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Federal Reserve Bank of Chicago

Price discovery in a market under
stress: the U.S. Treasury market in
fall 1998
Craig H. Furfine and Eli M. Remolona

WP 2005-06

Price discovery in a market under stress:
the U.S. Treasury market in fall 1998

Craig H. Furfine
Federal Reserve Bank of Chicago
230 South LaSalle
Chicago, IL 60604
United States
craig.furfine@chi.frb.org

Eli M. Remolona
Bank for International Settlements
Two International Finance Centre 78/F
8 Finance Street, Central
Hong Kong
eli.remolona@bis.org

The authors found helpful the comments of Claudio Borio, Wolfgang Bühler, Robert Engle,
Thierry Foucault, Eugene Kandel, Brian Sack, Asani Sarkar, Hyun Song Shin, Chester Spatt, Ilya
Strebulaev and participants in seminars at the Bank of Canada, Bocconi University, University of
Mannheim, the Federal Reserve Board of Governors, and the European Finance Association
meetings in Glasgow. They also wish to thank Lauren Gaudino and Marcus Jellinghaus for expert
data work. The views expressed are the authors' and not necessarily those of the Bank for
International Settlements, the Federal Reserve Bank of Chicago, or the Federal Reserve System.

Price discovery in a market under stress:
the U.S. Treasury market in fall 1998

Abstract
We analyze how price discovery in the inter-dealer market for U.S. Treasury
securities differs between stressful times and normal periods. Using tick-by-tick
data on inter-dealer transactions in the on-the-run two-year, five-year and 10-year
Treasury notes, we find that the impact of trades on prices tends to become
significantly stronger on stressful days. This effect remains after accounting for the
faster trading, wider spreads, and shallower depth observed on stressful days.

Keywords: price discovery, liquidity, depth, market makers, Treasury market

Price discovery in a market under stress:
the U.S. Treasury market in fall 1998

But “liquidity” is a straw man. Whenever markets plunge, investors
are stunned to find that there are not enough buyers to go around.
-- Lowenstein (2000), p. 42

Introduction
How different is price discovery in a market under stress? The U.S. Treasury market in

autumn 1998 was such a market. At that time, a hedge fund, Long-Term Capital Management
(LTCM), faced untenably heavy losses in Treasury securities, while some of its important
counterparties in other markets also happened to be dealers in the Treasury market. As a
consequence, the market experienced three unusual features. First, trading in Treasury securities
tended to be intense, with durations between transactions shorter than usual. Second, market
depth on both the buy and sell sides fell significantly. Third, bid-ask spreads widened noticeably.
It therefore appears that market makers became reluctant to take risks. The specific question we
ask is whether the relationship between trading flows and prices is qualitatively and
quantitatively different in such a market.
In the market microstructure literature, order flow affects prices because it conveys private
information regarding the value of the underlying asset. In Glosten and Milgrom (1985), for
example, market makers set a positive bid-ask spread as compensation for trades made with
counterparties with superior information. As a sequence of sell orders arrive, market makers

lower bid prices, incorporating the probability that the order flow implies that better-informed
investors believe the previous price was too high. In a general empirical framework, Hasbrouck
(1991) documents the positive relationship between order flow and price changes using a sample
of 80 NYSE and AMEX stocks.
The literature has since been extended to determine when order flow is expected to have
the greatest impact on prices. In particular, times of intense trading activity have been
distinguished from times of slow trading. In Admati and Pfleiderer (1988), discretionary liquidity
traders try to avoid losing money to the better informed by clustering their trading at around the
same time. Thus, the observation of multiple transactions occurring together suggests the
presence of predominantly uninformed traders. Order flow would then not be expected to have a
strong impact on prices. Contrast this intuition with that modeled by Easley and O’Hara (1992).
In their model, they allow for the possibility that no new information exists. As a result, an
increase in trading activity indicates that information has arrived, and therefore, order flow is
more informative when transactions are occurring rapidly.1 In a dynamic order-driven market,
Foucault, Kadan and Kandel (2005) distinguish between patient and impatient traders and show
that when waiting costs are large -- presumably when there is new information to exploit -traders will tend to be more aggressive in adjusting the prices in their limit orders.
The empirical evidence on when order flow is important suggests that it depends on the
market being considered. In foreign exchange markets, Lyons (1996) documents that trades are
less informative when they occur when transaction intensity is high, a finding consistent with the
theoretical prediction of Admati and Pfleiderer (1988). Lyons describes the phenomenon as “hot-

Diamond and Verrecchia (1987) model the interaction of short-sale restrictions on the information content of order
flow. Because of these constraints, a period of slow trading is likely to signal bad news. Further, these constraints
impart a delay in the reaction of prices to new information, especially to bad news.

