DOES PRICING DEVIATION OF EXCHANGE-TRADED FUNDS PREDICT ETF RETURNS?

Jung-Chu Lin

Associate Professor, Department of Banking and Finance, Takming University of Science and Technology, Taipei, Taiwan

ABSTRACT

This paper investigates whether the pricing deviation of inactive exchange-traded funds (ETFs) differs from that of active ETFs and can predict future ETF returns better and longer. The results show that, compared to active ETFs, inactive ETFs trade at a substantial, more volatile, mostly negative and more skewed-to-the-right pricing deviation. Inactive ETFs’ pricing deviation relates significantly and negatively to longer-day future ETF returns, indicating that the deviation may predict ETF returns better and longer. However, if an inactive ETF has corresponding futures for its underlying index, its pricing deviation may shrink and pricing efficiency may increase.

Keywords:Exchange-traded fund, Pricing deviation, ETF return, ETF pricing efficiency, Creation-redemption process, Arbitrage strategy

ARTICLE HISTORY: Received:13 April 2017Revised:10 May 2017 Accepted:5 June 2017Published:19 June 2017

Contribution/ Originality:: This study contributes the first logical analysis which classifies ETFs into four types to investigate whether inactive ETFs’ pricing deviation can predict future ETF returns better than active ETFs’. The results demonstrate that inactive ETFs’ pricing deviation does predict future ETF returns better and longer.

1. INTRODUCTION

Even though exchange traded funds (ETFs) resemble closed-end funds (CEFs) in many facets, ETFs have a unique feature that additional shares can be created and redeemed by investors through authorized dealers (Engle and Sarkar, 2006). The creation–redemption process allows investors to engage in an arbitrage strategy that adjusts the supply of ETF shares on the market, and thus helps ETF shares to trade at prices approximating the calculated net asset value (NAV) of the underlying portfolio (the underlying value). However, because the creation–redemption mechanism requires a minimum shares for each creation or redemption order (i.e., a creation and redemption unit), the arbitrage trading on ETFs with poor marketability may not be able to be executed smoothly and instantaneously. The deviation (pricing error) between the NAVs and market prices of these less marketable ETFs may be therefore much larger and mostly negative when compared with that of actively traded ETFs. Using actively traded ETFs as a benchmark, this article investigates the extent and properties of the less marketable ETFs’ pricing errors (premiums or discounts), how their NAVs and market prices lead each other, and whether their pricing errors can predict near-term returns better.

Taiwan currently has 13 domestic-component-security ETFs trading on the Taiwan Stock Exchange Corporation (TWSE), since the 2003 launch of the first ETF. While nine of the 13 ETFs have correspondent futures trading on the Taiwan Futures Exchange for their underlying indexes, only three of them have average daily share turnover that are greater than their corresponding creation and redemption unit during the data period August 31, 2006 to June 30, 2016. This study defines those ETFs with an average daily share turnover greater than their creation and redemption unit as active ETFs and the opposites as inactive ETFs. Further considering the existence of corresponding futures for the underlying indexes may affect the ETF pricing efficiency, this study divides the 13 ETFs into four types: (1) active ETFs that have futures markets for the underlying indexes; (2) active ETFs that do not have corresponding futures for the underlying indexes; (3) inactive ETFs that have corresponding index futures; and (4) inactive ETFs that do not have corresponding index futures. This paper compares the four different types of ETFs in terms of pricing errors, lead-lag relationship between NAVs and market prices and the ability of the pricing deviation to predict ETF near-term returns.

2. LITERATURE AND HYPOTHESES

A vast literature shows that CEF share prices generally trade at a substantial and long-lasting discount to the NAV. Explanations for the CEF discount include unrealized capital gains tax (Malkiel, 1977) portfolio illiquidity (Deli and Varma, 2002; Cherkes et al., 2009) managerial performance (Chay and Trzcinka, 1999; Berk and Stanton, 2007) agency costs (Barclay et al., 1993; Coles et al., 2000) and distribution policies (Johnson et al., 2006; Wang and Nanda, 2011). Investors who notice any discrepancy between the NAV and the fair market value have the opportunity to make a profit by buying at a discount and selling at a premium (Chalmers et al., 2001; Goetzmann et al., 2001; Boudoukh et al., 2002). Yet not until the development of the ETF creation and redemption mechanism are the arbitrage opportunities really exploited profitably. The creation and redemption process for ETFs allows arbitrage strategies to be executed effectively whenever the share prices deviate from the underlying value. If the creation–redemption process works efficiently, ETF shares should not trade at significant deviation from the fair value of the portfolio (Engle and Sarkar, 2006). The lower marketability in those inactive ETFs on the TWSE may block the efficient work of the creation–redemption process, making inactive ETF shares trade at significant deviation from the underlying value. For inactive ETFs, the bi-directional lead-lag relationship between NAVs and market prices of active ETFs, found in Lin (2011) may become a one-way lead-lag relationship that only NAVs lead market prices. However, having corresponding futures markets for the underlying indexes may improve the pricing efficiency and the connection between NAVs and market prices of inactive ETFs. Therefore, this paper develops three hypotheses to test as follows:

  1. This paper expects inactive ETFs, like CEFs, trade at a substantial and mostly-negative pricing error to the NAV. The distribution of their pricing errors is expected to be more skewed to the right and have a higher proportion for the negative than active ETFs. However, if an inactive ETF has corresponding futures for its underlying index, the deviation and the skewness to the right may shrink.
  2. While active ETFs generally display a bi-directional lead-lag relationship between NAVs and market prices, this paper expects a one-way lead-lag relationship for inactive ETFs where only NAVs lead market prices. However, if an inactive ETF has corresponding futures for its underlying indexes, this one-way lead-lag relationship may evolve into a bi-directional one that the market price also leads the NAV; that is, the creation–redemption process may work more effectively to enhance the connection between the market price and the NAV.
  3. Since the arbitrage on the pricing deviation of inactive ETFs needs more time (days) to accumulate enough shares for satisfying the requirement of the creation and redemption unit, the pricing errors of inactive ETFs may predict ETFs’ near-term returns better and longer.  

3. DATA AND DESCRIPTIVE STATISTICS

All the 13 ETFs, composed of the listed shares on TWSE, are included in the sample of this study. To identify the type of each ETF, I collect relevant information of the 13 ETFs summarized in Table 1, and categorize all these ETFs to one of the four types of ETFs as shown in Table 2. 

Table-1. The 13 ETFs with domestic component securities on the TWSE

ETF name
Stock code
Listing date
Creation/redemption unit (lot)
Average daily share turnover (lot)
With corresponding  index futures
Yuanta/P-shares Taiwan Top 50 ETF
50
June 30, 2003
500
12,581
Y
Yuanta/P-shares Taiwan Mid-Cap 100 ETF
51
August 31, 2006
1,000
296
N
Fubon Taiwan Technology Tracker Fund
52
September. 12, 2006
500
118
N
Yuanta/P-shares Taiwan Electronics Tech ETF
53
July 16, 2007
1,000
158
Y
Yuanta/P-shares S&P Custom China Play 50 ETF
54
July 16, 2007
1,000
148
N
Yuanta/P-shares MSCI Taiwan Financials ETF
55
July 16, 2007
1,000
2,723
Y
Yuanta/P-shares Taiwan Dividend Plus ETF
56
December 26, 2007
500
1,045
N
Fubon MSCI® Taiwan ETF
57
February 27, 2008
500
375
Y
Fubon Taiwan Eight Industries ETF
58
February 27, 2008
500
26
Y
Fubon Taiwan Finance ETF
59
February 27, 2008
500
48
Y
Yuanta/ P-shares MSCI Taiwan ETF
6203
May 12, 2011
500
336
Y
Sinopac TAIEX ETF
6204
September 28, 2011
1,000
296
Y
Fubon FTSE TWSE Taiwan 50 ETF
6208
July 17, 2012
500
104
Y

Note: One lot equals 1,000 shares. Average daily share turnovers are computed using daily data between August 31, 2006 and June 30, 2016. “Y” indicates the ETF has corresponding index futures on the market, while “N” means the ETF does not have corresponding index futures.
Source: the TWSE.

Table-2. Classification of the 13 ETFs

Type
Active ETFs with corresponding index futures
Active ETFs without corresponding index futures
Inactive ETFs with corresponding index futures
Inactive ETFs without corresponding index futures
ETF code
50
56
53
51
55
57
52
58
54
59
6203
6204
6208

Source: the Taiwan Futures Exchange and this study.

This study gathers daily data of the market price and the NAV of the 13 ETFs between August 31, 2006 and June 30, 2016 from the Taiwan Economic Journal (TEJ) database to compute the pricing error rates of the 13 ETFs of this data period. The movements of the pricing error rates for the four types of ETFs during this data period are plotted in Fig. 1 and the descriptive statistics of each ETF by types are presented in Table 3. For comparison purposes, the vertical axes of the four panels in Fig. 1 have the same maximum, minimum and spacing for the scale.

