Direct and Indirect Effects of Index ETFs on Spot-Futures Pricing and Liquidity: Evidence from the CAC 40 Index

This paper investigates how the introduction of an index security directly or indirectly impacts the underlying-index spot-futures pricing. Using intraday data for financial instruments related to the CAC 40 index, we do not find that the spot-futures price efficiency improvement observed after ETF introduction is explained either by the direct effect of ETF shares being used in arbitrage trades or by the indirect effect of ETF trading improving the liquidity of index stocks in the short run. Some of our findings suggest that the efficiency improvement could rather result from a structural change in the way index traders distribute across index markets, with the ETF market absorbing the liquidity demand from some hedgers or passive index traders.


Introduction
Exchange-Traded Funds (ETFs) are investment funds designed to replicate the performance of an index or a specified benchmark as closely as possible. Contrary to conventional index mutual funds, ETFs are listed on an exchange and can be traded at any time in the trading day at market prices. Their shares may also be created and redeemed by the issuer in large blocks on a daily basis, either in cash or in kind. ETFs replicating benchmark stock indices have rapidly developed since their first introduction in North America in the 1990s. Their number reached 2,422 funds at the end of November 2010, with 5,413 listings and assets of US$1,231.0 billion from 133 providers on 46 exchanges around the world. 1 Those liquid exchange-traded index securities offer new trading facilities for index portfolio managers, index risk hedgers, and arbitrageurs. They may therefore change trading equilibriums and cross-market pricing relations. In particular, the introduction of ETFs has been shown to tighten the spot-futures no-arbitrage price relation (see Park and Switzer (1995) for the case of the Toronto 35 Index, Switzer, Varson, and Zghidi (2000) for the S&P 500 Index, and Kurov and Lasser (2002) for the NASDAQ-100 Index). 2 However, previous literature has not yet investigated how this efficiency improvement actually formed. The present article aims to fill this gap and draws on high frequency data to identify the channel(s) by which the spot-futures price relation tightens.
Increased arbitrage trading is the traditional explanation of why the introduction of an ETF would tighten the spot-futures no-arbitrage price relation (Kurov and Lasser, 2002;Hegde and McDermott, 2004). Because of their low trading costs, 3 it is usually claimed that ETFs are used to establish the cash leg in arbitrage portfolios. With the opening of an ETF market, more arbitrage tools are available to arbitrageurs. Arbitrage trading is thus facilitated, which consequently improves the efficiency of futures prices. This effect stemming from the ETF shares being used in spot-futures arbitrage portfolios will be referred to as the direct effect of ETF trading on price efficiency.
Another explanation for the efficiency improvement following the introduction of an ETF lies in the linkage between liquidity and efficiency. Empirical studies on index spot-futures relations show that liquidity and trading costs play an important role in enforcing no-arbitrage pricing. Arbitrageurs do not trade unless the difference between the theoretical futures price and the market futures price is greater than the transaction costs incurred to implement arbitrage strategies. The higher these costs, or the lower the liquidity, the greater the price inefficiency must be before arbitrageurs trade on it. 4 For example, Roll et al. (2007) show that liquidity plays a significant role in the price reversion process. They provide evidence that the reversion of the basis on S&P 500 futures contracts occurs faster when aggregate NYSE liquidity is high. Due to this linkage between liquidity and price efficiency, if the introduction of an ETF improves the liquidity of underlying stocks, as has been shown by Hegde and McDermott (2004), Madura andRichie (2007), andDe Winne et al. (2011), this introduction could therefore 3 For instance, De Winne, Gresse, and Platten (2011) show that executing a round-trip trade in an ETF market is substantially less costly than a round-trip trade of the same size executed in the markets for the underlying stocks. 4 Chung (1991) and Miller, Muthuswamy, and Whaley (1994) argue that futures price deviations are more probably the reflection of transaction costs, market non-synchronicity, or market illiquidity, rather than exploitable profits. However, Neal (1996) relates actual S&P 500 arbitrage trades to the predictions of index arbitrage models and observes that price discrepancies do trigger arbitrage trades. Kempf (1996), Tse (2001), and Taylor (2007) show that arbitrage trading in futures markets drives, at least partially, price reversion toward theoretical values.
indirectly improve spot-futures price efficiency even if there is no arbitrage trading in the ETF itself. We refer to this as the indirect effect ETF introduction can have on spot futures price efficiency.
Our contribution is to investigate from which of the direct and direct effects the efficiency improvement generated by the inception of an ETF arises. Using highfrequency index, futures, and ETF data over two five-month periods surrounding the inception of the first ETF replicating the CAC 40 index, we do not find support for neither a direct effect of ETF trading nor a liquidity indirect effect at the intraday horizon. We rather interpret the post-ETF efficiency improvement as a structural change in the spatial distribution of traders across index related markets. This interpretation is based on the observation that a deterioration of the liquidity of index stocks causes ETF trading to increase and that the causal links between index stock liquidity and futures price deviations significantly change in periods of active ETF trading.
The remainder of this paper proceeds as follows. Section 2 presents the testable hypotheses. Section 3 describes our institutional framework and the data. Section 4 compares the level of mispricing in the pre-and post-ETF periods. Section 5 provides empirical tests of the direct and indirect effects of ETF trading on index spot-futures pricing. Section 6 seeks an alternative explanation for the efficiency improvement evidenced at Section 5. Section 7 sets forth our conclusions.

