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The link between monetary policy and stock and bondmarkets: evidence from the federal funds futurescontractO. David Gulley a & Jahangir Sultan ba Department of Economics, Bentley College, Waltham, MA 02452 USAb Department of Finance, Bentley College, Waltham, MA 02452 USA. Email:JSULTAN@BENTLEY.EDUPublished online: 07 Oct 2010.

To cite this article: O. David Gulley & Jahangir Sultan (2003) The link between monetary policy and stock andbond markets: evidence from the federal funds futures contract, Applied Financial Economics, 13:3, 199-209, DOI:10.1080/09603100110115165

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The link between monetary policy and stock

and bond markets: evidence from the

federal funds futures contract

O. DAVID GULLEY* and JAHANGIR SULTANz

Department of Economics, Bentley College, Waltham, MA 02452 USA andzDepartment of Finance, Bentley College, Waltham, MA 02452 USA. Email:JSULTAN@BENTLEY.EDU

This study examines the simultaneous response of both stock and bond marketreturns to changes in the CBOT 30-day federal funds futures rate. It is found thatchanges in the federal funds futures rate are negatively related to both stock andbond returns. It is also found that positive and negative changes in the federal fundsfutures rate have symmetric effects on the bond market, but somewhat asymmetriceffects on the stock market.

I . INTRODUCTION

On 4 February 1994, the Federal Reserve announced anincrease from 3% to 3.25% in the target level of the federalfunds rate. The reaction of financial markets to the surpriseannouncement was swift and decisive. The Dow JonesIndustrial Average fell by more than 96 points and interestrates on all categories of bonds rose generally by more thanone quarter of a percentage point. As there was little othernews that day, the Fed’s announcement is the only reason-able explanation for such dramatic changes in asset prices.From casual observations, the Fed’s announcement and

the public’s speculation over the Fed’s future policy actionsmay have affected both the level and volatility of assetreturns. The financial market’s response to policy informa-tion is important because it reflects the market’s eclecticviews and opinions on matters that affect the overall mar-ket microstructure and risk management. While such pub-lic announcements of policy changes are, unfortunately,rare,1 data are available that make it possible to inferhow actions by the Fed (and the expectation of thoseactions) affect asset prices. Specifically, the Fed influencesthe level and composition of reserves in the bankingsystem, and thus, the federal funds rate. Therefore, changesin the expected target for the federal funds rate should have

explanatory power for predicting changes in financial assetprices. As will be shown, the CBOT 30-day federal fundsfutures contract offers a convenient way to measurechanges in expected monetary policy.Using a multivariate GARCH model, the study exam-

ines the information content of the CBOT 30-day federalfunds futures contract as an indicator of the Fed’s mone-tary policy to infer financial market reaction to such infor-mation flows. In particular, it examines whetherinformation about changes in expected monetary policysimultaneously affects the level and volatility of stock andbond prices. This link between changes in the federal fundsfutures rate and changes in stock and bond prices in asystem of equations that incorporates stylized nonlinearityin asset returns has not been fully addressed in the litera-ture.Finally, the study examines whether positive and nega-

tive changes in the futures rate have asymmetric effects onthe financial market. If positive and negative changes inthis rate are perceived to be conveying either a pessimisticor an optimistic outlook on the economy, then the market’sreaction to the information flows could be asymmetric.Despite evidence that the market’s reaction to macro-economic information flows is asymmetric (Engle andNg, 1993), the possible asymmetric response of the stock

Applied Financial Economics ISSN 0960–3107 print/ISSN 1466–4305 online # 2003 Taylor & Francis Ltdhttp://www.tandf.co.uk/journalsDOI: 10.1080/09603100110115165

Applied Financial Economics, 2003, 13, 199–209

199

* Corresponding author. Email: DGULLEY@BENTLEY.EDU1 All subsequent policy changes have also been made public

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and bond markets to changes in the federal funds futuresrate has not been examined.2

The empirical analysis presented in this paper producesseveral important results. Changes in the 30-day federalfunds futures rate are inversely related to both stock andbond returns. Further, it is found that positive and negativechanges in the federal funds futures rate have symmetriceffects on the bond market, but somewhat asymmetriceffects on the stock market.

