市場效率和投資人情緒：以期貨和現貨市場間的價格動態調整為例 - 政大學術集成

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(1)國立政治大學財務管理研究所博士論文. 政治大 Market Efficiency 立 and Investor Sentiment: Evidence from ‧. ‧ 國. 學. the Pricing Dynamics between Futures and Spot Markets. n. er. io. sit. y. Nat 研究生：林楚彬. 撰. al. iv n Ch engchi U 指導教授：周冠男博士. 中華民國一百零四年十二月.

(2) 謝辭. 一轉眼，在指南山下踏過了十一個寒暑。回首來時路，得之於人者太多，出之於己者太少，這本論文得以付梓，必須感謝許多人對我的幫助。首先，我必須感謝我的指導教授周冠男老師，您在學業和生活上對我的照顧，是我可以完成博士學業的強力後盾。我也要感謝口試委員王衍智老師、陳聖賢老師、陳嬿如老師以及張紹基老師，有您們的建議和指導，才讓我順利走過博士學位的最後一個里程碑。. 政治大. 接著，我要感謝在我求學期間，財管系助教郁方、雪玲、偉峰以及溫柔的協助，. 立. 你們的熱心和關懷，讓財管系就像一個充滿人情味的大家庭。感謝同窗美菁、周燕以. ‧ 國. 學. 及威宏的切磋砥礪，我們得以共同享受知識的洗禮。我也要感謝博士班學長偉劭、文謙和肇榮的勉勵，我會永遠記得我們一起在體育館揮汗的時光。我也想感謝財管系博. ‧. 士班成員玉美、淑惠、淑華、玟惠、依婷、苡文、富德、品揚、維中、建霖、曉琳、. Nat. sit. n. al. er. io. 照應。. y. 晉吉、濰儒和舜芬的陪伴，我覺得自己很幸運，可以在尋求知識的路上，與你們互相. i n U. v. 如果政大是我第二個家，我也必須特別感謝這個家中待我如父母的臧國仁老師和. Ch. engchi. 蔡琰老師，感謝您們以身作則，教我欣賞生活中的真善美，也教我勇敢追求自己的人生。最後，我希望將這本論文獻給我最親愛的家人，你們的默默支持，是鼓舞我走到這裡的最大動力。謝謝所有在來時路上曾經陪伴我的師長、朋友和家人，我將以此謝誌為記，從此展開人生另一段未知的旅程。. i.

(3) Abstract. This study shows that investor sentiment plays an important role in affecting the pricing dynamics between the spot and futures markets. The empirical evidence suggests that investor sentiment has a positive impact on price volatility and the bid–ask spread on both the spot and futures markets, which induces higher arbitrage risk and trading costs during high sentiment periods. As a consequence, during high sentiment periods, informed traders become less willing to leverage their information advantages on the futures market, which diminishes. 政治大 findings provide support for the 立theory of limits to arbitrage.. the futures markets’ leading informational role and contributions to price discovery. My. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. ii. i n U. v.

(4) Table of Contents. CHAPTER I. INTRODUCTION ............................................................................................... 1 CHAPTER II. LITERATURE REVIEW AND HYPOTHESIS ................................................ 6 CHAPTER III. DATA AND MEASUREMENT OF VARIABLES ......................................... 11 1. DATA .................................................................................................................................. 11 2. MEASUREMENT OF VARIABLES ........................................................................................... 12. 政治大. CHAPTER IV. EMPIRICAL METHODS ............................................................................... 14. 立. 1. STRUCTURAL MODELS FOR VOLATILITY AND BID–ASK SPREADS ......................................... 14. ‧ 國. 學. 2. LEAD–LAG RELATION BETWEEN THE FUTURES AND SPOT MARKETS ................................... 15 3. INFORMATION SHARES AND FACTOR WEIGHTS .................................................................... 16. ‧. CHAPTER V. EMPIRICAL RESULTS ................................................................................... 20. sit. y. Nat. io. er. 1. INVESTOR SENTIMENT, PRICE VOLATILITY, BID–ASK SPREADS, AND THE LEAD–LAG. al. RELATION ........................................................................................................................... 20. n. v i n C h DISCOVERY PROCESS 2. INVESTOR SENTIMENT AND THE PRICE e n g c h i U ............................................... 24 CHAPTER VI. INVESTOR SENTIMENT AND THE FUTURES TRADING ACTIVITY .. 27 CHAPTER VII. CONCLUSION ............................................................................................. 29 REFERENCES ......................................................................................................................... 31. iii.

(5) List of Tables. TABLE 1: SUMMARY STATISTICS ..................................................................................... 35 TABLE 2: REALIZED VOLATILITY AND INVESTOR SENTIMENT............................... 36 TABLE 3: BID-ASK SPREAD AND INVESTOR SENTIMENT .......................................... 38 TABLE 4: VECM ESTIMATION FOR THE ETFS AND E-MINI FUTURES OF THE S&P 500 INDEX ............................................................................................................... 39. 政治大. TABLE 5: VECM ESTIMATION FOR THE ETFS AND E-MINI FUTURES OF THE. 立. NASDAQ 100 INDEX .............................................................................................. 40. ‧ 國. 學. TABLE 6: VECM ESTIMATION FOR THE ETFS AND E-MINI FUTURES OF THE DJIA INDEX ...................................................................................................................... 41. ‧. TABLE 7: INFORMATION SHARES AND INVESTOR SENTIMENT............................... 42. sit. y. Nat. io. al. er. TABLE 8: REGRESSION ANALYSIS OF INFORMATION SHARES ON INVESTOR. n. SENTIMENT ............................................................................................................ 43. Ch. engchi. i n U. v. TABLE 9: REGRESSION ANALYSIS OF GG FACTOR WEIGHTS ON INVESTOR SENTIMENT ............................................................................................................ 44 TABLE 10: TRADER COMPOSITIONS OF THE E-MINI INDEX FUTURES ................... 45. iv.

