investigating the relationships among oil prices, bond index returns and interest rates

International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 38 (2010)
© EuroJournals Publishing, Inc. 2010


Investigating the Relationships Among Oil Prices, Bond Index
Returns and Interest Rates


Manhwa Wu
Department of Finance, Ming Chuan University, 250 Zhong-Shan N. Rd., Sec. 5 Taipei
Taiwan 111, R.O.C
E-mail:
Tel: +886-2-2882-4564 ext. 2390; Fax: +886-2-2880-9769


Abstract

Fuerbringer (2004) reports that a sharp drawdown in American oil inventories on
the price of oil in turn helps push down longer-term interest rates. Browing (2004) finds
that the impact of oil prices produces an increase in the ten-year Treasury note yield, which
is similar to the finding of Fuervringer (2004). Browing (2005) reveals that the Dow Jones
Industrial Average index has the highest level in almost two months, partly as a result of
falling oil prices and declines in bond yields.
Most studies in the literature focus on the relationships of oil prices and
macroeconomic systems, or oil prices and stock indices. Few in the literature take a look at
oil prices and bond prices via interest rates. Thus, the above relationships should be further
investigated, since whether oil price changes affect bond investment decisions and
monetary policy by way of interest rates are still major concerns for investors and
government. Moreover, the massage transmission is also an essential matter in this paper,
which then leads to the lag-length chosen as another topic herein. Thus, we apply six lag-

length chosen criteria (AIC, SBC, BIC, S, HJC, and FPE) to study in either symmetric
models or asymmetric models. The important findings are that oil price changes affect both
interest rate and interest rate volatility. Bond returns also affect interest rate volatility and
oil price changes.


Keywords: Oil price changes, Bond index return, Interest rates
JEL Classification Codes: G15, E44

1. Introduction
The cost of inflation is a subject that has long troubled macroeconomists. While unexpected inflation
redistributes people’s wealth, it is difficult to show significant welfare losses from moderate inflation.
In Milton Friedman’s (1977) Nobel lecture, he stresses the potential of increased inflation to create
nominal uncertainty that lowers welfare and possibly even output growth, and the innovative model by
Ball (1992) formalizes Friedman’s insight. Besides, from the study of Grier and Grier (1998), the
results show that higher inflation causes increased uncertainty as predicted by Friedman and Ball.
Recently, Grier and Perry’s (1998) investigate that inflation and inflation uncertainty for G7
countries, and they find the bi-directional relationships between inflation and inflation uncertainty
among these countries. Due to the main source of inflation, which might be from the money
1
supply,
examining the effect from money uncertainty to inflation might be more appropriate than examining
the effect from inflation uncertainty to inflation.
International Research Journal of Finance and Economics - Issue 38 (2010) 148
From the traditional wisdom of Fisher’s (1922), he proposes the equation of exchange, which is
an identity relating the volume of transactions at current prices to the stock of money times the
turnover rate of each dollar. This identity is expressed as TPMV
TT
≡
. In view of the basic result of the

quantity theory of money, the behavior of money might be the main source of inflation.
In the paper, the contents will be organized into five sections. In section 2, the literatures will
be surveyed, and the variables retrieved in the paper will be explained. The methodology will be
introduced in section 3, and the empirical results will be shown and section 4. The conclusion will be
summarized in the final section.


2. Previous Research and Hypotheses
Many papers relate stock indices with oil prices (like Papapetrou, 2001), but only a few papers
investigate bond indices with oil prices. Therefore, we adopt a bond index instead of a stock index and
examine the relationships among oil price changes, bond returns, and interest rates. In this paper we
not only concerned about interest rate behavior, but also interest rate volatility. Moreover, the massage
transmission is also an essential matter in this paper, which then leads to the lag-length chosen as
another topic herein.
This section discusses four parts of the related literature as follows. Part 1 shows the
relationship between oil price changes and stock prices. Part 2 describes the behaviors of interest rates.
Part 3 discusses the methods of measuring interest rate volatility. The last part is about the chosen lag-
length criteria.

(1). Literature on the Relationships Between Oil Price Changes and Stock Prices
Sadorsky (1999) shows that oil prices and oil price volatility both play important roles in affecting real
shock returns. The evidence reveals that oil price volatility shocks have asymmetric effects on the
economy. Kim and Sheen (2000) reveal that monetary policy announcements have significant effects
on interest rates, as well as on their volatility in the short term. This implies that some macroeconomic
news announcements raise interest rate volatilities. Papapetrou (2001) provides empirical evidence that
oil price changes affect real economic activity. Maghyereh (2004) examines the dynamic linkages
between crude oil price shocks and stock market returns in emerging economies, finding that oil shocks
have no significant impact on stock index returns, especially in emerging economies. Manera et al.
(2004) investigate the correlations of volatilities in stock price returns and their determinants for the
most important integrated oil companies. The results reveal interdependence between the volatilities of

companies’ stock returns and Brent oil prices. Since oil price changes might affect interest rate
behavior and bond returns, the following are employed in this paper.
Hypothesis 1: There exist significant effects from the oil price changes to bond returns.

