On the Pricing Efficiency of China’s ETF Market
Yuexiang Jiang, Feng Guo and Tianjian Lan
Abstract: This study investigates to what extent the pricing efficiency of the SSE 50 ETF,
the first exchange traded fund in China. The empirical results demonstrate that the ETF
market price and its net asset value (NAV) are cointegrated and there is unidirectional
causality from the price to NAV. The conditional variance dynamics from the augmented
GARCH framework shows that the ETF market price spills significant information into
the NAV volatility, and therefore, can be used as price discovery vehicles. Meanwhile, we
find that the fund is priced closely to the NAV with occasional short excursions away,
particularly during the second half of 2007 when the Chinese stock market experienced
substantial volatilities, reflecting sudden increased market risks as well as potential
arbitrage opportunities during financial turbulences.
Keywords: Exchange traded funds; Price efficiency; GARCH model; Chinese market
JEL classification: G12, G15

Corresponding author. Dr. Feng Guo is Senior Economist and Faculty Fellow at Haile/US Bank College
of Business, Northern Kentucky University, Highland Heights, KY 41099, USA. Email: guof1@nku.edu.
Dr. YueXiang Jiang is Deputy Dean and Professor of Finance at College of Economics in Zhejiang
University, Hangzhou, China. Tianjian Lan is Research Assistant at College of Economics in Zhejiang
University, Hangzhou, China. We would like to thank Ying Sophie Huang and Johnny Chan (Editor) for
their valuable comments. Any remaining errors are the responsibility of the authors.
1
1. Introduction
Exchange traded funds (ETF) refer to an index-based equity instruments that
represent ownership in either a fund or a unit investment trust, and they give investors the
opportunity to buy and sell shares of an entire stock portfolio as a single security [Poterba
and Shoven (2002)]. Index-related ETFs are tradable securities which derive their value
from the market movements of the underlying stocks included in the portfolio. The
deviation in asset prices from their underlying value indicates price efficiency and
represents costs as well as opportunities for investors. Engle and Sarkar (2006) argue that
the long-run differences between market prices and Net Asset Values (NAV) in ETF
market sometimes are substantial, for example, if some of the transaction prices used in
calculating NAVs are stale or subject to bid-ask bounces.
Unlike index mutual funds trading at prices equal to the NAVs of the underlying
indices, ETFs are usually traded at prices determined by the supply and demand factors
of the market throughout the day. They also allow for the in-kind creation and
redemption of securities by deposits or withdrawals of actual shares, which tends to
eliminate long-run differences between market prices and NAVs to ensure a market price
approaching the NAV [e.g., see Gastineau (2001), Engle and Sarkar (2006)].1
There has been limited research concerning ETF performance, however, a few
studies have examined the pricing mechanism of ETFs and the relative performance of
on-market investment vehicles relative to the underlying benchmark and index fund
alternatives. For example, Engle and Sarkar (2006) examine the deviations of
international ETF prices from their NAVs and find substantial and longer lasting
deviations for international ETFs compared to domestic ETFs, which they attribute to
stale net asset values. Ackert and Tian (2000) analyze the arbitrage and valuation of
S&P500 SPDRs and find the tracking error of SPRDs to be only 0.069 percent with few
arbitrage opportunities between SPDRs and component stocks. Delcoure and Zhong
(2007) explore the pricing efficiency of iShares and report statistically significant
1
For example, in the case that the ETF price in the secondary market is less than the fund NAV, investors
can purchase the ETF in the secondary market, redeem the ETF unit and then sell the basket of stocks in the
secondary market. In contrast, if the ETF price in the secondary market is higher than the fund NAV,
investors may purchase a basket of stocks in the secondary market and create the ETF units which can then
in turn be sold in the secondary market to capture price discrepancies and get risk free returns.
2
premiums. However, the positive deviations of prices from NAVs are transitory. Jares
and Lavin (2004) find that ETFs in the Japanese and Hong Kong markets over-predict
next-day NAV returns and profitable trading strategies could have been devised to exploit
the overreaction of ETFs for traders who do not face large transactions costs. Other
related studies include Elton et al. (2002, 2004), Lin, Chan and Hsu (2006).
