The Shadow Price of Intermediary Constraints

Chris Anderson and Weiling Liu∗

November 2, 2018

JOB MARKET PAPER

Click here for most recent version

Abstract

Limits to the risk-taking activities of financial intermediaries are important for

understanding market stability as well as asset prices, yet they remain difficult

to pin down. We propose a novel measure of intermediary risk constraints called

the interdealer broker (IDB) ratio, which is the percent of total trade volume con-

ducted between dealers using an IDB. Theoretically, when aggregate risk constraints

tighten, dealers will use IDBs more in order to redistribute idiosyncratic risk. Em-

pirically, we test our measure in the U.S. Treasury market, where we find that the

IDB ratio has a 0.72 correlation with interest rate risk, as proxied by Value-at-

Risk. Furthermore, a one standard deviation increase in the IDB ratio forecasts a

1.8 percentage point higher annual excess return on a five-year bond. This return

predictability holds across different fixed income classes, over varying maturities,

as well as out-of-sample.

∗Weiling Liu (Job Market Paper) can be reached at wliu@hbs.edu and Chris Anderson at chan-

derson@hbs.edu. Harvard University. For helpful feedback we thank Malcolm Baker, John Campbell,

Lauren Cohen, Richard Crump, Matteo Maggiori, Chris Malloy, Michael Fleming, Robin Greenwood,

Sam Hanson, Derek Kaufman, Frank Keane, David Lucca, Or Shachar, Jeremy Stein, Adi Sunderam,

Jonathan Wright, Zack Yan, as well as the participants in the HBS Finance Lunch Seminar, the LBS

Transatlantic Student Conference, and the Federal Reserve Bank of New York’s Research and Markets

Group Seminars.

1

1 Introduction

The financial crisis in 2008 demonstrated how limits to the risk-taking activities of fi-

nancial intermediaries impact market stability as well as change real economic outcomes.

It also sparked the intermediary asset pricing literature, in which the risk constraints

of large intermediaries explain asset prices (Adrian et al., 2014; He and Krishnamurthy,

2013). These constraints may come from a number of sources, including internal risk tar-

gets, limited funding capital, or external regulatory pressures. Today, a crucial question

remains: how do we measure intermediary risk constraints?

The risk-taking activities of large financial intermediaries are difficult to pin down,

because their balance sheets are both expansive and complicated. For instance, the

broker-dealers, which are financial firms that trade securities for their own accounts as

well as for their clients, have strong incentives to veil their positions. Directly measuring

dealers’ risk exposure can be a Herculean task.

In this paper, we take a novel approach and instead infer dealers’ risk exposure from

their trading behavior, following the principle of revealed preference. In doing so, we

propose a novel measure of risk exposure relative to constraints called the interdealer

broker (IDB) ratio. The IDB ratio captures the percent of total dealer trading volume

that is conducted between dealers using an interdealer broker.

While there are some existing proxies for intermediary risk-taking, they are either

noisy or potentially biased. For example, Value-at-Risk (VaR) is an estimate of the

maximum potential loss on a portfolio, which many dealers use to manage risk. However,

VaR is released publicly by only a small number of firms; available for a short time period;

and usually supplemented by other stress tests, which are non-public. Another popular

proxy is leverage, which measures the ratio of a firm’s debts to its assets. Yet, in practice,

broker-dealer leverage is roughly measured, captured only once a quarter, and released

with a lag. To our knowledge, none of the empirical proxies show the tightness of dealer

risk constraints, which is only internally observed.

2

The IDB ratio circumvents many of the issues with existing measures, because it

does not rely on accurate nor complete disclosure of complicated holdings, and it can be

constructed from high-frequency trading volumes. Furthermore, in the U.S. bond market,

which is one of the largest and most liquid markets in the world, these trading volumes

are consistently reported by a group of the largest intermediaries: the primary dealers.

Perhaps most importantly, the IDB ratio tracks the tightness of dealer risk constraints,

a theoretically important quantity which is almost never directly reported.

Intuitively, in periods where risk constraints are binding, dealers are less likely to fulfill

customer orders directly from their own balance sheets. Instead, they are more likely to

resell parts of the order to other dealers, redistributing risk throughout the system. In

order to transact with other dealers anonymously and without incurring high transaction

costs, the dealers use the interdealer brokers (IDBs). We summarize this intuition using

a stylized model of dealer trade and risk-sharing, making two central predictions. First,

periods of higher risk exposures and tighter risk constraints are also periods with higher

IDB ratios. Second, in settings like the U.S. bond market where dealers are net long

holders of the risky asset, expected returns should be higher in order to compensate

dealers for bearing risk.

Empirically, we test our predictions in the U.S. Treasury market, where the primary

dealers serve as the dominant intermediaries. This is an ideal setting because Treasury

bonds are: (1) issued in standard maturities and at predictable intervals (2) uniform in

terms of credit risk (3) important assets, serving as a global risk-free benchmark as well

as a key indicator of macroeconomic conditions (4) traded by the primary dealers, who

consistently report their trade activity. Supportive of our first prediction, we find that

the IDB ratio rises when they bear more interest rate risk, as measured by interest rate

Value-at-Risk. The correlation between the IDB ratio and interest rate VaR is positive

and strong: 0.72 in levels and 0.58 in one-year changes.

Consistent with our second prediction, we find that that the IDB ratio significantly

forecasts future returns. A one standard deviation increase in the IDB ratio predicts a

3

1.8% higher annual excess return on a five-year Treasury bond. The return predictability

of the IDB ratio holds across a range of different maturities, is not spanned by the

forward rates, persists after controlling for macroeconomic conditions, and performs well

out-of-sample.

We provide additional evidence supporting our theory using U.S. Treasury auctions as

well as the cross-section of primary dealers. In our proposed model, the IDB ratio is higher

when dealers face positive inventory shocks that push them closer to risk constraints. U.S.

Treasury auctions provide a set of natural experiments in which dealers face significant

inventory shocks, because the primary dealers are required to bid competitively, but the

amount that they receive is determined by the strength of other bids. We find that when

the primary dealers unexpectedly receive a larger portion of the Treasury auction, the

contemporaneous IDB ratio increases.

In our model, we predict that dealers who are closer to constraints are more likely

to use the IDBs to offload risk. Using proprietary data, we then examine the IDB ratio

across individual dealers. We find that the dealers who have the highest IDB ratios also

have the highest risk exposures, and they are more likely to reduce risk exposure in the

future. Dividing the dealers into two halves, we further compare the IDB ratios of larger,

core dealers versus smaller, periphery dealers. We find that while all dealers rely on the

IDBs in order to manage risk, the IDB ratio constructed from large dealers drives most

of the return predictability.

Finally, we examine whether IDB ratios created from different market segments pos-

sess additional information. First, we look at IDB ratios created from bonds in different

maturity buckets: one- to three-year Treasuries, three- to six-year Treasuries, and 11-30

year Treasuries. When we add these ratios to the aggregate IDB ratio in return-forecasting

regressions, we find they can increase the R-squared almost five-fold— from 7% to 32%

when forecasting two-year bond returns. Next, we study two additional markets in which

primary dealers play a key role: non-mortgage agency securities and mortgage-backed se-

curities (MBS). We find that the agency and MBS IDB ratios positively forecast annual

4

excess returns in their respective markets, even after controlling for contemporaneous

Treasury returns. Combined, this evidence suggests that risk management is segmented,

and IDB ratios from different markets add valuable information.

In the remainder of Section 1, we discuss related literature and provide context for

trading in the U.S. bond market. In Section 2, we outline a stylized model which shows

how interdealer trade ratios can reveal dealer exposure in the presence of constraints.

We calibrate the model and produce several testable predictions. Section 3 describes our

data sources and time samples. Turning to empirical analysis, Section 4 presents our main

findings that the IDB ratio is closely related to risk exposure and it robustly forecasts

future returns. Section 5 provides supporting evidence from Treasury auctions as well

as the cross-section of primary dealers. In Section 6, we examine IDB ratios created

from different maturities and other fixed income markets, providing evidence that risk

management is segmented. Finally, Section 7 concludes.

1.1 Related Literature

Our work contributes to three main strands of research: intermediary asset pricing, fore-

casting bond returns, and the structure of bond markets.

First, this paper most naturally relates to the literature on intermediary asset pricing.

This literature is nascent but quickly growing, especially following the financial crisis.

On the empirical side, Adrian et al. (2014) documents that innovations to a measure

of broker-dealer book leverage can price the cross-section of asset returns. He et al.

(2017) instead uses shocks to the market leverage of primary dealers and expand the

analysis to include new asset classes such as commodities and currencies. Focusing on

the bond market and perhaps most similar to our paper in spirit, Haddad and Sraer

(2015) shows that banks’ natural activities them to interest rate risk, and that banks’

interest rate exposure significantly forecast long-run bond returns. Less related to our

paper but equally as important, theoretical work such as He and Krishnamurthy (2013),

Danielsson et al. (2010), and Adrian and Boyarchenko (2012) show how asset prices are

5

tied to intermediary capital in the presence of financial frictions.

Next, we contribute to the literature on bond return predictability by introducing

the IDB ratio as a novel predictor. This is a rich literature that extends back several

decades. One of the first seminal papers, Fama and Bliss (1987), find a strong ability to

forecast bond returns using forward rates. This work is updated and further extended by

many papers since, including Cochrane and Piazzesi (2005), who find that a single linear

combination of forward rates forecasts returns. Other important work in this literature

includes Campbell and Shiller (1991), which forecasts bond returns using yield spreads,

as well as Fama and French (1989), which shows that business cycle conditions forecast

both stock and bond returns. More recently, Greenwood and Vayanos (2014) relate excess

bond returns to the outstanding supply of Treasuries. Ludvigson and Ng (2009) expand

the work of Fama and French (1989) by using principal components over a broad number

of macroeconomic variables to forecast bond returns.

Finally, our work sheds light on trading in the U.S. bond market and the role of

interdealer brokers within it. While interdealer brokers are extremely important to two-

tiered over-the-counter markets like the Treasury market, little attention has been paid

to their activity until recently. Examining issues of liquidity and price discovery, Fleming

et al. (2017) details the microstructure of BrokerTec, an electronic interdealer broker.

Benos and Zikes (2017) show that when dealers are more constrained, they are less likely

to provide liquidity in the two-tiered U.K. gilt market. While not directly related to

interdealer trading, Boyarchenko et al. (2016) show that U.S. primary dealers can infer

private information from customer order flows, and thus may have incentives to share

that information with each other.

To our knowledge, our paper is the first to link trade flows to future long horizon

bond returns. Empircally, we are also the first to document a strong, positive relationship

between interdealer trading volumes and intermediary risk exposure in the bond market.

6

1.2 Background on the U.S. Bond Market

The U.S. bond market provides an ideal laboratory for testing our theory of intermediary

trade and risk constraints. One of the largest markets in the world, the U.S. bond market

had roughly $41 trillion outstanding at the end of 2017 (SIFMA, 2018). In comparison,

the equities market had $32 trillion outstanding. The U.S. bond market is also extremely

liquid, with roughly $765 billion dollars worth of securities being traded daily in 2017.

This dwarfs the equities market in comparison, which had $271 billion dollars traded daily.

The largest components of the bond market by volume are Treasuries and mortgage-

backed securities (MBS).

The bulk of our empirical analysis focuses on the cornerstone of the bond market:

the Treasury market. Treasury bonds are suitable for our study because they are:(1)

issued in standard maturities and at predictable intervals (2) uniform in terms of credit

risk (3) key assets that not only serve as a global risk-free benchmark but also important

indicators for macroeconomic conditions (4) traded by a central set of intermediaries, the

primary dealers, who report their weekly activity.

The U.S. Treasury market is broken into two segments: the primary market and

the secondary market. The primary market is conducted through regularly scheduled

Treasury auctions. These auctions are publically announced in advance, including details

such as the offering amount and auction time. In 2017, the government held 277 public

auctions and issued approximately $8.5 trillion in debt (Department of the Treasury,

2018). While both retail and institutional investors may bid, the primary dealers play a

central role, because they have an official obligation to participate and bid competitively

at every auction.

The primary dealers, who must be designated by the Federal Reserve Bank of New

York, are some of the largest intermediaries in the Treasury market. In addition to

participating in Treasury auctions, primary dealers are expected to make markets for

participants as well as serve as a counterparty for the Fed in its implementation of mon-

7

etary policy.1 As of January 2018, there are 23 primary dealers in total.

After auction, secondary trading in Treasuries is predominantly over-the-counter (OTC)

and decentralized. Most institiutional and retail institutions trade Treasuries through

their broker-dealers, who serve as the main market-makers. In order to accomodate

customer orders and hedge risk, dealers also trade with each other. While interdealer

trade can be done directly between two dealers, the overwhelming majority is conducted

through an interdealer broker (IDB). A recent study shows that roughly 88% of all inter-

dealer trade was facilitated by an IDB between 2017 and 2018 (Brain et al., 2018).

The interdealer brokers (IDBs) lie at the heart of the secondary market, facilitating

trade among institutional traders such as the broker-dealers. The IDBs have several

important features, including anonymous matching and work-up mechanisms, which help

reduce price impact and improve market liquidity. In the past, IDBs were platforms which

provided quotes through a voice service, but most activity on modern IDB platforms are

electronic.2 ESpeed and BrokerTec are two examples of the largest electronic platforms

today.