Testable hypotheses
The direct effect of the ETF being used for spot-futures arbitrage relies on the closeness of the ETF portfolio and the CAC 40 index. As evidenced by Blitz, Huij, and Swinkels (2010), ETFs tend to underperform their benchmark index on an annual basis and this may cast doubt on their closeness to their underlying index. However, in the case of the Lyxor CAC 40, the replication of the index is synthetic, which ensures very low tracking error: every day, the fund exchanges the return of its portfolio, possibly consisting of assets quite different from those constituting the index, against that of the index in the swap market. According to Deville (2002), over the first year of trading, the tracking error is less than 0.35%. Given its low trading costs and its tracking quality, the Lyxor CAC 40 ETF can thus be considered an appropriate cash instrument for index arbitrage. If the improvement of futures price efficiency following ETF introduction results from the direct effect of ETF shares being used in arbitrage portfolios, then we should observe that the more active the ETF market, the tighter the spot-futures pricing.
This leads us to posit hypothesis H1:

H1. spot-futures price deviations negatively correlate with trading volumes in the ETF.
However, a correlation analysis of daily data is insufficient to conclude as the relation between ETF trading volumes and index spot-futures mispricing may be dual, with (1) spot-futures mispricing inviting arbitrage trading and thus generating ETF trading volumes, and (2) ETF-based arbitrage trade execution making prices revert to no-arbitrage values. For this reason, we complement H1 by hypotheses H2, which will imply Granger-causality tests on intraday time series:

H2a. an increase in spot-futures price deviations invites ETF trading volumes;
H2b. an increase in ETF trading volumes causes a tightening of spot-futures price deviations.
Tests of an indirect effect of the ETF improving liquidity in the underlying stocks are motivated by the observation that illiquidity is an obstacle to the convergence of market prices toward no-arbitrage values. Any futures market price that deviates from the no-arbitrage value based on the well-known cost-of-carry model invites arbitrage trading. In practice, transaction costs and illiquidity in any of the cash or futures markets may discourage arbitrage activity and allow temporary price deviations from no-arbitrage values. Conversely, wide price deviations may trigger arbitrage trading, which may, in turn, affect liquidity by creating order imbalances, as noted by Roll, Schwartz, and Subrahmanyam (2007). This implies that there exists a two-way causal relation between the spot-futures joint price efficiency and liquidity, and any factor affecting liquidity is then likely to indirectly affect price efficiency. Therefore, if ETF trading affects the liquidity of index stocks, this change in liquidity caused by ETF trading may then modify the index spot-futures price equilibrium. This indirect effect can be examined by testing the following hypotheses:

H3. there exists a two-way causality between index-futures mispricing and index stock liquidity;
H3a. an improvement in index stock liquidity causes a decrease in the indexfutures mispricing; H3b. index stock liquidity deteriorates following an increase in the index-futures mispricing;

H4. an increase in ETF trading volumes causes an improvement in index stock liquidity.
Not rejecting H3a and H4 would validate that ETF trading indirectly cause spotfutures prices to converge towards efficiency by improving the liquidity of index stocks.
We will investigate H2a, H2b, H3a, H3b, and H4 by estimating a trivariate causal model between index stock liquidity, ETF trading volumes, and index spot-futures price deviations.

