Price discovery in stock and options markets*

Transcription

1 Price discovery in stock and options markets* VINAY PATEL**, TĀLIS J. PUTNIŅŠ*** and DAVID MICHAYLUK**** ** University of Technology Sydney, PO Box 123 Broadway, NSW, Australia, 2007 *** University of Technology Sydney, PO Box 123 Broadway, NSW, Australia, 2007 **** University of Technology Sydney, PO Box 123 Broadway, NSW, Australia, 2007 Abstract This study sheds new light on the contribution of stock and options markets to price discovery. We use a sample of large US stocks during the past decade and measures of price discovery that overcome a bias that is present in previous empirical work. We find that options markets contribute about one third to price discovery. This estimate is approximately two to five times larger in magnitude than documented in previous studies and suggests that options markets are an important source of informed trading and price discovery, consistent with theoretical predictions. We also find evidence that when a relatively high share of informed trading occurs in the options market (high options market price discovery share), bid-ask spreads in the options market tend to be wide compared to those in the stock market, consistent with relatively high adverse selection risks in the options market. Finally, our results indicate that the leverage offered by options is also a key driver of price discovery in the options market. Keywords: price discovery, stock, option, information share JEL classification: G14 * vinay.patel@uts.edu.au, talis.putnins@uts.edu.au and david.michayluk@uts.edu.au. We thank the Securities Industry Research Centre of Asia-Pacific (SIRCA) for providing access to data used in this study. In addition, we thank Larry Glosten, John Welborn, Ron Masulis, Robert Daigler, Petko Kalev, participants at the Financial Management Conference 2013 (Paris) and Behavioural Finance and Capital Markets Conference 2014 (Adelaide) and seminar participants at the University of Rhode Island and University of Technology Sydney for helpful comments.

2 1. Introduction There is a current debate in the literature regarding the level of price discovery that takes place in stock markets compared to options markets. Theory suggests several reasons why informed traders may prefer to trade in options markets rather than stock markets, including synthetic leverage, built-in downside protection and lack of short-sale restrictions (Black, 1975; Easley et al., 1998; Chakravarty et al., 2004). In addition, empirical research also provides indirect support for informed trading in the options markets. For example, abnormal trading volume and order imbalance in the options market can predict future stock returns (Easley et al., 1998; Pan and Poteshman, 2006; Johnson and So, 2012; Kehrle and Puhan, 2013; Hu, 2013) and is observed prior to earnings and takeover announcements (Amin and Lee, 1997; Cao et al., 2005, Augustin et al., 2014). 1 However, a number of studies find that price discovery in the options market is low relative to the stock market. Chakravarty et al. (2004) estimate that options account for about 17% of price discovery on average in US stocks between 1988 and 1992, and they interpret this share as a meaningful contribution to price discovery. In contrast, Muravyev et al. (2013) argue that there is no economically meaningful price discovery in the options market and report that only around 6% of price discovery occurs in US options between 2003 and The lack of consensus in the literature leads to several important questions. First, do stock options make a meaningful contribution to price discovery? Second, what are the factors that affect how much price discovery occurs in the options market? Third, how has the price discovery share of the options market changed over time, in particular in response to changes in market structure? This paper addresses the above questions. In doing so we hope to not only improve our understanding of price discovery across stock and options markets, but also reconcile the mixed findings in the existing literature. Understanding the contribution of the options market to price discovery and what drives variation in its contribution is important for understanding the behaviour of informed traders more generally, as well as the process of price discovery and informational efficiency. It also has a number of practical implications for market makers in both stock and options markets, in particular regarding management of hedging strategies and adverse selection risks, as well as regulatory bodies tasked with monitoring insider trading. There are three novel features of our empirical analysis which allow us to shed new light on the issues raised above. First, we utilize a considerably longer sample period than previous studies. We examine price discovery in the US stock and options markets over a ten year period from 2003 to This allows us to investigate time series variation in option information shares and reconcile differences documented in Chakravarty et al. (2004) and Muravyev et al. (2013). Second, we employ a new measure of price discovery, the information leadership share, stemming from Yan and Zivot 1 Augustin et al. (2014) find abnormal options trading volume prior to 25% of their sample of takeover announcements, in particular in short-term out-of-the-money call options. 2