Historically, use of the IDB platforms were highly selective, and up until 1994, only

primary dealers were allowed to be participants. In 1994, membership expanded to

members of Fixed Income Clearing Corporations (FICCs), although primary dealers still

played a dominant role (Potter, 2015). More recently, starting around 2004, additional

firms including principal trading firms (PTF’s) entered the market. In 2014, they ac-

counted for more than half of total volume on the electronic IDB platforms, although

their continuing impact on the market structure remains unclear (Department of the

Treasury et al., 2015). The most important and well-known members of these PTF’s are

the high-frequency algorithmic trading firms, also commonly known as HFT’s.

Due to the over-the-counter nature of the Treasury market, public data on trading

1The Federal Reserve Bank of New York states that: “Primary dealers are trading counterparties ofthe New York Fed in its implementation of monetary policy. They are also expected to make marketsfor the New York Fed on behalf of its official accountholders as needed, and to bid on a pro-rata basisin all Treasury auctions at reasonably competitive prices.”

2This is true to a lesser extent for off-the-run securities, but generally true for the on-the-run securities.

8

volumes and market activity are hard to find. Fortunately, the primary dealers are

required to publicly disclose their activities to the Federal Reserve through the FR2004

forms. Each week, their primary dealers report their weekly financing, net positions, and

transaction activity across a variety of bond classes. Transaction volumes are further

broken down by maturity buckets and by counterparty (trade with IDBs are separated

from trade with others). The public version of the FR2004 dataset aggregates information

across all of the dealers and provides the foundation for our study.

2 Theory and Predictions

In this section, we provide a stylized model of interdealer trade based on Viswanathan

and Wang (2004) that incorporates binding risk constraints and multiple time periods.

It demonstrates one example of how trade ratios can reveal dealers’ risk exposures and

the tightness of their risk constraints. We calibrate the model using a range of reasonable

parameters and simulate both trading activity as well as price paths. This ultimately

produces several hypotheses which we will test empirically.

Intuitively, in this model, the broker-dealers are both investors and market-makers

in a risky asset. We assume that dealers are net long holders of the asset in aggregate,

matching empirical observations in the U.S. bond market 3. Every period, they face

random inventory shocks in the form of customer orders. The dealers may accomodate

orders using their own balance sheets, which are subject to inventory constraints, as well

as by using the interdealer market, which is mediated by an interdealer broker. In periods

where dealers are closer to constraints, they accommodate less of the customer order from

their own balance sheets. Instead, dealers use the IDBs more in order to redistribute risk.

To compensate dealers for bearing risk, prices are lower and expected future returns are

higher.

3See Figure A1

9

2.1 Stylized Model

Our stylized model is a variant of Viswanathan and Wang (2004), a risk-sharing model

of trade in which N > 2 dealers serve as intermediaries in a market for a risky asset.

Each of the dealers hold initial inventory Ik ∼ Unif(0,1) of the risky asset, which has an

underlying asset value V ∼ N(v,τ−1v ). While the initial inventories may vary, the dealers

have homogeneous beliefs about the assets’ value. Each of the dealers maximize mean-

variance utility of profit and they share identical coefficient of risk aversion ρ. Finally,

we exogenously assign Nc < N dealers an inventory constraint of C.

In our model, we have multiple time periods, which can be thought of as monthly

observations. Dealers’ parameters, such as risk aversion, stay constant across periods

but their inventory accumulates from one period to the next. Each period is made up of

multiple iterations. In each iteration:

1. Random dealer w receives customer order O ∼ N(0,1).

2. Dealer w fulfills the customer order in its entirety, then he splits a portion of order

with other dealers using the IDB.

3. Dealer inventories update with trade amount and a fraction (1−τ) of assets matures,

expiring off the balance sheet.

IDB trading operates as a single price auction, in which the IDB essentially serves as

the auctioneer. We guess and verify that, in equilibrium, dealers submit the following

linear bidding strategies to maximize utility from profit:

1. xw = µ′ − γ′p+ β′(Iw +O)

2. xL = µ− γp− βIL

where subscript w refers to the dealer who received the order and L refers to all other

dealers. Note that the size of the customer order, O, is only known to dealer w. The IDB

market obeys the following market clearing condition: O = xw +∑N

j 6=w xj.

10

Solving for {µ′, γ′, β′, µ, γ, β}, we find that in equilibrium, dealers use the following

trading strategies,

1. For dealer w, who received the order, xw(p, o, Iw) = γ(v−p)+(

1N−B−1

)(Iw+O)−Iw

2. For dealer L, who did not receive the order but is not bound by constraints,

xL(p, IL) = γ(v − p)−(N−B−2N−B−1

)IL

3. For dealer b, for whom the constaint binds, xb(p, Ib) = C − Ib

where γ, the price elasticity of demand, is equal to: N−B−2(N−B−1)ρτ−1

v.

Finally, from the market clearing condition, we get equilibrium price:

p = v − α1

(N∑j=1

Ij +O

)+ α1α2

(CB − α3

∑Ib

)(1)

where α1 = ρτ−1v

(1

N−B

); α2 = N−B−1

N−B−2 ; and α3 = 1N−B−1 . Intuitively, this means that

price is higher if expected value is higher (first term), if inventory or the customer order

is larger (second term), or if the inventories of the constrained dealers are closer to

constraints (third term).

2.2 Model Calibration and Simulations

In this section, we calibrate the model and simulate 10,000 draws in order to predict

relationships between trading volumes, inventory holdings, dealer constraints, as well as

future returns. More specifically, we repeat 100 iterations per time period (month), and

we relate trading activity within a month to returns over the subsequent year. For illustra-

tive purposes, we only show one calibration of the model using the following parameters,

although the results generally hold across a broad spectrum of alternative assumptions.

• N=40

• Nc=30

• C=0.5

• Initial Ik ∼ Unif(0,1)

• O ∼ Norm(0,1)

• V ∼ Norm(1,0.1)

• τ = 99%

• ρ = 0.3

11

In our simulation, customer orders are noisy because they are independent and iden-

tically distributed according to a normal distribution. Since interdealer volume largely

reflects customer orders, it is also extremely noisy. In contrast, average dealer inventory

moves according to an autoregressive model of order one, or an AR(1), because it is a

function of inventory from the previous periods as well as new, random normal orders.

In periods where the average inventory is higher, prices are lower to compensate for the

risk of holding additional inventory. As a demonstration, Figure A3 shows one simulated

draw. Fom left to right, top to bottom, we show customer volume, interdealer volume,

market price, and average dealer inventory over time.

We summarize over all 10,000 simulations in order to relate monthly total trading

volumes to three main variables of interest: (1) the average dealer inventory over the

same time period, (2) the average number of dealers who have hit their constraints over

the same period, and (3) the one-year ahead return. Figure 1 summarizes our findings.

The size of each bar corresponds to the size of the R-squared from a univariate regression

of a variable of interest on one of three explanatory variables based on trade: (1) customer

volume (2) interdealer volume (3) a ratio of interdealer volume to total volume.

Examining the red bars in Figure 1, we see that customer volume has essentially

no relationship with average dealer inventory, number of dealers constrained, or future

returns. This is because customer orders are randomly drawn and they are always filled in

their entirety by the dealers. Next, following the blue bars, we see that interdealer trade

has a weak relationship with average dealer inventory (R-squared of 5.1%), the number

of dealers constrained (R-squared of 6.7%), and one-year ahead returns (R-squared of

2.7%). Dealers are more likely to trade with each other when average dealer inventory

is higher or there are more dealers who have hit constraints. These conditions also push

prices down, so that returns are higher in the future.

Finally, shown in the dark gray bars of Figure 1, the ratio of interdealer trade volume

to total volume has a strong relationship to our variables of interest. When the the ratio

is higher, average dealer inventory is higher, there are more dealers constrained, and

12

future returns are higher. In a univariate regression, the ratio can explain 49.0%, 62.2%,

and 13.1% of these key variables respectively. Although customer orders are random

and interdealer volume is largely driven by customer orders, taking a ratio of these two

components can remove part of the random noise.

To summarize, this stylized model demonstrates one way in which a simple ratio of

trade can reveal aggregate inventory and constraints. It generates the following predic-

tions:

1. Interdealer trade and dealer-to-customer volumes may not be informative of average

dealer inventory or number of dealers constrained on their own, since they are both

largely driven by idiosyncratic orders.

2. The ratio of interdealer trade to total trade volume is positively and strongly related

to inventory. It is also strongly and positively related to the number of dealers who

have hit constraints.

3. The ratio of interdealer trade to total trade is positively and strongly predictive of

future returns.

2.3 Thought Experiment

In this section, we propose and answer the following question: what if we don’t observe

all of the dealers’ balance sheets? In practice, dealers’ balance sheets are large and

complicated, so it is unlikely that we are able to observe all of the relevant assets. For

example, we may be able to observe all Treasury holdings and trades, but we cannot see

Treasury-based repos or interest rate swaps. However, they are still important drivers of

balance sheet risk.

To answer this question, we assign a random percent of trades to be in an unobserved

asset. Consequently, these trades do not count towards total trade volume nor do they

add to the observed inventory. Figure A2 shows how the informativeness of key variables

vary as the percent of the balance sheet which is missing increases. More specifically,

13

it plots the R-squared from a univariate regression of returns on the ratio of interdealer

trade (red) versus average inventory (black).

As more of the balance sheet becomes unobserved, both predictors become less in-

formative, but the trading ratio is much more robust to missing observations. Under

our standard calibration, if we observe less than 70% of total inventory risk, the IDB

ratio becomes an even better predictor than inventory. Furthermore, risk weights may

not be the same across all assets, and we may expect the risk weights on the unobserved

assets (eg. derivatives) to be much higher than the observed. Thus, while 30% missing

inventory may seem high, it may not be a large portion in dollar amounts, especially if

the risk weights on the missing assets are large.

Ultimately, this excercise shows that the IDB ratio is more robust to missing observa-

tions than direct measures of inventory. In observed trades, dealers are optimizing with

respect to the entire balance sheet, including the assets which we do not observe. Thus,

even if we cannot see those assets, we can glean information about them by observing

how dealers trade. In this thought experiment, we find that if reports of balance sheets

are incomplete, there may be substantial benefits from inferring the holdings through

actions instead.

3 Data

In this section, we provide detail on the sources used in our empirical analyses. First,

in Subsection 3.1, we focus on our proposed measure of dealer risk constraints called the

interdealer (IDB) ratio. We describe its construction as well as key considerations we

made in building this measure. Then, in Subsection 3.2, we give a general overview of

where our remaining data comes from and what date ranges we observe for each source.

14

3.1 Definition of the IDB Ratio

As shown in our stylized model, our ideal measure for dealer risk exposure is the fraction

of total trade conducted between dealers using an interdealer broker (IDB). In fact, this

ratio is more informative than either of its components: interdealer trade volume and

dealer-to-customer trade volume.

To create this ratio, we first obtain bond trading data from the FR2004 reports. Each

week, the primary dealers report the total volume of their trade with interdealer brokers

(IDBs) versus trade with others. We correct for a double-counting problem, which has

been highlighted in other recent work using the FR2004 data (Fleming and Krishnan,

2011). Every interdealer broker transaction could be reported by two dealers while dealer-

to-customer transactions will only be reported by the dealer involved. We correct for the

double-counting by dividing the total interdealer broker volume by two, and we will call

the subsequent measure interdealer trading volume.

Following the stylized model, we calculate a raw trading ratio, which is total inter-

dealer trading volume divided by the total trading volume.

Raw ratio =Interdealer Vol

Interdealer Vol + Other Vol· 100% (2)

Over time, the raw ratio appears mechanically related to the number of primary dealers.

Figure 2 plots the relationship between the raw ratio (blue line) and the number of

primary dealers designated by the Fed (black line). The two series are very closely

related and have a correlation of 0.86 over the full sample. This may not be surprising,

because when a firm becomes a dealer, its trade with other dealers may switch from being

classified as other trade to interdealer trade.4 This will mechanically raise the numerator

and the size of the raw ratio.5

4Until 1994, only primary dealers as designated by the Fed were allowed to be participants. In 1994,membership expanded to Fixed Income Clearing Corporations (FICCs) although primary dealers stillplayed a large role (Potter, 2015). Beginning in 2004, other firms including high frequency traders wereallowed to enter the market.

5Additions and removals to the list of primary dealers are largely driven by voluntary petition by theprospective and subject to approval from the New York Fed. Removals can also occur due to mergers or

15

In order to avoid the issue of primary dealers being added and removed throughout

our sample, we construct the IDB ratio as the part of the raw ratio which is orthogonal

to the number of primary dealers 6. To do this, we run a regression of log raw ratio on

log number of dealers, and we take the exponential of the residual.

ln(raw ratio)t = αt + β ∗ ln(num dealers)t + ln(ε)t (3)

IDB ratiot ≡ εt (4)

The results of the regression are shown in Table A1, and the resulting IDB ratio is plotted

in Figure 4 (blue line). Comparing it to the raw ratio and number of dealers in Figure 2,

we see that the IDB ratio no longer has the long-run persistence in each of its components.

The final transformed ratio, which we call the IDB ratio, is an index which is centered

at 1 (or 100%). This is due to the nature of the log regression in Equation (3), which

sets the mean of the log residual to 0. For ease of interpretation, in all regressions, we

will report the IDB ratio in units of standard deviations. Intuitively, when the IDB ratio

is higher, the primary dealers are trading a higher fraction of volume through the IDB.

This also suggests that each unit of trade is more likely to be intermediated through a

dealer-to-dealer transaction.