(6) Chapter I Introduction Price discovery is arguably one of the most important products of a financial market (Hasbrouck, 1995). When homogeneous or closely linked securities trade in multiple markets, it is often of interest to determine which market reacts to new information first and where price discovery occurs. In a perfectly frictionless world, price movements of stock index futures and the underlying spot market are contemporaneously correlated and are not cross-autocorrelated. However, if one market reacts to new information faster than the other, a lead–lag relation is observed (Chan, 1992).. 立. 政治大. The lead–lag relation between the spot and futures markets illustrates how fast one. ‧ 國. 學. market reflects new information relative to the other and how well they are linked. Several studies examine the temporal relation between spot and futures returns and find that futures. ‧. returns significantly lead spot index returns (Finnerty and Park, 1987; Ng, 1987; Kawaller, Koch,. Nat. sit. y. and Koch, 1987; Harris, 1989; Stoll and Whaley, 1990; Chan, 1992). Futures market reacts to. n. al. er. io. new information faster because informed traders prefer to trade on the futures markets, which,. i n U. v. compared to the spot markets, offer higher leverages, lower costs, and fewer short-sale. Ch. engchi. restrictions (Black, 1975; Kawaller et al., 1987; Stoll and Whaley, 1990; Käppi, 1997; Chan, 1992; Back, 1993; Mayhew, Sarin, and Shastri, 1995; Fleming, Ostdiek, and Whaley, 1996; Easley, O’Hara, and Srinivas, 1998). Chan (1992) points out that the most popular explanation for the asymmetric lead–lag relation is that the futures market is less costly for informed traders to utilize than the spot market, so the futures market is dominant in revealing information. Fleming et al. (1996) also argue that trading S&P 500 futures costs much less than trading an equivalent portfolio of index stocks does, and price discovery will tend to occur first in the lowest-cost market, as information-based trades are executed where they make the highest net profit. 1.

(7) In this paper, I conjecture that one form of investor behavioral bias, namely, investor sentiment, plays an important role in affecting the lead–lag relation and price discovery process between the spot and futures markets. I show that high investor sentiment significantly increases both price volatility and trading cost on the futures market, which makes it more risky and costly for informed traders to utilize their information on the futures market and diminishes the futures markets’ leading informational role and contribution to price discovery as a result. The literature shows that investor sentiment affects investors’ trading behavior (Kurov, 2008) and has a significant impact on stock returns and price volatility (Lee, Jiang, and Indro, 2002; Baker and Wurgler, 2006; Schmeling, 2009; Kurov, 2010; Berger and Turtle, 2011; Baker,. 政治大 expected return and volatility relation, 立 and Stambaugh, Yu, and Yuan (2012) find that investor Wurgler and Yuan, 2012). Yu and Yuan (2011) find that investor sentiment affects the market. ‧ 國. 學. sentiment is positively related to market anomalies. High investor sentiment attracts more noise traders into the market, which increases noise trader risk and undermines market efficiency.. ‧. Noise trader risk, driven by high investor sentiment, plays an important role in. sit. y. Nat. determining the participation of informed traders. Specifically, the theory of limits to arbitrage. n. al. er. io. argues that informed traders tend to be less willing to utilize their information when noise trader. v. risk is high (De Long, Shleifer, Summers, and Waldmann, 1990; Shleifer and Vishny, 1997;. Ch. engchi. i n U. Barberis, Shleifer, and Vishny, 1998). De Long et al. (1990) point out that the unpredictability of noise traders’ future beliefs creates a risk in asset prices that deters rational arbitrageurs from taking aggressive positions against them. Similarly, Barberis et al. (1998) present a model of investor sentiment that shows that informed traders who bet against mispricing run the risk that investor sentiment will become more extreme and prices will move even further away from fundamental values. Because informed traders are less willing to leverage their information when noise trader risk is high, asset prices can diverge significantly from fundamental values, and the cross-market price transmissions can be significantly affected, even in the absence of fundamental risk. 2.

(8) Jones and Seguin (1997) argue that because noise trades are not based on information about underlying values, these trades can move prices away from their intrinsic value, reducing price informativeness while increasing price volatility. In this study, price volatility serves as a proxy for noise trader risk with the expectation that investor sentiment has a positive impact on price volatility (Jones and Seguin, 1997; Brown, 1999; Yuan, 2012). Furthermore, prior research shows that price volatility driven by high sentiment is positively related to trading cost. Amihud and Mendelson’s (1987) theoretical model suggests a positive relation between the measured return volatility and the bid–ask spread. Roll (1984), French and Roll (1986), Glosten (1987), and others show a relation between the standard. 政治大 Whitcomb (1986) review previous 立 empirical studies of the relation between transaction price. deviation of transaction price changes and the bid–ask spread. Cohen, Maier, Schwartz, and. ‧ 國. 學. volatility and bid–ask spreads in security markets. In general, these studies find a positive relation between transaction price volatility and the bid–ask spreads. The bid–ask spread is one. ‧. of the most important measures of trading costs. I expect that investor sentiment also has a. sit. y. Nat. positive impact on the bid–ask spread and that the increased bid–ask spread during high. n. al. deterring informed traders from trading on the futures market.. Ch. engchi. er. io. sentiment periods makes it more costly for informed traders to exploit their information, thus. i n U. v. I examine the impact of investor sentiment on the price relations between 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. I find that, first, investor sentiment has a positive impact on both price volatility and the bid–ask spread. The minute-by-minute realized volatility of exchange-traded funds (ETFs) and futures contracts is significantly positively related to investor sentiment, which is consistent with Jones and Seguin (1997), Barberis et al. (1998), Brown (1999), Karlsson, Leowenstein, and Seppi (2009), and Yuan (2012) that sentimentdriven investors trade more actively during high sentiment periods and make the market noisier. 3.

(9) The bid–ask spreads of ETFs and futures contracts are significantly positively related to investor sentiment, which implies that trading cost becomes higher during high sentiment periods. My empirical evidence shows that the noise trader risk and trading cost increase significantly during high sentiment periods. Second, for the temporal relation between futures and spot returns, I find that the leading role of futures becomes significantly weaker when investor sentiment is high, consistent with the argument that informed investors tend to trade less aggressively on the futures markets when the market is characterized by higher risks and costs. Chan (1992) suggests that the lead–lag relation should change when it becomes more costly or less costly for traders to exploit the. 政治大 al. (1996), and Barberis et al. 立(1998), indicating that the futures market reacts to new. information on the market. My finding is in line with De Long et al. (1990), Chan, Fleming et. ‧ 國. 學. information relatively slowly during high sentiment periods.. Third, prior literature shows that futures prices contribute more to price discovery in. ‧. equilibrium than spot prices do, which implies that futures prices are more informative (Chan,. sit. y. Nat. 1992; Frino, Walter, and West, 2000). I observe that futures market information shares are. n. al. er. io. negatively related to investor sentiment, suggesting that investor sentiment not only has. v. temporal effects on the lead–lag relation but also affects the price discovery process between the two markets in equilibrium.. Ch. engchi. i n U. Finally, I provide direct evidence concerning the assertion that noise trading increases during high sentiment periods. I examine the Commitment of Traders report from the Commodity Futures Trading Commission (CFTC) and find that small traders tend to hold more open interests, especially long positions, when investor sentiment is high. This result shows that noise traders become more optimistic and buy more contracts on the futures market during high sentiment periods. Overall, my findings are in line with the theory of limits to arbitrage. I provide evidence showing that high investor sentiment increases price volatility and the bid–ask spread, which 4.