Institutional framework and data
We base our tests of H1, H2a, H2b, H3, and H4 on data relative to the inception of the first ETF replicating the CAC 40 index on NYSE-Euronext, that is the Lyxor CAC  Table 1 show that futures trading concentrates on the nearby maturity. Prior to the introduction of the ETF, 7,550 transactions a day are executed for the nearest contract (a figure that increases to more than 9,000 after), against 500 transactions for all other maturities.
This research is thus dedicated to the nearby-maturity contract, which is more likely to be subject to arbitrage trading. the index and the index return is tracked by way of synthetic replication through a daily settled swap, which guarantees a very small tracking error. Management fees equal 0.25% per year and apart from trading costs, no entrance or exit fees are charged by the fund. Share creation and redemption are always possible for a minimum amount of 50,000 units and are charged €10,000 per subscription request. The Lyxor CAC 40 ETF is continuously traded in the Euronext electronic order book in the same way as underlying stocks, but its trading session is delayed by five minutes compared with the cash stock market session, so that the price discovery process on underlying stocks precedes that on ETFs. Parallel to the order book trading, Liquidity Providers act as market specialists in two ways. They are committed to quote two-way bid and ask prices in the limit order book, with a minimum volume and within a maximum spread.
In addition, they execute a large portion of the ETF order flow in the OTC market.
The first panel of Table 1 reports Lyxor CAC 40 trading volume during its first year of trading and compares it to the average trading volume in each CAC 40 constituent stock. In terms of daily euro traded volume, the Lyxor CAC 40 ranks 28 th among the CAC 40 stocks. The number of trades recorded for the ETF is very small compared to stocks, with an average of 233 transactions per day, but trades in the ETF are much larger. On average, more than €155,000, representing approximately 3,100 shares (31 times the euro-denominated value of the CAC 40 index) are traded on each transaction, whereas the median trade size for a CAC 40 stock amounts to only €27,868.
These statistics indicate that the market for Lyxor CAC 40 shares is dominated by institutional traders rather than individuals, and that its trading level in its first year of existence was significant enough to affect market liquidity and arbitrage activity.

Observation periods and data
Our analysis is based on the comparison of two observation periods surrounding the ETF launch date of 22 January 2001. Although we hold data for the entire year following this inception date, we choose to make the post-ETF observation period starts once the Lyxor CAC 40 has gained enough assets and trading volumes, as we need to test the direct impact of ETF trading on other market characteristics. When examining the trading volumes of the ETF over its three first year of trading, we observe that the trading volume of the ETF substantially increases in June 2001. In that month, the average daily trading volume for the Lyxor CAC 40 reached a level comparable to that of 2002 and remains higher than that of 2003 until the end of 2001. In addition, in terms of size, the number of outstanding shares for the ETF substantially increases on the 30 th of July to exceed the threshold of ten million for the first time on that date. We therefore set the post-ETF period from 30 July to 31 December 2001. 11 September 2001 is excluded as extremely abnormal market conditions on that day could bias our results.
We then set the pre-ETF observation period symmetrically from 30 July to 31 December 2000 in order to avoid intra-year seasonal effects in the comparison of the two periods. Over these two periods, we use high-frequency data for the CAC 40 index, CAC 40 stocks, CAC 40 futures contracts, and the Lyxor CAC 40 ETF. Our calculations also require data on CAC 40 stock dividends and risk-free interest rates. The CAC 40 futures high-frequency data comprise information for all transactions recorded on the FCE contract and is time-stamped to the nearest second. The data report expiration month, futures price, and number of contracts traded for each transaction. As it is impossible to match night-session transactions with contemporaneous index values, these are omitted from the analysis.
For CAC 40 stocks, we use the best bid and ask quote data of Euronext Paris. These data are composed of the best limit prices and quantities, as displayed in the Euronext electronic order book. The timestamp frequency is the second and a new row appears in the database each time any characteristic of the best quotes, either price or quantity, changes. Quantities refer to displayed quantities only, but do not include hidden orders.
We hold similar data for the ETF security over 2001. We also use ETF tick-by-tick data, which report the price and volume of each trade at a second-by-second frequency.
Theoretically, dividends delivered by the index's constituent stocks must be accounted for in the derivation of the fair price of the futures contract. Kurov and Lasser (2002) argue that the dividend yield is so low on the NASDAQ 100 Index that it can be neglected in calculations of the theoretical price. Dividends on the French market are usually delivered on an annual basis and are highly concentrated around May and June.
It is thus inappropriate to work with a dividend yield since most of the observations concern futures contracts with less than one month to maturity traded during nodividend periods. Discrete dividends are extracted from Thomson Financial Datastream and expressed in terms of CAC 40 index points.
Finally, Euribor interest rates are used as the risk-free rate in the calculation of cash-futures bases. One-week to one-year Euribor interest rates are retrieved from Thomson Financial Datastream. Then, rates for non-rounded maturities are determined by linear interpolation.