Fig. 1 shows that inactive ETFs do have a larger-extent and more volatile pricing error than active ETFs. In particular, the inactive ETFs without corresponding index futures seem to have the largest-magnitude pricing error, and the volatility of their pricing errors seems the greatest. In addition to supporting the findings in Fig. 1, Table 3 shows that the distribution of pricing error rates of inactive ETFs are more skewed to the right and that their proportions of the negative pricing error are higher than those of active ETFs. All these results support the expectations of hypotheses (1) that inactive ETFs trade at a substantial and mostly-negative deviation to the NAV and that the existence of corresponding index futures does mitigate the deviation.

Fig-1. Pricing error rates of the four types of ETFs, August 31, 2006 to June 30, 2016.

Source: the TEJ database.

Table-3. Descriptive statistics of the four types, 13 ETFs’ pricing error rates, August 31, 2006 to June 30, 2016

ETFs
Mean (%)
Median (%)
Maximum (%)
Minimum (%)
Std. Dev.(%)
Skewness
Kurtosis
Obs.ervations
% of negative
Ⅰ. Active ETFs with corresponding index futures
50
-0.0603
-0.0676
2.8743
-4.5656
0.3415
-0.5174
23.2761
2436
58.5
55
-0.0814
-0.0884
4.6225
-3.5714
0.4782
0.662
12.8551
2222
56.84
Ⅱ. Active ETFs without corresponding index futures
56
-0.1033
-0.1676
4.7794
-5.283
0.5703
-0.1114
14.4013
2108
61.1
Ⅲ. Inactive ETFs with corresponding index futures
53
-0.3994
-0.4041
3.5384
-3.9683
0.6266
0.6175
7.8262
2222
79.3
57
-0.1761
-0.1664
7.3892
-4.6623
0.6516
2.2883
30.3901
2070
65.31
58
-0.3393
-0.2895
9.3393
-9.3105
1.2081
-0.1068
12.7568
2070
63.77
59
-0.2535
-0.2616
7.2385
-5.7845
0.9045
0.4912
12.633
2070
64.93
6203
-0.4577
-0.3834
7.1981
-3.804
0.756
0.2594
12.2817
1270
72.05
6204
-0.1575
-0.1121
5.746
-1.8966
0.3873
2.4887
50.8604
1173
64.79
6208
-0.6883
-0.6036
2.505
-3.4108
0.6761
-0.3038
4.6213
974
89.73
Ⅳ. Inactive ETFs without corresponding index futures
51
-0.0364
-0.1551
7.7717
-3.6124
0.8747
2.0637
13.4916
2436
58.62
52
-0.2652
-0.3321
11.7188
-4.9327
1.1941
2.1981
18.4974
2428
65.98
54
-0.4891
-0.5239
6.7214
-5.3526
0.7168
1.3014
17.159
2222
81.59

Source: The TEJ database and this study.

4. METHODOLOGY AND EMPIRICAL RESULTS

I first use the vector autoregression (VAR) to model the dynamic relationship between the NAV and the market price of each ETF. Through this model specification, I use Schwarz information criterion to decide the optimum lag length for each ETF’s NAV and market price relationship. Then I use the decided optimum lag length to execute the Granger Causality test to examining the causation between the NAV and the market price of each ETF. The results, presented in Table 4, show that the longest optimum lag length is 4 and that the length seems independent of ETF type. For all the 13 ETFs, the NAV does Granger cause the market price, yet only the active ETFs with corresponding index futures and some of the inactive ETFs with corresponding index futures display the reverse lead-lag relationship, i.e. the market price Granger causes the NAV. These results support the expectations of hypotheses (2) that inactive ETFs mostly have a one-way lead-lag relationship, compared to active ETFs. However, if an inactive ETF has corresponding futures for its underlying indexes, this one-way lead-lag relationship may evolve into a bi-directional one that the market price also leads the NAV.

Since all the NAV and market price series are non-stationary, I further test the presence of cointegrating relationship between each ETF’s NAV and market price. The results show that each ETF’s NAV and market price do have a cointegrating relationship between them. The properties of each cointegration equation (CE) are presented in Table 4. To investigate the ability of ETF pricing deviation to predict subsequent ETF returns, this paper constructs three testing equations as follows:

Table-4. The causality and cointegration relationship between NAVs and market prices of the 13 ETFs

ETFs
Optimum lag length
Null: Market price does not Granger Cause NAV
Null: NAV does not Granger Cause market price
Cointegration relationship
Ⅰ. Active ETFs with corresponding index futures
 
