Investor Sentiment and Price Discovery: Evidence from the Pricing Dynamics. between the Futures and Spot Markets

Transcription

1 Investor Sentiment and Price Discovery: Evidence from the Pricing Dynamics between the Futures and Spot Markets Robin K. Chou * National Chengchi University Chu Bin Lin National Chengchi University George H.K. Wang George Mason University August, 2014 JEL Classification: G02; G12; G14. Keywords: Behavioral finance; Information shares; Investor sentiment; Lead-lag relation; Pricing dynamics. * Robin K. Chou, Professor of Finance and Risk and Insurance Research Center, College of Commerce, National Chengchi University, Taipei, Taiwan, rchou@nccu.edu.tw; George H. K. Wang, Research Professor of Finance, School of Management, George Mason University, Fairfax, VA 22030, gwang2@gmu.edu; Corresponding author: Chu Bin Lin, PhD Candidate, Department of Finance, National Chengchi University, Taipei, Taiwan, Tel: ; @nccu.edu.tw. 1

2 Investor Sentiment and Price Discovery: Evidence from the Pricing Dynamics between the Futures and Spot Markets Abstract This study shows that investor sentiment has a positive impact on price volatility and bid-ask spread in both the spot and futures markets, which induces higher arbitrage risk and trading costs. We examine the pricing dynamics between the spot and futures markets during high and low sentiment periods and find that during high sentiment periods, informed traders are less willing to leverage their information advantages on the futures market to avoid exposing themselves to high noise trader risk, which in turn diminishes the futures markets informational leading role and contributions to price discovery. The findings provide support for the theory of limits to arbitrage. 2

3 1. Introduction The Efficient Market Hypothesis (EMH) proposes that market prices adequately reflect fundamentals and are set by a group of agents who update their information properly with rational preferences. Behavioral finance theories, on the other hand, argue that asset prices do not always reflect fundamentals and that the deviations are brought about by the presence of traders who are not fully rational (Barberis and Thaler, 2003; Ritter, 2003). Ritter (2003) points out that behavioral finance has two building blocks: cognitive psychology and limits to arbitrage. Investor s cognitive bias such as mistaken beliefs and distorted preferences result in transitory mispricing on financial markets, and the limits to arbitrage prolong the mispricing as rational arbitrageurs may fail to correct them due to short-sale constraints and arbitrage risk (De long, Shleifer, Summers, and Waldmann, 1990; Shleifer and Vishny, 1997; Barberis, Shleifer, and Vishny, 1998). Investor sentiment has been found to affect investors trading behavior (Kurov, 2008) and has significant impacts on stock returns and price volatility (Lee, Jiang, and Indro, 2002; Baker and Wurgler, 2006; Schmeling, 2009; Kurov, 2010; Berger and Turtle, 2011; Baker, Wurgler and Yuan, 2012). Yu and Yuan (2011) and Stambaugh, Yu, and Yuan (2012) find that investor sentiment plays an important role in affecting the extent of mispricing and market efficiency on the stock market. Yu and Yuan (2011) show that the market expected return and its volatility are positively related during low sentiment periods, but the relation is almost flat during high sentiment periods. Stambaugh et al. (2012) examine the profitability of long-short strategies on 11 market anomalies and find that each anomaly is stronger following high levels of sentiment. They argue that high investor sentiment attracts more noise traders into the market, which enhances anomalies and as a result undermines market efficiency. In this paper, we investigate how investor sentiment would impact the pricing dynamics between closely related markets, a topic that has rarely been studied in the literature. By examining the spot and futures markets simultaneously, we will shed light on how the informed 3

4 respond during different market sentiment periods and provide evidence on the relation among investor sentiment, informed and noise trading, price volatility, and price efficiency. This study offers a detailed picture on the effect of investor sentiment on the dynamic pricing relation between the spot and futures markets. Arbitrage activities, usually being carried out in closely related markets, play a crucial role in securities markets because they bring prices close to fundamental values and keep markets efficient (Shleifer and Vishny, 1997). The noise-trader model of De long et al. (1990) shows how traders acting on noises could affect prices in a systematic way. They point out that if noise traders act in concert during unusual market conditions, their trading may cause prices to deviate consistently from fundamental values. Also, the unpredictability of noise traders future beliefs creates a risk in asset prices that deters rational arbitrageurs from aggressively taking positions against them. Consequently, prices can diverge significantly from fundamental values and the cross-market price transmissions can be significantly affected, even in the absence of fundamental risk. Similarly, Barberis et al. (1998) present a model of investor sentiment, which shows that movements in investor sentiment could result in persistent mispricing due to the noise trader risk. They argue that arbitrage is limited because movements in investor sentiment are in part unpredictable, and therefore arbitrageurs betting against mispricing run the risk that investor sentiment becomes more extreme and prices move even further away from fundamental values. Furthermore, short-sale constraints are likely to make pricing errors more prevalent when investor sentiment is high. Stambaugh et al. (2012) document that noise traders usually push prices up from their fundamental values when sentiment is high, and short-sale constraints deter the informed from taking short positions to eliminate the overpricing. As a consequence, the risk of deepening mispricing and short-sale constraints cause arbitrage failing to eliminate the mispricing completely and investor sentiment affects security prices in equilibrium (Shleifer and Vishny, 1997). 4

