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 Exchange‐Traded Fund (ETF) 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 which replicate benchmark stock indices have developed rapidly since their introduction in North America in the 1990s. Their number reached 2,422 funds by 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 These 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 et al. (2000) for the S&P 500 Index, and Kurov and Lasser (2002) for the NASDAQ-100 Index). 2 However, the literature has not yet investigated how this efficiency improvement actually developed. The present paper 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. We refer to this effect, which stems from the ETF shares being used in spot-futures arbitrage portfolios, 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. These authors 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 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 of ETF introduction on spot-futures price efficiency.
Our contribution is to investigate from which of the direct and indirect effects the efficiency improvement generated by the inception of an ETF arises. Using highfrequency index, futures, and ETF data over two 5-month periods surrounding the inception of the first ETF replicating the CAC 40 index, we do not find support for either a direct effect of ETF trading or 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 in Section 5. Finally, 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 et al. (2010), ETFs tend to underperform their benchmark index on an annual basis and this may cast doubt on their closeness to their underlying indexes. 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 was 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 4 Chung (1991) and Miller et al. (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. 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 draw conclusions, as there may be a dual relation between ETF trading volumes and index spot-futures mispricing, 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 hypothesis H2, which implies Granger causality tests on intraday time series: H2. There exists two-way causality between index-futures mispricing and ETF trading; 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 noarbitrage 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 et al. (2007). This implies that there exists a two-way causal relation between 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 index-futures mispricing; H3b. Index stock liquidity deteriorates following an increase in 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 causes spotfutures prices to converge toward efficiency by improving the liquidity of index stocks. We 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 40. In Europe, ETFs emerged in 2000 on the Deutsche Börse and the London Stock Exchange, followed soon thereafter by Euronext Paris, the French subsidiary of NYSE-Euronext, which opened an ETF-dedicated segment, called NextTrack, in January 2001. The Lyxor CAC 40 was one of the first ETFs launched on NextTrack. When it began trading, on 22 January 2001, the CAC 40 index had long served as the underlying asset for futures and options contracts traded on NYSE Liffe, the derivative market of NYSE-Euronext. The characteristics of the CAC 40 index, its futures contracts, and the Lyxor CAC 40 ETF, as well as related descriptive statistics, are presented in Subsection 3.1. Subsection 3.2 describes our data.

The markets for the CAC 40 index
The CAC 40 index consists of the 40 most actively traded stocks listed on the Main Market of Euronext Paris. Components of the CAC 40 are traded in the electronic order book of Euronext on a continuous basis from 09:00 to 17:35. The trading session starts with a batch auction at 09:00, then switches to continuous trading. A closing auction takes place at 17:35 after a five-minute pre-auction period. Every 30 seconds during the continuous trading session, Euronext Paris calculates a weighted average of CAC 40 stock prices to determine the value of the index. 5 The trading of futures contracts on the CAC 40 index (ticker FCE) takes place on NYSE Liffe from 08:00 to 17:30 on the electronic trading system NSC-VF (day session) and from 17:30 to 22:00 on Globex (night session). The size of one contract is equal to the value of the CAC 40 index multiplied by €10, and the tick size is 0.5 index points. Eight maturities (three monthly, three quarterly, and two half-yearly) are continuously open with a quotation horizon of 19 to 24 months. Settlement is in cash with a liquidation price equal to the arithmetic average (rounded to one decimal) of each CAC 40 index value calculated and reported on the settlement day between 15:40 and 16:00, the first index value after 16:00 being included. Since its introduction in 1988, the FCE contract has experienced tremendous growth in trading volume and soon became one of the most liquid derivatives contracts trading on NYSE Liffe. In 2000, it reached a daily average of 71,568 contracts traded. Summary statistics in the first panel of Table 1 show that futures trading concentrates on the nearby maturity. Prior to the introduction of the ETF, 7,550 transactions a day were executed for the nearest contract (a figure that increases to more than 9,000 after the introduction of the ETF), 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 CAC 40 index currently serves as the benchmark for several ETFs, but the Lyxor CAC 40 ETF faced no competition until March 2005. One unit of the ETF is worth 1/100 of 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 Table 1 Spot and futures market trading activity around ETF introduction The first panel of this table reports the average number of trades and the average number of traded contracts per day for the near, far, and all-maturity contracts over the two sample periods. The second panel displays, for the two periods, the average daily euro trading volume in CAC 40 stocks, the corresponding average daily number of trades, the average bid-ask spread computed as the daily mean of the capitalization-weighted average of duration-weighted individual stocks' bid-ask spreads, and the daily mean of CAC 40 index volatility calculated with intraday values according to Parkinson (1980 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 for 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 28th 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 the volume of trades in the ETF is 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 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 begin the post-ETF observation period at the point where Lyxor CAC 40 has gained enough assets and trading volume, 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 first three years 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 remained 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 30 July 2001 to exceed 10 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.
