Investor Sentiment and Price Discovery Evidence

Investor Sentiment and Price Discovery: Evidence from the Pricing Dynamics between the Futures and Spot Markets SWJTU, Chengdu, 2015 Robin K. Chou National Chengchi University, Taiwan Chu Bin Lin National Chengchi University, Taiwan George H.K. Wang George Mason University, United States

Introduction Price discovery is arguably one of the most important products of a financial market. In a perfectly frictionless world, price movements of stock index futures and the underlying spot market correlated and not cross-autocorrelated (Hasbrouck, 1995; Chan, 1992). are contemporaneously However, if one market reacts to new information faster than the other, an asymmetric lead lag relation is observed (Chan, 1992). 2

Introduction Frictionless world Spot Futures 3

Introduction Real world Futures Spot 4

Introduction 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; K ppi, 1997; Chan, 1992; Back, 1993; Mayhew, Sarin, and Shastri, 1995; Easley, O Hara, and Srinivas, 1998). 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(Chan, 1992). 5

Introduction Lead-lag relation Spot Futures Investor sentiment 6

Introduction Investor sentiment has been found to affect investor trading behavior, stock returns, return volatility, and market efficiency (Lee, Jiang, and Indro, 2002; Baker and Wurgler, 2006; Schmeling, 2009; Kurov, 2010; Baker, Wurgler and Yuan, 2012; Berger and Turtle, 2011). Baker and Wurgler (2006) construct an index of investor sentiment and find that their index can predict subsequent returns for stocks. 7

Introduction Yu and Yuan (2011) discover a critical role for investor sentiment in the market efficiency. Specifically, there is a strong positive mean-variance tradeoff when sentiment is low but little if any relation when sentiment is high. Similarly, Stambaugh, Yu and Yuan (2012) examine the profitability of long-short anomalies and find that each anomaly is stronger following high levels of sentiment but little following low levels of sentiment. strategies on 11 market 8

Introduction Price volatility (+) Noise trader risk Sentiment (+) (+) Bid-ask spread 9

Introduction The theory of limits to arbitrage suggests that informed traders would become less willing to leverage their information when trading risk is high. Trading cost hypothesis suggests that informed trading decreases when it is more costly for informed traders to exploit their information. 10

Hypotheses Hypothesis 1: The leading role of the futures market is weakened during high investor sentiment periods. Hypothesis 2: The prices on the futures market become less informative during high investor sentiment periods. 11

Data and Methodology Three intraday ETFs-and-futures price pairs from 2002 to 2010 are examined: 1. S&P 500 ETFs and E-mini futures, 2. Nasdaq 100 ETFs and E-mini futures, 3. DJIA 30 ETFs and E-mini futures. Monthly sentiment index is from Baker and Wurgler (2006). 12

Data and Methodology Volatility proxies: Minute-by-minute returns for realized volatility. Bid-ask Spread and percentage bid-ask spread Lead-lag relationship: Vector error correction model (VECM). ? ??= ? + ?? ?? ?+ ??? 1+ ?? ?=1 Informativeness measure: (1) Information shares (Hasbrouck, 1995), and (2) Factor weights (Gonzalo and Granger, 1995) 13

