Impact study on the interest rate futures market

The Quarterly Review of Economics and Finance46 (2006) 495–512

Impact study on the interest rate futures market

Hyunyoung Choi a,∗, Joseph Finnerty b

a Statistics and Applied Probability Department, University of California, Santa Barbara CA, United Statesb Department of Finance, University of Illinois at Urbana Champaign, IL, United States

Received 15 May 2006; received in revised form 30 May 2006; accepted 2 June 2006Available online 28 July 2006

Abstract

Any announcement from the Federal Reserve has a huge impact on the interest rate markets. The pressreleases from the Federal Open Market Committee (FOMC) are major inputs to the market and the randomintervention model is applied to interest rate futures transaction data to measure FOMC announcementimpact. Missing prices during non-trading time periods are imputed iteratively during the estimation ofmodel parameters. The study shows that the market trading on the announcement day is different from themarket trading on a non-announcement for both the Eurodollar and T-Note futures market.© 2006 Board of Trustees of the University of Illinois. All rights reserved.

JEL classification: E43; E58; C32

Keywords: Eurodollar futures; Federal Open Market Committee; Impact study; Random intervention model; T-Notefutures

1. Introduction

As the central bank of the United States, the Federal Reserve (Fed) manages the nation’smoney supply and credit, supervises and regulates a large share of the nation’s banking andfinancial system. The most critical role of the Fed is to keep the economy healthy and the openmarket operation is one of the main means to control the market. The Fed’s monetary policyaffects prices, employment and economic growth by influencing the availability and the cost ofmoney and credit in the economy.

The FOMC meets eight times a year in Washington, D.C. and for each session, they set theFed’s monetary policy based on the extensive analysis of economic statistics. The press releases

∗ Corresponding author. Tel.: +1 805 893 5063; fax: +1 805 893 2334.E-mail address: [email protected] (H. Choi).

1062-9769/$ – see front matter © 2006 Board of Trustees of the University of Illinois. All rights reserved.doi:10.1016/j.qref.2006.06.001

mailto:[email protected]

dx.doi.org/10.1016/j.qref.2006.06.001

496 H. Choi, J. Finnerty / The Quarterly Review of Economics and Finance 46 (2006) 495–512

are issued after the FOMC meetings and they are very critical inputs to the interest rate markettraders. Strategies are set in advance of the announcement and trading plans are developed. Oncethe announcements are made, the traders react to the information according to their predeterminedplans.

There are two aspects of market reaction that this paper attempts to address. First, the pricechange at the announcement day is expected to be bigger, because the market is more activeand the price at the beginning of the second day reflects the market activity overnight. Withthe assumption that the short-term returns in trading defined as the price change are normallydistributed, this paper explains the average level price change and the extreme price change withthe mean and the tail behavior of the normal distribution, instead of explaining it with the priceof other instruments. Second, assuming that the baseline of 2 h around the day change does notchange, the differences in volatility of the prices with and without FOMC announcement can beexplained with the difference in the baselines.

The benefit of the random effect model is to identify the origin of variance by specifying thesource of variation in the model. The emphasis is on the distribution of the price level changeat the announcement day compared to the price level change at the non-announcement day.Depending on the information from the Fed, the returns and the baseline can be different. How-ever, the distribution explains the different expected behavior of the price level change. With theassumption that the FOMC announcement can affect the price level and the baseline structurewhich is associated with the volatility, this paper intends to identify the source of the differ-ence between the announcement days and non-announcement days with the random interventionmodel.

In this study, the tick data1 is used to analyze the FOMC impact on the interest rate futuresmarket. The tick data is recorded at the same time when the trade occurs. Because the tradingdoes not occur every minute, there are times when nothing is happening and the unobservedprices during non-trading hours are considered missing. Especially, during the earlier yearsof the study period, the market is not liquid and the trade occurs infrequently leaving manymissing prices. The continuous price process is a commonly accepted belief to participantsand those who study financial markets.2 When the data is missing, i.e., non-trading, the causeis presumed to be that the bid-ask spread is not enough to compensate for the risk that thetraders have to take in dealing with the futures and keeping the markets liquid. In this study,missing data is replaced with a model imputing the price bounded by two adjacent recordedprices. This allows the continuous price process to be assured over the entire period of thestudy.

The remainder of the paper is organized as follows: Section 2 provides background on therole of Federal Reserve and the interest rate futures market. Section 3 describes the tick dataand addresses the assumptions on the data analysis. Section 4 outlines the methodologies usedfor the analysis. Section 5 reports the results from the empirical study. Section 6 contains theinterpretation of the results, conclusions and future research direction. The statistical details onthe methodology are included in the Appendix A.

1 Data Source: TickData, Inc.2 The greater emphasis on timing by hedge fund, traders and other market participants has motivated the research on the

microstructure of the market and the high frequency data from the market enables them to study the continuous marketbehavior. The random intervention model is appropriate to study the microstructure of the market, with the assumption thatthe data from the daily market activities are independent samples. Besides the change in the mean due to the intervention,the random intervention model can be identify the sources of variability: day level and market level.

H. Choi, J. Finnerty / The Quarterly Review of Economics and Finance 46 (2006) 495–512 497

2. Background: Federal Reserve and interest rate futures market

Much research has been done on the impact of the Fed and the chairman of the Fed, AlanGreenspan, on the financial market and the economy. Sicilia and Cruikshank (2000) illustratevarious examples of how influential Alan Greenspan has been on the market and global economy.Fair (2002) used S&P 500 futures tick data to associate events with the price change bigger than0.75% in absolute value. He concluded that there is no simple model to determine price changesand many large price changes do not have corresponding events. Kohn and Sack (2003) discussedthe effects of central bank announcements by examining various financial variables and threetypes of communication by the FOMC: the FOMC press release, congressional testimony andmajor speeches by Alan Greenspan. They used a linear regression model and factor model torelate the FOMC’s activities to the short-term interest rate. Kuttner (2001) explained the termstructure with the Fed funds rate by separating the expected policy action from the unexpectedpolicy action. The daily spot futures rate on Fed funds rate is used to define the market basedproxy for the expectation of Fed policy. His study shows that the unexpected change in the Fedfunds rate has a strong impact on the change in the term structure of the long-term rates.