potato” trading whereby foreign exchange dealers rapidly and repeatedly lay off unwanted
inventory in response to an initial potentially informed trade. By contrast, in equity markets,
Dufour and Engle (2000) explicitly incorporate the role of inter-transaction time in the empirical
framework of Hasbrouck (1991) and find that when equity markets are most active, i.e., intertransaction times are short, the impact of order flow on prices is enhanced. Thus, the empirical
literature has found opposite relationships between inter-transaction times and the price impact
of trading depending on the market being examined.2
Our paper contributes in many ways to the understanding of when order flow exerts a
stronger influence on prices. To begin, we expand the model of Dufour and Engle (2000) to test
whether the relationship between trading and returns in on-the-run US Treasury securities differs
when those markets are under stress. After controlling for the differences in the rate of trade
arrival, we still find a noticeably higher price impact of a trade on stressful days. Having
proposed several alternative methods for identifying stressful days, we document that such days
generally witness more rapid trading, wider bid-ask spreads, and lower posted depth. Thus, to
further explore the result that stress is associated with greater price impact (lower liquidity), we
expand our analysis to explicitly consider the role that spreads and depth play in the price
discovery process for US Treasury securities. After controlling for inter-transaction time,
spreads, and depth, we are left with the finding that trades continue to move prices more on
stressful days. Further, we estimate the fraction of the stress-related price impact that the readily

For the U.S. Treasury market, Brandt and Kavajecz (2004) find that “overflow” affects prices especially when
liquidity is low. However, they do not specifically analyze the effect of inter-transaction times.

observable measures of liquidity can explain and find it to be quite small relative to the thusfar
unexplained decline in liquidity that occurs on stressful days. 3
The remainder of the paper is as follows. Because microstructure analysis of US Treasury
markets is relatively uncommon, we devote Section 2 to explain why private information can be
expected to play a large role in the price discovery process of a security ultimately valued
according to beliefs about the macroeconomy and for which there is frequent and public
information. We further provide suggestive evidence that prices in US Treasury markets in 1998
were particularly more susceptible to private, rather than public information. Section 3 discusses
the key sources of private information in US Treasury markets during 1998 and suggest why
these events may have affected the relationship between trading and prices in the Treasury
market. Section 4 develops four different methods of identifying days that might have been
particularly stressful for Treasury dealers. Section 5 describes the data used in the study and
present summary statistics to describe the nature of the stress periods in the market. In particular,
we document that regardless of which of our four stress-identification methods used, stressful
days in US Treasury markets during 1998 were associated with (1) faster trading, (2) wider bidask spreads, and (3) shallower depth. Section 6 estimates an extension of the Dufour and Engle
(2000) model on data on the 2-, 5-, and 10-year Treasury note and finds that trades move prices
by much more on days we previously identified as stressful. Section 7 extends the analysis
further to control for changing spreads and depth. We document that changes in trading

Goldstein and Kavajecz (2004) analyze liquidity provision in equity markets by limit order traders during and near
the time of the steep equity market decline in October 1997. They find that liquidity, as measured by the depth of the
limit order book, declined precipitously on the day after the steep market decline. Their study, however, was focused
on an analysis of the impact of market-wide circuit breakers rather than on the price impact of trading during a
crisis. Further, their analysis focused only on equity markets.

frequency, spreads, and depth explain very little of the decline in market liquidity we find on
stressful days. Section 8 concludes.

Public versus private information in Treasury market price discovery
The announcement literature would suggest that public rather than private information

drives price movements in US Treasury markets. Indeed it has been documented that
macroeconomic announcements are often the source of the largest moves in Treasury security
prices. For example, Furfine (2001) reports that of the 25 largest five-minute price moves in the
on-the-run 5-year Treasury note during 1999, 19 were associated with a macroeconomic
announcement, 4 with an announced change in the Federal Reserve’s target federal funds rate,
and 2 were coincident with testimony delivered by Federal Reserve Board Chairman Greenspan.
In a study of Treasury markets from the mid-1990s, Fleming and Remolona (1999a) report, too,
that public news releases explain virtually all of the largest high-frequency price movements in
Treasury markets. Fleming and Remolona (1999b) further indicate that prices generally adjust
rapidly in the wake of an announcement without a large increase in trading. Thus, previous
literature documents that at very high frequencies, public information is the source of the larges
moves of US Treasury prices, and that these movements occur without a large amount of trading.
Although news releases on occasion move prices in a matter of minutes, Treasury prices
move a lot even when such public announcements are absent. In the minutes and hours after a
news release, however, prices of Treasury securities are influenced by trading for the same
reasons assumed in equity and other markets. For instance, although there may be a public news
release of the monthly employment report, Treasury market participants will differ (at a
minimum) according to (a) their beliefs with regard to the implication of the news for interest