5 This study contributes to the literature in the following ways. We first provide evidence on the relation between investor sentiment and volatility by high frequency data. Brown (1999) shows that noise trading is positively related to investor sentiment, and noise traders cause volatility to increase, which induces higher market trading risk. Although Yu and Yuan (2011) and Stambaugh et al. (2012) argue that high investor sentiment attracts more noise trading to the market, they do not provide evidence showing that high sentiment empirically increases noise trading and volatility. According to Barberis et al. (1998) and Brown (1999), investor sentiment would have a positive impact on asset volatility. Furthermore, we empirically examine how informed traders respond to noise trading by investigating the impact of investor sentiment on the pricing dynamics between the spot and futures markets. Informed traders prefer to trade on the futures markets, which, compared to the spot markets, offer higher leverages, lower costs and fewer short-sale restrictions (Black, 1975; Kawaller, Koch, and Koch, 1987; Stoll and Whaley, 1990; Käppi, 1997; Chan, 1992; Back, 1993; Mayhew, Sarin, and Shastri, 1995; Easley, O Hara, and Srinivas, 1998). However, the effect of short-sale constraints may be enhanced by high investor sentiment, because it reinforces mispricing and makes it more difficult for the informed to correct the overpricing on the futures market during high sentiment periods. We show that high investor sentiment increases the risk of arbitrage and trading costs and makes the informed less willing to trade on the futures market for arbitrage purposes, which, in turn, decreases the leading role and the information shares of the futures prices. We examine the high frequency trade and quote data of the Standard & Poor s Depositary Receipts (S&P 500 ETFs), the Nasdaq 100 Index Tracking Stocks (Nasdaq 100 ETFs), the unit investment trust of the Dow Jones Industrial Average (DJIA ETFs), and their corresponding futures contracts and obtain the following findings. First, we show that investor sentiment has a positive impact on both price volatility and bid-ask spread. The minute-by-minute realized volatility of the ETFs and futures contracts is significantly positively related to investor 5

6 sentiment, which is consistent with Barberis et al. (1998), Brown (1999), Karlsson, Leowenstein, and Seppi (2005), and Yuan (2008) that sentiment-driven investors participate and trade more actively during high sentiment periods and make the market noisier. The bid-ask spreads of the ETFs and futures contracts are also found to be significantly positively related to investor sentiment. Both the noise trader risk and trading costs increase during high sentiment periods, which is likely to deter the informed from leveraging their information advantage on the futures market. Second, we find that the leading role of futures becomes significantly weaker when investor sentiment is high, consistent with our argument that the informed tends to trade less aggressively on the futures markets when the market is characterized by high sentiment with more noises. This finding is in line with De long et al. (1990) and Barberis et al. (1998) who argue that arbitrage is limited during high sentiment periods because informed traders bear higher arbitrage risk and trading costs during these periods. Third, it has been shown in the literature that the futures prices contribute more to price discovery than the spot prices do, which indicates that the futures prices are more informative (Chan, 1992; Frino, Walter, and West, 2000). However, we find that the futures market information shares are negatively related to investor sentiment, again implying that the informed trade less aggressively on the futures market during high sentiment periods because of the higher risk of arbitrage and trading costs (De long et al., 1990; Shleifer and Vishny, 1997; Barberis et al., 1998). Finally, we provide further evidence on the assertion that noise trading is more active during high sentiment periods. We examine the commitment of traders (COT) data from the Commodity Futures Trading Commission (CFTC) and show that small traders tend to hold more open interests when investor sentiment is high, especially the long positions, which shows that noise traders become more optimistic and buy more contracts on the futures market during high sentiment periods. 6

7 This paper is organized as follows. Section 2 reviews related literature on investor sentiment, limits to arbitrage and the lead-lag relation between the futures and spot markets, and proposes hypotheses. Section 3 describes data and methodologies. Section 4 presents our empirical results. Section 5 provides further supporting evidence for our empirical results, and Section 6 concludes. 2. Literature Review and Hypothesis The traditional finance paradigm seeks to describe financial markets by models in which agents are fully rational. Though this traditional framework is appealingly simple, after years of research, there is a growing stream of literature showing that the basic facts about the aggregate stock market, the cross-section of average returns and individual trading behavior are not easily understood in such a framework (Barberis and Thaler, 2003; Ritter, 2003). Behavioral finance, on the other hand, argues that some financial phenomenon can be better understood by models in which agents are less than fully rational. Economists increasingly turned to the extensive experimental evidence compiled by cognitive psychologists on the systematic biases that arise when people form beliefs, and on people s less than rational preferences (Tversky and Kahneman, 1974; Alpert and Raiffa, 1982; Buehler, Griffin, and Ross, 1994; Rabin, 2002). Ritter (2003) suggests that behavioral finance has two building blocks: cognitive psychology and limits to arbitrage. Researchers find abundant empirical evidence showing that market participants tend to be less than fully rational when making decisions under uncertainty. 1 Extensive evidence contrary to the tenets that underlie individual rationality in 1 Tversky and Kahneman (1974) argue that people often start with some arbitrary reference point and then adjust away from it when forming estimates. They also find that when judging the probability of an event, people will put more weight on more recent events and distort the estimates. Odean (1998) documents the disposition effect, where investors usually realize their profitable positions too soon and hold on to their losing positions too long. Shefrin and Statman (1994) and Odean (1998) find that some investors investment decisions are suboptimal due to overconfidence. De Bondt (1993) also observes that investors are over-optimistic in bull market, but are overpessimistic in bear market. Jegadeesh and Titman (1993) attribute momentum effect to a cognitive bias that investors underreact to the release of firm-specific information. Barber and Odean (2000) find that trading losses are attributable to investors overconfidence, and overconfidence also induces excessive trading. 7