3.2 Additional Data

Our main sample consists of monthly observations from 1964-2015. Transaction volumes

come from the Federal Reserve of New York’s FR2004 forms7. On a weekly basis, the

New York Federal Reserve reports total Treasury, mortgage-backed securities (MBS),

and non-mortgage Agency trading volumes made between primary dealers using IDB’s,

failures of the firm, although it is more rare.6We have also constructed two other versions of the IDB ratio, one which simply divides the raw ratio

by the number of dealers, and another which divides the raw ratio by the estimated total assets of theprimary dealers. The results are generally robust.

7While data dating back to 1960 has been published publically, it is only archived and downloadablefrom the New York Federal Reserve website beginning in 1998. For data between 1960 and 1998, weused the data series kindly shared from Fleming (2000).

16

or interdealer brokers, as well as between primary dealers and other entities. The data

are reported as of the week ending Wednesday, and are aggregated across all dealers. We

convert from weekly to monthly frequency by averaging trading volume. This aggregation

will help us avoid any monthly patterns arising from the supply effects of Treasury auc-

tions. The Treasury transaction data spans 1964-2015, while the MBS and non-mortgage

Agency transaction data spans 1998-2015.

In order to better understand dealer behavior, we utilize a proprietary, confidential

version of the FR2004 dataset, which covers July 1, 2001 through April 30, 2017 8.

This dataset contains weekly transations, long positions, and short positions of Treasury,

Agency, and MBS at the individual dealer level. This allows us to not only calculate

individual IDB ratios, but it allows us to match dealers’ IDB ratios to their reported

Value-at-Risk (VaR). In addition, this dataset breaks down each transaction by counter-

party (either with an interdealer broker or other) and across various maturity buckets.

This additional breakdown is not contained in the public historical data, although its

snapshot is available in real-time through the monthly Fed bulletins.

To measure primary dealer’s exposure to interest rate risk, we pull interest rate Value-

at-Risk (VaR) measures from Bloomberg and we convert them to the 95% confidence

interval for consistency. In some specifications, in order to normalize the measure by

size, we further divide the VaR by a firm’s total book equity.9 This reflects the amount

of interest rate risk that each dollar of shareholder equity bears. We focus on the sample

of primary dealers which provide public measures of VaR, and we exclude those who do

not publicly release VaRs in their 10Q. To create an aggregate measure of dealer VaR,

we simply average across all dealers in our sample 10. The earliest available reports begin

in April 1999 and continue to the present.

8This data was kindly provided to us jointly by the Markets Group at the New York Federal Reserveand the Board of Governors.

9We download both measures from Bloomberg. Interest rate risk is IS AVG VAR INT RATE RISKand book equity is TOTAL EQUITY.

10Note that this is a value-weighted average, where the largest dealers get more weight. If we adjustfor size using book equity and then equal weight, it gives us a similar measure and consistent results.For consistency, we choose to present results using the value-weight since the IDB ratio is also essentiallyvalue-weighted.

17

We calculate bond excess returns from two sources. First, we use Fama-Bliss synthetic

zero coupon bond data downloaded from CRSP. From that, we construct both annual

excess returns and forward rates for Treasury maturities up to five years. Second, we

obtain data on fitted yield curves from Gurkaynak et al. (2007). When the data overlap,

the GSW yields closely match the Fama-Bliss yields. GSW also contains data on longer

horizon maturities than Fama-Bliss, but these are not always available for our full sample

period. In particular, the five-year yields become available in 1961, 10-year yields in 1971,

20-year yields in 1981, and 30-year yields in 1985.

Measures of macroeconomic conditions, which include annual real GDP growth, an-

nual CPI growth, and Moody’s Baa-Aaa corporate bond credit spread, come from the

Federal Reserve Economic Database. While real GDP is measured quarterly, CPI and

the Baa-Aaa index are available monthly. They date back to the first quarter of 1947,

January 1947, and January 1919 respectively. To calculate annual growth at time t, we

measure change over the past year from time t-12 (t-4, if quarterly) to time t, and we

convert to a percentage by dividing by the measure at time t.

We also gather a number of Treasury auction statistics released by Treasury Direct.

These include the bid-to-cover ratio, the amount accepted by primary dealers as a percent

of total accepted, and the amount tendered by primary dealers as a percent of total

tendered. To create these measures, we considered all auctions of U.S. Treasury coupon

securities, excluding any Treasury Inflation Protected Securities (TIPS) and floating rate

notes. If there were multiple auctions in the same week, we use a value-weighted bid-to-

cover ratio based on total amount offered, and we simply combined the total accepted or

tendered amounts.

Finally, we proxy for aggregate U.S. MBS and Agency prices by using the Barclays

indices from Bloomberg. The MBS index is available from 1976 while the Agency index is

only available from 1990. While both series are available on a daily frequency, we take the

last value from each month in order to match the rest of the data’s monthly frequency.

Returns from holding a portfolio of MBS or agency portfolios are approximated using

18

the percent change in the index between month t and month t+ 12. We calculate excess

returns by subtracting the one-year Treasury rate.

4 Main Empirical Results

In this central section, we show the close link between the IDB ratio and intermedi-

ary risk exposure (Subsection 4.1), as well as the strongly ability of the IDB ratio to

forecast future bond returns (Subsection 4.2). Return forecastability holds even after a

number of robustness checks, including alternative standard errors and controlling for

macroeconomic conditions. The IDB ratio also forecasts well out-of-sample.

These analyses are focused on the U.S. Treasury market, although we also expand

to other markets in Section 6. We choose to study these relationships in the Treasury

market for several reasons. First, Treasuries are very uniform in terms of maturity, credit

risk, and issuance schedule. Second, as the most liquid goverment securities in the world,

U.S. Treasuries are an important asset class that not only serves as a global risk-free

benchmark but also an important indicator for macroeconomic conditions. Finally, in

the U.S. Treasury market, there is a clear group of designated intermediaries by the New

York Federal Reserve, the primary dealers. For more details on the structure of the U.S.

Treasury market, please see Section 1.2.

4.1 IDB Ratio and Interest Rate VaR

Empirically, dealers’ risk constraints are rarely reported. Thus, we instead proxy for

dealers’ inventory of risk, or risk exposure, using their reported Value-at-Risk (VaR).

VaR is one of the best empirical proxies because it is commonly used by financial firms to

measure risk exposure, and more importantly, it is used to limit risk exposure subject to

risk constraints. As a demonstration, Figure A4 shows an excerpt from Goldman Sach’s

2018 10Q filing. It describes how the VaR is regularly used by the firm to both manage

risk as well as set risk limits (Goldman, 2018). The VaR is calculated by estimating the

19

95th percentile of potential losses based upon historical risk factors. More details on this

measure can be found in Section 3.

More specifically, since we are studying U.S. bonds, we will focus on the sub-limit set

by the interest rate VaR. Examples of risk factors specific to the interest rate VaR include

“exposures to changes in the level, slope, and curvature of yield curves, the volatilities of

interest rates, prepayment speeds and credit spreads” (Goldman, 2018).

In Figure 3, we show the tight relationship between the IDB ratio and Interest Rate

VaR by plotting both over time. Consistent with our model’s predictions, we see that

the two series co-move positively and very closely. The empirical correlation between the

level of the two series is 0.72, and the correlation between their one-year changes is 0.58.

Another prediction from our model is that while the IDB ratio may be informative of

risk exposure, its underlying components may not be. We test this hypothesis in Table

A2. We see that over the same period, interdealer trade volume and other trade volumes

are not informative of interest rate VaR on their own (columns 1 and 2). 11 However,

when we create the IDB ratio using these components, it becomes very informative of

interest rate VaR with a univariate R-squared of 52%. A possible explanation, as shown in

the model, is that random customer orders may drive each of the individual components,

but taking their ratio can remove much of the noise.

4.2 IDB Ratio and Bond Returns

In this section, we demonstrate the strong and robust ability of the IDB ratio to forecast

future excess returns.

In Section 4.2.1, we establish a baseline relationship between the IDB ratio and future

excess returns using the five-year Treasury bond. Next, in 4.2.3, we show that return

predictability is robust across a variety of different specifications, including alternative

standard errors, across different maturities, controlling for the five forward rates, as well

11We normalize both series by dividing by the total amount of Treasuries outstanding in order toremove long-run trends as well as make the series stationary.

20

as controlling for macroeconomic conditions. Finally, in Section 4.2.7, we conduct a

rolling, out-of-sample forecasting excercise, and we find that the IDB ratio performs well

in real-time.

4.2.1 Baseline

As our model shows, the IDB ratio is higher in periods of tighter intermediary con-

straints, because intermediaries benefit more from sharing risk. Theories of intermediary

asset pricing show that risk premia will be higher when intermediaries have tighter risk

constraints. Thus, we should expect the IDB ratio to positively forecast bond returns.

In this section, we empirically test this prediction in the context of the Treasury market.

We begin by considering the ability of IDB trade to forecast bond excess returns on

its own. Figure 4 plots the IDB ratio against annual excess returns of a zero coupon

five-year Treasury bond, and there appears to be a strong, positive relationship. We will

statistically test this relationship in the next table.

Table 3 estimates our baseline regression, summarized by the following equation:

ert→t+12 ≡ r5,t→t+12 − r1,t→t+12 = α + β · IDB ratiot + εt→t+12 (5)

where t indexes months, rn,t→t+12 is the log return to holding the n-year Treasury over the

subsequent year, and ert→t+12 is the log excess return to holding the five-year Treasury

over the subsequent year. We run our baseline regression in the U.S. Treasury market

using a long time series of monthly data from January 1, 1964 through December 31,

2015. Since we are using overlapping monthly observations over a long time sample, we

compute Newey West adjusted standard errors with an 18 month lag as our baseline.

Section 4.2.3 considers alternative standard errors, including that of Hansen Hodrick.

Looking at column 1 of Table 1, we see that the IDB ratio predicts one year ahead

returns by itself with a univariate R-squared of 10.8%. More specifically, a one standard

deviation increase in the IDB ratio forecasts 1.8 percentage point increase in excess returns

21

over the subsequent year for Treasury bonds with a five-year maturity. The amount of

variation in expected returns is substantial. In comparison, the average annual excess

return on five-year Treasuries over our sample is 1.3% per year.

In column 2 of Table 1, we test the spanning hypothesis. We add in one-, two-, three-,

four-, and five-year forward rates, which are benchmark predictors of bond returns from

Cochrane and Piazzesi (2005). The coefficients on the forward rates generally match the

tent-shaped pattern that they identify. Looking at column 2, we see that the IDB ratio

continues to positively and significantly predict returns, controlling for all five forward

rates. In fact, the magnitude and significance is similar to column 1 (1.4% versus 1.8%).

Comparing column 2 to column 3, we see that the IDB ratio adds explanatory power to

a model using the forward rates alone, raising the adjusted R2 from 23% to 29%.

4.2.2 Robustness

4.2.3 Alternative Tests of Significance

First, we show that our results are robust to alternative specifications of standard errors.

In Table A3, we repeat the baseline regression in Table 3 using Hansen-Hodrick standard

errors, allowing for equal weights on the first 12 lags. While the standard errors become

slightly larger, across all specifications, we find that the results continue to hold at the

95% confidence level or higher.

As shown in Bauer and Hamilton (2017), traditional spanning tests may be misspeci-

fied and are subject to small sample distortions. Thus, we conduct an additional spanning

test using the bootstrap methodology outlined in their paper and either three or five prin-

ciple components of the forward rates. Using 5,000 simulations each, we find that we can

reject the null-hypothesis that the IDB ratio is spanned with p-values of 0.6% using a

three-factor model and 0.3% using a five-factor model.

22

4.2.4 Two- through Thirty-Year Maturities

In this section, we show that the predictability of the IDB ratio is not isolated to five-

year Treasury bonds. In Table 2, we present bond prediction regressions across a broad

spectrum of different maturities, ranging from two- through 30-years. We see that the

coefficient on the IDB ratio is consistently positive across all specifications. In all cases

except for the 30-year bond, the magnitude of the coefficient grows monotonically with the

maturity of the bond. While the predictive ability is strong up to ten-years in maturity,

we find that significance drops at the long end of the yield curve with the 30-year bond.

Reduced predictability at the long end of the yield curve may be due to several factors.

For instance, the IDB ratio is calculated using transactions across all maturity buckets,

which means that it will underweigh activity in the less liquid maturities, such as the

thirty-year bond. This suggests that there many be additional information in IDB ratios

calculated over different maturity buckets, and we will test this hypothesis in Section 6.1.

In addition, risk premia at the long end may be dominated by other risk factors, such as

fluctuating demand from institutional investors.

4.2.5 Long Run Time Trends

In order to make sure that we are not simply picking up long-run time trends, we add

both a general time trend as well as try a five-year difference of the ratio. For convenience,

the first column of Table 3 reproduces the baseline result from Table 1. In column 2, we

add a simple linear time trend. We find that the coefficient on the IDB ratio (1.4%) is

similar in magnitude to column 1, and while the relationship is slightly less significant,

it is still signifcant at the 95% confidence interval.

To check whether we are picking up non-linear, long-run trends, we also try a pre-

dictive regression using the five-year change in the IDB ratio in column 3. The five-year

change is calculated as the difference between the IDB ratio at month t and the IDB ratio

from five years ago at month t− 60. We find that the magnitude and significance of the

IDB ratio stays remarkably the same.

23

Finally, in the last column, we use five-year changes in the IDB ratio as well as add

a time trend. Again, the results remain consistent. Holding the time trend fixed, a

one standard deviation increase in the five-year change of the IDB ratio forecasts a 1.6

percentage point higher annual excess return for a five-year bond.