The studies between ED market and US financial market have been focused on the short-termT-Note and ED prices by investigating the daily/weekly/monthly prices. Hartman (1984) reportsthat the ED market and the domestic US market are closely linked and characterized by rapidadjustments to exogenous events affecting both markets. Because the US interest rates and theED rates move closely when measured monthly or quarterly, Hartman examined the associationbased on weekly data to improve their chance of disentangling the timing of the interest ratemarket’s response. Krol (1987) used monthly data to investigate the efficient market model of theterm structure of ED interest rates and its relationship with the T-Note market. Fung and Isberg(1992) applied the error correction model to daily data from the Wall Street Journal to examinethe relationship between the US and ED CD rates from 1981 to 1988.

Garbade and Silber (1979) show that the number of market participants and equilibrium pricevolatility determine the frequency of market clearing, the level and effect of dealer participation.The market participants prefer to trade in markets which minimize their exposure to liquidityrisk. The liquidity risk is decreasing as market participants in a given clearing increase. Dealer’sparticipation in the market decreases the liquidity risk and increases the optimal frequency ofclearing, which reduces the liquidity risk even further and ultimately leads to a continuous trading.This is consistent with Kalay, Wei, and Wohl’s (2002) study on the continuous trading. With theempirical example from the Tel Aviv Stock Exchange, they show that investors have a preferenceto the continuous market.

3. Data

This study examines the impact on the autocorrelation from the FOMC announcement as wellas the impact on the level of the returns with high frequency data. High frequency data refer totime series sampled at intervals of short period and tick data is used to explain the microstructureof interest rate market at the announcement day, compared to the non-announcement day. Theinformation arrives in the market continuously, and high frequency data can explain questionsabout how the market actually develops in real time at the FOMC announcement day, comparedto the normal days. The advantage of high frequency data is more detailed examination of both thesource and characteristics of return volatility. It is easier to see the dynamics of volatility becauseof the strong autocorrelation between the return at time t and the return at time t − 1.


Fig. 1. CME, CBOT and GLOBEX trading hours for Eurodollar and T-note. The light blocks indicates trading hours andthe black blocks indicates non-trading hours. CME floor trading hours are 7:20 a.m.–2:00 p.m. CST, while the GLOBEXtrading hours are 4:30 p.m.–4:00 p.m. CST on the following day and on Sunday, trading begins at 5:30 p.m. This studyfocuses on the time windows 1 h before the market closes and 1 h after the market opens, which is indicated taller blocks.T-Note is traded in CBOT and the trading hours are same as CME, 7:20 a.m.–2:00 p.m. CST. The GLOBEX trading hoursfor T-Note is 7:01 p.m. - 4:00 p.m. CST on the following day.

The ED and T-Note futures tick data are investigated from January 1996 to August 2004. Thetrading days 1 week after FOMC announcement are used for the reference. Chicago Mercan-tile Exchange (CME) and Singapore Exchange (SGX) are major players in ED futures and thecontract is traded via open outcry. They can trade futures in the GLOBEX system electronicallyand the GLOBEX market closes very shortly (30 min for the ED futures market and 3 h for theT-Note futures market), while the floor trading occurs from 7:20 a.m. to 2:00 p.m. CST. Trad-ing mechanism in open outcry and electronic trading are different, but prices from these twomarkets are same during the floor trading hours, otherwise there is arbitrage opportunity thatcan be taken advantage of because of the law of one price. Since the market reacts to the infor-mation immediately and the electronic markets outside of the CME and CBOT are closed veryshortly, the discontinuity of price in CME/CBOT floor trading between two days is assumed andjustified.

Each time series is defined with the 2 h time window including 1 h before the last trading atday 1 and 1 h after the first trading at day 2, so the center of each time series involves the 17 hand 20 min time period when the market closes overnight and the price level change from the firsthalf to the second half reflects the price change overnight. The FOMC press release is scheduledto be around 2:15 p.m. EST on each scheduled day. By including the time of announcement withthe 2 h time window, this study intend to explain the market behavior around the announcementin terms of the change in the baseline and the price level (Fig. 1).

The ED tick data with the nearest expiration is the most liquid in the ED market, so it is themost reactive to new market information. Among the available domestic interest rate futures tickdata, 2 year T-Note futures is the most liquid and relevant for this study. The trading did notoccur at certain time and assumptions on missing data had to be made for the analysis. This issueis addressed in Sections 1 and 4. The missing data is filled with the assumption that the priceis within the boundary of the adjacent recorded prices. The initial value for the missing valueimputation is assumed to be flat after the previously recorded data and it is simulated from themodel with this assumption and updated as a part of the MCMC iteration.


32.78% of ED futures trading occurred more than two times within a minute. The differencebetween highest and lowest price in ED futures within a minute is smaller than $0.03 over 99%and the maximum difference over the past 4 years is $0.345. Without the loss of generality, themedian of the prices at each minute is used for the analysis.

3.1. Weekday effect

Chamberlain, Cheung, and Kwan (1990) studied the day of week effect in the US stock marketand US futures market, using the opening and closing prices of the NYSE composite and thefutures written on the index between April 1982 (when the trading in the futures begins) andSeptember 1986. Wong, Hui, and Chan (1992) did additional research on the day of week effectin the stock markets of Singapore, Malaysia, Hong Kong, Thailand and Taiwan, using the datafrom 1975 to 1988. They reported that there is an evidence that the day of week effect exists inthe spot market, but not in the futures market.

The two way factorial design (Box, Hunter, & Hunter (1978, Chapter 7)) is used to test theeffects of year and weekday on the basis point. Let �Pi,j,t to be a basis point change at year i,weekday j and time t. Then�Pi,j,t can be presented as the sum of a general mean over all period(η), a year effect (βi), a weekday effect (τj), the interaction between year and weekday effect(ωi,j) and the error (εi,j,t),

�Pi,j,t = η+ βi + τj + ωi,j + εi,j,t . (1)

Table 1 shows that any of these factors is not influential to the change in the ED futures marketand that the year effect and the day of week effect in T-Note futures are significant with 1% level.The interaction between these two effects is significant with 5% level.

