Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

Resilience redux in the US Treasury market
Darrell Duffie
Graduate School of Business, Stanford University∗
Embargoed until August 25, 2023
August 13, 2023

Abstract
The resilience of the US Treasury market is limited by dealer balance sheets that are not sufficiently large and flexible to effectively
intermediate this market in a “dash for cash,” as when COVID became a global pandemic in March 2020. Since 2007, the total sizeof primary dealer balance sheets per dollar of Treasuries outstanding
has shrunk by a factor of nearly four. This trend continues becauseof large US fiscal deficits and regulatory capital constraints, which
are necessary for financial stability but reduce the flexibility of dealerbalance sheets. I review approaches for increasing the intermediation
capacity of the market and for backstopping Treasury market liquidity
with official-sector market-function purchase programs.

JEL codes: G14, D47, D82∗

I am grateful for comments or advice from Daron Acemoglu, Wenxin Du, Peter Glynn,
Linda Goldberg, Michael Harrison, Ben Hébert, Frank Keane, Arvind Krishnamurthy, Tiff
Macklem, Andrew Metrick, Sungjin Park, Chang Yong Rhee, Imène Rahmouni-Rousseau,
Jeremy Stein, Peter Van Tassel, and Annette Vissing-Jorgensen. This paper draws in parton work with Michael Fleming, Jean-Sébastien Fontaine, Frank Keane, Claire Nelson,
Or Shachar, and Peter Van Tassel. I am thankful for research assistance from Hannah
Firestone, Renhao Jiang, Rosemary Jiang, Isabel Krogh, Boyang Mu, and Tyler Ratcliffe.
This paper relies in part on work in Duffie (2022), Duffie and Keane (2023), and Duffie,
Fleming, Keane, Nelson, Shachar, and Van Tassel (2023). All opinions are my own.

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I

Introduction

On September 1, 1939, the opening of conflict in World War II triggered asurge of sales of US Treasury securities that threatened the ability of dealers
to make orderly markets. New York Fed First Vice President Allan Sproul
met with dealers at 9:30am, telling them that the Bank was “prepared tosee that no disorder develops” and that “we are willing to clean up thedealers’ net positions at a price 1/8 below last night’s late closing prices.”1
The Federal Open Market Committee authorized purchases of up to $500
million “toward maintaining orderly market conditions.”
In this paper, I describe new empirical evidence, with supporting theory,that the current intermediation capacity of the US Treasury market impairs
its resilience. The risks include losses of market efficiency, higher costs forfinancing US deficits, potential losses of financial stability, and reduced savehaven services to investors.
After investigating these implications, I discuss improvements in Treasury market structure and other measures that could increase the market’sintermediation capacity under stress. These include broader central clearing,
all-to-all trade, post-trade transaction reporting, substituting the Supplementary Leverage Ratio rule with higher risk-based capital requirements,and official-sector market-function purchase programs.
Central banks have occasionally had to rescue their government securities
1

See Garbade (2021) and Menand and Younger (2023).

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markets from dysfunction by relieving dealers of some of their inventories sothat dealers can intermediate the market more effectively. Notably, on March
12, 2020, when the World Health Organization declared COVID-19 to be a
global pandemic, some government securities markets became dysfunctional
as investors flooded dealers with demands for liquidity. In the US Treasury
market, dealers’ gross bond inventories and daily purchases of bonds from
customers surged to over ten times their 2017-2022 medians.2 The Fed responded by offering virtually unlimited Treasury financing to dealers andby purchasing nearly a trillion dollars of Treasury securities from them overthe next three weeks, among other major actions.3 It took several more
weeks for normal Treasury market functioning to resume. In the meantime
customers of dealers faced bid-offer spreads reaching more than ten times
normal and interdealer market depth nearly disappeared at some points.4
Treasury market prices were unstable and settlement failures soared.5
Figure 1 illustrates that normal investors in the US Treasury market trade
Treasuries exclusively with dealers. Dealers trade with each other bilaterally
2

From FR2004 data and market-implied yield volatilities, Duffie, Fleming, Keane, Nelson, Shachar, and Van Tassel (2023) provide statistics on the time series of gross and net
total primary dealer positions and dealer purchases from customers in Treasuries, agency
mortgage-backed securities, and corporate bonds. With and without risk-adjustment, total gross inventories and customer-to-dealer daily sales peaked at over ten times theircorresponding 2017-2022 sample medians.
3
See Fleming, Sarkar, and Tassel (2020); Garbade and Keane (2020); Fleming, Liu,
Podjasek, and Schurmeier (2022); Getz, Remache, Chen, Stowe, Mithal, Brifu, and Chu(2021). On April 1, the Fed temporarily exempted Treasuries and reserves from the
Supplementary Leverage Ratio.
4
See Figure 3 of Logan (2020), Figure 9 of Duffie (2020), and Fleming and Ruela (2020).
5
See Barone, Chaboud, Copeland, Kavoussi, Keane, and Searls (2022) and Fleming
and Keane (2021).

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c1

c2
d1
c5

MTP1

c3

MTP3

CLOB

d2

c6

d3
c7

MTP2

Figure 1: A schematic of the structure of the secondary market for trading US Treasury
securities. Blue dots represent investors. Green dots represent dealers. Black rectangles
represent trading venues. The Brokertec central limit order book (CLOB) market is inpractice used for on-the-run securities and only by dealers and a selection of high frequency trading firms. Multilateral trade platforms (MTPs) are arranged by firms such as
Bloomberg and Tradeweb.
or on a limit-order-book market for on-the-run securities. (High-frequency
trading firms also participate on the limit order book market.) Since 2007, as
illustrated in the bar chart in Figure 2, the amount of Treasuries outstanding
has grown by a factor of nearly four relative to the total size of primary dealerbalance sheets. The trend of declining relative market capacity continues because of large US deficits and regulatory capital constraints that keep banks
safe but reduce the flexibility of their balance sheets. Entry into the market for providing dealer services is limited.6 In describing what happened in
March 2020, the Federal Reserve Board wrote: “As investors sold less-liquid
Treasury securities to obtain cash, dealers absorbed large amounts of these6

The intermediation of trading treasuries a high fixed-cost business with significant
additional scale benefits due to the ability to net purchases against sales across customers(Wang, 2017).

4

Ratio of Treasuries Outstanding to Total Primary Dealer Assets

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0.6

0.4

0.2

0.0

2000

2005

2010

2015

2020

Figure 2: The ratio of US Treasury securities outstanding to primary dealer assets
over the period 1998-2022. Data: The Federal Reserve and company filings. Assets aremeasured at the holding company level.

Treasury securities onto their balance sheets. It is possible that some dealers
reached their capacity to absorb these sales, leading to a deterioration in
Treasury market functioning.”7 The situation in March 2020 raises concerns
over the capacity of dealers to intermediate this market under future stressed
economic conditions. Safe-haven investors face a wrong-way risk if Treasury
market intermediation capacity limits could plausibly bind just when theseinvestors have an emergency need to liquidate their positions.8
7

See Board of Governors of the Federal Reserve System (2020). Other accounts ofTreasury market dysfunction in March-April 2020 and its implications include those ofBrainard (2021), Duffie (2020), Hubbard et al. (2021), Group of Thirty (2021), Government Accounting Office (2021), Board of Governors of the Federal Reserve System (2021),
Vissing-Jorgensen (2021), and Committee on Capital Markets Regulation (2021). Fontaine
et al. (2021) covers the situation in Canada. Hauser (2020) discusses the situation in the
UK gilt market and the actions of the Bank of England.
8
He and Krishnamurthy (2020) discuss safe-haven services offered by US Treasuries inMarch 2020.