II . THE LITERATURE ON MONETARYPOLICY AND THE FINANCIAL MARKET

A large body of theoretical and empirical work indicatesthat markets respond to changes in monetary policy instru-ments (see, for example, Bernanke and Blinder, 1992).3 Thetransmission mechanisms through which the Fed’s policyvariables affect the nominal and the real economy incorpo-rates both direct and indirect effects of these variables,especially in the way market participants digest the infor-mation contents of these variables (Cornell, 1983b).Not surprisingly, there is a large body of literature on

how monetary policy affects interest rates. For the mostpart, studies that use the monetary aggregates as measuresof monetary policy find that expansionary policy is associ-ated with increases in short-term nominal interest rates (seeReichenstein (1987) for a survey).4 However, the evidenceon how money announcements affect long-term interestrates is mixed. For example, Shiller, et al. (1983) find thatunanticipated money announcements have no effect onlong-term forward rates, while Cornell (1983a) finds suchannouncements have positive effects on long-term rates.More recent studies using alternative measures of mone-tary policy (such as nonborrowed reserves) find that expan-sionary policies are associated with reductions in nominal

interest rates. Hardouvelis (1987) finds unanticipated

changes in net nonborrowed reserves are inversely associ-

ated with the federal funds rate, as well as various forward

rates, during the 1980–1984 period. Strongin and Tarhan

(1990) use net borrowed reserves as a measure of monetary

tightness and find that interest rates are affected by this

measure. However, they also find that the response of inter-est rates to the degree of tightness changes over time.5

Tarhan (1993) estimates ARCH models and finds that

open market operations affect bond prices all along the

yield curve, but only lowers the volatility of the federal

funds rate and the 30-year T-bond. He also finds open

market operations reduce the volatility of stock prices.

Bernanke and Blinder (1992) find that the federal funds

rate has more predictive power in forecasting various

macroeconomic variables than do several measures of themoney supply. Using VAR models, they also find that

the federal funds rate explains a significant percentage of

the variance in those same macroeconomic variables. These

findings lend support to the hypothesis that information

concerning monetary policy should affect the level and

volatility of asset prices. Jensen and Johnson (1993) find

that across various monetary policy regimes, stock prices

react negatively to increases in the discount rate, which in

previous years was often interpreted as a signal of tighter

policy. However, Pearce and Roley (1983) and Hafer(1986) find that unanticipated weekly money supply

increases are associated with lower stock prices.

Interestingly, Hafer finds that unanticipated reductions in

the money supply have no significant effects on stock

prices.6

Recent evidence also suggests that information can have

asymmetric effects on asset prices. Hafer (1986) finds that

unanticipated weekly money supply increases are associ-

ated with lower stock prices, but that unanticipateddecreases in the money supply have no effect on stock

200 O. D. Gulley and J. Sultan

2 However, it is important to note that while Kroner and Ng (1977) look at a symmetric news surface and perform conditional momentstests, the objective in this study is not to model conditional asymmetry in stock and bond returns. Rather, it asks: do positive andnegative changes in the Fedfunds futures have differential impacts on the stock and bond market? In essence, the results explicitlyaccount for possible asymmetry by including news as exogenous variables. Thus, by including news as exogenous variables, asymmetry istested for in the financial markets.3 Following Dueker (1993) and others, the Fed is assumed to operate in the following manner. First, the Fed has some long-term goal(s).In recent years (the Volker and Greenspan eras), this long-term goal seems to be a low and stable inflation rate. Next, the Fed selects anintermediate target(s) to help it achieve the long-term goal. The intermediate targets are either monetary aggregates or interest rates.Operating targets, such as the federal funds rate, are employed to achieve the intermediate targets. Finally, the Fed chooses a policyinstrument(s), such as a measure of reserves. Note that interest rates can be operating targets, intermediate targets, and/or long-termgoals. Presently, the Fed is targeting the federal funds rate.4 Cochrane (1989) is an exception. He uses band-pass filters on money and interest rate data and finds strong evidence of a liquidityeffect.5 Eichenbaum (1992), Christiano and Eichenbaum (1992) and Strongin (1991) report negative correlations between nonborrowedreserves and the federal funds rate.6 In addition, studies that find that monetary policy affects real interest rates and/or output imply that monetary policy affects stockprices. Huizinga and Mishkin (1986) find that monetary policy has statistically significant impacts on real interest rates. They find thatthe real rate undergoes structural shifts associated with the changes in monetary policy regimes.

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prices.7 Morgan (1993) finds that changes in the federal

funds rate have asymmetric effects on output growth,

which implies possible asymmetric effects on asset prices.

These results are important for studying the link between

the rate of information flow and asset price volatility.

Overall, it appears that the empirical evidence provides

mixed results concerning how monetary policy affects asset

prices. There may be a variety of reasons for such a con-

clusion. First, the findings may be sensitive to sample per-

iod, estimation technique, data, and other factors, thus not

allowing for consistent findings. Second, asset prices may

react differently across varying monetary policy regimes.

Lastrapes (1989) provides support for this idea using for-

eign exchange data. Third, market participants may have

heterogeneous views as to how policy affects assets prices.