The test on the tick data shows different results on the day of week effect from Chamberlain,Cheung, and Kwan (1990). These can be explained by the difference in the scope of studies. The

Table 1Analysis of variance table for two-way factorial design, the basis point change in Eurodollar and T-Note futures

Source d.f. Type III SS Mean square F Pr > F

EurodollarYR 8 29200.27 3650.03 0.94 0.48WKDAY 4 6102.91 1525.73 0.39 0.81YR × WKDAY 32 55772.12 1742.88 0.45 0.997Error 453740 1759432539 3878

Corrected total 453784 1759525527

T-NoteYR 8 1055056.85 131882.11 9.41 <.0001**

WKDAY 4 167869.24 41967.31 2.99 0.0176*

YR × WKDAY 32 1116789.54 34899.67 2.49 <.0001**

Error 233236 3270365893 14022

Corrected total 233280 3272592424

Two-way factorial design is fitted to see the mean difference associated with the weekday effect, year effect and theinteraction between weekday and year effects. WKDAY and YR represent weekday and year effect, respectively. EurodollarFutures market does not show the year and the day of week effect, while the year and the day of week effects are statisticallysignificant in T-Note futures market. (*) significance at 5% level; (**) significance at 1% level.


futures in their study is written on the NYSE composite index and the futures market at 1980smay not be liquid enough to capture the day of week effect.

The data shows an empirical evidence that the weekly pattern exists in the market. Becausethe FOMC releases the statement either on Tuesday or Wednesday, the reference days are chosenas the trading days one week after the FOMC press release. Choosing the reference days thisway resolves two concerns regarding the reference days. It guarantees that the effect from thisannouncement is already reflected to the price and the data is independent of the announcementdays. Since the reference days are close enough, it is assumed that two samples are under thesame economic conditions and have the same day of week effect, if any.

3.2. Overnight price change with FOMC announcement

The question in this study is whether the price change after FOMC announcement is differentfrom the price change without the announcement and how different the market activities are withthe announcement. From Fig. 2, it is clear that the price changes overnight and the announcementfrom the Fed amplifies the level of changes.

Define the price level of each day as the mean of price at the corresponding day and denotep̄i,1 and p̄i,2 as the price level at day 1 and 2, respectively. Table 2 presents the number of daysthat the price level went up/down between 2 days. The price level 1 h before the last trading at day1 is compared with the price level 1 h after the first trading at day 2. The χ2-test of independenceshows that the direction of market is indifferent to the announcement and the price could go upor down, depending on the announcement and other market conditions.

The question in this study is how much the market moves at the next day, not which directionthe market moves. In order to test how the information would affect the market without theconsideration of the direction, define the difference in the price level as |Δ| = |p̄i,2 − p̄i,1|. Theaverage price change for the reference days is $0.0632 with standard error of $0.0164, while theaverage price change for FOMC announcement days is $0.0791 with standard error of $0.0088.

In order to see the price change effects associated with the market, FOMC announcement andthe year, the generalized linear model is fitted to |�| with the following model (2)

|Δ| = η+ MKT + FOMC + YR + YR · FOMC + FOMC · MKT + ε, (2)

Table 2Market directional changes between 2 days, � = p̄i,2 − p̄i,1: Eurodollar and T-Note futures1

Direction Eurodollar T-Note

FOMC day Ref. day FOMC day Ref. day

+ 33 38 31 33− 28 24 26 27

Total 61 62 57 60

The number of days that the price levels went up/down between days is reported. Among FOMC announcement days,54.10% of ED futures price level went up after the announcement and 61.29% of the reference days have the higher meanlevel at the next day. The χ2-test of independence gives the statistic χ2

1 = 0.6517 (Pr-value = 0.4195) and χ21 = 0.0044

(Pr-value = 0.9468) for ED and T-Note futures respectively, which shows that the relationship between the direction andannouncement are not associated and the news from the Fed gives a positive or negative signal to the market with 50:50chance.


Fig. 2. Price quotes on four announcement days and four reference days1. The price of the ED and T-Note futures of fourannouncement days and four reference days are plotted. The time window in these plots is of 320 min around the daychanges. The center line indicates the day change and two dashed lines indicates the one hour time window studied inthis paper. The actual trading prices are plotted, leaving missing trade period blank. These plots show that two marketsare moving together and the Eurodollar future market is more active.

where MKT is 0–1 dummy variable to indicate ED and T-Note futures market, FOMC is 0–1dummy variable to indicate FOMC announcement day, YR is a class variable to indicate year1996–2004 and ε is the error. The interaction effect is included, if it is significant. The modelindicates that there is significant difference between ED futures market and the T-Note futuresmarket. FOMC announcement makes a significant difference in the price level change and thechange is different by year. The price level change is different by year and market.


Table 3Factorial design to test the price level change in futures market


Panel (A): Three-way factorial design is fitted to the ED and T-Note futures dataa

YR 8 0.11087348 0.01385919 1.77 0.0851*

FOMC 1 0.12210376 0.12210376 15.56 0.0001***

MARKET 1 0.08670427 0.08670427 11.05 0.001***

YR × FOMC 8 0.13862541 0.01732818 2.21 0.0279***

FOMC × MARKET 1 0.03321117 0.03321117 4.23 0.0409**

Error 220 1.72689707 0.00784953

Corrected total 239 2.21747385


Panel (B): Two-way factorial design is fitted to identify the influential factors to the price change on each marketb

EurodollarFOMC 8 0.06722212 0.00840276 0.86 0.5563YR 1 0.01484326 0.01484326 1.51 0.2216FOMC × YR 8 0.07700963 0.0096262 0.98 0.4556Error 105 1.03107154 0.00981973


T-NoteFOMC 1 0.14309729 0.14309729 22.1 <0.0001***

YR 8 0.11763705 0.01470463 2.27 0.0284**

FOMC × YR 8 0.09333437 0.0116668 1.8 0.0856*

Error 99 0.64112346 0.00647599


(*) denotes significance at 10 % level, (**) denotes significance at 5% level and (***) denotes significance at 1 % level.a YR, FOMC and MARKET represents year effect, announcement effect and market effect respectively. The FOMC

announcement makes a different in price change and the price change is different between ED and T-Note futures market.The FOMC announcement by year makes a difference in the price change. This preliminary analysis supports modelingthe FOMC announcement impacts to the price change with the random intervention model because the fixed effects modelover all time period and across market is not proper.

b The price change in ED futures market cannot be explained with year, weekday or the interaction between year andweekday effects. The price change in T-Note futures market is different by year, weekday and weekday at different years.