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II

Market resilience and safe-haven demands

US Treasury securities are the primary safe haven of global capital markets.
A safe-haven asset has two distinct roles. First, in a “flight to quality,” many
investors sell riskier assets and buy the safe-haven asset. US Treasury security
prices therefore tend to rise in a crisis, leading investors to own Treasuries
as a crisis hedge.
The second role of a safe-haven asset is manifest when a crisis induces
investors to sell the asset in order to raise cash.9 US Treasuries are expected to provide excellent safe-haven services in a “dash for cash” becauseof the anticipated depth and liquidity of the market in which they are traded,even during a crisis when many large investors are simultaneously liquidating their Treasuries (Das, Gopinath, Kim, and Stein, 2022). However, thisdash-for-cash safe-haven service generates a negative demand complementarity. During normal times, each investor who anticipates a need to raise cash
in a future crisis prefers to own less of a particular asset as a safe haven,other things equal, to the extent that other safe-haven-seeking investors own
more of that asset. Investors don’t want to suffer a cost of liquidation that ismagnified by the price impact of simultaneous sales of many other investors,
especially if the underlying market is not sufficiently resilient to efficiently intermediate a flood of demands for liquidity. Until now, despite this negative
9

US Treasuries are also particularly useful to many central banks to hold in their foreignexchange reserves because they can be sold at stable or elevated prices for US dollars, which
are often needed in a crisis because of dollar funding stresses (Das, Gopinath, Kim, andStein, 2022).

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complementarity,10 US Treasury securities remain the world’s clear go-to safe
haven, not only because they are safe if held to maturity, but also becauseof the expected depth and liquidity of Treasury markets.
In 2020, both of the safe-haven roles of US Treasuries were tested. With
the heightening risk of a global pandemic leading up to March 2020, a flightto quality caused US Treasury yields to decline more than the yields of otherdeveloped-market government securities, as shown in Figure 3. Then, oncethe onset of a severe global pandemic was clear by mid-March, a dash forcash caused severe selling of Treasuries. The resulting illiquidity in the US
Treasury market was worse than that of most other major government securities markets (Barone et al., 2022). The March 2020 dash for cash also hada significant adverse impact on liquidity in the UK gilt market, out of proportion to the extent to which gilts are held in foreign exchange reserves andperhaps related to the level of stressed demand for liquidity in gilts relative
to the intermediation capacity of the underlying market.
In short, for US Treasuries to maintain the high level of safe-haven services
that they have normally provided to global investors, the intermediation
capabilities of the underlying market must be sufficiently resilient to crisislevel selling.
10

Coppola, Krishnamurthy, and Xu (2023) show that the demand for US Treasuries israised by a positive complementarity associated with the ease of finding counterparties.

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Figure 1: Cumulative Yield Changes Across Sovereign Bond Markets
Bps
3/10

30

3/18

10
-10
-30
-50
-70
-90

U.S.

Germany

U.K.

Japan

-110
-130
-150

01/01/20

01/22/20

02/12/20

03/04/20

03/25/20

04/15/20

05/06/20

05/27/20

figure displays the cumulative yield changes for 10 year sovereign bonds, starting on January 1, 2020. U.S.,
Figure Note:
3: ThisCumulativechanges
10-yeargovernment
securities
yields,in basis points,
Gernany,
U.K., and Japan denote
Treasury, in
Bund,
Gilt, and Japanese
Government Bond
(JGB) securities,
respectively.

Source: Bloomberg
from January
1, 2020 to May 30, 2020, for Germany, Japan, the United Kingdom, and theUnited States. Source: Barone, Chaboud, Copeland, Kavoussi, Keane, and Searls (2022).

III

In addition to the increase in yields in March 2020, there was an increase in the implied volatility ofsovereign bond yields, reflecting in part investors’ uncertainty over the global economic repercussions of
the pandemic. Figure 2 charts a measure of this volatility and illustrates how, across a number ofsovereign bonds, this volatility started increasing in late February 2020 and peaked in March 2020.

Dealer capacity and liquidity: evidence

Alongside these changes in yields and volatility, sovereign bond liquidity deteriorated significantly inMarch 2020. A common measure of bond liquidity is the difference in prices that market makers offer topurchase andsell specific crisis
bonds, or(GFC)
the bid-ask spread.
An increasein this bid-ask
spread over late of capital
The global
financial
led toa majorstrengthening
February and March 2020, for U.S., German, U.K., and Japan 10-year sovereign bonds is illustrated in
Figure 3. This evidence, along with the aforementioned rise in volatility, suggests significant stress onrequirements
for large bank holding companies, further tightened in 2014
trading conditions across sovereign bond markets.

with the introduction of the enhanced Supplementary Leverage Ratio, followed by requirements under “GSIB scoring” (Tarullo, 2023). While highcapital requirements are necessary for financial stability, these capital regulations have reduced the short-run flexibility of liquidity provision to the US
4
Treasury market, given its heavy reliance on bank-affiliated dealers.11
Thelong-run rate of growth of the balance sheets of the largest dealers has also
11

See Tarullo (2023); Group of Thirty (2021); Adrian, Fleming, Shachar, and Vogt
(2017); Breckenfelder and Ivashina (2021); He, Nagel, and Song (2022). Du, Hébert, andLi (2022) provide theory and evidence of a change in the pricing of Treasuries caused bypost-GFC capital constraints on dealers.

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slowed dramatically since the GFC, especially in comparison with the sizeof the US Treasury market (Duffie, 2020). The underlying incentive is debt
overhang: dealers often refrain from issuing new equity or debt to undertake
profitable expansions of their balance sheets because this can adversely impact shareholder return.12 For example, since the GFC (but not before theGFC), dealers subject to quarter-end capital requirements forego significant
profits at quarter ends that could be obtained by arbitraging cross-currency
bases in the foreign exchange market (Du, Tepper, and Verdelhan, 2018).
Beyond the impacts of regulation and funding costs on the provision ofliquidity by dealers, the flexibility of space on dealer balance sheets for intermediating the Treasury market is also reduced by the complexity of internal
capital allocation processes and by agency costs, including the risk aversion
and career concerns of their traders and managers.
On typical trading days, Duffie, Fleming, Keane, Nelson, Shachar, and
Van Tassel (2023) show that illiquidity in the US Treasury market is welland simply explained by yield volatility. Figure 4 illustrates this nearly linear relationship. The scatter plot shows daily observations of a composite
measure of illiquidity versus the average volatility of 2-year, 5-year, and 10year yields. The yield volatilities are one-month swaption-implied volatilities.
The composite illiquidity measure is the first principal component13 of the
12

Beyond higher dealer capital requirements, increased dealer credit spreads inducedby other post-crisis reforms imply higher costs for debt and equity financing of dealer
inventories, as explained by Andersen, Duffie, and Song (2019) and Berndt, Duffie, and Zhu(2022). Klingler and Sundaresan (2023) analyze dealer balance sheet costs for Treasuries
in their Appendix B.4.
13
The first principal component places significant positive weight on each of the 18

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Figure 4: A scatter plot and estimated relationship between the principal-component
composite measure of Treasury market illiquidity and a composite measure of implied
volatility, as measured by the average of the standard deviations of benchmark swap
rates, in basis points, implied by swaptions on 2-year, 5-year, and 10-year swaps with onemonth expirations. The plotted ordinary-least-squares fit, for July 10, 2017 to December
31, 2022 (T = 1, 336), is the second-order polynomial y = −1.81 + 0.026x + 0.000005x2 ,where volatility x is in basis points, R2 = 79.5%. The constant and linear coefficientestimates have p-values of less than 1% under standard assumptions. Source: Duffie,
Fleming, Keane, Nelson, Shachar, and Van Tassel (2023).

z-scores of 18 metrics covering, for each of the 2-year, 5-year, and 10-year
maturity sectors of the Treasury market, six different measures of illiquidity.
These illiquidity measures are: interdealer market price impact, lack of interdealer market depth (the negative logarithm of depth),14 interdealer market
underlying illiquidity measures, and explains 61% of their variation, in the usual sense ofprincipal component analysis.
14
Fleming and Ruela (2020) and Fleming and Ruela (2020) find large losses in market
depth and increases in price impacts in March 2020. They estimate price impact as theslope coefficient associated with a regression of one-minute price changes on net order flow(buyer-initiated trades less seller-initiated trades). According to JP Morgan analysis by
Henry St. John, Joshua Younger, and Sejal Aggarwal, “Total depth at the top 20 levels
on both sides of the market collapsed, with a fairly staggering peak-to-trough decline

