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 the Hong Kong market. The efficiency hypothesis for the renminbi NDF market is rejected. Therefore, the NDF rate is not an unbiased predictor of the future spot rate.Renminbi, Non-deliverable forward (NDF), Foreign exchange market efficiency hypothesis

Hideki Izawa

English

Research Papers in Economics

 
Discussion Paper Series No.196 
 
 
An Empirical Test of the Efficiency Hypothesis 
on the Renminbi NDF in Hong Kong Market 
 
IZAWA  Hideki   Kobe  University 
 
 
November  2006 
 
 
 
 
 
The Discussion Papers are a series of research papers in their draft 
form, circulated to encourage discussion and comment. Citation and 
use of such a paper should take account of its provisional character. 
In some cases, a written consent of the author may be required.  1
An Empirical Test of the Efficiency Hypothesis on the Renminbi NDF in Hong Kong 
Market 
 
                            H i d e k i   I Z A W A  
(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 the 
Hong Kong market. The efficiency hypothesis for the renminbi NDF market is 
rejected.  Therefore, the NDF rate is not an unbiased predictor of the future spot 
rate. 
 
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 
JAPAN 
657-8501 
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 Monetary 
Authority) and acknowledges the excellent research assistance by Mr. Takeshi 
Hoshikawa (graduate student at Kobe University). 
 
 
 
  2
An Empirical Test of the Efficiency Hypothesis on the Renminbi NDF in Hong Kong 
Market 
 
1.  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 that 
the 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 the 
efficiency 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 3 
month 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 6 
month rate was overestimated. It seems that the valuation was not anticipated 
accurately.  
In the ilterature, the efficiency hypothesis in foreign exchange markets has been 
tested. For example, see Hai etc. (1997). However, the renminbi NDF has never been 
treated. 
 In Section 2, we show the empirical results.  In Section 3, we give remark and the 
conclusion. 
 
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 spot 
rates. We use NDF rates on contract date and the spot rates on valuation date, 
shown below. 
 
ɾNDF rate (F) on contract date 
ˣ two business days later (if holiday, next available business day) 
ɾinitial date of reckoning                       
ˣ 
ɾspot rate (S) on valuation date 
ˣ two business days prior to settlement 
ɾsettlement date  3
 
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 1 
shows.  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 of 
the 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 the 
efficiency 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 (϶) 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. W e also 
checked 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 of 
the difference of s and f are -6.718 and -26.641, respectively. Therefore both s and f 
have 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. In 
such 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 of 
the difference of s and f are -8.531 and -15.188, respectively. Therefore both s and f 
have unit roots. 
 
(2) Engle-Granger cointegration test 
  4
s(t) =  ЋʴЌf(t-k)ʴ̈́(t) 
where k=1, 3, 6 and 12 calendar months corresponding to the NDF contract. 
  
(1 month NDF case) 
As shown in Table 2,  Н(ADF), ADF t statistic of residual derived from OLS regression 
following Engle-Granger cointegration test is -4.4. The residual of OLS regression is 
stationary, 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 
c o i n t e g r a t i o n  t e s t  i s  - 0 . 6 1 .  T h e  r e s i d u a l  o f  O L S  r e g r e s s i o n  i s  n o t  s t a t i o n a r y .  A  
cointegration relationship does not exist. 
 
(3) Efficiency Hypothesis 
We test the null hypothesis, H(0) of efficiency hypothesis in 1 and 3 month NDF 
cases. 
 H(0)  :Ћ =0,  Ќ=1, and  ̈́  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, 
Ћ= 0.286 ,  Ќ=0.864, 
(0.045)    (0.022) 
  standard errors are in parentheses 
 If investors are risk neutral, the constant term (Ћ) is zero. However, if they are risk 
averse,  Ћ can be positive which may not necessarily imply the rejection of the 
efficiency hypothesis. However,  Ќ  is significantly different from 1.   
 And the residual, ̈́ is serially correlated according to Box-Pierce tests Q(6) with  
lag=6. 
Next, we estimate Stock and Watson’s dynamic OLS (DOLS) regression with six 
leads and lags.  5
6
,, ,
6
t k kt i kt i kt
i
sff u αβ γ ++
=−
=+ + ∆ + ∑  
 
As shown in Table 3,  Ћ= 0.267 ,  Ќ=0.873 
F statistic is 93.51 so that the joint hypothesis (Ћ=0 and  Ќ=1) is rejected. And  Ќ=1 is 
also rejected. 
 
(3 month NDF case) 
Ћ  = 0.618 ,  Ќ= 0.706, 
(0.052)    (0.025) 
Q(6) is 143.96. Therefore the residual is serially correlated. 
  F r o m  D O L S ,  Ћ= 0.513,Ќ =0.756. F statistic is 537.17 so that the joint hypothesis is 
rejected. And  Ќ=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 the 
Hong 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) 
 
 
 
  6
Figure 1    Chinese renminbi spot rate and non-deliverable forward (NDF) rates 
 
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  7
Table.1  Unit  root  tests 
 
 lag     lag     lag     lag    
            
ADF 0  0.469 5 0.234 0 -0.952 5 0.568  
PP   0.497  0.065  -0.871  0.57  
KPSS   2.606**   2.1**   1.159**    2.906  ** 
            
ADF 0  -12.085**  4 -6.718** 0 -9.142**  4  -8.531  ** 
PP   -11.999**    -12.569**   -9.201**   -15.266  ** 
KPSS   0.153  0.084  0.044  0.16  
            
ADF 1  -0.097 1 -0.006 0 -6.354** 0 -1.718  
PP   -0.246  -2.527 6 -5.853**  -1.634  
KPSS   2.63**   1.919** 6  0.22  1.93  **
            
ADF 0  -40.764**  0  -26.641**  - 0 -15.188  **
PP   -47.336**    -24.263**  -  -15.503  **
KPSS   0.292  0.344 -  0.174  
Note. ADF is the augmented Dickey-Fuller test of a unit root against no unit root. All 
lag lengths are chosen based on SBIC. PP and KPSS indicate Phillips-Perron test and 
Kwiatkowski-Phillips-Schmidt-Shin (1992) test (Bandwidth=6). Tests for variables 
in levels and in first differences include a constant term. **: 1% siginificance level. 
 
 
 
 
 
 
 
 
 
 
 
 
 
6,t s 12,t s
6,t s ∆ 12,t s ∆
6,t f 12,t f
6,t f ∆ 12,t f ∆
1,t s 3,t s
1,t s ∆ 3,t s ∆
1,t f 3,t f
1,t f ∆ 3,t f ∆ 8
Table 2   Engle-Granger cointegration tests 
,, tk k t k t sf u α β + =+ +  
 
k=1 k=3 k=12 
α  0.286   0.618   1.737  
 (0.045) (0.052)   (0.032)  
β  0.864   0.706   0.169  
 (0.022) (0.025)   (0.016)  
    
(ADF) -4.4** -6.42**  -0.61  
(PP) -4.47** -6.51**  -0.55  
Q(6) 320.09 143.96 -  
p-value [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 { , kt u } has a unit root. The 5% and 1% critical 
values 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 level 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
τ
τ 9
Table  3.  Cointegrating  regressions  (DOLS) 
6
,, ,
6
t k kt i kt i kt
i
sff u αβ γ ++
=−
=+ + ∆ + ∑  
 
  k=1     k =3  
α  0.267  0.513 
 (0.085)  (0.080) 
β  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 are 
in parentheses (lag truncation =6). **:1% significance level. 
. 
 

Understanding spot and forward exchange rates regressions”,

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

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

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