Empirical Results

Table 2 Realized volatility and investor sentiment Dependent Variable: Realized Volatility Empirical Results: Part I (1) (2) (3) (4) (5) S&P500 Nasdaq100 DJIA (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures Intercept 9.553 -16.983 7.416 -11.111 6.328 -7.520 11.903 17.432 8.464 13.849 7.632 13.323 11.478 -10.838 9.323 -6.273 8.104 0.180 (0.00) (0.00) (0.00) (0.00) (0.00) (0.05) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.15) (0.00) (0.97) High Sent. Dummy 4.814 7.502 3.919 5.018 3.610 4.511 3.891 5.652 3.418 4.454 3.635 4.641 4.756 7.214 3.959 5.192 3.401 4.731 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.01) (0.00) (0.01) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) LAG1_RV 0.853 0.862 0.632 0.550 0.593 0.483 0.907 0.961 0.605 0.602 0.549 0.535 0.835 0.873 0.613 0.585 0.584 0.540 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) LAG2_RV 0.256 0.342 0.192 0.244 0.341 0.373 0.259 0.308 0.259 0.327 0.189 0.241 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) LAG3_RV 0.126 0.188 0.150 0.138 0.128 0.187 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) - LAG1_TV ( 10 7) 0.119 1.576 0.091 57.618 0.115 71.459 -0.042 -530.008 0.078 -34.774 0.114 62.090 1.622 1.209 367.134 1.313 486.166 369.901 (0.03) (0.00) (0.00) (0.88) (0.03) (0.00) (0.01) (0.00) (0.11) (0.00) (0.05) (0.67) (0.01) (0.47) (0.00) (0.08) (0.00) (0.02) LAG2_TV ( 10 7) 0.002 -48.187 0.098 -1.939 -0.128 -401.612 -0.045 -225.362 0.089 -649.626 0.779 -242.040 (0.97) (0.00) (0.05) (0.92) (0.00) (0.00) (0.32) (0.01) (0.83) (0.00) (0.10) (0.28) LAG3_TV ( 10 7) -0.151 -67.030 -0.122 -271.767 -1.310 -732.610 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) LAG1_BAS ( 104) -0.175 12.682 -0.160 31.860 -0.144 38.961 -0.324 0.252 -0.694 25.929 -0.771 32.084 -0.218 21.503 -0.122 18.669 -0.116 19.273 (0.40) (0.00) (0.45) (0.00) (0.50) (0.00) (0.57) (0.73) (0.33) (0.00) (0.31) (0.00) (0.01) (0.00) (0.14) (0.01) (0.16) (0.01) LAG2_BAS ( 104) -0.109 -23.372 -0.180 -17.384 0.230 -25.888 0.187 -22.109 -0.138 -4.796 -0.100 -5.459 (0.60) (0.03) (0.40) (0.21) (0.75) (0.00) (0.81) (0.01) (0.09) (0.49) (0.23) (0.49) LAG3_BAS ( 104) -0.001 -15.317 -0.039 -10.012 -0.079 -7.694 (1.00) (0.17) (0.96) (0.16) (0.34) (0.30) Adj. R-Square 0.84 0.86 0.86 0.87 0.86 0.88 0.79 0.82 0.81 0.84 0.81 0.84 0.83 0.87 0.84 0.88 0.84 0.88 Obs. 1846 1846 1803 1803 1760 1760 1848 1848 1806 1806 1764 1764 1864 1864 1841 1841 1818 1818

Table 3 Bid-Ask Spread and Investor Sentiment Empirical Results: Part I Bid ask spread ( 104) Percentage bid ask spread ( 106) S&P500 Nasdaq100 DJIA S&P500 Nasdaq100 DJIA ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures ETFs Futures Intercept 41.48 1059.76 4.20 1713.23 109.35 5221.71 20.44 49.09 8.11 70.95 73.99 36.31 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) (0.00) High Sent. Dummy 6.78 523.04 2.46 481.82 39.43 2936.25 1.12 7.58 4.96 14.81 9.18 13.42 (0.12) (0.00) (0.02) (0.00) (0.00) (0.00) (0.78) (0.10) (0.05) (0.01) (0.33) (0.01) 0.24 10.26 0.01 9.51 0.41 65.30 -0.05 0.75 0.02 0.75 0.19 1.40 LAG1_RV ( 102) (0.08) (0.00) (0.24) (0.00) (0.02) (0.00) (0.50) (0.01) (0.74) (0.00) (0.22) (0.00) -0.81 78.81 -0.05 -404.39 -19.56 3219.00 -0.13 -8.49 -0.10 -144.98 -9.69 -241.75 LAG1_TV ( 10 3) (0.00) (0.13) (0.02) (0.40) (0.00) (0.62) (0.31) (0.08) (0.18) (0.00) (0.00) (0.00) LAG1_BAS 0.88 0.56 0.97 0.67 0.82 0.66 0.96 0.07 0.98 0.08 0.88 0.06 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) Adj. R-Square 0.89 0.72 0.97 0.69 0.78 0.76 0.92 0.80 0.97 0.81 0.81 0.83 Obs. 2,072 1,754 2,216 1,889 1,991 1,748 2,072 1,754 2,216 1,889 1,991 1,748

Empirical Results In summary, this paper finds adequate evidence showing that investor sentiment is positively correlated with the realized volatility and bid-ask spread. It is expected that the higher trading risk and cost caused by high sentiment to deter informed traders from trading on the futures market, which in turn diminishes the leading role of the futures market. 17

