 

changes over time. Next, we run a pooled regression with period d

indicating the precrisis, crisis, and post-crisis periods. Table 5 show

regressions for the maturity and downgrade events separately. We c

specifications that also include time-series variables that proxy for 

cost of capital. The third and fourth columns present estimates for regr

including dealer fixed effects. In addition to the point estimates, the fir

rows of the table convert the coefficients into half-life quantities us

transformation −log(2)/(1+β). The variables that proxy for dealer

bearing capacity are the VIX index like in Lou, Yan, and Zhang (20

aggregate leverage growth for broker-dealers from the Federal Reserv

16
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Precrisis −0.0960∗∗∗/6.9 −0.0869∗∗∗/7.6 −0.0788∗∗∗/8.5 −0.0752

(0.0052) (0.0105) (0.0127) (0.0151

Crisis −0.1371∗∗∗/4.7 −0.1334∗∗∗/4.8 −0.0929∗∗∗/7.1 −0.0907

(0.0092) (0.0200) (0.0128) (0.0206

Post-crisis −0.1171∗∗∗/5.6 −0.1043∗∗∗/6.3 −0.0993∗∗∗/6.6 −0.0920

(0.0059) (0.0132) (0.0139) (0.0181

VIX −0.0009 −0.0007

(0.0006) (0.0005

TED spread 0.0002∗∗ 0.0002

(0.0001) (0.0001

Dealer lev. gwth −0.0100 0.0175

(0.0262) (0.0192

Fixed effects No No Dealer Dea

Observations 569 569 569 56

R-square 0.6291 0.6319 0.7331 0.7366

t-test(post<pre) −2.668∗∗∗ −2.069∗∗ −1.702∗∗ −1.323∗

B. Downgrade exclusions (57 distinct dealers)

Precrisis −0.0919∗∗∗/7.2 −0.0884∗∗∗/7.5 −0.1042∗∗∗/6.3 −0.0968

(0.0065) (0.0118) (0.0382) (0.0385

Crisis −0.1205∗∗∗/5.4 −0.1046∗∗∗/6.3 −0.1231∗∗∗/5.3 −0.1092

(0.0147) (0.0292) (0.0396) (0.0450

Post-crisis −0.1250∗∗∗/5.2 −0.1154∗∗∗/5.7 −0.1296∗∗∗/5.0 −0.1186

(0.0131) (0.0192) (0.0357) (0.0374

VIX −0.0002 −0.0008

(0.0007) (0.0007

TED spread −0.0000 0.0001

(0.0001) (0.0001

Dealer lev. gwth 0.0554∗ 0.0192

(0.0304) (0.0315

Fixed effects No No Dealer Dea

Observations 345 341 345 34

R-square 0.4969 0.5005 0.7076 0.7000

t-test(post<pre) −2.261∗∗ −1.796∗∗ −1.879∗∗ −1.507∗

This table reports pooled regression estimates from regressing dealer- and event-specific inventory 

adjustments over period dummies and other control variables. The speed of adjustments, β, are estim

fitting the equation It −It−1 =β ∗(It−1 −α0 −α11[t>−3]) with iterated general method of moments 

with a Bartlett kernel (3 lags), for each dealer and event. It represents total inventory (across all bon

given dealer at event-time t, and α0 and α1 are two constants representing the desired level of invento

and after index exclusions. t = 0 represents the exclusion date. In addition to the point estimates, the fi

rows convert the coefficients into half-life quantities using the formula −log(2)/(1+β). The analysis is 

the inventories of the top-five dealers in each month. See Table 7 for variable definitions. Robust standa

are in parentheses. *** p<.01; ** p<.05; and * p<.1.

of Funds data11 like in Adrian, Etula, and Muir (2014). The VIX is suppo

proxy for the dealers’ funding constraints and the aggregate leverage gro

supposed to capture the dealers’ leverage constraints. When aggregate lev

growth is low, indicating it is more costly to obtain leverage, and when V

high, dealers face higher funding constraints. We also include the TED 

to proxy for money market stress.

11 These data are for primary dealers in the Treasury market. Schultz (2001) shows that the major corpor

dealers significantly overlap with the primary market dealers in the Treasury market.
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

a substantial 2-day difference. Note that this result is not due only to a ch

the composition of dealers over time, as it continues to hold even in regr

with fixed effects capturing within-dealer variation. We also test whe

increase in the speed of mean reversion is statistically significant. As 

seen from the last row of each panel, we reject the null hypothesis 

coefficient on the post-crisis dummy is equal to the coefficient on the p

dummy in favor of the alternative hypothesis that the coefficient becom

negative after the crisis.

In their model, Madhavan and Smidt (1993) derive inventory half-

function of holding costs and asset volatility. Because bond volatiliti

not increased from before to after the crisis, these results are consiste

increased holding costs.

4. Price Dynamics

Because dealers actively use their inventories to provide liquidity t

trackers, we expect them to earn a positive return on average as compe

for the inventory holding costs. The following section shows that dea

compensated for providing liquidity. The costs are higher for the dow

event compared to the low-maturity event as would be expected, beca

downgraded bonds are both more risky and kept longer on inventory.

4.1 Event study of index exclusions

Table 6 shows the dealer abnormal returns for the two exclusion events

of these returns is value-weighted either by the dealer buying volume (V

by the dealer inventory buildup (VW2) on the event date and over the p

2 days. Hence, those bonds purchased by dealers that increased inve

provided immediacy—are given more weight. Given the statistical sa

approach to replicating the index, indexers only hold some excluded bo

this reason, equally weighted returns may mistakenly give too much w

bonds for which traders do not seek immediacy.

Looking at Table 6, we see that the abnormal dealer returns for th

excluded due to low maturity are uniformly higher after the crisis rel

before the crisis. Both value-weighted returns show a much sharper i

(roughly a 100%) in the cost of immediacy for highly rated, short-term 

over the sample period. For example, at 1- and 30-day horizons, th

12 In Table A9 of the Internet Appendix, we report the average intertemproal bid-ask spreads used t

abnormal returns.

