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

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: Hypot

ISSN 1450-2887 Issue 38 (2010)

© EuroJournals Publishing, Inc 2010

http://www.eurojournals.com/finance.htm

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: manhwa@mail.mcu.edu.tw 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 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 money1 supply, examining the effect from money uncertainty to inflation might be more appropriate than examining the effect from inflation uncertainty to inflation

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 asMV T ≡P T T 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

(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-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 models1 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 HJC7 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

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 models8 equivalent to GARCH (2,2) models which allow the

N T

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 T N

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

T n SSR n

T n

T FPE = ( + + 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(

T SBC = ∑ +

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

) 2 log(

T

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

( ˆ ) 2 ln 2 2 ln ( ln )

2

j

T

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 1 2 1 1 2

−

−

−

+

)

1 2 1 3 1

If ρ in equation (2) is equal to 1.0, then the conditional variance contains a unit root If ρ<1.0 and ρ>α1+α2, 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

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 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 Interest volatility

Time

I RV1

I RV2

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

1998.1~2005.11

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

No -1.04 -0.27 -0.48 -0.27 Oil

No -0.64 -0.52 -0.58 -0.52 Bond

No -1.21 -0.99 -1.04 -0.99

Level

IR

No -6.61** -7.15** -7.19** -7.15**

Oil

No -6.22** -8.09** -8.09** -8.09**

Bond

No -3.76** -5.20** -5.07** -5.20**

Log Differencing

IR

Note: The lag length of ADF and that of APP are chosen by AIC criteria

Star (**) means significance at the 5% level

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

G IR = − G IR − − G IR − +ε

(4.02**) (2.98**)

(B )GARCH(1,1) Models

(-19.21**) (15.54**)

(21.35**) (37.70**) (41.10**)

( C )Component GARCH Models

G IR = − G IR − + G IR − + ε

(-19.21**) (15.54**)

(5.53**) (29.78**) (11.36**) (21.57**) (28.96**)

Note: GIRt : the growth of interest rate

t

a : the moving average terms; εt: 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

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

Bond (B) World Bond index

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 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

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 selecting different lags for each equation

(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)

H b :2.77*

(1) ( 20, 3 )

H a : 1.56 (2) ( 2, 21 )

GBOND = f(Ot−i, Bt−i)

Ha

H b : 1.93**

(1) ( 1, 1 ) (1) ( 1, 1 )

Ha: Oil does not Granger- cause

GOIL = f(Ot−i , Bt−i) (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 )

H b :1.22 (1) ( 1 , 1 )

H a : 1.39 (2) ( 1 , 1 )

H b : Bond does not Granger-cause

Oil

H b :2.77*

2 GOIL and GIR AIC (1) ( 1, 1 ) AIC (1) ( 1, 10 )

GIR = f(Ot−i, GIRt−i) H a : 3.15* H a : 3.46**

Ha: Oil does not Granger- cause

IR

GOIL = f(Ot−i, GIRt−i) BIC BIC (1) ( 1, 1)

Hb: IR does not Granger- cause

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

H a : 1.14 (2) (6 , 18 )

H b :1.32

(1) ( 1, 1 ) SBC (1) ( 1, 1 )

(2) ( 1, 1 ) (2) ( 1, 1 ) SBC

(1) ( 20, 24)

H a : 0.99 (2) ( 24, 20 )

H b : 1.07 (1) ( 1 , 1 )

H a : 1.57 (2) ( 1 , 1)

H b : 1.61

3 GOIL and IRV1 (1) ( 1, 1 )

H a : 9.26** (1) ( 1, 2 )

IRV1 = f(Ot−i, IRV1t−i)

Ha:

Ha: Oil does not Granger- cause

IRV1

H b : 0.31 (2) ( 24, 23 )

GOIL = f(Ot−i, IRV1t−i)

H b : 1.08

H a : 8.93**

Hb: IRV1 does not Granger-cause

H b : 1.16 (1) ( 12, 11 )

H a : 2.32**

(2) (7, 15 )

H b : 1.37 (1) ( 1, 1 ) SBC (1) ( 1, 5 )

(2) ( 1, 1 ) (2) ( 1, 1 ) SBC

(1) ( 24, 24 )

H a : 0.83 (2) ( 24, 24 )

H b : 0.97 (1) ( 1 , 1 )

H a : 7.07**

(2) ( 1 , 1 )

H b :1.72

4 GOIL and IRV2 AIC (1) ( 1 , 1 ) AIC (1) ( 1 , 1 )

IRV2 = f(Ot−i, IRV2t−i)

Ha:

(2) ( 1 , 1 ) (2) ( 24 , 21 )

(1) ( 1 , 2 )

Ha: Oil does not Granger- cause

IRV2

H a : 9.40**

GOIL = f(Ot−i , IRV2t−i)

H b

(2) ( 5 , 1 )

H b : 1.22 (1) ( 18 , 3 )

H a : 2.69**

(2) ( 9 , 13 )

H b : 1.03 (1) ( 1 , 1 ) SBC (1) ( 1 , 5 )

Hb: IRV2 does not Granger-cause

Oil

SBC (2) ( 1 , 1 ) (2) ( 1 , 1 )

H b : 1.59 H b : 2.43*

H a : 1.65

S

H b : 0.77

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