China has witnessed strong growth of its capital markets and undergone
significant reforms in its financial sector, which makes the country an attractive
destination for global investors in recent years. Nonetheless, accessing China’s capital
markets remains difficult for investors, who are only allowed to invest in China’s B-share
stock markets [e.g., see Cheng, Fung and Tse (2008)].2 Under these circumstances, the
Chinese ETFs that invest in the equities of companies based in China are naturally
becoming a convenient and appropriate alternative investment choice, as investors can
increase their exposure to the Chinese market and still achieve the diversification of an
index by holding a Chinese ETF.3 In addition, ETFs can provide investors with benefits
of improving tax efficiency relative to active portfolio management and lowering
transaction costs.
However, the Chinese stock market exhibits special characteristics, such as
government intervention, frequent regulatory changes, poor shareholder protections,
information transparency, and abundant speculative trading among retail investors [see,
e.g. Xu and Wang (1999)]. Instead of moving in accordance with the changes in
fundamental conditions of the companies, stock prices are also believed to be largely
affected by the liquidity shock stemming from hot money [Guo and Huang (2010)]. If the
price of ETF occurs as a premium or a discount to the NAV, the discrepancy can be an
arbitrage opportunity. Hence, investigating the relationship between NAV and market
price of ETF, and empirically examining the extent of price efficiency in the Chinese
2
International investors are not allowed to invest in the A-share markets, which have been reserved for
Chinese domestic investors. In December 2002, however, the Chinese government implemented a qualified
foreign institutional investor (QFII) program, which allows certain foreign institutional investors to invest
in the A-share market.
3
In overseas markets, the most popular China-related ETF is the iShares FTSE/Xinhua China 25 Index
Fund. To access the Chinese “A” Share market, the iShares FTSE/Xinhua A50 China Tracker is the only
ETF available to international investors, while domestic investors have a wider set of choices. Among the
local ETFs products, the SSE 50 ETF in the Shanghai Stock Exchange was the first to market and is most
popular currently. See section 2 for details.
3
ETF market not only warrants a timely study, but also could be of considerable value to
investors and market participants.
Toward this end, we utilize an augmented GARCH model that allows for shortterm deviations from the long-run equilibrium. Our empirical results demonstrate that
there is unidirectional causality from the market price to NAV and the two variables are
cointegrated. The conditional variance dynamics shows that the ETF market price spills
significant information to the volatility of net asset value, and therefore, can be used as
price discovery vehicles since such information may be used in decision-makings.
Meanwhile, we find that the SSE 50 ETF tends to trade at a small premium of just 0.023
percent on average, which disappears within three trading days. However, the Chinese
ETF market experienced substantial volatilities during mid-2007 and early 2008,
reflecting sudden increased market risks as well as enormous arbitrage opportunities
during the financial market turbulence.
The rest of the paper is organized as follows. In section 2, we offer some
discussions on China’s ETF market and related studies. The data and methodology are
provided in section 3. We provide the empirical results and their implications in section
4. The last section summarizes the main findings and draws some relevant policy
implications.
2. Background and Related Studies
Exchange traded funds (ETFs) represent diversified portfolios which track a
specific market index or group of market indexes. They trade like closed-end funds
because they can be bought and sold throughout the day, but in contrast to closed-end
funds, they allow for the creation and redemption of fund shares as needed. Currently
China has five ETFs, including the Shanghai 50 Index ETF (SSE 50 ETF), Shanghai
Dividend Index ETF, and the Shanghai 180 Index ETF, which are traded on the Shanghai
Stock Exchange. The other two are the Shenzhen 100 Index ETF and the Medium- and
Small-cap index ETF.
The SSE 50 ETF, the first Chinese ETF, was launched by China Asset
Management Co., Ltd., and began trading on the Shanghai Stock Exchange (SSE) from
4
December 30, 2004.4 It intends to track the Shanghai Stock 50 Index (SSE 50), which
consists of the 50 largest capitalization stocks with good liquidity that are representative
of the Shanghai securities market. Investing in the SSE 50 ETF, investors gain the same
return/risk characteristic as that of the SSE 50 Index. The process known as in-kind
transactions will direct the trade to the Shanghai stock exchange when investors purchase
SSE 50 ETF shares. The market maker in the exchange, authorized to create and redeem
shares of the SSE 50 ETF, will create or destroy ETF units as needed by buying and
selling shares of the underlying assets in the ETF. Investors may buy index baskets for
creation of the SSE 50 ETF units and then sell those units on the secondary market within
the same trading day.5 As a result, SSE 50 ETF will typically not be trading at a high
premium or discount, because the creation and redemption of shares keep the trading
prices closer to their NAVs.