18
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

of these bonds and the increased inventory risk that they pose. Moreov

Table 6

Dealer abnormal returns

Maturity exclusions Downgrade exclusions

[0,t] N EW VW1 VW2 N EW VW1 

Precrisis

1 830 20.22∗∗∗ 6.34∗∗∗ 6.17∗∗∗ 243 98.19∗∗∗ 96.18∗∗∗ 

(1.58) (0.69) (0.77) (22.39) (11.80) (

2 794 20.78∗∗∗ 7.31∗∗∗ 7.13∗∗∗ 245 157.89∗∗∗ 188.18∗∗∗ 1

(1.59) (0.69) (0.88) (41.48) (26.10) (

3 780 21.15∗∗∗ 7.66∗∗∗ 7.94∗∗∗ 243 160.68∗∗∗ 184.35∗∗∗ 1

(1.64) (0.76) (0.84) (40.61) (24.27) (

4 777 23.03∗∗∗ 7.87∗∗∗ 8.33∗∗∗ 234 168.71∗∗∗ 195.90∗∗∗ 1

(1.86) (0.99) (0.89) (34.01) (19.87) (

5 763 22.17∗∗∗ 7.59∗∗∗ 7.74∗∗∗ 229 193.42∗∗∗ 220.81∗∗∗ 1

(1.69) (0.87) (1.02) (37.09) (20.18) (

10 727 21.29∗∗∗ 8.05∗∗∗ 8.20∗∗∗ 226 251.28∗∗∗ 295.58∗∗∗ 2

(1.75) (1.29) (1.14) (71.83) (36.06) (

20 688 22.76∗∗∗ 7.20∗∗∗ 7.53∗∗∗ 215 173.15∗∗∗ 154.53∗∗∗ 1

(2.31) (0.86) (1.10) (36.87) (17.01) (

30 675 23.22∗∗∗ 7.92∗∗∗ 7.50∗∗∗ 209 173.25∗∗∗ 174.94∗∗∗ 1

(2.35) (1.11) (1.16) (63.66) (20.69) (

Crisis

1 269 46.33∗∗∗ 50.43∗∗∗ 43.02∗∗∗ 107 58.60 59.14 

(4.51) (7.51) (6.62) (43.07) (37.19) (

2 254 46.57∗∗∗ 50.86∗∗∗ 42.12∗∗∗ 101 80.74 65.61 1

(5.73) (8.13) (8.22) (74.52) (51.91) (

3 236 49.80∗∗∗ 56.52∗∗∗ 52.18∗∗∗ 102 42.16 74.38 1

(6.95) (9.91) (10.43) (88.86) (68.72) (

4 235 52.96∗∗∗ 56.89∗∗∗ 48.79∗∗∗ 93 50.22 118.90 1

(6.32) (7.75) (7.69) (135.23) (123.68) (

5 230 53.18∗∗∗ 56.27∗∗∗ 47.12∗∗∗ 87 82.48 152.41 2

(8.54) (8.86) (7.70) (157.06) (155.66) (1

10 211 63.28∗∗∗ 68.71∗∗∗ 54.53∗∗∗ 91 162.46 193.45 3

(8.59) (9.81) (10.72) (174.87) (145.00) (1

20 211 76.35∗∗∗ 72.47∗∗∗ 54.52∗∗∗ 77 234.47 334.32∗∗ 4

(13.67) (16.76) (17.55) (203.77) (169.83) (1

30 206 96.55∗∗∗ 102.75∗∗∗ 80.71∗∗∗ 71 −139.2 270.88∗ 3

(20.74) (26.35) (22.95) (381.10) (164.37) (1

Post-crisis

1 1,085 26.27∗∗∗ 13.53∗∗∗ 13.30∗∗∗ 213 99.91 292.93∗∗∗ 2

(2.06) (1.64) (1.56) (87.86) (110.71) (1

2 1,054 27.16∗∗∗ 13.79∗∗∗ 13.59∗∗∗ 208 149.92∗ 350.12∗∗∗ 3

(1.98) (1.39) (1.34) (85.42) (125.27) (1

3 1,041 26.47∗∗∗ 13.25∗∗∗ 13.06∗∗∗ 193 185.00∗ 488.51∗∗∗ 5

(2.06) (1.31) (1.29) (109.72) (174.48) (1

4 995 29.46∗∗∗ 13.99∗∗∗ 13.62∗∗∗ 185 203.06 577.79∗∗∗ 5

(2.41) (1.62) (1.56) (128.18) (204.04) (1

5 990 30.06∗∗∗ 14.35∗∗∗ 14.08∗∗∗ 188 231.84 651.57∗∗∗ 6

(2.45) (1.84) (1.79) (145.41) (218.76) (2

10 954 30.19∗∗∗ 14.87∗∗∗ 14.46∗∗∗ 177 173.39∗ 381.56∗∗∗ 4

(2.26) (1.61) (1.57) (101.57) (146.80) (1
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

20 861 34.06∗∗∗ 15.93∗∗∗ 16.02∗∗∗ 175 314.30 807.29∗∗∗ 

(3.25) (1.67) (1.74) (193.71) (281.61) 

30 814 34.20∗∗∗ 15.09∗∗∗ 14.37∗∗∗ 163 332.27 937.37∗∗∗ 

(3.29) (1.60) (1.65) (229.68) (313.65) 

This table shows the dealer-bond specific average returns of bonds excluded from the Barclay Corp

Index because of low maturity. Returns are calculated as log price changes between day 0 (the excl

and day t after exclusion. The returns are calculated from the dealer’s perspective. First, the intertempo

spread is calculated using the dealer-buy price (dealer-specific average buy price over days -2,-1, and 

average dealer sell price at day t (average across all dealers). Second, the abnormal return is the intertem

ask spread minus the return on a matched portfolio. The portfolio is matched on rating and time to mat

is weighted by the aggregate buying volume in the specific cusip for all dealers with a positive invent

in the bond. VW2 is weighted by the aggregate inventory buildup for dealers with a net positive invent

between day -3 and 0. The three time periods are 2002Q3–2007Q2, 2007Q3–2009Q4, and 2010Q

*** p<.01; ** p<.05; and * p<.1.

increase in the cost of immediacy because the precrisis period is muc

than the maturity exclusion case. As can be seen from the last two c

the increase ranges from more than 200% at the 1-day horizon (e.g., 8

294.79 for VW2) to more than 500% at the 30-day horizon (e.g., 14

965.48 for VW2).

4.2 Regression analysis of the cost of immediacy

Table 6 shows a remarkable increase in the price of immediacy since th

of the 2008 crisis. Next, we relate the higher returns earned by dealer

quantity of bonds transacted, and other variables likely to affect the sup

demand of immediacy. Generally, the price (p) and quantity (q) of imm

are jointly determined in the market. Therefore regressing the compensa

immediacy on its quantity subjects the econometrician to simultaneous e

bias. Importantly, we do not usually know whether such regression es

a supply function or a demand function. More formally, a suitable em

model to consider would be:

qD

t = α0+α1pt +et 

qS

t = β0+β1pt +ut 

qD

t = qS

t =qt, 

where et , ut contain both observable and unobservable demand and 

shifters, and the last equation imposes market clearing. To obtain unbia

consistent estimates of the slopes, a two-stage least squares (2SLS) is n

used.13 However, this is not necessary in our setting, which provides a 

identifying restriction.

13 See Choi et al. (2010) for a recent application of this methodology to the analysis of issue pr

underpricing for convertible bonds.

20
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

relation between prices and quantities as a supply relation, so a nonne

relation between prices and quantities in our data would provide supp

our assumption.

4.2.1 Model specification. The dependent variable in the regressions 

cumulative abnormal bond returns (a proxy for the cost of immediac

p(q)). The independent variable of interest is a measure of liquidity pro

(q). Assuming that dealers see the excluded bonds as reasonable substitut

define q as the aggregate dealer inventory imbalance (measured in milli

dollars) for each dealer from day -2 to 0 across all excluded bonds at the 

(downgrade and maturity separately). We drop all dealers with a net ne

inventory imbalance. We interact q with three dummies indicating wheth

observation takes place before, during, or after the 2008 crisis.

We expect our specification to capture a nonnegative supply relation be

the price and the quantity of immediacy. To this end, it is important to ac

for potential demand-side shifters likely to affect the price of immedi

is reasonable to assume that a large event, that is, an event during w

large portion of the index is reconstituted, is more likely to result in a 

demand of immediacy. For this reason, in our baseline regression we inclu

percentage of the index excluded each month as a control variable. In subse

regressions, we control for additional demand shifters, such as the dema

immediacy coming from buy-side institutions around index exclusions.

We also include other factors likely to influence the cost of imme

Specifically, we include the amount outstanding of the bond. Larger 

are likely more transparent and liquid than smaller bonds and are the

less risky to have on inventory. We include the variables proxying for de

risk-bearing capacity which we also used in the inventory half-life regre

Finally, we include industry (financials vs. nonfinancials), rating, and 

dummies that are interacted with each other. Lastly, we also include deale

effects. To save space, we have not reported the estimated coefficients 

dummies in the regression tables.