(10) makes it more risky and costly for informed traders to utilize their information on the futures market. As a consequence, during high sentiment periods, the leading informational role of the futures market is diminished and the futures market contributes relatively less to the price discovery process. This paper contributes to the literature by investigating how informed traders respond under different market sentiment regimes and by clarifying the relation between investor sentiment and price discovery. I offer a possible explanation on why some studies find that nonlinear or time-varying models are able to better describe the lead–lag relation between the spot and futures returns (Chan, 1992; Ng and Pirrong, 1996; Bekiros and Diks, 2008), because the time-varying investor sentiment plays an important role in affecting the lead–lag. 政治大 The remainder of this paper 立 is organized as follows. Section 2 reviews related literature. relation.. ‧ 國. 學. on the lead–lag relation between the spot and futures markets, on investor sentiment, and on the theory of limits to arbitrage and proposes my hypotheses. Section 3 describes the data and. ‧. measurement of variables used in this study, and Section 4 discusses the methodologies. Section. y. sit. n. al. er. io. concludes.. Nat. 5 presents my empirical results. Section 6 provides further supporting evidence, and Section 7. Ch. engchi. 5. i n U. v.

(11) Chapter II Literature review and hypothesis In perfectly frictionless and rational markets, the price movements of securities and security derivatives must simultaneously reflect new information. Otherwise, costless arbitrage profits would be possible. However, where friction exists and trading costs differ across markets, security and derivative prices can differ and trading activity can vary across markets. Fleming et al. (1996) suggest that, given the differences in trading costs, price discovery will tend to occur first in the lowest-cost market, as information-based trades are executed where the highest net profit is produced.. 治政 Several studies suggest that informed traders prefer大 to trade on the futures market and 立 find that the futures market reflects new information faster than the spot market does. Informed ‧ 國. 學. traders prefer to trade on the futures market because it 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;. y. Nat. io. sit. Stoll and Whaley, 1990; Käppi, 1997; Chan, 1992; Back, 1993; Mayhew et al., 1995). With. n. al. er. greater financial leverage and lower transaction costs, informed traders are able to maximize. Ch. i n U. v. their profits. Second, informed traders prefer the futures market because it has fewer short-sale. engchi. constraints than the spot market (Easley et al., 1998; Frino et al., 2000). 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 the volatility of the underlying stock prices can most easily utilize the information on the derivative market (Back, 1993; Cherian and Jarrow, 1998). Because price discovery tends to occur first in the lowest-cost market, the trading cost hypothesis suggests that the futures market should react more quickly to new information because the trading cost in the futures market is lower than that in the spot market. (Chan, 1992; Fleming et al., 1996). Empirical evidence shows that futures markets significantly lead spot 6.

(12) markets, yet spot returns only have limited predictability on futures returns. Kawaller et al. (1987) find that the S&P 500 futures lead the spot index by between 20 and 45 minutes whereas little evidence suggests that the spot index leads the futures index. Also, Stoll and Whaley (1990) find that the S&P 500 and the Major Market Index futures lead the stock indexes by about 5 minutes whereas the feedback time from the spot market to the futures market is much shorter. The literature generally suggests that the asymmetric lead–lag relation is due to the fact that informed traders prefer to trade on the futures market.1 Some theoretical models and empirical findings, however, suggest that increased risk and trading costs tend to decrease informed trading, which, in turn, affects the lead–lag relation. 政治大 sentiment, plays an important role 立 in affecting both trading risk and trading costs of informed. between futures and spot. I propose that one form of investor behavioral bias, namely, investor. ‧. ‧ 國. markets.. 學. traders and thus has a significant impact on the pricing dynamics between the spot and futures. The literature shows that investor sentiment is positively related to noise trader risk. Yu. sit. y. Nat. and Yuan (2011) show a strong positive tradeoff between expected returns and volatility of. n. al. er. io. stocks when investor sentiment is low, but the return–volatility tradeoff becomes much weaker. v. when investor sentiment is high. Other empirical studies find evidence that sentiment-driven. Ch. engchi. i n U. investors trade more aggressively during high sentiment periods (Karlsson et al., 2009; Yuan, 2012). Because sentiment traders tend to be inexperienced and naïve investors, they are likely to have a poor understanding of risk measurement and hence are likely to misestimate the variance of returns, which weakens the mean–variance tradeoff. Yu and Yuan’s (2011) findings are consistent with Barberis et al. (1998), who show that sentiment-driven traders increase their participation in the market when sentiment is high. This. 1. Chan (1992) and Frino et al. (2000) analyze the lead–lag relation between the cash market and stock index. futures market and show that the leading position of the futures market is in fact due to the information advantage of the futures market, not due to the infrequent trading problem of component stocks. 7.

(13) phenomenon pushes prices away from levels that would otherwise reflect a positive mean– variance tradeoff. 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, etc.) and find that each anomaly is stronger (i.e., the long–short strategy is more profitable) following high levels of sentiment and weaker following low levels of sentiment. Yu and Yuan and Stambaugh et al. both find that the market is less efficient during high sentiment periods due to the higher participation of noise traders. Noise trader risk driven by high sentiment is likely a source of limits to arbitrage, which deters informed traders from leveraging their information on the market. Informed trading plays. 政治大 investors can cause prices to deviate 立 from their fundamental values, but informed traders and. an important role in improving market efficiency (Shleifer and Vishny, 1997). Some naïve. ‧ 國. 學. arbitrageurs can choose to take positions against noise traders and bring prices back to their fundamental values. Theoretically, arbitrage requires no capital and entails no risk (Sharpe and. ‧. Alexander, 1990). Shleifer and Vishny (1997), however, argue that arbitrage is often risky in. sit. y. Nat. practice and that professional arbitrageurs can avoid extremely volatile positions. That is,. n. al. er. io. professional arbitrageurs may quit the market when it is highly volatile, which can cause asset. v. prices to deviate from fundamental values for an appreciable length of time (Gemmill and Thomas, 2002).. Ch. engchi. i n U. 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 bear the risk that investor sentiment may become more extreme causing prices to move even further away from fundamental values. The theory of limits to arbitrage suggests that informed trading tends to be less active when noise trader risk is high. 8.

