JFutM2006
Transcript of JFutM2006
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THE CHINESE INTERBANK
REPO MARKET: AN
ANALYSIS OF TERM
PREMIUMS
LONGZHEN FAN
CHU ZHANG*
Because of the lack of short-term government bonds, the interbank repomarket in China has been providing the best information about market-driven short-term interest rates since its inception. This article examinesthe behavior of the repo rates of various terms and their term premiums.The work in this article supplements the study by F. Longstaff (2000),which reports supportive evidence for the pure expectations hypothesis
over the short range of the term structure with the use of repo data fromthe United States. It is found that the pure expectations hypothesis is sta-tistically rejected, although the term premiums are economically small. Itis shown that the short-term repo rate, repo rate volatility, repo marketliquidity, and repo rate spreads are all important in determining the termpremiums. 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:153167, 2006
The authors would like to thank Bob Webb (the Editor) and an anonymous referee for their helpfulcomments and suggestions. Longzhen Fan acknowledges the financial support from National ScienceFoundation of China Grant No. NSFC-70471010. Chu Zhang acknowledges financial support fromDirect Allocation Grant No. DAG02/03.BM23 of HKUST. All remaining errors are the authors.*Correspondence author, Department of Finance, Hong Kong University of Science and Technology,
Clear Water Bay, Kowloon, Hong Kong; e-mail: [email protected]
Received October 2004; Accepted May 2005
I Longzhen Fan is an Associate Professor in the Department of Finance at FudanUniversity in Shanghai, China.
I Chu Zhang is an Associate Professor in the Department of Finance at Hong KongUniversity of Science and Technology in Hong Kong.
The Journal of Futures Markets, Vol. 26, No. 2, 153167 (2006)
2006 Wiley Periodicals, Inc.
Published online in Wiley InterScience (www.interscience.wiley.com).
DOI: 10.1002/fut.20191
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154 Fan and Zhang
INTRODUCTION
This article studies the interest-rate behavior in the Chinese interbank
repo market. A repo transaction is a pair of spot and forward transactions
of some securities in form, but short-term borrowing and lending with col-lateral in essence. In spite of its short history, the interbank repo market
in China has grown rapidly, taking over the interbank market for borrow-
ing and lending without collateral as the major form of interbank transac-
tions. The repo market facilitates borrowing and lending with enhanced
safety and plays a very important role in all businesses, including the stock
market and commodity futures markets.
The repo market in China is also important for another reason.
Because the Chinese government does not issue short-term bonds, the
repo rates become the only close substitutes of the benchmark risk-free
rates in the market, better than the Chinese interbank-offered rates(CHIBOR) because CHIBOR contain credit premiums. Although the
central government has tight control of the bank deposit rates, the inter-
bank repo rates do fluctuate according to the conditions of demand and
supply as billions of Renminbi (RMB, the Chinese currency) change
hands on the daily basis. The question is how interest rates of various
maturities at a given time reflect the expectations of the market partici-
pants about future interest-rate changes. In accordance with the litera-
ture, this question is examined in the context of testing the so-called
pure expectations hypothesis. This hypothesis basically states that the
term structure of interest rates at any given time is set such that theexpected return on rolling over short-term risk-free investments is
the same as the corresponding long-term risk-free rate. Although the
hypothesis has been tested repeatedly and rejected frequently in many
markets, the interest in reexamining it has never abated. Much has been
learned about the determination of interest rates in the process. Term
premiums, that is, longer-term rates in excess of what the pure expecta-
tions hypothesis predicts, and their determinants have been the most
important concept in decisions related to fixed-income investments. A
particularly relevant work by Longstaff (2000) documents that the pure
expectations hypothesis is supported in the U.S. repo market, in contrastwith the findings based on the U.S. Treasury market.
The results show that term premiums in the Chinese repo market
are positive and increasing with the term. The pure expectations hypothe-
sis is statistically rejected. However, the magnitude of the term premi-
ums is economically small relative to that found in the U.S. Treasury
market and elsewhere. The finding in Longstaff (2000) that the U.S.
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repo rates conform to the pure expectations hypothesis, though not strictly
observed in the Chinese interbank repo market, indeed has some merit
for repo markets outside the United States. The term premiums are
related to the short-term repo rate, to term spreads, to the trading
volumes of repo markets, and to the volatility of the repo rates. Allthese variables contribute to the determination of term premiums, as
the liquidity preference hypothesis, a classical alternative theory to the
expectations hypothesis, predicts.
