The Factors that Affect Market Interest Rates in

Chinese Bond Market

Fan Long-Zhen

School of Management

Fudan University

Shanghai, China

lzfan@fudan.edu.cn

Li Wan-Jun

Mathematical Department

Henan Business College

Zhengzhou, China

jcb407@sohu.com

Abstract— Unlike the central banks in the western countries,

the Chinese central bank controls the term structures of bank deposit interest rates, and lending interest rates. They are called as official interest rates in the paper. Heavily affected by these official rates, market interest rates in the bond market behave in a unique way. Theoretical model and empirical study indicate that changes of official rate and inflation rate, and difference in market rate and official rate are three important factors to explain the change of market rate. The empirical evidence also shows that during period of high real official rate, market rate is mainly determined by official rate; during the period of low real official rate, both market rate and inflation rate are key variables to determine market rate.

Keywords- market interest rate; bank deposit rate; inflation rate; Chinese bank market

I. INTRODUCTION

Although Chinese bond market has a short history, it develops rapidly. Bond trading was introduced in the Shanghai Stock Exchange just after its establishment in 1990. After 1997, Commercial banks are not allowed to trade in the stock exchanges market and to facilitate their trading of fixed income securities, inter-bank fixed income market was established then. Now the exchanges market and the inter-bank market are two major fixed income markets in China. Varieties of bonds are traded in the two markets; they include government bonds, financial institution bonds, corporate bonds, notes issued by the central bank, convertible bonds and some derivatives like repos and swaps. From prices of government bonds, term structure of market interest rates is obtained.

Term structure of interest rates is a key variable to determine prices of fixed income securities, and its behavior is the concern of both academic and industrial studies. Term structure of interest rates is closed related to money policy of the central bank. In the western countries, central banks may set a target for short-term interest rate, but long-term rates are determined by the market[1,2] . Two financial theories are proposed to explain behavior of term structure of interest rates, they are Fisher separation theorem [3] and expectations hypothesis [4].Fisher separation theorem says that market rates are determined by real interest rates and expected inflation rates; the expectations hypothesis says that long term rates are determined by expected future short rate and risk premium of long-term bonds.

Unlike in the western developed countries, China central bank has an unique procedure to regulate the economy. It uses money supply as a major tool to fulfill its target, but it also controls the deposit and lending interest rates of all the commercial banks. We call these interest rates as official interest rates. Long-term official rates are set to be higher than short-term rates during both higher inflation periods and lower inflation periods, and it is difficult to be explained with expectations hypothesis. The official interest rates change less 20 times during the sample period from 1996 to 2007, they are inconsistent with the Fisher separation theorem, because they could not fully reflect the changes of expected inflation rates and real interest rates from time to time. In other words, it is hardly to believe that expected inflation rates and real rates only change less than 20 times in the about 10 years. Market rates are affected heavily by these official interest rates; markets rates also reflect the views of investors about economic fundamentals. How does the term structure of market rates be determined? This paper gives both a theoretical and empirical study. The results indicate that changes of official interest rate and inflation rate, and difference in market rate and official interest rate are three key factors to explain market interest rate changes.

II. THORECTICAL NALYSIS OF THE FACTORS THAT

DTERMINE MARKET INTEREST RATE

Fisher separation theorem is the theory about how market rate is determined by economic fundamentals. According to Fisher separation theorem, market rate is determined by expected inflation rate and real interest rate, the formula for market rate based on the theorem is

( ) )12()12(

12

)12()12(~ n

t

n

ntt

n

t

n

t Ery ϕπ ++= ×+ (1)

Where )12( n

tr is real rate of n-years, )12(

12

n

nt ×+π is inflation rate

from month t to month 12×+ nt ,)12( n

tϕ is the risk premium

factor, and it is determined by risk of bond with maturity of n

years. )(~ n

ty is n-year theoretical interest rate according to

Fisher separation theorem. It is common sense that real rates

change slowly, and absolute value of risk premium)12( n

tϕ is

978-1-4244-2108-4/08/$25.00 © 2008 IEEE 1

relatively small compared to absolute values of real rate and

inflation rate [4, 5, 6].