(14) Furthermore, both theoretical and empirical studies find that price volatility driven by noise trading is positively related to the bid–ask spread (Roll, 1984; Cohen et al., 1986; French and Roll, 1986; Amihud and Mendelson, 1987; Glosten, 1987). McInish and Wood (1992) analyze the intraday pattern in bid–ask spreads for NYSE stocks and find that bid–ask spreads are positively related to risk. Consistent with the implications of a simple asymmetric information model for the bid–ask spread, Bollerslev and Melvin (1994) provide evidence showing that the bid–ask spread is positively related to the underlying uncertainty. Because the bid–ask spread is one of the most important measures of trading costs, I expect that the increased bid–ask spread during high sentiment periods makes it more costly for informed traders to. 政治大 Overall, as high sentiment 立increases noise trader risk and hence price volatility and the. exploit their information.. ‧ 國. 學. bid–ask spread on the futures market, based on the theory of limits to arbitrage and the trading cost hypothesis, I infer that informed traders are less willing to trade on the futures market. ‧. during high sentiment periods. Consequently, compared to low sentiment periods, the futures. sit. y. Nat. market reacts to new information relatively slowly during high sentiment periods. The. n. al. sentiment over time. I thus state the following hypothesis:. Ch. engchi. er. io. asymmetric lead–lag relation between the spot and futures markets changes with investor. i n U. v. Hypothesis 1: The leading role of the futures market is weakened during high investor sentiment periods.. Next, if high sentiment decreases informed trading on the futures market in a systematic way, I expect to observe not only changes in the temporal lead–lag relation between the two markets but also changes in the price discovery process across markets. The lead–lag relation, which usually manifests within minutes, illustrates which market reflects new information faster in a relatively short horizon. Informed trading, however, also affects prices in equilibrium. As 9.

(15) informed traders are less willing to leverage their information advantages on the futures market during high sentiment periods, I expect that futures prices become relatively less informative and contribute less to the price discovery process in equilibrium. Thus, I state my second hypothesis:. Hypothesis 2: The prices on the futures market become less informative during high investor sentiment periods.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 10. i n U. v.

(16) Chapter III Data and measurement of variables 1. Data The data used in this study consist of intraday trade and quote prices of three ETFs and their corresponding E-mini index futures, which include the S&P 500 ETFs and S&P 500 Emini 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 price series, I can better control for the potential biases caused by the infrequent trading. 治政 problem. My sample period is from January 1, 2002 to December 大 31, 2010. The tick-by-tick 立 quote data of ETFs are obtained from the Trade and Quote database. I take the midpoint of the 2. ‧ 國. 學. quoted bid and ask prices as the proxy for the fundamental values of the ETFs and, following. ‧. Hasbrouck (2003), use only regular quotes on the primarily listed market of the ETFs.3 Regular trading hour is between 9:30 AM and 4:00 PM EST.4. y. Nat. io. sit. Because the quote data for index futures are unavailable, I use trading prices of the. n. al. er. futures contracts. The trading prices of the corresponding index futures contracts, including the. Ch. i n U. v. E-mini versions of the S&P 500, Nasdaq 100, and DJIA index futures, are obtained from the. engchi. Chicago Mercantile Exchange (CME). These E-mini futures contracts are quite active. As. 2. 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, 2002. 3. For the S&P 500 ETFs and DJIA ETFs, I use the AMEX quotes before September 30, 2008 and the NYSE quotes. after October 1, 2008 since the AMEX is merged by the NYSE after October 1, 2008. Similarly, for the Nasdaq 100 ETFs, the quotes from the AMEX before November 30, 2004 and the quotes from NASDAQ after December 1, 2004 are used because the Nasdaq 100 ETFs transferred its listing from the AMEX to NASDAQ on December 1, 2004. 4. To avoid contaminating effects due to the financial crisis surrounding the end of 2008, I repeat my tests with. data before September 30, 2008. The empirical results are qualitatively similar. These results are not reported to save space but are available on request. 11.

(17) Hasbrouck (2003) shows, they dominate the price discovery process on the S&P 500 and Nasdaq 100 index markets. I use the nearby futures contracts because they are the most actively traded contracts. To construct a continuous time series for the futures prices, I 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 ETFs and futures contracts are not uniformly spaced in time. To assess the degree of comovement among the prices between different markets, I follow the method in Chan (1992) to synchronize price pairs. I construct a minute-by-minute data set for each price series. The daily trading hours are from 9:30. AM. to 4:00. PM,. which contain 390 minute-by-. 政治大 observation. If no price is observed 立 within that one-minute span, I use the price of the previous. minute intervals on each trading day. In each one-minute interval, I identify the last price. ‧ 國. 學. minute instead. 5 Returns are calculated as differences in log prices. 6 There 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 my nine-year sample period.7 I obtain trading volume for the ETFs and. n. al. er. io. sit. y. Nat. futures from the Trade and Quote database and the CME, respectively.8. 2. Measurement of variables. Ch. engchi. i n U. v. I measure investor sentiment using the monthly market-based sentiment index constructed by Baker and Wurgler (2006). Baker and Wurgler 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. 5. Because my sample ETFs and E-mini futures are actively traded, I use the price of the previous minute in less. than 1% of the sample. 6. 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. 7. Due to occasional market suspensions and trading halts, I remove sample days in which less than 120 one-minute. quote or trade prices can be identified. 8. The trading volume data for futures are available since July 1, 2003. 12.

(18) 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. 9 Similar to Yu and Yuan (2011), I define high (low) sentiment periods as those months in which Baker and Wurgler’s investor sentiment index is above (below) its median during my sample period from January 2002 to December 2010. To test the robustness of my results, I alternatively define high (low) sentiment periods as those months in which the investor sentiment index is above (below) its 75th (25th) percentile. To investigate the impact of sentiment on price volatility, I calculate the daily realized volatility for ETFs and futures as. 政治大 𝑅𝑒𝑎𝑙𝑖𝑧𝑒𝑑立 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 (𝑅𝑉 ) = √ ∑ (𝑟 ) 𝑡. 𝑚 𝑖=1. 𝑖. 2. × 10000,. (1). ‧ 國. 學. where m is the number of one-minute intervals during the regular trading hours on day t, and 𝑟𝑖. ‧. is the ith one-minute return on a trading day. Furthermore, I use quoted spreads to measure the. sit. y. Nat. market liquidity of the ETFs, which are defined as the differences between quoted ask and. n. al. er. io. quoted bid prices. Because the quote data are not available for the futures, I use the price reversal. v. method, suggested by Wang, Michalski, Jordan, and Moriarty (1994), to calculate the daily. Ch. estimated bid–ask spread for futures.10. 9 10. engchi. i n U. I download the data from Wurgler’s website: http://people.stern.nyu.edu/jwurgler/. The estimated bid–ask spread for the E-mini futures is calculated as follows: (a) an empirical joint price. distribution of ∆𝑃𝑡 and ∆𝑃𝑡−1 during a daily interval is created; (b) the subset of price changes that exhibited price continuity (i.e., a positive change followed by another positive change) is discarded; (c) absolute values of the price changes that are price reversals are taken; and (d) the mean of absolute values obtained in the third step is the estimated spreads. 13.