Table 7 provides descriptive statistics on the variables used in the regres

4.2.2 Cost of immediacy before and after the crisis. Table 8 repo

coefficient estimates of the regressions. As can be seen from the tab

price of providing liquidity is increasing in the amount of liquidity trans

14 Chacko, Jurek, and Stafford (2008) impose a similar restriction in their theoretical model of the 

immediacy, but do so in the context of a limit order book.
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

All VIX 131 20.40 8.91 14.38 17.74 

All Dealer lev. gwth 131 −0.01 0.21 −0.05 0.02 

All % idx excluded 131 1.15 1.17 0.74 0.91 

All Issue size (MIO) 3,314 664.91 569.02 300.00 500.00 

All Dealer inv. (q) 3,314 4.62 13.69 0.00 0.06 

All Log issue size 3,314 17.75 0.68 17.24 17.71 

All Ins. change (pct) 3,230 −0.01 0.03 −0.01 0.00 

All MF change (pct) 3,230 −0.01 0.03 −0.01 −0.00 

All Stk ret (excl.) 2,119 0.00 0.07 −0.02 0.01 

Downgrd Issue size (MIO) 695 655.59 593.82 300.00 500.00 

Downgrd Dealer inv. (q) 695 3.86 13.11 0.00 0.00 

Downgrd Log issue size 695 17.57 0.75 17.07 17.46 

Downgrd Ins. change (pct) 687 −0.02 0.06 −0.03 −0.00 

Downgrd MF change (pct) 687 −0.00 0.03 −0.01 0.00 

Downgrd Stk ret (excl.) 461 −0.00 0.08 −0.04 0.00 

Maturity Issue size (MIO) 2,619 667.38 562.35 300.00 500.00 

Maturity Dealer inv. (q) 2,619 4.82 13.83 0.00 0.08 

Maturity Log Issue Size 2,619 17.80 0.65 17.25 17.73 

Maturity Ins. change (pct) 2,543 −0.01 0.02 −0.01 0.00 

Maturity MF change (pct) 2,543 −0.01 0.02 −0.01 −0.00 

Maturity Stk ret (excl.) 1,658 0.00 0.06 −0.02 0.01 

This table presents descriptive statistics for the variables used in the regression analysis. The statistic

into the whole sample, the downgrade sample, and the low-maturity sample. The TED spread is the 

between the 3-month LIBOR rate and the 3-month Treasury-bill rate. VIX is the CBOR volatility ind

from the implied volatility on S&P 500 index options. Issue size is the offering amount for the bond 

Dealer lev gwth is the aggregate leverage growth for broker-dealers obtained from the Federal Reser

Funds data. Pct idx excluded is the percentage of the index being reconstituted. q is the dealer-specifi

imbalance. MF change (pct) and INS change (pct) are, respectively, mutual funds’ and insurance c

percentage changes in ownership of an excluded bond. Bond ownership data come from Lipper eMA

(excl.) is the issuer stock return at exclusion.

making the relation reminiscent of a supply curve. Comparing the inte

of q with the post-crisis dummy to the interaction of q with the p

dummy reveals that the supply curve is relatively steeper after the 

This result suggests that providing immediacy has become more costly a

crisis, and, consequently, dealers require higher returns for providing ad

immediacy. The results on the effect of q are also economically sign

Noting that the returns are measured in basis points, a one standard d

change in q after the crisis ($16.5 million) is roughly associated 

additional 18.5 bps of return over 3 days and 35 (16.5×2.10) bps ov

day horizon. The coefficient on the precrisis interaction is statistica

economically insignificant at all horizons, indicating that dealers’ stra

buy and temporarily hold excluded bonds could easily scale up.

The regressions include interacted fixed effects, which capture the f

bonds with the same rating might be priced differently before, during, a

15 We conduct t-tests of the difference in coefficients and find that the difference is generally statistically 

at conventional levels.

22
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

(0.308) (0.310) (0.471) (0.582) (0.683) (0.403) (0.699) 

q*Crisis 0.928 0.741 1.449 2.699∗ 3.725∗∗ 2.970∗ 4.904∗∗∗ 

(0.776) (0.980) (1.033) (1.417) (1.577) (1.699) (1.561) 

q*Precrisis 0.0617 0.180 0.130 0.190 0.217 0.255 0.0426 

(0.0874) (0.126) (0.117) (0.167) (0.142) (0.193) (0.129) 

Pct idx excluded 3.977 12.17 9.541 6.500 10.25 20.26 12.72∗∗ 

(4.006) (8.352) (8.054) (6.267) (7.560) (12.85) (5.938) (

Log Issue Size −15.16∗∗ −18.44∗∗ −13.04 −7.045 −14.60 −9.497 −14.91 

(6.610) (8.790) (11.08) (12.54) (14.19) (17.98) (16.49) (

Dealer lev. gwth −90.08∗ −94.07∗ −122.4∗ −89.27 −138.0 −101.2 −147.5 −2

(48.55) (49.74) (64.70) (73.04) (85.26) (90.99) (110.9) (1

VIX 2.446∗ 2.199 2.510 2.630 2.320 1.786 5.328∗ 

(1.345) (1.429) (1.865) (2.123) (2.294) (1.995) (2.852) 

TED spread 1.066∗∗ 1.220∗∗∗ 1.743∗∗∗ 1.832∗∗ 1.833∗∗ 1.346∗∗ 1.774∗ 

(0.416) (0.450) (0.593) (0.721) (0.816) (0.673) (0.966) 

Observations 15,713 15,338 14,993 14,779 14,634 14,101 13,401 

Adjusted R-squared 0.219 0.249 0.261 0.257 0.286 0.252 0.368 

Dealer FEs Yes Yes Yes Yes Yes Yes Yes 

Rating*Period FEs Yes Yes Yes Yes Yes Yes Yes 

F-test (FE interactions) 67.46 11.57 6.717 2.592 13.76 57.92 3.935 

Prob>F 0 0 3.86×10-10 0.00249 0 0 2.18×10-05 

This table presents regression coefficients for a series of regressions. The dependent variable is the b

dealer-specific abnormal returns over the period from the exclusion day 0 to day t after exclusion. Vari

defined in Table 7. The regressions include (interacted) period/industry/rating and dealer fixed effects. Th

are 2002Q3–2007Q2 (precrisis), 2007Q3–2009Q4 (crisis), and 2010Q1–2013Q4 (post-crisis). We con

industry categories (financial vs. nonfinancial) and six rating categories (AAA–AA, A, BBB, BB, B, a

C). Robust standard errors are clustered at the bond issuer and event date level. An F-test tests the null hy

that the interactions of the ratings and subperiod fixed effects are jointly zero. Robust standard erro

parentheses. *** p<.01; ** p<.05; and * p<.1.

the crisis. Interacting fixed effects mitigates the concerns that the inc

cost of immediacy and the increased supply price elasticity come only 

a higher level of risk aversion (hence risk premiums) in the market. 

bottom of Table 8, we test whether the interaction terms are jointly ze

find that these interactions explain some of the variation in dealer re

suggesting that it is important to control for potential changes in risk ave

However, controlling for changing attitudes toward risk does not explain 

our elasticity estimates.

Larger events during which a bigger fraction of the index is recons

might require dealers to take on more inventory resulting in larger dealer re

The positive coefficient on Pct Index Excluded is consistent with this int

but it is only significant at the 20-day horizon.