Elton et al. (2002) examine Spiders which track the S&P 500 index, and show that
while the ETF’s NAV is close to its fair market value, the NAV return is lower than the
S&P index return by 28 basis points if tracking errors include dividend reinvestments and
deduction of management expenses. Their research shows that a large determinant of the
underperformance arises from management fees and the costs associated with nonaccruing earnings on dividends. However, Blume and Edelen (2004), by studying
S&P500 index funds, argue that the tracking error is minimal and the index has been
tracked quite closely.
Cheng, Fung and Tse (2008) investigate the pricing relations in the US between
two exchange traded funds, namely the iShares FTSE/Xinhua China 25 Index (FXI) and
the S&P 500 Index Fund (IVV). They find the speculative pricing hypothesis that the
location of trading has stronger effects than the influence of domestic effects summarized
by FXI’s lagged returns. Regarding China’s domestic ETFs market, however, this issue
has not been discussed in the international literature with the exception of a small number
of works written in Chinese. By adopting the information share model [(Hasbrouck
4
China Asset Management Co. is one of the first national fund management companies approved by the
China Securities Regulatory Commission (CSRC). The fund adviser of the SSE 50 ETF is State Street
Global Advisors Asia Limited (SSgA Asia), a subsidiary of SSgA.
5
Creation and redemption fees for the SSE 50 ETF are no more than 0.5 percent of the creation or
subscription amount, and are generally lower than that of open-ended equity funds.
5
(2003)], Zou and Zhang (2008) examine the price discovery function of SSE 50 ETF and
find its contribution to be relatively insignificant compared to other markets’ ETFs,
which can be due to various market conditions and trading regulations. Wang (2006)
examines the relation between the volatility of ETFs and the volatility of its underlying
securities and finds that SSE 50 ETF enhances the volatility of its component stocks,
reflecting investors’ sentiment.
3. Data and Methodology
3.1. Data
Our daily data retrieved from the WIND Finance Database include the official
NAVs and market prices for the SSE 50 ETF from February 24, 2005 to September 26,
2008. Using higher frequency data allows us to better capture the fluctuations of ETF
market during periods of policy changes in China. Table 1 presents the summary statistics
of daily net asset values and market prices for the SSE 50 ETF over the sample period.
The average NAV (1.9508 Yuan) and market price (1.9516 Yuan) of SSE 50 ETF are
found to be very similar and highly correlated. The market price appears slightly higher
than the NAV, which implies that the SSE 50 ETF trades at a premium on average. The
table also indicates that both series evidence significant skewness and kurtosis. JarqueBera test statistic suggests rejection of the null hypothesis of normal distribution.
Figures 1 displays the movements of ETF market price and SSE stock index.
Overall, we see that behaviors of two series are quite similar, and both fluctuate slightly
around an upward trend until late 2007. The Shanghai Stock Index gained a dramatic 483
percent and reached an unprecedented level of 6000 points between the summer of 2005
and October 2007. However, with oil prices soaring, the financial turbulence in the U.S.
deepening, as well as large amounts of IPOs being approved, the Chinese A-share market
dropped drastically by two thirds to around 2000 points at the beginning of 2008 and
struggled to maintain at that level until the most recent. Similarly, the ETF price also
reached its apex at a historical record level around 4.6 Yuan in October 2007 before
taking a dramatic nosedive to a much lower level. Therefore, the SSE 50 ETF can provide
6
investors with a convenient means of replicating Shanghai stock market performance through a
single trade.
[Insert Table 1 here]
[Insert Figure 1 here]
3.2. Price-NAV volatility spillovers
The ETF market tends to exhibit periods of relative high volatility and periods of
stability, and this suggests that estimation of higher moment dependencies (volatility
spillovers) between market price and NAV can be made more efficient by modeling under
a generalized autoregressive conditional heteroscedasticity (GARCH) framework. A time
series regression that captures the autoregressive (AR) structure in both the mean and the
variance can be estimated as:
NAVt ETF     0 ( prt ETF )  ...   h ( prt ETF
 h )  t
q
p
i 1
j 1
2
2
t ~ N (0,  2 ); where  2  0   
1 t i   2 t  j
(1)
(2)
where net asset value ( NAVt ETF ) is the dependent variable and ETF price ( prt ETF ) is the
explanatory variable.
 
1
2
t i
is the ARCH term (the squared error term in the previous
time period) of q order, generally being news about volatility from the previous period;
 
2
2
t j
is the GARCH term (the conditional variance in the previous time period) of p
order. Thus, NAVt ETF follows an AR (h) process with a conditional variance equation
described by a GARCH (p, q) process.