8 traditional finance models has caused debates on the traditional finance paradigm and market efficiency. Investor sentiment has been found to affect investor trading behavior (Kurov, 2008) and to impact stock returns, return volatility, and market efficiency (Lee et al., 2002; Baker and Wurgler, 2006; Schmeling, 2009; Kurov, 2010; Baker et al., 2012; Berger and Turtle, 2011). Yu and Yuan (2011) show that there is a strong positive tradeoff between expected returns and volatility of stocks when investor sentiment is low, but the return-volatility tradeoff is weak when investor sentiment is high. They point out that other empirical studies find evidence that sentiment-driven investors participate and trade more aggressively in high-sentiment periods (Karlsson et al., 2005; Yuan, 2008). Because sentiment traders tend to be inexperienced and naïve investors, they are likely to have a poor understanding of how to measure risk and hence are likely to misestimate the variance of returns, which weakens the mean-variance tradeoff. Their findings are consistent with the theory of Barberis et al. (1998), which shows that there is a greater participation of sentiment-driven traders on the market when sentiment is high, and this phenomenon thereby perturbs prices away from levels that would otherwise reflect a positive mean-variance tradeoff. Overall, the increased presence and trading of sentimentdriven traders during high sentiment periods introduce more noise to the market and undermine market efficiency (Black, 1986). On the contrary, the market tends to be more efficient when investor sentiment is low. Stambaugh et al. (2012) examine the profitability of long-short strategies on 11 market anomalies (e.g., failure probability, net stock issues, total accruals, momentum, asset growth, return on assets and etc.) and find that each anomaly is stronger (i.e., the long-short strategy is more profitable) following high levels of sentiment, while it is weaker following low levels of sentiment. Yu and Yuan (2011) and Stambaugh et al. (2012) both find that the market is less efficient during high sentiment periods, due to higher participation of noise traders. 8

9 Arbitrage plays an important role in improving market efficiency (Shleifer and Vishny, 1997). Some naïve investors may cause prices to deviate from their fundamental values, but informed traders and arbitrageurs can choose to take positions against these noise trading and bring prices back to their fundamental values. Theoretically, arbitrage is defined as the simultaneous purchase and sale of the same, or essentially similar, security in two different markets for advantageously different prices (Sharpe and Alexander, 1990) and it requires no capital and entails no risk. Shleifer and Vishny (1997), however, argue that arbitrage is often risky in practice and that professional arbitrageurs may avoid extremely volatile arbitrage positions. That is, professional arbitrageurs may quit the market when market is highly volatile, and this phenomenon will make asset prices deviating from fundamental values for an appreciable length of time. De long et al. (1990) point out that the unpredictability of noise traders future beliefs creates a risk in the price of the asset that deters rational arbitrageurs from aggressively taking positions against them. Consequently, prices can diverge significantly from fundamental values even in the absence of fundamental risk. Barberis et al. (1998) argue that arbitrage is limited because movements in investor sentiment are in part unpredictable, and therefore arbitrageurs betting against mispricing run the risk that investor sentiment becomes more extreme and prices move even further away from the fundamental values. Furthermore, short-sale constraints are likely to make pricing errors more prevalent when investor sentiment is high. Stambaugh et al. (2012) document that impediments to short selling are the major obstacle to eliminating sentiment-driven mispricing. They find that noise traders usually push prices up from their fundamental values when sentiment is high, and shortsale constraints deter the informed from taking short positions to eliminate the overpricing. On the other hand, it is easier for the informed to take long positions against underpricing during low sentiment periods. Consequently, due to short-sale constraints, the overpricing during high sentiment periods is more prevalent than underpricing during low sentiment periods. 9