The article is organized as follows. The Chinese interbank repo
market is described. The unconditional term premiums and unconditional
tests of the pure expectation hypothesis are discussed. Results of the con-
ditional test of the pure expectations hypothesis and the determinants of
conditional term premiums are reported, and a conclusion is provided.
THE CHINESE INTERBANK REPO MARKET
The secondary markets for Chinese Treasury securities officially began
in 1990 when the securities exchanges were established. The trading
activities, however, have been limited. Unlike the case of the United
States, there are no regular cycles in Chinese Treasury issues. Although
the total number of Treasury bonds has now become nontrivial, most
bonds have long terms. There have been very few near-maturity bonds in
the last 5 years. As a result, there are no market-driven short-term rates
available from the Treasury market on a continual basis.The interbank market has always been the most important channel
for allocating resources across all sectors of the economy in China.
Imam (2004) has a brief account of the recent development in interbank
activities and its role in financial liberalization. Repo transactions are a
recent phenomenon in China. There are two major repo markets. One is
the market for exchange-traded repos and the other is the one for inter-
bank repos. Both mainly use Treasuries as general collateral. The trading
volume of the exchange-traded repo market was less than half of the
interbank repo market in 2003. The repo rates prevailing in the
exchange-traded repo market differ at times from those of the interbankmarket and are more affected by temporary factors in the stock market,
such as new issues. Therefore the focus here is on the interbank repo
market. Figure 1 shows the total amounts of interbank borrowing and
lending without collateral and with collateral (repo). As can be seen,
repo transactions have surpassed transactions without collateral since
1999 as the most important form of interbank borrowing and lending
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FIGURE 1
Trading volumes of the interbank borrowing-and-lending market and of the interbankrepo market. This figure shows the annual trading volumes in the two markets from
1999 to 2003.
1The overnight repo is approved by the central bank for trading in 2003. The trading volume growsimmediately, accounting for 22% of the total volume in 2004. However, the data series of the
overnight rate is too short for analysis.
transactions, totaling more than 10 trillion RMB in 2002 and 2003. As
the problem of nonperforming loans lingers in the Chinas banking
industry, the rise of the interbank repo market is no surprise.
The interbank repo rate data used in this study are from the
www.chinamoney.com.cn Web site. The sample includes weekly observa-
tions of the one-week rate , the 2-week rate , the 3-week rate , the1-month (4-week) rate , the 2-month (9-week) rate , and the
3-month (13-week) rate , from July 2, 1999 to June 25, 2004.
Although the interbank repo market began in 1997, the trading volume
before 1999 was too small to warrant study. Table I gives annual trading
volumes for these categories by the term of the repo, as well as the
overnight repos, over the period of 19992003 and their proportions in
the entire interbank repo market. There are also other terms of repo
transactions that are not included in the table. They are of relatively low
importance according to their trading volume.1
Repo rates are quoted in the Chinese interbank market on the actual/365 basis. In the analysis conducted in this article the actual quoted rates
are converted to continuously compounded rates. Table II reports the
descriptive statistics of the repo rates of various terms. Panel A gives the
Yt13
Yt9Yt
4Yt3Yt2Yt1
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The Chinese Interbank Repo Market 157
TABLE I
Trading Volume and Market Share of Repos by Term
Category 1999 2000 2001 2002 2003
A. Trading volume (billion RMB)
Overnight 1707.3
One-week 163.7 1054.0 3092.8 8227.0 7722.4
Two-week 93.4 239.0 470.4 1169.4 1320.4
Three-week 26.7 106.8 189.7 204.1 208.2
One-month 47.2 51.3 88.6 127.6 167.6
Two-month 31.5 65.3 49.7 75.2 86.1
Three-month 26.4 30.8 24.7 41.0 60.4
Entire market 394.9 1578.2 3924.3 9878.9 11306.0
B. Market share (%)
Overnight 15.1
One-week 41.5 66.8 78.8 83.3 68.3
Two-week 23.7 15.1 12.0 11.8 11.7Three-week 6.8 6.8 4.8 2.1 1.8
One-month 12.0 3.3 2.3 1.3 1.5
Two-month 8.0 4.1 1.3 0.8 0.8
Three-month 6.7 2.0 0.6 0.4 0.5
Sum 98.5 98.0 99.8 99.7 99.7
Note. Panel A of this table presents the trading volume of repos categorized by the term of the transactions.