However, there are limitations in the above GARCH model as the regression
results depend on the assumption that NAVt ETF and prt ETF are stationary, which may not
always be the case. If the two series are non-stationary, even if the empirical estimates of
the parameters  and  are consistent, their estimated standard errors will no longer be
reliable. The use of cointegration technique developed by Engle and Granger (1987)
suffices for straightforward inspection, in the sense that if the null hypothesis of lacking a
unit root for the error term t cannot be rejected at the conventional significance level,
then there exists a stationary long-run relationship in the two time series.
7
We employ Dickey-Fuller Generalized Least Squares (DF-GLS) methodology in
which the  t is de-trended prior to running the regression so that the linear time trend is
not necessarily included to take account of the deterministic components of the data
(Elliott, Rothenberg and Stock, 1996). Therefore, this technique provides more power
than the traditional ADF test and the application to China’s ETF market seems appealing,
given the historical nonlinear shifts in ETFs (see Figure 1).
As Granger (1988) argues, failure to include such an error correction term (ECT)
in a cointegrating model can lead to erroneous results. We thus slightly modify Equation
(1) to incorporate an ECT in order to examine the relation between NAVt ETF and prt ETF as
a factor that influences the variances of the two variables:
ETF
NAVt ETF   0   1prt ETF   2 NAVt ETF
1   3 prt 1   t    t 1
 t   t  t ; where  t2  0  1vt21  2 t21
(3)
(4)
The coefficient 2 actually reflects the error correction parameter, which embodies the
adjustment and control on the deviation, as well as maintains the relationship between the
price and NAV. Engle and Yoo (1987) show that the ECT has important predictive power
for the conditional variances of cointegrated series. This may imply that if the series
deviate further from each other they are harder to predict. The main virtue of this model
lies in its capability of pointing to a particular feature of cointegrated series, which is the
potential relationship between disequilibrium (measured by the ECT) and uncertainty
(measured by the conditional variance) (e.g., see Lee, 1994).
3.3. Persistence of the premium/discount
Premium/discount in ETF market has long been of interest to researchers and
investors. Elton et al. (2002) suggests that the difference between a fund’s market price
and NAV symbolizes the arbitrage opportunity, and the momentum intrigued by
arbitrages will lead the difference to vanish. By applying an AR(1) model to regress the
time series of closing price discount (premium) rate, the authors claim that the difference
will vanish in a day and the pricing is extremely efficient as the first-order lag coefficient
is insignificant in their model. This study further investigates the absolute difference
8
between price and NAV and the percentage difference to examine the pricing efficiency
of the SSE 50 ETF. The absolute difference ( dtETF ) is defined as ( prt ETF – NAVt ETF ),
while the percentage rate difference ( rd tETF ) can be calculated as [100( prt ETF –
NAVt ETF )/ NAVt ETF ]. Positive dtETF and rd tETF represent that the ETF is trading at a
premium, while negative values indicate a discount.
We also take a look at the conditional variance of the absolute difference ( dtETF )
to measure the persistence of any arbitrage opportunities. With greater arbitrage
opportunities for investor and market participants, not only differential rates but also the
variance would be larger over time. If we denote dtETF generically as the differential from
the two series, a time series model that extends Edwin (2002)’s autoregressive structure
to capture both the mean and the variance can be written as:
ETF
dtETF = 0 + 1 dtETF
1 +  +h d t  h +  t
q
p
i 1
j 1
 t  N(0, 2t), where  t2   0   1t2i    2 t2 j
(5)
(6)
The GARCH model is jointly implemented using maximum likelihood of the log
likelihood function. Numerical maximization is completed through the algorithm
developed by Bollerslev (1986) to get the final parameter estimates. The estimated
conditional variance 2t will give us an indication of the evolution of premiums/discounts
in the Chinese ETF market. In this paper, GARCH (1, 1) model is adopted, which is
sufficient to capture the dynamics of the conditional variance of dtETF . If the results come
up with significant coefficients, we can say that the premiums/discounts are persistent.
4. Empirical Results
4.1. Unit root and Granger causality effects
Given the time-series nature of the data, the first step in the analysis is to
determine the order of integration of each price series using Augmented Dickey-Fuller
(ADF, 1981) test. The properties of the market price of SSE 50 ETF and its underlying
net asset value are examined before we proceed with the empirical results, as the nonstationary assumption of individual series plays a very crucial role in our modeling
9
strategy. Table 2 presents the ADF test results with and without trend or intercept for unit
roots of both series at both levels and first-differences. The choice of lag length is based
on the Schwarz Information Criterion. It is clearly indicated that the null hypothesis of
unit root cannot be rejected at the significance level of 1 percent for both series, whereas
the differenced variables are confirmed to be stationary.