Bank deposit is an alternative investment opportunity to

bond. So market interest rates are also affected by official

interest rates. The risk of depositing in the banks is different

with the risk of investing in bonds. For a bank deposit, it can be withdrawn from bank anytime before its time to maturity,

but the cost of doing it is the loss of most part of interest,

although the principal is guaranteed. So value of bank deposit

is never less than its face value or principal. Bonds can also

be sold before their maturity dates, but the prices are

determined by the market, the bond holders have to face the

risk of capital loss, but they have no risk of interest loss. If no

other forces affect bond prices, only force that affects bond

trading is bank deposit as an alternative investment

opportunity, market interest rate and official interest rate of

the same term satisfies the following formula )12()12()12( n

t

n

t

n

t ORy λ+= (2)

Where )12( n

ty is n-year market interest rate determined by

official interest rate, )12( n

tOR is n-year deposit interest rate,

)12( n

tλ is the risk premium that are determined by the risk

difference of bank deposit and bond. Equations (1) and (2) determine market interest rates from

two angles. One comes from economic fundamentals; another comes from alternative investment opportunity. These two forces give two different market rate determination formulas. If they are the same, the actual market rate is determined by both equation (1) and (2). But it is rare that they are always the same. If they are inconsistent, the two forces are combined to affect the market interest rate. Actual market interest rate can only be in the between. Mathematically, market rate satisfies

)12()12()12()12()12( ~)1( n

t

n

t

n

t

n

t

n

t yyy θθ +−= (3)

Where )12( n

ty is market interest rate, )12( n

tθ satisfies

10)12( ≤≤ n

tθTo give a example to explain equation (3), we assume

that %6ˆ%,4 )12()12( == tt yy , actual market rate can’t be up

to 6%, if so, marginal investors will withdraw their bank deposits, and buy bonds instead, and such behavior will cause market rate to decline. If actual market rate is 4.3%, marginal investors will consider bond investing is preferable to bank deposit, but they will not withdraw their bank deposit because the cost is quite high. Market is still in equilibrium.

Let us discuss another situation. %5)12( =ty ,

%4ˆ )12( =ty , if actual market rate is 4.5%, marginal

investor will consider investing in bonds is worse than depositing money in banks, he will sell his bond and deposit money in the banks. Bond trading cost is relatively small. But if actual market rate is close to 5%, marginal investor will not trade. Market is in equilibrium.

From equation (3), annually change of market rate is

)12()12()12()12()12(

)12(

12

)12(

12

)12(

12

)12(

12

)12(

12

)12()12(

12

~))(1(

~))(1(

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

yOR

yORyy

θλθθλθ

−+−−

++−=− ++++++

[ ])(~)(

)~~())(1(

))(1(

)12()12()12()12()12(

12

)12()12(

12

)12(

12

)12()12(

12

)12(

12

)12()12(

12

)12(

12

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

ORy

yy

OROR

λθθθλλθ

θ

+−−+

−+−−+

−−=

+

++++

++

)](~)[(

)(

)]()([

)())(1(

))(1(

)12()12()12()12()12(

12

)12()12(

12

)12(

12

)12(

12

)12(

121212

)12(

12

)12()12(

12

)12(

12

)12()12(

12

)12(

12

)12()12(

12

)12(

12

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

ntt

n

ntt

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

ORy

EE

rr

OROR

ψθθϕϕθ

ππθθλλθ

θ

+−−+

−+

−+

−+−−+

−−=

+

++

×+×++++

++++

++

(4)

In the right side of equation (4), some variables are unobservable. To simplify the analysis, we make some assumptions based on common knowledge. We assume real rate are stable in one year, so we omit its change in one year, that is

0)12()12(

12≈−+

n

t

n

t rr

Risk premium is a factor to determine long-term rate, but it is common sense that absolute value of risk premium is much less than the absolute values of expected inflation rate and real rate, and some theoretical models[7,8,9] such as the Vasicek model further assume it is constant, so we omit its annually changes also, that is

