The intraday behavior of information misreaction across various categories of investors in the Taiwan options market

Available online at www.sciencedirect.com

Journal of Financial Markets 16 (2013) 362–385 www.elsevier.com/locate/finmar

The intraday behavior of information misreaction across various categories of investors in the Taiwan options market$ Chuang-Chang Changa, Pei-Fang Hsiehb, Chih-Wei Tanga, Yaw-Huei Wangc,n a Department of Finance, National Central University, Taoyuan 32001, Taiwan Department of Quantitative Finance, National Tsing Hua University, Hsinchu 30013, Taiwan c Department of Finance, National Taiwan University, Taipei 10617, Taiwan

b

Received 9 November 2011; received in revised form 28 September 2012; accepted 29 September 2012 Available online 1 November 2012

Abstract This study adopts a unique dataset that includes the complete history of transactions in the Taiwan options market to investigate the misreaction patterns for marketwise observations and the transactions of four different categories of investors in the high-frequency framework. Using the results from model-free tests as benchmarks, we find that model-based tests incorrectly indicate the existence of investor misreaction and show the differences of misreaction degree among investor categories. Our findings are robust to alternative observation frequencies and duration definitions. & 2012 Elsevier B.V. All rights reserved. JEL classification: G14 Keywords: Options; Misreaction; Stochastic volatility; Model-free implied variance; Investors

$ We are indebted to the seminar participants at the Financial Management Association Annual Meeting 2011, the Australasian Finance and Banking Finance Conference 2010, the National Taiwan University International Conference on Finance 2010 and Tamkang University for helpful comments and suggestions. The authors are grateful to the National Science Council of Taiwan for the financial support provided for this study. n Corresponding author. E-mail addresses: [email protected] (C.-C. Chang), [email protected] (P.-F. Hsieh), [email protected] (C.-W. Tang), [email protected] (Y.-H. Wang).

1386-4181/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.finmar.2012.09.004

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

363

1. Introduction Over the past decade or two, misreaction by investors has come to be regarded as a plausible explanation for certain stock market anomalies, such as short- and mediumhorizon momentum, as well as long-term reversals. Numerous prior studies investigate both the stock markets1 and the options markets. However, while Stein (1989) and Poteshman (2001) use model-based approaches to support the existence of some misreaction patterns in the options markets, Jiang and Tian (2010) use a model-free approach to argue that these anomalies are the result of model misspecification rather than market misreaction. Therefore, using a sophisticated dataset that includes the complete history of transactions in the Taiwan options market, we utilize both model-based and model-free approaches to reexamine the issues of market misreaction in a high-frequency framework.2 Using the results from the model-free tests as benchmarks, we find that the mode-based tests proposed by Poteshman (2001) incorrectly indicate the existence of market misreaction in the Taiwan options market. Several studies argue that investors tend to underreact over short horizons and overreact over long horizons.3 Although many studies have examined misreaction by stock market investors, an understanding of misreaction in the options markets is still quite limited. Investor misreaction is unlikely to be restricted to the stock markets alone as option markets provide informed traders several distinct advantages, such as higher leverage, lower margin, and volatility trading (Black, 1975; Mayhew, Sarin, and Shastri, 1995; Easley, O’Hara, and Srinivas, 1998; Chakravarty, Gulen, and Mayhew, 2004; Pan and Poteshman, 2006). For example, Stein (1989) finds the evidence of long horizon overreaction in the S&P 100 index options market and Poteshman (2001) finds the existence of short-horizon underreaction, long-horizon overreaction, and increasing misreaction in the S&P 500 index options market.4 However, these studies previously mentioned test for market misreaction by imposing particular dynamic processes for the price of the investigated asset, and therefore the results on a specific option pricing model. Jiang and Tian (2010) theoretically argue that the misreaction patterns found in previous studies are the inevitable consequences of model misspecification. They utilize a model-free approach to empirically reexamine the issues and find no evidence of market misreaction in the U.S. market. Therefore, whether market misreaction exists in options markets requires a more comprehensive investigation with an accurate methodology and a more sophisticated dataset.

1

Shleifer (2000) provides a review of the studies investigating stock market investor misreaction. Each transaction or order record contains a trader account number, artificial identification number, trader category indicator, strategy type, price, quantity, buy–sell indicator, product type, strike price, and time-toexpiration. 3 See, for example, Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer, and Subrahmanyam (1998), and Hong and Stein (1999). In particular, Barberis, Shleifer, and Vishny (1998) argue that underreaction is driven by conservatism and overreaction is attributable to an important heuristic that they referred to as ‘‘representativeness’’. The conservatism theory suggests that investors cling too firmly to prior beliefs and thus tend to underreact to a single piece of information, and the representativeness heuristic argument suggests that investors too readily find patterns in information and hence overreact to largely similar information. Barberis, Shleifer, and Vishny (1998) suggest that the interactions between investors’ short-horizon conservatism and long-horizon representativeness lead to increasing misreaction in the stock markets. 4 Cao, Li, and Yu (2005) study S&P 500 index options and long-dated S&P 500 leaps and have similar findings. 2

364

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

Although prior literature explores some issues related to market misreaction in the U.S. options markets, whether misreaction is discernible among investors in less matured markets, particularly those with a high participation rate of individual investors, remains an open question. Furthermore, because prior studies invariably adopt daily data, a strong assumption exists that investors attend to changes in information only once each day.5 Thus, the use of daily data can clearly hinder attempts to examine the instantaneous reactions of investors on receipt of certain information and subsequently the ways in which investors dynamically adjust following these reactions. We fill these gaps in the literature by investigating the issue of investor misreaction using a comprehensive record of all transactions in the Taiwan options markets with both Jiang and Tian’s (2010) model-free approach and Poteshman’s (2001) model-based approach. Thus, different from previous studies, we provide greater insights into the issues under investigation by exploring the transactions of different categories of investors in a less mature market with two different types of approaches using the high-frequency framework.6 In addition to providing further and more accurate evidence on how investors react to new information, our findings on the options market of Taiwan may also have important implications for other developing markets with similar characteristics, such as a high turnover rate and a high participation rate by individual investors.7 Our empirical investigation involves marketwise observations, along with the examination of the transactions undertaken by four different categories of investors (domestic institutional, foreign institutional, individual, and market makers).8 Our empirical results are summarized as the following. First, the model-based tests suggested by Poteshman (2001) indicate the existence of short-horizon underreaction and lead to incorrect conclusions, whereas the model-free tests show that investor misreaction does not exist in the Taiwan options market. This finding calls into question the validity of volatility anomalies identified in previous studies that use a model-based approach because the results are based on joint tests of market reaction and model specification. Second, employing the model-based approach to implement further tests, we find no evidence of long-horizon overreaction. The inconsistent results between short-horizon underreaction and long-horizon overreaction from the model-based tests again cast doubt on the validity of the model specification employed in previous studies. Our results do not rely on whether we investigate the marketwise observations or the transactions of various investor categories and are robust to different sampling frequencies and also to different maturity definitions of short- and long-term options. This empirical study contributes to the literature in several aspects. First, we use a correct (model-free) approach to re-investigate the issues on investor misreaction by examining the impact of volatility shocks on the relative pricing of long-term versus shortterm options in the high-frequency framework. Second, we clarify the mixed results found 5 Such an assumption may, of course, be far from the real-world situation, particularly nowadays, as technology is vastly improving the flow of information and the transaction times. 6 The Taiwan options market is typical of Asian or emerging financial markets, in which individual investors are the majority of traders and the dynamic of market prices is largely influenced by foreign capital flows. Chang, Hsieh, and Lai (2009) provide details of the characteristics of Taiwan options market. 7 According to statistics published by the Taiwan Stock Exchange, individual investors accounted for about 68% of all transactions in 2005, domestic institutional investors accounted for about 13%, and foreign investors accounted for about 17%. The total turnover rate in the Taiwan stock market in 2005 was about 127%. 8 Several studies report the existence of certain sophisticated investors who are capable of making profits in either the Taiwan stock or options markets (e.g., Barber, Lee, Liu, and Odean 2007; Mahani and Poteshman, 2008; Chang, Hsieh, and Lai, 2009; Han, Lee, and Yu, 2010).