[Insert Table 2 here]
The Granger causality test is employed to test whether using information
contained in the market price would be beneficial in forecasting the movements of NAV,
or vice versa. It is useful in inferring the relative predictability between the two variables
to ascertain a lead-lag structure. Based on AIC and SBC criteria, as well as error
autocorrelation for each system of equations, we use 5, 6 and 8 lags to analyze Granger
causality effects between price and NAV in the Chinese ETF market.
The estimated Granger-causality tests are reported in Table 3. Overall, the results
suggest that the change in market price can Granger-cause NAV, because the probability
of no causality effects can be rejected below the 1 percent statistical level. However, no
significant Granger causality is detected from the NAV to price in the Chinese market, as
shown by the Chi-square of p-values below 10 percent. The unidirectional feedback from
the market price to its underlying net asset value implies that knowing the market value
of the all the securities constituting 50ETF will help the investors to predict the NAV.
Price clustering is a widely-recognized phenomenon within financial markets, which
occurs as a result of traders using a discrete set of prices to specify the terms of their
trades. As the exchange traded funds can be bought and sold at anytime during trading
hours, investors in the Chinese ETF market could monitor the ETF returns, make
decisions based on observed profit patterns, and immediately reposition the market
during any given day.
[Insert Table 3 here]
4.2. Price-NAV volatility spillovers
Before we proceed with the GARCH model, a simple linear regression is first
estimated with net asset value ( NAVt ETF ) as the dependent variable and ETF price
10
( prt ETF ) as the explanatory variable. The regression results appeared in Panel A of Table
4 support the hypothesis that the NAV is positively related to the price, which is highly
significant at one percent significance level with an adjusted R-square of 95%. This
provides a clear indication that the NAV is priced in the ETF market and the two series
track closely with each other, which is consistent with a similar finding by Lin, Chan and
Hsu (2006) for the ETF market in Taiwan.
Information criteria and diagnostic statistics are used to select the final models from
various possible AR-GARCH specifications. The results of AR (1, 1)-GARCH (1, 1) process
are shown in Panel B of Table 4. The estimates of the coefficients of the mean equation
and the variance equation, including the volatility spillover parameters are presented as
well. We can see that the NAV is driven by AR (1) processes, as it is identified that the
estimated coefficients are highly significant. The maximum likelihood estimates evidence
the GARCH effects and that the changes in market price exhibit significant spillover
effects to its underlying net asset value.
[Insert Table 4 here]
For a system of non-stationary series, the presence of cointegration among them
has significant implications for modeling the dynamics of individual series. We now turn
to Engle and Granger’s technique to test for cointegration by applying ADF test. The
estimated residual term in the autoregressive equation is tested for stationarity. The result
shows that the residual term is stationary, which indicates the two series are
cointegrated.6 In the cointegration world, the existence of a long-term equilibrium
relationship between NAVt ETF and prt ETF clearly suggests that the in-kind creation and
redemption of securities by deposit or withdrawal of actual shares, which tends to
eliminate long-run differences between the two variables and the Chinese exchange
traded fund market is likely be stable over time.
In the presence of cointegration, an error correction term should be included when
one describes the time-series behavior of the first differences of the series. As the ETF
market price and NAV data used in this article are proved to be cointegrated with each
other, an error correction term should be incorporated in the subsequent GARCH analysis
6
To save space, the figures are not presented here but are available upon request.
11
to allow for the possible effect of deviations from the long–run relationship. The results
of augmented GARCH model by incorporating an ECT are reported in Panel C of Table
4. The coefficients of volatility spillover effects pick up the effect of lagged market prices
in explaining the volatility of NAV. We can see that the added variables (2, 3,) are all
significant, which add incremental explanatory powers to the original non-augmented
model. The volatility spillover from the ETF market price to the NAV means that the
information released by volatility transmission in the market has an important
informational role and therefore, has an effect on its net asset value which is exposed to
the volatility spillover.