rates and (b) the degree to which their current holdings of a particular security should be altered
in light of the news. As an illustration of both public and private sources of information
influencing Treasury market prices, Figure 1 graphs the price and trading volume of the on-therun 5-year Treasury Note on December 4, 1998. At 8:30 that morning, a surprisingly positive
employment report was announced. As the figure reports, Treasury prices fell quickly in the first
five minutes following the announcement. However, throughout the remainder of the day, heavy
trading pushed prices up and then back down, without the release of any new significant public
information. This suggests that although public information has a large impact on Treasury
prices over very short time intervals, the general relationship between trading and pricing can
still be modeled as being driven by private information.
Not only does private information have an important role in price discovery in Treasury
markets in general, but the relative importance of private versus public information during the
fall of 1998 appears to have been greater than was different from the periods examined by
Furfine (2001) and Fleming and Remolona (1999a). First, although late 1998 witnessed its share
of large and rapid price movements, these were less often associated with macroeconomic news
releases. Table 1 lists the largest 25 five-minute price changes of the 5-year on-the-run Treasury
Note occurring between May 1, 1998 and December 31, 1998. Of these, only five were
associated with macroeconomic news announcements, 4 with changes in the Fed’s policy rate,
and 2 with statements from Alan Greenspan. As Table 1 illustrates, the majority of large price
changes in late 1998 were not associated with an obvious, direct piece of macroeconomic news.
In this way, private interpretation by market participants of events such as a weakening dollar,
political anxiety, and the Russian economy played a larger role in price movements than is
typically seen.

3. Private information, Long-Term Capital Management, and Treasury markets in 1998
The importance of private information in the U.S. Treasury market should come as no
surprise. It is a multiple-dealer market in which, as in the classic model by Ho and Stoll (1980),
dealers face inventory risk in competing against one another. Unlike the model, however, U.S.
Treasury dealers also take highly leveraged proprietary positions and thus must rely on private
information.
Among the most significant sources of private information in Treasury markets during late
1998 related to the hedge fund Long-Term Capital Management (LTCM). This fund had taken
large positions in Treasury securities and Treasury related securities like swaps. As LTCM
became financially troubled in August 1998, market participants remained uncertain regarding
the size of LTCM’s positions, the hedge fund’s likely response to its difficulty, and the trading
response of other market participants that had taken similarly losing bets in financial markets.
Developments with LTCM were likely to result in less risk-taking by US Treasury dealers,
consistent with the empirical evidence we will provide.
By late August 1998, the partners of LTCM knew they were in trouble. Among other
losing positions, the hedge fund held long positions in swaps and short positions in on-the-run
Treasury securities.4 When spreads between 10-year swap yields and Treasury yields widened by
10 basis points on 21 August, the hedge fund faced untenably large losses. That Monday, the
partners started seeking new investors, while the spread continued to widen. The next day, the
10-year spread reached 84 basis points, the widest spread the fund had seen since it started

See the excellent accounts by the Committee on the Global Financial System (1999) and Lowenstein (2000). For
more on LTCM’s trading strategies, see Edwards (1999), President’s Working Group on Financial Markets (1999)
and Jorion (2000).

operating. The spread had increased 21 basis points over just three trading days. As volatility in
this spread continued in September, the fund failed to raise enough funds to cover its losses.
Finally, on 23 September, the fund's major creditors agreed to recapitalize it. Losses continued
into October as swap spreads widened further, reaching 93 basis points on 5 October, the day of
the single greatest rise in spreads. On 14 October, the 10-year swap spread reached its peak at 97
basis points.
There are good reasons to believe the troubles of LTCM affected price and trading
behavior in the U.S. Treasury market. The Johnson Report of the Committee on the Global
Financial System (hereafter, CGFS (1999)) points to three ways in which market strains were
exacerbated following the fund's admission in early September of large losses. First, market
participants traded on anticipation that LTCM would have to close out its positions. Second,
dealers apparently anticipated counterparty losses from their positions with LTCM and thus saw
their own capacity to absorb risk to be lower than before. And third, dealers began to harbor
doubts about the creditworthiness of other firms that had emulated LTCM's strategies, and thus
perceived a rise in the counterparty risk of dealing with these other firms.
Why would the knowledge that LTCM needed to close out its positions alter price and
trading behavior? At the very least, dealers may try to trade ahead of LTCM, a strategy described
as “predatory trading” by Brunnermeier and Pedersen (2005). Indeed Cai (2002) finds evidence
of such front-running behavior. More importantly, LTCM’s positions were thought to be very
large, but there was uncertainty about precisely how large these were and what LTCM’s
unwinding strategy would be. Gennotte and Leland (1990) model a similar situation in October
1987, when market participants knew that dynamic hedging strategies required program traders
to sell equities but were unsure about the size of the traders’ positions. The uncertainty about

order flows, even what are supposed to be just liquidity flows, gave prices an unusually critical
role in the formation of expectations, a situation that ultimately led to a sudden withdrawal of
market making and to the crash of 19 October 1987. In the case of the LTCM episode, CGFS
(1999) and Furfine and Remolona (2002) document that various spreads widened, including
spreads between swaps and Treasury securities and between off-the-run and on-the-run
Treasuries. Chordia, Sarkar, and Subrahmanyam (2005) also note wider bid-ask spreads in
Treasury markets during the last half of 1998 and therefore add dummy variables to distinguish
this period in their time series analysis of comovement of stock and bond liquidity.
There have been a few other studies based on the events surrounding LTCM. Kho, Lee and
Stulz (2000) document that the equity prices of the firms that would ultimately participate in the
bailout of LTCM declined on the days surrounding 2 September, when it first became public that
LTCM had suffered large losses in August. The magnitude of the decline even exceeded
similarly calculated declines around the time of the previous financial crises in Mexico, Korea,
Russia, or Brazil. Furfine (2006) finds that these same institutions were still able to maintain
their levels of overnight unsecured borrowing during the crisis period. Combined with the
findings of Kho, Lee and Stulz, Furfine’s finding suggests that although the LTCM episode had a
dramatic impact on bank equity valuations, it did not threaten any major bank’s solvency.
Furfine further finds that these same financial institutions dramatically began to curtail risktaking in the days leading up to LTCM’s resolution in ways consistent with reductions in shortterm trading activities.
All these studies suggest at least two reasons why the Treasury market on certain days in
autumn 1998 may be considered to have been fundamentally different from other days. First,
market depth fell noticeably. Second, most dealers may be expected to have become more