10 Due to the advantages of the futures markets, extensive studies have found that the futures prices tend to lead the spot prices (Finnerty and Park, 1987; Ng, 1987; Kawaller et al., 1987; Harris, 1989; Stoll and Whaley, 1990). Informed traders prefer to trade on the futures markets because the futures market offers several advantages for informed trading. First, greater financial leverage and lower transaction costs make the futures market more attractive than the spot market to informed traders (Black, 1975; Kawaller et al., 1987; Stoll and Whaley, 1990; Käppi, 1997; Chan, 1992; Back, 1993; Mayhew et al., 1995). With greater financial leverage and lower transaction costs, informed traders are able to maximize their profits. Second, informed traders prefer the futures market because of less short-sale constraints on the futures market (Easley et al., 1998). The derivative market allows informed traders to possess short positions more easily than they otherwise can on the stock market. Third, investors who have information about volatility of the underlying stock prices can most easily utilize the information on the derivative market (Back, 1993; Cherian, 1993). Empirical evidence shows that the futures markets significant lead the spot markets, while the spot markets have limited predictability on the futures returns. Kawaller et al. (1987) find that the S&P 500 futures lead the spot index between 20 to 45 minutes, while there is little evidence that the spot index leads the futures. Stoll and Whaley (1990) also find that the S&P 500 and the Major Market Index (MMI) futures lead the stock indexes by about 5 minutes, while the feedback time from the spot market to the futures market is much shorter. 2 Since high sentiment increases noise trader risk and hence price volatility on the futures market, based on the theory of limits to arbitrage, we argue that sentiment is likely to affect the pricing dynamics between the spot and futures markets, because the informed may be less 2 Some argue that the lead-lag relation is induced by the infrequent trading problem of component stocks, suggesting that many components stocks on the S&P 500 index are not traded frequently enough to allow prices to update information quickly. Chan (1992) further analyze the lead-lag relation between the cash market and stock index futures market and repels the critics above. His evidence indicates that when more stocks move together (market-wide information), the futures leads the cash index to a greater degree, suggesting that the leading position of the futures market is due to the information advantage in market-wide information. Frino et al. (2000) also find that the lead of the futures markets are greater around macroeconomic information releases, as the leverage benefits of derivatives and the lower costs futures environment attract informed traders. 10

11 willing to trade on the futures market during high sentiment periods, which decreases the amount of information on the futures market. Short-sale constraints further deter the informed from taking short positions to correct the overpricing on the futures market during high sentiment periods. Together, high sentiment is likely to weaken the leading role of the futures market. We thus have the following hypothesis: Hypothesis 1: The leading role of the futures market will be weakened during high investor sentiment periods. Next, since the informed are less willing or unable to leverage their information advantages on the futures market to avoid exposing themselves to high noise trading risk, the futures prices would become relatively less informative and contribute less to the price discovery process during high sentiment periods. Thus, we have our second hypothesis as follows: Hypothesis 2: The prices on the futures market will become less informative during high investor sentiment periods. 3. Data and Methodology The data used in this study consist of intraday trade and quote prices of three Exchangetraded Funds (ETFs) and their corresponding E-mini index futures, which include the S&P 500 ETFs and S&P 500 E-mini futures, the Nasdaq 100 ETFs and Nasdaq 100 E-mini futures, and the DJIA ETFs and DJIA E-mini futures. These three ETFs and futures price pairs are examined because they are among the most active index tracking ETFs and futures contracts on the market. By studying these markets, we reduce possible biases caused by the infrequent trading problem. Our sample period is from January 1, 2002 to December 31, The 3 For the DJIA ETFs and DJIA E-mini futures price pairs, the sample period is from May 1, 2002 to December 31, 2010 because the trading of the DJIA E-mini futures starts on May 1,

12 tick-by-tick quote data of the ETFs are obtained from the Trade and Quote (TAQ) database. We take the midpoint of the quoted bid and ask prices as the proxy for the fundamental values of the ETFs, and following Hasbrouck (2003), only regular quotes on the primarily listed market of the ETFs are used. 4 Regular trading hour is between 9:30 am and 4:00 pm EST. 5 Since the quote data for index futures are unavailable, we use trading prices of the futures contracts. The trading prices of the corresponding index futures contracts, including the E- mini versions of the S&P 500, Nasdaq 100, and DJIA index futures, are obtained from the Chicago Mercantile Exchange (CME). These E-mini futures contracts are quite active, as Hasbrouck (2003) shows, they dominate the price discovery process on the S&P 500 and Nasdaq 100 index markets. The nearby futures contracts are used in our analysis because they are the most actively traded contracts. To construct a continuous time series for the futures prices, we replace the prices of the nearby contract by those of the first deferred contract, once the daily trading volume of the first deferred contract exceeds that of the nearby contract. The prices of the ETFs and futures contracts are not uniformly spaced in time. To assess the degree of comovement among the prices between different markets, we follow the method in Chan (1992) to synchronize price pairs. A minute-by-minute data set is constructed for each price series. The daily trading hours are from 9:30 am to 4:00 pm, which contain 390 minuteby-minute intervals on each trading day. In each one-minute interval, the last price observation is identified. If no price is observed within that one-minute span, the price of the previous minute is used instead. 6 Returns are calculated as differences in log prices. 7 There 4 For the S&P 500 ETFs and DJIA ETFs, we use the American Stock Exchange (AMEX) quotes before September 30, 2008 and the New York Stock Exchange (NYSE) quotes after October 1, 2008 since the AMEX is officially merged by the NYSE after October 1, Similarly, for the Nasdaq 100 ETFs, the quotes from the AMEX before November 30, 2004 and the quotes from National Association of Securities Dealers Automated Quotations (NASDAQ) after December 1, 2004 are used because the Nasdaq 100 ETFs transferred its listing from the AMEX to NASDAQ on December 1, To avoid contaminating effects due to the financial crisis surrounding the end of 2008, we repeat our tests with data before September 30, The empirical results are qualitatively similar. These results are not reported to save space, but are available upon request. 6 Since our sample ETFs and E-mini futures are actively traded, this occurs in less than 1% of the sample. 7 To avoid data errors, the minute-by-minute returns are winsorized at the 0.5 and 99.5 percentiles. Empirical results are qualitatively similar with or without winsorization. 12