(2). Literature on the Behaviors of Interest Rates
Hiraki and Takezawa (1997) examine the sensitivity of volatility to the level of the interest rate in
Japan. They find that short-term interest rate volatility is sensitive to the level of interest rate. Siklos
and Skoczylas (2002) also show that real interest rate volatility is characterized by long periods of
relatively constant volatility interrupted by short periods of sharp increases in volatility, while volatility
clustering is positively correlated with financial market frictions and the nominal interest rate. Dotsey
et al. (2003) reveal evidence that high real rates are quite sensitive to the price series used. They also
find that real rate behavior varies over different sample periods and the cyclical properties of the ex-
ante and ex-post real rates are not identical. Seppala (2004) studies the behavior of the default-risk-free
real term structure and term premia in two general equilibrium endowment models. The evidence
shows that both models produce time-varying risk or term premia.
Hypothesis 2: There exist significant effects from oil price changes to interest rates and to interest
rate volatility.
149 International Research Journal of Finance and Economics - Issue 38 (2010)
(3). Literature on the Methods of Measuring Interest Rate Volatility
Niizeki (1998) applies several methods to estimate interest rate volatility and to investigate short-term
interest rate models by using both U.S. and Japanese data. The appropriate discrete-time specification
used to estimate the volatility in the short-term interest rate is the GARCH-M (1, 1) process. Edwards
and Susmel (2003) use data of Latin American and Asian countries to analyze the behavior of interest-
rate volatility through time and find some evidence of interest-rate volatility co-movements across
countries. In fact, current bond prices and interest rates are negatively related from the theoretical view
of financial markets. This implies that when the interest rate rises, the price of the bond falls, and vice
versa. Thus, it stimulates our interest to examine the relationship among oil price changes, bond prices,
and interest rate/interest rate volatility, and list the Hypothesis 1 as follows:
Hypothesis 3: The interest rate volatilities have significant GARCH effects.

(4). Literature of the Lag-Length Chosen Criteria
Since the massage transmission is also an essential concern for financial models, the lag-length chosen
will be emphasized in this paper. The lag-length chosen means how many lags are necessary to include
in the time series models. Thus, several scholars have their points of view as in the literature mentioned
below.
Hsiao (1981) proposes Akaike’s final prediction error criterion, which adopts a stepwise
procedure based on Granger’s concept of causality. This criterion is suggested as a practical means to
identify the order of lags for each variable in a multivariate autoregressive model. This model seems
useful, because it can serve as a reduced-form formulation to avoid imposing spurious restrictions on
the model.
Thornton and Batten (1985) similarly suggest that based on a standard, classical, and
hypothesis-testing norm, Akaike’s FPE criterion performs well in selecting the lag length for a model,
but the FPE criterion may not conform to all researchers’ prior beliefs about the appropriate trade-off
between bias and efficiency. Unlike the results of Thornton and Batten (1985), the evidence in Jones
(1989) reveals that one of the ad hoc methods for lag-length determination is found to perform
somewhat better than the statistical search methods in correctly assessing the causal relationships
involving money growth and inflation.
The lag terms selected by the FPE criterion are inadequate for the purpose of testing Granger
causality as suggested by Kang (1989). Kang reveals that lag terms are selected optimally in the most
efficient forecast equations obtained from univariate variable analyses and transfer function analyses.
This is done in order to test for the causality between industrial production and the leading indicator of
U.S. data by his new procedure. He applies his procedure showing that the ARIMA analysis is better
than using a pure AR process in the FPE to achieve optimal models. Furthermore, Hall (1994)
mentions there can be considerable gains in the power of the ADF test from estimating p rather than
fixing it at some relatively large number; i.e., he concludes that estimating appropriate lag terms for the
ADF test will get the power for the test. After surveying the above literatures, the following hypotheses
are taken into accounts as follows.
Hypothesis 4: The empirical results show no difference even when employing six lag-chosen
criteria.
Hypothesis 5: The empirical results show no difference between choosing symmetric models and

asymmetric models
1
.
This paper tests the relationships among oil price changes, bond returns, and interest rates with
more robustness concerns. We would like to find if our empirical results are sensitive to different lag-
length chosen criteria, such as AIC,
2
BIC,
3
FPE,
4
SBC,
5
S,
6
and HJC
7
criteria, and if the empirical

1
One model chooses the same lag-length for different variables, and the other one??? chooses different lag lengths for
different variables.
2
AIC (Akaike’s Information Criterion) criteria, proposed by Akaike in 1973 and 1974.
International Research Journal of Finance and Economics - Issue 38 (2010) 150
results concerning asymmetric lag length are different from those concerning symmetric lag length by
employing the above lag-length chosen criteria. Furthermore, we examine the interrelationships among
oil price changes, bond returns, and interest/interest rate volatility by time series models, in order to
compare if the evidence is different by retrieving interest rate volatility estimated by different methods,
and to test the robustness of causality by employing six different lag-length criteria.

3. Empirical Results
We obtain the monthly data of the MSCI World Bond index, Treasury Bill Rate, and the FOB cost of
crude oil imports for the U.S. from January 1998 to November 2005 in the AREMOS database
established by the Taiwan Economic Data Center and Economagic database, respectively. The FOB
cost of crude oil imports, the MSCI world bond index, and the Treasury bill rate are regarded as oil
price variables, bond variables, and interest rate variables, respectively, in this paper.
Since the volatilities of interest rates might cluster together (as shown in Figure 1), we apply
GARCH models to measure the conditional variance of the interest rate. In addition, Engle and Lee
(1993) propose component GARCH models
8
equivalent to GARCH (2,2) models which allow the

NTAIC 2log +∑=

Here, T is the number of usable observations, ∑ is the determinant of the variance/covariance matrix of the residuals,
and N is the total number of parameters estimated in all equations.
3
BIC (Bayesian Information Criterion) criteria, proposed by Rissanen in 1978.
T
TN
BIC
)log(
log +∑=

Here, T is the number of usable observations, ∑ is the determinant of the variance/covariance matrix of the residuals,
and N is the total number of parameters estimated in all equations.
4
FPE (Final Prediction Error) criteria, proposed by Akaike in 1969 and 1970.