The similar model without MKT variable can be fitted to test FOMC announcement effect,yearly effect and the interaction between these two effects in each market,

|Δ| = η+ FOMC + YR + YR · FOMC + ε. (3)

Panel B in Table 3 shows the difference between these two markets. In ED futures market, thedifference by year and FOMC announcement is not significant, while these are significant inT-Note futures market. From these preliminary analysis on the price level change, it is reasonableto expect the FOMC announcement impacts on the price level change between 2 days. Insteadof defining the price level as the mean of one hour trading before the last trading and after thefirst trading around the day change, the random intervention model considers the baseline as astochastic process and quantifies the changes in the price level. With the time series recorded fromdifferent days, the random intervention model represents the changes in the price level and thebaseline in distribution.


4. Methodology: statistical background

4.1. Random intervention model

Box and Tiao (1975) used the univariate intervention model to model the effects of the inter-vention and the noise in economic and environmental problems. The random intervention modelaims to answer the question if there is any evidence that the change in the baseline and the meanof a panel data can be associated with a known common event.

The following assumptions on the random intervention model are made. (1) Daily marketactivities are independent to each other, but they share common attributes as the instruments inthe short term interest rate market. (2) The price change in each day is independent to the stochasticbaseline process and the level of the price change is considered as random effects. (3) Within 1 htime windows before the market closes and after the market opens, there is no other major eventsto cause additional change in price level.

Let Pi,t be a price at day i and time t, where Si,t is a step function that indicates a commonmarket intervention such as an announcement from FOMC.

Assuming that the baseline model is ARIMA (p, d, q) process, the random intervention modelcan be written as

Pi,t = δ−1i (B)ωi(B)Si,t + φ−1

i (B)(1 − B)dθi(B)ai,t, (4)

where ωi(B) = Σsj=0ωi,jBj, δi(B) = 1 −Σrj=1δi,jB

j, θi(B) = 1 +Σqj=1θi,jB

j andφi(B) = 1 −Σpj=1φi,jB

j . The individual variance per each time series and the population variance is param-

eterized by ψ−1τ and ψ−1 respectively. The error structure of the random intervention modelcan be formulated as ai,0 = (ai,1, . . ., ai,T)′ follows N (0, ψ−1(IT + τJT)), JT = 1T·1′

T and B is abackshift operator. The impact and the speed of transition due to the intervention are measuredby the parameters, ωi and κi, where δi =Φ(κi).Φ(·) is the normal cumulative distribution functionand this transformation ensures the stability of the intervention model. βi = (ωi, κi)′ is assumed tofollow bivariate normal distribution.

In this study, the focus is on the overnight price level change associated with FOMC announce-ment, relative to the price level change without FOMC announcement and this difference can beconsidered as the ‘treatment’ effect in the usual observational study. In the random interventionmodel, the treatment effect is modeled through hyperprior parameters. Assume that the impacton the price level at the announcement days differs by ωi,F from the impact on the price level atthe normal day, ωi,0, then the model becomes

Pi,t = ωi,0 + ωi,F IF (i)

1 − (δi,0 + δi,F IF (i))BSi,t−d + ui,t, (5)

where IF(i) is the indicator for the announcement day and ui,t is the baseline ARIMA(1,1,0)process.

If the price gradually achieves another equilibrium after the intervention, δi captures the behav-ior how it reaches the new price level. Fig. 2 shows eight different days with/without FOMCannouncement. Because of the price discontinuity of 17 h and 20 min between 2 days, δi,0 andδi,F are assumed to be zero and the study focuses on testing the changes in the level of priceand baseline. Each announcement is independent to other announcements and the baseline pereach day is also independent. So the coefficients of the baseline and the price level change ateach day are considered to be random samples from common distributions. Since the random


intervention model assumes that there is no other event to the returns than FOMC announcement,the variability of the returns associated with all other events is considered as the variability in thebaseline and the variability across days and explained with the random sample from the normaldistributions.

4.2. Modeling missing data

Standard time series models have been developed to analyze equispaced time series and someof the values in the time series may not be observed. In the normal case, it is natural to treatthese unobserved values as missing and true underlying values would have been observed, if thetechnology is available or the data is collected more carefully. In this study, the price is recordedwhen the trade occurs and the missing prices are due to the lack of trading.

When the trading does not occur, the price is not recorded because the bid-ask spread is notbig enough. The price at the non-trading time is between the adjacent recorded prices and theimputation of the missing price can be done within the MCMC estimation procedure. Missingprice is considered as a latent variable and modeled with the observed value and parameters in theMarkov chain. The missing price is imputed with a sample drawn from the conditional distributiongiven data and other parameters. Let pi,t be a unobserved missing values at time t and Pi,t − 1 is theobserved price at time t − 1 or imputed price from the prices up to time t − 2. Then the conditionaldistribution given the past price and the parameters is

pi,t|Pi,1, . . . , Pi,t−1,Θ ∼ N(μi,t, σ2i,t) (6)

whereμi,t and σ2i,t are the mean and variance of the price at ith day and time t. With the assumption

that the missing price is between the adjacent observed prices at each day, the accept/reject ruleis applied to sample pi,t at each iteration. The simulated price from model (6) is accepted andreplaced, if the simulated price is between these two adjacent prices. Applying accept/reject ruleis equivalent to sample pi,t from the truncated normal distribution. Fig. 3 illustrates the samplingdistribution of N (99,1) with the adjacent prices $98 and $100.