CAC 40 index values at 30-second intervals, as well as high-frequency data for CAC 40 nearest futures, CAC 40 stocks, and the Lyxor CAC 40 ETF, are extracted from the Euronext Paris market database.
The CAC 40 futures high-frequency data comprise information for all transactions recorded on the FCE contract and are 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 to 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 no-dividend periods. Discrete dividends are extracted from Thomson Financial Datastream and are expressed in terms of CAC 40 index points.
Finally, Euribor interest rates are used as the risk-free rate in the calculation of cashfutures 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 CAC 40 Index-Futures Pricing Efficiency After Introduction of 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 measures: 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 contract with maturity date T at time t on day t, denoted F * t,T ,τ , should be such that: where B * t,T ,τ denotes the theoretical cash-futures basis; I t,τ is the value of the index at time t on day t; r t,T is the risk-free interest rate on a loan contracted at t and redeemed at T; and D t,T is the present value of the dividends delivered by the index stocks in the period [t;T], expressed in index points. Equation (1) defines the fundamental value of the futures contract in the absence of trading costs. When accounting for arbitrage transaction costs, the no-arbitrage cash-futures basis can differ from zero. Let us denote C t,T ,τ as the transaction cost borne to implement arbitrage trades at prices prevailing at time τ . The no-arbitrage cash-futures basis fluctuates inside a collar delimited by −C t,T ,τ and C t,T ,τ . Let us denote F t,T,τ and B t,T,τ as the actual futures price and the actual cash-futures basis, respectively, at time τ on day t for maturity T. If B t,T ,τ > C t,T ,τ (resp. < −C t,T ,τ ), the futures contract is overpriced (resp. underpriced) and the mispricing as a percentage of the index value 6 equals: A long (short) arbitrage portfolio 7 would yield a riskless return of t,T ,τ , provided that the trades implemented to build the portfolio are executed at prices F t,T ,τ and I t,τ . 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 ( t,T ,τ ), futures prices are synchronised with spot index values after aggregating futures trades executed within the same second at the same price for a given maturity. Since index-futures markets generally lead cash index markets (see for example, Kavussanos et al. 2008;Shyy et al., 1996;Stoll and Whaley, 1990), we match futures trade prices with the index value displayed at the time of the futures transaction or immediately following it. This procedure ensures that no more than 30 seconds has elapsed between the two values. Then, we determine the direction of futures trades. For each index-futures pairing, profit t,T ,τ is calculated according to the direction of the futures trade and after transaction cost.
Since the Euronext Paris market database does not include trade directions, estimating price deviations on futures trade prices may result in using buy (sell) futures trades to compute cash-and-carry (reverse cash-and-carry) profits, even though the strategy consists of selling (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 C t,T ,τ 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%. 8 Expected transaction costs to be supported at 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: where f = 0.01%; k = 0.125%; and B sell equals 1 for reverse cash-and-carry trades, zero otherwise. 7 A short, or sell arbitrage, also known as a reverse cash-and-carry trade, consists of shortselling the index portfolio and buying the futures contract, while a long or buy arbitrage, also known as a cash-and-carry trade, consists of buying the index portfolio and selling the futures contract. 8 As CAC 40 stock bid-ask spreads are more volatile than futures spreads, we also consider two other levels of transaction costs: 0.10% and 0.15%, i.e., respectively, 0.12% and 0.17% when including explicit costs. Results remain qualitatively unchanged.