4.2.6 Controlling for Macroeconomic Conditions

Since the prior literature has shown that macroeconomic cycles are strong predictors of

future bond returns, we test whether our measure is simply picking up macroeconomic

movements. To do this, we add several variables known to proxy for macroeconomic

conditions to the predictive regression in Table 4. In the first column, we include inflation

rates, as measured by CPI growth over the past year; in the second column, we add real

GDP growth over the past year; in the third column, we include the spread between Baa

and Aaa rated bonds in the spirit of Fama and French (1989); in the last column, we

include a multivariate specification with all three indicators.

Across all specifications, we find that the IDB ratio continues to positively and sig-

nificantly forecast returns. While the coefficients on the IDB ratio drops from 1.8 in

the univariate case to 1.3 when we include all three macroeconomic indicators, they are

similar in magnitude and both highly significant. This suggests that while the IDB ratio

may have some correlation with macroeconomic conditions, they do not drive its return

predictability.

4.2.7 Out-of-Sample Forecasting

Here, we show that the IDB ratio has strong ability to forecast returns out-of-sample.

We use data from 1964-1973 to train the initial estimate, and we conduct our rolling

out-of-sample excercise from 1974 to 2015, constructing forecasts only using previously

available data.

As in our main specification, we forecast the annual excess return on a five-year Trea-

sury. Our data set consists of overlapping monthly observations. Using only previously

24

available data, we estimate the univariate regression of annual excess returns on the IDB

ratio shown in Equation (5) of Section 4.2.1. Then, we use the fitted value from the

regression to forecast the upcoming year’s excess return as ert→t+12. To evaluate the

accuracy of our forecasts, we compute an out-of-sample R2 statistic following Campbell

and Thompson (2008):

R2OS = 1−

∑T−12t=1 (ert→t+12 − ert→t+12)

2∑T−12t=1 (ert→t+12 − ert)2

(6)

where ert ≡ 1/(t−12)∑t−12

i=1 eri→i+12 is the unconditional mean of excess returns prior to

time t. R2OS compares the forecasting performance of our model versus forecasting from

the previously realized unconditional mean.

The out-of-sample R2 from a univariate model using just the IDB ratio is 15.0%,

suggesting a strong out-of-sample forecasting ability. Furthermore, the out-of-sample R2

improves in more recent samples: R2OS is 16.3% after 1980, 19.0% after 1990, and 30.2%

after 2000. Figure A5 plots the time series of the actual versus the predicted returns.

In comparison, a real-time forecast using all five forward rates has a higher R2OS over

the entire sample, but its predictability steeply declines and becomes worse later in the

sample. A model using five forward rates has an out-of-sample R2 of 22.4% over the

entire sample; 21.5% after 1980; -3.7% after 1990; and -4.6% after 2000. Combining the

forward rates with the IDB ratio improves performance. For instance, over the entire

sample, a model using both the IDB ratio and forward rates has a R2 of 28.3%. We plot

the time series of the actual versus the predicted from this model in Figure A6.

Finally, we also try a version of the regressions that uses annual non-overlapping

observations. Qualitatively, our results remain the same. We find that the IDB ratio has

significant predictive power out-of-sample, and that this predicability strengthens over

time while the predictability using forward rate declines. The out-of-sample R2 for the

IDB ratio alone is 6.9% over the entire sample; 10.4% since 1980; 18.6% since 1990; and

32.3% since 2000. In comparison, the five forward rates have an out-of-sample R2 of 9.6%

25

over the entire sample; 13.6 since 1980; -15.1% since 1990; and -72.1% since 2000.

5 Supporting Evidence

5.1 Treasury Auctions as Natural Experiment

As shown in our model, the interdealer broker (IDB) ratio is higher when dealers face

inventory shocks that push them unexpectedly closer towards their constraints. One

natural, repeated instance of an inventory shock for the primary dealers are the U.S.

Treasury auctions. As part of their official designation, the primary dealers have to bid

competitively in all Treasury auctions. However, the amount they receive from the auc-

tion is heavily dependent on the competiveness of other participants’ bids. For instance,

in an especially weak auction, the primary dealers on average receive a bigger share of

the auction amount.

In Table 5, we explain the weekly IDB ratio using different Treasury auction shocks.

Since not all weeks contain auctions, we include a dummy indicator equal to one during

auction weeks. In column 1, the explanatory variable is the bid-to-cover ratio, which is

equal to total amount bid at auction divided by total amount accepted. When the bid-to-

cover ratio is high, it is indicative of an auction with strong demand, suggesting that the

dealers face a weaker supply shock from the auction. Consistent with this hypothesis,

we find a negative relationship between the bid-to-cover ratio and average IDB ratio.

However, it is not statistically significant.

In column 2, we explain the IDB ratio using the percent of total accepted at auction

which is specifically borne by the primary dealers. Consistent with our prediction, we

find a strongly positive and statistically significant relationship. This suggests that when

the primary dealers face bigger inventory shocks from auction, they use the IDB more in

order to redistribute the shock.

Dealers may accept a larger portion of the auction because of unexpected weak de-

mand from other bidders, or because they want to hold more Treasuries and thus bid

26

more competitively. To control for the latter, we additionally include the total percent

of all bids tendered which are accounted for by the primary dealers in column 3. We find

that not only is the positive and significant relationship robust to this additional control,

but it actually becomes stronger.

Supporting the idea that only unexpected inventory shocks matter, Figure 5 shows

a scatterplot of weekly IDB ratio against either the fraction of total amount accepted

(Panel A) or total amount tendered (Panel B) at auction. We see that while there is a

positive and fairly linear relationship in panel A, there is a much noisier and nonlinear

relationship in Panel B. In particular, looking closer at Panel B, primary dealers regularly

tender between 60 and 80 % of Treasury auctions. In this region, the relationship between

IDB ratio and percent tendered appears negative and insignificant.

Finally, we whether it is the fraction of total tendered to total accepted that matters

for inventory shocks and run a log regression in column 4. To make the results easier to

interpret, we remove all weeks without an auction as well as the auction week indicator.

We find that, again consistent with our prediction, there is a strong and positive rela-

tionship between the IDB ratio and the percent of total auction accepted by the primary

dealers. The magnitudes of the coefficients on percent accepted and percent tendered are

close to each other, suggesting that a simple ratio of accepted to tendered may be the

best explanatory variable for the IDB ratio. Column 4 also has the highest R-squared of

43%.

5.2 Variation across Dealers

5.2.1 Cross-Sectional Variation

As shown in our stylized model, the interdealer broker (IDB) ratio captures risk-sharing

between intermediaries. Thus, there should be important variation not only in the time

series but also in the cross-section of intermediaries. To examine the cross-section, we

use a proprietary version of the FR2004 trading data, which provides trading activity

27

at the dealer level for a shorter time sample between July 2001 to April 2017. Using

this data, we can create individual IDB ratios; and for the dealers who publicly report

Value-at-Risk, we can specifically match their VaR to their IDB ratio.

Intuitively, dealers who have the highest risk exposures, or who are closest to their

constraints, have the most to benefit from sharing risk using the interdealer brokers

(IDBs). This predicts that in the cross-section, dealers who have higher risk exposure

also have higher IDB ratios. And since these dealers are very close to or past their risk

constraints, we would also expect these dealers to reduce their risk exposure more than

others in the future 12.

In Panel A of Table 6, we run a monthly panel regression explaining interest rate

Value-at-Risk (VaR) 13. Each observation corresponds to one dealer and one month.

In the first column, we simply regress interest rate VaR on the IDB ratio and recover

the generally positive relationship depicted in Figure 3. To examine the whether this

relationship is driven by time series trends, we next control for dealer fixed effects in the

second column. We find that the relationship is positive and strong, suggesting that in

periods of higher risk exposure, dealers on average have higher IDB ratios. Finally, to test

whether this relationship is driven by the cross-section, we control for time fixed effects.

Looking at column 3, we see that consistent with our hypothesis, dealers with higher risk

exposure also have significantly higher IDB ratios. However, this cross-sectional effect is

roughly half the size in magnitude than that of the time series effect.

Next, in Panel B of Table 6, we run a monthly panel regression explaining six-month

ahead change in Value-at-Risk (VaR). In the first column, we regress six-month ahead

change in interest rate VaR on the IDB ratio, and we find a generally strong, negative

relationship. In the second column, we control for dealer fixed effects and look at whether

this trend is driven by variation across time. We find that the time-series relationship is

12Note that, alternatively, the dealer could choose to relax their risk constraints. This effect would goin the opposite direction of what we find and push our estimates towards zero. Also, there is reason tobelieve that constraints are slow-moving and the effect of its change is more long-run than our testedhorizon.

13To control for the fact that larger dealers tend to have larger risk constraints, we normal VaR bybook equity.

28

also negative as well as slightly larger in magnitude. This suggests that in periods where

IDB ratios are higher, dealers may be over-exposed to risk in the aggregate and are more

likely to reduce their inventory in the future. Finally, in the third column, we control for

time fixed effects and look at whether the relationship is driven by the cross-section of

dealers. We find that consistent with our prediction, dealers who have higher IDB ratios

are significantly more likely to reduce their risk exposure in the future. This effect is

statistically significant at the 95% confidence level and is similar to the baseline (column

1) in magnitude.

5.2.2 Core and Periphery Dealers

In a world where dealers trade to share risk, our model predicts that prices are driven by

the aggregate slackness in risk constraints. When the total capacity of the intermediary

system 14 shrinks, future returns are higher in order to compensate the intermediaries for

holding additional inventory, if they net positive holders of the risky asset. Empircally,

we know that capacity varies greatly among the primary dealers. As a result, we would

expect the dealers who supply a greater portion of the capacity to have more informative

IDB ratios.

To test this, we divide our dealers into two halves based on the size of their capacity.

We proxy for capacity using each dealer’s total interdealer broker(IDB) volume over the

last twelve months. The half of dealers with the highest capacity are designated as core

dealers. The remainder, which are the half of dealers with lower capacity, are designated

as the periphery dealers.

Figure 6 shows some summary measures of the core and periphery dealers over time.

Panels A and B show the total gross (long plus short) positions and total absolute net

positions of dealers in the U.S. Treasury market respectively. The black line represents

periphery dealers while the blue line represents core dealers. We see that in general,

periphery dealers hold smaller balance sheets than the core dealers, and they also have

14We can measure this using the gap between aggregate constraints and aggregate inventories.

29

smaller risk exposure, as proxied by the sum of the absolute value of their net positions.

Both the core and periphery dealers scaled back on their gross and net positions during the

financial crisis, but the drop is especially pronounced for the core dealers’ net positions.

Interestingly, while gross positions seem to have recovered post-crisis, the net positions

stay at a lower level post-crisis, especially for core dealers. This sugggests that while gross

capacity has recovered, risk limits were reduced post-crisis, perhaps due to regulatory

restrictions.

Panels C and D of Figure 6 show the relationship between interest rate VaR (black line)

and the IDB ratio (blue line) for periphery and core dealers respectively. We see that in

both cases, the VaR and IDB ratio are positively and strongly related. Their correlations

are 0.39 for the periphery dealers and and 0.69 for the core dealers, suggesting that both

core and periphery dealers use the IDBs to manage risk exposure. Interestingly, the

VaRs of periphery dealers are much flatter, shooting up only around the financial crisis.

One potential explanation for this pattern is that the periphery dealers increased their

risk constraints in order to take on more capacity during the crisis and account for the

declining capacity of the core dealers.

Finally, in Table 6, we test whether the IDB ratios of core dealers are more informative

than that of periphery dealers. We forecast annual excess returns on a five-year bond

using the IDB ratio from periphery dealers (column 1), core dealers (column 2), or the

standard IDB ratio including both core and periphery dealers (column 3). We find that

the IDB ratio of periphery dealers are uninformative of future exess returns. Its coefficient

is negative but also close to zero and statistically insignificant. On the other hand, as

predicted, the IDB ratio of core dealers are strongly and positively related to future

returns. A one standard deviation increase in the core IDB ratio forecasts a 1.5 percentage

point increase in annual excess returns. While this is slightly smaller in magnitude than

the aggregate IDB ratio, with a coefficient of 2.1 over the same period, its univariate

R-squared is actually larger (14% versus 11%). This suggests that among the primary

dealers, the activity of the largest, core dealers are the most informative.

30

6 Segmented Markets

In this section, we examine the question of whether risk management is segmented across

different maturities and asset classes. On one hand, we may believe that only aggregate

risks should matter for asset prices, and thus, individual IDB ratios created from different

market segments should not provide any additional information On the other hand, due

to market frictions like liquidity, risks in one sector of the market may not be easily

transferred to other sectors of the market.

First, in Section 6.1, we test whether IDB ratios created from different maturity buck-

ets provide additional explanatory power in forecasting excess bond returns. In Section

6.2, we test whether IDB ratios created from transactions in either Agency or mortgage-

backed securities (MBS) market can forecast returns in those respective markets. Then,

to test our null hypothesis that markets are not segmented, we check whether the Treasury

IDB ratio can also forecast returns in the Agency and MBS markets.

6.1 Multiple Maturity Buckets

The aggregate Treasury IDB ratio may be missing important information on movements

specific to parts of the yield curve. As we saw in Section 4.2.4, the aggregate IDB ratio is

not very informative of returns for thirty-year Treasury bonds. One possible explanation

is that the aggregate IDB ratio overweighs maturities with high transaction volumes (eg.

the two- and five-year notes) and it underweighs maturities with low transaction volumes

(eg. the thirty-year note).