Panel B gives their market share in percentage. The sample period is 19992003.
TABLE II
Descriptive Statistics of the Repo Rates
Term, n Mean SD 1 2 3 4
A. Rates (%)
One-week, Yt
1 2.3105 0.2654 0.8989 0.7643 0.6794 0.6136
Two-week, Yt
2 2.3385 0.2829 0.8789 0.7803 0.6664 0.5914
Three-week, Yt
3 2.3778 0.3016 0.8461 0.7438 0.6686 0.6170
One-month, Yt
4 2.4368 0.3139 0.8822 0.7825 0.7131 0.6771
Two-month, Yt
9 2.4764 0.3459 0.8858 0.7682 0.7133 0.7014
Three-month, Yt
13 2.5299 0.3459 0.8867 0.7958 0.7679 0.7294
B. Weekly changes in rates (%)
One-week, Yt1 Y
t11
0.0010 0.1169 0.1873 0.2614 0.1016 0.0762
Two-week, Yt
2 Y
t12
0.0007 0.1371 0.0979 0.0711 0.1732 0.0145
Three-week, Yt
3 Y
t13
0.0001 0.1651 0.1885 0.0737 0.0828 0.0651
One-month, Yt
4 Y
t14 0.0006 0.1464 0.0978 0.1096 0.1701 0.1024
Two-month, Yt
9 Y
t19 0.0015 0.1554 0.0118 0.2451 0.1099 0.0584
Three-month, Yt
13 Y
t113 0.0010 0.1533 0.0142 0.3035 0.0179 0.1349
Note. Panel A of this table presents the means, standard deviations, and autocorrelations up to order 4 of the
repo rates. Panel B presents the mean, standard deviation, and autocorrelations up to order 4 of the weekly
changes in repo rates. The sample consists of weekly observations in the period 1999.07.022004.06.25.
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FIGURE 2
The 1-week repo rate and the 3-month term spread. This figure shows the weekly timeseries of the 1-week repo rate (the solid line), and the 3-month term spread
(the dashed line), from 1999.07.02 to 2004.06.25.S13t Y13t Y
1t
Y1t
means, standard deviations, and autocorrelations up to the fourth order of
the weekly repo rates. Panel B gives the means, standard deviations, and
autocorrelations up to the fourth order of the weekly changes of the repo
rates.
As we can see from Panel A of Table II, the term structure of therepo rates is upward sloped on average. The standard deviation also
increases with the term from 1 week to 3 months. The pattern in the
standard deviations is in contrast with that observed in the United
States. Longstaff (2000) reports that, although the overnight repo rate
has the highest volatility, there is no apparent pattern in the volatilities of
the repo rates ranging from 1 week to 3 months. From Panel A, the repo
rates all have high correlations which are slowly decaying.
The numbers in Panel B of Table II show that the average weekly
changes in the repo rates are very small, less than one basis point for all
the terms. The standard deviations are more than 10 basis points, much
larger compared with the means. The rate changes are weakly autocorre-
lated, compared to the rates themselves.
In order to gain more insight of the analysis for the repo rates that
follows, some of the repo rates are plotted in Figure 2. All the repo rates
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are close to each other. To avoid clustering, only the 1-week rate ,
and the 3-month spread, , are plotted. As seen in the figure,
the repo rates drifted slightly down from July 1999 to early 2002. In the
second half of 2003, there were two rate spikes. The difference between
the rates of different terms is typically small, as evidenced by the 3-month
term spread in the figure. In late 2003 and early 2004, the 1-week rate
went through some volatile fluctuations. The interesting observation is
that the 3-month rate did not fluctuate with the 1-week rate on a one-to-
one correspondence, resulting in some fluctuation in the term spread. In
many cases, the market correctly expected that the fluctuation in the
1-week rate was temporary, so the longer-term rates were set much more
smoothly over time than were the shorter-term rates.