(19) Chapter IV Empirical methods 1. Structural models for volatility and bid–ask spreads I use two structural model equations to estimate the potential impacts of changes in investor sentiment on price volatility and bid–ask spreads with other control variables.11 The two empirical models are specified as follows, beginning with the price volatility equation;. ℎ𝑖𝑔ℎ−𝑠𝑒𝑛𝑡. 𝑅𝑉𝑡 = 𝛼0 + 𝛽0 𝐷𝑡. + ∑3𝑖=1 𝛾0𝑖 𝑅𝑉𝑡−𝑖 + ∑3𝑗=1 𝜃0𝑗 𝑇𝑉𝑡−𝑗 +. 政治大. ∑3𝑘=1 𝛿0𝑘 𝐵𝐴𝑆 𝑡−𝑘 + 𝜀𝑡 ,. 立. ℎ𝑖𝑔ℎ−𝑠𝑒𝑛𝑡. ‧ 國. is a dummy variable of high. 學. where 𝑅𝑉𝑡 is the realized volatility on day t, and 𝐷𝑡. (2). sentiment on day t, which is equal to 1 if the sentiment index is above its 75th percentile during. ‧. my sample period, and zero otherwise. 𝑅𝑉𝑡−𝑖 is the realized volatility on day t – i to take. sit. y. Nat. account of the cluster effects of volatility, 𝑇𝑉𝑡−𝑗 is the daily trading volume on day t – j, and. io. er. 𝐵𝐴𝑆 𝑡−𝑘 is the percentage quoted bid–ask spread for the ETFs and the percentage estimated. al. bid–ask spread for the futures on day t – k. 𝜀𝑡 is the error term. The percentage bid–ask spread. n. v i n is defined as the spread scaled by C price. price volatility to be positively related to h eI nexpect gchi U. investor sentiment. A significantly positive 𝛽0 would support the assertion that high sentiment introduces more noise traders to the market and makes the market more volatile. Similarly, the bid–ask spread equation is specified as. ℎ𝑖𝑔ℎ−𝑠𝑒𝑛𝑡. 𝐵𝐴𝑆𝑡 = 𝛼1 + 𝛽1 𝐷𝑡. + ∑3𝑖=1 𝛾1𝑖 𝑅𝑉𝑡−𝑖 + ∑3𝑗=1 𝜃1𝑗 𝑇𝑉𝑡−𝑗 +. ∑3𝑘=1 𝛿1𝑘 𝐵𝐴𝑆 𝑡−𝑘 + 𝜀𝑡 . 11. (3). To avoid the simultaneous equation bias, price volatility, trading volume and the bid–ask spreads are used as. lagged variables in Equations (2) and (3). Refer to Wang and Yau (2000) for further discussions on this issue. 14.

(20) A significantly positive 𝛽1 would support the assertion that high sentiment introduces more noise traders and increases trading costs measured by the bid–ask spreads. The ordinary least square method is used to estimate the parameters with Newey-West heteroscedasticity and autocorrelation consistent covariance matrix used to adjust for the standard errors of the parameters.. 2. Lead–lag relation between the futures and spot markets Next, I use the vector error correction model (VECM) to investigate the lead–lag. 政治大 futures are based on the same underlying 立 assets, so I assume that they share the same implicit. relation between the spot and futures markets. Index tracking ETFs and their corresponding. ‧ 國. 學. 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. sit. y. Nat. n. al. (4). er. io. ∆𝑃𝑡 = 𝜇 + ∑𝑘𝑖=1 𝐴𝑖 ∆𝑃𝑡−𝑖 + 𝛾𝑧𝑡−1 + 𝜀𝑡 ,. Ch. engchi. i n U. v. where ∆ is the difference operator, 𝑃𝑡 is a (2 × 1) vector of log prices on the two markets, 𝜇 is a (2 × 1) vector of constants, 𝐴𝑖 are (2 × 2) matrices of autoregressive coefficients, k is the number of lags, 𝛾 is a (2 × 1) vector of coefficients on the error correction terms, 𝑧𝑡−1 = 𝛼 ′ 𝑃𝑡−1 is a scalar of error correction terms, 𝛼 ′ is a (1 × 2) cointegrating vector, and 𝜀𝑡 is a (2 × 1) vector of price innovations. The coefficient, 𝛾, on the error correction term, also called speed of adjustment, measures the price reactions to the deviations from the long-term. 12. I apply the Johansen likelihood ratio 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. 15.

(21) equilibrium relation. In my VECM, ∆𝑃𝑡 = (∆𝐹𝑡 ∆𝑆𝑡 )′ , where 𝐹𝑡 and 𝑆𝑡 denote the prices for the index futures and their corresponding ETFs, respectively. The coefficient matrix 𝐴𝑖 in Equation (4) reveals the temporary lead–lag relation between the two markets. The coefficients in matrix 𝐴𝑖 are used to test Hypothesis 1 and are expected to change with investor sentiment over time. More specifically, if informed traders are reluctant to trade during high sentiment periods due to increased noise trader risk, the impact of the lagged futures returns on the ETFs returns will become smaller and less significant when sentiment is high. Such a finding supports my Hypothesis 1 that the leading role of futures is weakened during high investor sentiment periods.. 政治大 3. Information shares and factor 立 weights. ‧ 國. 學. Furthermore, I adopt two price information measures, 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. sit. y. Nat. (1995) suggests that the contribution to price discovery by each market (sharing a stochastic. al. er. io. common trend) is defined as the variation in efficient price innovations attributable to that. v. n. market’s innovation. According to Hasbrouck, the efficient price 𝑣𝑡 follows a random walk:. Ch. engchi. i n U. 𝑣𝑡 = 𝑣𝑡−1 + 𝑢𝑡 . 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:. ∆𝑃𝑡 = 𝛹(𝐿)𝜀𝑡 ,. 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: 16. (5).

(22) 𝜎𝑢2 = 𝛹𝛺𝛹 ′ ,. (6). where 𝛹 is a row vector composed of VMA coefficients and 𝛺 = 𝑣𝑎𝑟(𝜀𝑡 ). 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:. 𝐼𝑆𝑗 =. (𝛹𝐹)2𝑗 𝜎𝑢2. ,. (7). 政治大. where (𝛹𝐹)𝑗 is the jth element of the row matrix 𝛹𝐹. The larger information share of the jth. 立. market, the more predominant force it has in setting the common efficient price. By permuting. ‧ 國. 學. the order of the market prices, Equation (7) provides an upper and a lower bound for the information shares of each market. I compute the information shares for my three ETFs–futures. ‧. pairs each day and use the midpoint of the upper bound and lower bound as the measure for. sit. y. Nat. information shares.. n. al. er. io. In general, the market with larger information shares is expected to contribute more to. i n U. v. the discovery of the long-run equilibrium price. If the information shares of futures, 𝐼𝑆𝑓 , is. Ch. engchi. 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. Because the literature shows that information shares are related to liquidity and volatility (Eun and Sabherwal, 2003; Ates and Wang, 2005), the regression model for 𝐼𝑆𝑓 is specified as. ℎ𝑖𝑔ℎ−𝑠𝑒𝑛𝑡. 𝐼𝑆𝑓,𝑡 = 𝛼2 + 𝛽2 𝐷𝑡. + 𝛾2 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡 + 𝜃2 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦𝑡 + 𝜀𝑡 ,. 17. (8).