4.3. Bayesian estimation with Markov Chain Monte Carlo (MCMC) methods

In the Bayesian paradigm, the information from the data, a realization of x ∼ f(x|θ), is com-bined with the prior information, which is specified by π(θ), a prior distribution. The posteriordistribution, π(θ|x), is the summary of the information from data and prior distribution and canbe derived from the Bayes formula

π(θ|x) = f (x|θ)π(θ)∫f (x|θ)π(θ) dθ

, (7)

where m(x) = ʃf(x|θ)π(θ) dθ is the marginal density of x.On the basis of the support of the parameter space as well as the interpretation of the param-

eter, the assumptions on the prior distribution on model (5) are made. For example, the normaldistribution is used as the prior of parameters of the baseline and the price level change associatedwith the day change, assuming that these parameters have R

1 as a support. The support of thevariance is {�:0 < � < ∞} and the gamma prior is used for the prior of the variance. In the randomeffects model, the posterior distribution of a prior parameter has to be integrated over individualparameters and the posterior distribution does not have a closed form. Despite of these complica-


Fig. 3. Truncated normal distribution. Suppose the missing price is bounded by the adjacent prices, $98 and $100. Thedensity of normal distribution N (99,1). is in grey and the truncated normal distribution for the missing price is in black.Simulating the missing prices requires two steps: (1) draw random number from Normal distribution, N (99,1); (2) acceptif the random number is between the boundaries, $98 and $100. The relative density of the truncated normal distribution issame as the density of the normal distribution at the accepted area and the sum of the probability that the price is between$98 and $100 is 1.

tions, Gibbs sampling and Metropolis Hasting Algorithm (MHA) as standard sampling methodsin MCMC provide an easy solution.

4.4. Bayesian decision theory

The Bayesian decision theory is different from the Neyman Pearson framework of frequentists’decision theory. Let the null and alternative hypotheses be H0:θ ∈Θ0 and H1: θ ∈Θ1, where Θ0and Θ1 are subsets of the parameter space Θ =Θ0 ∪Θ1. Under the Bayesian framework, thenull hypothesis is accepted, if the posterior distribution of the null hypothesis is bigger than thedistribution of the alternative hypothesis, Pr(θ ∈Θ0|x) > Pr(θ ∈Θ1|x). If the posterior distributionis continuous, the probability of Pr(θ = θ0|x) is zero and it is impossible to test a null hypothesis,H0:θ = θ0. The best way to conduct such a test is to approximate the point with a small interval(θ0 − ε, θ0 + ε). After the data is observed, the probability of the wrong decision is defined asPr(error|x) = min (Pr(θ ∈Θ0|x), Pr(θ ∈Θ|x)) and it is possible to estimate the average probabilityof error over all possible measurements as Pr(error) = ʃxPr(error|x)f(x) dx. The test in this studyis interpreted in Bayesian framework and leave the frequentists’ interpretations up to the reader.

4.5. MCMC convergence diagnosis

In MCMC estimation, it is necessary to check if the chain is converged and if the chain exploresall parameter space to estimate the parameter. MCMC variance can explain if the estimator is thegrand solution or a local solution. After running multiple chain starting with the same initialvalues, MCMC variance can be calculated as the variance between chains. If MCMC varianceis relatively bigger than the variance within the chain, one can conclude that the chain has notexplored all possible parameter space and get the local solution. In other words, if the MCMCvariance is relatively smaller than ‘within variance’, one can conclude that the variance in MCMC


chain is caused by the limitation of MCMC chain, not by the random sampling process. Let θ be aparameter and m be the number of estimation chain with the length of N = 2n. Then the W (withinvariance) and B/n (between variance) are defined as follows:

W = 1

m(n− 1)

m∑j=1

2n∑t=n+1

(θ(t)j − θ̄·j)

2, (8)

B/n = 1

m− 1

m∑j=1

(θ̄·j − θ̄··)2, (9)

where θ̄j = 1/(n− 1)∑2nt=n+1θ

(t)j and θ̄·· = 1/m(n− 1)

∑mj=1∑2nt=n+1θ

(t)j . The ratio between W

and B/n is also considered as the MCMC variance and it is induced by the random samplingprocess in MCMC chain.

5. Empirical research: methodology and results

Consider the discrete model (Luenberger (1998, Chapter 11)) with N+1 time points, wherethe asset price at each time is characterized and denoted as St, t = 1, 2, . . ., N. The additive modeldescribes the price at a certain time as a price dependent to some extent on previous prices andthe random disturbance, εt.

St+1 = φSt + εt, (10)

where φ is the autocorrelation in the asset price over time. The additive model assumes εk aremutually statistically independent. Often εk is assumed to be independent normal random variable,even though it is not realistic because of the normal random variable can take negative infinitevalues. For this reason, the additive model with normal disturbance assumption is not accepted asa general model, but it is useful for the localized analysis. In the analysis of overnight tick data, itdoes give simplest model to explain the dynamic and the intervention associated with the FOMCannouncement.

The univariate intervention model mainly answers how the event affects on the baseline fora particular time series, not the expected level of effect due to the event in general. The randomintervention model can estimate the expected level of effect due to a common event and this studytries to answer a specific question about the price level changes at FOMC days, compared to thenormal days.

Choi (2005) proposed the random transfer function model as a model to explain the stochasticbehavior of a panel data associated with a common input. Random intervention model is describedas a special case of random transfer function model with a deterministic common input. Theproposed random effect model (11) is another application to analyze a bimodal mixture of twonormal distributions.

After observing the price discontinuity due to 17 h and 20 min between two days, the assumptionon the ramp-up effect is excluded. Assuming the baseline to be ARIMA(1,1,0) process, the modelbecomes

Pi,t = ωiSi,t + 1

(1 − φiB)(1 − B)(ai + εi,t), ωi ∼ N(ω0 + ωFIF (i), σ2

ω),

φi ∼ N(φ0 + φFIF (i), σ2φ), εi,t ∼ N(0, ψ−1), ai ∼ N(0, ψ−1

τ ), (11)


where IF(ωi) is the indicator function for the FOMC announcement day defined as

IF (ωi) ={

1, ith day is the FOMC announcement day

0, otherwise(12)

Let �Pi,t = Pi,t − Pi,t − 1, then the individual variance and the unit root is canceled. �Pi,t is thechange in quote at time t and ωi measures the change in price when the market opens,

�Pi,t = ωi �Si,t +�ui,t = ωi �Si,t + 1

1 − φiBεi,t . (13)

The ωi can be interpreted as the price change at day i, where the price change at the normalday follows N(ω0, σ

2ω) and the price change at the announcement day follows N(ω0 + ωF , σ

2ω).