Thus, monetary policy appears to have uncertain effects

on asset prices. This uncertainty implies that the volatility

of asset prices could be affected by information concerning

Fed policy. With the exception of Lastrapes (1989), who

uses foreign exchange data, and Tarhan (1993), there is

little empirical literature on this issue.

It is believed that this study makes several contributions.

First, unlike previous studies, daily data are employed

which allow the impact of monetary policy on financial

markets to be measured more accurately because monthly

(or even weekly) data may aggregate away (at least some

of) the effect of the policy shock. Second, the study exam-

ines the impact of monetary policy shocks on both the

mean (first moment) and the variance (second moment)

of asset price changes. Ross (1989) argues that evidence

of a link between information and the variance of an asset’s

price is also helpful for making inferences on the impact of

news on financial markets. Therefore, in addition to linking

policy shocks to the conditional mean, the effects of such

shocks on the conditional variance of asset prices are also

examined. Finally, in contrast to previous studies, whether

or not financial market volatility rises or falls is tested

depending on the information content of news. In general,

pessimistic news may raise stock market volatility while

optimistic news could reduce it. The implication is that

the management of interest rate exposure must incorporate

both the magnitude and the direction of changes in policy

variables when important official announcements are made

public. The evidence of a significant impact of the

announcements on asset price and volatility could be im-

portant for market participants in understanding how

macroeconomic information contributes to asset pricevolatility.

III . EMPIRICAL RESULTS

The data

Daily data from October 19888 through March 1995 areused. Stock prices are measured using the daily closingprice of the Dow Jones Industrial Average (DJIA). Themeasure of bond prices is the daily closing price of theDow Jones 20 Bond Index, consisting of 10 industrialand 10 utility bonds whose prices are compiled into theindex.There are many possible ways to measure monetary pol-

icy shocks. In previous years, changes in M1 and/or M2were employed to measure the stance of policy. However,numerous authors have pointed out that the monetaryaggregates are likely to be endogenous and are also heavilyinfluenced by the behaviour of banks and the non-bankpublic. Thus, economists turned to other indicators, suchas the overnight federal funds rate9 or some measure ofreserves, such as the ratio of borrowed to total reserves.However, these variables suffer from the same problems asthe monetary aggregates. In recent years, VAR modelshave been often used to generate policy shocks. For ex-ample, a monetary aggregate, the federal funds rate, orsome measure of reserves are included in a VAR model.The resulting innovations of the policy variable are takento be policy shocks. But as Gordon and Leeper (1994)point out, this technique requires implausible assumptionsconcerning elasticities of supply and/or demand forreserves. Gordon and Leeper also note that the resultingdynamic responses of macroeconomic variables are often atodds with predictions made by most models of monetarypolicy effects.10

Because of the various complications involved in usingmonetary aggregates, reserves, or the overnight federalfunds rate (or the innovations thereof), the CBOT 30-dayfederal funds futures contract rate was chosen as a measureof the market’s expectations of the future levels of thefederal funds rate. Carlson et al. (1995) note that despiteday to day variation, the average monthly level of the fed-eral funds rate is very close to the Fed’s target for the rate.The deviation is no more than a few basis points. Thus, tothe extent that the Fed’s target for the rate can be pre-

Monetary policy and stock and bond markets 201

7 Engle and Ng (1993) find that negative news shocks produce more volatility in Japanese stock prices than do positive news shocks.Sultan (1994) shows that unanticipated increases in the monthly US trade deficit are more likely to be associated with dollar depreciationthan are smaller than expected deficits.8 October 1988 is when the CBOT 30-day federal funds futures contract began trading.9 The federal funds rate has been explicitly targeted (in a narrow range) by the Fed at least since the stock market crash of 1987.10 Gordon and Leeper (1994) set up simple models of total reserves and monetary aggregates to measure money market supply anddemand shocks. The identified shocks are then employed in a VAR model.

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dicted, the average value of the federal funds rate oversome time period can also be predicted.11 Traded sinceOctober 1988, the CBOT 30-day federal funds futuresrate offers such a prediction. Krueger and Kuttner (1995)and Rudebusch (1996) both find that the federal fundsfutures rate is (at least close to) an unbiased predictor ofthe future average monthly federal funds rate. Krueger andKuttner (1995) also demonstrate that the futures rate is anefficient predictor of the future federal funds rate. Carlsonet al. (1995) find that the MSE of the futures contract’spredictions of the actual federal funds rate is superior tothe MSE’s of either a naive model or a univariate ARIMAmodel of the federal funds rate.12