(23) ℎ𝑖𝑔ℎ−𝑠𝑒𝑛𝑡. where 𝐼𝑆𝑓,𝑡 is the information shares of the futures contracts on day t; 𝐷𝑡. is a dummy. variable of high sentiment on day t, which is equal to 1 if the sentiment index is above its 75th percentile during my sample period, and zero otherwise; 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑡 is the liquidity measure on day t; and 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦𝑡 is the realized volatility on day t. I use three different proxies for liquidity: market share (MS), spread ratio (SR), and trading volume (TV). MS is the market share of futures, 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. 𝑀𝑆𝑡 =. 𝐷𝑜𝑙𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑜𝑛 𝑑𝑎𝑦 𝑡 𝐷𝑜𝑙𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑎𝑛𝑑 𝐸𝑇𝐹𝑠 𝑜𝑛 𝑑𝑎𝑦 𝑡. .. (9). 政治大. 立. SR is the ratio of the bid–ask spread of the ETFs to the bid–ask spread of the futures, and TV is. ‧ 國. 學. the daily trading volume of the futures contracts. The literature shows that liquidity is positively related to the contribution of price discovery (Eun and Sabherwal, 2003; Ates and Wang, 2005).. ‧. More important, I expect 𝛽2 in Equation (8) to be significantly negative, which would support. y. Nat. n. al. er. io. sentiment periods.. sit. Hypothesis 2 that the prices on the futures market are less informative during high investor. i n U. v. In a cointegrated system such as that in Equation (4), Gonzalo and Granger (1995;. Ch. engchi. hereafter GG) also propose a methodology to decompose the vector of market prices into permanent and transitory components:. 𝑃𝑡 = 𝑓𝑡 𝑖2 + 𝑧𝑡 ,. (10). where 𝑃𝑡 is a (2 × 1) vector of log prices on the futures and spot markets on day t, 𝑓𝑡 is a scalar of common long-memory component, 𝑧𝑡 is a (2  1) transitory component, and 𝑖2 is a (2  1) unit vector. The Johansen’s maximum likelihood framework suggests that the common long-memory factor can be estimated as 𝑓𝑡 = 𝛾⊥′ 𝑃𝑡 , where 𝛾⊥′ is a (1  2) vector, which is 18.

(24) orthogonal to the vector of speed of adjustment coefficients, 𝛾, on the error correction term in Equation (4). 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 1 and a larger factor weight of the jth market price suggests that the jth market price makes a larger contribution to the price discovery process. I expect that investor sentiment has a negative impact on the GG factor weights of the futures market. Finally, to show whether noise traders actually trade more on the futures market during. 政治大 100, and DJIA index futures published 立 by the CFTC. The CFTC requires traders to report their high sentiment periods, I use the Commitment of Traders report of the E-mini S&P 500, Nasdaq. ‧ 國. 學. 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 nonreportable traders. Reportable traders are further classified as. sit. y. Nat. either commercials or noncommercials based on information provided by the traders in the. n. al. and noncommercials are considered to be large speculators.. Ch. engchi. er. io. reports. In the finance research literature, commercials are typically considered to be hedgers,. i n U. v. Nonreportable positions are calculated by subtracting the reportable open interests from total open interests. They are typically small and considered to be coming from 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. I expect that nonreportable traders, who are likely to be noise traders, hold more open interests during high sentiment periods.. 19.

(25) Chapter V Empirical results 1. Investor sentiment, price volatility, bid–ask spreads, and the lead–lag relation This section presents empirical results on the impact of investor sentiment on price volatility, the bid–ask spread, and the lead–lag relation between the spot and futures markets. Table 1 reports summary statistics for the investor sentiment index and the minute-by-minute ETFs and futures returns.13 My nine-year sample period from January 2002 to December 2010 includes 108 monthly observations for the sentiment index. The sentiment index is a standardized statistics with zero mean and unit variance. The mean and median of the sentiment. 治政 index are both close to zero, which indicates that investor 大 sentiment during my sample period 立 is not leaning toward either high or low levels. The mean and median returns for the ETFs and ‧ 國. 學. futures are all close to zero.. ‧. Table 2 presents the regression results of the relation between investor sentiment and volatility. I use the minute-by-minute realized volatility as a proxy for price volatility and then. y. Nat. io. sit. regress it on the high sentiment dummy and other control variables. 14 The high sentiment. n. al. er. dummy equals 1 when the sentiment index is above its 75th percentile during my sample period. Ch. i n U. v. and zero otherwise. After controlling for lagged realized volatility, lagged trading volume, and. engchi. lagged bid–ask spread, I 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. I use the orthogonal investor sentiment index from Baker and Wurgler (2006) who 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. I 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 on request. 20.

(26) For example, with lag 1 control variables, the coefficients on the high sentiment dummy in Models (1) and (2) of Table 2 are, respectively, 4.81 and 7.50, significant at the 1% level, with S&P 500 ETFs and futures volatility as the dependent variables, respectively. This shows that investor sentiment significantly increases price volatility. The coefficients on the sentiment dummy remain significantly positive in Models (3) to (6) when lag 2 and 3 control variables are added. Similar results are found for the Nasdaq 100 and DJIA ETFs and futures volatilities in Table 2. 15 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 into the. 政治大 Table 3 presents the results 立 of regressing the bid–ask spread and the percentage bid–ask. market and in turn makes the markets noisier and riskier.. ‧ 國. 學. spread on the high sentiment dummies and other control variables and shows that investor sentiment has a significantly positive impact on both the bid–ask spread and the percentage bid–. ‧. ask spread. When the dependent variables are the bid–ask spread of the S&P 500, Nasdaq 100,. sit. y. Nat. and DJIA ETFs and futures, the coefficients on the high sentiment dummy are all positive, and. n. al. er. io. five out of six are statistically significant at the 5% level. Take the bid–ask spread of the Nasdaq. v. 100 ETFs and futures as an example: The coefficients on high sentiment dummy are 2.64 and. Ch. engchi. i n U. 481.82, respectively, significant at the 5% level. From Table 3, I further find that the high sentiment dummies have a positive impact on the percentage bid–ask spread, with all six coefficients being positive and four out of them being statistically significant at the 10% level.16 The bid–ask spread is generally considered an important measure for trading costs in the literature. The larger it is, the less informed traders are willing to leverage their information.. 15. I perform the regression specification error test, suggested by Hill, Griffiths, Lim (2008), and find that the. empirical models in Table 2 do not suffer from the model specification problem due to omitted variables. 16. I again perform the specification error test, suggested by Hill et al. (2008), and show that the empirical models. in Table 3 do not suffer from the model specification problem due to omitted variables. The results are qualitatively similar when the lag 2 and 3 control variables are added to the models. 21.