To test this hypothesis, we create four individual IDB ratios corresponding to Treasury

transactions across four different maturity buckets: one- to three-year notes, three- to

six-year notes, six- to 11-year notes, and 11- to 30-year notes. These individual ratios

are plotted over time in Figure 7. From this figure, we can see that while there is some

common comovement, there is also signifcant variation across maturity buckets. Overall,

all of the IDB ratios jumped up in year 2008 of the financial crisis and then have been

31

on a downward trend since the crisis.

To test whether individual ratios add forecasting power, we begin by adding them

one at a time to the aggregate IDB ratio in a regression forecasting one year-ahead bond

returns across different maturities (essentially Table 2). While they each seem to provide

additional explanatory power, we find that the three- to six-year IDB ratio generally

provides the most additional power across specifications. Thus, we show results when we

add the three- to six-year IDB ratio in Panel A of Table 8. For convenience of comparison,

the R-squareds from the univariate regression with just the aggregate IDB ratio over the

same period is reproduced in the second to last row 15.

Looking across the columns of Panel A in Table 8, we see that the coefficient on the

aggregate IDB ratio is positive while the coefficient on the three- to six-year IDB ratio is

negative and smaller in magntitude. The ratio between the coeffficients ranges between

roughly one-half (columns 2 and 3) to one-third (columns 4 and 5). The explanatory

power of the predictive regression increases significantly compared to the univariate case

across all of the columns. For example, the R-squared for forecasting two-year returns

jumps from 6.8% to 15%. While there was no explanatory power for the thirty-year note

in the univariate case, a combination of IDB ratios explain roughly 8% of variation in

future thirty-year returns.

Overall, this suggests that there is some spread between movements in different ma-

turity buckets that predicts returns. One possible interpretation is that, by subtracting

movements in the middle of the yield curve from movements across the entire curve, the

model picks up differential activity on the far ends of the yield curve. For instance, hold-

ing the aggregate level of the IDB ratio constant, higher use of the IDBs in the long end

of the yield curve forecasts higher future returns.

In Panel B of Table 8, we add in all of the IDB ratios across different maturity

buckets simultaneously. We see that we can get r-squareds of up to 32% for both the

two- and three-year maturity returns, which even outperform the forecasts from using all

15Note that compared to Table 2, which is over a much larger time sample, this period has generallylower r-squareds, with the exception of the ten-year maturity note.

32

five forward rates simultaneously (21% and 22% respectively, as shown in the last row).

While the coefficient on the three- to six-year IDB ratio is generally negative and the

coefficients on the other ratios positive, the magnitudes of the coefficients do not appear

to simply shift up or down by a common multiplier, unlike the Cochrane-Piazzesi factor.

For instance, the coefficient on the aggregate IDB ratio is much smaller than that of the

three- to five-year IDB ratio in columns 1-3, is roughly the same in column 4, and is

almost three-times bigger in columns 5-6.

Overall, Panel B of Table 8 shows us that IDB ratios across maturity buckets add

significant forecasting power and contain valuable information. In addition, there is

evidence that the drivers of returns across different maturities are not the same. Since the

IDB ratios across maturities have idiosyncratic variation and this idiosyncratic variation

carries variable information, it suggests that Treasuries of different maturities are not

fungible for managing risk exposure. Moreover, trading and risk-management across

different Treasury bonds durations may be quite segmented.

6.2 Agency and Mortgage-backed Securities

Although the Treasury market is an ideal laboratory to study our model of dealer con-

straints, the IDB ratio should be revealing of risk constraints in any market with an

over-the-counter (OTC) structure and heavy financial intermediation. In this section,

we provide preliminary evidence to support this by studying two other markets in which

primary dealers play a key role: mortgage backed securities (MBS) and non-mortgage

agency securities. These are also two large markets which are often used to hedge interest

rate risk. In the future, more work could be done on more disparate markets, such as the

Foreign Exchange market.

We begin by constructing the IDB ratio for both the MBS and Agency markets, which

is parallel to the consruction of the IDB ratio for the Treasury market. For example, to

calculate the MBS IDB ratio, we first calculate a raw ratio of total MBS interdealer

volume to total MBS volume (interdealer plus other volume). We then orthogonalize

33

the IDB ratio to the number of primary dealers using a log univariate regression, and

we designate the MBS IDB ratio as the exponential of the residual. We also calculate

excess returns by subtracting the one-year Treasury rate from the percent change in

end-of-month index values for either the Barclay MBS or Agency indices.

The Treasury, Agency, and MBS ratios possess significant co-movement , although

there is also individual variation. The first principal component of these three ratios

explains roughly 66% of variation. Furthermore, all three ratios share common slow-

moving trends, such as a general rise around mid-2007 and a steady decline beginning

in 2012. While the Treasury market has the highest portion of interdealer trade and the

highest IDB ratio, non-mortgage Agency securities have the lowest.

6.2.1 Forecasting Agency Returns

In this section, we test the forecasting ability of the Agency IDB ratio for future excess

Agency returns. In Table 9 Panel A, we find strong evidence that the IDB ratio in the

agency market is positively related to agency excess returns, similar to Treasuries. More

specifically, in column 1, we see that a 1 standard deviation increase in the IDB ratio

predicts a 1.2% increase in one-year ahead excess returns on an index of U.S. agency

bonds. The magnitude is smaller yet quite similar to that of the Treasury market (1.8%),

and it is also significant at the 95% confidence level. In column 2, we control for one-

through five-year forward rates, and we find that positive return predictability persists

although the significance and magnitude drops.

Since the Treasury IDB ratio is correlated with the Agency ratio and Treasury returns

are correlated with Agency returns, the strong forecastability of the Agency ratio is un-

surprisnig. Thus, we additionally check whether there is return predictability controlling

for ex-post Treasury returns. More specifically, we control for the three contemporaneous

principal components of Treasury bond excess returns in column 316. We find that the

agency IDB ratio continues to positively forecast returns on Agency markets orthogonal

16The loadings of the principal components on bond excess returns correspond to the traditional level,slope, and curvature factors.

34

to the Treasury market. Finally, we control for both forward rates and contemporaneous

Treasury returns in column 4, and again we find significant, positive predictability.

Finally, Panel B of Table 9 repeats Panel A, but it forecasts Agency returns using the

Treasury IDB ratio instead of the Agency IDB ratio. If fixed income markets are highly

integrated, and aggregate interest rate risk ultimately drives returns, we may expect the

Treasury IDB ratio to also forecast Agency returns. However, we find evidence suggesting

that this is not the case, instead suggesting a case of segmented markets. In particular,

the univariate regression with just IDB ratio is positive but insignificant, and once we

control for forward rates or contemporaneous Treasury returns, the relationship becomes

negative and insignificant.

6.2.2 Forecasting MBS Returns

Next, we turn to the MBS market. Panel A of Table 10 tests the relationship between

the MBS IDB ratio and MBS excess returns. We find that, similar to Treasuries and

agencies, there is a positive although weakly significant relationship. The magnitude is

roughly half of the Treasury and Agency regressions. A one standard deviation increase

in the MBS IDB ratio predicts a 0.67% increase in one-year ahead excess returns on the

Barclays MBS Index.

In column 2, we add in the five forward rates; and in column 3, we control for the three

contemporaneous principal components of Treasury excess returns. Finally, in column 4,

we control for both the forward rates as well as contemporaneous Treasury return factors.

We find that the significance and magnitude of our interdealer coefficient steadily drops

in magnitude and significance with these controls. However, it stays positive, similar to

Treasuries and agencies. It is possible that unobserved pricing factors such as credit risk,

which is especially important in this later sample covering the financial crisis, create noise

in the returns and attenuate our results.

Finally, in Panel B of Table 10, we repeat the excercise in Panel A, but we use

the Treasury IDB ratio instead of the MBS ratio. We find a positive and sometimes

35

statistically significant relationship between the Treasury IDB and MBS returns, yet it

drops near zero when we include contemporaneous Treasury returns. This suggests that

the Treasury IDB ratio is useful for forecasting MBS returns, because it explains the

component of MBS returns driven by interest rate risk. However, it is not useful for

forecasting the portion of MBS returns which is orthogonal to the Treasury market.

In conclusion, we find that consistent with the Treasury market, both excess Agency

and MBS returns are positively related to their respective IDB ratios. While there is

common comovement across the IDB ratios in all three markets, there is also evidence that

individual IDB ratios carry additional information. This suggests that risk management

across different asset classes, even within the fixed income market, may actually be quite

segmented.

7 Conclusion

In this paper, we propose a novel predictor of bond returns called the interdealer broker

(IDB) ratio, which rises when the risk constraints of intermediaries tighten. The IDB

ratio captures the percent of total intermediary trading volume that is conducted be-

tween intermediaries using an interdealer broker. Unlike other existing measures of risk

exposure, the IDB ratio does not depend on measuring a complicated balance sheet, and

it instead relies on the principle of revealed preference.

Theoretically, when intermediaries are closer to risk constraints, they are more likely

to trade with each other using the IDBs in order to spread risk around the system. Thus,

in periods when the IDB ratio is higher, risk exposure is higher. In order to compensate

intermediaries for bearing risk when they hold a positive inventory, future returns are

also higher. To our knowledge, this is the first paper to tie interdealer trading activity

with long horizon return predictability.

Empirically, we test our theory in the U.S. bond market, where the IDB ratio and

interest rate Value-at-Risk closely comove with a correlation of 72%. Furthermore, we

36

find that a one standard deviation increase in the IDB ratio significantly forecasts 1.8 per-

centage point higher annual excess returns for a five-year bond. This return predictability

persists across different maturities, controlling for one- through five-year forward rates,

controlling for several measures of macroeconomic conditions, and out-of-sample. We

find evidence of return predictability in Treasuries, MBS, as well as non-mortgage agency

securities.

Our findings are relevant for practioners, regulators, as well as academics who are

interested in understanding intermediary risk constraints. Although most measures of

risk exposure are slow-moving or non-public, the underlying data for the IDB ratio is

published weekly through the New York Fed. Thus, we hope that it can provide a simple

yet useful indicator for market conditions and increase understanding of dealer behavior.

Ultimately, the IDB ratio is not simply limited to the bond market. In theory, our

measure can be applied to any market with an over-the-counter trading structure and a

central set of large financial intermediaries. Thus, in the future, we hope that the IDB

ratio can be be extended to other markets, such as the foreign exchange (FX) market.

37

References

Adrian, T. and Boyarchenko, N. (2012). Intermediary leverage cycles and financial sta-

bility.

Adrian, T., Etula, E., and Muir, T. (2014). Financial Intermediaries and the Cross-

Section of Asset Returns. The Journal of Finance, 69(6):2557–2596.

Bauer, M. D. and Hamilton, J. D. (2017). Robust bond risk premia. The Review of

Financial Studies, 31(2):399–448.

Benos, E. and Zikes, F. (2017). Funding Constraints and Liquidity in Two-Tiered OTC

Markets.

Boyarchenko, N., Lucca, D. O., and Veldkamp, L. (2016). Taking orders and taking

notes: dealer information sharing in financial markets. Federal Reserve Bank of New

York Staff Reports, (725).

Brain, D., DePooter, M., Dobrev, D., Fleming, M., Johansson, P., Jones, C., Keane,

F., Puglia, M., Reiderman, L., Rodrigues, T., and Shachar, O. (2018). Unlocking the

treasury market through trace.

Campbell, J. Y. and Shiller, R. J. (1991). Yield Spreads and Interest Rate Movements:

A Bird’s Eye View. The Review of Economic Studies, 58(3):495–514.

Campbell, J. Y. and Thompson, S. B. (2008). Predicting Excess Stock Returns Out of

Sample: Can Anything Beat the Historical Average? Review of Financial Studies,

21(4):1509–1531.

Cochrane, J. H. and Piazzesi, M. (2005). Bond Risk Premia. American Economic Review,

95(1):138–160.

Danielsson, J., Shin, H. S., and Zigrand, J.-P. (2010). Risk appetite and endogenous risk.

Financial Markets Group.

38

Department of the Treasury (2018). Institutional - How Treasury Auctions Work.

Department of the Treasury, Board of Governors of the Federal Reserve System, Federal

Reserve Bank of New York, U.S. Securities and Exchange Commission, and U.S. Com-

modity Futures Trading Commission (2015). Joint Staff Report: The U.S. Treasury

Market on October 15, 2014. Technical report.

Fama, E. F. and Bliss, R. R. (1987). The Information in Long-Maturity Forward Rates.

The American Economic Review, 77(4):680–692.

Fama, E. F. and French, K. R. (1989). Business conditions and expected returns on

stocks and bonds. Journal of Financial Economics, 25(1):23–49.

Fleming, M. and Krishnan, N. (2011). The microstructure of the TIPS market.

Fleming, M. J. (2000). Financial market implications of the federal debt paydown. Brook-

ings Papers on Economic Activity, 2000(2):221–251.

Fleming, M. J., Mizrach, B., and Nguyen, G. (2017). The microstructure of a U.S.

Treasury ECN: The BrokerTec platform. Journal of Financial Markets.

Goldman (2018). Form 10-q. Report, United States Securities and Exchange Commission.

Greenwood, R. and Vayanos, D. (2014). Bond Supply and Excess Bond Returns. The

Review of Financial Studies, 27(3):663–713.

Gurkaynak, R. S., Sack, B., and Wright, J. H. (2007). The U.S. Treasury yield curve:

1961 to the present. Journal of Monetary Economics, 54(8):2291–2304.