Therefore, the federal funds futures contract rateshould be a good indicator of Fed policy. On anygiven day, the federal fund futures rate would changefor two possible reasons. First, market participantsexpect a change in Fed policy. For example, an increasein the futures rate implies that market participants placea higher probability on a given increase in the federalfunds rate and/or think that the federal funds rate willincrease by a larger amount than previously believed.The opposite interpretation would hold for a decreasein the futures rate. The second reason for a change inthe futures rate has nothing to do with Fed policy. Itcould just be the case that a few more buyers than sell-ers, for example, happen to show up at the market,causing the futures rate to fall. However, we can expectthat these changes will be random and relatively smallbecause of the efficient markets hypothesis and becauseof the empirical results cited above.The point is that the federal funds futures contract offers

a direct look at expected Fed policy because the federalfunds futures contract is based on average monthly valuesof the future (spot) federal funds rate. Based on Carlson etal.’s (1995) results, the Fed has excellent control over theaverage monthly value of the future (spot) federal fundsrate.The daily federal funds futures rate is based on the

nearby contract (current month contract). Each month,there is a roll over to the next nearby contract (deferredmonth contract) two weeks prior to the expiration of thecurrent month contract. This rolling over to nearby con-tracts is consistent with the literature on financial futures(see Kroner and Sultan, 1993).13

Diagnostics

First, Phillips-Perron unit root tests indicated that the log

differences of the stock, bond, and federal funds futures

data are stationary. Univariate statistics such as the

mean, variance, skewness, kurtosis, Bera-Jarque, and LM

facilitate tests for normality, fat tails and peakedness, and

serial correlations in the daily changes in the stock and

bond returns, as well as the federal funds futures rate.

In Panel A, Table 1, the first differenced variables are

skewed (skewness of 0 is considered normal) and highly

kurtotic (excess kurtosis of 0 is considered normal).

Based on the skewness and excess kurtosis, the Bera-

Jarque statistic indicates that the distributions of these

variables are not normal. Furthermore, Q(24) and Q2(24)

Ljung-Box statistics indicate that the null hypothesis of

serial correlation in both the level and the squares cannot

be rejected for stock and bond returns and changes in the

federal funds futures rate. Finally, Panel B reports Engle’s

LM test for detecting autoregressive conditional heterosce-

dasticity (ARCH) (time dependence in the variance) in the

daily returns and interest rate changes. Engle’s LM test

confirms that for all the returns and interest rate series,

the variances are time varying. The evidence of ARCH in

changes in the federal funds futures rate is confirmed at the

21st lag of the residuals. While this is quite unusual for high

frequency financial data, it is possible that the manner in

which the federal funds futures rate was constructed could

lead to such biases in the data. As noted earlier, the CBOT

trades two types of federal funds contracts on a given day:

the current month contract and the various deferred month

contracts. By rolling over from the current to the deferred

month two weeks prior to the current month’s contract

expiration, the rates are averaged using the one month

forward rate implied in the deferred contract and the

(approximately) 15-day yield implied in the current

month contract. It is important to note that this rolling-

over procedure allows one to avoid expiration-related

problems in the federal funds futures market.

Overall, the preliminary diagnostics confirm that the first

differences of the financial market data are not normal and

the variances are time varying. Therefore, it is appropriate

to use the GARCH technique to model the joint time vary-

ing distribution of stock and bond market returns and ex-

amine their responses to monetary policy shocks.

202 O. D. Gulley and J. Sultan

11 In fact, other macroeconomic variables should be good predictors of the federal funds rate. Simon (1990) finds that the spread betweenthe 90-day T-bill and the overnight (cash) federal funds rate is a good predictor of the future federal funds rate.12 Carlson et al. (1995) also note that all three forecasts of the funds rate exhibit a slight positive bias over the sample period October 1988to December 1994. This study also provides a detailed summary of the nature of the 30 day federal funds futures contract. The CBOT(1992) publication 30-Day Interest Rate Futures, is also an excellent source for many institutional details of this contract.13 The analysis was repeated allowing the contracts to run until expiration, at which time it was then rolled over to the next contract. Theresults were nearly identical to the ones reported in the paper.

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Bivariate GARCH regression model

A bivariate GARCH model allows one to jointly modelthe impact of changes in the federal funds futures rate onthe mean and variance of stock and bond returns.However, prior to estimating the model, the previouslymentioned serial correlation in both stock and bondreturns must be dealt with. There are a number of methodsfor doing so. The procedure was chosen as follows. First,separate ARIMA models of both stock and bond returnsare estimated:

Xt ¼ aþX5i¼1Xt�i þ

X4i¼1DAYDUMMYi þ "t

where Xt is the natural log of the daily change in either thestock or bond index. Five AR terms were included toinsure that the residuals for each equations are whitenoise. DAYDUMMY (Monday through Thursday) isincluded to model any day of the week effects.14