3 (2010) and Putniņš (2013). Importantly, the information leadership share (ILS) overcomes a key shortcoming of previously used metrics such as Hasbrouck s (1995) information share (IS) and Gonzalo and Granger s (1995) component share (CS), namely the bias inherent in these metrics when markets differ in the level of noise. Given the higher level of noise associated with the options price series due to trading frictions relative to the stock price series, previous studies are likely to have underestimated the contribution of options to price discovery, as well as mis-estimated the determinants of the options price discovery share. Third, we distinguish between competing drivers of price discovery including, (i) liquidity, (ii) uncertainty and (iii) leverage within a panel regression framework. This allows us to explain the overall levels of price discovery in options and stock markets and understand their time series trends. We use a sample of 36 US stocks (similar to Muravyev et al., 2013) during a ten-year period from April to April Using the information leadership share metric we find that the options market contributes about one third (33.20%) of the price discovery in US stocks during the past decade. This estimate is approximately two to five times larger in magnitude than documented in previous studies (e.g., Chakravarty et al., 2004; Muravyev et al., 2013). The difference compared to previous studies is largely because the information leadership share, unlike metrics used in previous studies, is not downward biased by the higher level of noise in the options market. This finding suggests options markets are an important source of informed trading and price discovery, consistent with early theoretical predictions. We also find a positive relation between the options market share of price discovery and the options market relative bid-ask spread (the bid-ask spread in the options market scaled by the bid-ask spread in the stock market). This result provides further evidence that informed trading in the options market contributes to price discovery when informed traders are more active in the options market, the options market spreads are relatively wider due to higher adverse selection risks for liquidity providers, and at the same time the options market makes a greater contribution to price discovery. This result differs from the findings of previous studies such as Chakravarty et al. (2004) who document that increased liquidity in the options market (or liquidity hypothesis) is associated with increased price discovery in the options market. Further, using the reduction in minimum tick size for options listed on the Chicago Board Options Exchange as an instrument for relative bid-ask spreads, we find no support for the liquidity hypothesis. Our findings also show a positive relation between relative trading volume in the options market to that of the stock market and price discovery in the options market, consistent with the pooling of uninformed and informed traders within the options market (Admati and Pfleiderer, 1988; Chowdhry and Nanda, 1991). Lastly, we find evidence which supports that the leverage inherent in options positions, specifically, the remaining time-to-maturity and distance between the underlying stock price and 3

4 strike price result in increased price discovery in the options market, consistent with theoretical predictions. The paper proceeds as follows. Sections 2 and 3 document the relevant literature and data sources. Section 4 describes our methodology and Section 5 contains our empirical findings. Section 6 concludes. 2. Related literature Two large strands of literature underlie the research conducted in this paper, (i) price discovery in the stock and options markets and (ii) empirical measures of price discovery. 2.1 Price discovery in the stock and options markets Early research focused on the lead-lag relation between the time series of stock and option prices with mixed findings. Manaster and Rendleman (1982) and Bhattacharya (1987) document that option price changes lead stock price changes, Stephan and Whaley (1990) and Finucane (1999) suggest otherwise. The lead-lag methodology has been refined since these early studies with more careful attention toward permanent price changes caused by informed trading. Chakravarty et al. (2004) calculate the implied stock price using the binomial model and were one of the first to apply the IS metric to compare price discovery in the stock and options markets. Their study examines 60 US firms between 1988 and 1992 and they document that at-the-money options contribute 17% to price discovery. The contribution of the options market to price discovery is found to increase when options market effective spreads are narrow and options trading volume is higher compared to the stock market, which is in support of the liquidity hypothesis as a driver of price discovery. Lastly, their study documents higher levels of price discovery in out-of-the-money options consistent with the view that options traders value leverage. Another method of comparing stock and option prices is to use the put-call parity relation to determine the implied stock price. 2 Holowczak et al. (2007) apply this methodology and examine 40 US stocks during May-July Using the IS metric they find that price discovery in the options market is approximately 11%, which is lower in magnitude when compared to Chakravarty et al. (2004). The authors attribute their result to a different method in calculating the implied stock price and thinner trading in options when compared to trading in the underlying stock during their sample period. More recently, Muravyev et al. (2013) support the view that there is very little price discovery in the options market. The authors apply a novel approach and the focus of their study compares the 2 Rourke (2013) outlines the advantages of using put-call parity rather than delta or vega hedging arguments to compute the implied stock price include, (i) put-call parity is model-free, (ii) does not require the use of unobservable parameters, and (iii) incorporates information given by both call and put prices. 4