reluctant to make markets during this period. They were unsure about the size of LTCM’s
positions and those of the fund’s emulators. Many of the dealers had already incurred trading
losses in August, especially from exposures to Russia.5 Some also happened to be counterparties
of LTCM and were concerned about the possibility of the hedge fund's default. Thus, dealers
may be expected to have withdrawn from risk taking, perhaps by increasing their bid-ask spreads
and by reducing the quantity they were willing to trade at posted prices (their posted depth).6
Note that there is no clear implication that trading activity should become more intense during
this period, but this is something we will find in the data.

Identifying stress days in 1998
For the purposes of our analysis of day-to-day stress, it is important that we try to identify

stress days independently of what is going on in the US Treasury market itself. This is to avoid
assuming what we are trying to show, which is that the market behaves differently during these
days. Narratives of the LTCM episode, for example, tend to focus on days when the spread of
swap yields over Treasury yields widened sharply. Using such spread movements as a criterion,
however, would mean choosing some days in which the Treasury yield fell, making it somewhat
difficult to disentangle our results from our choice of stress days. Since there is no established
alternative way of identifying these days, we propose four definitions. Table 2 reports the days
identified under the various definitions. The first definition is based on significant events
identified by two narratives of the LTCM episode. The others are based on information from
markets other than the Treasury market that would indicate reluctance by Treasury dealers to

See President's Working Group on Financial Markets (1999).

In a theoretical model of convergence trading, Xiong (2001) shows how capital losses would cause convergence
traders, such as LTCM and some dealers, to reduce their risk-bearing capacity.

perform their market-making role. These definitions give us different numbers of stress days,
ranging from four days to 70 days. We undertake the analysis for each of the four definitions.
1. Stress days I: For our first definition of stress days, we rely on events identified by CGFS
(1999) and Lowenstein (2000) as being significant for the LTCM crisis. As shown in Table
2, these events give us 21 days, starting on July 6, when Salomon began to wind down its
bond arbitrage operation, and ending on October 10 and 11, when Ellington Capital
Management auctioned $1.5 billion of mortgage securities. This definition does include two
days (September 10 and October 9) that refer to sharp movements in on-the-run Treasury
yields and one day (September 12) that is about a widening of the swap spread, which is
presumably calculated with the on-the-run Treasury yield.
2. Stress days II: For our second definition, we rely on information from the stock market.
Kho, Lee and Stulz (2000) identify four days in which the stocks of four banks exposed to
LTCM significantly underperformed the stocks of non-exposed banks. These exposed banks
were also dealers in the Treasury market. While news about LTCM’s losses became public
on September 2, Kho, Lee and Stulz find that the four banks had negative returns starting on
the day before and these losses continued for the next two days. As shown in Table 2, during
the three days in question, the banks suffered abnormal returns of -14.2% relative to nonexposed banks. On September 24 again, these banks’ stocks underperformed by 2.56%, after
market participants learned how much each bank would contribute to LTCM’s
recapitalization. This definition gives us four stress days.
3. Stress days III: For our third definition, we rely on information from the corporate bond
market. Rather than use corporate spreads directly, we rely on estimates by Reinhart and
Sack (2002). They use weekly interest rate data to decompose the spread of 10-year double-

A corporate bonds over on-the-run Treasury securities into various premia associated with a
credit risk factor, a liquidity factor and an idiosyncratic Treasury factor. The advantage of
using their estimates is that their decomposition is designed to isolate their estimates of credit
risk premia from any influence of the Treasury market, allowing us to consider their
estimates to be exogenous to the market we are analyzing. The corporate bond yields used
also happen to be the appropriate ones, because most bank dealers in the Treasury market
have double-A credit ratings. For 14 weeks during our sample period, shown in Table 2, the
estimated credit risk premium exceeds 60 basis points and is markedly higher than during
any other week. Using these weeks for our stress days gives us a continuous period of 57
trading days.
4. Stress days IV: For our fourth definition, we rely on information from the swaps market. We
identify the ten days in our sample period during which the five-year swap yield rose the
most. As shown in Table 2, each of these ten days saw swap yields rise by at least 7 basis
points. Since LTCM had long positions in swaps, sharp yield increases would have added to
its counterparties’ concerns that it might default. If, as reported, a number of dealers had
emulated LTCM’s swap positions, they themselves would have faced heavy losses from such
increases in swap yields.
The four definitions differ significantly in the specific stress days they identify. The most
apparent differences are in the number of days they each provide. The Johnson-Lowenstein
events (stress days I) provide 21 days, the Kho-Lee-Stulz bank returns (stress days II) four days,
the Reinhart-Sack credit spreads (stress days III) 57 days and the swap yield increases (stress
days IV) 10 days. There are also systematic differences in where in the calendar period they tend
to select stress days. The 20 days of stress days I are spread largely across August and

September, the four days of stress days II are all in September, the 57 days of stress days III
cover most of the trading days from September through November, and the 10 days of stress
days IV are found mostly in September through December.