TnSSRnTnTFPE /)()1/()1( −−++=

Here, T is the sample size, n is the lag-length being tested, SSR is the sum of squared residuals, and N denotes the
maximum lag-length over which the search is carried out.
5
SBC (Schwarz’s Bayesian Criterion) criteria, proposed by Schwarz in 1978.
)log(log TNTSBC +∑=

Here, T is the number of usable observations, ∑ is the determinant of the variance/covariance matrix of the residuals,
and N is the total number of parameters estimated in all equations.
6
S (Shibata Criterion) criteria, proposed by Shibata in 1980.
)2log(log NTTTS ++∑=

Here, T is the number of usable observations, ∑ is the determinant of the variance /covariance matrix of the residuals,
and N is the total number of parameters estimated in all equations.
7
HJC criteria, proposed by Hacker and Hatemi-J in 2001.
()
22
ln 2 ln(ln )
ˆ
ln det , 0,1, 2, ,
2
j
nT n T
HJC j j k
T
⎛⎞
+

=Ω+ =
⎜⎟
⎝⎠

Here, T is the sample size,
ˆ
j
Ω is the maximum likelihood estimate of the variance-covariance matrix Ω when the lag
order used in estimation is j, and n is the number of variables.
8
The component GARCH model allows the mean reversion level of the conditional variance to itself be time-varying.
The model, given by Equations (1) and (2) below, divides the conditional variance into permanent and transitory
components.
)()(
1
2
121
2
11
2
−−−−
−+−+=
tttttt
qqq
εε
σαεασ
(1)
)(
2
1

2
1310 −−−
−++=
tttt
qq
ε
σεαρα
(2)
If ρ in equation (2) is equal to 1.0, then the conditional variance contains a unit root. If ρ<1.0 and ρ>
21
α
α
+
, then q
t
is
the longer memory component of the conditional variance.
It is not obvious that the Component GARCH model is a superset of the GARCH(1,1) model, but Engle and Lee show
that it is equivalent to a GARCH(2,2) model with appropriate restrictions on the coefficients.
151 International Research Journal of Finance and Economics - Issue 38 (2010)
mean reversion level of the conditional variance to be time-variant. Therefore, we employ two kinds of
GARCH models to retrieve interest rate volatility variables and test if there are different results by
these two different approaches.

Figure 1: The interest rate volatility of the U.S.

0
0.02
0.04
0.06

0.08
0.1
0.12
1
3
5
7
9
11 1
3
1
5
17 1
9
21 2
3
2
5
27 2
9
31 3
3
3
5
37 3
9
41 4
3
4
5

47 4
9
51 5
3
5
5
57 5
9
61 6
3
6
5
67 6
9
71 7
3
7
5
77 7
9
81 8
3
8
5
Interest volati li ty
Ti me
IRV1
IRV2

Table 1: The Statistics for Oil, Bond, and IR

1998.1~2005.11
Va r i a b l e
Mean Standard Deviation Minimum Maximum
Oil (cents per barrel) 22.33 7.55 8.18 42.21
Bond 1041.30 163.04 850.88 1465.96
IR (percent per annum)
3.25
1.86 0.89 6.18

3.1. Unit Root Tests
From the results of the unit test, we find that the Dickey-Fuller (DF), Augmented Dickey-Fuller
(ADF), Phillips-Perron (PP), and Augmented Phillips-Perron (APP) values of the levels of Oil, Bond,
IR1, IR2, and IR are not all significant at the 5% level, and thus we do not reject this as non-stationary.
The PP, DF, and ADF values of Oil, Bond, and IR are significant after the first log transformation and
difference for these two series; i.e. these log-differential series are stationary. Moreover, the interest
rate volatility variables retrieved either by GARCH (1, 1) models or by Component GARCH models
are all stationary, as shown in Table 2.

Table 2: Unit Root Tests for Oil, Bond, and IR

Variable Trend ADF(t) DF(t) APP(t) PP(t)
No -1.04 -0.27 -0.48 -0.27
Oil
Yes -2.57 -2.04
No -0.64 -0.52 -0.58 -0.52
Bond
Yes -1.80 -1.66
No -1.21 -0.99 -1.04 -0.99

Level
IR
Yes -0.18 0.47
No -6.61** -7.15** -7.19** -7.15**
Oil
Yes -6.55** -7.16**
No -6.22** -8.09** -8.09** -8.09**
Bond
Yes -6.18** -8.05**
No -3.76** -5.20** -5.07** -5.20**
Log Differencing
IR
Yes -4.03** -5.39**
Note: The lag length of ADF and that of APP are chosen by AIC criteria.
Star (**) means significance at the 5% level.
International Research Journal of Finance and Economics - Issue 38 (2010) 152
3.2. Time Series Model of the Interest Rate
As suggested by Engle and Lee (1993), we set up an ARIMA model for interest rates and then retrieve
interest rate volatility variables by applying the GRACH models and the component GARCH models.
As a whole in the following models there exist clear GARCH effects during the data period for the
U.S., and the results imply the phenomenon of volatilities clustering together that exist during some
periods.