5 behaviour of stock and option quotes during periods when the actual stock price and the optionimplied stock price differ (which is termed a disagreement event). During these disagreement events option quotes are found to not convey any additional information about future stock prices when compared to stock quotes. In support of this conclusion and supplementary to their main analysis, the authors find using the IS metric that the upper bound of the contribution of the options market to price discovery is 6.7%. We would like to stress a key difference between the focus of this study and the Muravyev et al. (2013) study specifically, the disagreement events examined by Muravyev et al. (2013) occur only temporarily, whereas the ILS looks at price discovery on average during each trading day. A number of other recent studies present contrasting evidence to Muravyev et al. (2013). Czerwonko et al. (2013) document that the binomial model employed by Chakravarty et al. (2004) to calculate the implied stock price results in IS and CS metrics which understate the true price discovery share of the options market. The authors develop an alternative method which minimises the measurement error induced by the binomial model and find that the price discovery share of the options market is larger, especially following reductions in minimum tick size introduced by the Chicago Board of Options Exchange (CBOE) in Rourke (2013) uses the joint estimation of option-implied stock prices across different strike prices and the underlying stock price to calculate price discovery in the options market between 2007 and For a sample of 54 stocks, the option information share using the IS metric is 17.49%, approximately three times in magnitude compared to using option-implied stock prices from at-themoney options alone. Rourke concludes that away-from-the-money options make an additional contribution to price discovery, where out-of-the-money, at-the-money and in-the-money options all make a similar contribution to price discovery in the options market. In addition, Hu (2013) uses transaction data between 2008 and 2010 and finds that order flow within the options market has a permanent impact on price compared to the transitory price impact of stock order flow. The author also documents that options market order flow rather than stock market order flow can predict the following day s stock returns and that the predictive power of option order flow occurs in both at-the-money and in-the-money options. Further, Kehrle and Puhan (2013) use a sample of US stocks between 1996 and 2009 and also provide evidence which supports the finding that the options market order flow leads stock market order flow. 3 They suggest that out-of-the-money call options with one month till maturity earn returns of 25% (48%) when options market order flow indicates the dissemination of positive (negative) information. 3 Lin et al. (2013) document that option-implied volatilities based on skewness and spreads are able to predict analyst recommendation changes, analyst forecast revisions and earnings surprises in the underlying stock. Further, informed traders choose to trade in the options market when there are short-sale constraints on the underlying stock. 5

6 2.2 Empirical measures of price discovery The conventional empirical measures of price discovery between two price series are Hasbrouck s (1995) information share (IS) and Gonzalo and Granger s (1995) component share (CS) metrics. The IS metric decomposes the variance in efficient price changes due to both price series, whereas the CS metric is a linear combination of weights which makes the two price series converge to the common underlying asset value. Both the IS and CS metrics are based on a cointegrated price series which are related to the value of the same underlying asset. The parameter estimates from the vector error correction model (VECM) are used to calculate the IS and CS metrics. Baillie et al. (2002) documents that the IS and CS metrics are complementary, rather than substitutes, in the sense they measure different aspects of price discovery. In essence, the IS metric is variance-weighted version of the CS metric. Yan and Zivot (2010) extend this literature and develop a structural model in which two price series depend on one permanent and one transitory shock. In this model the IS metric is influenced by both permanent and transitory shocks and the CS metric is influenced by transitory shocks only. Given that both the IS and CS metrics are heavily influenced by transitory shocks (which in theory should not have a large impact upon long run prices), the authors combine the IS and CS metrics together to strip out the influence of transitory shocks upon the two price series. A problem with the Yan and Zivot (2010) information leadership metric is that it can range from 0 to making it difficult to interpret and compare to the IS and CS metrics. More recently, Putniņš (2013) provides a detailed critique of the current empirical measures of price discovery and introduces a new price discovery metric Yan-Zivot-Putniņš information leadership share (ILS). In response to previous price discovery metrics, the author uses simulations to show that the IS and CS metrics will understate price discovery shares for the more noisy price series. The ILS metric overcomes this problem and can reliably calculate price discovery shares when the two price series have different levels of noise. Further, in contrast to the Yan and Zivot (2010) metric, the ILS metric is easy to interpret and comparable to the IS and CS metrics as the information share ranges between 0 and 1. More importantly, Putniņš (2013) provides evidence in four circumstances in which the IS and CS metrics lead to incorrect conclusions when compared to the ILS metric, specifically, futures versus spot/options market for US treasuries, European Union emissions trading scheme, Taiwanese stock index and JPY/USD to EUR/USD currency pairs. 3. Data This study examines whether price discovery initially occurs in the options or stock market for a sample of 36 stocks and two exchange-traded funds (ETF) during a ten year sample period between 6

7 April and April We obtain intraday trade and quote data for both stocks and options from the Thomson Reuters Tick History (TRTH) database provided by the Securities Industry Research Centre of Asia-Pacific (SIRCA). In our calculation of price discovery measures we use the national best bid and offer (NBBO) consolidated quotes from Options Price Reporting Authority (OPRA) listed options. The sample of stocks examined and the beginning of our sample period coincide with Muravyev et al. (2013). This particular sample consists of several large technology stocks which had the highest options trading volume in March Methodology To examine the level of price discovery in the stock and options markets we calculate the options implied stock price in a similar manner to Muravyev et al. (2013). Following on we calculate the IS, CS and ILS metrics to determine the price discovery shares of both the stock and options markets. Lastly, we describe our panel regression approach to examine competing drivers of price discovery in the options market and two-stage least squares (2SLS) approach to address an endogeneity concern between relative price discovery shares and relative liquidity. 4.1 Options implied stock price Muravyev et al. (2013) begin with the European put-call parity relationship to calculate the implied stock price using options data documented in equation (1), ( ) ( ) ( ( )) ( ) (1) where, is the stock price at time t, ( ) is the call option price with strike price K, ( ) is the put option price with strike price K, ( ( )) is the present value of cash dividends at time t, r is the continuously compounded risk-free rate of interest per annum and T t is the time to maturity. 5 The options in both the Muravyev et al. (2013) and our sample are American-style options, so equation (1) is adjusted to incorporate the ability to exercise early. ( ) ( ) ( ) ( ( )) ( ) (2) Specifically, the term ( ) captures the early exercise premium of American call and put options. We calculate ( ) by first estimating the error from the put-call parity relationship at every quote update for either the stock, call or put option, 4 We report findings for 39 different ticker codes in Table 2 because the QQQ ticker changed to QQQQ during our sample period. 5 The continuously compounded risk-free rate of interest is obtained from OptionMetrics. 7