High-frequency data from the inter-dealer Treasury market
Our U.S. Treasury data cover eight months of tick-by-tick quotes and transactions in the

inter-dealer market. The source of the data is GovPX, which consolidates data from five of six
inter-dealer brokers, accounting for perhaps half of all transactions in the market. The data
include the best bid and offer quotes for each security, the depths for both ask and bid quotes, the
price and size of each trade, and an indicator for whether the trade was initiated by a buyer or a
seller. Our analysis uses data on the 2-year on-the-run Treasury notes, 5-year on-the-run
Treasury notes and 10-year on-the-run Treasury notes.7
Our data sample runs from May 1, 1998 to December 31, 1998. To avoid times of very
slow trading activity, we exclude trades occurring outside of US business hours, with business
hours being defined, as in Fleming and Remolona (1999a and 1999b), as 7:30 AM to 5:00 PM
ET. We further drop the data for 8 days that are all associated with an extended market break
involving a major US holiday. This criterion excludes one day that otherwise would have been
considered stressful, October 9, because of its proximity to the Columbus Day weekend. Because
we are interested in the typical relationship between inter-transaction time and market dynamics,
we would like to avoid the possibility of atypically slow trading days influencing our results. We
also drop observations on 3 days where there were problems with the GovPX data for at least
part of the day. Finally, to avoid confounding the data with large overnight price changes, we

follow Dufour and Engle and drop observations near the beginning and end of each business day.
After these adjustments to the data, we are left with 67,428, observations for the 2-year note,
103,377 observations for the 5-year note, and 83,999 observations for the 10-year note.
As shown in Table 3, our 8 months of data covers 156 trading days. The three different
securities have different typical levels of trading (as captured by GovPX), with the 2-year note
having the most value traded, but the 5-year note having the highest number of trades. For all
three securities, buyer initiated transactions are more common than those initiated by a seller.
This is consistent with the role of the primary securities dealers. These market participants buy
new Treasury securities at auction and then gradually liquidate their position by the next auction.
In combination with their commitment to make markets in these securities, major dealers would
gradually reduce their position in on-the-run issues through the posting of limit orders, which
ultimately will lead to buyer-initiated trades. All three securities are relatively actively traded,
with a transaction occurring approximately once a minute. Depths and spreads are also reported
in Table 3 to give a basis of comparison to interpret the magnitude of changes that occurred on
particularly stressful days. For example, the average posted depth was just over $17 million for
the 2-year note.
Our empirical analysis in the following sections will be an attempt to quantify the degree to
which stress affects the price discovery process in Treasury markets. These markets are where
LTCM held losing positions. As mentioned above, LTCM held short positions in on-the-run
Treasury securities and long positions in swaps. Some dealers in the market had emulated
LTCM's strategies and thus held similar positions. To unwind these positions, LTCM and its
emulators would have had to buy Treasury securities, and many market participants seem to have

The on-the-run security is the most recently issued security of a given original maturity. This is the security (of a

known this. Some of the same dealers were also LTCM's counterparties in the swap contracts
and were thus exposed to risk that LTCM would default. The data allow us to examine the
dynamics of prices and trade flows for on-the-run Treasury securities under these conditions.
Before turning to a more formal analysis, we provide some indicative evidence to suggest
changes that occurred in the Treasury market on stressful days. To do so, we first converted the
tick-by-tick data into data observed at 15-minute intervals. For instance, transactions within a
given 15 minute interval were combined (e.g. depth was averaged, trading volume was totaled).
We then ran a simple linear regression of various characteristics of the data (e.g. volume, depth)
on intraday dummy variables (to control for intraday variation) and a single indicator for one of
the four definitions of stress. The coefficients and robust standard errors on the stress coefficients
are reported in Table 4. There are many features of the data apparent in this preliminary data
exploration that are worth highlighting for the purposes of our subsequent price discovery
analysis.
First, the number of transactions and average dollar value traded rose noticeably on
stressful days. For example, the dollar value traded of the 2-year note rose between $2.7 billion
per day and $5.2 billion per day depending on the definition of stress being considered. Although
theory does not necessarily predict a positive relationship between trading volume and stress, we
find this to be the case for all three securities whenever the coefficient is statistically significant
(9 out of 12 times). This increase in trading activity maps directly into a reduction in the average
time between trades for all three securities.
We also find evidence that market makers became more risk averse, consistent with our
discussion in Section 3. For example, the average quoted depth in the market became shallower

given original maturity) with the most active trading.