The coefficient (2) of the error correction term provides some insight into the
adjustment process of NAV and market prices towards equilibrium. The coefficient is
negative 0.3315 and statistically significant. This implies that the ECT responds
negatively in order to correct a shock in the system before reaching the long-run
equilibrium. For example, NAVt will increase when the deviation from the equilibrium is
negative ( ecmt 1  0 ). In response to a positive deviation from their equilibrium
relationship at period t-1, NAV in the next period decreases in value to eliminate any
disequilibrium. Hence, the augmented AR-GARCH model provides a good description of
the interaction between the two time series.
4.3. Analysis of the premium/discount
The redemption system in the Shanghai Stock Exchange may trigger arbitrage
trading when there is a substantial difference between the market price and the NAV.
Theoretically, the level of premium/discount of the ETF is not supposed to be substantial
provided that the arbitrage in-kind mechanism exists. If the difference is significant and
exceeds the transaction costs, the SSE 50 ETF is considered to be pricing inefficient and
arbitrage opportunities may arise.
Table 5 illustrates the statistics and distribution of absolute differences and
percentage differences between prices and NAVs. We employ t-statistics to test the
hypothesis that the mean of premium/discount equals zero. The average dtETF and
12
rd tETF is 0.0008 Yuan and 0.0226 percent, respectively. This implies that the average
market price is slightly higher than the NAV and the SSE 50 ETF trades at a premium on
average. Both series do not conform to a normal distribution with high levels of kurtosis.
Although the SSE 50 ETF generally trades at a premium, t-test results show an
insignificant premium level.
Of the 878 trading days in the sample, Panel B of Table 5 shows that about 86
percent of premium/discount rates concentrate in the interval of ±0.5 percent, meaning
the SSE 50 ETF is priced relatively close at its NAV.7 By comparison, Elton et al. (2002)
show that on average the SPDRs have been trading on discount of US$0.014 dollar or
0.018 percent. In addition, Engle and Sarkar (2006) suggest that on about 97 percent of
trading business days for SPDR, the range of discount/premium phenomenon is in the
interval of ±0.5 percent. Furthermore, it is discovered that the discount/premium
phenomenon will not continue for more than one trading day. It is eliminated quickly by
market demand and supply or by arbitragers.
[Insert Table 5 here]
In the Chinese ETF market, the average arbitrage trading cost for a brokerage and
an institutional investor is about 0.4-0.5 percent and 0.6-0.8 percent, respectively, while
an individual investor has about 1 percent arbitrage trading cost. However, we find that in
the distribution table, only 3.3 percent of the sample has a discount (premium) rate larger
than 1 percent. This probably means that the arbitrage opportunities are only available to
the brokerages and large institutional investors. In the period of June 20, 2005 to June 28,
2005, ETF is consistently overpriced, and the average premium rate is 1.709 percent.
Wang (2006) points out that this may be intrigued by the special pricing method used by
the eight companies in the portfolio of SSE 50 ETF as pilot stocks in China’s split share
structure reform during that period.
When the SSE 50 ETF sells at a premium, investors can achieve arbitrage profits by applying a “T+0”
strategy when the “secondary market price” is larger than [Fund’s Net Value (claim day) + Commission
charged to purchase the target stock portfolio in the secondary market + Fee charged to subscribe fund
shares in the primary market + Commission charged to sell the target stock portfolio in the secondary
market+ Custodial fees]. Investors could subscribe the fund share in the primary market and sell it in the
secondary market to make a risk-free profit. On the other hand, when the former is smaller than the latter,
investors could purchase the fund in the secondary market and sell it in the primary market to realize the
arbitrage.
13
7
Figure 2 illustrates the absolute difference, dtETF , which is defined as ( prt ETF –
NAVt ETF ) over the sample period. The figure shows that the SSE 50 ETF does not continuously
trade at either a premium or a discount as they are randomly scattered around the horizontal axis.
However, the figure shows that the variation of dtETF magnifies in recent years, in
particular after the period of mid-2007. This coincides with the increased volatility in the
Chinese stock market. Since bottoming out in the summer of 2005, the Shanghai stock
index has gone parabolic, gaining 483 percent from trough to a historical record-high
around 6000 in October 2007. However, with the oil prices soaring, the financial
turbulence in the U.S., large IPOs approved, the Chinese A-share market has dropped
drastically by two thirds to around 2000 points (Guo and Huang, 2010).