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bid-ask spreads,15 the yield spread between off-the-run and on-the-run Treasuries, the within-security dispersion of off-the-run transaction yields,16 andthe root mean squared error (RMSE) of yield-curve fitting noise.17
Volatility alone explains about 80% of the variation in Treasury market
illiquidity. When volatility is higher, dealers tend to reduce their provisionof liquidity for a range of reasons unrelated to capacity limits, including thetypical risk-versus-return incentives of their traders and the fear of having
their quotes adversely selected by informed counterparties, which tends torise with volatility. The total demand by investors for liquidity provision fromdealers, and by dealers for liquidity provision from other dealers, is expected
to rise with volatility. As volatility rises, higher demands for liquidity and areduced supply of liquidity at any given level of dealer compensation imply
that the cost or ease of obtaining liquidity rises.
Although yield volatility explains most of the variation in Treasury market illiquidity, Duffie, Fleming, Keane, Nelson, Shachar, and Van Tassel(2023) also show that dealer balance-sheet loading plays an important role,of 92%.” (The Life Aquatic: Deeper Depth in the Treasury Market Infrastructure, JPMorgan Fixed Income Strategy, June 5, 2020.)
15
The interdealer data are from BrokerTec. The dealer-to-customer transaction data
are from TRACE.
16
See Jankowitsch et al. (2011).
17
The Hu, Pan, and Wang (2013) noise measure of Treasury market illiquidity is thesquare root of the mean squared error (RMSE) obtained when fitting the prices of Treasury
securities to a smooth mathematical model of the yield curve. The yield-curve fitting model
used in this case is the non-parametric model of Filipović et al. (2022), derived from CRSP
end-of-day quotes. Using data from 1990 to 2017, Goldberg (2020b) shows that the supplyof liquidity by dealers to the US Treasury market goes down as RMSE rises, along with adecline in dealer gross positions.

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but only when balance sheets are heavily loaded–a highly nonlinear effect.
This supports the proposition that dealer balance-sheet capacity constrains
Treasury market intermediation during a dash for cash. When dealer balance
sheets are sufficiently loaded, the propensity of dealers to supply liquidity is
reduced and the demand for liquidity that dealers request from other dealers rises. Both effects increase illiquidity, and this is consistent with thedata. Figure 4 shows that during March 2020 Treasury market illiquidity
was at times over three standard deviations worse than predicted by volatility. Figure 5 shows that a significant fraction of this excess illiquidity canbe explained by much heavier-than-normal loading of dealer balance sheets.
Duffie et al. (2023) estimate dealer capacity utilization based on dealer grosspositions, dealer net positions, gross dealer-customer volume, and net dealercustomer volume, all adjusted for risk. When the estimated capacity utilization of dealers is around 20%, Figure 5 shows little estimated marginal impact
of increases in capacity utilization on Treasury market illiquidity. However,when dealer capacity utilization rises from 40% to 80%, Treasury market
illiquidity is estimated to increase by roughly three standard deviations beyond the level of illiquidity predicted by volatility. The scatter plot reveals astriking nonlinear relationship between balance sheet utilization and market
liquidity.
Volatility is likely to be the primary driver of illiquidity in most financial markets, under normal operating conditions. One might therefore viewilliquidity that is significantly in excess of the level predicted by volatility
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Figure 5: The relationship between the average dealer capacity utilization and the residual component of Treasury market illiquidity that remains after controlling for averageswaption-implied volatility (the residuals associated with the fitted relationship in Figure4). The average capacity utilization is the average of the dealer capacity utilization measures based on dealer gross positions, dealer net positions, gross dealer-customer volume,and net dealer-customer volume. The plotted ordinary-least-squares fit, for July 10, 2017
to December 31, 2022, is the second-order polynomial y = 0.363 − 0.048x + 0.0013x2 , with
R2 = 43.6%. All three coefficient estimates have p-values of less than 1% using NeweyWest standard errors. Source: Duffie, Fleming, Keane, Nelson, Shachar, and Van Tassel(2023).

to be a sign of market dysfunction. Despite some limitations, this “excess
illiquidity” may be viewed as a index of market dysfunction.
Using quantile regressions, Duffie et al. (2023) also show that extreme levels of illiquidity are predicted to depend heavily on dealer capacity utilization,
before or after controlling for volatility. For example, in a univariate quantile
regression, the 99th percentile of daily Treasury market illiquidity is predicted
to rise 1.2 standard deviations18 for each one-standard-deviation increase in
18

Based on 1336 observations, the estimated standard error of this coefficient is 0.038.

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estimated utilization of dealer capacity, as measured by risk-adjusted grosspositions. The pseudo-R2 measure of this fit is 70%. The 50th percentile ofTreasury market illiquidity, on the other hand, has a much more muted dependence on dealer capacity utilization, especially after controlling for yieldvolatility. This again supports the concept of capacity constraints. Marginalchanges in balance-sheet loading have only small effects on Treasury market
liquidity on normal days, but the same marginal changes in balance-sheet
loading have large predicted effects when illiquidity is very high.
Some of the increase in Treasury market illiquidity in March-April 2020
can likely be ascribed to the increased willingness of investors to pay for
immediacy from dealers. This increase in the demand for liquidity could
be caused not only by a heightened need for cash but also heightened yieldvolatility or by macroeconomic factors that increase with volatility, consistent with the evidence in Figure 4. An additional increase in illiquidity canbe caused by a change in the propensity of dealers to supply immediacy.
Some of that change in dealers’ supply of liquidity is likely to be related toheightened costs of taking or holding customer positions, which increase withyield volatility, again consistent with the evidence in Figure 4. Additional
shifts in the supply of immediacy by dealers could be caused by higher likelihoods of hitting balance-sheet limits in the near future, consistent with theeffects shown in Figure 5.
In his analysis of Treasury market liquidity during March and April of2020, Goldberg (2020a) estimates both an outward shift in the investor de14

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mand curve for liquidity and an inward shift in dealers’ supply of liquidity.19
A shift in the supply curve is assumed to lead to opposite-sign changes in priceand quantity, proxied by weekly changes in dealer gross positions (FR2004
data). A shift in the demand curve is assumed to lead to same-sign changes
in the same two variables. The increase in demand for liquidity in March
2020 is estimated at about 26%, the largest such shift in the sample period,
1990 to 2020. The estimated 17% reduction in the supply of liquidity is thefifth largest of the sample period, the largest being the 29% estimated reduction in liquidity supply that occurred in October 2008, following the Lehman
bankruptcy.
Huang et al. (2023) find that transactions costs in the foreign exchange
market rise when variables that are correlated with the cost of dealer balance
sheet space rise, after controlling for dealer-provided volume.
The implications of dealer capacity limits for Treasury market resilience
may worsen in future years because the quantity of Treasury securities thatinvestors may wish to liquidate in a crisis is growing far more rapidly than
the size of dealer balance sheets. In 2020 alone, the stock of marketable US
Treasuries held by the public increased from about $17 trillion to about $21
trillion. In July 2023, The US Congressional Budget Office (2023) projectedthat the total amount of Treasury security debt will rise from 98% of US
gross domestic product (GDP) in 2023 to 177% of GDP in 2052, far above
19

This is based on the vector autoregressive modeling approach developed in Goldberg(2020b).

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the previous peak of 106% of GDP in 1946. Yet the dealer balance sheets
are not even keeping up with GDP. For example, from 2010 to 2022, theratio of total primary-dealer assets, at the holding company level, to GDP
went down by 18.5%.20 The stress on dealer balance sheets of handling future
surges in trade demands could also be magnified by increases in the volatilityof Treasury prices.