Changes in the CAC 40 index-futures pricing efficiency after the introduction of the Lyxor CAC 40 ETF
In a preliminary stage leading to our main empirical work, we check to what extent the price efficiency of CAC 40 futures contracts improves after inception of the Lyxor CAC 40. To do so, we conduct pre/post-ETF univariate comparisons of several mispricing pleasures: the frequency of positive index-futures arbitrage profits, the average value of non-zero index-futures arbitrage profits, and the average duration of arbitrage opportunities.

Mispricing measures
According to the cost-of-carry model, the theoretical price of an index-futures , should be such that: . Let us denote F t,T, and B t,T, as the actual futures price and the actual cash-futures basis, respectively, at time  on day t for maturity T.
), the futures contract is overpriced (resp. underpriced) and the mispricing equals: (2) A long (short) arbitrage portfolio 6 would yield a riskless return of Although in practice the actual arbitrage profit might differ from the observed price deviation, for sake of simplicity, the expressions "mispricing," "price deviation," and "arbitrage profit" are used interchangeably henceforth.
To compute arbitrage profit series   Since the Euronext Paris Market Database does not contain trade directions, estimating price deviations on futures trade prices may result in using buy (resp. sell) futures trades to compute cash-and-carry (resp. reverse cash-and-carry) profits, even though the strategy consists of selling (resp. buying) the futures contract. This would increase both the frequency and the value of arbitrage opportunities. We thus apply the tick rule to infer the direction of futures trades. A transaction is classified as a buy (sell) if its price is above (below) the price of the preceding trade. If there is no price change, the transaction is classified according to the preceding tick change. Opening trades are unclassified. When more than 10 orders are executed within the same second, the actual trade sequence is unknown. We do not classify such observations and drop them from the final sample. Less than 4% of trades remain unclassified.

Transaction cost
in Equation (2) is calculated as follows. Given that futures trade prices are inclusive of implicit trading costs, each futures trade is charged an explicit cost of only 0.01%. Concerning the cash market, it is reasonable to assume that, on average, a one-way CAC 40 basket trade costs a half bid-ask spread of 0.125% plus 2 basis points for explicit fees, for a total cost of 0.145%. 7 Expected transaction costs to be supported at the liquidation of the arbitrage portfolio are estimated on the basis of the initial index value. For short arbitrages, we consider an additional short-selling cost on the cash leg, equal to 0.10% of the index value pro rata temporis. As a result, the total cost charged on an arbitrage strategy may be written: ,T t may differ from the actual profit that an arbitrage portfolio would provide because of execution delays. In order to assess the actual profit accessible to an arbitrageur whose trades are triggered by the observation of an ex post price deviation at time , we simulate ex ante profits in the manner of Yadav and Pope (1994). An ex ante profit is the profit obtained from an arbitrage strategy executed at prices prevailing a few seconds after the observation of the mispricing signal, i.e., at time . This ex ante simulated profit is positive provided that price deviations persist long enough before prices revert to no-arbitrage values; it is negative when prices revert to fair values before trade execution. We consider two values for lag : one minute and two minutes.
When no trade occurs in the market after the considered delay and before the close, the observation is omitted from the sample.
We then focus on the durations of ex post arbitrage opportunities. Observing a price deviation at time  triggers arbitrage transactions that move prices until they revert to equilibrium or violate the no-arbitrage rule in the opposite direction at trade time *.
The time elapsing between  and * is the duration of the arbitrage opportunity and is a measure of price adjustment speed. The shorter *, the more efficient the markets. Let us assume that a buy arbitrage profit buy T t   , , is observed on day t at time . To determine the time at which the buy arbitrage opportunity vanishes, we seek the nearest following trade time within day t at which either the price deviation is null or a sell arbitrage profit appears. We follow the same reasoning to determine the durations of sell arbitrages.
Profits observed at times between  and *  are considered time- opportunity perpetuating and are not taken as new observations for the calculation of arbitrage durations. For this reason, the number of observed durations is much lower than that of sampled arbitrage profits. Finally, the finding of Taylor (2007) (1) and (2) report a highly significant decline in the ex post mispricing frequency consecutive to the introduction of ETFs. The proportion of observations deviating from the no-arbitrage relation falls from 0.58% in the pre-ETF to 0.21% in the after-period. The comparison of ex ante profits presented in columns (3) to (6) of Table   2 shows that the introduction of the ETF reduces arbitrage profit opportunities with respect to any statistic. The proportion of positive profits persisting after a 2-minute delay is divided by 10 after the inception of the ETF, with a decline from 52.63% to 5.24%. Furthermore, mean and median profit values decline substantially to become negative in the post-ETF period for any execution lag and any category of arbitrage trades. 9 Comparison of average and median values of arbitrage durations, reported in columns (7) and (8) These findings are all supportive of improved spot-futures price efficiency, which is consistent with the findings of Park and Switzer (1995), Switzer et al. (2000), and Kurov and Lasser (2002) for the introduction of the Toronto 35, the S&P 500, and the NASDAQ 100 ETFs, respectively.