8 ( ) ( ) ( ( )) ( ) (3) The early exercise premium is then calculated as the average error term for each trading day, ( ) (4) By recognizing that we can replicate a stock position using options contracts we can rewrite equation (2) in terms of the options implied bid price and implied ask price at time t: ( ) ( ) ( ) ( ( )) ( ) ( ) (5) ( ) ( ) ( ) ( ( )) ( ) ( ) (6) For comparative purposes we apply the following criterion applied by Muravyev et al. (2013): (a) Time to maturity (in days) is between 10 and 70 calendar days (inclusive), (b) Options are near-the-money satisfying ( ), (c) Present value of dividends with ex-dividends dates during the remaining life of the option satisfying ( ( )), (d) Bid price of option. 6 As a result our analysis focuses on near-the-money short-term liquid options contracts. 4.2 Information leadership share (ILS) We expect the level of noise in the stock and options price series to differ due to differences in liquidity and trading activity between both markets. Putniņš (2013) explains that inferences made from the IS and CS metrics will be biased when the level of noise between two prices differs. Extending the work of Yan and Zivot (2010), Putniņš develops an alternative measure, the information leadership share (ILS), which is not influenced by differences in the levels of noise. Similar to Putniņš (2013) we calculate the ILS using a vector-error-correction model (VECM) of options and stock prices sampled at a frequency of one-second intervals with 200 lags for each stockday: 6 We exclude the ticker DIA from our analysis due to an insufficient number of observations after applying criterion (a) to (d). 8

9 ( ) (7) ( ) where is the implied stock price calculated using the midquote of the implied bid (equation 5) and implied ask (equation 6) prices at time t, and is the midquote of the stock price at time t. 7 We calculate the ILS metric for each stock i for each stock-day which meet criteria (a) to (d) in Section 4.1 using the VECM coefficients and reduced form errors (see Appendix A) obtained from equation (7). As noted by Putniņš (2013) the ILS metric ranges between 0 and 1, allowing for a direct comparison with the IS and CS metrics. 4.3 What factors affect the level of price discovery in the options market? In this study we examine several competing hypotheses, specifically, i) liquidity, ii) uncertainty and iii) leverage, within a panel regression framework to determine the key drivers of price discovery in the options market. Chakravarty et al. (2004) provide the only other examination of the competing determinants of price discovery in the options and stock market using the IS metric as the dependent variable. The underlying intuition behind the liquidity hypothesis is that informed traders prefer to trade in the most liquid market (Chowdhry and Nanda, 1991) so they can hide the price impact of their trades and prolong the value of their information (Kyle, 1985). Further, Fleming et al. (1996) examine trading costs and price discovery within stock, futures and options markets and provide evidence that suggests that price discovery will occur in the market with lower transaction costs (or the more liquid market). Chakravarty et al. (2004) measure liquidity using the bid-ask spread and trading volume in the stock and options markets. We apply a similar method and, given the differences in liquidity between the stock and options market, expect a negative (positive) relation between relative bid-ask spreads (trading volume) and option price discovery shares, if liquidity is a key determinant of price discovery. Capelle-Blancard (2001) models the strategic interaction of individuals informed about the underlying stock (directional-informed traders) and individuals informed about volatility (volatility traders) and examines the impact of their interaction upon the bid-ask spread in the options market. The author concludes that the presence of volatility traders removes directional-informed traders from 7 Muravyev et al. (2013) find that the VECM coefficients are insignificant after 200 lags for the option price series. In addition, we use midpoint prices rather than trade prices, as the latter increases the amount of noise in each price series. 9