Second, the bivariate conditional distribution of thedaily stock and bond returns is parameterized with thefollowing GARCH model that has been previously usedin the literature:15

St ¼ �0 þ "S;t

Bt ¼ �0 þ "B;tð1Þ

"S;t

"B;t

� �j t�1 � Dð0;HtÞ ð2Þ

Ht ¼

hS;t

hSB;t

hB;t

2664

3775 ¼

�S

�SB

�B

2664

3775þ

a11 0 0

0 a22 0

0 0 a33

2664

3775

"2S;t�1

"S;t�1"B;t�1

"2B;t�1

2664

3775

þ

b11 0 0

0 b22 0

0 0 b33

2664

3775

hS;t�1

hSB;t�1

hB;t�1

2664

3775 ð3Þ

where St and Bt in the mean Equations 1 are the residualsfrom the ARIMA equations of the daily stock and bondreturns, respectively.16 Equation 2 describes the joint den-sity functions, and in Equation 3, hS;tðhB;t) is the con-ditional variance of the stock (bond) returns, and "S and"B are the residuals from the mean Equations 1. InEquation 3, � are constant terms in the Ht matrix,a11 . . . a33 are ARCH coefficients, and b11 . . . b33 areGARCH coefficients. Note that to avoid convergenceproblems, the (a) (ARCH) and (b) (GARCH) matricesare usually assumed to be diagonal. This implies that thevolatilities are determined by the lagged squared residualsas well as the past volatilities much the same way as anautoregressive moving average (ARMA) time series model

Monetary policy and stock and bond markets 203

Table 1.

Variable � � Skewness Kurtosis Bera-Jarque Q(24) Q2(24)

Panel A: Descriptive statistics (first-differenced data)

Stock returns 0.04 0.80 �0.37 9.33 5955.19 36.64 68.03Bond returns 0.00 0.19 �1.04 19.11 25 128.39 70.82 10.78Fed funds futures �0.01 0.93 1.17 33.27 75 600.48 106.06 47.19

Panel B: Engle’s LM Test

TR2 Order

Stock returns 26.90 (1)Bond returns 8.65 (1)Fed funds futures 48.91 (21)

Note: Daily stock returns are based upon the Dow Jones equally weighted index of 30 stocks. Daily bond returns are constructed usingthe equally weighted index of 20 corporate bonds. Fed funds futures is the daily federal funds futures rate. The federal funds futures rateis based upon the nearby contract and rolls over to the next active contract two weeks prior to the expiration of current month contract.The first-differenced data are also highly kurtotic and the Bera-Jarque statistic indicates that the data are not normally distributed.Ljung-Box Q and Q2 tests show that daily returns are serially correlated both in the level and in squares. Finally, the evidence of timedependence in daily returns is confirmed with Engle’s LM test.

14 The authors thank the referee for this suggestion. The results of the ARIMA equations are available on request.15 See Chan et al. (1991) and Kroner and Sultan (1993).16 As mentioned, there are a number of alternatives to dealing with the serial correlation of the stock and bond returns. We tried using thechanges in the natural logs of the daily stock and bond prices directly in the GARCH equations above, rather than the residuals from theARIMA equations. This method required the use of AR terms in the GARCH equations themselves. Overall, the results using thismethod are fairly similar to those reported, except that for stock returns somewhat less evidence for asymmetry was found.

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204 O. D. Gulley and J. Sultan

Table 2. Bivariate GARCH estimation of the effects of fed funds futures rate

Mean equation�0 0.014

(0.854)�0 0.002

(0.403)�1 �0.043

(�2.973)c�1 �0.025

(�7.807)c

Variance equation�1 0.004

(1.924)b

�2 0.000(0.851)

�3 0.025(6.903)c

a11 0.018(3.714)c

a22 0.007(1.499)

a33 0.172(4.993)c

b11 0.973(128.840)c

b22 0.984(75.846)c

b33 0.093(0.878)

11 �0.005(�1.194)

21 �0.000(�0.784)

31 0.000(0.460)

1=v 0.168(12.989)c

Log-likelihood �1214.710� 3.000

Post-estimation diagnostics with standardized residuals

Skewness Kurtosis Q(24) Q2(24)

Stock returns �0.766 10.601 11.852 4.482Bond returns �1.755 25.413 10.829 0.954

Note: The following bivariate GARCH model was estimated:

St ¼ �0 þ �1� lnFF þ "t;S

Bt ¼ �0 þ �1� lnFF þ "t;B ð5Þ

Ht ¼

ht;S

ht;SB

ht;B

2664

3775 ¼

�S

�SB

�B

2664

3775þ

a11 0 0

0 a22 0

0 0 a33

2664

3775

"2t�1;S

"t�1;S"t�1;B

"2t�1;B

2664

3775þ

b11 0 0

0 b22 0

0 0 b33

2664

3775

ht�1;S

ht�1;SB

ht�1;B

2664

3775þ

11

21

31

2664

3775½� lnFF ð6Þ

where St and Bt in the mean Equations 5 are the residuals from the ARIMA models of the Dow Jones daily stock and bond returns,respectively. � lnFF represents changes in the federal funds futures rate. ht;Sðht;B) is the conditional variance of the daily stock (bond)returns, and "t;S and "t;B are residuals from the mean Equations 5. 1=v is the reciprocal of degrees of freedom. L is the log-likelihoodvalue. � is the log-likelihood ratio test statistics for the null hypothesis that H0: 11 ¼ 21 ¼ 31 ¼ 0 in the variance equation. The criticalvalue for the chi-square with three degrees of freedom is 7.89 (5%). Significance levels for the t-statistics: a (10%), b (5%), and c (1%).

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is defined. The bivariate GARCH models are estimatedusing the Berndt, Hall, Hall, and Hausman (BHHH)(1974) procedure.The robustness of the results depends on post-estimation

diagnostics using the standardized residuals ð"ij;t=ðhij;tÞ1=2Þand ("2ij;t=ðhij;tÞ1=2Þ from GARCH models. To deal withexcess kurtosis in the residuals, a conditional bivariateelliptical t-distribution (Muirhead, 1982, pp 48–9) isassumed for the residuals. The likelihood function is:

f ð"tÞ ¼�ðnþ �Þ

2

�

�

2

�ðð ð� � 2ÞÞ1=2Þn

� jHtj�1=2 1þ 1

� � 2"t 0H

�1t "t

� ��ððnþ�Þ=2Þð4Þ

where n is the number of variables, � denotes the degrees offreedom, and the time varying covariance matrix (Ht) isobtained from Equation 3.

Changes in the federal funds futures rates

We now turn to the link between the federal funds futuresrate and stock and bond returns. Table 2 presents theresults of the following GARCH model:

St ¼ �0 þ �l� lnFFt þ "S;t

Bt ¼ �0 þ �l� lnFFt þ "B;tð5Þ

Ht ¼

ht;S

ht;SB

ht;B

2664

3775 ¼

�S

�SB

�B

2664

3775þ

a11 0 0

0 a22 0

0 0 a33

2664

3775

"2t�1;S

"t�1;S"t�1;B

"2t�1;B

2664

3775

þ

b11 0 0

0 b22 0

0 0 b33

2664

3775

ht�1;S

ht�1;SB

ht�1;B

2664

3775þ

11

21

31

2664

3775½� lnFF ð6Þ

where again St and Bt in the mean Equations 5 are theresiduals from the ARIMA equations of the daily stockand bond returns, respectively. � lnFFt represents thedaily changes in the natural log of the federal funds futuresrate. Of particular importance to this study are �1, �1, andthe coefficients. �1 and �1 measure how changes in thefutures rate affect the mean returns in the stock and bond

markets, respectively. 11 and 31 measure the correspond-ing effects of this variable on the conditional volatility of

stock and bond market returns, respectively.

As can be seen, both stock and bond returns are inver-

sely related to changes in the futures rate. For example, an

increase in the futures rate implies that market participants

place a higher probability on a given increase in the federal

funds rate and/or think that the federal funds rate will

increase by a larger amount than previously expected.

This change in expectations is associated with decreases

in stock and bond prices. The reverse is true for a decrease

in the futures rate.17 Note that the results are actually

biased towards zero. Recall that the futures rate can change

for reasons that have nothing to do with expected changes

in policy, like a few more buyers than sellers on a given

day. Since these changes are random, � lnFFt contains an

element of random noise.

The results in Table 2 also indicate that changes in the

futures rate do not have a statistically significant effect on

the volatility in either the stock or bond markets, implying

that changes in expected Fed policy influence only the level

of asset prices, not the volatility.18 Post estimation diag-

nostics using the standardized residuals ("ij;t=ðhij;tÞ1=2Þ and("2ij;tÞ=ðhij;tÞ1=2Þ reveal that the GARCH models fit the data

quite well. The residuals are close to being white noise.

While kurtosis values are quite high, estimated

standard errors are robust to high kurtosis because of the

elliptical t-distribution. Finally, Ljung-Box Q statistics

show that the residuals are not serially correlated in levels

or in squares.