(27) In sum, my results in Tables 2 and 3 show that investor sentiment increases both arbitrage risk and trading costs on the futures market during high sentiment periods, which is likely to make informed traders less willing to leverage their information advantage on the futures market when investor sentiment is high. I next examine how informed traders respond to the more risky and costly trading environment during high sentiment periods by testing the impact of investor sentiment on the lead–lag relation between ETFs and futures. Tables 4, 5 and 6 report the coefficient matrix, 𝐴𝑖 in Equation (4), and show 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. 政治大 indicating that a two-way Granger 立causality relation exists between ETFs and futures returns.. in Tables 4, 5, and 6, I find that the spot and futures markets significantly lead each other,. ‧ 國. 學. More important, futures tend to lead ETFs more significantly, because the impact of lagged futures returns on the ETFs returns are larger and more significant than those of the. ‧. lagged ETFs returns on the futures returns. Take the S&P 500 index as an example: From the. sit. y. Nat. baseline regressions in Table 4, the coefficients on the first three minutes lagged futures returns. n. al. er. io. are 0.579, 0.434, and 0.307, respectively, with ETFs returns as the dependent variable. The. v. coefficients on the first three minutes lagged ETFs returns are smaller at 0.138, 0.104, and 0.072,. Ch. engchi. i n U. respectively, with futures returns as the dependent variable. 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, although a two-way causal relation exists between ETFs and futures prices, the futures market assumes a more significant role in reflecting new information, which is consistent with the prior literature. To investigate the effect of investor sentiment on the lead–lag relation, I add several sentiment dummies representing different levels of investor sentiment in the VECM. First, I add a low sentiment dummy, which is equal to 1 when the sentiment index is below the 25th percentile of its distribution, and zero otherwise. Again, take the S&P 500 index as an example: 22.

(28) From Table 4, the coefficients on the interactions between the low sentiment dummy and the first three lagged futures returns are respectively 0.091, 0.071, and 0.068, significant at the 1% level, with ETFs returns as the dependent variable. This result indicates that the futures tend to lead ETFs more significantly during low sentiment periods. On the other hand, when the sentiment dummy is set with respect to the sentiment index at greater than either the 50th or the 75th percentiles, from Table 4, the coefficients on the interactions between the high sentiment dummies and the first three lagged S&P 500 futures returns are, respectively, –0.055, –0.053, and –0.055 (–0.079, –0.099, and –0.088) for the 50th (75th) percentile sentiment dummy, all significant at the 1% level, with ETFs returns as the. 政治大 significantly weakened during 立 high sentiment periods. Tables 5 and 6 report the results for the. dependent variable. These results show that the leading informational role of the futures is. ‧ 國. 學. 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 leading informational role of the futures, likely due to a riskier and more. sit. y. Nat. costly trading environment during these periods.. n. al. er. io. The effect of investor sentiment on the pricing dynamics between the spot and futures. v. markets is not only statistically significant but also economically significant. For instance, from. Ch. engchi. i n U. Table 4, for the model of the 75th percentile sentiment dummy, the coefficient on the first lagged futures returns is 0.593, whereas the coefficient on the interaction term between the first lagged futures returns and the sentiment dummy is –0.079 with ETFs returns as the dependent variable. This number indicates that, when investor sentiment is high, the coefficient on the first lagged futures returns drops by 13%. Similarly, from Table 6, for the model of the 75th percentile sentiment dummy of the DJIA index, the coefficient on the first lagged futures return drops by 23%, which is also economically significant. The coefficients on the interaction terms between. 23.

(29) the two- to five-lag returns and the high sentiment dummy show similar patterns in signs and magnitudes.17 I 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 informed traders 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.. 2. Investor sentiment and the price discovery process. 政治大 relation between the spot and futures 立 markets is affected by investor sentiment. Next I present. In the previous section, the VECM estimation reveals that the temporary lead–lag. ‧ 國. 學. the impact of investor sentiment on the information shares and GG factor weights to show whether investor sentiment affects the spot and futures prices in equilibrium. I use the intraday. ‧. data to calculate the daily information shares for the ETFs and their corresponding futures. As. sit. y. Nat. pointed out in the research methodology section, the ordering of time series in the Hasbrouck. n. al. er. io. (1995) model affects the calculations of information shares, so I focus on the average of the. v. upper and lower bounds (i.e., the midpoint) of information shares.. Ch. engchi. i n U. Table 7 reports the changes in the information shares during different sentiment regimes. 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 my VECM results in the previous section and shows that the futures prices are, unconditionally, more informative than ETFs prices. Table 7, however, shows that as investor sentiment increases, the average information shares of the futures market decrease and those of ETFs increase. For example, the information share midpoint of the S&P 500 futures during high sentiment periods is 0.021 lower than that. 17. The VECMs in my tables are estimated in an AR(6) framework. To save space, I only show the coefficients on. the first three lags. Interested reader can obtain the complete results from the authors. 24.

(30) during low sentiment periods. Similar results are obtained for the Nasdaq 100 and DJIA indexes. From Table 7, I observe that the futures market becomes relatively less informative, whereas the spot market becomes relatively more informative, during high sentiment periods.18,19 I next perform multivariate regressions to investigate the relation between investor sentiment and the futures information shares with control variables, including realized volatility and liquidity measures. Table 8 shows that investor sentiment again has a significantly negative impact on the futures information shares. I regress the futures information shares of the S&P 500, Nasdaq 100, and DJIA indexes on the high sentiment dummies, set with respect to the sentiment index at greater than the 75th percentile, and on control variables in different model. 政治大 negative. Take the information立 shares of the S&P 500 futures for example: From Table 8, the specifications and find that the coefficients on high sentiment dummies are mostly significantly. ‧ 國. 學. coefficients on high sentiment dummies in Models (1), (2), and (3) are –0.104, –0.044, and – 0.005, respectively, for three different sets of liquidity controls, and two of them are significant. ‧. at the 1% level.. sit. y. Nat. Table 8 provides similar results for the Nasdaq 100 and DJIA futures, implying that. n. al. er. io. futures prices contribute relatively less to price discovery when investor sentiment is high. The. v. results reported in Tables 7 and 8 are in line with Shleifer and Vishny (1997) and Barberis et al.. Ch. engchi. i n U. (1998) who argue that informed traders 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 futures prices relatively less informative during such periods. I next report the results with GG factor weights as an alternative information measure. The larger the GG factor weights are, the more the prices contribute to the price discovery 18. The results are similar when the high sentiment period is defined as the sentiment index being greater than its. 75th percentile. 19. In unreported univariate analysis, I also find the correlations between investor sentiment and information shares. of the S&P 500, Nasdaq 100, and DJIA futures are significantly negative. 25.