Does ETF trading directly or indirectly explain the improvement in spot-futures price efficiency?
In this section, we set out to identify the channel(s) by which the efficiency improvement observed after the introduction of the ETF is formed. Direct and indirect effects of ETF trading on index spot-futures mispricing are tested through regressions of daily aggregates as well as a multivariate vector autoregressive model estimated on intraday data.

Regression analysis
Our multivariate analysis consists in regressing daily measures of arbitrage profits onto ETF-related variables after controlling for acknowledged determinants of arbitrage trading. The advantage of this procedure is two-fold. First, it allows us to check that the enhancement of joint spot-futures price efficiency measured at Section 4 is due to the inception of the ETF rather than to financial factors that ease or impede arbitrage trading, such as dividends, volatility, liquidity, or maturity. 10 Second, including a measure of ETF trading in the regressions will provide a test for hypothesis H1.
The first measure of price deviation that we consider is t  , the equally weighted mean of ex post index-futures arbitrage profits measured on day t assuming no trading costs. We use two ETF-related independent variables: 10 These factors were proved to explain arbitrage opportunities in futures markets by Switzer et al. (2000). 11 The CAC 40 turnover is the total euro trading volume in CAC 40 stocks reported to the CAC 40 index capitalization. which denotes the cross-sectional capitalization-weighted mean of CAC 40 stocks' duration-weighted average quoted bid-ask spreads on date t.
The liquidity of the underlying stocks is a factor of particular interest, because the introduction of ETFs is proven to influence the spreads of underlying stocks (Hegde and McDermott, 2004;De Winne et al. 2011). In preliminary regressions of t  on control variables, the explanatory power of the spread variable appears to be unstable: its coefficient is not significantly different from 0 prior to ETF inception but becomes strongly significant thereafter. This leads us to model the daily average price deviation t  as follows: A 2-order moving average model (MA(2)) model is applied to correct a significant degree of autocorrelation in the error terms.
The daily multivariate analysis is also conducted on daily average deviations after transaction costs calculated according to Equation (   is significantly negative would support hypothesis H1 according to which futures price deviations decrease when the ETF is more actively traded. The results of the regressions are displayed in Table 3. Volatility turns out to have no statistical significance for our sample. Concerning the effect of underlying stock turnover, opposite arguments can be put forward. On the one hand, it may be that the   coefficients are significantly negative at the 5% level in the two regressions, confirming that futures price efficiency improves in the post-ETF without it being driven by arbitrage trading factors unrelated to the ETF. However, the ETFturn t coefficients ( 7  ) do not significantly differ from zero in any of the MA(2) OLS or Tobit regressions, which provides no support for H1. The fact that the level of trading in the ETF does not add explanatory power beyond the period binary variable undermines the direct effect of the use of ETF securities in arbitrage strategies on joint price efficiency.