Asymmetric effects of the federal funds futures rate

As pointed out above, various authors have shown that

news can have asymmetric effects on economic variables

depending upon whether the market views the news to be

good or bad (Engle and Ng, 1993). Therefore, the federal

funds futures rate is decomposed into two variables: Pos,

which is equal to � lnFF if � lnFF 0, and zero other-

wise; and Neg, which is equal to � lnFF if � lnFF < 0,

and zero otherwise. The model is:

St ¼ �0 þ �1 Posþ �2Negþ "t;S

Bt ¼ �0 þ �1 Posþ �2Negþ "t;B

Monetary policy and stock and bond markets 205

17 One drawback of the methodology is that it does not allow for a clean interpretation of the �1 and �1 coefficients because the series Stand Bt are residuals. However, using the daily changes in the natural logs of the stock and bond prices in the GARCH models (seeFootnote 16), we found an estimated value of �0.10 for �1. If the DJIA was at 9000 and the federal funds futures rate rose by 5%, theDJIA would be predicted to fall by 45 points.18 There was also an attempt to measure volatility spillover between the markets by allowing several of the off-diagonal elements of the [a]and [b] matrices to be non-zero. Thus, a13 measures the effect of bond market volatility on stock market volatility and a31 measuresreverse causality in bond market volatility. b13 and b31 are interpreted analogously. It was found that there is no volatility spilloverbetween the two markets, nor is there reverse causality in the variances. These results are available on request.

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206 O. D. Gulley and J. Sultan

Table 3. Bivariate GARCH estimation of the effects of fed funds futures (positive and negative changes in fed funds futures rates)

Mean equation�0 0.017

(0.944)�0 0.001

(0.188)�1 �0.051

(�2.711)c�1 �0.024

(�3.594)c�2 �0.035

(�1.535)�2 �0.027

(�3.870)c

Variance equation�1 0.006

(1.700)a

�2 0.000(0.750)

�3 0.024(6.699)c

a11 0.019(3.613)c

a22 0.005(1.090)

a33 0.166(4.983)c

b11 0.971(111.990)c

b22 0.973(48.829)c

b33 0.076(0.711)

11 �0.007(�1.250)

21 0.000(0.096)

31 0.003(1.262)

12 �0.006(�0.947)

22 �0.002(�1.240)

32 �0.003(�0.809)

1=v 0.166(12.986)c

Log-likelihood �1211.586� 8.448

Post-estimation diagnostics with standardized residuals

Skewness Kurtosis Q(24) Q2(24)

Stock returns �0.752 10.523 11.766 4.207Bond returns �1.842 26.812 10.712 0.944

Note: The following bivariate GARCH model was estimated:

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Ht ¼

ht;S

ht;SB

ht;B

2664

3775 ¼

�S

�SB

�B

2664

3775þ

a11 0 0

0 a22 0

0 0 a33

2664

3775

"2t�1;S

"t�1;S"t�1;B

"2t�1;B

2664

3775

þ

b11 0 0

0 b22 0

0 0 b33

2664

3775

ht�1;S

ht�1;SB

ht�1;B

2664

3775þ

11

21

31

2664

3775½Pos

þ

12

22

32

2664

3775½Neg ð8Þ

The effects of positive changes in the federal funds futuresrate on the stock market variables are measured with �1 (inthe conditional mean equation) and 11 (in the conditionalvariance equation). Similarly, negative changes in the fed-eral funds futures rate are measured with �2 (in the con-ditional mean equation) and 12 (in the conditionalvariance equation). �1 and �2 measure the effects of posi-

tive and negative changes in the federal funds futures rateon the bond market returns, respectively, and the corre-sponding coefficients from the conditional variance equa-tions are 31 and 32. 21 and 22 capture the effects of theexogenous variables on the conditional covariance betweenthe two markets.Table 3 presents the results. �1, �2, �1, and �2 are all

negative and statistically significant, indicating the changesin the futures rate are inversely associated with stock andbond returns. Recall that the positive signs on the coeffi-cients of �2 and �2 must be reversed for usual interpret-ation of the coefficient since they measure the impact ofnegative changes in the exogenous variables. Comparisonof the coefficients shows that positive and negative changesin the futures rate have fairly symmetric effects on bondprices (�0:024 and �0:027) and somewhat asymmetriceffects on stock prices (�0:051 and �0:035, with the lattercoefficient not being statistically different from zero). As inTable 2, positive and negative changes in the federal fundsfutures rate do not influence the conditional volatility ofthe stock and bond markets.