IV

Dealer capacity and liquidity: theory

As the basis for a theoretical exploration of the impact of dealer capacity
limits on market liquidity and the benefits of a “buyer of last resort,” thissection extends the dealership model of Amihud and Mendelson (1980).21
The main theoretical findings are: (1) a dealer’s bid and offer prices “benddown” sharply when their bond inventories near capacity; (2) simultaneously, the rate at which the dealer purchases bonds from customers suffers a20

In 2010, based on holding company public filings and FRED (for GDP), this ratio was$26.05 trillion in dealer assets divided by $15.05 trillion of GDP, which is 1.73. By theend of 2022, this ratio had declined by 18.5% to $35.88 trillion divided by $25.46 trillion.
21
Here, the dealer’s objective is maximization of the present value of dealing profits.
In Amihud and Mendelson (1980) the dealer’s objective is maximization of the steadystate expected net rate of dealer revenue. Amihud and Mendelson (1980) illustrate asolution for the case of linear demand and supply schedules. This model is also in thespirit of those of Garman (1976) and Ho and Stoll (1981). Eisenbach and Phelan (2022)
provide a model in which a safe asset market functions well if deep enough, but can break
down, with prices falling precipitously, if intermediated by dealers subject to balance sheet
constraints. Kalsi, Vause, and Wegner (2023) go beyond the buyer-of-last-resort benefit ofcreating more dealer balance-sheet space by modeling the ability of a buyer of last resort
to reduce self-fulfilling firesale equilibria. Other models of the impact of limited dealer
intermediation capabilities or incentives for market liquidity include those of Gromb and
Vayanos (2010), Geromichalos, Herrenbrueck, and Lee (2023), Weill (2007), and He andKrishnamurthy (2020).

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sharp decline as inventory limits approach; and (3) both of these effects are
mitigated by an official-sector market-function purchase program.
The time discount rate is r > 0. A dealer’s inventory x of a given asset
must remain below some integer capacity x > 0 and above some minimum
level, which is taken to be zero without loss of generality for our purposes.
With an inventory of x, the total dividend paid to the dealer, net of dealer
holding costs, is d(x). For example, if the asset is a perpetual bond that pays
one per unit of time, then d(x) = x, unless the dealer has holding costs.
At each ask price a, the intensity (mean arrival rate) at which customers
arrive and agree to sell a unit to the dealer is A(a). At each bid price b,
the intensity at which customers arrive and agree to buy a unit from thedealer is B(b). These intensity functions A and B, which are assumed tobe differentiable, reflect trading motives that can arise from investor liquidity shocks, changes in risk preferences, and frictions such as attention andsearch costs. This setup is illustrated in Figure 6. This model does not incorporate general-equilibrium effects stemming from dealer competition22 andendogenous changes in the asset holdings of each type of non-dealer investor.

1

2

x−1

B(bx )x

A(ax )

x+1

x−1

x

Figure 6: Mean dealer purchase rate A(ax ) and sale rate B(bx ) from the current inventory
level x at the dealer’s chosen ask price ax and bid price bx . The dealer’s upper bound on
inventory is x̄. The lower bound of zero, chosen for simplicity, could be replaced with any
integer less than x̄, including a negative lower bound.
22

Ho and Stoll (1983) analyze a related model of dealer competition.

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Some of the price elasticity embedded in the mean supply and demandrates, A(a) and B(b), could arise from the cross-sectional distribution ofwillingness-to-pay of investors and some could stem from the ability of investors to trade with other dealers under imperfect competition (Ho and Stoll,1983). For example, suppose that investors hoping to buy contact the dealer
at some mean frequency λ(b) that could depend on the dealer’s posted bid b.
For any such investor, let ρ be the larger of (i) the investor’s preference-basedvalue of owning the asset and (ii) the lowest alternative bid quote available(or prospectively available) to the investor from other intermediaries. The
cumulative probability distribution function of this reservation price ρ is denoted by F . In this example, investors accept a bid b with probability F (b),so the mean frequency of investor purchases is B(b) = λ(b)F (b).
At each initial inventory level x, the dealer’s maximum expected present
value V (x) of future discounted cash flow is achieved by an optimal price quotation policy.23 At any inventory level x other than the boundary points24
0 and x, the dealer’s optimal present value V (x) of inventory and intermediation profits satisfies the Hamilton-Jacobi-Bellman (HJB) optimality
23

A complete mathematical specification of the dealer’s problem is stated in the Appendix.
24
For the boundary cases: maxa {−V (0)(r + A(a)) + d(0) + A(a)(V (1) − a)} = 0 andmaxb {−V (n)(r + B(b)) + d(n) + B(b)(b + V (n − 1))} = 0.

18

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condition25max{−rV (x)+d(x)+B(b)(b+V (x−1)−V (x))+A(a)(V (x+1)−V (x)−a)} = 0.
a,b

The first-order necessary condition for an interior optimal ask price a is

A0 (a)(V (x + 1) − V (x) − a) − A(a) = 0,0 ≤ x < x,

(1)

0 < x ≤ x.

(2)

Similarly, an optimal interior bid price b satisfies

B 0 (b)(V (x − 1) − V (x) + b) + B(b) = 0,

Example 1. Exponential supply and demand.

SupposeB(b) = ce−βb ,A(a) = keαa ,(3)for positive parameters k, α, c, and β. In this case, we can verify optimality
and compute optimal dealer quotes given a solution V of the HJB equation.
25

The condition is that dealer’s optimal expected net rate of gain is equal to the “required
return” rV (x). At given quotes (a, b), the expected net rate of gain in value is the sum(i) of the dividend payout d(x) net of holding cost, (ii) the mean rate of gain from selling,which is the product of the selling rate B(b) and the gain in value b + V (x − 1) − V (x) froma sale, and (iii) the mean rate of gain from buying, which is the product of the buying rate
A(a) and the gain V (x + 1) − V (x) − a from a purchase. That a function V solving the
HJB equation is in fact the optimal present value of future profits is verified by a standard
martingale argument.

19

Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

The optimal bid and ask at inventory level x areb = V (x) − V (x − 1) +1,
βa = V (x + 1) − V (x) −

1
.
α

(4)

The bid b is the sum of the dealer’s indifference price V (x) − V (x − 1) andthe direct markup β −1 . The indifference price V (x) − V (x − 1) embeds thepresent value of future markups from other investors and future dividends(net of dealer holding costs). Similarly, the optimal offer a reflects the direct
rent α−1 taken from a seller. The bid-ask spread isα−1 + β −1 + 2V (x) − V (x + 1) − V (x − 1).

(5)

The first two terms of the bid-ask spread are the rents taken directly fromsellers and buyers, respectively. The remainder of the bid-ask spread, 2V (x)−V (x + 1) − V (x − 1), is the concavity of the value function V at inventory
level x, in a discrete sense. The concavity of the dealer’s value for inventory
naturally increases as the inventory x nears the capacity x because of theincreasing marginal cost to the dealer of using up its shrinking balance-sheet
space. This is consistent with the empirical results of Duffie, Fleming, Keane,
Nelson, Shachar, and Van Tassel (2023) summarized in Section III and withsolved numerical examples found below.26
For example, consider the parameters r = 0.10, n = 50, c = e40 , k = e−20 , α = β = 3,
and d(x) = x for all x. At the efficient-market bid price of b = 1/r = 10, the dealer buys
at the mean arrival rate of B(10) = e−20 e3×10 = e10 units per year. If the dealer reduces
its bid price by 0.1% from 10 to 9.99, the mean purchase rate declines to B(9.99) = e9.97 .
Similarly, at an ask price of a = 10, the mean arrival rate of sales is A(10) = e40 e−3×10 =26

20

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Example 2. Isoleastic supply and demand.

