Discussion Paper Series No.196

An Empirical Test of the Efficiency Hypothesison the Renminbi NDF in Hong Kong Market
IZAWA Hideki

Kobe UniversityNovember

2006

The Discussion Papers are a series of research papers in their draft
form, circulated to encourage discussion and comment. Citation anduse of such a paper should take account of its provisional character.
In some cases, a written consent of the author may be required.

An Empirical Test of the Efficiency Hypothesis on the Renminbi NDF in Hong KongMarket
Hideki IZAWA(Kobe University)
Abstract
In this paper we analyze empirically the efficiency hypothesis after the revaluation
on July 21, 2005, using daily non-deliverable forward (NDF) renminbi rates in theHong Kong market. The efficiency hypothesis for the renminbi NDF market isrejected. Therefore, the NDF rate is not an unbiased predictor of the future spotrate.
Key words: renminbi; non-deliverable forward (NDF); foreign exchange market
efficiency hypothesis
JEL classification: F31, F37(corresponding address)
Prof. Hideki IZAWA
Research Institute for Economics and Business Administration,
Kobe University
2-1 Rokkodai-cho Nada-ku, Kobe
JAPAN657-8501
tel/ fax (81)78-803-7004
izawa@rieb.kobe-u.ac.jp-------------------The author is grateful for data contributed by Dr. Li-Gang Liu (Hong Kong MonetaryAuthority) and acknowledges the excellent research assistance by Mr. Takeshi
Hoshikawa (graduate student at Kobe University).

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An Empirical Test of the Efficiency Hypothesis on the Renminbi NDF in Hong Kong
Market1.

Introduction

The Chinese govenment revalued the renminbi (RMB) per dollar by about 2
percentage points, to 8.11 from 8.2765 at 7 p.m. on July 21, 2005. It announced thatthe exchange rate regime would change trom the de facto dollar peg to a
managed float in reference to the currency basket. However, the exchange rates
have not appreciated very much. In this paper, we analyze empirically theefficiency hypothesis after the revaluation, using daily non-deliverable forward(NDF) renminbi rates in the Hong Kong market. If the efficiency hypothesis holds,
the NDF rate is an unbiased predictor of the future spot rate. Could the NDF market
forecast the valuation on July 21, 2005? The 1 month NDF rate was 8.2397, the 3month rate was 8.1829, the 6 month rate was 8.0464, and the 12 month rate was
8.1731. Therefore, the 1, 3, and 12 month rates were underestimated while the 6month rate was overestimated. It seems that the valuation was not anticipatedaccurately.
In the ilterature, the efficiency hypothesis in foreign exchange markets has beentested. For example, see Hai etc. (1997). However, the renminbi NDF has never beentreated.
In Section 2, we show the empirical results. In Section 3, we give remark and theconclusion.
2. Empirical Results
Figure 1 shows the RMB spot rates and NDF (1, 3, 6, and 12 calendar months) rates.
NDF rates are shifted to the right to compare with the corresponding future spotrates. We use NDF rates on contract date and the spot rates on valuation date,shown below.
・NDF rate (F) on contract date↓

two business days later (if holiday, next available business day)・initial date of reckoning↓
・spot rate (S) on valuation date↓

two business days prior to settlement・settlement date2

Daily data by CEIC Data Company Ltd. are used in this paper. But the estimation
periods start from each date corresponding to 1, 3 and 6 month NDFs terms
contracted on July 21, 2005 because the NDFs suddenly appreciated, as Figure 1shows. In the case of the 12 month NDF, the estimation period of spot rates starts
from July 21, 2005, corresponding to the 12 month NDF on July 21, 2004. The end ofthe data is May 10, 2006.
We start from unit root tests. If both spot and NDF variables have unit roots, we test
Engle-Granger cointegration and then dynamic OLS (DOLS). Finally we test theefficiency hypothesis.
(1) Unit root test
(1 month NDF case)As shown in Table 1, Augmented Dickey-Fuller (ADF) statistic of logarithm of spot
rate, s, is 0.469 and ADF t statistic of logarithm of NDF rate, f, is -0.097. Moreover,ADF t statistics of the difference (Δ) of s and f are -12.085 and -40.764, respectively.
Therefore both s and f have unit roots, i.e. I(1) at 1% significance level. We alsochecked PP and KPSS unit root tests and got robust results(3 month NDF case)
The ADF t statistic of s is 0.234 and ADF t statistic of f is -0.006. The ADF t statistics ofthe difference of s and f are -6.718 and -26.641, respectively. Therefore both s and fhave unit roots, i.e. I(1)(6 month NDF case)
The ADF t statistic of s is -0.952 and ADF t statistic of f is -6.354. f does not have unit
root. The ADF t statistics of the difference of s is -9.142. Therefore s has a unit root. Insuch a case we will not test cointegration.
(12 month NDF case)
The ADF t statistic of s is 0.568 and ADF t statistic of f is -1.718. The ADF t statistics ofthe difference of s and f are -8.531 and -15.188, respectively. Therefore both s and fhave unit roots.
(2) Engle-Granger cointegration test3