The other control variables behave as expected although they are not a

significant. Larger bonds have a lower cost of immediacy when consi

short horizons, but the effect is insignificant at long horizons. When d

are more constrained, that is, a low leverage growth or a high VIX, th

of immediacy is higher. Finally, when the money market undergoes stres

is, a high TED spread, the cost of immediacy increases. Money marke
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

4.3 The hidden cost of bond index investment

The cost of immediacy includes a price pressure component as wel

bid-ask spread. From the perspective of the institutional investor, th

pressure component is the more interesting part (Hendershott and M

2014). Because the bid-ask spread or the half-spread is in some sense 

cost once the investor owns the asset and wants to sell, variation in the 

buying price is what constitutes the true opportunity cost. Table 9 sh

abnormal event return calculated like in Table 6 but using only dealer buy 

This is thus the return that the institutional investor could have gotten 

equal) had she waited to sell instead of selling at the event date. The neg

indicate the return from before the exclusion date and up to the exclusio

A negative return before the exclusion date thus means that the price de

leading up to the event. From Table 9, we see that for the maturity exc

the bid price decreases leading up to the exclusion and it also decreas

exclusion. The dealer return from Table 6 is therefore driven by an i

in the bid-ask spread rather than a rebound of the price. For the dow

exclusions, the bid price decreases leading up to the event and increas

the event, indicating that much of the dealer return from these exclus

generated by a rebound of the price level.

The bid-to-bid returns pick up a hidden cost of index tracking (s

Chen, Noronha, and Singal, 2006, Pedersen, 2018, Petajisto, 2011). 

this, consider that the bond index return is calculated using the averag

from day 0 and that this price will be heavily depressed by the conce

selling from index trackers. Although index trackers obtain potentially 

tracking error by trading on the exclusion date, the actual returns attai

based on severely discounted prices. It is in principle possible to outp

the index on average by avoiding the price pressure and selling sever

away from the rebalancing date.

On average 1.2% of the index (in market values) is excluded each 

Using a back of the envelope calculation, the hidden cost of index tra

the average (monthly) abnormal bid-to-bid exclusion return times the 

excluded from the index (multiplying by 12 gives a rough estimate of the 

costs). The ratio of low- maturity exclusions to downgrade exclusion is 

3:1 (in market values). For downgraded bonds it is optimal to sell out 

after the event, whereas for maturity exclusions it is optimal to sell out 

before the event according to Table 9. The hidden cost of index tracking 

roughly 0.012×12×(0.25×0.0966+0.75×0.00129)= 34 bps.

The cost estimate can be compared to the hidden cost from stoc

investment calculated in Petajisto (2011) of 21–28 bps annually for t

500. Note that this annual cost estimate is only indicative, because we 

24
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Intertemporal bid-ask spreads

−10 888 −15.04∗∗∗ −7.20∗∗ −6.66∗∗ 179 −236.2∗∗ −357.3∗∗ −3

(2.83) (2.89) (3.03) (112.38) (153.68) (1

−5 973 −10.41∗∗∗ −2.91 −2.96 198 −286.9∗∗ −216.4∗∗∗ −1

(2.20) (1.90) (2.03) (132.66) (75.00) 

−4 1,059 −9.56∗∗∗ −1.77 −1.70 192 −217.0∗ −117.1∗∗∗ −

(2.09) (1.64) (1.65) (127.68) (42.04) 

−3 1,216 −7.86∗∗∗ −1.28 −1.68 202 −190.0 −111.4∗∗ −

(2.24) (1.78) (1.65) (123.68) (48.42) 

1 947 5.87∗∗∗ −2.01∗ −2.40∗ 208 83.49 380.83∗∗ 4

(1.65) (1.13) (1.36) (118.02) (167.58) (1

2 911 5.60∗∗∗ −2.13∗ −2.63∗∗ 214 158.80 488.26∗∗ 5

(1.73) (1.13) (1.27) (130.18) (197.33) (1

3 904 6.37∗∗∗ −1.05 −1.46 204 210.10 621.78∗∗ 6

(1.56) (0.99) (1.13) (161.63) (253.37) (2

4 885 7.29∗∗∗ −1.28 −1.34 188 231.39 736.97∗∗ 7

(1.30) (1.02) (1.17) (192.10) (304.91) (3

5 880 8.34∗∗∗ −1.96∗ −2.53∗∗ 181 264.08 830.50∗∗ 8

(1.48) (1.15) (1.28) (220.66) (343.04) (3

10 895 13.16∗∗∗ 1.15 1.02 174 131.33 475.54∗∗ 5

(2.50) (1.96) (2.11) (147.23) (218.24) (2

20 871 18.79∗∗∗ 4.16 3.61 166 357.55 1043.1∗∗∗ 11

(3.36) (2.79) (2.56) (301.68) (373.96) (3

30 832 23.88∗∗∗ 7.10∗∗ 6.02∗∗ 174 524.61 1406.5∗∗∗ 14

(4.40) (3.02) (2.87) (355.04) (443.29) (4

Abnormal returns

-10 888 −21.61∗∗∗ −13.00∗∗∗ −12.91∗∗∗ 179 −322.3∗∗ −566.6∗∗ −5

(2.03) (2.00) (2.03) (152.23) (257.04) (2

-5 973 −15.35∗∗∗ −7.64∗∗∗ −7.78∗∗∗ 198 −354.9∗∗ −385.2∗∗ −3

(1.32) (1.32) (1.48) (154.12) (153.03) (1

-4 1,059 −14.44∗∗∗ −6.66∗∗∗ −6.86∗∗∗ 192 −290.3∗∗ −293.7∗∗ −2

(1.50) (1.24) (1.18) (146.19) (121.61) (1

-3 1,216 −12.01∗∗∗ −5.12∗∗∗ −5.65∗∗∗ 202 −262.7∗ −287.9∗∗ −2

(1.82) (1.33) (1.06) (144.22) (119.64) (1

1 947 4.89∗∗∗ −2.60∗∗∗ −2.76∗∗∗ 208 55.66 304.63∗∗ 3

(1.65) (0.80) (0.91) (100.57) (136.67) (1

2 911 3.77∗∗ −3.51∗∗∗ −3.78∗∗∗ 214 110.44 358.86∗∗ 3

(1.52) (0.69) (0.68) (100.82) (146.05) (1

3 904 3.94∗∗∗ −3.05∗∗∗ −3.25∗∗∗ 204 149.10 463.94∗∗ 5

(1.49) (0.76) (0.82) (124.28) (188.31) (1

4 885 4.14∗∗∗ −3.73∗∗∗ −3.49∗∗∗ 188 167.47 563.32∗∗ 5

(1.29) (0.82) (0.83) (146.60) (224.34) (2

5 880 4.61∗∗∗ −4.75∗∗∗ −5.10∗∗∗ 181 198.02 647.02∗∗ 7

(1.26) (0.88) (0.94) (173.08) (262.52) (2

10 895 7.00∗∗∗ −3.35∗∗ −3.17∗∗ 174 105.16 438.89∗∗ 5

(1.86) (1.35) (1.51) (135.07) (198.27) (2

20 871 8.59∗∗∗ −2.46∗∗ −2.28 166 264.48 781.47∗∗∗ 8

(2.06) (1.22) (1.40) (231.05) (287.87) (2

30 832 6.83∗∗∗ −5.27∗∗∗ −5.21∗∗∗ 174 312.39 935.26∗∗∗ 9

(2.21) (1.34) (1.43) (257.10) (315.03) (3

This table replicates Table 6, except that the time ±t price is an average (across all dealers) of the buy 

negative t, we compute bid returns from −t to 0; for positive t, we compute bid returns from 0 to t. C

with Table 6, prices at time zero are dealer specific. Returns are only calculated for the most recent tim