An alternative special case isisoelastic demand and supply,

B(b) = cb−γ ,A(a) = kaν ,(6)

for positive constants c, k, ν, and γ. In this case, the dealer quotes areproportional to the dealer’s indifference prices, in thata=ν(V (x + 1) − V (x)),
ν+1

b=

γ
(V (x) − V (x − 1)).
γ−1

(7)

For example, with ν = γ = 400 and at the median inventory level, the bidask spread is about 50 basis points of the dealer’s indifference price. Because
actual bid-ask spreads in the Treasury market are even smaller, higher elasticities would be needed to calibrate the model to the relatively high degreeof competition that normally obtains in the wholesale Treasury market. A
large investor’s decision to trade with a particular dealer is highly sensitive
to the dealer’s quotes because of the investor’s outside option to search for abetter price from another dealer. For the 10-year customer-to-dealer sector of
the US Treasury market, for example, Duffie et al. (2023) estimate yield dispersion, a proxy for bid-ask spread in the off-the-run market, at roughly 0.5
basis points on average across days during their sample period, July 2017 to
December 2022, and about 1.2 basis points at the 95th percentile. For large
e10 . For the present purposes, the model is solved by “value iteration,” meaning iterative
solution of HJB equation.

21

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elasticities, the bid-ask spread of the isoelastic model is approximately27 tothe concavity of the value function, as for the exponential model.
Panel of Figure 7 illustrates the solution of the optimal quotation policy
for a completely specified isoelastic model. As suggested, when the dealer’s
inventory approaches capacity, bids and offers decline as the dealer conserves
on remaining balance sheet space by discouraging investor sales and encouraging investor purchases. As inventory rises toward the boundary, the bid-ask
spread widens as a reflection of the increasing marginal indirect cost to thedealer of balance-sheet space.
Consumer surplus is reduced in this setting by dealer pricing power, captured by the elasticity-dependent markups relative to the dealer’s indifference price V 0 (x). Surplus is also reduced by the effect of dealer rationing ofbalance-sheet space through pricing, reflected in the concavity of the valuefunction. Figure 8 illustrates expected investor surpluses added by trades.
For example, suppose the value u to a potential buyer of owning the asset
is distributed exponentially with parameter µ, identically and independently
across buyers. At a dealer bid b, the expected surplus of a buyer conditionalon a trade is E(u − b | u > b) = 1/µ. The expected time rate of buyer surplus
at inventory level x is B(bx )E(u − bx | u > bx ). The case of a selling investors
is analogous.28
27

For large ν and γ, the formulas shown for a and b imply that b − a is approximately
2V (x) − V (x + 1) − V (x − 1).
28
Suppose the value of owning the bond for a randomly chosen potential seller is π.
Then the expected time rate of seller surplus is A(ax )E(ax − π | π < ax ).

22

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100.4

Bid-ask spread (basis points)

66

100.2

bid

Price

100
99.8
99.6

ask
99.4
0

10

20

30

40

64
62
60
58

with CB purchases
56

50

0

10

20

30

40

50

Dealer inventory

Dealer inventory(a) Bid and ask prices for an isoelastic model. Buyer(b) Bid-ask spreads for the isoelastic model shown

elasticity is γ = 400. Seller elasticity is ν = 300. The
trade-rate constants are c = 100, 000 and k = 50, 000.
The discount rate is r = 0.1. The bond dividend rateis d(x) = 0.1x, implying a perfect-markets bond priceof 0.1/r = 1. The prices shown are scaled by 100.

in Panel (a), with and without a central-bankmarket-function purchase program. The heightof the blue shaded area is the reduction in bidoffer spread caused by the central-bank marketfunction purchase program through its impact on
the shape of the dealer’s value function V .

Figure 7: Dealer pricing for an isoelastic model. The central-bank market-function
purchase program whose effect on bid-ask spread is shown in Panel (b) is active whenever
the inventory level x is at or above x = 45. Central bank purchases from the dealer are at
the mean rate λ(x) = 0.1B(bx ) and executed at the mid-price (ax + bx )/2.

The value to a buyer of owning the asset may be much higher than the
trade reservation price of the buyer when facing a given dealer because thebuyer’s reservation value reflects not only the value of owning the asset, butalso expected cost of obtaining the asset from an alternative dealer, including
delay and search costs (Duffie, Dworczak, and Zhu, 2017).
To illustrate how a buyer of last resort can increase the dealer’s capacity
to absorb customer sales, suppose the central bank purchases units of theasset from the dealer at mean frequency λ(x), paying the mid-price m(x) =(ax + bx )/2. When facing the central bank, the dealer takes m(x) as given,23

probability of bid
acceptance
expectedbuyer surplusbprobability of offer
acceptancebid-ask

Dealer quotes

Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

a
expected seller
surplus

P (b) P (a)Probability of quote acceptance

Figure 8: An illustration of the expected buyer surplus (the blue shaded area) and
expected seller surplus (the red shaded area) at dealer bid b and ask a quotes, respectively.

not influenced by dealer quotes.29
The theoretical impact of a central bank market-function purchase program on dealer pricing at high inventory levels is illustrated in Panel (b) of
Figure 7 and in Figure 9. For this parametric example, the central bankpurchases a unit from the dealer at the mean frequency λ(x) = KB(bx ), forsome constant K, whenever the dealer’s inventory x exceeds some thresholdx. The central bank’s purchases liberate space on dealer balance sheets tohandle more customer sales. That is, with the prospect of these central-bank
29

The modified HJB equation is0=sup{−V (x)(r + A(a) + B(b) + λ(x)) + d(x) + A(a)(a + V (x − 1))a,b+λ(x) (m(x) + V (x − 1)) + B(b)(V (x + 1) − b)},with the obvious elimination of b at x = x and a at x = 0.

24

Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

purchases, the dealer expects to be less constrained in the future by balancesheet space. The concavity of the dealer’s value function therefore declines,
and at high levels of inventory the dealer optimally raises its quotes to moresocially efficient levels than would apply without the market-function purchase program. (I am ignoring the welfare effect of increasing the size ofthe central bank’s balance sheet.) For the illustrated example, the central
bank purchases at a mean rate equal to K = 10% of the rate of purchases ofother investors whenever the dealer’s inventory is within 90% of its capacity.
Although buyers pay a higher price than would be the case without a buyerof last resort, the total surplus is improved whenever the mean rate of gainfrom trade of sellers is raised sufficiently relative to the lost mean rate of gainfrom trade of buyers, which is to be expected when prices would otherwise
be depressed by elevated inventory levels.

V

Market-function purchase programs

Consistent with the theory in Section IV, empirical research supports theeffectiveness of central-bank government-securities purchases in March-April
2020 in support of market functionality.30 These official-sector purchases
reduced the inventories of dealers, liberating space on dealer balance sheets
to handle more investor demands for liquidity. For example, Boneva et al.
(2020) show that in reverse auctions conducted by the Bank of England,30

See Vissing-Jorgensen (2021); Bernardini and De Nicola (2020), and Fleming et al.
(2022).

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100.4

Mean rate of dealer purchaseswith CB purchases
100.2

bid

Price

100
99.8

with CB purchases
99.6

ask
99.4
25

30

35

40

45

50

with CB purchases
25,00020,000dealer purchases

15,00025

Dealer inventory

30

35

40

45

50

Dealer inventory(a) Bid and ask prices for the isoelastic model de- (b) Mean time rate of dealer purchases from cusscribed in the caption of Figure 7. The between
the quotes with a central-bank market-function purchase program and without are the height of the blue
shaded area.

tomers for the isoelastic model. The difference between the dealer purchase rate with a central-bankmarket-function purchase program and without isthe height of the blue shaded area.