Table 4 VECM estimation of ETFs and E-mini Futures of S&P 500 Baseline D=1 if sentiment < 25th pctl. D=1 if sentiment > 50th pctl. D=1 if sentiment > 75th pctl. D(ETFs(-1)) D(ETFs(-2)) D(ETFs(-3)) D(Futures(-1)) D(Futures(-2)) D(Futures(-3)) C D(ETFs(-1))*Dummy D(ETFs(-2))*Dummy D(ETFs(-3))*Dummy D(Futures(-1))*Dummy D(Futures(-2))*Dummy D(Futures(-3))*Dummy Adj. R-square Sum sq. resids Akaike AIC ETFs 0.574 [ 237.60] 0.419 [ 145.61] 0.297 [ 99.23] 0.579 [258.48] 0.434 [155.74] 0.307 [104.41] Futures 0.138 [52.95] 0.104 [33.43] 0.072 [22.36] 0.167 [ 69.02] 0.115 [ 38.09] 0.082 [ 25.87] 0.006 0.240 12.247 [ 177.29] 0.396 [ 108.09] 0.273 [ 71.56] [185.85] [113.17] [74.25] [ 1.14] 0.066 [ 13.17] 0.054 [ 8.93] 0.058 [ 9.28] [20.02] [12.44] [11.23] 12.404 ETFs 0.546 Futures 0.157 [47.27] 0.114 [28.73] 0.082 [19.87] 0.186 [ 59.03] 0.123 [ 31.81] 0.089 [ 21.93] 0.000 [ 0.83] 0.046 [ 8.39] 0.024 [ 3.67] 0.026 [ 3.80] 0.045 [9.18] 0.020 [3.23] 0.017 [2.60] 0.007 0.240 12.247 [ 188.61] 0.442 [ 116.25] 0.321 [ 81.53] [208.79] [125.56] [85.83] [ 1.10] [12.01] [8.79] [9.31] 0.055 [ 11.96] 0.053 [ 9.33] 0.055 [ 9.15] 12.403 ETFs 0.599 Futures 0.129 [37.46] 0.103 [25.20] 0.069 [16.27] 0.165 [ 53.08] 0.119 [ 30.13] 0.085 [ 20.36] 0.000 [ 0.80] 0.022 [4.17] 0.002 [ 0.24] 0.003 [0.46] 0.005 [ 1.05] 0.012 [1.87] 0.009 [1.38] 0.007 0.240 12.247 [ 219.53] 0.435 [ 135.69] 0.313 [ 93.93] [241.69] [146.99] [99.34] [ 1.10] [13.05] [11.56] [10.73] 0.079 [ 13.15] 0.099 [ 13.57] 0.088 [ 11.54] 12.403 ETFs 0.590 Futures 0.133 [45.66] 0.102 [29.43] 0.069 [19.04] 0.168 [ 63.42] 0.113 [ 34.00] 0.083 [ 23.37] 0.000 [ 0.81] 0.021 [3.02] 0.005 [0.59] 0.009 [1.03] 0.002 [0.33] 0.002 [ 0.28] 0.005 [0.58] 0.006 0.240 12.247 0.542 0.601 0.593 0.406 0.457 0.454 0.280 0.331 0.325 0.000 0.000 0.000 0.059 0.083 0.051 0.086 0.056 0.083 0.091 0.071 0.068 0.074 0.205 12.403 0.074 0.205 0.074 0.205 0.074 0.205