Table 3: Time Series Model for Interest Rates

(A )ARMA Models
13
0.3774 0.2834
tttt
GIR GIR GIR

ε
−−
=− − +

(4.02**) (2.98**)
(B )GARCH(1,1) Models
13
0.3592 0.0890
tttt
GIR GIR GIR
ε
−−
=− + +
(-19.21**) (15.54**)
222
11
0.000082 1.1711 0.4169
ttt
ε ε
σ
εσ
−−
=− + +

(21.35**) (37.70**) (41.10**)
( C )Component GARCH Models
13
0.4108 0.3801
tttt
GIR GIR GIR

ε
−−
=− + +

(-19.21**) (15.54**)
22222
12 1 2
0.000077 0.6092 0.3298 0.2632 0.2440
ttttt
ε εε
σεεσσ
−− − −
=+ + + +

(5.53**) (29.78**) (11.36**) (21.57**) (28.96**)
Note: GIR
t
: the growth of interest rate
t
a : the moving average terms;
t
ε
: noise term
2
t
ε
σ
：the conditional heteroscedasticity of the growth of interest rate
Star (**) means significance at the 5% level.

3.3. Granger Causality Results
This section investigates three topics, such as the relationship between oil price changes and bond
returns, the relationship between oil price changes and the growth of interest rates, and the relationship
between oil price changes and interest rate volatility, including retrieving volatilities by both models.
Six lag-length chosen criteria - AIC, SBC, BIC, S, HJC, and FPE - are also employed in either
symmetric models or asymmetric models.
Since the structure of presenting empirical results is quite complicated, it might be necessary to
set up a table containing the above information for readers to understand what we have done in this
paper. In addition, in order to save space, we put all of the information in a table instead of putting
them in several tables. Since these several variables and lag-chosen criteria are mentioned many times,
we use the abbreviated symbols for them instead of presenting their full name, as shown in Table 4.
153 International Research Journal of Finance and Economics - Issue 38 (2010)
Table 4: The Abbreviated Symbols of Variables and Criteria

AIC Akaike’s Information Criterion
BIC Bayesian Information Criterion
FPE Final Prediction Error
HJC Hacker and Hatemi-J’s Criterion
SBC Schwarz’s Bayesian Criterion
S Shibata Criterion
Oil Oil price
Bond (B) World Bond index
IR Treasury bill rate
GOIL (O) The change in oil price
GBOND The bond returns
GIR The growth of the interest rate
IRV1 Interest rate volatility generated by GARCH(1,1) models
IRV2 Interest rate volatility generated by Component GARCH models

3.3.1. The Relationships of Oil Price Changes, Bonds, Interest Rates, and Interest Rate Volatility

by Applying Symmetric Models
In the systematic models, there are four kinds of VAR models investigated as follows: (1) Granger
causality tests for GOIL and GBOND with different lag-chosen criteria, (2) Granger causality tests for
GOIL and GIR with different lag-chosen criteria, (3) Granger causality tests for GOIL and IRV1 with
different lag-chosen criteria, and (4) Granger causality tests for GOIL and IRV2 with different lag-
chosen criteria.
In the first and second Granger causality tests, the results selected by AIC and SBC criteria
show some significant effects, such as the effect from GBOND to GOIL, and that from GOIL to GIR.
Similar results are shown in the third and fourth Granger causality tests for GOIL and IRV1, and for
GOIL and IRV2. These all imply there are significant effects from oil price changes to interest
volatility even though the retrieved volatilities are by different GARCH models.

3.3.2. The Relationships of Oil Price Changes, Bond Returns, Interest Rates, and Interest Rate
Volatility by Applying Asymmetric Models
While separating 2x2 VAR models into two OLS equations, different lag lengths could be selected for
different variables in each OLS equation by these six lag-chosen criteria. The results for the Granger
causality tests could be obtained by these six different lag-chosen criteria, as shown in Table 5.
In the case of GOIL and GBOND, the unidirectional effects are found from GBOND to GOIL
by employing six lag-chosen criteria, except for the S criteria. In the case of GOIL and GIR, the
unidirectional effects from GOIL to GIR are also detected by the AIC lag-chosen criteria. As for GOIL
and IRV1, there exist significant effects from GOIL to IRV1 for all criteria except for the S criteria. In
addition, similar results are shown in the case of GOIL and IRV2, i.e. the unidirectional effects are
found from oil price changes to IRV2 for all of the criteria except for the S criteria.
International Research Journal of Finance and Economics - Issue 38 (2010) 154
Table 5: Granger Causality Results for Symmetric Lag Models and Asymmetric Models Concerning Six
Lag-chosen Criteria (The relationships of oil price changes, bond returns, interest rates, and interest
rate volatility)

Models
Granger

Causality
The symmetric lag models after
selecting same lag length for each
equation
The asymmetric lag models after selectin
g

different lags for each equation
1. GOIL and GBOND
(1) ( 1, 1 ) (1) ( 1, 1 )
H
a
: 0.17 H
a
: 1.39
(2) ( 1, 1 ) (2) ( 2, 22 )
AIC
H
b
: 3.18*
AIC
H
b
: 1.97**
(1) ( 1, 1 )
H
a
: 1.39
GBOND = f ( a , b )
a and b mean the lag lengths

chosen for the oil variable and
bond variable for equation (1)
(2) ( 1, 1 )
GOIL = f ( c , d) c and d mean the
lag lengths chosen for the oil variable
and bond variable for equation (2)
BIC BIC
H
b
:2.77*
(1) ( 20, 3 )
H
a
: 1.56
(2) ( 2, 21 )
GBOND = f(O
it−
, B
it−
)
Ha
FPE