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

365

in previous studies by documenting the patterns of investor misreaction in the Taiwan options market with a very sophisticated dataset including the complete record of transactions and orders. Third, we confirm that the model-based approach, which depends on the specification of option pricing models, leads to unreliable conclusions. The remainder of this paper is organized as follows. A description of the data used for our empirical investigation is provided in Section 2, followed in Section 3 by details of the empirical methods adopted for this study. The empirical results are presented in Section 4, followed by some tests for robustness in Section 5. Finally, the conclusions drawn from this study are presented in Section 6. 2. Data description The primary dataset for our empirical investigation consists of a comprehensive record of all options transactions written on the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX). These TAIEX options contracts are traded on the Taiwan Futures Exchange (TAIFEX) with a ticker symbol of TXO. Our dataset is obtained directly from the TAIFEX and contains a highly detailed history of transactions, including the identification of traders, the characteristics of the contracts, and the transaction contents. A complete record of transactions in TAIEX futures is also obtained from the TAIFEX. We are motivated to study TAIEX options due to the availability of a comprehensive and sophisticated dataset and because the Taiwanese market shares several common characteristics with other developing markets, such as a high turnover rate and a high participation rate by individual investors.9 These characteristics differ markedly from those of the major U.S. and European option markets. Therefore, in addition to providing greater insights into the issues under investigation, our findings on the Taiwan market may also have important implications for other developing markets. Our dataset covers all trading dates from January 2, 2002 to December 31, 2005, as well as maturity months from January 2002 to June 2006. Following similar standard datafiltering criteria to those employed in prior studies (e.g., Aı¨ t-Sahalia and Lo, 1998; Poteshman, 2001), we exclude those contracts with a time-to-expiration period of less than six calendar days, essentially as a result of liquidity concerns, as well as those with a BlackScholes implied volatility level of lower than zero or higher than 0.7 to avoid extreme options prices.10 We also exclude in-the-money options, essentially because they are in general regarded as being less actively traded and thus less informative than corresponding out-of-the-money contracts.11 We use the same dataset in both the model-free and modelbased volatility estimations to compare the results from these two approaches. Due to the liquidity concern, we define short-maturity options as the most nearby contracts and long-maturity options as those contracts with other maturity dates.12 The 9 Based on the annual report and statistics at the website of the World Federation of Exchanges, the TAIEX index options and futures are two of the most actively traded derivatives in the world. The TAIFEX was ranked as having the fifth largest trading volume in the world in 2008. 10 Different from Poteshman (2001), we do not incorporate the criteria about bid–ask spreads because we use transaction prices. 11 Moneyness is defined as the ratio of the strike price over the corresponding futures price. 12 In the Taiwan options market, most investors trade the contracts with the first two nearby maturities only. During our sample period, these contracts take about 59.88% and 27.32% of trading volume, respectively. As the model-free approach requires the model-free implied variance calculated with a wide range of strikes, we exclude

366

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

risk-free rates (which are proxied by the three-month deposit rates) are obtained from the website of the Central Bank of Taiwan. Our intraday investigation is based on five-minute trading intervals, resulting in a total of 59,640 trading intervals.13 For each interval, we select all of the qualified contracts traded two minutes before the closing timestamp. Whenever necessary, we match every contract in our analysis with its corresponding futures price from the futures transaction dataset. The summary statistics for our final sample are presented in Table 1. The total number of observations on call options, 6,047,083, is much larger than the total number of observations on put options, 4,826,047. The average Black-Scholes implied volatility for call (put) options is 21.9% (23.1%). Furthermore, the time to maturity ranges between 6 and 212 days, and the moneyness ranges between 0.63 and 1.62. The general patterns of the summary statistics for every investor category are similar to those for the marketwise observations. To save space, we do not report the results here, but they are available on request. The comparison among investor categories shows that (a) foreign institutional investors clearly trade more put options, whereas individual investors trade more call options and (b) the positions of foreign (domestic) institutional investors exhibit the longest (shortest) average time to maturity, with the trading patterns obviously differing across different investor categories.

3. Methodology Our investigation, which follows the analysis framework of Jiang and Tian’s (2010) model-free approach and checks the validity of Poteshman’s (2001) model-based approach, focuses on the reaction to information by investors based on some variance sequences, which represent the corresponding series of options prices. The two approaches define investor misreaction differently between long- and short-maturity options with the estimates of the variance sequences and thus employ different procedures to estimate the required variance sequences. Therefore, in this section, we first define the model-free and model-based estimation frameworks and then describe how these frameworks measure investor misreaction. 3.1. Model-free estimation of implied variance Based on the framework of Jiang and Tian (2010), we take a model-free approach to estimate the implied variance sequences. Model-free implied volatility is extracted from option prices without using any option pricing model or assuming any process of the (footnote continued) the maturities with less than three strike prices, and, consequently, the contracts with maturities longer than the second nearby one are often not included in the long-maturity group for the model-free tests. Therefore, in our main analysis of the model-free tests, the long-maturity group includes the second nearby contracts only. Since the third nearby contracts take about 6.10% of trading volume, we are also capable of generating sufficient and reliable model-free variance information from the marketwise observations of the third nearby contracts. Therefore, for the robustness check, we also provide the model-free results based on defining the third nearby contracts as the long-maturity group for the marketwise analysis, but not for the cross-investor-category analysis. 13 We also implement the analysis based on the 15-minute, 30-minute, 60-minute, and 1-day frequencies. The results based on the 60-minute frequency will be reported and discussed in the robustness analysis.

Variables

Mean

S.D.

Min

Percentiles

Max

1%

10%

50%

90%

99%

Panel A: Calls (n ¼6,047,083) Price (NT$) B-S implied volatility Time to maturity (per year) Strike price Risk-free rate Moneyness

59.180 0.219 0.064 6,075 0.013 1.034

41.016 0.086 0.042 551 0.002 0.030

0.100 0.010 0.016 3,800 0.011 1.000

3.000 0.085 0.016 4,400 0.011 1.001

14.000 0.129 0.022 5,400 0.011 1.005

51.000 0.199 0.060 6,100 0.012 1.026

113.000 0.342 0.099 6,700 0.016 1.070

194.000 0.473 0.197 7,300 0.018 1.142

600.000 0.700 0.581 7,300 0.022 1.620

Panel B: Puts (n¼ 4,826,047) Price (NT$) B-S implied volatility Time to maturity (per year) Strike price Risk-free rate Moneyness

56.094 0.231 0.066 5,690 0.013 0.964

44.542 0.093 0.051 562 0.002 0.030

0.100 0.038 0.016 3,500 0.011 0.633

2.600 0.104 0.016 4,000 0.011 0.862

12.000 0.144 0.022 5,000 0.011 0.924

47.000 0.204 0.060 5,800 0.012 0.972

109.000 0.359 0.101 6,300 0.016 0.994

210.000 0.569 0.268 6,800 0.018 0.999

1,050.000 0.700 0.581 7,200 0.022 1.000

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

Table 1 Summary statistics for options. This table presents the summary statistics of the intraday (five-minute) observations on the full sample of options written on the Taiwan Stock Exchange Capitalization Weighted Stock Index, with the sample period running from January 2, 2002 to December 31, 2005. We exclude those contracts with a time-to-expiration period of less than six calendar days, those with a Black-Scholes (B-S) implied volatility of lower than zero or higher than 0.7, and those that are in-the-money, with moneyness defined as the ratio of the strike price to the corresponding futures price. We use the average three-month deposit rates as proxy for the risk-free rates, which are obtained from the website of Central Bank of Taiwan.