during the stressful days. In the case of the 5-year note, average bid depth fell by between $1.13
million and $3.37 million (from its average value of $9.3) on stressful days. We find that depth at
both the bid and ask price generally declined on stressful days, and fell most using stress
definition III (wide credit spreads). Using this measure of stress, depth in Treasury markets was
roughly 40% lower on stressful days than its full-sample average.
Table 4 also documents that bid-ask spreads in the Treasury market were wider on stress
days relative to the entire sample period. In general, bid-ask spreads for on-the-run Treasury
notes range from 0.6 basis points for the 2-year note to 2.2 basis points for the 10-year note.
Although the point estimates vary across securities and across stress definitions, we find that
spreads were generally wider by roughly 30%-40% on stressful days. In sum, we can
characterize Treasury markets to (1) be more active, (2) have lower posted depth, and (3) have
wider spreads on stressful days.

A VAR representation of price discovery in the U.S. Treasury market
The results in the previous section suggest that dealers became more reluctant to make

markets during stressful days of 1998. This would imply a reduction in market liquidity. In
Hameed, Kang and Viswanathan (2005), a decline in the collateral value of market makers leads
to a fall in liquidity. To explore this possibility more formally for the U.S. Treasury market, we
estimate a price discovery model that builds upon the work of Hasbrouck (1991) and Dufour and
Engle (2000). We do this in two steps. First, we simply adopt Dufour and Engle’s approach of
explicitly incorporating inter-transaction time into Hasbrouck’s VAR model of prices and trades
and calculate a benchmark for the price impact of a trade in US Treasury markets. We then
expand the model to allow price impact to vary according to whether or not the day was

considered stressful. In this way, we are able to determine whether price impact was changed on
stressful days after controlling for the aforementioned reduction in inter-transaction time.
Our empirical model consists of two equations: one for returns (quote revisions) and one
for direction of trades. We define our measure of returns, rt , as the change in the log mid-quote
price between the trade at time t and trade at t+1. Hence, rt ≡ 100(ln qt +1 − ln qt ) . For trade
direction, we use Hasbrouck's (1991) indicator variable xt0 , which is equal to +1 if the trade is a
take (it is initiated by the buyer) and –1 if it is a hit (seller initiated).8 Recall that the GovPX data
includes information as to whether the trade was buyer or seller initiated so there is not an issue
of correctly identifying trades as there often is in studies of US equity markets.
Dufour and Engle’s (2000) model explicitly accounts for trading intensity by interacting a
duration variable ln (Tt ) with xt0 , where Tt is measured as one plus the number of seconds
between trades at times t and t-1.9 Our benchmark equations, therefore, can be expressed as
shown in equations (1) and (2).
5

rt = ∑ a r + ∑ b r ln (Tt −i ) + ∑ c x + ∑ dir xt0−i ln (Tt −i ) + v1t
r
i t −i

i =1

r
i t −i

i =1

r 0
i t −i

i =0

(1)

i =0

i =1

xt0 = ∑ aix rt −i + ∑ bix rt −i ln (Tt −i ) + ∑ cix xt0−i + ∑ dix xt0−i ln (Tt −i ) + v2t

(2)

Note that our equations differ from Dufour and Engle's in that we add lags of rt ln (Tt ) to both
equations to account for an interaction between quote revisions and durations in addition to the
interaction between trading and durations. We follow Dufour and Engle (2000) and make the

Also following Hasbrouck (1991) we estimated the model replacing the trade indicator variable with a continuous
variable measuring the size of the given trade. All of our empirical results were qualitatively unchanged.
9

The data contain a few cases in which measured duration between trades is zero. To keep log values finite, we add
one second to each inter-transaction time.

assumption that the lag polynomials may be truncated after the fifth lag. Also, like Dufour and
Engle (2000), we identify the system by assuming that a trade at t affects the returns from t to

t+1, but that this return can only affect trades beginning at t+1. This is reflected in the 0-lag
terms in equation (1).
To measure the effect of stressful days arising from the risk aversion of market makers, we
estimate a slightly expanded system, shown in equations (3) and (4). For these equations, we
further define a dummy variable DtS that takes on the value of 1 if t occurs on one of the days we
have identified as stressful and 0 otherwise. As described above, we consider four different
definitions of stress days. We then add lagged interactions of this dummy variable with the trade
indicator variable to our benchmark equations. In this way, we will examine whether trades
affect prices differently on stressful days after controlling for the possible changes in intertransaction time (trading intensity).
5

i =1

i =0

i =1

rt = ∑ air rt −i + ∑ bir rt −i ln (Tt −i ) + ∑ cir xt0−i + ∑ dir xt0−i ln (Tt −i ) + ∑ eir xt0−i DtS−i + v1t
xt0 = ∑ aix rt −i + ∑ bix rt −i ln (Tt −i ) + ∑ cix xt0−i + ∑ dix xt0−i ln (Tt −i ) + ∑ eix xt0−i DtS−i + v2t