UNCONDITIONAL TERM PREMIUMS
The analysis of term premiums is conducted in the backdrop of a dis-
cussion of the pure expectations hypothesis. There are many different
versions of the pure expectations hypothesis, as explained by Cox,
Ingersoll, and Ross (1981). Consequently, there are different definitions
of term premiums, that is, deviations from the pure expectations
hypothesis. However, as argued by Campbell (1986), the differences
among different versions of the pure expectations hypothesis are of the-
oretical importance only. The numerical magnitude of such differences
are negligible in practice. Fama (1984a, 1984b), Fama and Bliss (1987),
and Campbell and Shiller (1991) examine the various notions of term
premiums on U.S. Treasuries and reject the pure expectations hypoth-
esis. The interest in testing the expectations hypothesis, however, has
never abated. Balfoussia and Wickens (2004) identify macroeconomic
sources of the nonzero term premiums. Thornton (in press) clarifies the
Campbell-Shiller result from an econometric point of view. One line of
research extends the work to the international arena. For example,
Robinson (1998), Fernandez and Frutos (2000), and Hejazi, Lai, and
Yang (2000) analyze the Australian, Spanish, and Canadian markets,
respectively.
A study that is most relevant to this one is that of Longstaff (2000),
who analyzes the repo rates in the U.S. market and presents supporting
evidence for the pure expectations hypothesis for the short end of the
term structure of interest rates. This article follows one of the formula-
tions in Campbell and Shiller (1991).
For the continuously compoundedn-week repo rate at t, , one ver-
sion of the pure expectations hypothesis says that it equals the expected
Ytn
St13 Yt
13 Yt
1
Yt1
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TABLE III
Unconditional Term Premiums in the Repo Rates
Term rates 1-week rate Term premium Newey-West Sample sizeTerm, n Y
t
n Rt
n Yt
n R
t
n t statistics T
A. Sample period for t: 1999.07.022004.04.02
Two-week 2.3368 2.3119 0.0249 3.6060 249
Three-week 2.3705 2.3106 0.0599 3.6907 249
One-month 2.4217 2.3098 0.1120 4.6609 249
Two-month 2.4627 2.3059 0.1568 4.3515 249
Three-month 2.5156 2.3033 0.2123 5.0175 249
B. Sample period for t: 1999.07.022002.08.30
Two-week 2.3352 2.3196 0.0156 4.2148 166
Three-week 2.3570 2.3179 0.0391 5.8306 166
One-month 2.3978 2.3166 0.0811 7.4061 166
Two-month 2.4285 2.3112 0.1173 5.5984 166
Three-month 2.4902 2.3069 0.1834 6.2590 166
C. Sample period for t: 2002.09.062004.04.02
Two-week 2.3399 2.2965 0.0433 3.2554 83
Three-week 2.3975 2.2960 0.1015 2.9553 83
One-month 2.4697 2.2961 0.1737 3.3341 83
Two-month 2.5311 2.2952 0.2359 2.9200 83
Three-month 2.5662 2.2960 0.2702 2.7086 83
Note. This table presents the average repo rates of various terms, , for n equal to 2 weeks,
3 weeks, 1 month, 2 months, and 3 months. In comparison is the average of corresponding average 1-week
repo rates, The term premium refers to their difference. The Newey-West t ratios are used to
test the hypothesis that term premium is zero. The sample size is the number of weeks T in the sample.
(1 T)aT
t1Rnt.
(1 T) aT
t1Ynt
n-week average of 1-week rates in the future, . That is,
(1)
Note that the 1-month,2-month, and 3-month rates are not exactly 4-week,
9-week, and 13-week rates, so the matching here is not perfect. But
because some have more days and others have fewer days, the difference
should not cause systematic bias, given that they are all annualized rates.
Panel A of Table III is for the entire sample period of 1999.07.02
2004.06.25. It reports the sample mean of , , and with the
autocorrelation and conditional heteroskedasticity consistent t statisticssuggested by Newey and West (1987). The lag in the autocorrelation
adjustment is chosen to be 30 weeks to account for the high autocorre-
lations in and the overlapping components in . The results show
that, on average, the longer repo rates are higher than the corresponding
rolling-over short rates; that is, tends to be positive. As indicated
by the t statistics, the difference in the averages as an estimate of the
term premium is significantly positive for all the terms considered in this
Ynt Rnt
RntYtn
Ynt RntR
ntYt
n
E[Ytn Rt
n] 0
Rtn
1ngj1n Ytj1
1
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article and the term premium increases with the length of the term. The
magnitude of the term premiums is small, however. The largest one is
about only 21 basis points on the annual basis that occurs for the
3-month ( ) term premium.