367

368

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

underlying asset price. Jiang and Tian (2010) define their model-free forward variance as    Z 1  Ct T2 ,K=Bðt,T2 Þ Ct T1 ,K=Bðt,T1 Þ 2 dK, ð1Þ vðt; T1 ,T2 Þ ¼ K2 T2 T1 0 where trT1 oT2 and the expectation is conditional on the information set at time t. vðt; T1 ,T2 Þ is a forward integrated variance over a future time period T1 to T2 measured at time t. Bðt,T Þ is the time t price of zero coupon bond that pays $1 at time T, and Ct ðT,K Þ is the time t price of a call option with strike price K and maturity date T. The model-free forward volatility is the squared root of the right-hand side of Eq. (1). The model-free spot variance is a special case of the model-free forward variance when T1 ¼ t and T2 ¼ T and formularized as  Z 1  Ct T,K=Bðt,T2 Þ maxf0,St K g 2 dK ð2Þ vðt; t,T Þ ¼ K2 Tt 0 where St is the price of the underlying asset at time t. To estimate the model-free variance sequences defined in Eqs. (1) and (2), we follow Jiang and Tian’s (2005) estimation procedure. First, we collect the qualified option prices Table 2 Summary statistics for model-free and model-based variances. This table presents the summary statistics of the estimated variances of Taiwan Stock Exchange Capitalization Weighted Stock Index using both the model-free and model-based approaches, with the sample period running from January 2, 2002 to December 31, 2005. The model-free measures include the model-free implied spot and forward variance. The vðt,T1 Þ and vðt,T2 Þ indicate the spot variances implied from options with time to maturities T1 and T2 , respectively. vðT1 ,T2 Þ is the forward variance implied from options with time to maturities T1 and T2 . T1 and T2 correspond to the most and second nearby maturity dates, respectively. The model-based instantaneous variance vt is the high-frequency series of instantaneous variance estimated from full sample by assuming the underlying asset and vShort are the high-frequency series of price follows the Heston (1993) stochastic volatility model. vLong t t instantaneous variance estimated from long- and short-maturity options, respectively. We define short-maturity options as the most nearby contracts and long-maturity options as those contracts with other maturity dates. Variance Panel A: Model-free implied variance Statistics Mean Median S.D. Skewness Kurtosis

vðt,T1 Þ 0.0636 0.0529 0.0410 1.1392 1.5307

vðt,T2 Þ 0.0470 0.0352 0.0315 1.6044 3.0546

vðT1 ,T2 Þ 0.0626 0.0511 0.0386 1.4309 2.7823

Panel B: Model-based instantaneous variance Statistics Mean Median S.D. Skewness Kurtosis

vt 0.0654 0.0524 0.0526 2.1859 8.4269

vLong t 0.0425 0.0280 0.0450 1.9822 6.7593

vShort t 0.0663 0.0521 0.0537 2.2071 8.3858

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

369

over an available finite range of strike prices at the five-minute frequency. Using the available contracts, we apply the cubic spline curve fitting approach to fit a smooth function of the Black-Scholes implied volatility across all observed strike prices.14 Second, we estimate the model-free variance sequences with a numerical integration method. The series of model-free variances are not only extracted from the marketwise observations but also individually from the transactions of the four categories of investors: domestic institutional, foreign institutional, individual, and market makers. We calculate model-free implied variance associated with two option maturities ½t,Ti  for i¼ 1 and 2, which, respectively, represent the nearby and second nearby option contracts for short- and long-maturity groups. Similarly, we calculate the forward variance associated with every pair of option maturities ½T1 ,T2 . Panel A of Table 2 describes the summary statistics of the high-frequency series of model-free implied variance. The average short-maturity spot variance is larger than long-maturity spot variance (6.36% vs. 4.70%, respectively). However, the distribution of long-maturity spot variance is more leptokurtic than that of short-maturity spot variance. 3.2. Model-based estimation of instantaneous variance In line with Poteshman (2001), we generate the instantaneous variance by assuming that the underlying asset price follows the Heston (1993) stochastic volatility model. See the Appendix for a full description of the model. The model is estimated from options prices based on a two-stage procedure. Because the model describes the dynamic process of the underlying asset price, the parameters should not rely on data frequency. Therefore, in the first stage, we use the weekly closing prices of the options over our sample period, selected on Wednesdays, and then generate the estimates of the risk-neutral parameters, kn , yn , Z, and r, by minimizing the sum of the squared option pricing errors.15 Essentially, the prices for a spot option and a futures option with the same underlying asset, maturity, and strike price should be identical if both contracts are European and the futures contract has the same expiration date as the options contract. As a result, to avoid the challenge of determining the underlying asset price and dividend yield separately, we replace the underlying asset with the futures contract under the assumption of spot-futures parity. The parameters estimated from our marketwise sample are kn ¼ 1.13, yn ¼ 0.12, Z ¼ 0.65, and r ¼ 0.64. Our parameter estimates except the long-term mean of volatility yn and the volatility of volatility Z are very close to those reported by Bakshi, Cao, and Chen (1997) for the S&P 500 index. In terms of volatility, the mean level for the Taiwan market is 0.35, while that for the U.S. market is only 0.20. Different from the situation in the U.S. market, individual investors are the majority of market participants in the Taiwan stock market. Indeed, the long-term mean level of volatility for this market is higher than that for a more mature one. Meanwhile, the volatility of volatility for the Taiwan stock market is also higher than that for the U.S. market, with a difference of about 0.26. 14 Beyond the maximum and minimum available strike prices, the option prices are replicated from the closest available strike prices to reduce truncation errors. 15 The marketwise sample for the first-stage estimation provides a total of 198 observations. Following Bakshi, Cao, and Chen (1997), we set the initial values of the parameters for estimation as k0n ¼ 1.15, yn0 ¼0.04, Z0 ¼0.39, and r0 ¼ 0.64.

370

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

Taking the parameter estimates as given, in the second stage we generate a highfrequency series of instantaneous variance within which each observation minimizes the cross-sectional sum of the squared pricing errors of the options at the corresponding timestamp. The series of instantaneous variance is generated on the basis of marketwise observations, as well as individually from the transactions undertaken by the four categories of investors. Let fvt g, t ¼ 1. . .T be the high-frequency series of instantaneous variance, where T is the total number of observations in our sample. Because the price dynamic of the underlying asset is correctly specified by the model, the change in instantaneous variance from trading time t1 to t can be decomposed into expected and unexpected elements, which are, respectively, denoted as Dvexpected and Dvunexpected and formulated as t t   Dvexpected ¼ vt1 ekt þ y 1ekt vt1 ð3Þ t and Dvunexpected ¼ ðvt vt1 ÞDvexpected , t t

ð4Þ

where t refers to the number of years of an observation interval. Given that the price dynamic of the underlying asset follows the Heston (1993) model, also follows Eq. (19) in Cox, Ingersoll, and Ross (1985). The the formula for Dvexpected t values of k and y follow the relation of kn ¼ k þ l and yn ¼ ky=ðk þ lÞ, respectively, with the parameters kn and yn being estimated in the first stage. Following Poteshman (2001), we assume that the volatility risk parameter is l ¼ kn =2.16 We use the same procedure to estimate the high-frequency series of short- and longhorizon instantaneous variances. Panel B of Table 2 describes the summary statistics of the high-frequency series of model-based instantaneous variance. The average instantaneous variance at the five-minute frequency is 6.54%; the average long-maturity instantaneous variance is smaller and its distribution is less fat tailed than that of short-maturity instantaneous variance. 3.3. Model-free and model-based estimations of investor misreaction Jiang and Tian (2010) and Poteshman (2001) detect investor misreaction differently. In the section, we detail how they measure investor misreaction. Jiang and Tian’s (2010) model-free approach measures the spot and forward variance directly from option prices without making any specific model specification or assumptions. The model-free approach investigates whether long-maturity implied volatility overreacts to changes in shortmaturity implied volatility, which is based on the error of using the forward variance proxy to forecast the corresponding future spot variance. The forecasting error is defined as       Dvt T1, T2 ¼ v T1, T2 ^v t; T1, T2 , ð5Þ   where v T1, T2 is the spot variance at time T1 with maturity date T2 and calculated using Eq. (2), and v^ t; T1, T2 is a proxy for forward variance constructed from the corresponding   long- and short-maturity spot variances and calculated by Eq. (1). Therefore, Dvt T1, T2 16

Poteshman (2001) also shows the robustness of alternative settings such as l¼ 0 and l¼ k*; the results are essentially unchanged.