At each futures trade time, we compute arbitrage profit t,T ,τ (Equation 2) conditioned on a total transaction cost of C t,T ,τ (Equation 3). Negative profits correspond to noarbitrage prices and are set to zero. Arbitrage profits calculated in this way are stated as ex post because they represent the profitability of an arbitrage trade assuming that observed prices can instantaneously be executed at the observed price. In practice, t,T ,τ 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 τ , 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 observation of the mispricing signal, i.e., at time τ + δ. This ex ante simulated profit is positive provided that price deviations persist long enough before prices revert to noarbitrage values; it is negative when prices revert to fair values before trade execution. We consider two values for lag δ : 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. A price deviation at time τ triggers arbitrage transactions that move prices until they revert to equilibrium or violate the no-arbitrage rule in the opposite direction at trade time τ *. The time elapsed between τ and τ * is the duration of the arbitrage opportunity and is a measure of price adjustment speed. The shorter is τ * − τ , the more efficient the markets. Let us assume that a buy arbitrage profit buy t,T ,τ is observed on day t at time τ . 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 τ and τ * are considered time-τ 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) that arbitrage activity falls dramatically just before the close of trading suggests that arbitrageurs do not wish to hold arbitrage positions overnight. This leads us not to compute the duration of arbitrage opportunities that do not vanish prior the end of the trading day. 9 4.2. Changes in frequency, magnitude, and persistence of mispricing after ETF introduction Table 2 presents a complete view of the variation in mispricing frequency and level around the introduction of the Lyxor CAC 40 ETF.
Columns (1) and (2) report a highly significant decline in ex post mispricing frequency following introduction of ETFs. The proportion of observations deviating from the noarbitrage relation falls from 0.58% in the pre-ETF to 0.21% in the post-ETF period. 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 9 While we do not compute durations in these cases, we keep these observations in the sample of arbitrage profits. The percentage of observations dropped from the duration sample is only 0.004%.  (7) and (8), the table displays the number of observations, the number and percentage of deviations and the mean and median mispricing value as a 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) (7) and (8) (3) (3) a factor of 10 after inception of the ETF, with a decline from 52.63% to 5.24%. Further, 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. 10 Comparison of average and median values of arbitrage durations, reported in columns (7) and (8), confirms those results. The mean of arbitrage durations significantly declines from 15.65 seconds in the pre-ETF period to 4.94 seconds in the post-ETF period. 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 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 through a multivariate vector autoregressive model estimated on intraday data.

Regression analysis
Our multivariate analysis consists in regressing daily measures of arbitrage profits on 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 in Section 4 results from inception of the ETF rather than from financial factors that ease or impede arbitrage trading, such as dividends, volatility, liquidity, or maturity. 11 Second, including a measure of ETF trading in the regressions provides a test for 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: ETF t , which is a binary variable equal to 0 (1) in the pre-ETF (post-ETF) period, and ETFturn t , which equals the ETF turnover -calculated as the number of ETF shares traded on date t as a percentage of the number of outstanding shares -when t belongs to the post-ETF period, and zero otherwise.
On given day t, control factors are measured as follows: volatility is measured as the price range of the futures contract taken in logarithm and denoted Fσ t ; dividend yield is denoted d t,T and measured as discounted dividends paid by CAC 40 stocks 10 Given that the level of an ex ante profit obviously depends on the value of the initial price deviation, which serves as an arbitrage signal, we also examine ex ante profit values relative to ex post profit values to provide a more accurate picture of the effective impact of ETF inception. We compare differential profits calculated as the ex ante profit minus the initial ex post profit. The results, unreported for the sake of brevity, are in the same direction and are even more significant. They are available on request. 11 These factors are proven to explain arbitrage opportunities in futures markets by Switzer et al. (2000). from date t to futures maturity date T as a percentage of the value of the index; Fmat t denotes futures maturity in number of days taken in logarithm. Liquidity is assessed via two variables: CACturn t , the CAC 40 turnover 12 on day t, and CACspr t , the crosssectional capitalisation-weighted mean of CAC 40 stocks' duration-weighted average quoted bid-ask spreads on date t.
