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Structural vector autoregressive model (SVAR)

CHAPTER 3 : HYPOTHESES AND DATA

3.2 HYPOTHESIS DEVELOPMENT AND MODEL SPECIFICATION

3.2.3 Structural vector autoregressive model (SVAR)

This study will employ a structural vector-auto-regression (SVAR) model of index futures returns and sentiment, modified from the VAR model introduced by Tetlock (2007). This model will include the contemporaneous effect (same day) and up to 5 previous days for all variables.

Brown and Cliff (2004) find a contemporaneous relationship between sentiment measures and market returns for weekly data, only one lag of returns is included in the regressions because the autocorrelation in returns is relatively small and dies out quickly. In this study, the rationale for the contemporaneous relationship is about the timing of the market events and news going public. Investors read newspapers in the morning comprehend yesterday’s events and form today’s sentiment. It is likely that trading decisions are influence by the information gather in the morning and reflect on the trading activity data on the same day.

I estimate a three variables SVAR model to test the hypotheses. The specification of the model as follows:

𝑁𝑁𝑑𝑑 =𝛼𝛼1+βˆ‘5𝑖𝑖=1𝛽𝛽1π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛾𝛾1π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛿𝛿1π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘14𝑗𝑗=1πœ†πœ†1𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€1𝑑𝑑 (3.1)

𝑅𝑅𝑑𝑑 =𝛼𝛼2+βˆ‘5𝑖𝑖=0𝛽𝛽2π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=1𝛾𝛾2π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛿𝛿2π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘14𝑗𝑗=1πœ†πœ†2𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€2𝑑𝑑 (3.2)

𝛾𝛾𝑑𝑑 =𝛼𝛼3+βˆ‘5𝑖𝑖=0𝛽𝛽3π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛾𝛾3π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=1𝛿𝛿3π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘14𝑗𝑗=1πœ†πœ†3𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€3𝑑𝑑 (3.3)

where

𝑅𝑅𝑑𝑑= Daily returns of the Hang Seng Index Futures (HSIF), Kuala Lumpur Composite Index

Futures (KLCIF) and Morgan Stanley Singapore Free Index Futures (SiMSCIF) on day t.

𝑁𝑁𝑑𝑑= News factor score obtain by performing principal component analysis (PCA) for day t.

The GI category variables are demeaned by day of week using the prior year mean to ensure the media factor generated in PCA does not systematically capture the day of the week variation in the news. The sources of news are Wall Street Journal Asia, New Straits Times, South China Morning Post and The Straits Times.

𝛾𝛾𝑑𝑑= Detrended log volume obtain by subtract a 60-day backward moving average15 for day

t. The volume of HSIF, KLCIF and SiMSCIF are proxy by the number of contract traded and open interest at market close.

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗=Exogenous variables.

Equation (3.1) tests hypotheses 1, I expect the 𝛾𝛾1𝑖𝑖to be negative because reporters

tend to use more optimistic (pessimistic) words when past returns are high (low). Equation (3.2) tests Hypotheses 2 to 5, in which, I expect 𝛽𝛽2𝑖𝑖 to be negative when i= 0 and 1, and

positive when i=3, 4, and 5. This is based on the sentiment argument that highly pessimistic news lead to lower returns, but soon investors will realise that they have overreacted and the prices will reverse.

I estimate a four variables SVAR model to test Hypotheses 6 and 7. The specification of the model as follows:

𝑁𝑁𝑑𝑑=𝛼𝛼1+βˆ‘5𝑖𝑖=1𝛽𝛽1π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0πœƒπœƒ1𝑖𝑖|π‘π‘π‘‘π‘‘βˆ’π‘–π‘–| +βˆ‘π‘–π‘–=05 𝛾𝛾1π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛿𝛿1π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘π‘—π‘—=114 πœ†πœ†1𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€1𝑑𝑑 (3.4)