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

371

indicates the forecasting error measured by the difference between forward variance of maturities ½T1 ,T2  at time t and the real spot variance of maturity T2 at time T1 . As in Poteshman (2001), the variable FarMisProjt measures the extent to which the unexpected change in instantaneous variance, from trading time t1 to t, is overprojected into the distant future. This variable is defined as    FarMisProjt  sign Dvunexpected DvShort DvLong ð6Þ t t t  Short  Dvt is the change in the instantaneous variance, from trading time t1 where DvLong t to t, for long- (short-) maturity options. Poteshman (2001) argues that if the Heston (1993) option pricing model is appropriate, the change in prices measured in instantaneous variance should be exactly the same. On the contrary, a positive FarMisProjt (negative) indicates that the current unexpected change in instantaneous variance is positive (negative). That is, when the current changes in instantaneous variance for long-maturity options are greater (less) than those for short-maturity options, the projection is made too far (less) into the distant future. As defined, FarMisProjt increases the extent to which investors misproject the unexpected changes in instantaneous variance into the distant future. Therefore, if investors underreact to the unexpected changes in instantaneous variance, FarMisProjt will decrease with the magnitude of the unexpected change in instantaneous variance. Thus, we can determine whether investors exhibit a short-horizon underreaction by investigating the relation between FarMisProjt and jDvunexpected j. t Stein (1989) successfully showed the long-horizon overreaction of investors by demonstrating that the prices of long-maturity options were too high. If such overreaction does exist, we would expect to find a positive relation between the level of instantaneous variance and the difference between the changes in instantaneous variance for longmaturity options and short-maturity options. Therefore, Poteshman (2001) also uses VtLong VtShort to explore the negative relation of long-horizon overreaction. 4. Empirical results Unlike prior studies, we use intraday data rather than daily data to investigate investor misreaction to information. Consequently, we can provide potentially greater insights into the issue of investor misreaction, particularly considering the current availability of technology-assisted trading as investors are able to trade on their information promptly. Our investigation is based on the marketwise viewpoint, as well as on the level of alternative investor categories (domestic institutional, foreign institutional, individual, and market makers). It is clear that the model-based approach is subject to the model specification. In addition, the estimation method proposed by Poteshman (2001) has some shortcomings. For example, it does not consider whether or not the market prices of options with different strikes or maturities are correlated. Moreover, the results can be severely impaired by parameter misestimation since the shock in the instantaneous variance can be correctly inferred only when kn is estimated accurately. Therefore, in our empirical analysis, we use the results from the model-free approach as benchmarks to check whether

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

372

the model-based approach can generate consistent results. Consequently, our conclusions are mainly based on the results from the model-free tests. In we first examine whether any intraday pattern exists either for the  particular,  Dvt T1, T2 or FarMisProjt variables in the Taiwan options markets, and then we test for the existence of investor misreaction with both the model-free and model-based approaches. Moreover, we investigate whether any of the four categories of investors exhibit different misreaction behavior. 4.1. Intraday patterns of investor misreaction to new information   After generating the five-minute series of marketwise Dvt T1, T2 and FarMisProjt , we calculate the averages levels of the variables for each intraday interval. Fig. 1 illustrates their intraday across the observation intervals. First, we find that the intraday averages  patterns  of Dvt T1, T2 are all positive. Namely, the forecasting error of forward variance for future spot variance is, on average, positive. Second, in contrast to the findings of the prior studies  using daily data on the U.S. markets and to the results based on Dvt T1, T2 , we find that the intraday averages of FarMisProjt are all negative. In other words, although investor

0

FarMisProjt

-0.002 -0.004 -0.006 -0.008 -0.01 -0.012 08:50 09:00 09:10 09:20 09:30 09:40 09:50 10:00 10:10 10:20 10:30 10:40 10:50 11:00 11:10 11:20 11:30 11:40 11:50 12:00 12:10 12:20 12:30 12:40 12:50 13:00 13:10 13:20 13:30 13:40

-0.014

08:50 09:00 09:10 09:20 09:30 09:40 09:50 10:00 10:10 10:20 10:30 10:40 10:50 11:00 11:10 11:20 11:30 11:40 11:50 12:00 12:10 12:20 12:30 12:40 12:50 13:00 13:10 13:20 13:30 13:40

Δvt(T1,T2)

Trading Interval 0.064 0.062 0.06 0.058 0.056 0.054 0.052 0.05 0.048 0.046

Trading Interval Fig. 1. Intraday pattern of Jiang and Tian’s (2010) and Poteshman’s (2001) misreaction variables. (A) Jiang and Tian’s (2010) model-free forward variance forecast error. (B) Poteshman’s (2001) investor misreaction variable. Note: Panel A shows the average value of the model-free forward variance forecast errors, Dvt ðT1 ,T2 Þ, for each intraday interval for the period from January 2, 2002 to December 31, 2005. Panel B shows the average value of the FarMisProjt variable for each intraday interval for the same period.

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

373

misreaction to current unexpected information occurs in the high-frequency data, the unexpected changes in instantaneous variance tend to be projected relatively more by investors into short-maturity options rather than long-maturity options. Regardless of whether the signs of the unexpected changes in instantaneous variance are positive or negative and of whether we look at the model-free or model-based variance measures, the reactions in variance for short-maturity options are invariably larger than those for long-maturity options. This finding from the high-frequency data may well reveal that when investors receive unexpected information, they usually trade short-maturity options first, essentially because nearby contracts in the Taiwan options markets are much more liquid than others.17 Hence, the instantaneous adjustments from long-maturity options are invariably relatively smaller, and it may take some time for comparable adjustment to take place in options with longer maturity. In addition, we find that the magnitudes of both variables of investor misreaction are higher during the market open (8:45 AM–9:15 AM) and during the noon hour (12:00 PM–12:30 PM). We hypothesize that the larger misreaction during the open period may be attributable to the relatively higher level of information asymmetry caused by the long nontrading overnight period. We posit that the larger misreaction during the noon time period may be attributable to the relatively higher level of information asymmetry caused by the absence of certain  market  participants who simply go out for lunch. However, during the market close, Dvt T1, T2 is particularly low, whereas FarMisProjt is particularly high. 4.2. Investor misreaction from the marketwise viewpoint Because the results shown in Poteshman (2001) are inconsistent with those presented in Jiang and Tian (2010), we now use a more sophisticated dataset to reexamine the existence of investor misreaction by using both approaches and again compare their results. Since Jiang and Tian’s (2010) model-free approach is free from model misspecification, we adopt their analysis framework as the benchmark to test for investor misreaction by using the following regression: Dvt ðT1 ,T2 Þ ¼ a þ bvðt,T1 Þ þ

3 X

gj Dj,t vðt,T1 Þ þ et ,

ð7Þ

j¼1

where  vðt,T  1 Þ is spot variance implied from option prices for maturity date T1 at time t. and overreact to the Dvt T1, T2 is the forecasting error as defined in Eq. (6). If  investors  forward variance related with spot variance at time t, Dvt T1, T2 would be negatively correlated with short-maturity spot variance. Referring to the intraday pattern showed in Fig. 1, we control for the intraday effect by including three dummy variables in the model, D1, D2 and D3, each of which equals 1 for the respective open, noon, and close intervals, and zero otherwise.18 We use the Newey-West robust standard errors in all of our empirical regressions to adjust for serial correlation and heteroskedasticity. 17

In almost all of the options markets around the world, nearby contracts are invariably found to be the most liquid; however, in the Taiwan options market, the difference between the liquidity of nearby and non-nearby contracts is extremely large. This huge difference in liquidity could result in the prices of non-nearby contracts being insensitive to information flow. 18 As the model-free regression is not a time-series regression, we do not control for the lagged values of the dependent variable.