Figure 9: Dealer quotes and purchase rates for the isoelastic model described in thecaption of Figure 7. The central-bank purchase program is active whenever the inventory
level x is at or above x = 45. Central bank purchases from the dealer are at the mean rate
λ(x) = 0.1B(bx ) and at the mid-price (ax + bx )/2.

dealers sell gilts more aggressively when they have unwanted inventory, or
when they took additional gilt positions just before the reverse auctions, orwhen they are more constrained by the leverage-ratio rule. They find that“by acting as a backstop in the secondary market for gilts, the BoE’s QE
purchases have played a role in helping to alleviate market dysfunction andreducing price volatility.”
In his Presidential address to the American Economics Association, Bernanke(2020) said: “A possible interpretation is that the initial [2008-2009] roundsof QE were particularly effective because they were introduced, and provided critical liquidity, in a period of exceptional dysfunction in financial

26

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markets.” Busetto et al. (2022) write that “In exceptionally stressed circumstances, when dealers’ capacity to intermediate trades is limited, large-scaleasset purchases can improve wider market liquidity and mitigate the risk ofa broader tightening in financial conditions that might disrupt the monetarytransmission mechanism. The strength of this channel therefore depends onthe degree of market dysfunction and the amount of gilts held by dealers.”
Buiter et al. (2023) offer a policy discussion of emergency market-function
programs, including both lending of last resort and buying of last resort.
A market-function purchase program would naturally be triggered only if
lending of last resort by the central bank is insufficient, as was the casein March 2020. Within the first few days of Treasury market dysfunction
in mid March, the Fed had saturated dealers with virtually unlimited repo
financing of their Treasuries, quickly returning repo rates to normal levels(Copeland et al., 2021). However, in the “cash” market for trading Treasury
securities, extreme illiquidity persisted for several more weeks. In response,
the Fed purchased an enormous quantity of Treasuries, nearly $1 trillion in
the first three weeks of the crisis, as depicted in Figure 10, in addition tolarge quantities of mortgage-backed securities.
For the largest dealers, those affiliated with US bank holding companies,
these purchases failed to liberate as much balance-sheet space as one might
have hoped because the Fed paid dealers for its purchases with new reservebalances, which have the same capital requirement under the Supplementary
Leverage Ratio Rule (SLR) as any other asset, including the Treasuries that27

Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

the Fed purchased. On April 1, 2020, the Fed temporarily exempted bothTreasuries and reserves from the SLR for bank holding companies, although
it was not until the middle of May that the Fed, the Office of the Comptrollerof the Currency, and the Federal Deposit Insurance Corporation adopted asimilar SLR exemption for commercial bank subsidiaries. Treasuries held bybank-affiliated dealers remained subject to risk-based capital requirements,
given their obvious re-pricing risk.
He, Nagel, and Song (2020) and Breckenfelder, Grimm, and Hoerova(2022) analyze the implications of bank leverage constraints on market liquidity during the COVID-19 crisis. He, Nagel, and Song (2020) estimate
significant “inconvenience yields” for Treasuries associated with the SLR and“find that during the two weeks of turmoil, Treasury yields rose substantiallyabove maturity-matched OIS rates, reflecting the inconvenience yield.” The
SLR exemptions expired on April 1, 2021.
The Fed’s March 2020 program of market-function purchases eventuallybecame a quantitative-easing (QE) program. Market participants may nothave had a clear perception at each point of time of how much of current
purchases would have sufficed for monetary policy objectives alone. Thissuggests the transparency value to monetary policy transmission of a clearly
demarcated market-function purchase program (Duffie and Keane, 2023).
Purchases that are designated to cure a market dysfunction would be expected have the same monetary-policy impact as concurrent QE purchases,
dollar for dollar, but the opposite conclusion applies only to the extent that28

Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

markets are actually dysfunctional.
Moreover, market-function purchases may be needed just when monetary
policy objectives imply tightening, thus sales of government securities! For
example, on September 22, 2022, the Monetary Policy Committee of the
Bank of England voted to begin selling gilts for the purpose of quantitative
tightening. Within a day of this announcement, a UK fiscal policy shock
triggered fire sales of gilts by liability-driven investors that destabilized thegilt market. On September 28, the Financial Policy Committee of the Bank ofEngland instituted a program of gilt purchases that restored market stability.
On October 22, Bank of England Governor Andrew Bailey stated that “There
may appear to be a tension here between tightening monetary policy as wemust, including so-called Quantitative Tightening, and buying government
debt to ease a critical threat to financial stability. This explains why wehave been clear that our interventions are strictly temporary and have been
designed to do the minimum necessary.”31
Hauser (2021) proposed that central banks need “new tools” such as
market-function purchase programs to deal with dysfunction in government
securities markets. Duffie and Keane (2023) provide a cross-jurisdictional
discussion of market-function purchase programs, covering their objectives,effectiveness, and design. They emphasize that the transparency of these programs and the intent to use them in a market-function emergency supports
financial stability, the transparency of monetary policy, and the safe-haven
31

See Bailey (2022).

29

Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

400

Purchases ($ billions)

350
300
250
200
150
100
50

25
-M
ay

17
-M
ay

11
-M
ay

pr

pr
4M
ay

27
-A

pr

20
-A

pr

13
-A

6A

30
-M
ar

23
-M
ar

16
-M
ar

0

Figure 10: Total weekly purchases of Treasuries by the Fed from the week of March 16,
2020. Data: Federal Reserve. Source: Duffie (2020).
quality of government securities. At the point of issuance of government securities, investors will treat the existence of market-function programs thatcan be activated in a future liquidity crisis as a feature of the securities forwhich they are willing to pay a premium. Governments would then benefit from stronger primary-market demand, lowering the cost to taxpayersof financing government deficits. The extra price premium associated withimproved future safe-haven services would also lead to a more efficient allocation of the securities across investors, given the heterogeneity of investor
preference for safe-haven services.
Knowledge of the existence of a liquidity backstop from a buyer of lastresort could, however, lead some investors to take additional leverage. This
moral hazard can be addressed with improvements in regulation and market structure, discussed in the next section, that promote increased market
capacity and stability.
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Duffie and Keane (2023) note that, at least in some jurisdictions and insome situations, a fiscal authority can conduct market-function purchases in
the form of buybacks. As for the United States, where buybacks are likely
to be reinitiated, the Treasury Borrowing Advisory Committee stated that
“Treasury buybacks are intended to support healthy market functioning but
not mitigate episodes of acute stress in markets.”32
Depending on the setting, fiscal-authority market-function purchase programs might reduce potential tensions over monetary policy communicationand in extreme cases could mitigate fiscal dominance concerns. However,there are limits on the speed with which the fiscal authority can conduct
purchases, relative to the central bank, which has the ability to immediately
fund its purchases by creating reserve balances.

VI

Market structure and capacity

Over time, reforms to the structure of the US Treasury market have been considered primarily for their potential to improve market efficiency and stability.33 Some key potential improvements in market structure may also increase32

See Treasury Borrowing Advisory Committee (2023). In his May 2023 Quarterly refunding statement, Assistant Treasury Secretary Josh Frost stated that “Based on feedback
from a broad variety of market participants, including the Treasury Borrowing Advisory
Committee and primary dealers, Treasury believes it would be beneficial to conduct regular buyback operations for cash management and liquidity support purposes. Treasury
anticipates designing a buyback program that will be conducted in a regular and predictable manner, initially sized conservatively, and not intended to meaningfully change
the overall maturity profile of marketable debt outstanding.” See Frost (2023).
33
See, for example, US Department of the Treasury and Federal Reserve (1969), US
Department of the Treasury, Board of Governors of the Federal Reserve System, Federal

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the intermediation capacity of the market, which is my main focus here.
These include, especially, broad central clearing and all-to-all trade, which
are the main focus of this section. Central clearing increases the amount oftrade that can be effectively intermediated on existing dealer balance sheets.
All-to-all trade adds intermediation capacity to the market through better
matching efficiency for some types of trade and by allowing some trade that
does not necessarily require dealer intermediation.
Improving post-trade price transparency with the real-time publication ofTreasuries transactions34 would also improve market intermediation capacity through a more efficient matching of specific types of trades to specificdealer balance sheets (Duffie, Dworczak, and Zhu, 2017). The Fed’s new
Treasury financing facilities, the Standing Repo Facility (SRF), the Bank
Term Funding Program (BTFP), and the Foreign and International Monetary Authorities (FIMA) Repo Facility,35 could also reduce the likelihood ofstressing the intermediation capacity of the US Treasury market by making
it easier for some investors that need cash, and do not necessarily need to sell
their securities, to instead obtain financing for their Treasuries from the Fed.
Reserve Bank of New York, US Securities and Exchange Commission, and US Commodity
Futures Trading Commission (2015), US Department of the Treasury (2017), and Adrian,Fleming, Goldberg, Lewis, Natalucci, and Wu (2013). The most recent broad US officialsector discussions of reforms, Interagency Working Group for Treasury Market Surveillance(2021) and Interagency Working Group for Treasury Market Surveillance (2022), were
triggered by the market dysfunction in March 2020.
34
See Brain et al. (2018).
35
The BTFP provides financing for banks. FIMA was also established as a special repo
facility that allows foreign monetary authorities with a custodial account at the Federal
Reserve Bank of New York to obtain repo financing for the securities held in their custodial
accounts.