Figure 2 reveals that, over the entire sample period, there is a slightdownward trend in the level of repo rates. If the downward trend is totally
unexpected, then it is likely to observe a positive realized average value of
even when the pure expectations hypothesis holds. To see
whether or not this is the case, subperiod results are examined. Panels B
and C of Table III report the same statistics for two subperiods:
1999.07.022002.08.30 and 2002.09.062004.06.25. From Figure 2, it
can be seen that the first period is a period in which the level of the repo
rates declined overall, whereas in the second subperiod, the repo rates
fluctuated more without following a clear trend. If the positive realized
term premiums are entirely due to unexpected realizations, one should
anticipate higher realized term premiums in the first subperiod than for
those in the entire period and basically no realized term premiums in the
second subperiod. The numbers in Panels B and C, however, show the
opposite results. The realized term premiums are in fact slightly smaller
in the first subperiod than in the second one. This means that the posi-
tive realized term premiums found in the entire sample period are not
from unexpected changes in the level of repo rates, at least not entirely.
Figure 3 plots the difference for the 1-month rate ( )
and for the 3-month rate ( ). For both series, the difference
remains positive for almost all the time. The negative spike of
the difference in late 2003 is due to the large temporary fluctu-
ation of the level of the rates. Overall, although the repo rates in early
2004 fall back to the 2002 level, the realized term premiums are positive
on average.
CONDITIONAL TERM PREMIUMS
The pure expectations hypothesis can also be tested at the conditional
level. The hypothesis is stated as
(2)
where represents the expectation conditioned on time t information.
The hypothesis says that the value of should not be predicted by
any variable known at t. As a result, one can test the conditional version
of the pure expectations hypothesis by regressing on time tvari-
ables and testing whether the regression coefficients are all zero.
Ynt Rnt
Ynt Rnt
Et
Et[Ytn Rt
n] 0
Ynt Rnt
Ynt Rnt
n 13
n 4Ynt Rnt
Ynt Rnt
n 13
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FIGURE 3
Longer-term repo rates in excess of rolling-over 1-week rates. This figure shows theweekly time series of the 1-month repo rate in excess of the rolling-over 1-week reporates, (dashed line), and the 3-month repo rate in excess of the rolling-over
1-week repo rates, (the solid line), from 1999.07.02 to 2004.04.02.Y13t R13t
Y4t R4t
The conditional version of the pure expectations hypothesis is
stronger than the unconditional version and, therefore, is easier to
reject. Given that the unconditional version of the hypothesis is rejected
in the last section for the Chinese interbank repo rates, it seems that
testing the conditional version of the hypothesis is beating a dead horse.
This view, however, is too scholastic. The purpose of testing a tightly
specified economic theory should not be the end of the academic inquiry,
but, rather, the beginning point of discussing broader issues surrounding
the extreme case represented by the theory. Tests of the conditional ver-
sion of the pure expectations hypothesis can provide important informa-tion about the determinants of conditional term premiums. Indeed,
many early tests of the pure expectations hypothesis are of the nature of
conditional tests.
In choosing conditioning variables, both the classical and modern
theories of the term structure of interest rates are examined. Among
several classical theories, the liquidity preference hypothesis stands
out as the main alternative theory that has more concrete predictions.
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2Casual observations show that the bidask spread of the repos is also increasing with the length ofthe term. However, the data on bidask spread for the sample period are not available.
The thrust of liquidity preference hypothesis is that a long-term bond is
less liquid than a short-term one and, therefore, investors who prefer
liquidity demand a term premium on the long-term bond with the term
premium increasing with the length of the term. A liquidity measure will
be constructed based on trading volumes of the repos to test whether itcontributes to the term premiums. There are many term structure models
that imply nonzero term premiums. In the most popular one-factor models,
such as those by Vasicek (1977) and Cox, Ingersoll, and Ross (1985), the
instantaneous rate serves as the only factor. Longstaff and Schwartz
(1992) add the conditional volatility of the instantaneous rate as a second
factor. More recently, Duffie and Kan (1996) use several key rates as
the factors of the entire term structure and as the determinants of term
premiums.
To construct the liquidity variable, the trading volumes of repo con-
tracts of different terms are used.2As Table I shows, the 1-week repo is
the most liquid, whereas repos of longer terms are less so. The trading
volumes of longer terms are not only smaller, but also more volatile
across terms and over time. The trading volume of the repo of any given
term is therefore not very informative. To create a meaningful variable,
the trading volumes are smoothed by taking averages across time and
across term. More specifically, let
(3)
where is the trading volume of thej-week repo in weekt. represents
how illiquid longer-term repos relative to the 1-week repo.