By assuming the same variance, the distribution of the price change at the announcement dayis considered as the translation of the distribution of the price change at the non-announcementday. The same analogy applies to the AR(1) coefficient on the baseline and this measures thedifference in baseline in announcement day and reference day.

The hyperprior distributions for the price change due to the day change are assumed asω0 ∼ N(ω∗

0, s2ω,0) for the normal days and ωF ∼ N(ω∗

F , s2ω,F ) for the difference at FOMC

announcement days from the normal days. σ−2ω ∼ Γ (pω, λω) measures the variability of the

price change overnight. The baseline of the random effect model is assumed to be an AR(1)process with φi as the linear filter coefficient at day i. φ0 ∼ N(φ∗

0, s2φ,0) measures the baseline

behavior at the ordinary days without FOMC announcement and φF ∼ N(φ∗F , s

2φ,F ) measures the

AR(1) baseline coefficient difference at FOMC announcement day. σ−2φ ∼ Γ (pφ, λφ) presents

the variability of the AR(1) coefficient at each day and ψ∼Γ (pψ, λψ) for the error variance. Theposterior distribution of each parameter is presented in Appendix A.

5.1. Parameter constraints

To measure the level of mean change without the consideration of the market direction, di =sign(p̄i,2 − p̄i,1) is computed and multiplied to �Pi,t, where p̄i,1 and p̄i,2 are the price level atday 1 and the price level at day 2. By construction, �P∗

i,t = di �Pi,t preserves the change in theprice level from the day 1 to day 2 positive.

Prior distributions of the ωi, �0 and ωF are imposed as normal distributions,

ωi ∼ I{x|x>0}(ωi)N(ω0 + ωFIF (i)σ2ω),

ω0 ∼ I{x|x>0}(ω0)N(ω∗0, s

2ω,0),

ωF ∼ N(ω∗F , s

2ω,F ), (14)

where I{x|x> 0} is the indicator function for positive value of ωi and ω0. Since the change in pricelevel for ith day, ωi, is presumed to be positive, ωi is generated from the truncated normal distri-bution. Considering that ω0 represents the price level change at the normal day without FOMCannouncement and ωF represents the additional price level change with FOMC announcement,ω0 is also imposed to be positive, whereas ωF can be either positive or negative. If ωF is positive,it implies that the price level change after FOMC announcement is bigger than normal days andvice versa.


5.2. MCMC estimation procedure

The Gibbs Sampling and the MHA are used to implement the Bayesian paradigm and analyzerandom intervention model. The hierarchical Bayesian nonlinear model is adapted to estimatethe effects over all series. No assumption on the baseline is imposed and there is possibility thatsome of the baseline can be nonstationary. Nandram and Petruccelli (1997) shows that restrictingnonstationary series to be stationary does not add new information and restricting nonstationaryseries to be stationary leads to substantially different estimators and predictors from those withoutthe restriction.

The model (11) has parameter set,Θ = {ψ, τ, φ1, . . . , φn, σ2φ, φ0, φFω1, . . . , ωn, ω0, ωF , σ

2ω}

andΘ(θ) denotes all parameters except θ, where θ ∈Θ. Gibbs Sampling and MHA is used forthe estimation and the estimation procedure suggested in Hsiao (2002, Chapter 6) is used for theinitial estimates. The MCMC chain is generated as follows:

(1) Start with initial valuesΘ(0) = {ψ(0), τ(0), φ(0)1 , . . . , φ(0)

n , σ2(0)φ , φ

(0)0 , φ

(0)F ω

(0)1 , . . . , ω(0)

n , ω(0)0 ,

ω(0)F , σ

2(0)ω }

(2) After kth iteration, define Θ* =Θ(k). (k + 1)th iteration is done with the following steps.(a) Generate φ(k+1)

i , i = 1, . . . , n fromφi|Pi,1, . . . , Pi,n, Si,1, . . . , Si,n−d,Θ∗(φi) and update

Θ∗ withφ(k+1)i

(b) Generate φ(k+1)0 fromφ0|Θ∗(φ0) and updateΘ∗ withφ(k+1)

0

(c) Generate φ(k+1)F fromφF |Θ∗(φF ) and updateΘ∗ withφ(k+1)

F

(d) Generate σ2(k+1)φ from σ2

φ|Θ∗(σ2φ) and updateΘ∗ with σ2(k+1)

φ

(e) Generate ψ(k + 1) from ψ|Pi,1, . . .,Pi,n, Si,1, . . ., Si,n−d,Θ*(ψ) and updateΘ* with ψ(k + 1)

(f) Generate ω(k+1)i , i = 1, . . . , n from the truncated normal distribution

ωi|Pi,1, . . . , Pi,n, Si,1, . . . , Si,n−d,Θ∗(ωi) to ensureω(k+1)i to be positive and update Θ*

with ω(k+1)i , i = 1, . . . , n

(g) Generate ω(k+1)0 from the truncated normal distribution �0|Θ*(ω0) to ensure ω(k+1)

0 to

be positive and update Θ* with ω(k+1)0

(h) Generate ω(k+1)F from ωF|Θ*(�F) and update Θ* with ω(k+1)

F

(i) Generate σ2(k+1)ω from σ2

ω|Θ∗(σ2ω) and update Θ* with σ2(k+1)

ω

(j) Use the MHA to generate �(k + 1) and update Θ* with τ(k + 1)

(k) Define the parameter set after (k + 1)th iteration as Θ(k + 1) =Θ*

(3) Repeat 2 until MCMC generates M samples after burn-in periodΘ(1), . . .,Θ(M). These samplesare random samples from the joint posterior distribution of Θ.