10 the options market (due to wider spreads in the options market) into the stock market. 8 Based on this theory, Chakravarty et al. (2004) find weak evidence that an increased level of uncertainty proxied by volatility in the underlying stock price results in reduced price discovery within the options market. In support of the uncertainty hypothesis, we also expect a negative relation between volatility (which is represented by the daily standard deviation of one-minute midquote returns in the underlying stock market) and option price discovery shares. Theory suggests that informed traders will prefer to trade in the options market due to the synthetic leverage advantage (Black, 1975, Easley et al., 1998). Chakravarty et al. (2004) examine price discovery across different strike prices and find a higher level of price discovery in the options market for out-of-the-money (OTM) options when compared to near-the-money (ATM) and in-themoney (ITM) options. 9 We develop our own leverage measure in equation (8): ( ( ) ( ( ))) (8) which we construct in the following manner: i) we find the natural logarithm of the ratio of daily time-weighted average midquote stock price to that of the midquote call option price multiplied by the delta of a call option ( ( )), ii) we find the natural logarithm of the ratio of daily time-weighted average midquote stock price to that of the midquote put option price multiplied by the delta of a put option ( ( )) and iii) take the average of steps i) and ii). 10 We multiply our measure by delta to take into account the sensitivity of option prices to changes in the underlying asset price. The intuition behind our measure is to capture the additional units of exposure that we get from an options position when compared to a similar investment in the underlying stock. Thus, lower priced call or put options reflect out-of-the-money options, or increased leverage. We expect a positive relation between our leverage measure and option price discovery shares to support the leverage hypothesis. Following a similar set-up to Chakravarty et al. (2004) we examine the competing drivers of price discovery using the following panel regression and stock-day observations: ( ) (9) 8 An alternative explanation is that there is increased price discovery in the stock market when there is higher volatility in the underlying asset price. 9 OTM (ITM) options are defined when the strike price is more (less) than 5% above (under) the stock price. 10 Note, ( ) ( ), where is the underlying spot price at time t, is the strike price, ( ) is the present value of dividends, is the continuously compounded risk-free rate of interest per annum, is the implied volatility of the underlying asset price and is the number of days till expiration of the options contract. 10

11 where is the price discovery share of the options market for stock i on day t using the Yan- Zivot-Putniņš information leadership share (ILS) metric. is the ratio of the time-weighted average quoted bid-ask spread in the options market to that of the stock market, is the ratio of options market traded volume to that of the stock market, is the standard deviation of one minute midquote returns in the stock market only, and is calculated using equation (8) Changes in market structure In this section we investigate an endogenous concern between price discovery shares and relative liquidity between the options and stock markets. Specifically, price discovery shares and liquidity can be co-determined by informed traders choice of market. For instance, if informed traders choose to trade in the options market for some exogenous reason perhaps more stringent informed trading regulation which affects trading in the stock market only, then this will result in increased price discovery in the options market and wider spreads in the options market consistent with adverse selection risks from informed traders (Glosten and Milgrom, 1985; Kyle, 1985). We use the reduction in the minimum tick size for options listed on the CBOE as an instrumental variable for relative liquidity. We measure relative liquidity using, the ratio of the timeweighted average quoted bid-ask spread in the options market to that of the stock market. Our instrumental variable is calculated when the minimum tick size was reduced to $0.01 for option classes less than $3 and $0.05 for option classes greater or equal to $3. 12 The CBOE gradually reduced (on different dates) the minimum tick size for 13 option classes on January to a total of 369 option classes on July The reduction in minimum tick size applies to 29 of 36 stocks and the two ETFs in our sample. 13,14 The reduction in minimum tick size for options listed on the CBOE should cause the bid-ask spread in the options market to fall due to the removal of a binding constraint on the width of the spread (Harris, 1999). Thus, we could expect that an exogenous increase in liquidity caused from this event will result in increased price discovery in the options market consistent with the liquidity hypothesis and it being cheaper to trade in the options market (Chowdhry and Nanda, 1991; Fleming et al., 1996). Note however, that we expect that the reduction in the minimum tick size for CBOE option classes will not directly affect option price discovery shares other than via changes in relative spreads between the options and stock markets. 11 To reduce the impact of outliers we express all regression variables in natural logarithm form and we winsorize the 1 st and 99 th percentiles of all regression variables. 12 Previously, the minimum tick size for options listed on the CBOE was $0.05 for options classes less than $3 and $0.10 for options classes greater or equal than $3 (Battalio et al., 2004). 13 Six stocks within our sample changed ticker or merged prior to January For our sample the reduction in minimum tick size took place on a number of different dates including: February , February , September , March , November , February and August for two stocks, one stock and two ETF s, eight stocks and one ETF, nine stocks, three stocks, four stocks and two stocks from our sample, respectively. 11