Monetary policy and stock and bond markets 207

St ¼ �0 þ �1 Posþ �2Negþ "t;S

Bt ¼ �0 þ �1 Posþ �2 negþ "t;B ð7Þ

Ht ¼

ht;S

ht;SB

ht;B

2664

3775 ¼

�S

�SB

�B

2664

3775þ

a11 0 0

0 a22 0

0 0 a33

2664

3775

"2t�1;S

"t�1;S"t�1;B

"2t�1;B

2664

3775þ

b11 0 0

0 b22 0

0 0 b33

2664

3775

ht�1;S

ht�1;SB

ht�1;B

2664

3775þ

11

21

31

2664

3775½Pos þ

12

22

32

264

375½Neg ð8Þ

where St and Bt in the mean Equations 7 are the residuals from the ARIMA models of the Dow Jones daily stock and bond returns,respectively. POS and NEG are positive and negative changes in the log of the federal funds futures rate. ht;Sðht;B) is the conditionalvariance of the daily stock (bond) returns, and "t;S and t;B are residuals from the mean Equations 7. 1=v is the reciprocal of degrees offreedom. L is the log-likelihood value. � is the log-likelihood ratio test statistics for the null hypothesis thatH0: 11 ¼ 21 ¼ 31 ¼ 0 in thevariance equation. The critical value for the chi-square with three degrees of freedom is 7.89 (5%). Significance levels for the t-statistics: a(10%), b (5%), and c (1%).A test was also conducted to check for asymmetry in the returns of the stock and bond markets. A bivariate GARCH model with no

asymmetry in the model specification was estimated. This model has no good news/bad news in the mean or variance equations. Fromthis model, the residuals and the conditional covariance matrix were retrieved. Then standardized residuals were calculated as:("ij;t=ðhij;tÞ1=2) and ð"2ij;t=ðhij;tÞ1=2). This was repeated for the bond market. Next, the cross correllogram between squared standardizedresiduals and lagged level standardized residuals were estimated. Finally, the Ljung-Box statistic was estimated using the partial auto-correlation functions (PACF) as:

T*ðT þ 2Þ*X36i¼1p2t�i

!�ðT � 2Þ

where T ¼ 1631 (number of observations) and pi is the PACF. If there is asymmetry in the model then the Ljung-Box statistics should besignificant with 36 degrees of freedom. The results are

Ljung-Box TStock 29.668 1631Bond 22.106 1631

The critical chi-square (Ljung-Box) is 36.42. The null hypothesis of no serial correlation is not rejected. Thus, it was concluded that thereis not enough evidence to support asymmetry in either stock or bond returns.

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As above, post-estimation diagnostics using the standar-dized residuals ("ij;t=ðhij;tÞ1=2Þ and ð"2ij;t=ðhij;tÞ1=2Þ reveal thatthe GARCH models fit the data quite well. The residualsare quite close to being white noise. Finally, Ljung-Box Qstatistics show that the residuals are not serially correlatedin the levels or in squares.19

IV. SUMMARY AND CONCLUSIONS

The understanding of the role of the central bank and theeffects of its policy variables is crucial for developing effec-tive risk management strategies for a firm operating in aglobal capital market. In particular, to effectively managerisk, market participants need to extract information aboutthe central bank’s future policies and carefully examinethe extent to which such information can affect financialmarket variables. This study examined how the level andvolatility of stock and bond returns are influenced bychanges in the 30-day federal fund futures contract rate.It was found that changes in the 30-day federal fundsfutures rate are inversely related to stock and bond returns.Evidence was also found that information shocks concern-ing the futures rate have asymmetric effects on the stockmarket, but symmetric effects on the bond market.These results are important for several reasons. First, the

econometric model employed in this paper addresses sty-lized features of the distribution of financial market returnsand provides statistical inferences that are robust to thenon-normal distribution of the data. Such a careful analy-sis of market response to information shocks clearlyimproves understanding of the link between informationand market volatility. The unique feature of the empiricalresults is that they are obtained from a regression modelthat incorporates the joint distribution of stock and bondmarket returns and yet allows each market to express itsown views on monetary policy. Finally, the econometricmodel also offers a useful guide to study the asymmetriceffects of information variables on the market dependingupon whether market participants view such informationas optimistic or pessimistic.Several important issues are left for future research.

First, Garfinkel and Thornton (1995) find that the federalfunds rate does not appear to provide any unique informa-tion regarding monetary policy. Thus, it would be of inter-est to see if the results hold up using other short-terminterest rates. Second, Ederington and Lee (1993) use intra-day data to examine the impact of news on asset prices.Such data could be employed using these techniques, whichwould allow for finer distinction as to how monetary policyaffects asset prices. Third, why do the stock and bond

markets appear to react differently to the same informationconcerning Fed policy? Do participants in these marketshave different views of the same information?

ACKNOWLEDGEMENTS

We thank James Zeitler for excellent research assistance,David Simon for his insightful comments, and theEconomics Department Seminar at Bentley College forvery helpful suggestions. Thanks are also expressed to ananonymous referee for helpful suggestions that substan-tially improved the paper. Gulley is a Gibbons ResearchProfessor.

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