5.3. Results and Interpretation

Ten runs of 5000 iterations are done for each model of ED futures and T-Note futures. Table 4shows the estimates, the standard errors of the estimates and the convergence criteria. The impactsassociated with FOMC announcement are measured through φF and ωF as the translations of thedistributions at the reference days. The sample within the MCMC chain is considered as thesample from the posterior distribution and the prior/hyperprior parameters are estimated as theaverage of the sample. By the central limit theorem, each estimate will have a limiting distributionapproaching a normal distribution.


Table 4Estimates of the random intervention model

Estimates S.E. r.v. B/n W B/n/W (%) R

Eurodollarψ−1 4.28e−4 5.39e−6 ψ 3.40e−1 8.68e2 0.04 1.00φ0 −1.09e−1 2.66e−2 φ0 8.49e−6 7.09e−4 1.20 1.01φ1 −9.50e−2 2.94e−2 φ1 1.18e−5 8.64e−4 1.37 1.01σ2φ 5.25e−3 6.45e−4 σ−2

φ 6.98e−1 5.48e2 0.13 1.00ω0 4.37e−3 2.51e−3 ω0 3.61e−10 6.29e−6 0.01 1.00ω1 3.70e−3 2.98e−3 ω1 3.21e−9 8.90e−6 0.04 1.00σ2ω 4.15e−2 5.39e−3 σ−2

ω 7.32e−3 9.78 0.07 1.00

T-Noteψ−1 2.35e−3 3.68e−5 ψ 4.32e−2 4.45e1 0.10 1.00φ1 −1.19e−1 1.77e−2 φ0 3.17e−6 3.14e−4 1.01 1.01φ2 −4.13e−2 2.15e−2 φ1 2.56e−6 4.63e−4 0.55 1.00σ2φ 2.79e−3 2.14e−4 σ−2

φ 8.18e−1 7.57e2 0.11 1.00ω0 2.06e−3 1.56e−3 ω0 l.Ole−9 2.43e−6 0.04 1.00ω1 −1.48e−5 2.57e−3 ω1 1.63e−9 6.61e−6 0.02 1.00σ2ω 9.32e−3 1.24e−3 σ−2

ω 2.12e−1 2.03e2 0.10 1.00

Estimates and S.E. are the mean and the standard error of the chain after the initial burn in period. W and B/n are withinand between variance respectively. R is the reduction factors for the convergence diagnostic. Estimates and SE is reportedin terms of the parameters in the model for the easier interpretation. W and B/n are reported in terms of the random samplegenerated in MCMC chain.

From the random intervention model, one can conclude that there are more than 99% chancethat the baseline will deviate from the baseline in the normal day and the volatility increases inED futures market. In T-Note futures market, the probability that the baseline will change withFOMC announcement is close to 95%. From the frequentist point of view, one can conduct ahypothesis test, H0:φF = 0 versus H1:φF �= 0, and conclude that the change is significant with99% significance level for ED futures market and 90% significance level for T-Note futuresmarket.

The change in the price level is not as notable as the change in the baseline. There are99% of chance that the price level change in ED futures market after FOMC announcementis higher than normal day without FOMC announcement and 50% of chance for the same eventin T-Note futures market. With these results, frequentists will conclude that there is no signif-icant difference between FOMC announcement days and the ordinary days in T-Note futuresmarket.

When the absolute value of AR(1) coefficient increases, prices are more strongly autocorre-lated and the market becomes more volatile. The baseline of each day is assumed to be AR(1)process and AR(1) coefficient (φi) follows, N (−0.109–0.095 IF(i), 0.0722) for ED futures andN(−0.119–0.041 IF(i), 0.0532) for T-Note futures. When the absolute value of the AR(1) coef-ficient at FOMC announcement day increases, the variance of the price also increases. Harveyand Huang (2002) discuss the impact of the Fed open market operations as an example of themarket reaction to the private information trading. They reported that the high volatility duringthe trading time windows, which can be associated with the intervention associated with the Fedopen market operation. The results from the random intervention model also suggest that theFOMC announcement increases the volatility in the ED/T-Note futures market and this is due tothe change in the baseline at FOMC announcement days.


The error variance of the returns defined as the price difference between tick is modeled asεi,t ∼ N (0,ψ−1) andψ−1 are estimated as 4.28e−4 and 2.35e−3 for ED futures and T-Note futuresrespectively. The inverses of σ2

φ and σ2ω are assumed to follow gamma distribution and the within

variance and between variance of these two parameters are calculated with the random samplefrom each distribution.

Gelman and Rubin’s potential scale reduction factor (R) is used for the convergence diagnos-tic. It is based on the comparison of within-chain and between-chain variances and the valuessubstantially bigger than one indicate lack of convergence. Table 4 presents that the reductionfactors are all close to one and the chain is converged.

6. Conclusion

This paper studies the impact due to FOMC announcement by looking at the microstructureof the futures market. The purpose of the study is to examine how differently market would reactto the information from the FOMC and the difference is measured as the translation of normaldistribution. The preliminary test based on the generalized linear model shows that there are dif-ferences in the overnight price level changes between the reference day and FOMC announcementday. The study shows that the FOMC announcement changes the autocorrelation structure andthe overnight price level change. The ED futures market is more volatile and price level changeis bigger at the announcement day.

By specifying the source of variation, the random intervention model can identify the originof the difference between the announcement day and non-announcement day. The study showsthat the difference in autocorrelation structure exist at both markets, but the price level differenceis not noticeable at T-Note market. The difference is more obvious in Eurodollar futures marketand this can be explained by the fact that the short-term interest rate reacts to the Fed monetarypolicy more actively, compared to the long-term interest rate. There is strong correlation amongthe interest rates of T-Bonds and these rates are highly correlated to the federal funds rate. Twoyear T-Note futures are used in this study because it is the most liquid instrument among theavailable domestic interest rate futures and it is easier to see the dynamics how the price reflectsthe information in the liquid instrument. Despite of all the considerations, the difference in thematurity seems to have an affect on the magnitude of the FOMC impact. Also the greater liquidityin the ED market helps the impact to be reflected in the price more efficiently.