12 We use this exogenous event as an instrumental variable for relative liquidity between the options and stock markets within a two-stage least squares regression model. In the first stage model (equation (10)) we regress upon a dummy variable which is equal to 0 (1) before (after) the reduction in minimum tick size for option classes listed on the CBOE ( ). (10) In the second stage regression (equation (11)) we examine the relation between relative liquidity between the options and stock markets using fitted values of relative bid-ask spreads ( ) obtained from the first stage regression and relative price discovery shares ( ( ). The control ) variables include: the ratio of options market traded volume to that of the stock market ( ), the standard deviation of one minute midquote returns in the stock market only ( ), the average of the ratio of the time-weighted average midquote stock price to that of the call option price and to that of the put option price ( ) and a time trend variable which is equal to 1 on the first stock-day of our sample and increases by 1 for each subsequent trading day ( ). 15,16 ( ) (11) 5. Results 5.1 Descriptive statistics Table 1 presents descriptive statistics for the options (Panel A) and stock (Panel B) markets. We observe that the time-weighted quoted bid-ask spreads in the options market are almost four times larger (using median values) than the stock market. In addition, we observe that the options market has lower trading activity represented by 0.02% trading volume and 13% of the number of quote updates when compared to the stock market. The leverage advantage of options is clearly evident, as on average stock prices are approximately 24 times larger in magnitude than options prices or 3.34 times larger using our leverage metric. We note that for our sample of stocks and ETFs that volatility or the level of uncertainty represented by the daily standard deviation of one-minute midquote returns is similar between both the stock and options markets. 15 Our variable controls for the general trends in liquidity overtime which are not related to our exogenous event in the first stage regression and general trends in price discovery shares overtime in the second stage regression. We use a time trend variable rather than time fixed effects as the reduction in minimum tick size affects our sample of stocks at a specific point in time (Foley and Putniņš, 2013). 16 Again to mitigate the impact of outliers within our analysis we express all regression variables (except dummy variables) in natural logarithm form and we winsorize the 1 st and 99 th percentiles of all regression variables. 12

13 < Table 1 here > Overall, the differences in bid-ask spreads, traded volume and the number of quotes changes provide some evidence to suggest that the options and stock price series contain different levels of noise which will create bias in the conclusions drawn from the IS and CS metrics. In section 5.2 we use the ILS metric which can accurately calculate the share of price discovery in the options market when the two price series in question contain different levels of noise and we compare these findings with the IS and CS metrics. Further, a combination of wider bid-ask spreads and lower trading activity (represented by trading volume and the number of quote updates) indicates that the options market for our sample of 36 stocks and two ETFs has higher transaction costs and is less liquid than the stock market. In section 5.3 we test competing hypotheses to document the determinants of price discovery in the options market. 5.2 Price discovery in the stock and options markets We present the price discovery shares of the options market in Table 2 for the IS, CS and ILS metrics using estimates based on data pooled from all sample days over the last decade. 17,18,19 Consistent across price discovery metrics and with previous studies, the majority of price discovery is found in the stock market. The mean IS, CS and ILS levels of price discovery in the options market for our sample of 36 stocks and two ETFs is equal to 14.21%, 22.63% and 33.20%, respectively (Panel C). 20 Of particular note, we document using the ILS metric that the price discovery share in the options market is 33.20%, approximately two to five times larger in magnitude when compared to Chakravarty et al. (2004) and Muravyev et al. (2013), respectively. 21 This finding suggests options markets are an important source of informed trading and price discovery, consistent with early theoretical predictions. < Table 2 here > In addition, this finding is also consistent with the intuition underlying the ILS metric (Putniņš, 2013), for example, wider spreads in the options market create more noise in the option price series 17 For instances where a component share (CS) estimate is negative or greater than one, we truncate the estimates to zero and one, respectively. This procedure is consistent with a price discovery interpretation of the component share, in which a price series can contribute between zero and all of the price discovery for an asset, and thus its price discovery share can take the range [0,1] (Harris et al., 2002). 18 The following ticker codes merged or changed code during the sample period: AOL, CPN, MWD, SBC and NXTL, which explains the lower number of observations associated with these tickers. 19 There are approximately 2,520 trading days in 10 years but it is possible for each ticker to have more than 2,520 observations if more than one put-call pair meets the criterion outlined in Section We find similar results for day by day estimates of the IS, CS and ILS metrics for our sample of stocks and ETFs. 21 We acknowledge that our sample of stocks and sample period is different to Chakravarty et al. (2004). 13

14 relative to the stock price series, which creates a downward bias in the magnitude of the IS and CS metrics. In our study, the IS and CS metrics understate price discovery in the options market by approximately a factor of two when compared to the ILS metric. Only on three occasions (AMGN, AOL and CPN) does either the IS or CS metrics estimate a larger level of price discovery in the options market than the ILS metric. Also consistent with Putniņš (2013), the IS and CS metrics measure different aspects of price discovery. Specifically, relative to the CS metric, the IS metric places more weight on the speed of adjustment of a price series to new information. Our findings support this conclusion as the mean and median IS (approximately 14%) and CS (approximately 22%) estimates are different for our sample stocks and period. < Table 3 here > In Table 3 we examine the time-series of the IS, CS and ILS metrics by year. During the sample period the mean and median IS and CS metrics show an upward trend. In contrast, the ILS metric shows a downward trend particularly in median yearly values. Muravyev et al. (2013) only use the IS metric to document the information share of the options market during the period April to October and they find that the mean (median) option information share is approximately 6.25% (2.60%). We confirm Muravyev et al. s (2013) claim that the option information share is lower during their sample period when compared to Chakravarty et al. (2004). In Panel A we calculate that the mean (median) option information share using the IS metric from 2003 to 2006 is 8.80% (3.38%). 22 Further comparison during the same time period shows that the mean (median) price discovery shares calculated using the ILS metric is 42.06% (22.26%), approximately six times larger in magnitude than the IS metric, providing further support that the IS metric understates price discovery in the options market. Similarly, throughout the remainder of the sample period the IS metric continues to understate the information share in the options market when compared to the ILS metric, however, the ILS metric is approximately only twice as large in magnitude in In addition, comparing the CS metric (Panel B) with the ILS metric over our sample period provides mixed findings. Initially, we document that the mean (median) CS metric understates the price discovery share in the options market when compared to the ILS metric throughout the entire sample period (up to 2007). However, the median CS metric overstates option price discovery shares between 2007 and Lastly, we examine option price discovery shares in the three months before and after the introduction of the pilot uptick rule on May and the permanent removal of the uptick rule on 22 This figure includes approximately three additional months of data compared to Muravyev et al. (2013). Note that we exclude the ticker DIA due to a low number of observations, otherwise our sample is identical with the same stocks and ETFs. 14