To construct the conditional volatility of the short-term rate, an
autoregressive model of order 3 is estimated with exponential general-
ized autoregressive and conditional heteroskedasticity of order (1,1), or
in short, AR(3)-EGARCH(1,1), as follows:
(4)
(5)
(6)
where is the conditional variance of . The order of the AR model is
chosen by the insignificance of the slopecoefficients of additional termsand
the order of the GARCH model for the conditional variance is chosen by its
popularity in the literature. Although these choices of the orders may affect
Yt1Ht
log Ht g u[et 2Ht1] a[|et| 2H
t1] b log Ht1
Vart1(et) Ht1
Yt1 f0 f1Yt1
1 f2Yt2
1 f3Yt3
1 et
LtVtj
Lt log a14a3
i0
Vti1 b log a1
5 aj2,3,4,9,13
14a
3
i0
Vtij b
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TABLE IV
Descriptive Statistics of Conditioning Variables
0 1 2 3
A. Estimation of the AR(3)-EGARCH(1,1) model for
Parameter 0.159 0.855 0.200 0.275 0.420 0.033 0.617 0.984
t ratio (3.428) (19.510) (6.025) (4.303) (9.643) (1.738) (18.435) (54.787)
Lt Ht
B. Mean and standard deviation of conditioning variables
Mean 2.309 2.681 2.880 0.023 0.057 0.108 0.149 0.200
SD 0.267 0.760 8.746 0.058 0.092 0.116 0.164 0.177
C. Correlation matrix of conditioning variables
1.000 0.508 0.188 0.217 0.206 0.155 0.188 0.147
Lt
1.000 0.004 0.034 0.133 0.096 0.052 0.011
Ht 1.000 0.047 0.072 0.227 0.198 0.1791.000 0.637 0.306 0.261 0.213
1.000 0.455 0.470 0.417
1.000 0.757 0.746
1.000 0.851
1.000
Note. Panel A of the table presents parameter estimates of the model
,
where is the 1-week repo rate. Panel B presents the mean and standard deviation of the 1-week rate , liquidity Lt, the
conditional varianceH
t (multiplied by 100), and the yield spreads 3, 4, 9, 13. Panel C presents the correlationmatrix of , L
t, H
t, and , , 3, 4, 9, 13. The sample is weekly observations from 1999.07.02 to 2004.06.25.n 2SntY
1t
S
n
t, n
2,
Y1tY
1t
logHt g u[et 2Ht1] a[|et| 2Ht1] b log Ht1
Vart1(et) Ht1
Y1t f0 f1Y1
t1 f2Y1t2 f3Y
1t3 et
S13t
S9t
S4t
S3t
S2t
Y1t
S13tS9tS
4tS
3tS
2tY
1t
Y1t
3In an early version of the article a more complicated vector autoregressive (VAR) model is estimatedfor , where for , 3, 4, 9, 13, with the conditional variancefollowing an EGARCH model, similar to those of Bekaert, Hodrick, and Marshall (1997) andLongstaff (2000). The resultant Ht is very similar to the much simpler model discussed here.
n 2Snt Ynt Y
1t(Yt
1, S2t , S3t , S
4t , S
9t , S
13t )
the parameter estimation, the resultant Ht is not very sensitive to the order
of the model. The model is estimated with a quasi-maximum-likelihood
(QML) approach.3 It should be noted that, although Ht is the conditional
variance of the 1-week rate, it can be viewed as a multiplier of the condi-
tional variance of the repo rate of other terms as well because of the strong
correlations among repo rates of all the terms.
Panel A of Table IV presents the estimation results of (4)(6). The
first slope coefficient, , shows that the 1-week rate is quite persistent.The logarithm of the conditional variance is even more persistent with a
slope coefficient of its lagged value, , near one. In addition, the con-
ditional variance shows a slight asymmetry measured by the insignificant .u
b
f1
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The conditional variance tends to be greater when the unexpected shock
to the repo rate is negative.
Panels B and C report the mean, standard deviation, and the corre-
lation matrix of all the variables as candidates of the conditional term
premiums. The increasing pattern in the means and standard deviationsof is consistent with that observed in Table II. The correlations among
the variables are low except for that between Yt and Lt and those among
s.