50
2
7.6493
15.6358
A CE with intercept and trend; linear deterministic trend in data
(0.0005)***
(0.0000)***
55
4
7.74165
3.19969
A CE with intercept and trend; linear deterministic trend in data
(0.0000)***
(0.0125)**
Ⅱ. Active ETFs without corresponding index futures
 
56
2
1.4372
77.1551
A CE without intercept and trend; no deterministic trend in data
-0.2378
(0.0000)***
Ⅲ. Inactive ETFs with corresponding index futures
 
53
3
1.012
53.6837
A CE with intercept and trend; linear deterministic trend in data
-0.3863
(0.0000)***
57
1
9.1918
183.901
A CE with intercept but without trend; no deterministic trend in data
(0.0025)***
(0.0000)***
58
2
3.0569
206.355
A CE with intercept but without trend; no deterministic trend in data
(0.0472)**
(0.0000)***
59
2
3.8528
142.793
A CE without intercept and trend; no deterministic trend in data
(0.0214)**
(0.0000)***
6203
1
5.7821
174.389
A CE with intercept but without trend; no deterministic trend in data
(0.0163)**
(0.0000)***
6204
2
0.7657
40.7755
A CE with intercept and trend; linear deterministic trend in data
-0.4653
(0.0000)***
6208
4
0.8761
25.3851
A CE without intercept and trend; no deterministic trend in data
-0.4776
(0.0000)***
Ⅳ. Inactive ETFs without corresponding index futures
 
51
2
1.7569
133.334
A CE without intercept and trend; no deterministic trend in data 
-0.1728
(0.0000)***
52
3
0.3753
135.77
A CE without intercept and trend; no deterministic trend in data
-0.7708
(0.0000)***
54
2
0.0475
132.445
A CE without intercept and trend; no deterministic trend in data
-0.9536
(0.0000)***

Note: The optimum lag lengths are selected by Schwarz information criterion. The results of the Granger causality test are reported by F-statistics and their p-values in the parentheses. Johansen cointegration tests and Schwarz criteria are applied to decide whether NAVs and market prices are cointegrated and which type their cointegration relationship (cointegration equation, CE) is. *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively.

The regression results, presented in Table 5, show that all the four-type ETFs’ pricing deviation is significantly and negatively related to one-day future ETF returns, indicating that a discount in ETF pricing predicts one-day future positive returns and vice versa. However, only inactive ETFs have pricing deviation significantly and negatively related to two- to four-day future ETF returns, supporting the hypothesis (3) that the pricing errors of inactive ETFs may predict ETF returns better and longer. In a few cases, the connection between future ETF market price returns and current pricing deviation in a rising market is stronger than that in a non-rising market.

Table-5. Regression results based on various-period future ETF returns against the market condition dummy and the pricing errors rates