15 July ,24 Specifically, we expect that these changes in market structure will result in a decrease in option price discovery shares as it becomes easier for investors to short-sell the underlying stock. In Panel D, inconsistent with our prediction, we observe that the IS and CS metrics increase following the introduction of the pilot uptick rule. In contrast, the mean and median ILS metric decrease, providing more evidence supporting the validity of the ILS metric when measuring price discovery shares between two markets. Following the permanent removal of the uptick rule, the median IS, CS and ILS metrics produce similar conclusions, i.e., a decrease in price discovery in the options market. In summary, our findings suggest options markets are an important source of informed trading and price discovery, consistent with theoretical predictions. Using the ILS metric we document that the level of price discovery in the options market is approximately 33%, which is almost two and five times larger in magnitude than Chakravarty et al. (2004) and Muravyev et al. (2013), respectively. Our findings confirm that the IS and CS metrics used in previous studies largely understate the true level of price discovery in the US options market between 2003 and In the next section we examine competing drivers of price discovery in the options and stock markets. 5.3 What factors affect the level of price discovery in the options market? In Table 4 we examine the drivers of price discovery in the options market for our sample of 36 stocks. 25 We present four model specifications and all regression variables are expressed in logarithmic form and as a ratio. The exceptions include which is defined as the daily standard deviation of one-minute midquote returns within the stock market only and which is defined as the implied volatility for each put-call pair which makes the market price of the call and put option prices consistent with the Black-Scholes call and put option prices. < Table 4 here > In model (1) we begin with a similar specification to Chakravarty et al. (2004), by regressing market characteristics against option price discovery shares calculated using the IS metric. Similarly, we find a negative relation between option price discovery shares and relative bid-ask spreads. This 23 The uptick rule restricts short selling to take place in the following circumstances, i) on an uptick a price greater than the last traded price, or ii) on a zero-plus tick at the last traded price if the last trade was made on an uptick. 24 The pilot uptick rule removed the uptick rule for a random sample of stocks between May and August , including ten stocks from our sample. 25 For the remaining sections we exclude the two ETFs in our sample from our analysis as ETFs have different characteristics than stocks including, i) ETFs are used for trading the market and ii) there is a considerable adverse selection problem in stocks which is likely to be marginal in ETFs. 15

16 result implies that increased price discovery in the options market is associated with lower transaction costs or spreads in the options market when compared to the stock market. 26 Given the bias inherent in the IS metric, our analysis focuses on the drivers of price discovery in the options market using the ILS metric. In contrast to Chakravarty et al. (2004) and in model (2), we observe that a 1% increase in the relative bid-ask spread results in a 2.22% increase in relative option price discovery shares. In particular, this finding is consistent with increased levels of adverse selection as a result of informed trading in the options market. Thus, wider spreads in the options market correspond with increased price discovery in the options market. Further, this positive relation between bid-ask spreads and the ILS metric is consistent with the work of Putniņš (2013). Specifically, wider spreads create more noise in the options price series relative to the stock price series and as a result cause a downward bias in the IS and CS metrics. In contrast, the ILS metric is able to reliably calculate option price discovery shares when the two price series have a different level of noise. We also document in model (2) a significant and positive relationship between relative trading volume and option price discovery shares. Firstly, this result is consistent with informed traders hiding their trades by trading in the market in which uninformed traders predominantly trade within, or the pooling of uninformed and informed traders (Admati and Pfleiderer, 1988; Chowdhry and Nanda, 1991). Thus, a larger proportion of uninformed traders trading in the options market rather than the stock market will mean informed traders also predominantly trade in the options market resulting in increased price discovery in the options market. Secondly, increased trading activity by informed traders as a proportion of total volume in the options market will by chance be the market first to reflect innovations in the efficient price (Barclay and Warner, 1993). We do not find any evidence to support the uncertainty hypothesis as we document a positive relation between underlying stock volatility and relative option price discovery shares. Lastly, we examine whether leverage is a key driver of price discovery in the options market. In model (3) and consistent with theoretical predictions, we find that our leverage measure has a significantly positive relationship with option price discovery shares. Specifically, a 1% increase in the leverage from holding an options position results in a 1.82% increase in relative option price discovery shares. We note, that there are several factors which determine the leverage advantage inherent in holding an options position including, i) implied volatility, ii) time-to-maturity and iii) distance of the stock price to the strike price (termed distance to ATM). As a result we re-run our analysis using implied volatility, time-to-maturity and distance to ATM as explanatory variables (instead of our leverage variable) to provide a richer characterisation of how various option-level characteristics individually affect option price discovery shares. The theory underlying the relationship between 26 In unreported results, we observe similar findings when option price discovery shares are calculated using the CS metric. 16