Haddad, V. and Sraer, D. A. (2015). The Banking View of Bond Risk Premia.

He, Z., Kelly, B., and Manela, A. (2017). Intermediary asset pricing: New evidence from

many asset classes. Journal of Financial Economics, 126(1):1–35.

He, Z. and Krishnamurthy, A. (2013). Intermediary Asset Pricing. American Economic

Review, 103(2):732–770.

39

Hlavac, M. (2013). stargazer: LaTeX code and ASCII text for well-formatted regression

and summary statistics tables.

Ludvigson, S. C. and Ng, S. (2009). A factor analysis of bond risk premia. Technical

report, National Bureau of Economic Research.

Potter, S. (2015). Challenges posed by the evolution of the Treasury market. Speech 162,

Federal Reserve Bank of New York.

SIFMA (2018). Data and statistics on u.s. capital markets. https://www.sifma.org/

resources/archive/research/.

Viswanathan, S. and Wang, J. J. (2004). Inter-dealer trading in financial markets. The

Journal of Business, 77(4):987–1040.

40

Figures

Figure 1: Simulation Results

Notes: The figure above summarizes the findings from 10,000 simulations of the stylized model,

calibrated using the baseline assumptions outlined in Section 2.1. There are three main ex-

cercises in which we try to predict three key parameters, and they shown along the x-axis:

(1) predicting average inventory (2) predicting number of constrained dealers (3) predicting

future returns. Each bar corresponds to the R-squared from a univariate regression of the key

parameter on each of the three explanatory variables: (1) customer volume (red), (2) inter-

dealer volume (blue), and (3) ratio (dark gray), calculated as (interdealer volume)/(interdealer

volume+ customer volume).

41

Figure 2: Number of Dealers and Raw IDB Ratio over Time

Notes: The figure above shows the monthly number of primary dealers designated by the Federal

Reserve Bank of New York (left hand side, black line) and the monthly raw ratio (right hand

side, blue line), where the raw ratio is calculated as: (total U.S. Treasury interdealer broker

(IDB) volume) /(total U.S. Treasury IDB volume+ total U.S. Treasury non-IDB volume). To

calculate U.S. Treasury volume, we used the transaction volume data from the FR2004 report

of U.S. primary dealers, and we excluded non-coupon securities. To calculate the number of

primary dealers, we use the historical list of primary dealer additions and removals provided

by the Federal Reserve Bank of New York. The data sample covers January 1, 1964 through

December 31, 2015.

42

Figure 3: Primary Dealer Interest Rate Value at Risk and IDB Ratio

Notes: The figure above shows monthly average interest rate Value-at-Risk (VaR)(left hand

side, black line) and average interdealer broker (IDB) ratio (right hand side, blue line) for the

sample of primary dealers who publicly report interest rate VaR. Interest rate VaR comes from

quarterly 10Q financial filings and are converted to be at the 95% confidence level. The IDB

ratio is calculated from Treasury transaction volume data collected from Primary Dealers in

the FR2004 reports, and it represents the fraction of total trade which is conducted with other

dealers through an IDB. More details on its construction can be found in Section 3.1. We use

the confidential dealer-level version of the FR2004 data to exclude dealers who do not report

interest rate VaR. The data sample covers July 1, 2001 to April 30, 2017.

43

Figure 4: IDB Ratio and Annual Excess Return

Notes: The figure above shows monthly average interdealer broker (IDB) ratio (right hand

side, blue line) and future annual excess returns for a five-year Treasury bond (left hand side,

black line). The IDB ratio is calculated from Treasury transaction volume data collected from

Primary Dealers in the FR2004 reports, and it represents the fraction of total trade which is

conducted with other dealers through an IDB. More details on its construction can be found in

Section 3.1. Annual excess return is estimated using Fama Bliss zero coupon bonds, and it is

calculated as the return from holding a five-year maturity bond over the following year minus

the risk-free rate. The data sample covers January 1, 1964 through December 31, 2015.

44

Figure 5: Primary Dealer Amount Tendered and Accepted at Auction

Notes: The figures above show the interdealer broker (IDB) ratio (y-axis) against the percent

of total auction volume accepted by the Primary Dealers (x-axis, panel A) and the percent

of total auction volume tendered by the Primary Dealers (x-axis, panel B). Each observation

represents one Treasury auction, exluding any re-openings, TIPS, floating rate notes, and bills.

Both percent accepted and percent tendered by Primary Dealers comes from auction summaries

provided by Treasury Direct. The IDB ratio is measured over the same week as the auction,

and is calculated from Treasury transaction volume data collected from Primary Dealers in the

FR2004 reports. Itrepresents the fraction of total trade which is conducted with other dealers

through an IDB. The data sample covers April 1, 2008 to April 30, 2017.

45

Figure 6: Core and Periphery Dealers

Notes: The figures above summarize the average position, interdealer broker (IDB) ratio, as

well as interest rate Value-at-Risk (VaR) for two subgroups: the core dealers and the periphery

dealers. The core dealers are designated as dealers whose IDB trade volume over the past year is

in the top 50th percentile, and the remainder of the sample are designated as periphery dealers.

Panels A and B show the monthly U.S. Treasury gross positions and absolute value of net

positions of the core (blue line) and peripery (black line) dealers over time respectively. Gross

and net positions come from the confidential dealer-level version of the FR2004 data. Panels

C and D show the monthly interest rate VaRs and IDB ratios for periphery and core dealers

respectively. The IDB ratio is calculated from Treasury transaction volume data collected from

Primary Dealers in the FR2004 reports, and it represents the fraction of total trade which is

conducted with other dealers through an IDB. Interest rate VaR comes from quarterly 10Q

financial filings and are converted to be at the 95% confidence level. We use the confidential

dealer-level version of the FR2004 data to separate dealers into a core and periphery group.

The data sample covers January 1, 2002 to April 30, 2017.

46

Figure 7: IDB Ratio using Different Maturity Buckets

Notes: The figure above shows the monthly Treasury IDB ratio measured over five non-

overlapping maturity buckets. For example, the 1-3Y IDB Ratio only uses trading volumes

from U.S. Treasury secuities with maturities ranging between one and three years, excluding

TIPs. More specifically, the IDB ratio is calculated from Treasury transaction volume data

collected from Primary Dealers in the FR2004 reports, and it represents the fraction of total

trade which is conducted with other dealers through an IDB. Confidential data was used to mea-

sure transaction volumes by both the maturity bucket as well as counterparty type (interdealer

broker or other). The data sample covers July 1, 2001 to December 31, 2017.

47

Tables

Table 1: Forecasting Annual Excess Bond Returns using IDB Ratio

Annual Ex Ret on 5Y Treasury Bond (%)(1) (2) (3)

IDB Ratio(sd) 1.801*** 1.443***(0.494) (0.484)

1Y Forward Rate(%) -1.898*** -1.978***(0.637) (0.639)

2Y Forward Rate(%) -0.315 -0.818(0.899) (0.939)

3Y Forward Rate(%) 2.406*** 2.203**(0.901) (1.009)

4Y Forward Rate(%) 1.609** 2.150***(0.682) (0.649)

5Y Forward Rate(%) -1.517** -1.295*(0.696) (0.716)

Constant 1.366** -1.895 -2.230(0.628) (1.603) (1.577)

Observations 624 624 624R-squared 0.108 0.289 0.232

Notes: The table above shows the results from forecasting the one-year excess return of a

Fama-Bliss five-year zero coupon bond. The independent variables are the interdealer broker

(IDB) ratio and the one- through five-year forward rates. The IDB ratio is calculated from

Treasury transaction volume data collected from Primary Dealers in the FR2004 reports, and

it represents the fraction of total trade which is conducted with other dealers through an IDB.

The data sample is monthly and covers January 1, 1964 to December 31, 2015. Newey-west

standard errors with 18-month lags are shown in parentheses. *p<.05; **p<.01; ***p<.001

48

Table 2: Forecasting Returns Across Multiple Maturities using IDB Ratio

Annual Ex Ret on Treasury Bonds (%)

2Y 3Y 4Y 5Y 10Y 30Y

(1) (2) (3) (4) (5) (6)

IDB Ratio(sd) 0.561*** 1.018*** 1.452*** 1.801*** 3.534*** 0.293(0.165) (0.302) (0.407) (0.494) (1.348) (3.664)

Constant 0.491** 0.902** 1.240** 1.366** 2.107 6.917**(0.212) (0.379) (0.519) (0.628) (1.329) (2.755)

Observations 624 624 624 624 533 362R-squared 0.105 0.103 0.107 0.108 0.092 0.000

Notes: The table above shows the results from forecasting the one-year excess return of a zero

coupon bond ranging from two- (column one) through thirty- (column 6) years in maturity.

Two- through five-year maturity bonds are Fama-Bliss zero coupon bonds from CRSP, while

the 10 and 20-year maturity bonds come from from Gurkaynak et al. (2007). The independent

variable is the interdealer broker (IDB) ratio, which calculated from Treasury transaction

volume data collected from Primary Dealers in the FR2004 reports. The IDB ratio represents

the fraction of total trade which is conducted with other dealers through an IDB. The data

sample is monthly and the main sample (columns one through four) covers January 1, 1964 to

December 31, 2015. 10-year returns only become available in August 1, 1971 (column five)

and 30-year yields in November 1, 1985 (column 6). Newey-west standard errors with

18-month lags are shown in parentheses. *p<.05; **p<.01; ***p<.001

49

Table 3: Controlling for Long Run Trends

Annual Ex Ret on 5Y Treasury Bond (%)(1) (2) (3) (4)

IDB Ratio(sd) 1.801*** 1.408**(0.494) (0.649)

5Y Chg in IDB Ratio(sd) 1.166*** 1.564***(0.451) (0.569)

Time Trend 0.003 0.010**(0.003) (0.004)

Constant 1.366** 0.370 1.545** -1.800(0.628) (1.337) (0.717) (1.793)

Observations 624 624 564 564R-squared 0.108 0.114 0.047 0.120

Notes: The table above shows the results from forecasting the one-year excess return of a

Fama-Bliss five-year zero coupon bond. The independent variables are the interdealer broker

(IDB) ratio, five-year change in the IDB ratio, and a linear time trend. The IDB ratio is

calculated from Treasury transaction volume data collected from Primary Dealers in the

FR2004 reports, and it represents the fraction of total trade which is conducted with other

dealers through an IDB. More details on its construction can be found in Section 3.1. The

data sample is monthly and covers January 1, 1964 to December 31, 2015. Newey-west

standard errors with 18-month lags are shown in parentheses. *p<.05; **p<.01; ***p<.001

50

Table 4: Forecasting using IDB Ratio and Controlling for Macro Conditions

Annual Ex Ret on 5Y Treasury Bond (%)(1) (2) (3) (4) (5)

IDB Ratio(sd) 1.801*** 1.675*** 1.579*** 1.744*** 1.332***(0.494) (0.616) (0.416) (0.523) (0.433)

Annual GDP Growth(%) -0.155 -0.083(0.348) (0.385)

Annual CPI Growth(%) -0.302 -0.437(0.307) (0.297)

Baa-Aaa Credit Spd(%) 1.415 1.948(1.403) (1.780)

Constant 1.366** 1.815 2.520** -0.109 1.245(0.628) (1.222) (1.070) (1.304) (2.540)

Observations 624 624 624 624 624R-squared 0.108 0.111 0.127 0.122 0.156

Notes: The table above shows the results from forecasting the one-year excess return of a

Fama-Bliss five-year zero coupon bond. The independent variables are the interdealer broker

(IDB) ratio, annual GDP growth, annual CPI growth, as well as the credit spread between

Baa- and Aaa-rated corporate bonds. GDP growth, CPI growth, and credit spread data

comes from the Federal Reserve Economic Database. The IDB ratio is calculated from

Treasury transaction volume data collected from Primary Dealers in the FR2004 reports, and

it represents the fraction of total trade which is conducted with other dealers through an IDB.

The data sample is monthly and covers January 1, 1964 to December 31, 2015. Newey-west

standard errors with 18-month lags are shown in parentheses. *p<.05; **p<.01; ***p<.001

51

Table 5: Explaining IDB Ratio using Supply Shocks from U.S. Treasury Auctions

Dependent Variable:

IDB Ratio IDB Ratio IDB Ratio Ln Ratio

(1) (2) (3) (4)

Bid-to-Cover Ratio -1.699(1.549)

Accepted by Primary Dealers(%) 48.941*** 77.646***(3.873) (6.426)

Tendered by Primary Dealers(%) -84.004***(15.255)

Ln(Accepted by Primary Dealers) 0.283***(0.022)

Ln(Tendered by Primary Dealers) -0.427***(0.086)

Auction Week Indicator 4.355 -22.370*** 24.358***(4.452) (1.904) (8.684)

Constant 106.603*** 106.603*** 106.603*** 0.146***(0.721) (0.624) (0.605) (0.020)

Observations 471 471 471 300R-squared 0.003 0.255 0.300 0.430

Notes: The table above shows the results from weekly regressions explaining either the

interdealer broker (IDB) ratio (columns one through three) or the natural log of the IDB ratio

(column four). In the first column, the explanatory variable is the average bid-to-cover ratio

measured over all Treasury auctions held in the same week. In the second and third columns,

the explanatory variables are the percent of total accepted and tendered at Treasury auctions

in the same week, which is accounted for by the primary dealers. In the last column, the

explanatory variables are the natural logs of the explanatory variables in columns two and

three. Auction data comes from Treasury Direct and excludes auctions pertaining to bills,

floating rate notes, or Treasury Inflation Protected Securities (TIPS). The IDB ratio is

calculated from Treasury transaction volume data collected from Primary Dealers in the

FR2004 reports, and it represents the fraction of total trade which is conducted with other

dealers through an IDB. The data sample covers April 17, 2008 through April 19, 2017.