Vector autoregressive (VAR) analysis
In addition to the regression analysis of daily aggregates, we examined the causal links between joint spot-futures price efficiency, CAC 40 stock liquidity, and ETF trading activity, in a VAR analysis at the intraday level. This not only provides a more refined test of the direct effect of ETF trading but also provides tests for the indirect effect (H3a and H4). To conduct the VAR analysis, we divided the trading day into It is well acknowledged that trading volumes and spreads exhibit intraday patterns, and it is likely that spot-futures price deviations exhibit a similar phenomenon. Before performing vector autoregressions, we thus removed intraday seasonalities from the time series. We actually found that average bid-ask spreads of CAC 40  (6) In Equations (5) and (6) (5) and (6)  were related in a trivariate VAR model over the post-ETF observation period:   We report the estimated coefficients of Model (8) until the third lag of each exogenous variable, the total number of lags used to estimate the model, and pairwise Granger causality tests in Table 4. According to these estimates and statistics, we did not reject the null hypothesis that price deviations did not Granger-cause the trading activity in the ETF. In other words we failed to prove that an increase in spot-futures mispricing invited ETF trading (rejection of H2a). With respect to the opposite causal link, ETF turnover was found to Granger-cause index-futures price deviations at the 5%-threshold according to the Chi-square statistic. However, coefficients 3 i  have signs opposite to what H2b predicts: instead of tightening the spot-futures price relation, ETF trading volumes were followed by increasing price deviations on the sample period. We thus rule out the direct effect of ETF trading.
As for indirect effects, we found evidence for a two-way causal relation between liquidity and price efficiency. A liquidity deterioration over a given 30-minute period significantly caused an efficiency deterioration in the next 30-minute period, with 2 1  being significantly positive at the 1% level. The reverse effect of efficiency onto liquidity was also significant but mixed in directions: an increase in futures price deviations produced tensions on CAC 40 stocks spreads in the next 30-minute period  1 1  being positive with a 5% significance  but was followed by a reduction in stock CAC 40 spreads two 30-minute periods later  1 2  being negative with a 5% significance. This partially supports H3b. Regarding the short-term impact of ETF trading on index stock liquidity, null hypothesis (4) was rejected based on a Wald test significant at the 1% threshold and ETF turnover was found to Granger-cause CAC 40 stock spreads, yet not in the way expected according to H4. The coefficients of the lagged ETF turnover variables appeared to be positive with a strong statistical significance at the third lag ( 3 3  ) and a 10%-level significance at the first lag ( 3 1  ). This led us to also reject the hypothesis that ETF trading has an indirect effect on efficiency by enhancing index stock liquidity at the intraday horizon. 12

Interpreting the tightening of the index spot-futures price relation after ETF introduction
In the absence of direct and indirect effects of ETF trading onto index-futures price efficiency at the intraday horizon, how can we then explain the price efficiency improvement observed just after the ETF market has become significantly active? It appears from the statistics displayed in Table 4 that there exists a causal relation between CAC 40 stock spreads and the Lyxor CAC 40 turnover according to which a deterioration of spreads in a given 30-minute period results into an increase in ETF 12 As a robustness check, we conducted the same VAR analysis with 15-minute periods. Results, available upon request, remain qualitatively unchanged.
trading volumes in the next 30-minute period. This suggests that the ETF market could play the role of a second resort market when CAC 40 stocks are less liquid. In addition, the lack of any direct effect of ETF trading on futures price efficiency indicates that the traders who divert their orders to the ETF market are probably not arbitrageurs in their majority but rather hedgers or liquidity traders. Assuming that hedgers and liquidity traders prefer to trade the index in the ETF market when spreads enlarge in the CAC 40 stock markets but that most arbitrageurs remain in the individual stock markets for technical constraints, 13 times of higher volumes in the ETF market should correspond to greater proportions of arbitrageurs -relatively to other categories of traders -in the stock and futures markets. As arbitrage trading is particularly sensitive to trading costs, the greater proportion of arbitrageurs in the stock and futures markets may then result in a tighter causality between spreads and spot-futures price deviations.
To check this hypothesis we divided the post-ETF observation period into two subsamples of dates: the days on which the total ETF trading volume was higher than the median value of ETF daily trading volumes over the period, and the days on which the ETF trading volume was below the median level. We estimated VAR model (8) on each sub-sample. Results are displayed in Table 5. One of these constraints could be the low frequency of trading in the ETF market. While long-term position hedgers and long-term liquidity traders care more about immediacy and market depth, arbitrageurs are mainly concerned by execution speed, which is undoubtedly higher in the stock market than in the ETF market (cf. last panel of Table 1).
estimates corresponding to heavy trading in the ETF are similar to those obtained for the whole sample (Table 4), while Panel A estimates differ in several ways. All the causal links involving the ETF turnover that were significant for the whole sample turn out to be insignificant in times of light ETF trading. More unexpectedly, the two-way causality between index stock spreads and price deviations is also modified. It weakens substantially on days when the ETF turnover is low. Price deviations do not Grangercause spreads any more. Only the opposite-way causality of spreads onto mispricing remains significant; yet the causal impact of spreads on price deviations takes longer to realize: with low ETF trading, the causality is related to the third-lag of spreads while with high ETF trading it is related to the first-lag.
We consider that those differences reflect long-term indirect effects of the creation of the ETF market which cannot be captured at the intraday level. We conjecture that under some market conditions, some group of index traders, most probably those with long-term trading horizon as long-term position hedgers or long-term liquidity traders, shift to the ETF market, leaving other markets with a greater proportion of arbitrageurs.
This results in strengthening the dual causality between liquidity and price efficiency and in dampening the liquidity tensions in the stock and futures markets that would be unfavorable to arbitrage and thus price efficiency otherwise. All in all, mispricing is reduced on average.