Panel A: one-day future ETF return
ETFs
c
a
b
γ
Adj. R2 (%)
Ⅰ. Active ETFs with corresponding index futures
50
0.0644 (0.1749)
-0.1037 (0.0709)*
0.1003
-0.0142 (0.6283)
-0.3640 (0.0278)**
0.7788
0.0669 (0.1610)
-0.1783 (0.0042)***
-0.2756 (0.3026)
-0.3351 (0.2839)
1.1667
55
-0.0070 (0.9024)
-0.0091 (0.9027)
-0.0444
-0.0294 (0.4522)
-0.2233 (0.0451)**
0.3234
-0.0160 (0.7835)
-0.0301 (0.6990)
-0.2018 (0.2300) 
-0.0549 (0.8046)
0.2512
Ⅱ. Active ETFs without corresponding index futures
56
0.0052 (0.9090)
-0.0203 (0.7126)
-0.0409
-0.0478 (0.0689)*
-0.4145 (0.0001)***
3.5651
0.0200 (0.6935)
-0.1990 (0.0017)***
-0.3346 (0.0317)**
-0.3661 (0.0379)**
4.3345
Ⅲ. Inactive ETFs with corresponding index futures
53
0.0566 (0.2765)
-0.1110 (0.0802)*
0.0988
-0.2045 (0.0000)***
-0.5048 (0.0000)***
4.6559
-0.0990 (0.1132)
-0.2206 (0.0087)***
-0.5141 (0.0000)***
-0.0349 (0.7774)
5.0775
57
0.0565 (0.2644)
-0.0843 (0.1779)
0.0334
-0.0920 (0.0042)***
-0.5877 (0.0000)***
6.744
-0.0281 (0.6037)
-0.1265 (0.0550)*
-0.5602 (0.0000)***
-0.0868 (0.5098)
6.8276
58
0.0378 (0.4103)
-0.0575 (0.3247)
-0.0104
-0.1510 (0.0000)***
-0.4670 (0.0000)***
14.6493
-0.0407 (0.3952)
-0.2433 (0.0001)***
-0.4082 (0.0000)***
-0.1556 (0.0441)**
15.3688
59
0.0055 (0.9271)
-0.0157 (0.8379)
-0.0466
-0.1638 (0.0001)***
-0.6372 (0.0000)***
9.5441
-0.1538 (0.0090)***
-0.0217 (0.7869)
-0.6156 (0.0000)***
-0.0541 (0.6830)
9.4792
6203
0.0574 (0.2792)
-0.1057 (0.1048)
0.1363
-0.2354 (0.0000)***
-0.5168 (0.0000)***
11.7472
-0.1749 (0.0020)***
-0.1108 (0.1415)
-0.5559 (0.0000)***
0.0735 (0.3937)
12.0689
6204
0.0812 (0.0875)*
-0.1206 (0.0369)**
0.3052
-0.0757 (0.0103)**
-0.5856 (0.0000)***
5.4732
-0.0228 (0.6579)
-0.0916 (0.1490)
-0.6820 (0.0000)***
0.2151 (0.1854)
5.9241
6208
0.0767 (0.1243)
-0.0909 (0.1415)
0.1454
-0.1808 (0.0002)***
-0.2985 (0.0000)***
4.8653
-0.1059 (0.1139)
-0.1396 (0.1073)
-0.2880 (0.0000)***
-0.0287 (0.7437)
5.1123
Ⅳ. Inactive ETFs without corresponding index futures
51
0.0196 (0.6959)
-0.0412 (0.5145)
0.0234
-0.0190 (0.5378)
-0.4434 (0.0000)***
6.3298
0.0825 (0.0867)*
-0.2035 (0.0010)***
-0.4186 (0.0000)***
-0.1125 (0.2813)
6.7447
52
0.0771 (0.1537)
-0.1297 (0.0655)*
0.0947
-0.1283 (0.0005)***
-0.5067 (0.0000)***
1.9085
0.0196 (0.7227)
-0.2910 (0.0001)***
-0.4768 (0.0000)***
-0.0926 (0.2534)
12.5039
54
0.0265 (0.6025)
-0.0679 (0.2824)
0.0036
-0.3028 (0.0000)***
-0.6005 (0.0000)***
7.8012
-0.1958 (0.0019)***
-0.2623 (0.0009)***
-0.5557 (0.0000)***
-0.1738 (0.1650)
8.1855

Note: The panel reports estimates from the OLS regressions of one-day future ETF returns on the dummy variable for market condition and the pricing error rate. Robust p-values following White or Newey and West (1987) corrected t-statistics with optimum lag length are reported in parentheses. *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively. The sample period is from August 31, 2006 through June 30, 2016.