0)12()12(

12 ≈−+n

t

n

t ϕϕFinally, we assume the risk and risk premium differences between bond and bank deposit are stable in one year, and assume that

0)12()12(

12 ≈−+n

t

n

t λλWith above assumptions, equation (4) becomes

)](~)[(

)]()([

))(1(

)12()12()12()12()12(

12

)12(

12

)12(

121212

)12(

12

)12()12(

12

)12(

12

)12()12(

12

n

t

n

t

n

t

n

t

n

t

n

ntt

n

ntt

n

t

n

t

n

t

n

t

n

t

n

t

ORy

EE

ORORyy

ψθθππθ

θ

+−−+

−+

−−=−

+

×+×++++

+++

(5)

Expectation of inflation rate in equation (5) is another unobservable variable, to relate it to observable variables, we assume one-year inflation rate follow AR(1) time-series process. It is considered that inflation rate is highly persistent, and many papers such as Anderson, et al

[5] assume it follow AR(1) or unit root process. That is

12

)12()12(

12 ++ ++= ttt ba υππ )10( ≤< b (6)

From equation (6), the expected change of inflation rate is as follows

( ) ( )]...[

1 )12(

)1(12

)12(

312

)12(

21212

)12(

12

)12(

121212

+×+×+×++

×+×+++

+++=

−

ntttt

n

ntt

n

ntt

En

EE

πππ

ππ

978-1-4244-2108-4/08/$25.00 © 2008 IEEE 2

]...[1 )12(

12

)12(

212

)12(

12 nttttEn

×+×++ +++− πππ

( )

=−

<−−−

=

+

+

1

11

1

1

)12()12(

12

)12()12(

12

b

bnb

b

tt

tt

n

ππ

ππ

)( )12()12(

12 tt ππξ −= + (7)

Where

=

<−−

=11

11

1

1

b

bnb

bn

ξ

)12(~ n

ty in the right of equation (5) is also an unobservable

variable, we try to be instead of it with observable variables. From equation (3), we have

)](~[)()12()12()12()12()12()12()12( n

t

n

t

n

t

n

t

n

t

n

t

n

t ORyORy λθλ +−=+−

(8)

With equation (8), the last term in the right of equation (5) becomes

( )[ ])12()12()12()12()12(

12

)12()12()12()12()12(

12

)1/(

)](~)[(

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

ORy

ORy

λθθλθθ

−−−=

+−−

+

+ (9)

Combining equations (5) , (7) and (9), equation (5) becomes

))(1()/1( )12()12(

12

)12(

12

)12()12()12(

12

)12()12(

12

n

t

n

t

n

t

n

t

n

t

n

t

n

t

n

t

OROR

yy

−−+−=

−

+++

+

θλθθ))(/1()( )12()12()12()12(

12

)12()12(

12

)12(

12

n

t

n

t

n

t

n

ttt

n

t ORy −−−−+ +++ θθππξθ (10)

From equation (10), we get the conclusion that change of market rate is affected by the change of official interest rates, change of inflation rate, and the difference between market interest rate and official interest rate. The risk premium term

)12( n

tλ has been assumed to be small and constant. If it changes,

maybe it is another factor.

III. EMPIRIAL STUDY ON THE FACTORS THAT AFFECT

INTEREST RATE

Theoretically, we have obtained three factors that determine market interest rates changes, They are official interest rate changes, inflation rate change, and difference in market interest rate and official interest rate. Now we use data to test if that is true. The sample period is from July 1997 to July 2007. The monthly data include market interest rates with maturities of 1 to 5 years, 1-year bank deposit interest rate, and annually inflation rate. Fig. 1 gives annually changes of one-year market rate, one-year deposit interest rate, and one-year inflation rate. From the figure, it can be seen that market rate is closely related to inflation rate, especially in the second half of the sample period; market rate is also closely related to official interest rate, especially in the first half of the sample period.