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Group of Thirty (2021) and Hubbard et al. (2021) recommend broadening
access to the SRF.

VI.A

Central clearing

Broad central clearing in the US Treasury market, recently proposed by the
Securities and Exchange Commission,36 could increase the intermediation
capacity of the market through several different channels that I outline here.
The main purpose of central clearing, however, is to lower counterparty risk
and, from that, improve financial stability.37
When a trade is centrally cleared, the original buyer and seller are nolonger exposed to each other for the settlement of their trade—they instead
face the central counterparty (CCP). In case of a default, the surviving
clearing members of the CCP are mutually responsible for covering mostof ultimate losses.38 US Treasuries transactions between primary dealers arecentrally cleared by the Fixed Income Clearing Corporation (FICC).39
36

See “SEC Proposes Rules to Improve Risk Management in Clearance and Settlement
and to Facilitate Additional Central Clearing for the US Treasury Market,” Securities andExchange Commission, press release, September 14, 2022.
37
See Duffie (2020), Hubbard, Kohn, Goodman, Judge, Kashyap, Koijen, Masters,
O’Connor, and Stein (2021), Group of Thirty (2021), Liang and Parkinson (2020), andrelevant reports of The Treasury Markets Practices Group (TMPG) (Treasury Markets
Practices Group, 2018, 2019; Treasury Market Practices Group, 2021a,b). The TMPG
states at its web site that “The TPMG is composed of senior business managers and legal
and compliance professionals from a variety of institutions–including securities dealers,banks, buy side firms, market utilities, and others and is sponsored by the Federal Reserve
Bank of New York.”
38
Typically, a CCP operator contributes a comparatively small amount of capital.
39
In the current market structure, transactions by principal trading firms (PTFs) in theinterdealer market are not cleared by the CCP, but rather are cleared on the balance sheetsof interdealer brokers. Customer-to-dealer Treasuries securities trades are not centrally

33

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On average, a participant in the US Treasuries market is protected by
FICC on about 22% of market transactions.40 By comparison, central clearing covers virtually 100% of exchange traded derivatives and equities, and the
majority of swap-market transactions. In the bilateral non-centrally-cleared
Treasury repo market, which is larger than the centrally cleared componentof the market, Hempel, Kahn, Mann, and Paddrik (2022) found that a majority of repos have no “haircut” to cover default losses. The lack of central
clearing in this market therefore increases both counterparty credit risk andleverage.
Figure 11, from Fleming and Keane (2021), shows a comparison between the daily settlement commitments of Treasuries dealers in the opening
months of 2020 and the much smaller settlement commitments that would
have applied in a counterfactual market with broad central clearing. As thefigure shows, for the same set of trades, central clearing of the entire market
would have reduced peak daily settlements in March 2020 from about $1
trillion to about $300 billion, a vast reduction of dealer balance-sheet commitments. Baranova et al. (2023) conduct an analogous study for the UK
gilt market, with directionally similar but not as dramatic balance-sheet efficiency gains from central clearing. Chen et al. (2022) show the significant
netting benefits of clearing in Canada’s government securities market.
cleared. Some Treasury repos are cleared by “sponsors.” FICC clearing members are also
responsible for covering the liquidity needs of the CCP, through the Capped Contingent
Liquidity Facility.
40
This is from a simple calculation (Duffie, 2020), based on data from Treasury Markets
Practices Group (2018).

34

Billio

100

50
Embargoeduntil presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023
0
1/1/202/1/203/1/204/1/205/1/20Source: Authors’ calculations, based on FINRA TRACE data.
Note: The figure plots dealers’ gross settlement obligations in U.S. Treasury securities by day under apotential structure in which all trades are centrally cleared and netted.

Figure 7 – Dealers' Gross Settlement Obligations by Market Structure
1200

Billions of Dollars

1000
800
600
400
200
0
1/1/202/1/203/1/20Current Structure

4/1/205/1/20Market Wide Central Clearing

Source: Authors’ calculations, based on FINRA TRACE data.

FigureTotalplots
daily
settlementsof US
Treasury
securities
transactions
under
Note:11:
The figure
dealers’
gross settlement
obligations
in U.S.
Treasury securities
by day under
the the cur-rent market
structureandin a interdealer
counterfactual
structure
withandmarket-wide
centralcurrent structurein whichdealers’
trades aremarket
centrally cleared
and netted
under apotential
structurein which all
tradesare centrally
cleared and netted.
clearing.
Source:Flemingand
Keane(2021).

In addition to benefiting financial stability, the netting of purchases against
14

sales that is achieved by central clearing also improves the efficiency withwhich dealers use their balance sheets.41 Broader central clearing of Treasuries could also, depending on its design, promote the introduction of all-toall trade of Treasuries by making it simpler for trade platform operators andinvestors to arrange for safe and efficient trade settlement, without necessarily requiring the intermediation of a dealer. All-to-all trade would further
increase the capacity and resilience of US Treasury markets, as I discuss inthe next subsection.
Central clearing also improves market safety and economizes on dealer
41

In current accounting practice for the determination of US regulatory capital under
the SLR requirement, commitments to settle a cash-market Treasuries transaction do notcount toward assets, unless the settlement fails. This is not consistent with the regulatory
capital accounting treatment for the closing leg of a Treasury repo, which is economically
identical, but does count toward assets. Because of this accounting inconsistency, theshareholders of large dealer banks have a regulatory-capital incentive in favor of broader
central clearing in the repo market that does not apply to the market for cash Treasuries
trading.

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balance-sheet commitments by reducing settlement delivery failures, whichrose significantly during the most stressful days in March 2020. Fleming and
Keane (2021) show that broad central clearing would dramatically reduce delivery failures, which reached $85 billion per week in March 2020, finding that“nearly three-fourths (74%) of fails in specific issues are effectively “daisychain” fails, which could be paired off and hence eliminated with increased
central clearing. Moreover, the percentage of fails that pair off tends to behigher when fails are higher and in issues where they are higher. It follows
that expanded central clearing not only reduces the balance sheet resources
needed for intermediation overall through reduced settlement fails, but thatthe benefits are greatest when they are most needed and for the securities
for which they are most needed.”
Central clearing comes with some costs. The Brattle Group (2022) collected a range of views of market participants regarding the costs and benefitsof central clearing in US Treasury markets. Among the concerns expressed inthis survey is the risk of concentrating settlement at a central counterparty.
A CCP like FICC is systemically important and, effectively, too big to fail.
Because of these concerns, large US CCPs are designated by the Financial Stability Oversight Council as systemically important, which implies aheightened level of supervision by US regulators. Without careful regulation,
supervision,42 and failure resolution planning, CCPs risk financial instability
42

Hubbard et al. (2021) and Group of Thirty (2021) offer policy recommendations forthe case of FICC.