*** p<.01; ** p<.05; and * p<.1.
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

at the Vanguard Total Bond Market Index Fund as an example. The 

Capital Corporate Bond Market Index constitutes around one third 

index that the Vanguard fund is tracking. The Vanguard fund had an 

yearly tracking error of -20 bps over 1993-2017. The tracking error pr

comes from transaction costs and management fees. Following the 

from above (using intertemporal returns) and selling out 10 days be

event for maturity exclusions and 30 days after the event day for dow

exclusions, the Vanguard fund could improve its tracking error by betw

9 bps, depending on our assumptions about how the fund samples th

However, the improvement in tracking error comes with an increas

standard deviation of the tracking error, which increases from 20.0 bps 

bps. Hence, there is a trade-off between size and stability of the trackin

Thus, the strategy of selling out very close to the exclusion date c

explained by a desire to keep the tracking risk low.

Although the increase in tracking error variance that we calculate m

modest, the fund could have a fear of realizing a very large negative even

would cause additional variation in the tracking error. This dislike for t

risk also could be seen in 2002, when the Vanguard fund underperform

benchmark by 2.00%. This lead the fund to change its tracking strateg

a strategy that used to overweight some sectors. In the semiannual repo

June 2002, fund managers stated that they would make this change desp

belief that the overweighting had rewarded them over the long run. Ave

such tail risk is consistent with findings that the flow-to-performance 

for corporate bond funds is concave (Goldstein, Jiang, and Ng 2017).

5. Exploring Additional Channels

5.1 Evolution of bond ownership structure

The discussion so far has ignored changes in the market structure tha

potentially affect the price of immediacy. Based on data from the 

eMaxx institutional bond database, Table 10 and Figure 6 show that 

fund investors have risen in importance in both relative and absolute 

Figure 6 further shows that high-yield funds, which can be seen as 

buyers for bonds that exit an investment-grade index to join a hig

index, have also risen in importance, but have grown less than other 

funds. Table 10 reports absolute and relative frequencies (by subpe

fund*quarter observations in the Lipper eMaxx database. As can b

insurance companies are a major player in the corporate bond market. H

mutual funds have gained importance in this space. While before th

holding reports by mutual funds represent about a third of insurance c

26
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

% 28.65% 9.88% 1.06% 2.28% 

Crisis Count 10,894 5,643 163 1,364 

% 9.21% 4.77% 0.14% 1.15% 

Post-crisis Count 28,100 16,490 305 4,053 

% 23.76% 13.94% 0.26% 3.43% 

This table reports the absolute and relative frequencies of the investment categories represented in th

eMAXX institutional Bond holdings database. The observations for which the frequencies are compu

the fund*date level.Par amount (USD bn)

0 200 400 600 800 1,000

2003Q1 2005Q1 2007Q1 2009Q1 2011Q1 2013Q1

Total par amount

Spec. par amount

Figure 6

Mutual fund growth

The figure shows the total bond par value held by mutual funds covered by Lipper eMAXX. The other lin

holdings by mutual funds specializing in speculative-grade bonds.

reports, after the crisis their number has grown to be more than half. 

types of investors are negligible, so we ignore them going forward.

Next, we explore how mutual funds and insurance companies trade a

exclusion events. Figure 7 shows that, compared to the crisis, mutual 

hold a much larger share of excluded bonds. This figure shows the perc

of bonds held by insurance companies and mutual funds before and 

after the exclusion event and provides prima facie evidence of the t

direction of these corporate bond investors around the exclusion event. A

be seen, insurance companies (left graphs) reduce their holdings, espe

for downgrade exclusions (Figure 7C). In addition to showing the inc

relevance of mutual funds, Figures 7B and 7D show that mutual fund

net buyers of excluded bonds before the crisis, and have become net 

since. This change in behavior by mutual funds apparently contrasts the 

in Choi and Huh (2017), who suggest that some liquidity provision is pro

by nondealers after the crisis. A related paper by Anand, Jotikasthir

Venkataraman (2017) is more consistent with our study in that it suggest
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

C D 0.00 0.06 0.12 0.18 0.24 0.30

Precrisis Crisis Post−crisis

Before excl. After excl.

0.00 0.03 0.06 0.09 0.12

Precrisis Crisis Post−

Before excl. After exc

0.00 0.06 0.12 0.18 0.24 

Precrisis Crisis Post−crisis

0.000 0.015 0.030 0.045 0

Precrisis Crisis Post−

Downgrade - Insurance Downgrade - Mutual fund

Figure 7

Institutional ownership before and after index exclusions

The figure shows the holdings as a percentage of the issue size held by insurance companies (left 

mutual funds (right charts) in bonds that exit the Barclays Investment-Grade Index either because they 

1 year of maturity (top charts) or because the median bond rating falls below investment grade (bott

Each chart reports bond ownership for each subperiod considered in this study. Within each subperiod

also report bond ownership before exclusion (blue, left bars) and up to 2 months after exclusion (red, ri

while some mutual funds could be supplying liquidity in some instances

they are still liquidity takers. We note, however, that our findings pertain 

exclusions, so they do not have the same breadth as the two studies ab

We test the relationship between institutional ownership and tradin

exclusion events in a regression. Contrasting holdings from the 3 

preceding a bond exclusion against the month of the exclusion and the 2 

following exclusion, Table 11 regresses aggregate holdings (as a percen

issue size) on a dummy (Post) indicating the month of or the 2 mont

exclusion. This setup accounts for the quarterly reporting frequency of 

funds and insurance companies. The regression also includes the intera

28
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Insurance companies

Intercept 0.4686 0.3562 0.1372 0.0723 0.0653 

(97.61)∗∗∗ (49.47)∗∗∗ (29.58)∗∗∗ (1.25) (0.74) (

Post −.0233 −.0373 −.0440 −.0067 −.0131 −

(−2.43)∗∗ (−2.59)∗∗∗ (−2.59)∗∗∗ (−1.48) (−2.57)∗∗ (−

High inv*Post −.0074 −.0034 0.0303 0.0001 0.0061 −

(−0.54) (−0.13) (1.12) (0.01) (0.71) (−

Adjusted R-square 75.41% 70.09% 91.45% 81.07% 93.01% 8

Num. of observations 630 304 298 1,596 404 

Mutual funds

Intercept −.0023 0.0064 0.0058 0.0013 0.0261 −

(−1.43) (2.27)∗∗ (1.75)∗ (0.27) (1.64) (−

Post 0.0008 −.0066 −.0199 0.0008 −.0050 −

(0.34) (−1.17) (−2.20)∗∗ (0.84) (−2.36)∗∗ (−

High inv*Post 0.0038 −.0019 0.0132 −.0004 −.0006 −

(0.77) (−0.31) (0.94) (−0.33) (−0.18) (−

Adjusted R-square 37.67% 85.66% 93.13% 35.90% 69.81% 5

Num. of observations 912 372 476 2,248 616 

This table presents coefficient estimates of a regression of aggregate bond holdings (as a percentage of 

size) held by insurance companies (top panel) and mutual funds (bottom panel). The regression includ

and time (event month) fixed effects. Robust standard errors are clustered at the issuer level. Post is a 

equal to one if the holding refers to either the month of exclusion or the next 2 months following exclus

inv (absorbed by the time fixed effects) is a dummy equal to one if the exclusion event was characte

above-median inventory buildup. High inv*Post is an interaction term meant to capture changes in ins

holdings after exclusions characterized by higher than usual inventory buildup. Robust standard erro

parentheses. *** p<.01; ** p<.05; and * p<.1.