(31) process. Table 9 reports the regression results of the relation between investor sentiment and the futures GG factor weights. The coefficients on the 75th percentile sentiment dummies are all negative in various model specifications, and most of them are statistically significant. For example, with the GG factor weights of the DJIA futures as the dependent variable, the coefficients on the high sentiment dummies are respectively –0.229, –0.183, and –0.053, significant at the 1% level, for the liquidity measures of MS, SR, and TV; see Models (7), (8), and (9), respectively. Results for the S&P 500 and Nasdaq 100 futures are similar, which again imply that the futures prices contribute less to the price discovery process when investor sentiment is high.20. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. 20. Ch. engchi. i n U. v. To address the endogeneity concerns, I replace all control variables in Tables 8 and 9 with their lagged terms. and re-estimate the coefficients. The results are both qualitatively and quantitatively similar. 26.

(32) Chapter VI Investor sentiment and the futures trading activity Finally, I provide supporting evidence on the increase of noise trading activity during high sentiment periods. I collect the weekly Commitment of Traders report for the S&P 500, Nasdaq 100, and DJIA E-mini futures from the CFTC and analyze the trader composition. Panel A of Table 10 summaries the combined open interests held by commercial, noncommercial, and nonreportable 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. 治政 and low sentiment periods. High (low) sentiment periods are 大those months in which Baker and 立 Wurgler’s (2006) investor sentiment index is above (below) its median. ‧ 國. 學. I find that nonreportable traders, who are usually less informed and are most likely to. ‧. be affected by investor sentiment (Röthig and Chiarella, 2011), tend to hold significantly more open interests in all sample E-mini futures when investor sentiment is high. For the combined. y. Nat. io. sit. long and short positions results in Panel A of Table 10, compared to low sentiment periods,. n. al. er. nonreportable traders hold on average 85,742, 9,566, and 9,139 more open interests during high. Ch. i n U. v. sentiment periods in the S&P 500, Nasdaq 100, and DJIA futures, respectively. These results. engchi. indicate that noise traders tend to trade more actively on the futures market when investor sentiment is high. Panel A of Table 10 also shows the percentage changes in open interests for nonreportable traders and commercial traders. The percentage changes in open interests from low to high sentiment periods for the commercial traders, who are the major participants on the E-mini index futures market, are –2.41%, 6.58%, and 37.19 for the S&P 500, Nasdaq 100 and DJIA futures, respectively, without obvious patterns. However, the percentage changes in open interests from low to high sentiment periods for nonreportable traders are sizable and positive at 22.87%, 13.57%, and 39.06% for the S&P 500, Nasdaq 100 and DJIA futures, respectively. 27.

(33) This result suggests that nonreportable trading disproportionately increases during high sentiment periods. By breaking the combined positions into long and short positions, I further find that the increased open interests held by nonreportable traders during high sentiment periods are mostly due to increases in long positions. Panel B of Table 10 shows that during high sentiment periods nonreportable traders hold significantly more long positions, both in the absolute and in percentage terms, while no clear the patterns exist for commercial traders. For example, for nonreportable traders, the percentage increases in the long positions from low to high sentiment periods are 41.83%, 45.65%, and 26.39% for the S&P 500, Nasdaq 100 and DJIA futures,. 政治大 not consistent for both commercial 立 and nonreportable traders.. respectively. However, the absolute and percentage changes of short positions in Panel C are 21. ‧ 國. 學. The results that nonreportable traders tend to hold more long positions when investor sentiment is high are in line with the argument that during high sentiment periods noise traders. ‧. tend to buy more stocks and that informed traders have difficulty correcting overpricing due to. sit. y. Nat. short-sale constraints on the stock market. These findings are consistent with Baker and Wurgler. n. al. er. io. (2006) and Stambaugh et al. (2012), who find that noise traders driven by high sentiment are. v. usually overly optimistic and push prices up, away from their fundamental values for an. Ch. engchi. i n U. appreciable length of time. Overall, Table 10 shows that nonreportable traders trade more actively on the futures market during high sentiment periods, and this excessive trading increases informed traders’ risk and cost to trade on the futures market during high sentiment periods. This phenomenon, in turn, undermines the informativeness of the futures market.. 21. When high (low) sentiment periods are defined as those months in which the investor sentiment index is above. (below) its 75th (25th) percentile, the results are more significant. For nonreportable traders, the percentage increases in the combined positions from low to high sentiment periods are 57.79%, 3.20%, and 79.21% for the S&P 500, Nasdaq 100 and DJIA futures, respectively. For nonreportable traders, the percentage increases in the long positions from low to high sentiment periods are 79.07%, 69.76%, and 50.40% for the S&P 500, Nasdaq 100 and DJIA futures, respectively. 28.

(34) Chapter VII Conclusion The literature extensively shows that the futures market reflects new information more quickly than the spot market does because lower trading costs in the futures market attract more informed traders who can better utilize their information. As a consequence, an asymmetric lead–lag relation is observed between the spot and futures markets. Some studies, however, suggest that the lead–lag relation can be time-varying if trading risk and trading cost change over time. I empirically investigate the effect of time-varying investor sentiment on the lead– lag relation and on the price discovery process between the spot and futures markets. Using the. 治政 trade and quote data of the S&P 500, Nasdaq 100, DIJA ETFs, 大 and their corresponding futures 立 contracts, I first show that investor sentiment has a positive impact on both price volatility and ‧ 國. 學. the bid–ask spread, which implies that informed traders bear higher trading risk and trading. ‧. costs during high sentiment periods. Based on the theory of limits to arbitrage and trading cost hypothesis, I hypothesize that informed traders become less willing to leverage their. y. Nat. io. sit. information advantages on the futures market during high sentiment periods.. n. al. er. My investigation on the lead–lag relation and on the price discovery process between. Ch. i n U. v. the spot and futures markets provides several findings that are consistent with the literature and. engchi. my hypotheses. First, the leading role of the futures markets becomes significantly weaker during high sentiment periods, indicating that informed traders tend to trade less on the futures market when noise trader risk and trading cost are high. Second, investor sentiment negatively impacts both the information shares and the GG factor weights of the futures market. These results suggest that the futures prices become relatively less informative during high sentiment periods. Finally, nonreportable small traders tend to hold more long positions in futures during high sentiment periods, which indicates that investor sentiment indeed has a positive impact on the noise trader risk.. 29.

(35) My study provides support for the theory of limits to arbitrage. That is, increased noise trader risk and trading costs during high investor sentiment periods discourage informed traders from leveraging their information advantages on the futures market. This study contributes to the literature by showing that investor sentiment not only affects asset prices and volatility but also has an important effect on the price discovery process across informationally linked markets.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 30. i n U. v.

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