FPE
H
b
: 1.93**
(1) ( 1, 1 ) (1) ( 1, 1 )
Ha: Oil does not Granger- cause
Bond

H
a
: 0.17 H
a
: 1.39
GOIL = f(O
it−
, B
it−
)
(2) ( 1, 1 ) (2) ( 1, 1 )
H
b

SBC
H
b
: 3.18*
SBC
H
b
:2.77*
(1) ( 22, 24 )
H
a
: 0.94
(2) ( 24, 22 )
S S
H
b

:1.22
(1) ( 1 , 1 )
H
a
: 1.39
(2) ( 1 , 1 )
H
b
: Bond does not Granger-cause
Oil
HJC HJC
H
b
:2.77*
2. GOIL and GIR
AIC (1) ( 1, 1 ) AIC
(1) ( 1, 10 )
GIR = f(O
it−
, GIR
it−
)
H
a
: 3.15* H
a
: 3.46**
Ha
(2) ( 1, 1 )
(2) ( 2, 20 )

Ha: Oil does not Granger- cause
IR
H
b
: 0.93 H
b
:1.47
GOIL = f(O
it−
, GIR
it−
)
BIC BIC
(1) ( 1, 1)
H
b

H
a
: 1.57
H
b
: IR does not Granger- cause
Oil

(2) ( 1, 1 )
H
b
:1.61
(1) ( 15 , 10 )

H
a
: 1.14
(2) (6 , 18 )
FPE FPE
H
b
:1.32
(1) ( 1, 1 )
SBC (1) ( 1, 1 )
H
a
: 3.15* H
a
: 1.57
(2) ( 1, 1 )
(2) ( 1, 1 )

SBC
H
b
: 0.93 H
b
:1.61
155 International Research Journal of Finance and Economics - Issue 38 (2010)
(1) ( 20, 24)
H
a
: 0.99
(2) ( 24, 20 )

S S
H
b
: 1.07
(1) ( 1 , 1 )
H
a
: 1.57
(2) ( 1 , 1)
HJC HJC
H
b
: 1.61
3. GOIL and IRV1
(1) ( 1, 1 )
H
a
: 9.26**
(1) ( 1, 2 )
IRV1 = f(O
it−
, IRV1
it−
)
Ha:
(2) ( 1, 1 ) H
a
: 8.93**
Ha: Oil does not Granger- cause
IRV1

H
b
: 0.31
(2) ( 24, 23 )
GOIL = f(O
it−
, IRV1
it−
)
AIC

AIC
H
b
: 1.08
H
b

(1) → (1, 2 )
H
a
: 8.93** H
b
: IRV1 does not Granger-cause
Oil (2) → ( 5, 1 )
BIC BIC
H
b
: 1.16
(1) ( 12, 11 )

H
a
: 2.32**
(2) (7, 15 )
FPE FPE
H
b
: 1.37
(1) ( 1, 1 ) SBC
(1) ( 1, 5 )
H
a
: 9.26** H
a
: 6.93**
(2) ( 1, 1 )
(2) ( 1, 1 )
SBC
H
b
: 0.31 H
b
:1.72
(1) ( 24, 24 )
H
a
: 0.83
(2) ( 24, 24 )
S S
H

b
: 0.97
(1) ( 1 , 1 )
H
a
: 7.07**
(2) ( 1 , 1 )

HJC HJC
H
b
:1.72
4. GOIL and IRV2
AIC (1) ( 1 , 1 ) AIC (1) ( 1 , 1 )
H
a
: 12.17** H
a
: 10.31**
IRV2 = f(O
it−
, IRV2
it−
)
Ha:
(2) ( 1 , 1 ) (2) ( 24 , 21 )

H
b
: 1.59 H

b
: 2.06*
(1) ( 1 , 2 )
Ha: Oil does not Granger- cause
IRV2
H
a
: 9.40**
GOIL = f(O
it−
, IRV2
it−
)
H
b

(2) ( 5 , 1 )
BIC BIC
H
b
: 1.22
(1) ( 18 , 3 )
H
a
: 2.69**
(2) ( 9 , 13 )
FPE FPE
H
b
: 1.03

(1) ( 1 , 1 ) SBC (1) ( 1 , 5 )
H
a
: 12.17** H
a
: 6.19**
H
b
: IRV2 does not Granger-cause
Oil
SBC
(2) ( 1 , 1 ) (2) ( 1 , 1 )
International Research Journal of Finance and Economics - Issue 38 (2010) 156
H
b
: 1.59 H
b
: 2.43*
S (1) ( 24 , 24 )
H
a
: 1.65
(2) ( 21 , 23 )
S
H
b
: 0.77
HJC (1) ( 1 , 1 )
H
a

: 10.31**
(2) ( 1 , 1 )
HJC

H
b
: 2.43*
Note: 1. Star (*) means significance at the 10% level, and two stars (**) mean significance at the 5% level.
2. The criteria for BIC, S, and FPE are selected equation by equation. Since symmetric lag models select the same
lag length for each variable in each equation, the spaces are therefore empty due to this reason.