July 96 July 98 July 00 July 02 July 04 July 06-8

-6

-4

-2

0

2

4

6

∆yt+12(12)

∆πt+12(12)

∆ORt+12(12)

Fig. 1 Annually changes of one-year market interest rate ( )12(

12+∆t

y ), one-year

inflation rate ( )12(

12+∆ tπ ), and one-year bank deposit rate ( )12(

12+∆t

OR )

To test if the theoretical model is right, the following regression equation is constructed,

)12(

12

)12()12(

3

)12(

122

)12(

1210

)12(

12

)(n

ttt

tt

n

t

ORy

ORy

+

+++

+−+

∆+∆+=∆

εαπααα

(11)

)5,43,2,1( =n

Where )12()12(

12

)12(

12

n

t

n

t

n

t yyy −=∆ ++ , )12()12(

12

)12(

12 ttt OROROR −=∆ ++ ,

)12()12(

12

)12(

12 ttt πππ −=∆ ++ . The regression results of equation (11)

are in table 1. The estimated results of the total sample period in table 1 tell us that the coefficients of the three variables are significant, and this indicates that they are obvious to explain interest rate change. The coefficients of change of official rate and change of inflation rate are positive, this indicates that when official interest rate or inflation rate increase, market interest rate also increases. The coefficient of the difference in market rate and official rate is negative. This indicates when market rate is high relative to official rate, it will decrease in the next period.

From fig. 1, we have seen that although change of inflation and change of official rate are closely related to market rates, but in different period, their relationships with market rate are different. So we divide the total sample period into two sample periods, the first period is from July 1996 to December 2000, and the second sample period is from January 2001 to July 2007. The results in the two sample period are different. In the first period, change of inflation rate is not significant to explain market rate change, but change of official rate and difference in market rate and official rate are significant. In the second period, all the variables are significant. Why the difference occurs in the two different periods, fig. 2 gives us some intuition. Fig. 2 shows market rate is higher than official rate most of time. We can interpret that as investors consider bond is more risky than bank deposit of the same term, so once market rate is lower than official rate, investor sell their bonds and deposit the money in the to bank, and this activity cause

978-1-4244-2108-4/08/$25.00 © 2008 IEEE 3

market rate to rise above official rate. In the first period, inflation rate is quite low and official rate is relatively high. This results in that real official rate is high. Maybe )12(~ n

ty is

lower than)12( n

ty most of time. But market rate is still higher

than official rate. This indicates 0)12( ≈n

tθ . In this situation,

according equation (10), inflation rate shows no power to explain market interest rate change. In the second sample period, most of time inflation rate and official interest rate are

close to each other, so )12(~ n

ty is higher than )12( n

ty quite often.

During these times the market rate is in the between, that is

10)12( << n

tθ . According to equation (10), now change of

inflation rate and change of official rate both have power to explain market interest rate change.

TABLE 1. ESTIMATED RESULTS OF EQUATION (11)

n Constant )12(

12+∆ tOR )12(

12+∆ tπ yt(12)

-ORt(12)

R2

Total sample period ( from July 1996 to July 2007)

1 -0.20 0.80 0.18 0.68

(-1.95) (4.87) (3.25)

1 0.38 0.82 0.05 -0.75 0.81

(3.48) (6.32) (0.84) (-7.97)

2 -0.17 0.75 0.20 0.67

(-1.83) (4.49) (2.79)

2 0.48 0.82 0.06 -0.86 0.81

(2.76) (6.27) (0.75) (-5.47)

3 -0.18 0.67 0.22 0.61

(-1.72) (3.85) (2.60)

3 0.47 0.79 0.07 -0.93 0.78

(1.90) (5.34) (0.72) (-3.82)

4 -0.18 0.61 0.23 0.56

(-1.40) (3.36) (2.46)

4 0.62 0.81 0.07 -1.00 0.76

(2.05) (5.30) (0.72) (-3.72)