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(Powell, 2017). Market participants also expressed concern over their participation costs for central clearing, which include fees, operational costs, andthe cost of funding margin requirements. These costs reduce the incentives ofindividual firms to participate in central clearing. In effect, each participant
is incurring costs to insure other market participants against its own default.
Central clearing costs are likely to be more tangible and internalized by market participants than are the broader public benefits of increased financial
stability and intermediation capacity. The promotion of public goods is moreeasily addressed by the official sector.43

VI.B

All-to-all trade

The advent of all-to-all trade in the US Treasury market could significantly
increase the intermediation capacity of the market, among other benefits suchas improved competition and market efficiency.
All-to-all trade means that a broad set of market participants, dealers
and non-dealers alike, are able to trade at quotes supplied by each other.
This can be achieved on a continuous limit order book, or via all-to-all requests for quotes on an electronic trade platform, or with occasional batch
auctions, or by size-discovery trading on dark pools, among other trade protocols. Analysis of the benefits of all-to-all trade in government securities
markets has usually focused on the associated improvements in competition
43
Treasury Markets Practices Group (2019) wrote that “the TMPG believes that to theextent that public policy interests are served by moving to more widespread utilization ofcentral clearing, that is something best addressed by the official sector.”

37

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and allocative efficiency (Allen and Wittwer, 2023; Kutai et al., 2022). Like
Chaboud et al. (2022), my main focus here is the impact of all-to-all tradeon market intermediation capacity and resilience.
In 2022, the Securities and Exchange Commission (2022) discussed reforms that may encourage all-to-all trade in the US Treasuries market, including the removal of exemptions for Treasuries securities to fair-access rules.44
As I mentioned earlier, central clearing also lowers barriers to all-to-all tradeby making it simpler for trade platform operators and investors to arrange
for safe and efficient trade settlement without necessarily trading directlywith a dealer.
Currently, there is a “done-with” norm in the US Treasury market, meaning that an investor who arranges with a dealer for the central clearing ofa trade must also conduct the trade with that same dealer. This done-withpractice, among other disadvantages such as reducing competition, also lowers the ability or incentives to conduct all-to-all trade. Anonymous central
clearing and a greater flexibility for done-away trades would promote the introduction and adoption of all-to-all trade and thus a likelihood of increased
market capacity.
In a future US Treasury market that includes all-to-all trade, investors
would continue to conduct some trades directly with dealers but could also
44

The SEC proposed a new definition of “exchange” that would have the effect of covering the principal interdealer and multidealer-to-client platforms for Treasury securities
and therefore require them to comply with Regulations ATS and SCI. Group of Thirty(2021) and Group of Thirty (2022) explain the implications.

38Embargoed until presentation time of 9:55 a.m. Mountain Daylight Time, August 25, 2023

expose some of their trading interests simultaneously to many non-dealersand dealers at all-to-all trade venues. Although some all-to-all trade has
emerged in the corporate bond market, bilateral trade with dealers retains
the dominant share of market intermediation. The option to source liquidity either way would increase market efficiency and the total intermediation
capacity of the market (Allen and Wittwer, 2023). I conjecture that market illiquidity on all-to-all trade venues in March 2020 did not significantly
exceed levels that are predicted by contemporaneous price volatility. Illiquidity could be measured by bid-ask spread, price impact, and negative log
depth. Like a pure dealership market, an all-to-all market has capacity limits
related to the willingness of investors to commit capital to the provision ofliquidity. However, coupling a dealership market with all-to-all trade venues
increases the sources of potential capital commitments to the provision of
immediacy by including dealers and many non-dealers. Beyond the wider
sourcing of capital, the capacity of all-to-all venues benefits from matchingefficiency, relative to pure dealership markets, which have lower pre-trade
price transparency and limited bilateral trade relationships. Matching efficiency can be especially impaired if some dealers are nearing their capacity
for intermediation. Duffie, Fleming, Keane, Nelson, Shachar, and Van Tassel(2023) provide evidence of high excess illiquidity for the US Treasury market
in March 2020 (Section III), and also at the failure of Lehman Brothers in
2008. They show that this excess illiquidity is predicted by the unusually
heavy loading of dealer balance sheets at these times.
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VII

Final remarks

Volatility is likely to explain the majority of variation in illiquidity in manyfinancial markets, except when a market becomes dysfunctional. The extent
of illiquidity in excess of that predicted by volatility could be viewed as anindex of market dysfunction, despite some limitations of this measure. In
the US Treasury market, this dysfunction index is reasonably well explainedby heavy loading of dealer balance sheets, which places the resilience of theTreasury market at risk just when safe-haven investors are most dependent
on intermediation.
A resilient US Treasury market supports financial stability, dollar dominance, effective monetary policy, capital market efficiency, and the provisionof safe-haven services to global investors.
The total amount of Treasuries outstanding will continue to grow rapidly
relative to the intermediation capacity of the market because of large andpersistent US fiscal deficits and the limited flexibility of dealer balance sheets,
unless there are significant improvements in market structure. Broad central
clearing and all-to-all trade have the potential to add importantly to market
capacity and resilience. Additional improvements in intermediation capacity
can likely be achieved with real-time post-trade transaction reporting andimprovements in the form of capital regulation, especially the Supplementary
Leverage Ratio. Backstopping the liquidity of this market with transparent
official-sector purchase programs will further buttress market resilience.

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Appendix
The dealer model and its solution
The dealer problem described in Section IV is more completely formulated
as follows. We fix a probability space and an information filtration satisfying
the usual conditions. Because A and B are differentiable, for each pair (a, b)of bounded and predictable ask and bid processes there is a non-explosive
counting process M a of dealer purchases with integrable intensity process{A(at ) : t ≥ 0} (Brémaud, 1981) and a non-explosive dealer-sales counting
process N b with integrable stochastic intensity {B(bt ) : t ≥ 0}. For each
initial inventory x in S = {0, 1, . . . , x̄}, let Cx be the space of such (a, b) withthe property that the resulting inventory process
(a,b)

{Xt

= x + Mta − Ntb : t ≥ 0}

remains in S. The dealer’s optimal expected present value of future cash
flows is finite and well defined by

V (x) =

supE(a,b) ∈ Cx"∞
X

e−rSj b(Sj ) −

j=1

Z ∞
=

sup
(a,b) ∈ Cx

∞
X

E

i=1
−rt

e

e−rTi a(Ti ) +

Z ∞

#
(a,b)

e−rt d(Xt) dt ,

0(a,b)[bt B(bt ) − at A(at ) + d(Xt )] dt

,0where Ti = inf{t : Mta = i} is the time of the i-th dealer purchase and Sj =inf{t : Ntb = j} the time of the j-the dealer sale. By the usual martingale
41

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verification method, any solution of the HJB equation shown in Section IV
can be verified as the value function V and the associated Markov quotation
policy x 7→ (ax , bx ) can be verified as optimal.
The model is solved by value iteration, as follows. We begin with some
initial “guess” V0 (0), ..., V0 (x̄) of the solution of the HJB equation, and thebid and ask policies b1 , ..., bx̄ and a0 , ..., ax̄−1 that solve the associated optimization problems in the HJB equation, after replacing V with V0 . By
algebraic rearrangement of the HJB equation, we can update our guess toV1 (0), ..., V1 (x̄), whered(0) + A(a0 )(V0 (1) − a0 )r + A(a0 )d(x) + B(bx )(bx + V0 (x − 1)) + A(ax )(V0 (x + 1) − ax ),V1 (x) =r + A(ax ) + B(bx )d(x̄) + B(bx̄ )(bx̄ + V0 (x̄ − 1))V1 (x̄) =.
r + B(bx̄ )V1 (0) =0 < x < x̄,

Following this update method, successive iterations V0 , V1 , V2 , . . . are generated until maxx |Vn (x) − Vn−1 (x)| is within a given error tolerance. Any limitof V0 , V1 , V2 , . . . is the unique solution of the HJB equation.

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