Post with a dummy indicating whether aggregate dealer inventory buildu

above the median (High Inv).

As can be seen from the top panel of Table 11, on average, insu

companies reduce their positions in downgraded bonds substantially, 

the reduction for low-maturity bonds is less pronounced and less statis

significant. Lack of significance of the interaction term suggests that insu

companies do not take liquidity at a time when dealers are providing 

of it. With regard to mutual funds (bottom panel), before the crisis ch

in holdings were practically zero, but over time the reduction in holdin

become more pronounced and statistically significant. Similarly to insu

companies, selling by mutual funds does not happen during events when d

are building up inventory more than usual.

The analysis of institutional holdings reveals a steady change in m

structure that potentially affects the demand and pricing of immediac

statistical insignificance of High Inv*Post indirectly suggests that the gr

mutual fund sector is not driving the increased price of immediacy that d

charge, because we do not find that selling by mutual funds is elevated 

times when dealers provide above-median immediacy. Nevertheless, as a 
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Event day

Av. daily volume (U

0 50 100 150 

−100 −50 0 50 100

Cumulative inventory at downgrade date

Event day

Cum. dealer inventory (USD mill.)

−20 0 20 40 60

−50 0 50 100

B

Figure 8

Trading and inventory around the downgrade date

These graphs show the average trading volume and cumulative dealer inventory around the down

The downgrade date is the date at which the bond changes index rating from investment grade to 

grade. Trading volume is aggregated across all the downgraded bonds. The cumulative inventory is 

like in Figure 4, except that the referencing point is now event day -50 and the event time is now rel

downgrade date.

robust approach we control for institutional trading behavior directly 

main specification.

Table 12 presents regression estimates for a specification that mim

of Table 8, but with the addition of two regressors capturing the 

in percentage holdings of excluded bonds by mutual fund and in

companies. Indeed, the coefficient on MF Change (Pct) and Ins. Chan

suggest that the cost of immediacy is larger when mutual funds and in

companies reduce their position in the bonds that exit the index. Howe

note that, while these coefficients are marginally statistically signific

coefficients on the interaction of q with the post-crisis dummy do not 

and remain statistically significant. For instance, comparing Table 8 to T

30
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

(0.259) (0.376) (0.419) (0.523) (0.597) (0.388) (0.646) 

q*Crisis 0.863 0.744 1.403 2.614∗ 3.648∗∗ 2.826∗ 4.946∗∗∗ 

(0.893) (0.997) (1.001) (1.421) (1.747) (1.479) (1.558) 

q*Precrisis 0.0636 0.176 0.133 0.195 0.225 0.246 0.0512 

(0.169) (0.122) (0.120) (0.118) (0.145) (0.175) (0.133) 

MF change (pct) −303.5 −246.7 −505.2 −538.5 −342.9 311.9 −429.5 −9

(328.8) (370.4) (385.8) (497.1) (613.5) (545.5) (675.1) (5

Ins. change (pct) −275.3∗ −302.3∗ −125.3 −68.72 −51.15 −621.6∗ −129.7 −8

(162.2) (178.5) (304.4) (298.3) (385.0) (345.4) (379.1) (3

% idx excluded 3.406 11.64 9.356 6.441 10.16 18.61 12.41∗∗ 

(3.802) (7.961) (8.062) (6.389) (7.476) (11.73) (5.773) (

Log issue size −14.95∗∗ −18.15∗ −13.69 −8.257 −16.10 −8.562 −15.59 

(7.248) (9.682) (11.72) (13.09) (16.09) (17.93) (19.01) (

Dealer lev. gwth −83.88∗ −91.61∗ −113.6∗ −77.83 −123.5 −88.97 −134.9 −2

(47.18) (49.58) (62.32) (70.22) (82.52) (91.26) (110.6) (1

VIX 2.546∗ 2.228 2.566 2.675 2.468 2.130 5.430∗ 

(1.294) (1.403) (1.863) (2.082) (2.270) (2.015) (2.873) 

TED spread 1.058∗∗ 1.215∗∗∗ 1.720∗∗∗ 1.805∗∗ 1.787∗∗ 1.335∗∗ 1.730∗ 

(0.405) (0.443) (0.575) (0.692) (0.780) (0.669) (0.952) 

Observations 15,443 15,079 14,714 14,506 14,371 13,851 13,153 

Adjusted R-squared 0.221 0.251 0.266 0.262 0.299 0.245 0.376 

Dealer FEs Yes Yes Yes Yes Yes Yes Yes 

Rating*Period FEs Yes Yes Yes Yes Yes Yes Yes 

This table presents regression coefficients for a series of regressions. The dependent variable is the b

dealer-specific abnormal returns over the period from the exclusion day 0 to day t after exclusion. Vari

defined in Table 7. The regressions include (interacted) period/industry/rating and dealer fixed effects. Th

are 2002Q3–2007Q2 (precrisis), 2007Q3–2009Q4 (crisis), and 2010Q1–2013Q4 (post-crisis). We con

industry categories (financial vs. nonfinancial) and six rating categories (AAA–AA, A, BBB, BB, B, a

C). Robust standard errors are clustered at the bond issuer and event date level. Robust standard erro

parentheses. *** p<.01; ** p<.05; and * p<.1.

we see that the 1-day coefficient on q ∗P ost −crisis goes from 0.630 to 

and that the 30-day coefficient goes from 1.887 to 1.815.

5.2 Search frictions and inventory costs

In this subsection, we test a set of predictions derived from search 

models (e.g., Duffie, Garleanu, and Pedersen, 2007). The predictions 

dealer inventory costs to dealer behavior and market power.

The increase in the cost of immediacy seen in Table 6 could be drive

change in dealers’ market power (Lagos and Rocheteau 2007). The fa

during the crisis many dealers merged or exited the market could pote

increase the market power of the remaining dealers. Alternatively, an in

in the collective market power of dealers could entice new dealers to the m

Table 13, panel A, shows the number of dealers participating in the even

the number of dealers with at least one buy transaction during event d

to 0). Panel A also shows the Herfindahl-Hirschman index for dealer 

at the event. The table shows that the number of dealers has increase

time and that the concentration is lower. Based on these two findings it 

that competition among dealers has not decreased after the crisis. We 
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

(p

Number of participating dealers

Maturity exclusion 54.0 71.6 77.8 6.

(2.32) (12.86) (2.30)

Downgrade exclusion 36.4 35.2 49.0 1.

(7.01) (9.68) (6.61)

Herfindahl index for dealer market share

Maturity exclusion 0.132 0.114 0.101 −2.

(0.0095) (0.0110) (0.0094)

Downgrade exclusion 0.264 0.275 0.234 −0.

(0.0267) (0.0526) (0.0303)

Riskless principal trading fraction

Maturity exclusion 0.106 0.121 0.116 0.

(0.010) (0.019) (0.009)

Downgrade exclusion 0.118 0.109 0.152 1.