Concerning the effect of underlying stock turnover, opposing arguments may be put forward. On the one hand, it may be that the occurrence and magnitude of price deviations increase trading activity by inviting more arbitrage services. On the other hand, higher volumes, if initiated by arbitrageurs, may lead to a tighter spot-futures relation. Active trading would accelerate price reversion and cause profits to vanish more rapidly. Spreads are 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 zero prior to ETF inception, but becomes strongly significant thereafter. This leads us to a model of the daily average price deviation t as follows: A two-order moving average model (MA (2)) is applied to correct a significant degree of autocorrelation in the error terms. It is Ordinary-Least-Square (OLS) estimated. Multivariate analysis is also conducted on daily average deviations after transaction costs, calculated according to Equation (3). As the distribution of average deviations net of trading costs is characterised by a substantial number of values equal to 0, the model is estimated using a censored Tobit methodology. The same independent variables as those of Model (4) are used.
Finding a significantly negative value for γ 1 in both the OLS regression of price deviations before trading costs and the Tobit regression of price deviations after trading costs would constitute a robustness check for the univariate tests of Section 4. Finding that γ 2 is significantly negative would support 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. Our main interest lies in the effects of ETF variables. The γ 1 coefficients are significantly negative at the 5% level in the two regressions, confirming that futures price efficiency improved in the post-ETF observation period without it being driven by arbitrage trading factors unrelated to the ETF. However, the ETFturn t coefficients (γ 2 ) 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.
With respect to control variables, volatility Fσ t turns out to have no statistical significance for our sample. We find a positive coefficient for CAC 40 turnover; yet, this coefficient is weakly significant in the MA(2) analysis and insignificant in the Tobit Table 3 Regressions of average ex post price deviations This table displays the estimates for regressions of daily average ex post index-futures arbitrage profits calculated upon signed futures trade prices for the nearby maturity. An MA(2) is used to model ex post price deviations before transaction costs. Censored Tobit regressions are implemented to analyze ex post price deviations net of transaction costs. Fσ t is the price range of the futures contract over day t, taken in logarithm. CACturn t is the trading volume on CAC 40 stocks on day t as a 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. Fmat t denotes the futures maturity in number of days taken in logarithm. The dividend yield d t,T is measured as discounted dividends paid by underlying stocks from date t to futures maturity T as a percentage of the value of the index. ETF t equals zero before the ETF inception date and 1 thereafter. ETFturn t is ETF turnover on date t. η t−1 and η t−2 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. deviations before transaction costs increase because trading costs discourage arbitrage trading (positive γ 7 in the OLS regression). Simultaneously, trading costs reduce net arbitrage profits, as indicated by the negative sign for γ 7 in the Tobit regression.

Vector autoregressive (VAR) analysis
In addition to the regression analysis of daily aggregates, we examine 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 effects (H3a and H4). To conduct the VAR analysis, we divide the trading day into 16 periods of 30 minutes from 09:15 to 17:15. For each 30-minute period, indexed by h, we calculated: (1) the average of ex post index-futures price deviations assuming no trading costs, denotedπ h ; (2) the duration-weighted average relative quoted spread of each component of the CAC 40 index, and then the cross-sectional mean of these average spreads, denoted cacspr h ; and (3) the turnover of the ETF, denoted etfturn h . 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 remove intraday seasonalities from the time series. We find that average bid-ask spreads of CAC 40 stocks (cacspr h ) are greater during the first four and the final 30-minute periods of the day, and that the ETF's turnover (etfturn h ) is higher, on average, in the final 30-minute period. We therefore adjust the (cacspr h ) and the (etfturn h ) time series by regressing them on dummies as follows: cacspr h = a 0 + a 1 I 1 + a 2 I 2 + a 3 I 3 + a 4 I 4 + a 16 I 16 + ε In Equations (5) and (6), variables I k are binaries that equal 1 when the dependent variable is measured over the kth 30-minute period of the day, 0 otherwise. ε  (5) and (6) representing the adjusted average spread and the adjusted ETF turnover, respectively.