374

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

In the Poteshman’s (2001) model-based framework, if investors underreact to the unexpected changes in instantaneous variance, FarMisProjt decreases in the magnitude of the unexpected change in instantaneous variance. Therefore, a regression test that   determines the relation between FarMisProjt and Dvunexpected  should clarify whether t short-horizon underreaction to information exists within the Taiwan options market. The model is specified as 6   X 3   X     FarMisProjt ¼ a þ bi Dvunexpected gj Dj,t Dvunexpected ð8Þ þ  þ et , ti ti i¼0

j¼1

where FarMisProjt is as defined in Eq. (5) and Dvunexpected is as defined in Eq. (2). In t addition to the contemporaneous relation between the two variables, we also consider the time that it may take investors to react fully to the unexpected shock, as well as the frequently found autocorrelation in the intraday financial time series, by adding into the model the absolute value of the unexpected changes in instantaneous variance over the previous 30-minute period. As before, we also control for the intraday effect by including three dummy variables in the model, D1, D2 and D3, each of which equals 1 for the respective open, noon, and close intervals, and zero otherwise. If long-horizon overreaction does exist, we would expect to find a positive relation between the level of instantaneous variance and the difference in the changes in instantaneous variance between long- and short-maturity options. Thus, a regression model that regresses VtLong VtShort on Vt serves as an appropriate channel for exploring the issue of long-horizon overreaction. Based on the same concerns relating to the inclusion of lagged instantaneous variance and dummy variables in the model we used to test for short-horizon underreaction, we specify the regression model for testing long-horizon overreaction as VtLong VtShort ¼ a þ

6 X i¼0

bi Vti þ

3 X

gi Dj,t Vt þ et ,

ð9Þ

j¼1

  where VtLong VtShort is the instantaneous variance implied from long- (short-) maturity options, and Vt is the instantaneous variance for the corresponding trading interval, and D1 , D2 , and D3 are as defined in Eq. (7). Tables 3 and 4 show the regression results from the five-minute marketwise observations for the model-free and model-based approaches, respectively. As shown in Panel A of Table 3, the model-free regression provides no evidence of investor misreaction as the b coefficient is significantly positive and is not significantly negative in any instance. Note that although a significantly negative b coefficient is associated with investor overreaction, a significantly positive b coefficient does not indicate investor underreaction. The significantly positive b coefficient may be related to the volatility level. In other words, the forecasting error defined by the difference between the forward variance and the corresponding future spot variance is high (low) when the variance level is high (low). To detect this potential cause for the positive significantly positive b coefficient, we scale the forecasting error with the average of the forward variance and the corresponding future spot variance and then rerun the model-free regression. Panel B of Table 3 shows that the b coefficient becomes statistically insignificant although it is negative. As shown in Table 4, the results from the model-based regression are completely unique from the model-free regression results. The results from the model-based regression for

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

375

Table 3 Model-free tests for the full sample with the five-minute frequency. This table presents the results based on Jiang and Tian’s (2010) regression as Dvt ðT1 ,T2 Þ ¼ a þ bvðt,T1 Þ þ

3 X

gj Dj,t vðt,T1 Þ þ et ,

j¼0

  where Dvt T1, T2 is defined in Eq. (5), and vðt,T1 Þ is spot variance implied from option prices. T1 and T2 correspond to the most and second nearby maturity dates, respectively. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the five-minute marketwise observations, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. For the results shown in Panel B, the dependent variable is rescaled by the average of the forward variance and the corresponding future spot variance. The figures in the parentheses are t-statistics. nnn indicates significance at the 1% level. g1

g2

g3

Adj. R2 (%)

Panel A: Original dependent variable 0.0048 1.0479 (35.07nnn) (3.41nnn)

0.0143 (0.39)

0.0590 (1.49)

0.0094 (0.24)

30.78

Panel B: Rescaled dependent variable 3.9604 0.9860 (0.76) (0.01)

36.101 (0.68)

128.269 (1.62)

71.856 (1.53)

0.00

Coefficients

a

b

Table 4 Model-based tests for the full sample with the five-minute frequency. Model (1) is based on Poteshman’s short-horizon underreaction regression, where FarMisProjt is defined in Eq. (6), and Dvunexpeced is defined in Eq. (4). Model (2) is based on Poteshman’s long-horizon overreaction regression, t is the instantaneous variance implied from long maturity options, vShort is the instantaneous variance where vLong t t implied from short maturity options, and vt is the instantaneous variance for the corresponding trade interval. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the five-minute marketwise observations, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. n, nn, and nnn indicate significance at the 10%, 5%, and 1% levels, respectively. Regression parameters

Model (1) t-stat.

Coeff. a b0 b1 b2 b3 b4 b5 b6 g1 g2 g3 Adj. R2 (%)

Model (2)

nnn

0.0012 0.8531 0.0098 0.0410 0.0134 0.0391 0.0005 0.0410 0.1122 0.0979 0.0694

5.62 24.63nnn 0.49 1.83n 0.58 1.96n 0.03 0.03 1.93n 2.58nn 0.88 29.52

Coeff.

t-stat.

0.0059 0.4884 0.0489 0.0340 0.0549 0.0600 0.0222 0.0620 0.0113 0.0094 0.0362

4.47nnn 16.84nnn 2.88nnn 1.883n 3.51nnn 3.91nnn 0.19 3.34nnn 0.53 0.44 1.85n 13.66

376

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

short-horizon underreaction (Model (1)) are consistent with prior studies that adopt daily data for the U.S. market because the b0 estimate is significantly negative at the 1% level. In other words, the model-based test supports the existence of short-horizon underreaction in the Taiwan options market. However, different from the previous studies, we find strong evidence against the instantaneous long-horizon overreaction hypothesis because the b0 estimate in Model (2) is negatively significant at the 1% level. Because some of the coefficients of lagged variables in the two models are significantly positive, an obvious subsequent attempt to correct the misreaction occurs. The correction is nonetheless insufficient as all are very small compared to the b0 estimate. In sum, our findings using Taiwan high-frequency data are in line with Jiang and Tian’s (2010) study using U.S. daily data. That is, the model-free approach does not support the investor misreaction detected by the model-based approach. As previously mentioned, using the model-free approach to estimate the series of variance is free from model misspecification. Therefore, contradictory findings from the model-based tests indicate that a model misspecification problem exists in the model-based investigation on investor misreaction and the conclusions derived from the model-based approach are unreliable.

4.3. Misreaction across investor categories Due to the uniqueness of our dataset, we can explore the transactions of four categories of investors individually: domestic institutional, foreign institutional, individual, and market makers. To examine whether the misreaction patterns found in the marketwise observations apply to every investor category, we run both the model-based and modelfree regressions for the variance series compiled from the transactions of the four categories of investors individually. Tables 5 and 6 provide the results for the model-based and model-free analyses on the five-minute frequency, respectively. The findings in Tables 5 and 6 for all of the four categories of investors are consistent with those from the marketwise transactions. That is, the model-based tests support the existence of investor misreaction, whereas the model-free tests do not. According to the results of Model (1) for short-horizon underreaction and Model (2) for long-horizon overreaction in Table 5, all of various categories of investors exhibit short-horizon underreaction, but do not behave long-horizon overreaction. When further comparing the results between the four categories of investors, we find that the foreign institutional investors exhibit the lowest underreaction, as the value of b0 the estimate is just half of that for the other investor categories. This result may indicate that foreign institutional investors are the most sophisticated investors in the Taiwan options markets, which is consistent with the findings reported in the prior studies of their superior information advantage and profit-making ability. However, the model-free results in Table 6 do not confirm the misreaction patterns reported by the model-based tests for the various investor categories. That is, the modelfree tests provide no evidence to support the existence of investor misreaction across investor categories because none of the b coefficients with nonscaled forecasting errors are negatively significant (Panel A) and all of those with scaled forecasting errors are statistically insignificant (Panel B). Therefore, the model-based findings could be incorrect and should be interpreted cautiously because they are not supported by the modelfree tests.