The regression model of the following form is then estimated:
(7)
with various combinations of the conditioning variables. Some of the
results are reported in Table V. The regression coefficients are estimated
Ynt Rnt an bnY
1t cnLt dnHt enS
nt e
nt
Snt
Snt
TABLE V
Conditional Term Premiums in the Repo Rates
an bn cn dn en R2
n 2 0.2520 0.0990 0.0158 0.0021 0.1315
(2.7888) (3.0178) (2.5230) (5.7249)
0.0636 0.0250 0.0002 0.0022 1.0723 0.6265
(1.1682) (1.2458) (0.0482) (8.6403) (16.6620)
n 3 0.5571 0.2118 0.0437 0.0035 0.2217
(3.1976) (3.5330) (2.7725) (5.3191)
0.2340 0.0914 0.0069 0.0035 0.9501 0.6136
(2.0961) (2.2021) (0.9519) (11.2421) (13.5747)
n 4 0.5615 0.2363 0.0402 0.0067 0.3204
(3.1824) (3.9871) (2.1295) (6.6869)
0.4006 0.1620 0.0160 0.0048 0.7504 0.6125
(2.6876) (2.9410) (1.7365) (17.3479) (16.0226)
n 9 1.1878 0.5090 0.0543 0.0081 0.4702
(3.3499) (3.9005) (2.0210) (7.1384)
0.9925 0.4144 0.0305 0.0064 0.6165 0.6631
(3.5436) (3.7853) (1.7061) (13.3084) (9.1243)
n 13 1.2698 0.5771 0.0462 0.0080 0.4389
(4.0637) (5.0366) (1.7374) (4.7307)
1.1769 0.4944 0.0295 0.0058 0.7461 0.6981
(4.2120) (4.5183) (1.3013) (8.2322) (10.9914)
Note. This table presents the regression results for term premiums conditioned on either the term rate , or
the term spread , and the conditional volatility , of the 1-week repo rate,
where is the n-week repo rate, is the n-week rolling average of one-week rate, Ltis the liquidity measure
from trading volumes, Htis the conditional volatility, obtained from an AR(3)-EGARCH(1,1) model (and is multi-
plied by 100), and is the yield spread between the n-week rate and the 1-week rate. Numbers in the paren-
theses under the parameter estimates are Newey-West t ratios. R2s are the adjusted Rsquares. The sample is
weekly observations from 1999.07.02 to 2004.06.25.
Snt
RntY
nt
Ynt R
nt an bnY
1t cnLt dnHt enS
nt e
nt
H1tS
nt
Ynt
-
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166 Fan and Zhang
Journal of Futures Markets DOI: 10.1002/fut
by OLS. The t ratios of the coefficient estimates are adjusted by the
Newey-West scheme with the use of a lag of 30 weeks.
The variables , and Ht are all useful in predicting the term pre-
miums. The signs of the slope coefficients are consistent with the theory,
and their estimates are mostly significant. The most useful variable, how-ever, is . The R2 with inclusion of jumps to more than 60%. In addi-
tion, substantially reduces the role of and totally subsumes the role
ofLt. Although the estimate of the slope coefficient of the conditional
volatility, Ht, is basically unchanged, its t ratio increases because of a
much smaller residual variance.
In summary, the results show that the conditional version of the
pure expectations hypothesis does not hold. The conditional term premi-
ums are related to the short-term rate, to term spreads, to the liquidity
measure, and to the conditional variance of the repo rates.
CONCLUSIONS
This article studies the behavior of the Chinese interbank repo rates with
terms from 1 week to 3 months. The repo rates have been used as the
benchmarks for market-determined short-term risk-free interest rates in
Chinese financial markets. Casual observations reveal that the market
has reached a certain level of sophistication. To some degree, the longer-
term repo rates reflect expectations of future fluctuation of the shorter-
term repo rates.One version of term premiums is analyzed as a deviation of the term
rates from the pure expectations hypothesis. The results show that the
term premiums are positive and increase with the length of the term.
The pure expectations hypothesis is statistically rejected, although the
magnitude of the term premiums is economically small. The conditional
term premiums are found to be related to the short-term repo rate, to
term spreads, to a liquidity measure constructed from trading volumes,
and to the volatility of the repo rates.
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