[Insert Figure 2 here]
We turn to the conditional variance of the absolute difference ( dtETF ) to measure
the persistence of the arbitrage opportunities. With greater arbitrage opportunities for
investors and market participants, not only differential rates but also the variances would
be larger over time. Results of fitting AR-GARCH models to changes in dtETF are
reported in Table 6. Information criteria and diagnostic statistics are used to try various
possible AR-GARCH specifications and the final selection is fitted with an AR (3)GARCH (1, 1) model. We find that the maximum likelihood estimates confirm that
dtETF exhibits significant conditional heteroskedasticity. The coefficients of the three days
lagged premium are statistically significant, which indicates a premium on one day has
predictability for the premium on the next three days.8 The AIC suggests that the selected
specifications explain the data fairly well.
[Insert Table 6 here]
Figure 3, which plots out the GARCH conditional variance for the absolute
difference between the price and NAV, confirms our earlier finding that the Chinese ETF
8
We also tried the fourth day lagged variable in the regression model, but found that the variable is close to
zero and not statistically significant, indicating the deviations of price from net asset value vanish within
three days.
14
market experienced substantial volatilities between mid-2007 and early 2008. The
conditional variance jumped to extremely high levels, reflecting sudden increased stock
market risks and large arbitrage opportunities during the financial market turbulence.
According to Engle and Sarkar (2006), compared to the U.S. ETFs that are priced very
close to their true NAVs with only brief excursions away, the international ETFs are less
actively traded and less accurately priced as they operate in a more stringent environment
and may still be performing according to expectations.
[Insert Figure 3 here]
5. Conclusions
Existent examinations on the price efficiency of Chinese exchange traded funds
are de facto quite few. Thus, there is scope for this paper to contribute to the ongoing
exploration of costs of funds as well as arbitrage opportunities in the Chinese ETF market
for investors and market participants. The performance and the trading characteristics of
the first and most popular fund in China, Shanghai 50 ETF, during the time period from
February 24, 2005 to September 26, 2008 are investigated in this paper.
Our study reports a number of important results. By explicitly modeling an
augmented GARCH model that allows for short-term deviations from the long-run
equilibrium, this paper first investigate the interactions between the market price and
NAV of ETFs. The empirical results demonstrate that the two variables are cointegrated
and there is unidirectional causality from the market price to NAV. In response to a
positive deviation from their long-run equilibrium relationship, NAV decreases in value
to eliminate any disequilibrium when the system is disturbed by external shocks.
Moreover, the conditional variance dynamics shows that the ETF market price spills
significant information to the volatility of net asset value, and therefore, can be used as
price discovery vehicles since such information may be used in decision-making
processes.
To gauge the degree of pricing efficiency in the Chinese ETF market, we then
measure the deviation of price from NAV and investigate the extent of persistency of
premium/discount within a GARCH framework. Previous research suggests that such
15
deviations should be small as the participants can create new shares and redeem existing
ones to arbitrage away any discrepancies between the price and NAV. Consistent with
this assertion, we find that the SSE 50 ETF tends to trade at a small premium at just 0.023
percent on average, and not statistically significant. Also, the deviations do not persist
over time and disappear within three trading days. Hence, we conclude that the SSE 50
ETF is pricing efficient. However, the Chinese ETF market experienced substantial
volatilities during mid-2007 and early 2008, as the conditional variance jumped to
extremely high levels, reflecting sudden increased market risks as well as large arbitrage
opportunities during the financial market turbulence.
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17
Table 1 Summary statistics of NAV and market price of SSE 50 ETF (February 24,
2005 to September 26, 2008)
Net Asset Value
Market Closing Price
Mean
1.9508
1.9516
Std. dev.
1.1713
1.1727
Max
4.5850
4.5990
Min
0.7060
0.7050
Skewness
0.6449
0.6467
Kurtosis
2.0536
2.0576
Jarque-Bera
92.884
92.943
Beginning Value
0.8770
0.8760
Ending Value
1.8700
1.8660
% Change
113.227%
113.014%
Correlation Coefficient
0.9998
Table 2 ADF test of the price and NAV series
Variable
Exogenous Variable
T-value
P-value
Lags
NAV
Trend and intercept
-0.482458
0.9843
16
Intercept
-1.152089
0.6966
16
None
-0.165844
0.6262
16
Trend and intercept
-5.891114
0.0000***
15
Intercept
-5.792366
0.0000***
15
None
-5.773856
0.0000***
15
Trend and intercept
-0.599060
0.9785
15
Intercept
-1.184389
0.6830
15
None
-0.213731
0.6092
15
Trend and intercept
-5.873202
0.0000***
15
Intercept
-5.611559
0.0000***
14
None
-5.595381
0.0000***
14
D(NAV)
PRICE
D(PRICE)
Notes:
1. the choice of lag length is based on the Schwarz Information Criterion.