(0.014) (0.021) (0.021)

B. Selling priority

Downgrade exclusions Maturity exclusions

q*Post-crisis 0.256∗∗∗ 0.379∗∗∗

(0.016) (0.024)

q*Crisis 0.098∗∗∗ 0.256∗∗∗

(0.006) (0.081)

q*Precrisis 0.063∗∗∗ 0.204∗∗∗

(0.004) (0.059)

Period fixed effects Yes Yes

N 237,310 45,450

t-test (pre vs. post) 9.60∗∗∗ 2.73∗∗∗

Panel A shows the number of dealers participating in buying the excluded bonds over day -2 to 0. The 

index is calculated using each dealers share of the event dealer-buying volume from day -2 to 0. Riskle

trading is a dealer-buy in a specific bond that is reversed with a sell from the same dealer within 6

The riskless principal fraction is the ratio of these trades to the total dealer specific buying volum

-2 to 0. All numbers are averages over dealers and then months. Panel B shows selling priority as 

of dealer-specific inventory. Selling priority is equal to 1 if the dealer executes a principal at risk se

of riskless principal) and 0 otherwise. Inventory is event and dealer specific and is set to 0 at the st

date -2. The regression includes all customer buys from day -2 to 0. Inventory is measured in $100 m

periods are 2002Q3–2007Q2 (precrisis), 2007Q3–2009Q4 (crisis), and 2010Q1–2013Q4 (post-crisis)

is for no difference in estimates between precrisis and post-crisis. Robust standard errors are in p

*** p<.01; ** p<.05; and * p<.1.

unlikely that the entry of new dealers is driven by an increase in the co

market power of dealers because dealers were already in a situation 

they could extract maximal rent from the price inelastic index tracke

bargaining power of index trackers is likely primarily determined by the 

of participating dealers, because, with fewer dealers, the index tracke

fewer outside options when negotiating with a specific dealer.

The entry of new dealers could be consistent with an increase in holdi

of the old dealers. Such an increase in holding costs would allow new 

to enter the market and compete at the (now) higher prices of imm

The dominating precrisis dealers were likely those who were most affe

32
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

inventory costs.

Our setting is close to that modelled in An and Zheng (2017). While 

search based models assume that investors randomly switch preferenc

holding a security, in their model customers will not regain a positive pref

for the security. This resembles the situation for index trackers, although 

models assume that the loss of preference happens randomly wherea

deterministic for index trackers. In An and Zheng (2017) dealers can 

use their inventory (provide immediacy) or just match customers (ri

principal trading or agency trading). In the latter case customers have t

in order to be matched. When inventory costs increase the price of imm

should also increase (like in Table 6), and we should see a higher fract

riskless principal trading. The bottom section of panel A in Table 13 sho

fraction of riskless principal trading out of the total trading volume. Sim

Bessembinder et al. (2018), we define riskless principal trading as a cus

sell that can be matched to a customer buy by the same dealer within 

frame of 60 seconds. We find a minor increase in riskless principal tradin

only minor increase should be seen in connection to index trackers ha

preference for selling the asset and being price inelastic. Therefore, even t

dealers had an increase in their holding costs, their costs are still much 

than the holding costs for index trackers hanging on to the bond after excl

Another prediction regarding inventory cost from An and Zheng (20

that dealers should be more prone to service incoming customers seek

buy a bond by using their inventory instead of matching to waiting cust

when inventory costs increase. To test this, we classify each buy by a cus

as either having been served using existing inventory (principal at risk) or 

a waiting seller (riskless principal). Again, we classify it as a customer 

if the same dealer made two opposite transactions in the same bond w

same volume within 60 seconds. We then construct an indicator that 

1 if the customer buy was serviced using the inventory and 0 otherw

Table 13, panel B, the indicator is the dependent variable and the level 

dealer inventory is the independent variable. The inventory is dealer sp

and accumulated from the start of day -2 up to the specific transaction 

for calculating the principal at risk indicator (up to day 30). The dealer 

be more prone to using her inventory when inventory costs increase and 

inventory holdings are large. The increase in the estimated coefficient

time thus suggests that inventory costs are higher after the crisis.

5.3 Information and trading

New information about the issuer around the time of the index exc

could affect the observed cost of immediacy for the bonds. Focusing 
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

could then coincide with the price pressure reversal from the index excl

To investigate the potential impact of contemporaneous informatio

the bonds, we first look at the downgrade date compared to the exclusi

Figures 8A and 8B show that the downgrade date itself also sees a lot of 

activity. Average trading volume is of the same size as that seen on the ex

date but the inventory buildup on the downgrade date is far smaller th

on the exclusion date. While inventory peaked at the exclusion date a

decreased, here the peak is delayed consistent with a larger inventory 

at the exclusion date instead of at the downgrade date.

Figure 9 shows both the downgrade date and the exclusion date fo

with exactly 17 days between the downgrade and exclusion. This is t

common number of days between the two events. The volume figure 

shows two spikes in trading activity, first on the downgrade date and the

exclusion date. The inventory graph shows a minor inventory increas

downgrade date, but the second increase at the exclusion date is large

after the inventory spike at the exclusion event, dealer inventory imm

starts to decrease.

The figures suggest that the downgrade date and the exclusion d

two separate events. To test whether information spillover or a slow r

from the downgrade could be a contributing factor to the exclusion 

we augment the main regression from Table 8 with two variables. F

include the abnormal stock return of the bond issuer over event day 

Abnormal returns are calculated by benchmarking the issuer using s

book-to-market value to a matching Fama-French portfolio (Barber an

1997). We also include an indicator that equals 1 if the downgrade ha

in the second half of the month. If the exclusion event return is affe

a slow recovery from the downgrade date, then we would expect tha

with a recent downgrade had a higher return than bonds with a more 

downgrade.

Table 14 shows the estimated regression model for downgraded bon

abnormal stock return is clearly significant and important. However, 

not affect the significance of the other coefficients of interest. This s

that contemporaneous new information is of course important but th

not a main driver of the results. The indicator for a recent downgrad

significant at long horizons and has the opposite sign compared to exp

when it is significant. This suggests that a slow recovery from the dow

does not contribute on average to the exclusion returns. A possible rea

16 See, for example, Katz (1974), Grier and Katz (1976), and Norden and Weber (2004) for a review of o

change studies.

34
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Event day

Total daily volume (U

0 500 1,500 

−30 −20 −10 0 10 20

Inventory: 17 days lag

Event day

Cum. dealer inventory (USD mill.)

−400 0 400 800

−30 −20 −10 0

B

Figure 9

Trading and inventory for specific downgrade constellations

The graphs show trading activity (calculated like in Figure 3) and cumulative inventory (calculated like 

4). The event time in these graphs is relative to the index exclusion date (the right vertical line). The lef

line is the downgrade date. The time lag between the downgrade date and index exclusion is kept cons

days, which is the most common number of days between the two events. Volume and inventory are not 

like in the former graphs.

this is that to the extent that a slow recovery is predictable it becomes part 

negotiation surplus in the bargaining between dealer and index tracker

high dealer competition the dealer compensation would still just reflect th

of providing immediacy.