s(t) = α＋βf(t-k)＋ｕ(t)where k=1, 3, 6 and 12 calendar months corresponding to the NDF contract.
(1 month NDF case)As shown in Table 2, τ(ADF), ADF t statistic of residual derived from OLS regression
following Engle-Granger cointegration test is -4.4. The residual of OLS regression isstationary, I(0). A cointegration relationship exists.
(3 month NDF case)
The ADF t statistic of residual derived from OLS regression following Engle-Granger
cointegration test is -6.42. The residual of OLS regression is stationary, I(0). A
cointegration relationship exists.
(12 month NDF cae)
The ADF t statistic of residual derived from OLS regression following Engle-Granger
cointegration test is -0.61. The residual of OLS regression is not stationary. A
cointegration relationship does not exist.
(3) Efficiency Hypothesis
We test the null hypothesis, H(0) of efficiency hypothesis in 1 and 3 month NDFcases.
H(0) : α=0, β=1, and ｕ is serially uncorrelated (or white noise)
If the null hypothesis is not rejected, efficiency hypothesis holds.
(1 month NDF case)As shown in Table 2,α= 0.286 , β=0.864,(0.045)(0.022)standard errors are in parentheses
If investors are risk neutral, the constant term (α) is zero. However, if they are risk
averse, α can be positive which may not necessarily imply the rejection of theefficiency hypothesis. However, β is significantly different from 1.
And the residual, ｕ is serially correlated according to Box-Pierce tests Q(6) withlag=6.
Next, we estimate Stock and Watson’s dynamic OLS (DOLS) regression with six
leads and lags.

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st + k = α + β f k ,t + ∑ γ i ∆f k ,t + i + uk ,ti =−6

As shown in Table 3, α= 0.267 , β=0.873
F statistic is 93.51 so that the joint hypothesis (α=0 and β=1) is rejected. And β=1 isalso rejected.
(3 month NDF case)α = 0.618 , β= 0.706,(0.052)(0.025)

Q(6) is 143.96. Therefore the residual is serially correlated.
From DOLS, α= 0.513,β =0.756. F statistic is 537.17 so that the joint hypothesis isrejected. And β=1 is also rejected.

3. Conclusion
In this paper we analyze empirically the efficiency hypothesis after the revaluation
on July 21, 2005, using daily non-deliverable forward (NDF) renminbi rates in theHong Kong market. The efficiency hypothesis in the renminbi 1 and 3 month NDF
market is rejected. The NDF rate is not an unbiased predictor of the future spot rate.
This phenomenon is generally referred to as “forward premium (or bias) puzzle”.
REFERENCES
Hai Weike, Nelson C. Mark, and Yangru Wu, (1997) “Understanding spot and forward
exchange rates regressions”, Journal of Applied Econometrics, vol.12, no. 6,
November/December, pp.715-34, collected in Sarno L., and M. Taylor, New
Developments in Exchange Rate Economics, vol. II, Elgar Reference Collection,(2002)

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2005/11/10

2005/10/27

2005/10/13

7.6

2005/9/29

7.7

2005/9/15

7.8

2005/9/1

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2005/8/4

2005/7/21

Figure 1 Chinese renminbi spot rate and non-deliverable forward (NDF) rates

8.3

8.2

8.1

8

7.9

spot
12m
6m
3m
1m

7.5

Table.1

Unit root tests

lag

lag

s1,tADF0s3,t0.469

PP0.497

KPSS

2.606**
0 -12.085**

lag

s6,t5

0.234

00.065∆s3,t4s12,t-0.952

50.571.159**

2.906**∆s6,t-6.718**

00.568-0.871

2.1**∆s1,tADF

lag∆s12,t-9.142**

4-8.531**

PP-11.999**-12.569**-9.201**-15.266**

KPSS

0.153

0.084

0.044

0.16

f1,tADFPPKPSS

1f 3,t-0.097

1-0.246
2.63**∆f1,tADF

0 -40.764**

f 6,t-0.006

0-6.354**-2.527

6-5.853**

1.919**

60.22∆f 3,t0f12,t0-1.718-1.634
1.93**∆f 6,t∆f12,t-26.641**-0-15.188**

PP-47.336**-24.263**--15.503**

KPSS

0.292

0.344

-0.174Note. ADF is the augmented Dickey-Fuller test of a unit root against no unit root. Alllag lengths are chosen based on SBIC. PP and KPSS indicate Phillips-Perron test andKwiatkowski-Phillips-Schmidt-Shin (1992) test (Bandwidth=6). Tests for variablesin levels and in first differences include a constant term. **: 1% siginificance level.

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Table 2 Engle-Granger cointegration tests

st + k = α + β f k ,t + uk ,tαβτ (ADF)τ (PP)
Q(6)p-value

k=1

k=3

k=12

0.286

0.618

1.737

(0.045)(0.052)(0.032)

0.864

0.706

0.169

(0.022)(0.025)(0.016)-4.4**-6.42**-0.61-4.47**-6.51**-0.55

320.09143.96

-

[0]

[0]

-

Note. Newey-West HAC standard errors are in parentheses (lag truncation =6).

τ (ADF) and τ (PP) are Studentized coefficients for the augmented Dickey-Fuller and
the Phillips-Perron tests, respectively, that { u k , t } has a unit root. The 5% and 1% criticalvalues are -3.37 and -4.00, respectively (Engle and Yoo, 1987). Q(6) is the Box-Pierce
statistics with 6 lags for the residuals and the associate p-values are reported. **:1%
siginificance level8

Table 3.

Cointegrating regressions (DOLS)
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st + k = α + β f k ,t + ∑ γ i ∆f k ,t + i + uk ,ti =−6k=1

αβk =3

0.267

0.513

(0.085)(0.080)

0.873

0.756

(0.041)(0.038)t-value( α =0)3.13 **

6.42 **

t-value( β =1)9.66 **

40.40 **F( α =0, β =1)93.51 **

537.17 **Note. Estimates of cointegrating regression coefficients using Stock and Watson’s
method with six leads and lags are reported. Newey-West HAC standard errors arein parentheses (lag truncation =6). **:1% significance level.
.

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