Conclusion
Using high-frequency index, futures, and ETF data over two five-month periods surrounding the introduction of the first ETF tracking the CAC 40 index, we find a significant improvement of the no-arbitrage pricing relation in the post-ETF period.
This finding is consistent with those of Switzer, Varson and Zghidi (2000) and Kurov and Lasser (2002). However, in contrast with Kurov and Lasser (2002), we do not attribute the observed improvement to the increased ease in establishing the cash position in cash-futures arbitrage trades by using ETF shares.
First, in a multivariate analysis that controls for financial factors known to impact the spot-futures price relation, index-futures mispricing was found to decrease following ETF introduction, but ETF trading did not explain this improvement. Second, our VAR analysis shows that index-futures mispricing did not invite ETF trading and that ETF trading did not contribute to reducing index-futures mispricing. Although those two findings do not rule out the use of ETF securities in arbitrage strategies, they fail to support that the efficiency improvement mainly stems from the direct effect of ETF trading. Furthermore, although our VAR analysis provides evidence of a two-way causality between CAC 40 stock liquidity and CAC 40 futures price deviation, it shows that the efficiency improvement following ETF introduction cannot be assigned to an indirect effect of ETF trades improving the liquidity of the underlying index stocks at the intraday level.
Some complementary empirical work suggests that the post-ETF efficiency improvement may rather have arisen from a long-run indirect effect of the creation of the ETF market caused by a structural change in the way index traders distribute across markets. The ETF market is likely to provide a second resort trading venue to some specific categories of traders such as long-term position hedgers or liquidity traders, and this may leave other index markets with a greater proportion of arbitrageurs.   (7) and (8), it displays the number of observations, the number and percentage of deviations and the mean and median mispricing value in percentage of the index value. Observations considered in columns (7) and (8) are ex post deviations for which prices revert to no-arbitrage values before the market close. Mean and median deviation values displayed in columns (7) and (8) are those of arbitrage durations reported in seconds. Odd columns correspond to the pre-ETF period, while even columns correspond to the post-ETF period. Pre/post ETF difference statistics are reported in even columns. Ex post results in columns (1) and (2) are based on signed futures trades matched with the contemporaneous index value; ex ante results in columns (3) to (6) for arbitrage strategies triggered by the observation of a cash-futures mispricing (ex post signal) are computed on the basis of signed futures trades matched with contemporaneous index values; duration results in columns (7) and (8)    CACturn is the trading volume on CAC 40 stocks on day t in percentage of their market value. CACspr t is the cross-sectional capitalization-weighted mean of CAC 40 stocks' duration-weighted average quoted bid-ask spreads at date t. t Fmat denotes the futures maturity in number of days taken in logarithm. The dividend yield T t d , is measured as the discounted dividends paid by the underlying stocks from date t to the futures maturity T in percentage of the value of the index. t ETF equals 0 before the ETF inception date and 1 thereafter.
t ETFturn is ETF turnover on date t. 1  t  and 2  t  are the lagged variables in the MA(2). *** , ** , * indicate statistical significance at the 1%, 5%, and 10% levels, respectively. p-values are given between brackets.  h are, respectively, average index stock bid-ask spread, ETF turnover, and average index-futures price deviation calculated over 30-minute period h and adjusted for time-of-day effects. The table displays the estimated coefficients of the model until the third lag of each exogenous variable, the number of lags used to estimate the model determined according to the Akaike information criterion, the number of observations, and pairwise Granger causality tests. The null hypothesis that variable X Granger-causes variable Y is tested by running a Wald test based on a chi-square statistic. Chisquare statistics and associated p-values are reported. *** , ** , * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.