The study suggests that the price change between 2 days is due to the baseline and the mar-ket volatility. Measuring the impact associated with the announcement, the market direction wasnot considered and the future research will be focused on the study of the reaction of futuresto the content of the announcement such as surprise/anticipated policy change, positive/negativechange. For example, the announcement from the Federal Reserve can affect the market posi-tively or negatively and this difference in the market can be detected. Assuming the baseline ofthe Eurodollar futures market does not change overnight, the classification by the random inter-vention model can provide the information at the FOMC day with the hyperprior distribution ofinterest.

This study is focused on the comparison of the market reaction between the announcement dayand non-announcement day. Another research direction can be the investigation of the short-termimpact at the announcement. The price reflects the market information quickly and dependingon the liquidity of the market, it takes some time to reach new equilibrium. Especially, when themarket is not liquid, it takes more time for the market to reflect the information to the price. This


can be modeled by another random intervention model with transition effect as,

Pi,t = ωi

1 − δiBSi,t−d + ui,t, (15)

ui,t is the baseline ARIMA (1,1,0) process and δ measures the speed of the information to theprice.

Appendix A

Let the set of all parameters in the model to be Θ = {ψ, τ, φ1, . . ., φn, σ�, φ0, φF, ωi, . . ., ωn,ω0, ωF, σω}. Θ(θ) denotes all parameters except θ, where θ ∈Θ. Then the conditional posteriordistribution of the bimodal hyperprior parameters given the prior and the hyperprior distributionsare calculated as follows:

ω0|Θ(ω0) ∼ N

(Σi/∈IF (ωi/σ2

ω) +Σi∈ IF (ωi − ωF )/(σ2ω + ω∗

0)/s2ω(N/σ2

ω) + (1/s2ω),

(N

σ2ω

+ 1

s2ω

)−1)(16a)

ωF |Θ(ωF ) ∼ N

(Σi∈ IF (ωi − ω0/σ

2ω) + (ω∗

2/s2ω)

(nF/σ2ω) + (1/s2ω)

,

(nF

σ2ω

+ 1

s2ω

)−1)

(16b)

σ−2ω |Θ(σω) ∼ Γ

(N

2+ pω, λ

∗ω

),

λ∗ω ∼ N

⎛⎝1

2

∑i/∈IF

(ωi − ω0)2 + 1

2

∑i∈ IF

(ωi − ω0 − ωF )2 + 1

λω

⎞⎠

−1

(16c)

φ0|Θ(φ0) ∼ N

⎛⎝Σi/∈IF (φi/σ2

ω) +Σi∈ IF (φi − φF/σ2ω) + (φ∗

0/s2φ)

(N/σ2φ) + (1/s2φ)

,

(N

σ2φ

+ 1

s2φ

)−1⎞⎠

(16d)

φF |Θ(φF ) ∼ N

⎛⎝Σi∈ IF (φi − φ0/σ

2ω) + (φ∗

0/s2φ)

(nF/σ2φ) + (1/s2φ)

,

(nF

σ2φ

+ 1

s2φ

)−1⎞⎠ (16e)

σ−2ω |Θ(σω) ∼ Γ

(N

2+ pφ, λ

∗φ

),

λ∗φ =

⎛⎝1

2

∑i/∈IF

(φi − φ0)2 + 1

2

∑i∈ IF

(φi − φ0 − φF )2 + 1

λφ

⎞⎠

−1

(16f)

where nF is the number of announcement days.


References

Box, G., Hunter, W., & Hunter, S. (1978). Statistics for experiments: An introduction to design data analysis, and modelbuilding. John Wiley & Sons.

Box, G., & Tiao, G. (1975). Intervention analysis with applications to economic and environmental problems. Journal ofthe American Statistical Association, 70, 70–79.

Chamberlain, T., Cheung, C., & Kwan, C. (1990). Day-of-the-week patterns in futures prices: Some further results.Quarterly Journal of Business and Economics, 29, 68–88.

Choi, H. (2005). Topics in nonlinear time series. Ph.D. thesis, University of Illinois at Urbana Champaign.Fair, R. (2002). Events that shook the market. Journal of Business, 75, 713–732.Fung, H., & Isberg, S. (1992). The international transmission of Eurodollar and US interest rates: A cointegration analysis.

Journal of Banking and Finance, 16, 757–769.Garbade, K., & Silber, W. (1979). Structural organization of secondary markets: Clearing frequency, dealer activity and

liquidity risk. Journal of Finance, 34, 577–593.Hartman, D. (1984). The international financial market and US interest rates. Journal of International money and Finance,

3, 91–103.Hsiao, C. (2002). Analysis of panel data. Cambridge University Press.Harvey, C., & Huang, R. (2002). The Impact of Federal Reserve Bank’s open market operations. Journal of Financial

Markets, 5, 223–257.Kalay, A., Wei, L., & Wohl, A. (2002). Continuous trading or call auctions: Revealed preferences of investors at the Tel

Aviv Stock Exchange. Journal of Finance, 57, 523–542.Krol, R. (1987). The term structure of eurodollar interest rates and its relationship to the US Treasury-Bill market. Journal

of International Money and Finance, 6, 339–354.Kohn, D., & Sack, B. (2003). Central Bank Ralk: Does it matter and why? Board of Governors of the Federal Reserve

System.Kuttner, K. (2001). Monetary policy surprises and interest rates: Evidedence from the Fed Funds futures market. Journal

of Monetary Economics, 47, 523–544.Nandram, B., & Petruccelli, J. (1997). A Bayesian analysis of autoregressive time series panel data. Journal of Business

and Economic Statistics, 15, 328–334.Luenberger, D. (1998). Investment science. Oxford University Press.Sicilia, D., & Cruikshank, J. (2000). Greenspan effect: Words that move the world’s markets. McGraw-Hill Companies.Wong, K., Hui, K., & Chan, C. (1992). Day-of-the-week effects: Evidence from developing stock markets. Applied

Financial Economics, 2, 49–56.

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