Table 5 Model-based tests for different investor types with the five-minute frequency. This table presents the results based on Poteshman’s (2001) short-horizon underreaction and long-horizon overreaction regressions specified, respectively, as FarMisProjt ¼ a þ

6 X i¼0

  X   3     bi Dvunexpeced gj Dj,t Dvunexpeced þ  þ et t ti

ð1Þ

j¼0

vShort ¼aþ vLong t t

6 X

bi vti þ

i¼0

3 X

gj Dj,t vt þ et

ð2Þ

j¼0

is defined in Eq. (4). Model (1) is based on Poteshman’s (2001) short-horizon underreaction regression, where FarMisProjt is defined in Eq. (6), and Dvunexpeced t is the instantaneous variance implied from long maturity options, vShort is the Model (2) is based on Poteshman’s long-horizon overreaction regression, where vLong t t instantaneous variance implied from short maturity options, and vt is the instantaneous variance for the corresponding trade interval. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the five-minute observations of four investor types, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. n,n and nnn indicate significance at the 10%, 5%, and 1% levels, respectively. Investor types Regression

Domestic institutional investors

Foreign institutional investors

Individual investors

Model (1)

Model (1)

Model (1)

Parameters

Coeff.

t-stat.

Model (2) Coeff.

t-stat.

a 0.001 3.25nnn 0.000 0.06 b0 0.852 43.6nnn 0.813 27.2nnn b1 0.000 0.01 0.010 0.92 b2 0.001 0.14 0.017 1.81n 0.009 0.84 0.022 2.18nn b3 b4 0.001 0.09 0.005 0.70 b5 0.026 2.42n 0.009 0.97 b6 0.001 0.19 0.005 0.64 Intraday Yes Yes dummy Adj. R2 (%) 47.88 60.38

Coeff.

t-stat.

Model (2) Coeff.

t-stat.

0.002 5.53nnn 0.413 8.27nnn 0.002 0.14 0.013 0.88 0.004 0.25 0.017 1.41 0.014 1.01 0.008 0.57 Yes

0.008 16.64nnn 0.506 14.0nnn 0.073 4.82nnn 0.038 3.19nnn 0.048 3.82nnn 0.030 2.80nnn 0.041 3.07nnn 0.031 2.52nn Yes

13.99

42.40

Coeff.

t-stat.

Market makers Model (2) Coeff.

t-stat.

0.002 7.23nnn 0.013 15.00nnn 0.884 41.75nnn 0.851 56.3nnn 0.010 0.72 0.038 3.26nnn 0.015 0.90 0.058 4.47nnn 0.023 1.62 0.041 3.83nnn 0.016 0.93 0.047 4.37nnn 0.038 2.08n 0.027 2.32nn 0.023 1.54 0.035 2.92nnn Yes Yes 35.98

40.48

Model (1) Coeff.

t-stat.

Model (2) Coeff.

t-stat.

0.002 6.65nnn 0.013 16.86nnn 0.811 43.3nnn 0.837 68.8nnn 0.030 2.01n 0.016 1.96n 0.031 2.66nnn 0.001 0.07 0.007 0.61 0.018 2.12nn 0.016 1.31 0.011 1.20 0.011 0.88 0.012 1.51 0.003 0.26 0.011 1.13 Yes Yes 40.49

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

and

56.28 377

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

378

Table 6 Model-free tests for different investor types with the five-minute frequency. This table presents the results based on Jiang and Tian’s (2010) regression as Dvt ðT1 ,T2 Þ ¼ a þ bvðt,T1 Þ þ

3 X

gj DDj,t vðt,T1 Þ þ et ,

j¼0

where Dvt ðT1 ,T2 Þ is defined in Eq. (5), and vðt,T1 Þ is spot variance implied from option prices. T1 and T2 correspond to the most and second nearby maturity dates, respectively. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the five-minute transactions of the four categories of investors, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. For the results shown in Panel B, the dependent variable is rescaled by the average of the forward variance and the corresponding future spot variance. nn and nnn indicate significance at the 5% and 1% levels, respectively. Variables

Domestic institutional investors Coeff.

t-stat.

Panel A: Original dependent variable a 0.012 24.05nnn b 1.212 70.58nnn Intraday dummy Yes Adj. R2 (%) 59.93 Panel B: Rescaled dependent variable a 0.7251 0.49 b 50.884 0.65 Intraday dummy Yes Adj. R2 (%) 0.00

Foreign institutional investors Coeff.

t-stat.

0.007 1.082

14.26nnn 42.03nnn Yes 45.03

0.2198 6.189

3.50nnn 0.35 Yes 0.04

Individual investors Coeff.

t-stat.

0.005 3.30nnn 1.056 35.67nnn Yes 31.42 3.2144 1.11 61.957 0.91 Yes 0.00

Market makers

Coeff.

t-stat.

0.006 6.21nnn 1.085 50.63nnn Yes 37.38 4.0421 2.13nn 39.358 1.10 Yes 0.00

In sum, we find that the model-based tests indicate the existence of investor misreaction in the Taiwan options market whereas the model-free tests do not. These findings do not rely on whether we explore the marketwise observation or the transactions of a particular investor category. In other words, even using a high-frequency dataset of a less mature market, our results are still consistent with Jiang and Tian (2010), who employ U.S. market data. Therefore, the validity of volatility anomalies identified in previous studies using a model-based approach should be questionable because their findings are based on joint tests of market misreaction and model specification and not supported by a correct (modelfree) approach. In other words, using the model-free approach as the benchmark, we find that the model-based approach leads to incorrect conclusions. 5. Robustness analysis The main results of this empirical investigation are based on a five-minute observation frequency. To conduct a check of the robustness of our results, we also run the model-free and model-based tests with alternative sampling frequencies of 15, 30, and 60 minutes and one-day observations. We comprehensively analyze the results with the 60-minute frequency here and the results with the other frequencies are similar and available upon request. Moreover, since theoretical works such as Berberis, Shleifer, and Vishny (1998) do not provide guidance on how to define the duration of short- and long-maturity options,

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

379

Table 7 Model-free tests for the full sample with the 60-minute frequency. This table presents the results based on Jiang and Tian’s (2010) regression as Dvt ðT1 ,T2 Þ ¼ a þ bvðt,T1 Þ þ

3 X

gj Dj,t vðt,T1 Þ þ et ,

j¼0

  where Dvt T1, T2 is defined in Eq. (5), and vðt,T1 Þ is spot variance implied from option prices. T1 and T2 correspond to the most and second nearby maturity dates, respectively. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the 60-minute marketwise observations, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. For the results shown in Panel B, the dependent variable is rescaled by the average of the forward variance and the corresponding future spot variance. The figures in the parentheses are t-statistics. * and nnn indicate significance at the 10% and 1% levels, respectively. b

Intraday dummy

Adj. R2 (%)

Panel A: Original dependent variable 0.0058 (1.77n)

1.0588 (14.75nnn)

Yes

30.63

Panel B: Rescaled dependent variable 0.2491 (0.86)

0.3716 (1.05)

Yes

0.00

Coefficients

a

we also implement the model-free investigation based on an alternative duration definition to further validate our empirical findings.19 5.1. The analysis based on an alternative observation frequency Using the observations with the 60-minute sampling frequency, we re-implement all of the tests reported in Tables 3–6. The corresponding 60-minute results are shown in Tables 7–10. Tables 7 and 8 show the model-free and model-based regression results for the 60-minute marketwise observations, respectively. Consistent with the findings from the five-minute marketwise observations, the model-free tests do not support the existence of investor misreaction since the b coefficient is not negatively significant, which does not rely on whether the original or rescaled dependent variable is used. Once again, the results from the model-based regression are completely different from the model-free regression results. The model-based regression results still indicate that investors exhibit short-horizon underreaction, but do not have long-horizon overreaction because the b0 estimate in both Models (1) and (2) are negatively significant at the 1% level. The model-based and model-free regression results for the 60-minute observations of various investor categories are shown in Tables 9 and 10, respectively. The results are also consistent with those with the five-minute frequency. Namely, the model-based tests support the existence of investor misreaction and show different misreaction patterns across investor types, whereas the model-free tests do not no matter whether we examine the original or rescaled dependent variable. 19

As the model-based approach requires time-series regressions, we are unable to compute the long-maturity instantaneous variance for several days when the long-maturity group includes the contracts with maturities longer than the second nearby one. Therefore, the analysis with this alternative duration definition is conducted for the model-free tests only.