Standard errors are shown in parentheses. *p<.05; **p<.01; ***p<.001

52

Table 6: Cross-Section versus Time Series Variation in IDB Ratio and VaR

(1) (2) (3)

Panel A. Predicting IR VaR / Tot Equity(%)

IDB Ratio(sd) 0.027*** 0.021* 0.014*(0.008) (0.011) (0.007)

Constant 0.102*** 0.061*** 0.156***(0.010) (0.020) (0.033)

Observations 1,549 1,549 1,549R-squared 0.0456 0.393 0.293Dealer FE NO YES NOTime FE NO NO YES

Panel B. Predicting Chg in IR VaR / Tot Equity(%)

IDB Ratio(sd) -0.007** -0.012* -0.006**(0.003) (0.007) (0.002)

Constant -0.003 -0.021* 0.003(0.003) (0.012) (0.013)

Observations 1,525 1,525 1,525R-squared 0.0129 0.0459 0.241Dealer FE NO YES NOTime FE NO NO YES

Notes: The table above shows the results from a monthly panel regression explaining either

average interest rate Value-at-Risk (VaR) (panel A) or the six-month change in average

interest rate VaR (panel B). To control for the fact that larger dealers have larger VaRs, we

normalize the VaR using total book equity. Both VaR and book equity come from public 10Q

reports. The explanatory variable is the interdealer broker (IDB) ratio, which calculated from

Treasury transaction volume data collected from Primary Dealers in the FR2004 reports, and

it represents the fraction of total trade which is conducted with other dealers through an IDB.

We utilize a confidential version of the FR2004 data in order to calculate an IDB ratio for

each dealer and month. In column (2), we control for dealer fixed effects, and in column (3),

we control for time fixed effects. The data sample covers July1, 2001 through April 30, 2017.

Standard errors are shown in parentheses. *p<.05; **p<.01; ***p<.001

53

Table 7: Forecasting Annual Ex Ret using Core and Periphery IDB Ratio

Annual Ex Ret on 5Y Bond (%)(1) (2) (3)

Periphery IDB Ratio(sd) -0.150(0.529)

Core IDB Ratio(sd) 1.501***(0.448)

IDB Ratio(sd) 2.145**(0.883)

Constant 2.774*** 2.529*** 1.406(0.761) (0.671) (0.928)

Observations 168 168 168R-squared 0.00195 0.144 0.107

Notes: The table above shows the results from forecasting the one-year excess return of a

Fama-Bliss five-year zero coupon bond. The independent variables are the interdealer broker

(IDB) ratio calculated from core dealers, and the IDB ratio calculated from periphery dealers,

and the IDB ratio calculated from all dealers. The IDB ratio is calculated using Treasury

transaction volume data collected from Primary Dealers in the FR2004 reports, and it

represents the fraction of total trade which is conducted with other dealers through an IDB.

The core dealers are designated as dealers whose IDB trade volume over the past year is in the

top 50th percentile, and the remainder of the sample are designated as periphery dealers. We

use the confidential version of the FR2004 data in order to calculate the IDB ratio for core

and periphery dealers separately. The data sample covers July1, 2001 through April 30, 2017.

Newey-west standard errors with 12-month lags are shown in parentheses. *p<.05; **p<.01;

***p<.001

54

Table 8: Forecasting Annual Ex Ret using IDB Ratios across Different Maturity Buckets

Annual Ex Ret on Treasury Bonds (%)

2Y 3Y 4Y 5Y 10Y 30Y

(1) (2) (3) (4) (5) (6)

Panel A. Forecasting with IDB Ratio and 3-6Y IDB Ratio

IDB Ratio(sd) 1.621*** 3.354*** 4.932*** 6.188*** 10.362*** 24.312***(0.506) (0.978) (1.256) (1.514) (2.980) (9.249)

3-6Y IDB Ratio(sd) -0.700** -1.510** -2.243*** -2.638*** -3.992*** -12.260**(0.323) (0.626) (0.753) (0.850) (1.182) (5.919)

Constant -0.321 -0.479 -0.557 -0.660 -0.676 -6.026(0.339) (0.646) (0.884) (1.108) (2.162) (6.567)

Observations 174 174 174 174 174 174R-squared 0.150 0.163 0.172 0.179 0.168 0.081

Panel B. Forecasting with IDB Ratios across All Buckets

IDB Ratio(sd) 0.036 0.352 1.186 2.119 7.023 30.911**(0.426) (0.878) (1.513) (2.221) (5.345) (14.080)

1-3Y IDB Ratio(sd) 0.919*** 1.735*** 2.117*** 2.252** 1.426 -5.478(0.251) (0.494) (0.765) (1.079) (2.565) (7.373)

3-6Y IDB Ratio(sd) -0.601*** -1.322*** -2.008*** -2.383*** -3.784*** -12.680**(0.209) (0.405) (0.548) (0.630) (1.092) (5.142)

11-30Y IDB Ratio(sd) 0.024 0.057 0.179 0.297 1.168* 3.515*(0.148) (0.275) (0.377) (0.442) (0.624) (1.880)

Constant 0.554* 1.179** 1.514* 1.590 1.181 -9.630(0.299) (0.570) (0.904) (1.218) (2.632) (7.233)

Observations 174 174 174 174 174 174R-squared 0.320 0.322 0.291 0.267 0.206 0.125

Univ. R-Squared 0.068 0.063 0.057 0.077 0.117 0.001

R-Squared using Forwards 0.206 0.218 0.250 0.232 0.250 0.179

Notes: The table above shows the results from forecasting the one-year excess return of a zero

coupon bond ranging from two- (column one) through thirty- (column 6) years in maturity.

Two- through five-year maturity bonds are Fama-Bliss zero coupon bonds from CRSP, while

the 10 and 20-year maturity bonds come from from Gurkaynak et al. (2007). In Panel A, the

independent variable is the interdealer broker (IDB) ratio and the IDB ratio calculated from

only three- to six-year maturity securities. In Panel B, we add ratios calculated over

additional maturity buckets. The IDB ratio is calculated from Treasury transaction volume

data collected from Primary Dealers in the FR2004 reports; it represents the fraction of total

trade which is conducted with other dealers through an IDB. The data sample is monthly and

the main sample covers January 1, 1964 to December 31, 2015. 10-year returns only become

available in August 1, 1971 (column five) and 30-year yields in November 1, 1985 (column

six). Newey-west standard errors with 18-month lags are shown in parentheses. *p<.05;

**p<.01; ***p<.001

55

Table 9: Forecasting Agency Ex Ret using Agency and Treasury IDB Ratios

Annual Ex Ret on Barclarys Agency Index (%)

(1) (2) (3) (4)

Panel A. Forecasting using Agency IDB Ratio

Agency IDB Ratio (sd) 1.120*** 0.831* 0.449*** 0.368***(0.422) (0.450) (0.142) (0.138)

Constant 2.196*** -1.915* 2.077*** 2.114***(0.489) (1.033) (0.152) (0.493)

Observations 215 215 215 215R-squared 0.123 0.279 0.783 0.798Control for Forward Rates NO YES NO YESControl for Treasury PCs NO NO YES YES

Panel B. Forecasting using Treasury IDB Ratio

Treasury IDB Ratio (sd) 0.042 -0.080 -0.003 -0.017(0.063) (0.059) (0.020) (0.017)

Constant -1.890 5.457 2.641 3.406*(6.860) (5.874) (2.169) (1.893)

Observations 312 312 312 312R-squared 0.006 0.199 0.816 0.834Control for Forward Rates NO YES NO YESControl for Treasury PCs NO NO YES YES

Notes: The table above shows the results from forecasting the one-year excess return based on

the Barclays Agency Index, which comes from Bloomberg. The excess return is calculated as

the percent change in the Agency index minus the short rate. In Panel A, the independent

variable is the interdealer broker (IDB) ratio calculated using all agency transactions; and in

Panel B, the the independent variable is the interdealer broker (IDB) ratio calculated using all

Treasury transactions. The IDB ratio is calculated from transaction volume data collected

from Primary Dealers in the FR2004 reports, and it represents the fraction of total trade

which is conducted with other dealers through an IDB. The data sample is monthly and

covers March 1, 2001 to December 31, 2015. Newey-west standard errors with 18-month lags

are shown in parentheses. *p<.05; **p<.01; ***p<.001

56

Table 10: Forecasting MBS Ex Ret using MBS and Treasury IDB Ratios

Annual Ex Ret on Barclarys MBS Index (%)

(1) (2) (3) (4)

Panel A. Forecasting using MBS IDB Ratio

MBS IDB Ratio (sd) 0.665* 0.317 0.259 0.151(0.364) (0.311) (0.219) (0.214)

Constant 2.795*** -2.116* 2.641*** 1.390*(0.472) (1.109) (0.211) (0.773)

Observations 215 215 215 215R-squared 0.0357 0.210 0.721 0.708Control for Forward Rates NO YES NO YESControl for Treasury PCs NO NO NO YES

Panel B. Forecasting using Treasury IDB Ratio

Treasury IDB Ratio (sd) 0.148* 0.173*** 0.004 0.007(0.076) (0.060) (0.024) (0.020)

Constant -12.790 -20.286*** 2.459 0.747(8.523) (6.754) (2.598) (2.392)

Observations 480 480 362 362R-squared 0.00567 0.0842 0.815 0.799Control for Forward Rates NO YES NO YESControl for Treasury PCs NO NO YES YES

Notes: The table above shows the results from forecasting the one-year excess return based on

the Barclays Mortgage-backed Securities (MBS) Index, which comes from Bloomberg. The

excess return is calculated as the percent change in the MBS index minus the short rate. In

Panel A, the independent variable is the interdealer broker (IDB) ratio calculated using all

MBS transactions; and in Panel B, the the independent variable is the interdealer broker

(IDB) ratio calculated using all Treasury transactions. The IDB ratio is calculated from

transaction volume data collected from Primary Dealers in the FR2004 reports, and it

represents the fraction of total trade which is conducted with other dealers through an IDB.

The data sample is monthly and covers March 1, 2001 to December 31, 2015. Newey-west

standard errors with 18-month lags are shown in parentheses. *p<.05; **p<.01; ***p<.001

57

8 Appendices

Figure A1: Fixed Income Assets of U.S. Broker-Dealers over Time

Notes: The figure above shows the total fixed income assets held by the U.S. security broker-

dealers on an annual basis between 1945 and 2016. The data comes from the flow of funds

(FOF) accounts of the United States and is provided in the Z1.statistical release by the Board

of Governors. Total fixed income holdings is calculated as the sum of the broker dealers total

assets in Treasury bonds, municipal bonds, corporate bonds, agency bonds, and commercial

paper.

58

Figure A2: Robustness to Incomplete Data

Notes: The figure above shows the percent of variation in future returns explained by the inter-

dealer broker (IDB) ratio (red) versus average dealer inventory (black), based upon simulations

from the stylized model. The x-axis shows the percent of customer orders which are unobserved,

so that they are neither recorded in the observed average inventory nor the observed transaction

volumes that create the IDB ratio. However, they still affect market prices and, thus, future

returns. Each dot corresponds to a regression from 10,000 random simulations.