5.4 Banks versus Nonbanks

The increase in the cost of immediacy coincides with the spin-off of prop

trading for the largest dealers. The spin-off is likely a strong contri

factor to the lower levels of inventory for dealers after the crisis com

to before the crisis. In their motivation for the spin-off, dealers cite 
[17:21 17/12/2018 RFS-OP-REVF180082.tex] Page: 36 1–41

Table 14 Accounting for information Event window: (0,t] 1 2 3 q*Post-crisis 1.429 2.202∗ 4.201∗∗ 

(1.329) (1.204) (1.781) 

q*Crisis 3.092∗∗ 3.829∗∗ 4.656∗∗ 

(1.313) (1.576) (1.997) 

q*Precrisis 0.112 0.118 0.110 

(0.145) (0.168) (0.204) 

Recent downgrd −74.92∗∗∗ −94.36∗∗∗ −115.9∗∗∗ −1

(23.22) (33.39) (39.05) (

Stk ret (excl.) −872.9∗∗ −1,048∗∗ −1,166∗∗ 

(350.5) (420.4) (478.6) (5

MF change (pct) −298.3 −132.7 −391.3 −1

(257.7) (355.9) (396.8) (4

Ins. change (pct) −183.5 −349.0 −72.76 

(272.5) (246.0) (435.9) (4

% idx excluded 11.14∗∗ 28.43∗∗∗ 23.96∗∗ 

(5.383) (10.38) (9.704) (

Log issue size −43.64∗∗∗ −43.96 −37.87 −

(16.00) (27.00) (36.05) (

Dealer lev. gwth −94.61 −248.2 −283.1 

(189.6) (284.2) (341.1) (4

VIX 6.287 0.460 1.886 

(4.623) (6.175) (7.557) 

TED spread 2.922∗∗ 4.752∗∗∗ 4.304∗∗∗ 

(1.110) (0.868) (1.292) 

Observations 2,805 2,783 2,732 Adjusted R-squared 0.376 0.409 0.420 Dealer FEs Yes Yes Yes Rating*Period FEs Yes Yes Yes This table presents regression coefficients for a series of regressions. The dependent varday 0 to day t after exclusion. Variables are defined in Table 7. The regressions include ((precrisis), 2007Q3–2009Q4 (crisis), and 2010Q1–2013Q4 (post-crisis). We consider two iBB, B, and CCC–C). Robust standard errors are clustered at the bond issuer and event 

36
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

Buy share Inv share Buy share Inv share

Post-crisis 0.696 0.874 0.663 0.640

(0.016) (0.035) (0.017) (0.038)

Crisis 0.779 0.844 0.552 0.759

(0.017) (0.030) (0.048) (0.160)

Precrisis 0.760 0.906 0.769 0.825

(0.013) (0.025) (0.024) (0.047)

t-test (pre vs. post) 3.02∗∗∗ 0.75 3.61∗∗∗ 3.05∗∗∗

B. Diff-in-diff. of bank versus nonbank elasticity estimate

Window: (0,t] 1 3 5 10 20 

q*Post-crisis*Bank 0.872*** 1.247*** 1.848*** 1.444*** 2.673*** 

(0.317) (0.437) (0.641) (0.539) (0.688) 

q*Precrisis*Bank -0.142 -0.531* -0.294 -0.562** -0.0419 

(0.191) (0.272) (0.336) (0.277) (0.283) 

Controls and lower-level interactions included

Observations 15,443 14,714 14,371 13,851 13,153 

Adj. R-squared 0.222 0.266 0.300 0.246 0.377 

Dealer FEs Yes Yes Yes Yes Yes 

Rating*Period FEs Yes Yes Yes Yes Yes 

t-test (Diff-in-diff) 13.47∗∗∗ 24.89∗∗∗ 13.87∗∗∗ 14.40∗∗∗ 19.71∗∗∗ 

Panel A shows the market share fraction of the event buying volume handled by banks. The buy sh

market share of the buying volume handled over event day -2 to 0. Inv share is the share of the total i

buildup held by banks over event day -2 to 0. Note that the later measure is not bounded between 0 and 1 

inventory buildup could be negative. All numbers are average across events for downgrade exclusions and 

exclusions. The t-test is for no difference in estimates between precrisis and post-crisis. Panel B repo

interactions of the form q ∗P eriod ∗Bank, where P eriod is one of two subperiods: 2002Q3–2007Q2 (

and 2010Q1–2013Q4 (post-crisis). The triple interactions, including the one involving 2007Q3–200

reported to save space), are from regressions that are otherwise identical to those estimated in Table 12

for the difference in the post-crisis interaction and the precrisis interaction is reported at the bottom of 

Robust standard errors are in parentheses. *** p<.01; ** p<.05; and * p<.1.

regulation prohibiting proprietary trading, that is, the Volcker rule, as w

other regulations.

To test this potential channel, we follow Bao, O’Hara, and Zhou (201

classify dealers as either banks or nonbanks. The Volcker rule was not ac

implemented during our sample period but the regulation was expected 

applicable only to bank dealers. A differential increase in the cost of imm

between banks and nonbanks from before to after the crisis could thus s

that anticipation of tighter banking regulation was a contributing factor.

Table 15, panel A, shows the market share for banks versus nonbanks 

events. Market share for banks is the fraction of the buying volume hand

bank dealers over day -2 to 0. Panel A also shows the share of the inv

buildup over the same days for banks versus nonbanks. Inventory share 

inventory buildup for banks divided by the total inventory buildup for all d

hence, if either banks or nonbanks are net sellers at the event the inventory 

will not be bounded by 0 and 1, although it is in most cases. The table show

the market share for banks have decreased after the crisis, they handle 
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

be a contributing factor explaining why the cost of immediacy has in

more for downgrades compared to maturity exclusions. For downgrade 

nonbanks have not yet taken over the supply of immediacy.

As an additional test, we augment the main regression with som

interactions to capture banks’ change in trading behavior. The speci

that we adopt is given by

P =β1q ∗P ost −crisis ∗Bank+β2q ∗P ost −crisis

+β3q ∗Crisis ∗Bank+β4q ∗Crisis

+β5Q∗Pre−crisis ∗Bank+β6q ∗Pre−crisis

+f ixed eff ects +controls +

The coefficients β1,β3, and β5 in Equation (6) measure the differ

elasticity between banks and nonbanks after, during, and before th

respectively. A positive coefficient indicates that banks have a higher e

than nonbanks. We are interested in assessing whether β1 is larger than 

is whether the extent to which banks’ supply function is more elastic 

to nonbanks has increased after the crisis.

For brevity, Table 15, panel B, shows only the triple interaction t

interest. As the t-test at the bottom of the table shows, the differenc

difference (β1−β5) from before to after the crisis is positive and sign

This shows that the elasticity increases significantly more for banks co

to nonbanks from before to after the crisis. This finding complements 

Bao, O’Hara, and Zhou (2018) and Bessembinder et al. (2018), who s

effect at the implementation date of the Volcker rule. Our finding sugge

for the cost of immediacy there is also an earlier anticipation effect.17

6. Conclusion

The cost of immediacy for corporate bonds has significantly increased a

2008 crisis. We show that the supply of immediacy has become more 

with respect to its price and that dealers have become more reluctant 

risky bonds on inventory for longer periods of time. This post-crisis ch

pricing and dealer behavior is most pronounced for banks, consistent w

dealers closing down proprietary trading and operating with lower inve

Furthermore, these findings are consistent with Duffie’s (2012) predict

the post-crisis regulatory regime would impede market making.

17 Bao, O’Hara, and Zhou (2018) did not find a large anticipation effect, but their study was focused o

in connection to the downgrade date. As shown in Section 5.3, that event may not be as focused on 

provision as the event used in this study.

38
[17:21 17/12/2018 RFS-OP-REVF180082.tex] 

sector (Johnson 2012; Richardson 2012). However, the lower willingn

use balance sheet for market making might make it more difficult for dea

mitigate the selling pressure originating from shocks to other segments 

economy.

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