13 are 879,916, 880,802, and 847,103 one-minute price pairs for the S&P 500, Nasdaq 100, and DJIA ETFs and futures, respectively in our nine-year sample period. 8 In addition, trading volume for the ETFs and futures are obtained from the TAQ database and the CME, respectively. 9 We measure investor sentiment using the monthly market-based sentiment index constructed by Baker and Wurgler (2006). Baker and Wurgler (2006) (BW) form their sentiment index by taking the first principal component of six sentiment-related measures. The six measures are the closed-end fund discount, the number and the first-day returns of IPOs, NYSE turnover, the equity share in total new issues, and the dividend premium. The principal component analysis filters out idiosyncratic noise in the six measures and captures their common component. 10 We define high (low) sentiment periods as those months in which the BW investor sentiment index is above (below) its median during our sample period from January, 2002 to December, To test the impact of sentiment on volatility, we first calculate the daily realized volatility for each ETFs and futures contract as follows: Realized Volatility (RV t ) = m i=1 (r i ) , (1) where m is the number of one-minute intervals during the regular trading hours on day t, and r i is the i th one-minute return on the trading day. We follow the literature to control for other important factors that are likely to influence price volatility (Wang and Yau, 2000). The model is as follows: 3 RV t = α 0 + β 0 D high sent t + i=1 γ i RV t i + j=1 θ j TV t j + k=1 δ k BAS t k, (2) Due to occasional market suspensions and trading halts, some sample days are removed when there are less than 120 one-minute quotes or trade prices on a trading day, 9 The trading volume data for futures are available since July 1, We download the data from Wurgler s website: 13

14 where RV t is the realized volatility on day t, and D t high sent is a dummy variable of high sentiment on day t, which is equal to 1 if the sentiment index is above its 75 th percentile during our sample period and zero otherwise. RV t i is the realized volatility on day t - i, TV t j is the daily trading volume on day t j, and BAS t k is the percentage quoted bid-ask spread for the ETFs, and percentage estimated bid-ask spread for the futures on day t - k. Since the quote data are not available for the futures, the price reversal method, suggested in Wang, Michalski, Jordan, and Moriarty (1994), is used to calculate the daily estimated spread for futures. 11 Percentage bid-ask spread is defined as the spread divided by price. We expect price volatility to be positively related to investor sentiment. A significantly positive β 0 would support the assertion that high sentiment introduces more noise traders to the market, which makes the market more volatile. Next, we use the vector error correction model (VECM) to investigate the lead-lag relation between the spot and futures markets. Index tracking ETFs and their corresponding futures are based on the same underlying assets, so it is expected that they share the same implicit efficient price component. Therefore, prices on these two markets form a cointegration system. 12 If two prices are cointegrated, based on the Granger representation theorem (Engle and Granger, 1987), price changes can be represented by a VECM as follows: k P t = μ + i=1 A i P t i + γz t 1 + ε t, (3) where is the difference operator, P t is a (2 1) vector of log prices on the two markets, μ is a (2 1) vector of constants, A i are (2 2) matrices of autoregressive coefficients, k is 11 The estimated bid-ask spread for the E-mini futures is calculated as follows: (a) an empirical joint price distribution of P t and P t 1 during a daily interval was created, (b) the subset of price changes that exhibited price continuity (i.e., a positive change followed by another positive change) was discarded, (c) absolute values of the price changes that were price reversals were taken, and (d) the mean of absolute values obtained in the third step is the estimated spreads. 12 We apply the Johansen likelihood ratio test and a maximum eigenvalue test and confirm that each matched daily price pairs of spot and future prices form a cointegrated system. The estimation results are omitted to save space and are available upon request. 14

15 the number of lags, γ is a (2 1) vector of coefficients on the error correction terms, z t 1 = α P t 1 is a (1 1) scalar of error correction terms, α is a (1 2) cointegrating vector, and ε t is a (2 1) vector of price innovations. The coefficient, γ, on the error correction term, also named speed of adjustment, measures the price reactions to the deviations from the long-term equilibrium relation. In our VECM, P t = ( F t S t ), where F t and S t denote the prices for the index futures and their corresponding ETFs, respectively. The coefficient matrix A i in Equation (3) is used to test Hypothesis 1 and is expected to change with investor sentiment over time. More specifically, if the informed are reluctant to trade during high sentiment periods due to increased noise trader risk, then the coefficients of the ETFs returns on the lagged futures returns will become smaller when sentiment is high. Such a finding will support our Hypothesis 1 that the leading role of futures will be weakened during high investor sentiment periods. Furthermore, we adopt two measures, the information shares (Hasbrouck, 1995) and factor weights (Gonzalo and Granger, 1995), to investigate the effect of investor sentiment on the price discovery process between the spot and futures markets. Hasbrouck (1995) suggests that the contribution to price discovery by each market (sharing a stochastic common trend) is defined as the variation in efficient price innovations attributable to that market s innovation. According to Hasbrouck (1995), the efficient price v t follows a random walk: v t = v t 1 + u t. The observed prices of several cointegrated markets contain the same random walk component and components incorporating the effects of market frictions. Hasbrouck (1995) shows that the following vector moving average model (VMA) can be derived from the VECM: P t = Ψ(L)ε t, (4) 15