|𝑁𝑁𝑑𝑑| =𝛼𝛼2+βˆ‘5𝑖𝑖=0𝛽𝛽2π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=1πœƒπœƒ2𝑖𝑖|π‘π‘π‘‘π‘‘βˆ’π‘–π‘–| +βˆ‘5𝑖𝑖=0𝛾𝛾2π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛿𝛿2π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘14𝑗𝑗=1πœ†πœ†2𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€2𝑑𝑑 (3.5) 𝑅𝑅𝑑𝑑=𝛼𝛼3+βˆ‘5𝑖𝑖=0𝛽𝛽3π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0πœƒπœƒ3𝑖𝑖|π‘π‘π‘‘π‘‘βˆ’π‘–π‘–| +βˆ‘π‘–π‘–=15 𝛾𝛾3π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0𝛿𝛿3π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘π‘—π‘—=114 πœ†πœ†3𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€3𝑑𝑑 (3.6) 𝛾𝛾𝑑𝑑=𝛼𝛼4+βˆ‘5𝑖𝑖=0𝛽𝛽4π‘–π‘–π‘π‘π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=0πœƒπœƒ4𝑖𝑖|π‘π‘π‘‘π‘‘βˆ’π‘–π‘–| +βˆ‘π‘–π‘–=05 𝛾𝛾4π‘–π‘–π‘…π‘…π‘‘π‘‘βˆ’π‘–π‘–+βˆ‘5𝑖𝑖=1𝛿𝛿4π‘–π‘–π›Ύπ›Ύπ‘‘π‘‘βˆ’π‘–π‘–+βˆ‘π‘—π‘—=114 πœ†πœ†4𝑗𝑗𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝑗𝑗+πœ€πœ€3𝑑𝑑 (3.7)

15 This is to transform the trading volume and open interest into a stationary time series. Campbell, et al. (1993) and Fung and Patterson (1999) employ the same method, but 100-day backward moving average is used. Fung and Patterson (1999) have also tried with 20-day backward moving average, and yield similar results.

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I expect 𝛽𝛽4𝑖𝑖 to be negative because highly optimistic (pessimistic) news implies over- confidence, causing the liquidity and trading volume to increase (decrease) sharply. I expect πœƒπœƒ4𝑖𝑖to be positive because both optimistic and pessimistic news triggers buying and selling between the non-information and the risk-averse utility maximisers that increase trading volume.

Index futures returns, bad news factors and volume are endogenous variables in these two SVAR systems. I calculate close-to-close returns (log ( 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑠𝑠

𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,π‘ π‘ βˆ’1)). The volume is measure in number of contracts traded daily and daily open interest. Volume series usually contain trend component and are non-stationary. I employ a simple detrending method to address these issues. I subtract a 60-day backward moving average from the log volume series, which is similar to the geometrically declining average of volume growth rates.

EXOG represents all exogenous variables. The exogenous variables are five lags of the detrended squared index futures residuals to proxy for volatility (j=1 to j=5); dummy variable for Chinese New Year effect (j=6); dummy variable for 1997 Asian financial crisis (j=7); dummy variable for 2008 Wall Street financial meltdown (j=8); dummy variable for January effect (j=9); dummy variables for day-of-the-week effect (Monday to Thursday, i.e. j=10 to j=13); and finally dummy variables for four days prior to settlement date and inclusive the settlement day (i.e. j=14 to j=17).

I calculate the proxy for volatility as follows. Firstly, the variable Rt will be regressed on

12 lags of Rt to obtain a residual. The residual is then squared, and a past 60-day moving

average of the squared residual is subtracted from the squared residual16.

Yen, Lee, Chen and Lin (2001) confirm the existence of a Chinese New Year effects in Hong Kong, Japan, South Korea, Malaysia, Singapore and Taiwan. The study finds a consistent up-moving trend from 15 days before Chinese New Year and lasts up to 15 days after that. A dummy variable will be created and 1 will be assigned to 15 days before and after Chinese New Year, and 0 for other days. Table 3.1 lists the month and date for Chinese New Year from 1995 to 2008.

Table 3.1Chinese New Year Days in the Gregorian Calendar

Year Month Date

1995 January 31 1996 February 19 1997 February 7 1998 January 28 1999 February 16 2000 February 5 2001 January 24 2002 February 12 2003 February 1 2004 January 22 2005 February 9 2006 January 29 2007 February 18 2008 February 7

Lean, Smyth and Wong (2007) find evidence of weekday effect and January effect in Hong Kong, Malaysia and Singapore Market. I create dummy variables for Monday, Tuesday, Wednesday, Thursday, and the month of January.

16 Tetlock (2007) define the trend as 60-day moving average; Ciner (2006) define the trend as 200-day moving average and Bessembinder and Seguin (1992) define the trend as 100-day moving average. These studies conclude that the results are robust to the number of days used to calculate the trend.

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The onset of the 1997 and 2008 financial crises had a great impact on equity markets. The 1997 crisis period is refers to the period from August 1997 to December 1997, following Hassan, Mohamad, Ariff and Nasir (2007). In addition, the 2008 financial crisis refers to the period of October 2008 to December 2008, because the equity markets in the samples started to plunge from October 2008.

Trading volume is exceptionally high from about four days before the settlement date. Settlement date and four days prior settlement date equal to 1, and 0 for other days

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