3.3.3. The Relationships of Bond Returns, Interest Rates, and Interest Rate Volatility by
Applying Symmetric Models
In the systematic models, three VAR models are investigated as follows: (1) Granger causality tests for
GBOND and GIR with the same lag-chosen criteria, (2) Granger causality tests for GBOND and IRV1
with the same lag-chosen criteria, and (3) Granger causality tests for GBOND and IRV2 with the same
lag-chosen criteria.
In the first Granger causality tests, the results selected by AIC and SBC criteria show some
significant phenomena, with an effect from GBOND to GIR. However, there exists no relationship
between GBOND and IRV1, and between GBOND and IRV2. This implies no significant effects from
bond returns to interest volatility as retrieved by different GARCH models.

3.3.4. The Relationships of Bonds, Interest Rates, and Interest Rate Volatility by Applying
Asymmetric Models
After separating 2x2 VAR models into two OLS equations, different lag lengths are selected for
different variables in each OLS equation by these six lag-chosen criteria. The results for Granger
causality tests are obtained by these six different lag-chosen criteria, as shown in Table 6.
In the case of GBOND and GIR, the results selected by the AIC, BIC, and S criteria show some
significant phenomena, with an effect from GBOND to GIR. However, there are significantly
unidirectional effects from GIR to GBOND by employing the FPE and S lag-chosen criteria. In the

case of GBOND and IRV1, there are unidirectional effects from GBOND to IRV1 by the AIC and BIC
lag-chosen criteria. Similar results are shown in the case of GBOND and IRV2, and there are
unidirectional effects from bond returns to interest rate volatility for the AIC, BIC, HJC, and SBC lag-
chosen criteria.
157 International Research Journal of Finance and Economics - Issue 38 (2010)
Table 6: Granger Causality Results for Symmetric Lag Models and Asymmetric Models Concerning Six
Lag-chosen Criteria (The relationships of bond returns, interest rates, and interest rate volatility)

Models
Granger
Causality
The symmetric lag models after
selecting the same lag length for
each equation
The asymmetric lag models after
selecting different lags for each
equation
(1) ( 1 , 1 ) (1). ( 1 , 3 ) 1 GBOND and GIR
H
a
: 3.17* H
a
:2.59*
(2) ( 1 , 1 ) (1). ( 1 , 1 ) (1) GIR = f (B , GIR ) Ha:
AIC
H
b
: 2.04
AIC
H

b
:2.35
- Ha: Bond does not Granger- cause IR (1) ( 1 , 3 )
H
a
: 2.59*
(2) ( 1 , 1 )
(2) GBOND=f(B , GIR ) H
b

BIC

BIC
H
b
: 2.35
(1) ( 15 , 10 )
H
a
: 1.34
(2) ( 7 , 17 )
FPE

FPE
H
b
: 1.96**
(1) ( 1 , 1 ) (1) ( 1 , 1 )
H
a

: 3.17* H
a
:1.58
(2) ( 1 , 1 ) (2) ( 1 , 1 )
SBC
H
b
: 2.04
SBC
H
b
: 2.35
(1) ( 24 , 23 ) S

S
H
a
: 1.93*
(2) ( 24 , 17 )
H
b
: 2.22**
(1) ( 1 , 1 )
H
a
: 1.58
(2) ( 1 , 1 )
- H
b
: IR does not Granger- cause Bond

HJC

HJC
H
b
:2.35
2 GBOND and IRV1 (1) ( 1 , 1 ) (1) ( 1 , 2 )
H
a
: 0.01 H
a
: 3.68**
(2) ( 1 , 1 ) (2) ( 1 , 1 )
(1) IRV1 = f (B ,
it−
IRV1
it−
) Ha:
AIC
H
b
: 0.07
AIC
H
b
: 0.92
BIC (1) ( 1 , 2 )
H
a
: 3.68**

- Ha: Bond does not Granger- cause IRV1
(2) ( 1 , 1 )


BIC
H
b
: 0.92 (2) GBOND=f(B , IRV1 ) Hb
(1) ( 13 , 9 )
H
a
: 1.06
(2) ( 4 , 17 )
FPE

FPE
H
b
: 1.77*
(1) ( 1 , 1 ) (1) ( 1 , 1 )
H
a
: 0.01 H
a
: 2.25
(2) ( 1 , 1 ) (2) ( 1 , 1 )
SBC
H
b
: 0.07

SBC
H
b
: 0.92
(1) ( 23 , 24 )
H
a
: 0.71
(2) ( 23 , 24 )
S

S
H
b
: 1.60
(1) ( 1 , 1 )
H
a
: 2.28
(2) ( 1 , 1 )
- H
b
: IRV1 does not Granger- cause Bond
HJC

HJC
H
b
:0.92
3 GBOND and IRV2 (1) ( 1 , 1 ) (1) ( 1 , 2 )

H
a
: 0.0001 H
a
: 5.16**
(2) ( 1 , 1 ) (2) ( 1 , 1 )
(1) IRV2=f(B
it−
, IRV2
it−
) Ha:
AIC
H
b
: 0.25
AIC
H
b
:1.04
- Ha: Bond does not Granger- cause IRV2 BIC BIC (1) ( 1 , 2 )
International Research Journal of Finance and Economics - Issue 38 (2010) 158
H
a
: 5.16**
(2) ( 1 , 1 )
H
b
:1.04
(1) ( 7 , 15 )
H

a
: 1.45
(2) GBOND=f(B
it−
, IRV2
it−
) H
b

(2) ( 12 , 11 )
FPE

FPE
H
b
:1.84*
(1) ( 1 , 1 ) (1) ( 1 , 2 )
H
a
: 0.0001 H
a
: 5.16**
(2) ( 1 , 1 ) (2) ( 1 , 1 )
SBC
H
b
: 0.25
SBC
H
b