16 where Ψ(L) is a polynomial in the lag operator. The VMA coefficients can be used to calculate the variance of the underlying efficient price: σ u 2 = ΨΩΨ, (5) where Ψ is a row vector composed of VMA coefficients and Ω = var(ε t ). Using the Cholesky factorization to transform Ω into a lower triangular matrix F, and Ω = FF, the information share of market j is calculated as: IS j = (ΨF) j 2 σ u 2, (6) where (ΨF) j is the j th element of the row matrix ΨF. The larger information share of the j th market, the more predominant force it has in setting the common efficient price. By permuting the order of the market prices, Equation (6) will provide an upper and a lower bound for the information shares of each market. We compute the information shares for our three ETFsfutures pairs each day and use the midpoint of the upper bound and lower bound as the measure for information shares. In general, the market with larger information shares is considered to contribute more to the discovery of the long-run equilibrium price. If the information shares of futures, IS f, is negatively related to investor sentiment, then Hypotheses 2 is supported, which indicates that the futures market would experience relatively lower information shares and thus contribute less to the price discovery process during high investor sentiment periods. Since the information shares has been found to be related to the liquidity and volatility in the literature (Eun and Sabherwal, 2003; Ates and Wang, 2005), the regression model for IS f is specified as follows: 16

17 IS f,t = β 0 + β 1 D t high sent + β 2 liquidity t + β 3 volatility t + ε t, (7) where IS f,t is the information shares of the futures contracts on day t, D t high sent is a dummy variable of high sentiment on day t, which is equal to 1 if the sentiment index is above its 75 th percentile during our sample period and zero otherwise, liquidity t is the liquidity measure on day t, and volatility t is the realized volatility on day t. We use three proxies for liquidity: market share (MS), spread ratio (SPRA), and trading volume (TV). MS is the market share of futures, which is defined as the ratio of dollar volume of futures to the sum of dollar volume of futures and the corresponding ETFs. It is calculated as: MS t = Dollar volume of futures on day t Dollar volume of futures and ETFs on day t. (8) SPRA is the ratio of the bid-ask spread of the ETFs to the bid-ask spread of the futures, and TV is the daily trading volume of the futures contracts. Liquidity is found in the literature to be positively related to the contribution of price discovery (Eun and Sabherwal, 2003; Ates and Wang, 2005). More importantly, we expect β 1 in Equation (7) to be significantly negative, which would support Hypothesis 2 that the prices on the futures market will become less informative during high investor sentiment periods. In a cointegrated system such as that in Equation (3), Gonzalo and Granger (1995) (GG) also propose a methodology to decompose the vector of market prices into permanent and transitory components as follows: P t = f t i 2 + z t, (9) where P t is a (2 1) vector of log prices on the futures and spot markets on day t, f t is a scalar of common long-memory component, z t is a (2 1) transitory component, and i 2 is a 17

18 (2 1) unit vector. Under the Johansen s maximum likelihood framework, it is suggested that the common long-memory factor can be estimated as f t = γ P t, where γ is a (1 2) vector which is orthogonal to the vector of speed of adjustment coefficients on the error correction term in Equation (3). The common factor has been interpreted as the implicit efficient price, which is common to the related market prices. The normalized GG factor weights, γ, are used as a measure of the contribution to price discovery by each related market. The GG factor weights are summed to one and a larger factor weight of the j th market price suggests that the j th market price has a larger contribution to the price discovery process. We expect that investor sentiment has a negative impact on the GG factor weights of the futures market, relative to those of the spot market. Finally, to show whether noise traders actually trade more on the futures market during high sentiment periods, we use the Commitments of Traders (COT) Report of the E-mini S&P 500, Nasdaq 100, and DJIA index futures published by the CFTC. The CFTC requires traders to report their daily open positions when their trading positions are larger than the specified reporting thresholds. This report provides information on the open interests of a particular futures contract held by reportable traders and non-reportable traders. Reportable traders are classified as either commercials or non-commercials based on information provided by the traders in the reports. In the finance research literature, commercials are typically considered to be hedgers, and non-commercials are considered to be large speculators. Non-reportable positions are calculated by subtracting the reportable open interests from total open interests. They are typically small and are considered to be noise traders in the literature. Röthig and Chiarella (2011) suggest that small traders tend to follow large speculators and that they are less informed than large hedgers and speculators. We expect that non-reportable traders, who are likely to be noise traders, hold more open interests during high sentiment periods. 18

19 4. Empirical Results 4.1 Investor sentiment and the lead-lag relation between the spot and futures markets This section presents empirical results on the relation between investor sentiment and price volatility and the lead-lag relation between the spot and futures markets. We first report summary statistics for the investor sentiment index and the minute-by-minute ETFs and futures returns in Table There is a total of 108 monthly observations for the sentiment index in our nine-year sample period from January, 2002 to December, The sentiment index is a standardized statistics with zero mean and unit variance. The mean and median of the sentiment index are both close to zero, which indicates that investor sentiment during our sample period is not leaning towards either high or low levels. The mean and median returns for the ETFs and futures are all close to zero. (Insert Table 1 Here) Table 2 presents the regression results of the relation between investor sentiment and volatility. We use the minute-by-minute realized volatility as a proxy for price volatility and then regress it on the high sentiment dummy and other control variables. 14 The high sentiment dummy equals one when the sentiment index is above its 75 th percentile during our sample period and zero otherwise. After controlling for lagged realized volatility, lagged trading volume, and lagged bid-ask spread, we find that the sentiment dummy has a significantly positive impact on volatility for all sample ETFs and futures returns. The results are robust with control variables of various lags. 13 In this study, we use the orthogonal investor sentiment index from Baker and Wurgler (2006). Baker and Wurgler (2006) regress each of the six raw proxies for sentiment on industrial production index, growth in consumer durables, nondurables, and services, and a dummy variable for NBER recession. They argue that the residuals from these regressions are cleaner proxies for investor sentiment. The orthogonal investor sentiment index is the first principal component of the correlation matrix of these six residuals. 14 We also use daily standard deviation and variance of returns as dependent variables, and the results are qualitatively similar. The estimation results are not presented here to save space and are available upon request. 19

