Investor Sentiment and Price Discovery: Evidence from the Pricing Dynamics

between the Futures and Spot Markets

SWJTU, Chengdu, 2015

Robin K. ChouNational Chengchi University, Taiwan 

Chu Bin LinNational Chengchi University, Taiwan

George H.K. WangGeorge Mason University, United States

 

2

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 are contemporaneously correlated and not cross-autocorrelated (Hasbrouck, 1995; Chan, 1992).

However, if one market reacts to new information faster than the other, an asymmetric lead–lag relation is observed (Chan, 1992).

3

Introduction

Spot Futures

Frictionless world

4

Introduction

Spot Futures

Real world

5

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; Käppi, 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).

6

Introduction

Spot Futures

Lead-lag relation

Investor sentiment

7

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.

8

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 strategies on 11 market anomalies and find that each anomaly is stronger following high levels of sentiment but little following low levels of sentiment.

9

Introduction

Sentiment

Price volatility

Bid-ask spread

Noise trader risk(+)

(+)

(+)

10

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.

11

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.

12

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).

13

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).

Informativeness measure:

(1) Information shares (Hasbrouck, 1995), and

(2) Factor weights (Gonzalo and Granger, 1995)

Empirical Results

Empirical Results: Part I

Table 2 Realized volatility and investor sentiment Dependent Variable: Realized Volatility

S&P500 Nasdaq100 DJIA

(1) (2) (3) (4) (5) (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 -369.901 1.209 367.134 1.313 486.166

(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) (0.03) (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

Empirical Results: Part ITable 3 Bid-Ask Spread and Investor Sentiment

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)

LAG1_RV (× 102) 0.24 10.26 0.01 9.51 0.41 65.30 -0.05 0.75 0.02 0.75 0.19 1.40

(0.08) (0.00) (0.24) (0.00) (0.02) (0.00) (0.50) (0.01) (0.74) (0.00) (0.22) (0.00)

LAG1_TV (× 10−3) -0.81 78.81 -0.05 -404.39 -19.56 3219.00 -0.13 -8.49 -0.10 -144.98 -9.69 -241.75

(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

17

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.

Baseline D=1 if sentiment < 25th pctl. D=1 if sentiment > 50th pctl. D=1 if sentiment > 75th pctl.

ETFs Futures ETFs Futures ETFs Futures ETFs Futures

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

Table 4VECM 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.

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

Table 5VECM estimation of ETFs and E-mini Futures of Nasdaq 100

Baseline D=1 if sentiment < 25th pctl. D=1 if sentiment > 50th pctl. D=1 if sentiment > 75th pctl.

ETFs Futures ETFs Futures ETFs Futures ETFs Futures

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

Table 6VECM estimation of ETFs and E-mini Futures of DJIA

21

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.

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 8 Regression Analysis of the Information Shares 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)

TV (× 10−7) –0.188 6.070 –18.059

(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

Table 9 Regression Analysis of the GG Factor Weights on Investor Sentiment

24

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.

25

Conclusion

Investor sentiment has a positive impact on both price volatility and bid-ask spread.

The leading role of futures market becomes significantly weaker when investor sentiment is high.

The information shares of futures market have a negative relation with investor sentiment.

26

Thank you.