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

380

Table 8 Model-based tests for the full sample with the 60-minute frequency. This table presents the results based on Poteshman’s (2001) short-horizon underreaction and long-horizon overreaction regressions specified, respectively, as FarMisProjt ¼ a þ

3 X i¼0

  X 3       bi Dvunexpeced gj Dj,t Dvunexpeced þ  þ et t ti

ð1Þ

j¼0

and vShort ¼aþ vLong t t

3 X i¼0

bi vti þ

3 X

gj Dj,t vt þ et :

ð2Þ

j¼0

Model (1) is based on Poteshman’s short-horizon underreaction regression, where FarMisProjt is defined in Eq. (6), and Dvunexpeced is defined in Eq. (4). Model (2) is based on Poteshman’s long-horizon overreaction regression, t is the instantaneous variance implied from long maturity options, vShort is the instantaneous variance where vLong t t implied from short maturity options, and vt is the instantaneous variance for the corresponding trade interval. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the 60-minute marketwise observations, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. n, nn¸and nnn indicate significance at the 10%, 5%, and 1% levels, respectively. Regression parameters

a b0 b1 b2 b3 Intraday dummy Adj. R2 (%)

Model (1)

Model (2)

Coeff.

t-stat.

Coeff.

t-stat.

0.0009 0.8861 0.0003 0.0494 0.0231

1.61 12.97nnn 0.01 0.93 0.50

0.0146 0.8885 0.1067 0.0771 0.0974

7.72nnn 22.72nnn 2.85nnn 2.25nn 2.69nnn

Yes 32.09

Yes 41.25

It is clear that the size and significance of the coefficients estimates reported in Tables 7–10 are very similar to their corresponding ones presented in Tables 3–6. Combining with the unreported results with other sampling frequencies, we show that our empirical findings are robust to alternative sampling frequencies.

5.2. The analysis based on an alternative maturity definition During our sample period, the third nearby contracts took about 6.1% of trading volume. Although these contracts are much less liquid than the most and second nearby contracts, the amount of data for the third nearby contracts is still sufficient for us to generate reliable model-free variance measures for the marketwise analysis. However, when narrowing down to the cross-investor-category analysis, we do not have sufficient observations to construct the model-free variance variables for most of the days. Therefore, the analysis in which T2 corresponds to the third nearby maturity date is implemented for the marketwise observations only and the results are shown in Table 11. For both the five-minute and 60-minute frequencies, none of the b coefficients is negatively significant. When examining the rescaled dependent variables, all b coefficients

Table 9 Model-based tests for different investor types with the 60-minute frequency. This table presents the results based on Poteshman’s (2001) short-horizon underreaction and long-horizon overreaction regressions specified, respectively, as FarMisProjt ¼ a þ

3 X i¼0

  X   3     bi Dvunexpeced gj Dj,t Dvunexpeced þ  þ et t ti

ð1Þ

j¼0

vShort ¼aþ vLong t t

3 X

bi vti þ

i¼0

3 X

gj DDj,t vt þ et

ð2Þ

j¼0

is defined in Eq. (4). Model Model (1) is based on Poteshman’s (2001) short-horizon underreaction regression, where FarMisProjt is defined in Eq. (6), and Dvunexpeced t is the instantaneous variance implied from long maturity options, vShort is the (2) is based on Poteshman’s long-horizon overreaction regression, where vLong t t instantaneous variance implied from short maturity options, and vt is the instantaneous variance for the corresponding trade interval. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the 60-minute observations of four investor types, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. n, nn, and nnn indicate significance at the 10%, 5%, and 1% levels, respectively. D Regression Parameters

Domestic institutional investors

Foreign institutional investors

Model (1)

Model (1)

Coeff.

t-stat.

Model (2) Coeff.

t-stat.

Coeff.

t-stat.

a 0.000 0.04 0.001 0.22 0.004 2.87nnn b0 0.807 15.73nnn 0.792 11.45nnn 0.582 5.75nnn b1 0.021 0.54 0.057 1.45 0.012 0.29 b2 0.011 0.48 0.007 0.41 0.003 0.11 0.008 0.45 0.004 0.17 0.003 0.12 b3 Intraday dummy Yes Yes Yes Adj. R2 (%) 44.98 60.48 25.14

Model (2) Coeff.

t-stat.

Individual investors Model (1) Coeff.

t-stat.

Market makers

Model (2) Coeff.

t-stat.

Model (1) Coeff.

t-stat.

Model (2) Coeff.

t-stat.

7.80nnn 0.001 0.88 0.014 8.27nnn 0.003 3.88nnn 0.014 8.29nnn 7.92nnn 0.96 17.81nnn 0.928 29.14nnn 0.895 17.99nnn 0.862 29.95nnn 1.62 0.036 0.74 0.137 3.67nnn 0.086 1.82n 0.070 1.98nn 1.13 0.014 0.22 0.067 1.99n 0.092 1.93n 0.017 0.44 1.76n 0.049 0.98 0.076 2.22nn 0.040 1.12 0.012 0.39 Yes Yes Yes Yes Yes 39.99 39.68 44.24 48.20 56.93

0.007 0.601 0.048 0.031 0.047

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

and

381

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

382

Table 10 Model-free tests for different investor types with the 60-minute frequency. This table presents the results based on Jiang and Tian’s (2010) regression as 3 X gj Dj,t vðt,T1 Þ þ et , Dvt ðT1 ,T2 Þ ¼ a þ bvðt,T1 Þ þ   j¼0 where Dvt T1, T2 is defined in Eq. (5), and vðt,T1 Þ is spot variance implied from option prices. T1 and T2 correspond to the most and second nearby maturity dates, respectively. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the 60-minute transactions of the four categories of investors, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. For the results shown in Panel B, the dependent variable is rescaled by the average of the forward variance and the corresponding future spot variance. n, nn, and nnn indicate significance at the 10%, 5%, and 1% levels, respectively. Variables

Domestic institutional investors Coeff.

t-stat.

Foreign institutional investors t-stat.

Coeff.

Panel A: Original dependent variable a 0.0145 11.68nnn b 1.2066 29.39nnn Intraday dummy Yes Adj. R2 (%) 59.64 Panel B: Rescaled dependent variable a 0.0328 1.15 b 0.1074 0.17 Intraday dummy Yes Adj. R2 (%) 0.00

Individual investors

0.0053 1.0303

0.0026 0.0927

Coeff.

Market makers

t-stat.

6.62nnn 12.44nnn Yes 45.36

0.0054 1.66n 1.0642 14.83nnn Yes 30.91

3.55 0.70 Yes 0.22

0.2600 0.91 10.6759 0.97 Yes 0.28

Coeff.

t-stat.