(3)

(4)

Tables 5(a), 3(b) and 3(c) summarize our coefficient estimates from estimating equations
(1)-(4) on data for the 2-year, 5-year and 10-year on-the-run Treasury notes respectively. The
tables report the sum of the estimated coefficients on lagged values for each variable and the pvalues for a Wald test of the significance of this sum. The first column in each table reports the
results for the estimation of benchmark equations (1) and (2). The other four columns report the
results for equations (3) and (4), with each column representing a different definition of stress
days. The estimates for the return equations are shown in the top half of each table and the
estimates for the trade-side equations are shown in the bottom half.
20

Our results suggest that the dynamics of the Treasury market have features in common
with other markets. For example, as shown in the first row for the return equations, we find that
Treasury market returns are negatively related to past returns. Furthermore, the second row
indicates that the coefficient on trade sign is positive. This is the result one would expect. That is,
buying should lead to a price rise and selling to a price fall. Hasbrouck (1991) and Dufour and
Engle (2000) have documented these results for equity markets. We also document that both of
these relationships are greater in magnitude as the maturity of the bond increases.
Our coefficient estimates on the terms interacted with inter-transaction time suggest that
the above-mentioned relationships become stronger during periods of intense trading. For
example, as shown in the third row, the sum of the coefficients on the lags of the interaction
between returns and inter-transaction times is positive. This indicates that during periods of more
intense trading (smaller inter-transaction time), current returns become even more strongly
negatively related to past returns. As shown in the fourth row, the sign of the coefficients on the
interaction term between inter-transaction time and the price impact of a trade is negative. This
indicates that periods of more intense trading are associated with a stronger price impact of a
given trade. The stronger price impact of trades during busy times is consistent with Easley and
O’Hara (1992), where informed traders seem impatient to trade, perhaps because the value of
their information deteriorates with time. It is also the same empirical relationship found by
Dufour and Engle (2000) in their study of equity markets. Thus, periods of intense trading
involve on average more trades that are perceived by market makers as informed, and therefore
each individual trade has a larger influence on price.
The results for the trade-side equation suggest that there is a positive relationship between
past returns and current trades. This is in contrast to the result found by Hasbrouck in equity

markets. However, it supports the findings of Cohen and Shin (2001), who also analyze data
from GovPX. These authors find that on busier trading days, a positive feedback mechanism
appears whereby, in the very-short run, an increase in the price of a Treasury security leads to
more buy-side transactions, and a decline in the price of a security leads to an increase in sellside transactions. As shown in the second row of the bottom panels of Table 5, trades are
positively related to past trades. This finding is typical in the empirical microstructure literature.
It may reflect partly an effort by informed traders to break down their desired trades into smaller
pieces in order to reduce the impact on prices. The relationship between past returns and
subsequent trading becomes even more positively related during times of intense trading. This is
the implication of the fact that the sum of the coefficients on rt ln (Tt ) , the interaction of return
and inter-transaction time, is negative.
To explore how stress may change the price discovery process, we report our estimates of
equations (3) and (4) in the last four columns of Table 5. The coefficients on the variables
discussed earlier change very little. The key new result, however, suggests that the price impact
of a trade becomes stronger on stressful days, indicating a decline in market liquidity on such
days. The magnitude of the effect depends on the specific on-the-run security and the definition
of stress days. The relevant variable is xt0 dtS , which interacts a dummy variable for stress days
with our signed trade variable. The sums of the estimated coefficients for this interaction variable
are shown in the fifth row of Tables 5(a) to 5(c). In all specifications, the estimated coefficients
are positive, and with only 2 exceptions out of 12, highly statistically significant.
To quantify the differential impact of a stressful day on the price impact of a trade, we
calculate a benchmark cumulative impulse response function plotting the impact of a positive
trade shock on the returns to each of the Treasury notes based on the coefficients estimated from

equations (1) and (2). This response function is plotted as the solid black line in each panel of
Figure 2. To estimate the impact of stress, we consider another trade shock, only this time using
estimates from equations (3) and (4) and also setting the stress dummy variables equal to 1.
These impulse responses are graphed as dotted lines in Figure 2. For these two impulse
responses, we set the inter-transaction time equal to the mean value for the given security that
was reported in Table 3. By holding inter-transaction time constant, we are estimating the
marginal price impact of a stressful day, without considering that stressful days are also
associated with faster trading. Thus, the dotted lines in Figure 2 understate the total difference
between the price impact of a trade on a normal day and that on a stressful day. To jointly
consider the impact of stress and stress-induced reduction in inter-transaction time, the solid gray
line in Figure 2 plots the impulse response of returns from a trade shock when we both set the
stress dummy variable equal to 1 and also reduce the presumed inter-transaction time to the level
witnessed on stressful days of the given type.
As an illustrative example, the picture at the top-left corner of Figure 2 graphs the
impulse response of a trade shock on prices for the 2-year note on a non-stressful day compared
with a similar response to a trade occurring on a Johnson-Lowenstein day, calculated both for
average inter-transaction time and Johnson-Lowenstein-day inter-transaction time. The other
pictures in Figure 2 repeat this exercise for each on-the-run security and for each definition of
stress. In all 12 specifications, market stress is associated with decreased liquidity (higher price
impact). For example, the ultimate price impact of a trade of the 5-year note is estimated to be
around 0.4 basis points on normal days. Stressful days increase the price impact of a trade
significantly. For example, using the Johnson-Lowenstein identification method, the price impact
of a trade of the 5-year note increases to approximately 0.7 basis points, an increase of 75%.