: 1.04
(1) ( 24 , 24 )
H
a
: 1.37
(2) ( 24 , 23 )
S

S
H
b
: 0.51
(1) ( 1 , 1 )
H
a
: 3.77**
(2) ( 1 , 1 )
- H
b
: IRV2 does not Granger- cause Bond
HJC

HJC
H
b
: 1.04
Note: 1. Star (*) means significance at 10% level, and two stars (**) mean significance at 5% level.
2. The criteria for BIC, S, and FPE are selected equation by equation. Since symmetric lag models select the same lag
length for each variable in each equation, the spaces are thus empty due to this reason.

3.4. Analysis of the Factors that Affect the Bond Returns
The results of Tables 7, 8, and 9 reveal no significant effects from any variable to the bond returns. It
implies that we cannot find any factors that affect bond returns in this sample period. The following
describes the contemporaneous relationships among variables. The results show a weakly feedback
effect between GOIL and IRV2, which implies that oil price changes affect interest rate volatility
retrieved by the Component GARCH model, and interest rate volatility also effects oil price changes at
the 10% significant level. However, there is stronger evidence that IRV1 and IRV2 have significant
feedback effects at the 5% significant level. This reveals that interest rate volatility retrieved by the
GARCH models and Component GARCH models will affect each other.
159 International Research Journal of Finance and Economics - Issue 38 (2010)
Table 7: The Contemporaneous Relationships of GOIL, GBOND, GIR, IRV1, and IRV2

Independent
variable
Dependent variable
GOIL GBOND GIR IRV1 IRV2
GOIL
- -0.51 0.96 -1.05 1.75*
GBOND
-0.51 - 1.32 -1.39 1.60
GIR
0.96 1.32 - -0.07 -0.36
IRV1
-1.05 -1.39 -0.07 - 11.66**
IRV2
1.75* 1.60 -0.36 11.66** -
Note: 1. Numbers in the table represent the coefficients of estimated equations.
2. * means at the 10% significance level, and ** means at the 5% significance level.

3.4.1. The Effect of the Symmetric Model

In the systematic models, we also employ 3x3 VAR models and 5x5 VAR models in order to find
detailed empirical results. In the case of 3x3 VAR symmetric models, by choosing the same lag-length
for each variable, we find there are effects from GBOND to GOIL, from GBOND to GIR, and from
GOIL to GIR. This reveals that bond returns will affect oil price changes and the growth in the interest
rate, and oil price changes will affect the growth of the interest rate at the 10% significant level. Thus,
the evidence shows that GBOND will affect GOIL at the 10% significant level in the case of the 5x5
VAR models. This provides robust evidence of the unidirectional effect from GBOND to GOIL by the
VAR models.

Table 8: The Relationships of GOIL, GBOND, GIR, IRV1, and IRV2 for Symmetric Model

Panel A
Independent
variable
Dependent variable
GOIL(1) GBOND(1) GIR(1)
GOIL
7.06** 3.06* 0.83
GBOND
0.85 0.11 1.87
GIR
3.41* 3.43* 33.56**
Panel B
Independent
variable
Dependent variable
GOIL(1) GBOND(1) IRV1(1)
GOIL
5.87** 2.41 0.29
GBOND

0.09 1.63 0.59
IRV1
0.74 0.30 75.46**
Panel C
Independent
variable
Dependent variable
GOIL(1) GBOND(1) IRV2(1)
GOIL
5.50** 2.59 0.29
GBOND
0.02 1.34 1.78
IRV2
0.36 0.94 75.23**
Panel D
Independent
variable
Dependent variable
GOIL(1) GBOND(1) GIR(1) IRV1(1) IRV2(1)
GOIL
4.78** 2.80* 0.78 0.04 0.05
GBOND
0.0002 0.85 0.58 0.22 1.45
GIR
2.05 0.12 39.51** 2.64 0.90
IRV1
0.31 0.05 1.67 32.82** 0.39
IRV2
0.16 1.37 0.56 0.48 21.69**
Note: 1. Numbers in the table represent the coefficients of estimated equations.

2. Number in the parentheses represents the lag-chosen for the variable.
3. * means at the 10% significance level, and ** means at the 5% significance level.

International Research Journal of Finance and Economics - Issue 38 (2010) 160
3.4.2. The Effect of the Asymmetric Model
After separating the 3x3 or 5x5 VAR models into three or five OLS equations, the different lag lengths
are selected for different variables in each OLS equation by the AIC and SBC lag-chosen criteria. In
the case of three OLS models, we find significant effects from GBOND to GOIL and from GOIL to
GIR, revealing that bond returns will affect oil price changes and oil price changes will affect the
growth of the interest rate at the 5% significant level. This provides robust evidence of the
unidirectional effect from GBOND to GOIL and from GOIL to GIR by symmetric models and
asymmetric models.