59

Figure A3: A Sample Simulation

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

0 200 400 600 800 1000 1200

01

23

45

Time

Ord

er V

olum

e

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●●

●

●

●

●●

●●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●●

●

●

●●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●●●

●●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●●

●●

●

●●

●

●●

●●

●

●●

●

●●

●

●

●

●

●

●

●

●●

●

●

●

●

●●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

●●

●

●

●

●

●

●

●

●

●

0 200 400 600 800 1000 1200

02

46

8

Time

Inte

rdea

ler

Vol

ume

●

●

●

●●

●

●

●

●●●

●●●●

●●●●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●●●●

●●●

●●●

●

●●●

●

●●●

●●●

●●●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●●

●

●

●

●●

●

●

●

●●●

●

●●

●●

●

●●●●

●

●

●

●●

●

●●

●●

●

●●

●●●

●●●

●●●

●

●

●●

●

●●●

●

●

●

●●●●

●●●

●

●

●●●●

●

●

●●

●●●

●

●

●

●

●

●

●●

●

●●

●●

●●●

●●

●

●

●

●

●●●●

●

●●●●

●

●●●●

●

●

●●

●●●●

●

●

●●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●●

●●●●

●●●●

●

●

●●●

●

●

●

●●●●

●●●

●

●

●●●

●

●

●●

●

●●●

●

●●●●●●

●

●

●●

●

●●

●●

●

●●●

●●●

●

●●

●●●

●●

●●●

●●

●

●●●

●

●●

●●●

●

●

●

●●

●●

●

●

●●●

●●●●●

●

●

●●

●

●

●●●

●●●

●●

●

●●

●●

●

●

●●●

●●

●●

●●●●●●

●●

●

●

●

●

●●●

●●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●●●

●

●

●●

●●

●●

●●●●

●●

●●

●●●●

●

●

●●

●●●

●●●●

●

●●

●●

●

●

●●

●●●

●●●●

●●

●

●●●

●●

●

●●●

●●

●

●●●

●

●●

●

●●●●

●

●●

●●

●

●●

●

●●●●

●

●●

●

●●

●

●●●●●●

●

●●

●

●

●●

●

●

●●

●●

●●●●●●

●

●

●●●●●●

●

●

●

●●●●

●●

●

●●●●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●●

●●●●

●

●

●●●●●●●●

●●●●●●

●●

●●

●

●

●

●●●

●

●●

●●

●●

●●

●●

●●●

●

●

●

●●

●●

●●

●

●●

●

●

●●

●●●●

●●●●

●●

●●●

●

●

●

●●●

●

●●●

●●

●●

●

●●

●

●

●

●●●

●

●

●●●

●

●●●●●

●

●

●●●

●●

●●

●●

●●

●

●

●●●

●●●

●

●●●

●●

●

●

●●

●●

●●●●●

●●

●

●

●

●●

●●●

●●●

●●●●●

●

●●●

●

●●●

●

●●●

●●

●●

●

●

●●

●●

●●●●

●●●●●●

●

●

●●

●

●

●●

●

●

●

●●

●●

●●

●●

●●

●

●●●●●

●●●

●●●●

●●

●

●

●

●●

●

●●

●

●●

●

●

●●●

●

●

●●

●

●

●●

●●

●

●

●●

●●●

●●

●●

●●●

●●●●●

●

●●●●●

●●

●

●●●

●●●●

●●●●●

●●●●●

●●●

●

●

●

●●

●●

●●

●●●

●

●

●●

●●

●

●

●

●

●●

●●

●●

●●●

●●

●

●

●●●

●

●

●●

●

●●●●

●

●

●●

●

●●

●●●●●●●

●

●●

●

●

●●●●

●●●

●●●●●

●

●●●●

●●

●●

●●

●●

●●

●●

●●

●●●●●●

●

●●

●

●●

●●●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●●●

●

●

●

●

●●●●●●

●

●●●●

●

●

●●●●

●●●●●

●●●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●●●

●●

●●

●●

●●

●●●

●

●

●

●

●

●●●

●

●

●●●●

●

●

●●

●

●●

●

●

●●

●●

●●

●

●

●●●●

●●●

●

●●●●●

●●●

●

●

●●

●●●●

●

●

●

●

●

●●

●

●●●●

●●

●

●●

●

●●●

●

●

●●

●●

●●●●

●

●

●●

●

●

●

●●●

●

●

●●●●

●●●

●●●●●

●●

●●

●

●●

●

●

●

●

●

●●●

●●●●

●●●●●

●●●●

●

●●

●●

●●●●●●●●

●

●

●●

●

●

●

●

●

●

●

●●●●

●●●

●

●

●●●

●

●

●

●

●●●●

●●

●●●

●

●

●

●●●

●●

●●

●

●●●●●●

●●●

●●

●

●

●●●

●

●●●●●

●

●

●

●

●●

●

●

●

●●●

●●●

●●●●

●

●

●●

●

0 200 400 600 800 1000 1200

0.98

0.99

1.00

1.01

1.02

Time

Pric

e

●●●

●

●●

●

●

●

●●●

●●●●

●●●●

●

●

●●

●●●

●

●

●

●●

●

●●

●

●

●

●

●

●●

●●

●●●

●

●

●

●

●●●

●

●●●

●●●

●●●

●

●●●

●

●

●

●

●

●

●

●●

●●

●●

●●

●

●

●

●●

●

●

●

●●●

●

●●

●●

●

●●●

●

●

●

●

●●

●

●●

●●

●

●●

●●●

●●●

●●●

●

●

●●

●

●●●

●

●

●

●

●●

●

●●●

●

●

●

●●●

●

●

●●

●

●●

●

●

●

●

●

●

●●

●

●●

●●

●●●

●●

●

●

●

●

●●

●

●

●

●●●●

●

●●●●

●

●

●●

●●●●

●

●

●●

●

●

●

●●

●●

●

●●

●

●

●

●

●

●●●

●

●

●●

●

●

●

●

●●

●●●●

●●●●

●

●

●●●

●

●

●

●●●

●

●●●

●

●

●●●

●

●

●●

●

●●●

●

●●●●●●

●

●

●●

●

●

●

●●

●

●●●

●●●

●

●●

●●

●

●●

●●●

●●

●

●●●

●

●

●

●●●

●

●

●

●●

●

●

●

●

●●●

●●●●●

●

●

●●

●

●

●●●

●●●

●●

●

●●

●●

●

●

●●●

●●

●●

●●●●●●

●●

●

●

●

●

●●●

●●

●●

●

●

●

●

●

●

●●

●●

●

●

●

●●●

●

●

●●

●●

●●

●●●●

●●

●●

●●●●

●

●

●

●

●●●

●●●●

●

●●

●●

●

●

●●

●●

●

●●●●

●●

●

●●●

●●

●

●●●

●●

●

●●●

●

●●

●

●●

●●

●

●●

●●

●

●●

●

●●●●

●

●●

●

●●

●

●●●●●●

●

●●

●

●

●●

●

●

●●

●●

●●●●●●

●

●

●●●

●●●

●

●

●

●●●●

●●

●

●●●●

●●

●

●●

●

●

●●●

●

●

●

●

●

●

●●

●

●●●

●

●

●●●●●●●●

●●●●●●

●●

●●

●

●

●

●●●

●

●●

●●

●●

●●

●●

●●●

●

●

●

●●

●●

●●

●

●●

●

●

●●

●●●●

●●●●

●●

●●●

●

●

●

●●●

●

●●●

●●

●●

●

●●

●

●

●

●●●

●

●

●●●

●

●●●●●

●

●

●●●

●●

●●

●●

●

●

●

●

●

●●

●●●

●

●●●

●●

●

●

●●

●●

●●●●●

●●

●

●

●

●●

●●●

●●●

●●●●●

●

●●●

●

●●●

●

●

●●

●

●

●●

●

●

●●

●●

●●●●

●●●●●●

●

●

●●

●

●

●●

●

●

●

●

●

●●

●●

●●

●●

●

●●●●●

●●●

●●●●

●

●

●

●

●

●●

●

●●

●

●●

●

●

●

●●

●

●

●●

●

●

●●

●●

●

●

●●

●●

●

●

●

●

●

●●●

●●●●●

●

●●●

●●

●●

●

●●●

●●●●

●●●●●

●●●●●

●●●

●

●

●

●●

●●

●●

●●●

●

●

●●

●●

●

●

●

●

●

●

●●

●●

●●●

●●

●

●

●●●

●

●

●●

●

●●●●

●

●

●●

●

●●

●●●●●●●

●

●●

●

●

●●●●

●●●

●●●●●

●

●●●

●

●●

●●

●

●

●

●

●●

●●

●●

●●●●●●

●

●●

●

●●

●●●

●●

●

●

●●

●

●●

●

●

●

●

●●

●

●

●

●

●

●●

●●

●●●●

●

●

●

●

●●●●●●

●

●●●●

●

●

●

●●●

●●●●●

●●●●

●●

●

●

●

●

●●

●

●

●

●●

●

●

●

●●

●●

●

●

●●

●●

●●●

●

●

●

●

●

●

●●

●

●

●●●

●

●

●

●

●

●

●●

●

●

●●

●●

●●

●

●

●●●●

●●●

●

●●●●●

●●●

●

●

●●

●●●●

●

●

●

●

●

●●

●

●●●●

●●

●

●●

●

●●●

●

●

●●

●●

●●●●

●

●

●●

●

●

●

●●●

●

●

●●●●

●●

●

●●●●●

●

●

●●

●

●●

●

●

●

●

●

●●

●

●●●●

●●

●●●

●●●●

●

●●

●●

●●●●●●●●

●

●

●●

●

●

●

●

●

●

●

●●●

●

●●●

●

●

●●●

●

●

●

●

●●●

●

●●

●●●

●

●

●

●●●

●●

●●

●

●●●●●●

●●●

●●

●

●

●●●

●

●●●●●

●

●

●

●

●●

●

●

●

●●●

●●●

●●●●

●

●

●●

0 200 400 600 800 1000 1200

−0.

6−

0.2

0.2

0.4

Time

Avg

Inve

ntor

y

Notes: The figure above shows one sample draw from the stylized model with parameters set

in Section 2.2. From left to right, top to bottom, we show total order volume, total interdealer

volume, market clearing prices, as well as average inventory over time.

60

Figure A4: Excerpt from Goldman Sachs 2018 10Q

Notes: The figure above shows an excerpt on Value-at-Risk (VaR) measures taken from the

2018 Goldman Sachs 10Q report. The highlighted text shows the relevant lines regarding use

of the VaR in managing risk as well as setting sub-limits on day-to-day risk exposures.

61

Figure A5: Out-of-Sample Prediction with IDB Ratio Alone

Notes: The figure above shows annual excess returns for a five-year Treasury bond (black

line) and its rolling out-of-sample forecast (blue line) using a univariate model just using the

interdealer broker (IDB) ratio. For each month, we use only data available up until that month

to fit the model and then forecast returns over the next 12 months. The IDB ratio is calculated

from Treasury transaction volume data collected from Primary Dealers in the FR2004 reports,

and it represents the fraction of total trade which is conducted with other dealers through an

IDB. More details on its construction can be found in Section 3.1. Annual excess return is

estimated using Fama Bliss zero coupon bonds, and it is calculated as the return from holding

a five-year maturity bond over the following year minus the risk-free rate. The forecasting

excercise covers January 1, 1974 through December 31, 2015.

62

Figure A6: Out-of-Sample Prediction with IDB Ratio and Forward Rates

Notes: The figure above shows annual excess returns for a five-year Treasury bond (black line)

and its rolling out-of-sample forecast (blue line) using a model which includes the one- through

five-year forward rates and the interdealer broker (IDB) ratio. For each month, we use only

data available up until that month to fit the model and then forecast returns over the next

12 months. The IDB ratio is calculated from Treasury transaction volume data collected from

Primary Dealers in the FR2004 reports, and it represents the fraction of total trade which is

conducted with other dealers through an IDB. Annual excess return is estimated using Fama

Bliss zero coupon bonds, and it is calculated as the return from holding a five-year maturity

bond over the following year minus the risk-free rate. The forecasting excercise covers January

1, 1974 through December 31, 2015.

63

Table A1: Orthogonalizing Raw Ratio to Number of Dealers

Ln(raw ratio)(1)

Ln(# dealers) 0.716***(0.019)

Constant -3.551***(0.063)

Observations 624R-squared 0.701

Notes: The table above shows the results from explaining log raw ratio using log number of

primary dealers. The raw ratio comes from Treasury transaction volume data collected from

Primary Dealers in the FR2004 reports, and it is calculated as total interdealer broker (IDB)

volume divided by total volume (IDB volume plus other volume). The number of primary

dealers comes from a historical list published by the Federal Reserve Bank of New York. The

data sample is monthly and covers January 1, 1964 to December 31, 2015. Standard Errors

are shown in parentheses. *p<.05; **p<.01; ***p<.001

64

Table A2: Trade Volumes and Interest Rate VaR Regression

Interest Rate VaR

(1) (2) (3)

IDB Trade(%) 0.002(0.003)

Other Trade(%) 0.002(0.002)

IDB Ratio(sd) 19.16∗∗∗

(19.159)Constant 0.09 0.08 −52.565∗∗∗

(0.12) (0.11) (1.33)

Observations 156 156 156Adjusted R2 0.10 0.12 0.52

Notes: The table above shows the results from explaining the average interest rate

Value-at-Risk (VaR) using trade volumes and the IDB ratio. Average VaR comes from the

10Q reports of the primary dealers, when available. The independent variables are interdealer

broker (IDB) trade volumes as a percent of total Treasuries outstanding, other trade volumes

as a percent of total Treasuries outstanding, as well as the interdealer broker (IDB) ratio.

These variables are calculated from Treasury transaction volume data collected from Primary

Dealers in the FR2004 reports. The IDB ratio represents the fraction of total trade which is

conducted with other dealers through an IDB. More details on its construction can be found

in Section 3.1. The data sample is monthly and covers January 1, 1999 to December 31, 2015.

Newey-west standard errors with 18-month lags are shown in parentheses. *p<.05; **p<.01;

***p<.001

65

Table A3: Hansen Hodrick Standard Errors

Annual Ex Ret on 5Y Treasury Bond (%)(1) (2) (3) (4)

IDB Ratio(sd) 1.801*** 1.443***(0.553) (0.535)

1Y Forward Rate(%) -1.898*** -1.978***(0.679) (0.680)

2Y Forward Rate(%) -0.315 -0.818(0.841) (0.889)

3Y Forward Rate(%) 2.406*** 2.203**(0.912) (1.040)

4Y Forward Rate(%) 1.609** 2.150***(0.660) (0.601)

5Y Forward Rate(%) -1.517** -1.295*(0.657) (0.674)

Constant 1.366* -1.895 -2.230(0.714) (1.791) (1.762)

Observations 624 624 624R-squared 0.108 0.289 0.232

Notes: The table above shows the results from forecasting the one-year excess return of a

Fama-Bliss five-year zero coupon bond. The independent variables are the interdealer broker

(IDB) ratio and the one- through five-year forward rates. The IDB ratio is calculated from

Treasury transaction volume data collected from Primary Dealers in the FR2004 reports, and

it represents the fraction of total trade which is conducted with other dealers through an IDB.

The data sample is monthly and covers January 1, 1964 to December 31, 2015. Hansen

Hodrick standard errors, imposing equal weights on the first 12 lags, are shown in parantheses.

*p<.05; **p<.01; ***p<.001

66