5 -0.18 0.56 0.24 0.52

(-1.20) (3.00) (2.34)

5 0.72 0.82 0.08 -1.04 0.75

(2.15) (5.17) (0.76) (-3.81)

Subperiod 1 (from July 1996 to December 2000)

1 -0.25 0.77 0.19 0.56

(-1.60) (5.08) (1.95)

1 0.98 1.12 -0.14 -1.13 0.72

(3.55) (10.09) (-2.25) (-8.39)

2 -0.16 0.80 0.17 0.52

(-1.00) (4.58) (1.40)

2 1.19 1.19 -0.13 -1.28 0.76

(4.19) (9.72) (-2.12) (-10.53)

3 -0.15 0.77 0.15 0.43

(-1.08) (4.61) (1.11)

3 1.26 1.25 -0.13 -1.39 0.78

(4.48) (7.94) (-2.17) (-9.34)

4 -0.15 0.74 0.14 0.36

(-0.96) (4.08) (0.93)

4 1.34 1.23 -0.10 -1.42 0.80

(4.34) (7.76) (-1.82) (-10.06)

5 -0.15 0.72 0.12 0.32

(-0.91) (3.74) (0.80)

5 1.39 1.21 -0.08 -1.43 0.81

(4.24) (7.74) (-1.53) (-11.19)

Subperiod 2 (form January 2001 to December 2007)

1 -0.12 0.06 0.17 0.36

(-1.05) (0.19) (3.68)

1 0.46 -0.20 0.15 -0.86 0.75

(10.14) (-0.82) (16.73) (-12.78)

2 -0.14 0.35 0.23 0.58

(-1.78) (1.75) (6.68)

2 0.34 0.29 0.18 -0.68 0.78

(5.88) (1.47) (17.60) (-8.00)

3 -0.17 0.43 0.30 0.67

(-2.60) (3.10) (10.10)

3 0.16 0.49 0.23 -0.52 0.76

(2.21) (2.25) (12.16) (-5.02)

4 -0.21 0.52 0.35 0.70

(-2.72) (4.00) (12.81)

4 0.13 0.61 0.27 -0.46 0.75

(1.34) (2.29) (9.39) (-3.80)

5 -0.23 0.54 0.39 0.71

(-2.49) (3.59) (14.38)

5 0.10 0.66 0.30 -0.41 0.74

(0.89) (2.14) (8.17) (-3.16)

Numbers in parentheses are Newey-West t values with lags of 12.

July 96 July 98 July 00 July 02 July 04 July 06-4

-2

0

2

4

6

8

10

12

ORt(12)

πt(12)

yt(12)

Fig. 2 Market rate ( )12(

ty ), official rate ( )12(

tOR ) and inflation rate ()12(

tπ )

978-1-4244-2108-4/08/$25.00 © 2008 IEEE 4

IV. CONCLUSION REMARKS

Unlike in the western countries, Chinese central bank controls the term structures of bank deposit interest rates, lending rates, long-term official rates are always set to be higher than official short-term rates. This situation is difficult to explain by expectations hypothesis. Heavily affected by the official rates, Chinese market interest rates behave in a unique way. Chinese market rates are higher than bank deposit rate most of time in the sample period. This indicates that investors consider bonds are more risky than bank deposits. Official rates represented by bank deposit rates are one source to determine market interest rates. Economic fundamentals such as inflation rate are other sources to determine market interest rates. Market rates are determined by both economic fundamentals and official rates. Our theoretical model and empirical study indicate that change of official rate, change of inflation rate, and difference in market rate and official rate are significant to explain the change of market rate. Rising in official rate and inflation rate cause market rate to increase, high difference in market rate and official rate indicate market rate is higher on average and will decrease in the coming year. The empirical evidence also show that during period of high real official rate, market rate is mainly determined by official rate; during the period of low real official rate, both market rate and inflation rate are key variables to determine market rate.

ACKNOWLEDGMENT

This paper is supported by the foundation for New Century Excellent Talents in Universities (NCET).

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