Panel B: two-day future ETF return
ETFs
c
a
b
γ
Adj. R2 (%)
Ⅰ. Active ETFs with corresponding index futures
50
0.0812 (0.3465)
-0.1222 (0.2354)
0.0572
0.0029 (0.9551)
-0.1993 (0.3562)
0.0819
0.0801 (0.3545)
-0.2167 (0.0494)**
0.1204 (0.6889)
-0.9304 (0.0153)**
0.7706
55
0.0179 (0.8686)
-0.0824 (0.5238)
-0.0176
-0.0324 (0.6730)
-0.1171 (0.5387)
0.0056
0.0149 (0.8946)
-0.1024 (0.4398)
-0.0688 (0.8196)
-0.1279 (0.7114)
0.0317
Ⅱ. Active ETFs without corresponding index futures
56
-0.0324 (0.7092)
0.0391 (0.6928)
-0.0355
-0.0541 (0.2961)
-0.4202 (0.0077)***
1.7669
-0.0177 (0.8440)
-0.1381 (0.1723)
-0.3259 (0.1519)
-0.3690 (0.1637)
1.9914
Ⅲ. Inactive ETFs with corresponding index futures
53
0.0585 (0.5294)
-0.1210 (0.2791)
0.0428
-0.2212 (0.0026)***
-0.5373 (0.0000)***
2.6931
-0.0907 (0.3904)
-0.2870 (0.0329)**
-0.4936 (0.0003)***
-0.1590 (0.3659)
2.9559
57
0.0847 (0.3798)
-0.1130 (0.3182)
0.0286
-0.0892 (0.1153)
-0.6351 (0.0000)***
4.1028
-0.0074 (0.9385)
-0.1591 (0.1639)
-0.6080 (0.0000)***
-0.0981 (0.5981)
4.2028
58
0.0398 (0.6468)
-0.0469 (0.6502)
-0.0343
-0.1747 (0.0008)***
-0.5576 (0.0000)***
11.6961
-0.0569 (0.4988)
-0.2555 (0.0090)***
-0.5023 (0.0000)***
-0.1491 (0.2467)
12.0796
59
0.0525 (0.6415)
-0.1112 (0.3998)
-0.002
-0.1865 (0.0102)**
-0.7174 (0.0000)***
6.266
-0.1336 (0.2098)
-0.1006 (0.4305)
-0.7223 (0.0001)***
0.0104 (0.9580)
6.2371
6203
0.0618 (0.4864)
-0.1134 (0.3000)
0.047
-0.2747 (0.0000)***
-0.6023 (0.0000)***
8.0834
-0.2081 (0.0386)**
-0.1197 (0.3391)
-0.6488 (0.0000)***
0.0878 (0.5035)
8.2332
6204
0.0668 (0.4357)
-0.0686 (0.4954)
-0.0208
-0.0600 (0.2849)
-0.5801 (0.0000)***
2.6777
-0.0410 (0.6439)
-0.0263 (0.7976)
-0.7211 (0.0000)***
0.3128 (0.1564)
2.7901
6208
0.0803 (0.2441)
-0.0587 (0.4974)
-0.0538
-0.1770 (0.0437)**
-0.3282 (0.0001)***
2.7645
-0.1192 (0.3246)
-0.1118 (0.4427)
-0.3161 (0.0024)***
-0.0299 (0.8245)
2.6952
Ⅳ. Inactive ETFs without corresponding index futures
51
0.0146 (0.8742)
-0.0389 (0.7264)
-0.0332
-0.0260 (0.6499)
-0.5480 (0.0000)***
4.8247
0.0847 (0.3321)
-0.2450 (0.0229)**
-0.4660 (0.0014)***
-0.2606 (0.1041)
5.2776
52
0.1172 (0.2347)
-0.1933 (0.1068)
0.1229
-0.1491 (0.0143)**
-0.6045 (0.0000)***
9.2099
0.0468 (0.6365)
-0.3771 (0.0024)***
-0.5865 (0.0000)***
-0.0754 (0.5191)
9.7251
54
0.0250 (0.7943)
-0.0831 (0.4640)
0.0073
-0.3209 (0.0001)***
-0.3184 (0.0000)***
4.2716
-0.2169 (0.0517)*
-0.2363 (0.0896)*
-0.6053 (0.0005)***
-0.0865 (0.6590)
4.408

Note: The panel reports estimates from the OLS regressions of two-day future ETF returns on the dummy variable for market condition and the pricing error rate. Robust p-values following White or Newey and West (1987) corrected t-statistics with optimum lag length are reported in parentheses. *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively. The sample period is from August 31, 2006 through June 30, 2016.