Table 9: Relationships of GOIL, GBOND, GIR, IRV1, and IRV2 for Asymmetric Model

Panel A
Independent
variable
Dependent variable
GOIL GBOND GIR
GOIL(2) GBOND(2) GIR(2)
GOIL
-0.95 -2.41** 1.44
GOIL(1) GBOND(1) GIR(1)
GBOND
0.19 1.59 1.37
GOIL(2) GBOND(2) GIR(2)
GIR
2.16** -1.19 3.85**
Panel B

Independent
variable
Dependent variable
GOIL GBOND IRV1
GOIL(3) GBOND(3) GIR(3)
GOIL
-1.05 -1.42 0.02
GOIL(1) GBOND(1) GIR(1)
GBOND
0.31 1.28 0.77
GOIL(1) GBOND(1) GIR(1)
IRV1
-0.86 -0.55 8.69**
Panel C
Independent
variable
Dependent variable
GOIL GBOND IRV2
GOIL(1) GBOND(1) GIR(1)
GOIL
2.52** -1.53 0.58
GOIL(1) GBOND(1) GIR(1)
GBOND
0.22 1.20 1.36
GOIL(1) GBOND(1) GIR(1)
IRV2
-0.60 0.98 8.74**
Panel D
Independent
variable

Dependent variable
GOIL GBOND GIR IRV1 IRV2
GOIL(1) GBOND(1) GIR(1) IRV1(1) IRV2(1)
GOIL
2.40** -1.56 0.71 0.20 0.22
GOIL(1) GBOND(1) GIR(1) IRV1(1) IRV2(1)
GBOND
0.08 0.98 0.69 -0.46 1.22
GOIL(1) GBOND(1) GIR(1) IRV1(1) IRV2(1)
GIR
1.43 -0.36 6.42** 1.63 -0.96
GOIL(1) GBOND(1) GIR(1) IRV1(1) IRV2(1)
IRV1
-0.57 -0.23 -1.31 5.77** -0.63
GOIL(1) GBOND(1) GIR(1) IRV1(1) IRV2(1)
IRV2
-0.42 1.18 -0.75 0.69 4.69**
Note: 1. Numbers in the table represent the coefficients of estimated equations.
2. Number in the parentheses represents the lag-chosen for the variable.
3. * means at the 10% significance level, and ** means at the 5% significance level.
161 International Research Journal of Finance and Economics - Issue 38 (2010)
4. Summary and Concluding Remarks
The paper uses the monthly data of the MSCI world bond index, Treasury bill rate, and the FOB cost
of crude oil imports for the U.S. from January 1998 to November 2005 in the AREMOS database
established by the Taiwan Economic Data Center and Economagic database, respectively. This final
section summarizes several important findings relevant to the five hypotheses provided in this paper.
1) We find that the interest rate volatility series in the U.S. have significant GARCH effects
by employing the GARCH models. Thus, it might be appropriate to use GARCH models
to retrieve interest rate volatility by the Treasury bill rate.
2) The empirical results are similar by either choosing symmetric models or asymmetric

models. In the case of investigating the relationships among GOIL, IRV1, and IRV2, the
results still show significant effects from oil price changes to interest volatility.
3) The empirical results are somewhat different by choosing six different lag-chosen criteria
for the empirical results of bond returns and interest rate/interest rate volatility. There is
an essential finding for applying different lag-chosen criteria, since it means that different
lag-chosen criteria might cause different empirical results.
4) There exist significant effects from oil price changes to interest rate/interest rate
volatility, no matter what interest rate volatilities are retrieved.
5) In the case of GOIL, GBOND, and GIR, choosing the asymmetric model’s effects reveals
that bond returns will affect oil price changes and oil price changes will affect the growth
of the interest rate.
From the above important findings, we conclude that oil price changes will affect the growth of
the interest rate and interest rate volatility, and bond returns will either affect the interest rate volatility
or affect oil price changes.
The important finding for this research is similar to previous mentioned literature
(Wongbangpo & Sharma (2002), Mauro (2003), and Broome & Morley (2004)). They find that a stock
index will affect economic variables, but economic variables seldom affect the stock index.
9
This
means that the Dow Jones Industrial Average Index can be taken as a leading indicator. In this study
our empirical results explore another leading indicator - the bond index, which seldom mentioned in
past studies - since bond returns, similar to stock returns, Granger cause macroeconomic variables,
such as output or oil price changes. Furthermore, this result is robust with the sub-period’s result.
10
In
addition, other findings are that oil prices affect the interest rate and its volatilities, the Treasury bill
rate and its volatilities, and bond returns affect the interest rate and its volatilities as well.


9

From the literature of Wongbangpo & Sharma
9
(2002), Mauro
9
(2003), and Broome & Morley
9
(2004), we want to
explore the relationship between stocks and macroeconomics. Therefore, we obtain the monthly data of the Dow Jones
Industrial Average Index and industrial production index, which are regarded correspondingly as stock variables and
macroeconomics variables. The results show that the returns of the Dow Jones Industrial Average Index affect output
growth. It implies that the leading indicator (stock returns) do Granger cause macroeconomic variables (output growth).
10
Furthermore, we divide the entire sample into sub-sample periods, from January 2002 to November 2005, and compare
the structure change of the sub-sample period with the entire sample for new findings. From the empirical results, we
find a similar result that bond returns affect oil price changes. It provides robust evidence that bond returns are one of
the leading indicators. Like stock prices, they also play an important influential role on macroeconomic variables.
International Research Journal of Finance and Economics - Issue 38 (2010) 162
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