2. *** rejects the null hypothesis at the 1 percent level.
18
Table 3 Granger-causality test for the price and NAV series
Lags
Causality
chi-square
P value
Conclusion
5
price  nav
9.93
0.0773*
Rejection
nav  price
4.71
0.4525
Acceptation
price  nav
11.24
0.0812*
Rejection
nav  price
5.21
0.5176
Acceptation
price  nav
15.79
0.0455**
Rejection
nav  price
7.95
0.4382
Acceptation
6
8
Note: The lag selection is based on AIC criteria.
19
Table 4 Estimation results of the GARCH model
Panel A: Linear Model


0.0014
(2.59)
0.9988*
(4196.21)
Panel B: GARCH Model 1

0
0
1
2
0.0021*
(3.50)
0.9981*
(2495.25)
7.79e(-8)
(1.49)
0.1398*
(12.26)
0.8986*
(126.56)
Panel C: GARCH Model 2
0
1
2
3

0
1
2
0.0003**
(3.00)
0.9438*
(337.07)
- 0.3315*
(3.87)
0.3314*
(3.87)
0.3223
(8.76)
2.01E(-7)*
(3.10)
0.1427*
(7.51)
0.8811*
(62.49)
Notes:
1. * and ** indicate significant level at the 1 percent and 5 percent, respectively.
2. GARCH model 1 refers the model without error correction term while GARCH model 2
includes an error correction term 2.
20
Table 5 Summary statistics of discount/premium of SSE 50 ETF (February 24, 2005
to September 26, 2008)
Panel A: Summary
dtETF
rd tETF
0.0008
0.0083
0.057
-0.053
1.094
12.590
3539.852
2.96*
0.0226
0.4219
2.704
-2.078
1.086
9.978
1953.991
1.54
Interval (%）
Days
Percentage（%）
[-0.5,+0.5]
[-0.5,-1]or[0.5,1]
Absolute value> 1
757
92
29
86.2
10.5
3.3
Mean
Std. dev.
Max
Min
Skewness
Kurtosis
Jarque-Bera
t-statistic
Panel B: Distribution
Note:
ETF
1. The absolute difference ( dt
can be calculated as 100( prt
) is defined as ( prt
ETF
– NAVt
ETF
ETF
)/ NAVt
– NAVt
ETF
ETF
ETF
) while the rate difference ( rd t
ETF
. Positive dt
ETF
and rd t
represent that the
ETF is trading at a premium, while negative values indicate a discount.
2. t-statistic is based on the test of hypothesis: Mean= 0; * indicates a significance level at 1 percent.
21
)
Table 6 AR (3)-GARCH (1, 1) model for premium/discount of SSE 50 ETF
Conditional Mean Parameters
0
Conditional Variance Parameters
0
R2
-2.16e-05
(-0.149)
0.334*
(8.19)
0.092**
(2.17)
0.161*
(4.65)
0.0497
(1.37)
62.51
R2
0.069
F-statistic
13.38
F-statistic
11.82
AIC
-1.92
AIC
-7.46
1
2
3
4
0.017*
(4.78)
0.107*
(4.66)
0.774*
(17.77)
1
2
Notes:
1. * and ** indicate significant level at the 1 percent and 5 percent, respectively.
2. The numbers in parenthesis are t-statistics.
2. AR (3)-GARCH (1, 1) model for premium/discount of SSE 50 ETF is defined as:
q
p
i 1
j 1
ETF
ETF
2
2
2
2
dtETF = 0 + 1 dtETF
1 + +2 d t  2 +3 d t 3 +  t,  t  N(0,  t), where  t   0   1 t i    2 t  j
22
Figure 1 Movement of SSE 50 ETF and SSE stock index
6000
5
5000
SSE Stock Index
(right scale)
4
4000
3000
3
2000
2
1000
SSE 50 ETF
(left scale)
1
0
0
05:07
06:01
06:07
07:01
07:07
08:01
08:07
Figure 2 Trend of premium/discount in the Chinese ETF market
.08
.06
.04
.02
.00
-.02
-.04
-.06
05M03 05M07 05M11 06M03 06M07 06M11 07M03 07M07 07M11 08M03 08M07
23
Figure 3 GARCH conditional variance of premium/discount in the Chinese ETF
market
.0005
.0004
.0003
.0002
.0001
.0000
05M03 05M07 05M11 06M03 06M07 06M11 07M03 07M07 07M11 08M03 08M07
24