Table 5 VECM estimation of ETFs and E-mini Futures of Nasdaq 100 D(ETFs(-1)) D(ETFs(-2)) D(ETFs(-3)) D(Futures(-1)) D(Futures(-2)) D(Futures(-3)) C D(ETFs(-1))*Dummy D(ETFs(-2))*Dummy D(ETFs(-3))*Dummy D(Futures(-1))*Dummy D(Futures(-2))*Dummy D(Futures(-3))*Dummy Adj. R-square Sum sq. resids Akaike AIC Baseline D=1 if sentiment < 25th pctl. ETFs 0.519 [ 198.15] 0.368 [ 121.96] 0.255 [ 82.03] 0.595 [227.09] 0.426 [134.81] 0.293 [88.50] 0.000 [ 2.28] 0.056 [ 13.34] 0.036 [ 7.45] 0.037 [ 7.29] 0.109 [25.93] 0.092 [17.54] 0.068 [12.27] 0.103 0.326 11.941 D=1 if sentiment > 50th pctl. ETFs 0.560 [ 204.82] 0.397 [ 124.50] 0.284 [ 86.82] 0.652 [238.24] 0.480 [141.47] 0.338 [94.42] 0.000 [ 2.23] 0.044 [10.71] 0.032 [6.74] 0.036 [7.33] 0.045 [ 10.97] 0.052 [ 10.26] 0.048 [ 9.12] 0.102 0.326 11.939 D=1 if sentiment > 75th pctl. ETFs 0.542 [ 225.78] 0.385 [ 137.75] 0.275 [ 95.69] 0.636 [263.52] 0.467 [156.60] 0.325 [103.80] 0.000 [ 2.24] 0.004 [0.92] 0.007 [1.42] 0.021 [3.92] 0.011 [ 2.45] 0.032 [ 5.82] 0.032 [ 5.51] 0.102 0.326 11.939 ETFs 0.540 [ 265.02] 0.382 [ 161.50] 0.268 [ 110.19] 0.631 [309.64] 0.455 [182.07] 0.315 [119.80] 0.000 [ 2.19] Futures 0.093 [45.64] 0.057 [23.95] 0.034 [14.16] 0.119 [ 58.26] 0.068 [ 27.22] 0.044 [ 16.72] 0.000 [ 1.34] 0.004 0.327 11.937 Futures 0.098 [37.32] 0.054 [17.73] 0.035 [11.37] 0.119 [ 45.38] 0.066 [ 20.77] 0.042 [ 12.64] 0.000 [ 1.32] 0.013 [ 3.00] 0.009 [1.86] 0.001 [ 0.28] 0.004 [ 0.84] 0.006 [ 1.20] 0.009 [ 1.69] 0.004 0.327 11.937 Futures 0.089 [32.39] 0.060 [18.87] 0.036 [10.91] 0.128 [ 46.60] 0.073 [ 21.48] 0.048 [ 13.55] 0.000 [ 1.31] 0.009 [2.14] 0.009 [ 1.84] 0.004 [ 0.75] 0.017 [4.22] 0.011 [2.21] 0.010 [1.89] 0.004 0.327 11.937 Futures 0.101 [42.02] 0.065 [23.42] 0.038 [13.35] 0.137 [ 56.79] 0.078 [ 26.22] 0.053 [ 16.82] 0.000 [ 1.31] 0.030 [ 6.64] 0.030 [ 5.69] 0.013 [ 2.48] 0.061 [13.35] 0.033 [6.01] 0.028 [4.81] 0.005 0.327 11.937 0.102 0.326 11.939

Table 6 VECM estimation of ETFs and E-mini Futures of DJIA Baseline D=1 if sentiment < 25th pctl. D=1 if sentiment > 50th pctl. D=1 if sentiment > 75th pctl. D(ETFs(-1)) D(ETFs(-2)) D(ETFs(-3)) D(Futures(-1)) D(Futures(-2)) D(Futures(-3)) C D(ETFs(-1))*Dummy D(ETFs(-2))*Dummy D(ETFs(-3))*Dummy D(Futures(-1))*Dummy D(Futures(-2))*Dummy D(Futures(-3))*Dummy Adj. R-square Sum sq. resids Akaike AIC ETFs Futures [ 188.79] 0.365 [ 112.48] 0.251 [ 75.00] [194.34] [112.04] [74.27] [ 0.35] 0.107 [ 23.10] 0.091 [ 16.69] 0.076 [ 13.43] [28.88] [20.13] [14.32] 12.436 ETFs Futures [ 207.69] 0.437 [ 125.07] 0.308 [ 84.99] [220.56] [127.41] [84.86] [ 0.32] [21.75] [16.36] [12.14] 0.093 [ 21.71] 0.083 [ 16.28] 0.062 [ 11.82] 12.436 ETFs Futures [ 240.00] 0.418 [ 144.06] 0.296 [ 98.34] [255.68] [147.50] [98.23] [ 0.33] [20.38] [15.54] [13.21] 0.138 [ 25.36] 0.119 [ 18.82] 0.094 [ 14.49] 12.436 ETFs Futures 0.573 [ 257.60] 0.398 [ 153.54] 0.277 [ 103.35] 0.572 [271.04] 0.391 [155.66] 0.270 [103.00] 0.000 [ 0.30] 0.072 [30.56] 0.050 [18.36] 0.033 [11.59] 0.079 [ 35.69] 0.056 [ 20.99] 0.037 [ 13.41] 0.000 [ 0.28] 0.002 0.213 12.329 0.532 0.081 [27.13] 0.049 [14.17] 0.030 [8.43] 0.090 [ 31.70] 0.054 [ 16.28] 0.032 [ 9.30] 0.000 [ 0.28] 0.021 [ 4.23] 0.006 [0.96] 0.007 [1.23] 0.027 [5.90] 0.004 [ 0.77] 0.014 [ 2.35] 0.002 0.213 12.329 0.616 0.060 [19.11] 0.047 [12.79] 0.034 [8.88] 0.074 [ 25.40] 0.057 [ 16.14] 0.042 [ 11.30] 0.000 [ 0.26] 0.028 [5.86] 0.005 [0.97] 0.005 [ 0.91] 0.013 [ 2.92] 0.005 [0.97] 0.014 [2.46] 0.002 0.213 12.329 0.594 0.063 [24.18] 0.048 [15.61] 0.032 [9.94] 0.074 [ 30.02] 0.053 [ 17.87] 0.038 [ 12.19] 0.000 [ 0.27] 0.045 [7.53] 0.011 [1.62] 0.002 [0.23] 0.033 [ 5.76] 0.010 [ 1.54] 0.006 [0.86] 0.002 0.213 12.329 0.525 0.612 0.600 0.354 0.429 0.417 0.243 0.300 0.290 0.000 0.000 0.000 0.098 0.117 0.086 0.102 0.066 0.089 0.125 0.106 0.079 0.086 0.191 0.085 0.191 12.435 0.086 0.191 0.086 0.191