Panel C: three-day future ETF return
ETFs
c
a
b
γ
Adj. R2 (%)
Ⅰ. Active ETFs with corresponding index futures
50
0.0966 (0.4189)
-0.1392 (0.3184)
0.0432
0.0003 (0.9966)
-0.3444 (0.1260)
0.202
0.0972 (0.4181)
-0.2484 (0.0943)*
-0.0655 (0.8395)
-0.8541 (0.0454)**
0.6218
55
0.0300 (0.8463)
-0.1291 (0.4820)
-0.0017
-0.0424 (0.7017)
-0.0869 (0.7170)
-0.0271
0.0317 (0.8432)
-0.1605 (0.3898)
0.0399 (0.9221)
-0.2931 (0.5320)
0.0183
Ⅱ. Active ETFs without corresponding index futures
56
-0.0709 (0.5598)
0.0978 (0.4735)
0.0005
-0.0688 (0.3662)
-0.5009 (0.0167)**
1.5967
-0.0538 (0.6688)
-0.1099 (0.4319)
-0.3758 (0.2124)
-0.4396 (0.2276)
1.7491
Ⅲ. Inactive ETFs with corresponding index futures
53
0.0699 (0.5849)
-0.1497 (0.3231)
0.0436
-0.2364 (0.0234)**
-0.5656 (0.0000)***
1.9588
-0.0974 (0.5021)
-0.2958 (0.0831)*
-0.5544 (0.0038)***
-0.0946 (0.6780)
2.1438
57
0.1113 (0.3977)
-0.1425 (0.3450)
0.0326
-0.0999 (0.2149)
-0.7637 (0.0000)***
3.9298
0.0070 (0.9562)
-0.2179 (0.1403)
-0.6877 (0.0000)***
-0.2302 (0.3043)
4.0469
58
-0.0020 (0.9870)
0.0423 (0.7624)
-0.0404
-0.1707 (0.0191)**
-0.5667 (0.0000)***
8.4444
-0.1043 (0.3631)
-0.1477 (0.2395)
-0.5324 (0.0009)***
-0.0914 (0.6313)
8.4703
59
0.0932 (0.5684)
-0.1956 (0.3049)
0.045
-0.2077 (0.0468)**
-0.7958 (0.0000)***
5.0144
-0.1278 (0.3999)
-0.1482 (0.4058)
-0.8579 (0.0002)***
0.1543 (0.5382)
5.0601
6203
0.0406 (0.7309)
-0.0739 (0.5961)
-0.0414
-0.2779 (0.0037)***
-0.6095 (0.0000)***
5.8068
-0.2369 (0.0755)*
-0.0674 (0.6670)
-0.6693 (0.0000)***
0.1188 (0.4614)
5.8167
6204
0.0622 (0.5973)
-0.0307 (0.8182)
-0.0769
-0.0499 (0.5331)
-0.6048 (0.0003)***
1.9151
-0.0312 (0.7998)
-0.0288 (0.8350)
-0.6344 (0.0097)***
0.0652 (0.8290)
1.7661
6208
0.0635 (0.6084)
0.0100 (0.9427)
-0.1023
-0.1569 (0.2242)
-0.3307 (0.0039)***
1.863
-0.1508 (0.3872)
-0.0141 (0.9426)
-0.3397 (0.0172)**
0.0131 (0.9399)
1.6692
Ⅳ. Inactive ETFs without corresponding index futures
51
0.0060 (0.9623)
-0.0307 (0.8355)
-0.0379
-0.0332 (0.6905)
-0.6340 (0.0000)***
4.2813
0.0819 (0.4917)
-0.2728 (0.0550)*
-0.5030 (0.0054)***
-0.3850 (0.0802)*
4.7924
52
0.1451 (0.2866)
-0.2365 (0.1418)
0.1289
-0.1449 (0.0880)*
-0.6067 (0.0000)***
6.4173
0.0736 (0.5840)
-0.4174 (0.0085)***
-0.5985 (0.0000)***
-0.0588 (0.6190)
6.8439
54
0.0047 (0.9714)
-0.0634 (0.6762)
0.0308
-0.3894 (0.0007)***
-0.7384 (0.0000)***
3.9606
-0.2698 (0.0703)*
-0.2924 (0.0963)*
-0.6883 (0.0030)***
-0.1932 (0.4432)
4.0666

Note: The panel reports estimates from the OLS regressions of three-day future ETF returns on the dummy variable for market condition and the pricing error rate. Robust p-values following White or Newey and West (1987) corrected t-statistics with optimum lag length are reported in parentheses. *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively. The sample period is from August 31, 2006 through June 30, 2016.