0.0046 2.01nn 1.0908 20.50nnn Yes 38.55 0.0116 0.47 0.9508 0.51 Yes 0.02

Table 11 Model-free tests with an alternative duration definition. This table presents the results based on Jiang and Tian’s (2010) regression as Dvt ðT1 ,T2 Þ ¼ a þ bvðt,T1 Þ þ

3 X

gj Dj,t vðt,T1 Þ þ et ,

j¼0

where Dvt ðT1 ,T2 Þ is defined in Eq. (5), and vðt,T1 Þ is spot variance implied from option prices. T1 and T2 correspond to the most and THIRD nearby maturity dates, respectively. D1, D2, and D3 are dummy variables, which, respectively, equal 1 for the open, noon, and close intervals, and zero otherwise. The regression model is estimated from the five- and 60-minute marketwise observations, respectively, with the t-statistics calculated using Newey-West robust standard errors. The sample period runs from January 2, 2002 to December 31, 2005. For the results shown in Panel B, the dependent variable is rescaled by the average of the forward variance and the corresponding future spot variance. The figures in the parentheses are t-statistics. n, nn, and nnn indicate significance at the 10%, 5%, and 1% levels, respectively. Coefficients

a

b

Panel A: Original dependent variable Five-minute 0.0115 0.2324 (13.32nnn) (14.34nnn) 60-minute 0.0046 1.0908 (2.01nn) (20.50nnn) Panel B: Rescaled dependent variable Five-minute 2.9333 0.1717 (1.51) (0.89) 60-minute 0.0116 0.9508 (0.47) (0.51)

g1

g2

g3

0.0086 (0.63) 0.0046 (0.13)

0.0189 (0.91) 0.0654 (1.82n)

0.0259 (1.43) 0.0449 (1.06)

21.7439 (1.41) 1.7203 (0.80)

9.3772 (0.44) 0.7739 (0.39)

30.1044 (1.63) 0.4645 (0.24)

Adj. R2 (%)

9.28 38.55

0.00 0.02

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

383

turn to insignificant. These findings are consistent with those with the previous analysis in which T2 corresponds to the second nearby maturity date. In other words, the model-free tests provide no evidence to support the existence of investor misreaction in the Taiwan options market, which is robust across alternative duration definitions of short- and long-term options. 6. Conclusions Using a unique and comprehensive dataset consisting of complete transaction records on all trades in Taiwan’s options market, we employ both the model-free and model-based approaches to examine the reactions of investors to information contained in intraday changes in instantaneous or implied variance. We conduct our empirical investigation on marketwise observations, as well as on the individual transactions of four different categories of investors (domestic institutional, foreign institutional, individual, and market makers). In general, our findings are in line with the model-free tests of Jiang and Tian (2010). Using the model-free approach as the benchmark, we find that the model-based tests incorrectly indicate the existence of some types of investor misreaction, which is not supported by the model-free tests under all different empirical designs. Thus, although some interesting conclusions can be drawn from the evidence based on a model-based comparison between patterns of misreaction across various categories of investors, the findings could be the natural outcomes caused by model misspecification and must be regarded cautiously. Investigating the Taiwan market enhances our knowledge on the misreaction to information by investors in a less mature market, whereas the use of high-frequency data relaxes the assumption that investors react to information changes only once each day. In addition, using two different approaches helps clarify the inconsistent findings from previous studies. The findings therefore provide further understanding of the existence of investor misreaction, as well as greater insight into the ways in which investors react to changes in information and how researchers should interpret the results on investor misreaction from previous studies. Appendix A. The stochastic volatility model of Heston (1993) We generate the instantaneous variance by assuming that the underlying asset price follows the Heston (1993) stochastic volatility model. The model, under a real-world measure, is specified as pffiffiffiffi dSt ¼ mðSt ,vt ,tÞdt þ vt dwSt St

ðA1Þ

pffiffiffiffi dvt ¼ kðyvt Þdt þ Z vt dwvt

ðA2Þ

where k, y and Z are constant parameters. Within this system, the time t price and the instantaneous variance of the underlying asset, which are respectively denoted by St and vt , are driven by the two standard Wiener processes, with increments of dwSt and dwvt , and correlation r.

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

384

The risk-neutral process of the option pricing model is obtained as pffiffiffiffi dSt ¼ ðrdÞdt þ vt dwSt St   pffiffiffiffi dvt ¼ kn yn vt dt þ Z vt dwvt ,

ðA3Þ ðA4Þ

n

where kn ¼ k þ l and y ¼ ky=ðk þ lÞ: The resulting price of a call option with strike price X is derived as C ¼ SedT P1 XerT P2 ,

ðA5Þ

where P2 is the probability of ST 4X under the risk-neutral Q measure, and P1 is the probability of the same event under another measure, say Q*. For the details on the P1 and P2 functions, refer to Heston (1993).

References Aı¨ t-Sahalia, Y., Lo, A.W., 1998. Nonparametric estimation of state-price densities implicit in financial asset prices. Journal of Finance 53, 499–547. Bakshi, G., Cao, C., Chen, Z., 1997. Empirical performance of alternative option pricing models. Journal of Finance 52, 2003–2049. Barber, B.M., Lee, Y.T., Liu, Y.J., Odean, T., 2007. Just how much do individual investors lose by trading? Review of Financial Studies 22, 609–632. Berberis, N., Shleifer, A., Vishny, R., 1998. A model of investor sentiment. Journal of Financial Economics 49, 307–343. Black, F., 1975. Fact and fantasy in the use of options. Financial Analysts Journal 31, 61–72. Cao, C., Li, H., Yu, F., 2005. Is investor misreaction economically significant? Evidence from short- and longterm S&P 500 index options. Journal of Futures Markets 25, 717–752. Chakravarty, S., Gulen, H., Mayhew, S., 2004. Informed trading in stock and option markets. Journal of Finance 59, 1235–1258. Chang, C.C., Hsieh, P.F., Lai, H.N., 2009. Do informed option investors predict stock returns? Evidence from the Taiwan Stock Exchange. Journal of Banking and Finance 33, 757–764. Cox, J.C., Ingersoll, J.E., Ross, S.A., 1985. A theory of the term structure of interest rates. Econometrica 53, 385–407. Daniel, K.D., Hirshleifer, D., Subrahmanyam, A., 1998. Investor psychology and securities market under- and overreactions. Journal of Finance 52, 1839–1885. Easley, D., O’Hara, M., Srinivas, P., 1998. Option volume and stock prices: evidence on where informed traders trade. Journal of Finance 53, 431–465. Han, B., Lee, Y.T., Liu, Y.J., 2010. Investor trading behavior and performance: evidence from Taiwan Stock Index options. Working Paper, University of Texas at Austin. Heston, S.L., 1993. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6, 327–344. Hong, H., Stein, J.C., 1999. A unified theory of underreaction, momentum trading and overreaction in asset markets. Journal of Finance 54, 2143–2184. Jiang, G.J., Tian, Y.S., 2005. The model-free implied volatility and its information content. Review of Financial Studies 18, 1305–1342. Jiang, G.J., Tian, Y.S., 2010. Misreaction or misspecification? A re-examination of volatility anomalies. Journal of Banking and Finance 34, 2358–2369. Mahani, R.S., Poteshman, A.M., 2008. Overreaction to stock market news and misevaluation of stock prices by unsophisticated investors: evidence from the options market. Journal of Empirical Finance 15, 635–655. Mayhew, S., Sarin, A., Shastri, K., 1995. The allocation of informed trading across related markets: an analysis of the impact of changes in equity-option margin requirements. Journal of Finance 50, 1635–1653.

C.-C. Chang et al. / Journal of Financial Markets 16 (2013) 362–385

385

Pan, J., Poteshman, A.M., 2006. The information in option volume for future stock prices. Review of Financial Studies 19, 871–908. Poteshman, A.M., 2001. Underreaction, overreaction and increasing misreaction to information in the options market. Journal of Finance 56, 851–876. Shleifer, A., 2000. In: Inefficient Markets: An Introduction to Behavioral Finance. Oxford University Press, Oxford, UK. Stein, J., 1989. Overreactions in the options market. Journal of Finance 44, 1011–1022.