Index-futures price deviations (π h ) are found to be greater in the first and last 30minute periods of the day. In addition, we know from the previous section that price deviations are determined by CAC 40 stock turnover, futures contract maturity, and amounts of dividends paid by index stocks. Average deviations (π h ) are thus controlled for all these effects, as follows: where: CACturn h is CAC 40 turnover over 30-minute period h; Fmat h is futures maturity at period h, in number of days and taken in logarithm; and d h,T is dividend yield measured as discounted dividends paid by CAC 40 stocks from the day of period h to futures maturity date T as a percentage of the value of the index. ) are related in a trivariate VAR model over the post-ETF observation period: The Akaike criterion is used to set q*. vπ h , v cacspr h , and v et f turn h are error terms. For each pair of variables, the null hypothesis that variable X Granger-causes variable Y is tested by running a Wald test based on a chi-square statistic.
Testing the two-way Granger causality between ETF trading (ε et f turn ) and spot-futures price deviations (ε π ) consists in testing the null hypotheses that: (1) coefficients (δ 3 i ) q * i do not jointly differ from zero; and (2) coefficients (λ 1 i ) q * i do not jointly differ from zero. Rejecting (1) and (2) would be in support of H2a and H2b, respectively (i.e., the direct effect), provided that (λ 1 i ) q * i are found to be significantly positive and that (δ 3 i ) q * i are found to be significantly negative. Positive values of (λ 1 i ) q * i would indicate that an increase in price deviations invites ETF-based arbitrage trades and is followed by an increase in ETF volumes, while negative values of (δ 3 i ) q * i would indicate that ETF arbitrage trading contributes to reducing mispricing and is followed by a decrease in price deviations.
The indirect effect of ETF trading at the intraday horizon relies on the presence of two-way causality between liquidity and efficiency (H3a and H3b). Evidence for this causality would come from finding a Granger causality between ε cacspr and ε π with positive values for (ϕ 1 i ) i . The null hypothesis (3) that ε etfturn does not Ganger-cause ε cacspr combined with the null hypothesis (4) that ε cacspr does not Grangercause ε π then provides a test for the indirect effect of ETF trading. Rejecting (3) with significantly positive values of (ϕ 3 i ) q * i and rejecting (4) with significantly positive values of (δ 2 i ) q * i would support H3a and H4, respectively. 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 cannot reject the null hypothesis that price deviations do not Granger-cause the trading activity in the ETF. In other words, we fail to prove that an increase in spot-futures mispricing invites ETF trading (rejection of H2a). With respect to the opposite causal link, ETF turnover is found to Granger-cause index-futures price deviations at the 5%-threshold according to the Chi-square statistic. However, coefficients δ 3 i have signs opposite to what H2b predicts: instead of tightening the spot-futures price relation, ETF trading volumes are followed by increasing price deviations over the sample period. We thus rule out the direct effect of ETF trading.