Panel D: four-day future ETF return
ETFs
c
a
b
γ
Adj. R2 (%)
Ⅰ. Active ETFs with corresponding index futures
50
0.1008 (0.5004)
-0.1354 (0.4304)
0.019
-0.0073 (0.9400)
-0.5693 (0.0652)*
0.4598
0.1038 (0.4901)
-0.2673 (0.1393)
-0.3328 (0.4218)
-0.7591 (0.1255)
0.7342
55
0.0369 (0.8513)
-0.1666 (0.4625)
0.0096
-0.0488 (0.7308)
-0.0196 (0.9449)
-0.0444
0.0473 (0.8167)
-0.2163 (0.3467)
0.2354 (0.6085)
-0.5721 (0.2821)
0.0672
Ⅱ. Active ETFs without corresponding index futures
56
-0.1034 (0.4995)
0.1455 (0.3838)
0.032
-0.0802 (0.4223)
-0.5375 (0.0353)**
1.3707
-0.0846 (0.5916)
-0.0687 (0.6918)
-0.4086 (0.2545)
-0.4272 (0.3279)
1.4461
Ⅲ. Inactive ETFs with corresponding index futures
53
0.0825 (0.5980)
-0.1497 (0.3231)
0.0436
-0.2429 (0.0618)*
-0.5656 (0.0000)***
1.9588
-0.0539 (0.7528)
-0.2958 (0.0831)*
-0.5544 (0.0038)***
-0.0946 (0.6780)
2.1438
57
0.1210 (0.4538)
-0.1434 (0.4312)
0.015
-0.0938 (0.3628)
-0.7864 (0.0000)***
3.2002
0.0177 (0.9103)
-0.2311 (0.2020)
-0.6904 (0.0006)***
-0.2850 (0.2962)
3.3023
58
-0.0243 (0.8719)
0.0929 (0.5863)
-0.018
-0.1711 (0.0675)*
-0.5838 (0.0000)***
7.0023
-0.1244 (0.3833)
-0.1210 (0.4307)
-0.5229 (0.0056)***
-0.1471 (0.5229)
7.0406
59
0.1356 (0.5183)
-0.2828 (0.2375)
0.1023
-0.2034 (0.1286)
-0.7693 (0.0000)***
3.6039
-0.0691 (0.7237)
-0.2593 (0.2529)
-0.7923 (0.0025)***
0.0581 (0.8387)
3.6619
6203
0.0252 (0.8661)
-0.0462 (0.7815)
-0.0678
-0.2844 (0.0187)**
-0.6235 (0.0000)***
4.6821
-0.2423 (0.1478)
-0.0766 (0.6837)
-0.6458 (0.0000)***
0.0407 (0.8306)
4.5842
6204
0.0805 (0.5883)
-0.0367 (0.8217)
-0.0765
-0.0447 (0.6552)
-0.6776 (0.0002)***
1.7806
-0.0199 (0.8954)
-0.0433 (0.7937)
-0.6887 (0.0061)***
0.0226 (0.9449)
1.6264
6208
0.0860 (0.5869)
0.0123 (0.9422)
-0.1023
-0.1378 (0.4171)
-0.3342 (0.0232)**
1.3995
-0.1252 (0.5858)
-0.0218 (0.9292)
-0.3339 (0.0669)*
-0.0020 (0.9923)
1.1964
Ⅳ. Inactive ETFs without corresponding index futures
51
-0.0280 (0.8592)
0.0238 (0.8955)
-0.0397
-0.0411 (0.7041)
-0.7367 (0.0000)***
4.3625
0.0587 (0.6942)
-0.2562 (0.1435)
-0.5728 (0.0017)***
-0.4595 (0.0758)*
4.8223
52
0.1679 (0.3212)
-0.2365 (0.1418)
0.1289
-0.1488 (0.1725)
-0.4174 (0.0085)***
-0.6067 (0.0000)***
6.4173
0.0854 (0.6063)
-0.5985 (0.0000)***
-0.0588 (0.6190)
6.8439
54
-0.0112 (0.9448)
-0.0634 (0.6762)
0.0308
-0.4119 (0.0043)***
-0.7384 (0.0000)***
3.9606
-0.2837 (0.1113)*
-0.2924 (0.0963)*
-0.6883 (0.0030)***
-0.1932 (0.4432)
4.0666

Note: The panel reports estimates from the OLS regressions of four-day future ETF returns on the dummy variable for market condition and the pricing error rate. Robust p-values following White or Newey and West (1987) corrected t-statistics with optimum lag length are reported in parentheses. *, ** and *** indicate significance at the 10%, 5% and 1% levels, respectively. The sample period is from August 31, 2006 through June 30, 2016.

5. CONCLUSION

This study examines whether the poor marketability of inactive ETFs block the efficient work of the creation-redemption process, making their pricing deviation, lead-lag relationship between the NAVs and market prices and ability to predict future ETF returns distinct from those of active ETFs. The empirical results show that inactive ETFs do trade at a substantial, more volatile and mostly negative pricing deviation to the NAV and that the existence of corresponding index futures trading may mitigate the deviation and improve the pricing efficiency. While active ETFs display a bi-directional lead-lag relationship between NAVs and market prices, most of the inactive ETFs only display a one-way lead-lag relationship, i.e. only NAVs Granger cause market prices. However, if an inactive ETF has corresponding futures market for its underlying index, the pricing deviation may shrink and the one-way lead-lag relationship may evolve into a bi-directional one that market prices also lead NAVs. Finally, the regression results show that both active and inactive ETFs’ pricing deviation relates significantly and negatively to one-day future ETF returns, indicating that a discount in ETF may predict a positive one-day future return and a premium predict a negative return. However, only inactive ETFs’ pricing deviation relates significantly and negatively to longer-day future ETF returns, indicating that since the arbitrage on the pricing deviation of inactive ETFs needs more days to accumulate enough shares for satisfying the requirement of the creation and redemption unit, their deviation may predict ETF returns better and longer.

Funding: This study received no specific financial support.
Competing Interests: The author declares that there are no conflicts of interests regarding the publication of this paper.

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