20 (Insert Table 2 Here) For example, with lag 1 control variables, the coefficients of the S&P 500 ETFs and futures volatilities on the high sentiment dummy in Model (1) of Table 2 are 4.81 and 7.50, respectively, significant at the 1% level, which shows that investor sentiment significantly increases price volatility. The coefficients on the sentiment dummy remain significantly positive in Models (2) and (3), when lag 2 and 3 control variables are added. Similar results are found for the Nasdaq 100 and DJIA ETFs and futures volatilities. These results suggest that investor sentiment has a positive impact on price volatility and are consistent with Barberis et al. (1998), Brown (1999), Yu and Yuan (2011), and Stambaugh et al. (2012), who argue that high sentiment introduces more noise trading to the market and in turn makes the markets noisier and riskier. In Table 3, we show the results of regressing the bid-ask spread on the high sentiment dummies and other control variables. We find that the impact of investor sentiment on the percentage bid-ask spread is generally positive, although not statistically significant. However, we further find that investor sentiment has a much more significantly positive impact on the bid-ask spread. Specifically, the coefficients of the bid-ask spread for the S&P 500, Nasdaq 100, and DJIA ETFs and futures on the high sentiment dummy are all positive, and five of them are statistically significant at the 5% level. Take the bid-ask spread for the S&P 500 ETFs and futures as an example, the coefficients of the S&P 500 ETFs and futures spreads on high sentiment dummy are 30.1 and 7.1, respectively, significant at the 1% level, which suggests that sentiment has a positive impact on the bid-ask spread. The bid-ask spread is generally considered an important measure for trading costs. Since investor sentiment increases the bid-ask spread, the informed likely become less willing to trade during high sentiment periods due to increased trading costs. Overall, our results show that investor sentiment increases both arbitrage risk and trading costs on the futures market during 20

21 high sentiment periods, which is likely to make the informed less willing to leverage their information advantage on the futures market when investor sentiment is high. (Insert Table 3 Here) We next examine how the informed would respond to the riskier and nosier trading environment during high sentiment periods by testing the impact of investor sentiment on the lead-lag relation between the ETFs and futures. Tables 4, 5 and 6 report the lead-lag relations between the ETFs and the corresponding futures for the S&P 500, Nasdaq 100, and DJIA indexes, respectively. From the baseline VECM in Tables 4, 5, and 6, we find that both markets significantly lead each other, indicating there is a two-way Granger causality relation between the ETFs and futures returns. (Insert Table 4 Here) (Insert Table 5 Here) (Insert Table 6 Here) More importantly, the futures tend to lead the ETFs more significantly, because the coefficients of the ETFs returns on lagged futures returns are larger and more significant than those of the futures returns on the lagged ETFs returns. Take the S&P 500 index as an example, from the baseline regressions in Table 4, the coefficients of the S&P 500 ETFs returns on the first three minutes lagged futures returns are 0.579, 0.434, and 0.307, respectively, while those of the S&P 500 futures returns on the first three minutes lagged ETFs returns are smaller at 0.138, and 0.072, respectively. Tables 5 and 6 present respectively the VECM results for the Nasdaq 100 and DJIA indexes, and the results are qualitatively similar. These results indicate that while there is a two-way casual relation between the ETFs and futures, the futures 21

22 market assumes a more significant role in price discovery, which is consistent with prior literature. Next, to investigate the relation between investor sentiment and the pricing dynamics, we add several sentiment dummies with respect to different levels of investor sentiment in the regression model. First, we add a low sentiment dummy, which is equal to one when the sentiment index is below the 25 percentile of its distribution and zero otherwise. Again, take the S&P 500 index as an example, from Table 4, the coefficients of the ETFs returns on the interactions between the low sentiment dummy and the first three lagged futures returns are 0.091, 0.071, and 0.068, respectively, significant at the 1% level. This result indicates that the futures tend to lead the ETFs more significantly during low sentiment periods. On the other hand, when the sentiment dummy is set with respect to the sentiment index being greater than either the 50 th or the 75 th percentiles, from Table 4, the coefficients of the ETFs returns on the interactions between the high sentiment dummies and the first three lagged S&P 500 futures returns are , , and for the 50 th percentile sentiment dummy and are , , and for the 75 th percentile sentiment dummy, all significant at the 1% level. These results show that the informational leading role of the futures is significantly weakened during high sentiment periods. Tables 5 and 6 report the results for the Nasdaq 100 and DJIA indexes, respectively, and the results are similar to those of the S&P 500 index in Table 4. Consistent with Hypothesis 1, these findings suggest that high investor sentiment weakens the informational leading role of the futures, likely due to a riskier and nosier trading environment during these periods. The effect of investor sentiment on the pricing dynamics between the spot and futures markets is not only statistically significant but also economically significant. For instance, from Table 4, for the model of the 75 th percentile sentiment dummy, the coefficient of the S&P 500 ETFs returns on the first lagged futures returns is 0.593, while the coefficient on the interaction term between the first lagged futures returns and the sentiment dummy is