17 these variables and leverage is as follows, increased levels of volatility in the underlying stock price increase options prices as there is a greater probability that the options contract will be in-the-money, thus decreasing the numerator of equation (8) and thus leverage. 27 Further, as the options contract approaches maturity results in lower option prices as there is a lower probability that the options contract will be in-the-money, thus increasing the numerator of equation (8) and thus leverage. Lastly, the further the distance (or difference) between the stock price and strike price will decrease the moneyness of the call option (if stock price < strike price) or the put option (if stock price > strike price). When the stock price is greater than (or increases relative to) the strike price than the increased leverage of out-of-the-money put options will dominate the lower levels of leverage associated with in-the-money call options, resulting in an increase in our leverage measure documented in equation (8). In summary, to support the expected positive relation between leverage and option price discovery shares, we expect a negative relation between implied volatility and option price discovery shares, a positive relation between time-to-maturity and option price discovery shares and a positive relation between distance to ATM and option price discovery shares. 28 We define as the implied volatility of the underlying stock price for each put-call pair which makes the market price of the call and put options consistent with the Black-Scholes call and put options prices, is a dummy variable equal to 1 if there is between a and b days (inclusive) till the expiration of the options contract and is the absolute value of the distance between the underlying stock price and strike price. Firstly, in model (4) inconsistent with our predictions, we observe a positive relation between implied volatility and option price discovery shares. To measure time-to-maturity we include weekly dummy variables beginning 10 calendar days till the expiration of the options contract. 29 All four dummy variables document a positive relation between time-to-maturity and option price discovery shares, however, only is significant. In particular, this finding suggests that informed traders prefer the leverage advantages of American near-the-money options contracts which have approximately two weeks remaining till maturity, which potentially provide sufficient time to trade upon their private information. Lastly and also consistent with our predictions, we see a significantly positive relation between distance to ATM and option price discovery shares. This result supports the notion that informed traders prefer the leverage advantages of using out-of-the-money options 27 We could expect different findings using implied volatility which is forward looking and less subject to microstructure noise when compared to using historical stock volatility ( ). 28 We expect a positive relation between time-to-maturity and option price discovery shares rather than a negative relation because the dummy variables measure shorter time-to-maturity relative to the base case, where the base case is the omitted category (which is option contracts which have a time-to-maturity of between 38 to 70 days). 29 Sample selection criteria (a) in Section 4.1 restrict our analysis including the 10 calendar days prior to the expiration of the options contract. 17

18 contracts. Future research can confirm leverage as a key driver of price discovery in the options market using deep out-of-the-money options contracts. In summary, we document new evidence that increased relative bid-ask spreads and trading volume are associated with increased price discovery in the options market. In addition, we show that our leverage variable and option-level determinants of leverage are also key drivers of option price discovery shares. 30 In contrast, Chakravarty et al. (2004) suggests that both relative liquidity and leverage increase price discovery in the options market. 5.4 Changes in market structure To address an endogeneity concern between relative liquidity and option price discovery shares we use the reduction in minimum tick size for option classes listed on the CBOE as an instrumental variable. Table 5 reports the output from the first stage regression in which is regressed upon a dummy variable representing our exogenous event. We run two specifications, in model (1) we use, and as control variables, and in model (2) we use option-level determinants of leverage as control variables including:,,,, and. Consistent with our predictions we observe in both models (1) and (2) that after the reduction in minimum tick size that the significantly falls. The F-statistics reported for models (1) and (2) are much greater than ten which provides some support to the validity of our instrumental variable (Bound et al., 1995). < Table 5 here > Table 6 presents the results from the second stage regression. In contrast to our OLS findings we observe an insignificant relationship between relative bid-ask spreads and option price discovery shares in both models (1) and (2). Thus, in contrast to the findings of Chakravarty et al. (2004) our 2SLS instrumental variable approach does not find any evidence to support the liquidity hypothesis as a key driver of price discovery in the options market. < Table 6 here > In addition, consistent with our OLS results in models (2 to 4) reported in Table 4, we observe a similar relationship in terms of sign and magnitude between relative volume, leverage and the optionlevel determinants of leverage and option price discovery shares. In particular, these results are consistent with theoretical predictions that informed traders may prefer to trade in the options market 30 Our findings in Table 4 are robust to including stock fixed effects and a time trend variable (similar to the methodology explained in Section 4.4). 18