Empirical Results Tables 4 to 6 support Hypothesis 1 that the leading role of the futures market is weakened during high investor sentiment periods. This indicates that the informed and/or arbitrageurs are reluctant to trade when the noise trading risk is particularly high. 21

Table 8 Regression Analysis of the Information Shares on Investor Sentiment Dependent variable: Midpoint of information shares for the E-mini futures S&P500 Nasdaq100 DJIA (1) (2) (3) (4) (5) (6) (7) (8) (9) Intercept 0.212 0.506 0.558 0.457 0.556 0.622 0.421 0.563 0.672 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) High Sent. Dummy 0.104 0.044 0.005 0.004 0.047 0.048 0.129 0.114 0.047 (0.00) (0.00) (0.43) (0.56) (0.00) (0.00) (0.00) (0.00) (0.00) MS 0.366 0.345 0.253 (0.00) (0.00) (0.00) SR 0.029 0.048 0.010 (0.00) (0.00) (0.00) TV ( 10 7) 0.953 1.087 9.360 (0.00) (0.01) (0.00) RV 0.037 0.016 0.085 0.030 0.040 0.072 0.053 0.050 0.004 (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.79) Adj. R-Square 0.14 0.09 0.13 0.24 0.06 0.08 0.14 0.19 0.14 Obs. 1,846 2,207 1,846 1,644 1,878 1,644 1,784 2,062 1,784

Table 9 Regression Analysis of the GG Factor Weights on Investor Sentiment Dependent variable: GG factor weights for the E-mini futures S&P500 Nasdaq100 DJIA (1) (2) (3) (4) (5) (6) (7) (8) (9) Intercept 0.083 0.478 0.538 0.730 0.780 0.798 0.083 0.416 0.615 (0.38) (0.00) (0.00) (0.00) (0.00) (0.00) (0.37) (0.00) (0.00) High Sent. Dummy 0.123 0.025 0.021 0.025 0.094 0.102 0.229 0.183 0.053 (0.00) (0.27) (0.44) (0.34) (0.00) (0.00) (0.00) (0.00) (0.07) MS 0.494 0.292 0.530 (0.00) (0.00) (0.00) SR 0.036 0.064 0.016 (0.00) (0.00) (0.00) 0.188 6.070 18.059 TV ( 10 7) (0.48) (0.00) (0.00) RV 0.045 0.022 0.019 0.153 0.140 0.249 0.073 0.059 0.005 (0.11) (0.28) (0.62) (0.00) (0.00) (0.00) (0.01) (0.00) (0.90) Adj. R-Square 0.014 0.008 0.001 0.053 0.029 0.053 0.055 0.061 0.057 Obs. 1,889 2,264 1,889 1,890 2,265 1,890 1,887 2,181 1,887

Empirical Results The results reported above support our Hypothesis 2 that the prices on the futures market become less informative during high investor sentiment periods. This study is in line with Shleifer and Vishny (1997) and Barberis, Shleifer, and Vishny (1998) that informed traders will avoid exposing themselves to extreme risk during high sentiment periods. 24

Conclusion Investor sentiment has a positive impact on both price volatility and bid-ask spread. The significantly weaker when investor sentiment is high. leading role of futures market becomes The information shares of futures market have a negative relation with investor sentiment. 25

Thank you. 26