Across all three securities and all definitions of stress, stressful days are associated with between
a 30% and 200% increase in price impact.
These calculations are hold inter-transaction time constant and therefore neglect to
consider that on stressful days, trading is more rapid, which would increase a trade’s price
impact even further. However, in practice, the decline in average inter-transaction time has a
negligible impact on the price impact of a trade. This can be seen visually by comparing the
dotted line with the solid gray line, which demonstrates that the shorter inter-transaction time on
stress days increases the price impact of a trade by a trivial amount.

Controlling for other factors
The results in section 6 indicate that market liquidity in on-the-run Treasury markets

declined on stressful days in the latter part of 1998. As discussed earlier, some signs of stress
were apparent in both available depth and in posted bid-ask spreads. It could be, therefore, that
the higher price impact of a trade on stressful days reported in section 6 merely reflects this
lower level of depth and wider spreads. In this section, we expand our empirical framework to
explicitly account for both spreads and depth to see if there remain differences in the price
impact of a trade on normal versus stressful days, or whether or not any differences merely
manifest themselves in these observable measures of liquidity.
To control for the possible influence of declining depth, we interact the trade indicator
with a variable Pt , which measures the size of the depth in the direction of the given trade. For
example, Pt would be the posted depth at the ask price if xt0 = 1 and would be equal to the

posted depth at the bid price if xt0 = −1 . We would expect trades will have a greater impact on

prices when depth is lower. We follow an analogous approach to incorporating the information

contained in bid-ask spreads. We interact the trade indicator with a variable BAt , which
measures the bid-ask spread at the time of trade t.10 Our hypothesis is that trades occurring when
spreads are wide will move prices more than trades arriving when spreads are narrow. To test the
influence of spreads and depth, we add lags of the depth interaction variable and the spread
interaction variable to our equations (3) and (4) to see whether depth affects the relationship
between trade flows and prices.
To conserve space, we do not report the coefficient estimates from this expanded empirical
specification. However, the additional coefficients were of the expected sign. That is, lower
depth and higher bid-ask spreads were correlated with greater price impact. We do, however,
report analogous impulse response functions in Figure 3. In each panel, the solid line is the
benchmark impact of a trade on returns (keeping the stress-day indicator equal to 0), estimated
from the depth- and spread- expanded versions of equations (3) and (4). These solid lines are
very close to those plotted in Figure 2. The dotted line is the cumulative impulse response of
returns to a trade shock from the same model, only setting the stress dummy variable equal to 1.
The simulations plotted by the dotted line keep the inter-transaction time, depth, and spread
variables at their full-sample mean value. As Figure 3 indicates, the increase in price impact
shown in the dotted line in Figure 3 is quite close to the effect reported in Figure 2. This is due to
the fact that changes in spreads and depth that accompany stressful days have a negligible impact
on the price impact of a trade as indicated by the close proximity of the dotted line to the solid
gray line, which estimates the impact of a trade shock on a stress day and allows inter-transaction
time, depth, and spreads to adjust to their stress-day average level. Thus, we conclude that the
price discovery process on stressful days is different than on normal days, even after controlling

Technically, this variable measures the “touch”, or the difference between the best bid and best ask price. This is

for changes in inter-transaction times, spreads, and depth that typically accompany such days. In
particular, the price impact of a trade is much greater.

Conclusions

This paper has studied the price impact of a trade in the U.S. Treasury market during the
particularly turbulent period of fall 1998. The main empirical findings are as follows: Overall,
the dynamics of trading in the Treasury market are much like those founds in equity markets. In
particular, returns are negatively related to past returns, trades are positively related to past
trades, and order flow moves prices in the expected direction. We further find that the intensity
of activity in the market, as measured by the inter-transaction time, affects the liquidity of the
market, as measured inversely by the price impact of a trade. Busy times, because they are times
of information-based trading, witness a significant increase in the price impact of a trade.
Most significantly, we document that stressful days during the crisis period of 1998 saw a
dramatic increase in the price impact of a given trade. Even after controlling for the shorter intertransaction times, shallower depth, and wider bid-ask spreads witnessed in the market, trading
during the crisis moved prices much more than trading during the more normal times of 1998.
This finding is robust across securities of different maturities as well as for various definitions of
stressful days.

what GovPX reports rather than the spreads posted by any of the individual dealers.

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Table 1
Largest Five Minute Price Changes in the 5-Year
on-the-run Treasury Note: May – Dec 1998
Date

Time

Change in price
(Basis points)

Discussion in financial press

9-Oct-98