23 These numbers indicate that, when investor sentiment is high, the coefficient on the first lagged futures returns drops by 13%. Similar results are found in Tables 5 and 6 for the Nasdaq 100 and DJIA indexes, respectively. The coefficients on the interaction terms between the two- to five-lag returns and the high sentiment dummy show similar patterns in signs and magnitudes. 15 We show that investor sentiment has a significant impact on the lead-lag relation between the spot and futures markets. The leading role of the futures is significantly weakened when investor sentiment is high. These results imply that the informed are less willing to leverage their information advantage on the futures market during high sentiment periods, when the noise trader risk and trading costs are high. 4.2 Investor sentiment and the price discovery process Next we present the impact of investor sentiment on the information shares and GG factor weights. We use the intraday data to calculate the daily information shares for the ETFs and their corresponding futures. As pointed out in the research methodology section, the ordering of time series in the Hasbrouck (1995) model will affect the calculations of information shares, so we focus on the average of the upper and lower bounds, i.e., the midpoint, of information shares. The changes in the information shares during different sentiment regimes are reported in Table 7. From Table 7, the midpoints of the futures information shares are higher than those of the ETFs during both high and low sentiment periods. This pattern is consistent with our VECM results, showing that the futures prices are more informative than the ETFs prices. Table 7 further shows that as investor sentiment increases, the average information shares of the futures market decrease, while those of the ETFs increase. For example, the information share midpoint of the S&P 500 futures during high sentiment periods is lower than that during low sentiment periods. Similar results are obtained for the Nasdaq 100 and DJIA 15 The VECM in our tables are estimated in an AR(6) framework. To save space, we only show the coefficients on the first three lags in our tables. Interested reader can obtain these results from the authors. 23

24 indexes. From Table 7, we find that the futures market becomes relatively less informative, whereas the spot market becomes relatively more informative during high sentiment periods. 16 (Insert Table 7 Here) We next perform multivariate regressions to investigate the relation between investor sentiment and the futures information shares by controlling for the effects of other variables, including realized volatility and liquidity measures. From Table 8, it is shown that investor sentiment again has a significantly negative impact on the futures information shares. We regress the futures information shares of the S&P 500, Nasdaq 100, and DJIA indexes on the high sentiment dummies and control variables in different model specifications and find that the coefficients on high sentiment dummies are mostly significantly negative. For example, from Table 8, the coefficients of the S&P 500 futures information shares on high sentiment dummies in models (1), (2) and (3) are , , and , respectively, with respect to three different liquidity controls, and two of them are significant at the 1% level. (Insert Table 8 Here) Similar results for the Nasdaq 100 and DJIA futures are also obtained in Table 8. The futures prices contribute relatively less to price discovery when investor sentiment is high. The results reported in Tables 7 and 8 are in line with Shleifer and Vishny (1997), and Barberis et al. (1998) who argue that the informed will avoid exposing themselves to extreme risk when investor sentiment is high and thus are less willing to leverage their information advantages on the futures market, which in turn makes the futures prices relatively less informative during such periods. 16 In unreported results, we also find the correlations between investor sentiment and information shares of the S&P 500, Nasdaq 100, and DJIA futures are significantly negative. 24

25 In addition to the information shares, the GG factor weights are also frequently used to investigate the price discovery process in the literature. more the prices contribute to the price discovery process. The larger the GG factor weights, the Table 9 reports the regression results of the relation between investor sentiment and the GG factor weights. The coefficients of the GG factor weights on the high sentiment dummies are all negative in various model specifications, and most of them are statistically significant. For example, the coefficients of the GG factor weights on the high sentiment dummies for the DJIA index are , , and , significant at the 1% level, for the liquidity measures are MS, SPRA, and TV (Models (7), (8), and (9)), respectively. Results for the S&P 500 and Nasdaq 100 indexes are similar, which, again, implies that the futures prices contribute less to the price discovery process, when investor sentiment is high. (Insert Table 9 Here) 5. Further Evidence on the Futures Trading Activity So far we have shown that investor sentiment has a positive impact on price volatility and bid-ask spread on both the spot and future markets, and that both the leading role and the information content of the futures prices are diminished during high sentiment periods. This section provides further evidence on the trading activity of the futures market by trader types. We collect the COT data of the S&P 500, Nasdaq 100, and DJIA E-mini futures reported by the CFTC each week and analyze the trader composition. Panel A of Table 10 summaries the combined open interests held by commercial, non-commercial, and non-reportable traders in different sentiment periods, and Panels B and C break the total open interests into long and short positions, respectively. The last four columns in Table 10 show the absolute and percentage changes in open interests for different types of traders between high and low sentiment periods. 25