As for indirect effects, we find evidence for a two-way causal relation between liquidity and price efficiency. A liquidity deterioration over a given 30-minute period significantly causes an efficiency deterioration in the next 30-minute period, with δ 2 1 being significantly positive at the 1% level. The reverse effect of efficiency on liquidity C 2012 Blackwell Publishing Ltd Table 4 Trivariate VAR analysis in post-ETF period This  is also significant but mixed in direction: an increase in futures price deviations produces tensions on CAC 40 stock spreads in the next 30-minute period -ϕ 1 1 being positive with 5% significance -but is followed by a reduction in stock CAC 40 spreads two 30minute periods later -ϕ 1 2 being negative with 5% significance. This partially supports H3b. Regarding the short-term impact of ETF trading on index stock liquidity, null hypothesis (4) is rejected based on a Wald test significant at the 1% threshold and ETF turnover is found to Granger-cause CAC 40 stock spreads, yet not in the way expected from H4. The coefficients of the lagged ETF turnover variables appear to be positive with strong statistical significance at the third lag (ϕ 3 3 ) and a 10%-level significance at the first lag (ϕ 3 1 ). This leads us to also reject the hypothesis that ETF trading has an indirect effect on efficiency by enhancing index stock liquidity at the intraday horizon. 13

Interpreting Tightening of the Index Spot-Futures Price Relation after ETF Introduction
In the absence of direct and indirect effects of ETF trading on index-futures price efficiency at the intraday horizon, an explanation is required for the price efficiency improvement observed just after the ETF market becomes active. It appears from the statistics set forth in Table 4 that there exists a causal relation between CAC 40 stock spreads and Lyxor CAC 40 turnover, according to which a deterioration of spreads in a given 30-minute period results in an increase in ETF trading volumes in the next 30-minute period. This suggests that the ETF market may act as an alternative market when CAC 40 stocks are less liquid. In addition, the lack of a direct effect from ETF trading on futures price efficiency indicates that the majority of traders who divert their orders to the ETF market are probably not arbitrageurs, 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, but that most arbitrageurs remain in individual stocks because of technical constraints, 14 times of higher volumes in the ETF market should correspond to greater proportions of arbitrageurs-relative 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 tighter causality between spreads and spot-futures price deviations.
To check this hypothesis, we divide the post-ETF observation period into two subsamples of days: those days on which total ETF trading volume was higher than the median value of ETF daily trading volume over the period, and those days on which ETF trading volume was below the median level. We estimate VAR model (8) on each subsample. Results are delineated in Table 5.
Comparing Panel A and Panel B of Table 5 shows that the causal links between liquidity, price efficiency, and ETF trading change dramatically between days of low 13 As a robustness check, we conducted the same VAR analysis with 15-minute periods. Results, available upon request, remain qualitatively unchanged. 14 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 about execution speed, which is undoubtedly higher in the stock market than in the ETF market (cf. last panel of Table 1).  (Table 4), while Panel A estimates differ in several ways. All the causal links involving ETF turnover that are 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 ETF turnover is low. Price deviations do not Granger-cause spreads any longer. Only the opposite-way causality of spreads on mispricing remains significant; yet, the causal impact of spreads on price deviations takes longer to realise: with low ETF trading, this causality is related to the third lag of spreads, while with high ETF trading it is related to the first lag. We consider that these 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 index traders, most probably those with longterm trading horizons 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 liquidity tensions in the stock and futures markets that would be unfavorable to arbitrage otherwise. The end result is that mispricing is reduced on average.

Conclusion
Using high-frequency index, futures, and ETF data over two 5-month periods surrounding the introduction of the first ETF tracking the CAC 40 index, we find a significant improvement in the no-arbitrage pricing relation in the post-ETF period. This finding is consistent with those of Switzer et al. (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 cash positions in cash-futures arbitrage trades through use of ETF shares.
In a multivariate analysis that controls for financial factors known to impact the spot-futures price relation, index-futures mispricing is found to decrease following ETF introduction, but ETF trading does not explain this improvement. Further, our VAR analysis shows that index-futures mispricing does not invite ETF trading and that ETF trading does not contribute to reducing index-futures mispricing. Although these two findings do not rule out the use of ETF securities in arbitrage strategies, they fail to support the hypothesis that the efficiency improvement mainly stems from the direct effect of ETF trading. In addition, 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.
Complementary empirical work suggests that the post-ETF efficiency improvement may rather arise 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 and liquidity traders, and this may leave other index markets with a greater proportion of arbitrageurs.