Short-Sale Constraints and Option Trading: Evidence from Reg SHO. Sheng-Syan Chen * National Taiwan University

Transcription

1 Short-Sale Constraints and Option Trading: Evidence from Reg SHO Sheng-Syan Chen * National Taiwan University Yiwen Chen ** National Chengchi University Robin K. Chou * National Chengchi University August, 2014 Keywords: Option Trading; Pilot Program; Short-sales; Substitutability JEL Classification: G12, G14, G18 * Sheng-Syan Chen, Professor of Department of Finance, College of Management, National Taiwan University, Taipei, Taiwan, fnschen@management.ntu.edu.tw; Robin K. Chou, Professor of Finance and Risk and Insurance Research Center, College of Commerce, National Chengchi University, Taipei, Taiwan, rchou@nccu.edu.tw. ** Corresponding author: Yiwen Chen, PhD Candidate, Department of Finance, National Chengchi University, Taipei, Taiwan, Tel: ; @nccu.edu.tw. 1

2 Short-Sale Constraints and Option Trading: Evidence from Reg SHO Abstract We study the substitutability of the stock and the option market trading surrounding a temporary suspension of short-sale constraints introduced by Reg SHO from 2005 to The Security and Exchange Commission (SEC) designated a set of pilot securities for the suspension, i.e., the Pilot Program. We find a significant decrease in put volume for the pilot stocks. The pilot stock put prices decrease significantly relative to the pilot stock call prices after Reg SHO. We also find that information content of the option trading decreases significantly. These results suggest that the option market is a substitute to the stock market, because the short-sale constraints relaxation allows traders to switch part of their trading demand to the stock market. 2

3 1. Introduction Extensive evidence in the literature shows that short-sale constraints have significant impacts on the stock market price efficiency, liquidity, and price discovery (e.g., Jones and Lamont, 2002; Bris, Goetzmann, and Zhu, 2007; Boehmer, Jones, and Zhang, 2008; Saffi and Sigurdsson, 2011; Beber and Pagano, 2013). A trader who wants to reflect a negative view about a security can either sell the security if he happens to own it, sell the security short, or buy (write) put (call) options. Due to short-sale constraints on the stock market, it might be difficult and costly to short sell. Hence, there is a potential for short-sale constraints on the stock markets to affect the option trading activity as traders seek to trade on the option markets instead. Compared with the extensive studies on the effect of short-sale constraints on the stock market, the cross-market effects of stock market short-sale constraints on the option market receive relatively less attention from the literature (notable exceptions include Figlewski and Webb, 1993; Ofek, Richardson, and Whitelay, 2004; and Grundy, Lim, and Verwijmeren, 2012). In this paper, we explore the substitutability of stock short sales and option trading, and further investigate the effects of the stock market short-sale constraints on option prices and the relation between option prices and stock prices. We further examine the changes in information content of the option market due to changes in short-sale constraints. Purchasing (Writing) a put (call) option or establishing a short position is common alternatives for traders to make profits when expecting a price decline. Thus, any trading rule changes in one market are likely to affect the price and trading of the other. Exchanges are constantly competing for order flows and thus it is important to know how short-sale constraints on the stock market would impact the option market. It seems straightforward to view the option trading as a substitute for selling a stock short directly and if this is the case, then there will be a negative relation between stock 3

4 market short-sale activity and option trading. The empirical studies, however, offer mixed evidence. Some papers show that, instead of sell short directly, the option market is an alternative trading venue for investors with unfavorable information (Figlewski and Webb, 1993; Danielsen and Sorescu, 2001; Beber and Pagano, 2013), whereas some papers do not find the stock and option markets being substitutes (Battalio and Schultz, 2011; Grundy, Lim, and Verwijmeren, 2012). Next, if investors anticipate a drop in a stock price, they are more likely to buy put options to capitalize on their information. This will lead to a price increase in the put options. Several recent papers demonstrate that the difference in the prices (implied volatilities) between puts and calls can arise in the presence of short-sale constraints on the underlying stocks (e.g., Figlewski and Webb, 1993; Lin, Lu, and Driessen, 2014), and that the difference can significantly predict future equity returns (Bollen and Whaley, 2004; Xing, Zhang, and Zhao, 2010; Jin, Livnat, and Zhang, 2012). The results indicate that, in the presence of short-sale constraints, it is easier for informed traders with negative information to capitalize on their private information by trading options. In addition, prior research analyzes the effect of short-sale constraints on put-call parity. Lamont and Thaler (2003), Ofek and Richardson (2003), Ofek et al. (2004), and Evans, Geczy, Musto, and Reed (2009) find that deviations from put-call parity arise in the presence of short-sales constraints on the underlying stocks. Short-sales constraints cause price pressures on put relative to call options, because trading strategies of buying puts or writing calls are used to circumvent short-sale constraints. Further, short-sales constraints tend to cause stock price overvaluation (Miller, 1977; Morris, 1996; Scheinkman and Xiong, 2003; Chang, Cheng, and Yu, 2007), and without short sales, it is difficult for the overvalued stock prices to converge to those implied by put-call parity. 4

5 Thus, it is expected that short-sale constraints are positively related to the probability of put-call disparity. Furthermore, it is interesting to examine the markets in which traders with negative private information would first release their information, because it has implications for the cross-market information linkage, price discovery and hence market efficiency (Ofek et al.,2004; Chakravarty, Gulen, and Mayhew, 2004). Studies find that in the presence of short-sales constraints, traders with negative information are forced to sit out of the stock market and may trade options to circumvent the short sale constraints (Miller, 1977; Damodaran and Lim, 1993). 1 In this paper, we examine the effect of stock market short-sales constraints on the option market, which include option volume, option prices, put-call parity, and information content of the option market. We take advantage of a temporary suspension of short-sale constraints mandated by the Security and Exchange Commission (SEC) from 2005 to 2007 for a set of designated pilot securities, i.e., the Pilot Program. The Pilot Program is an experiment which requires a temporary suspension of short-sale price tests, i.e., a form of short-sale constraint relaxations. Specifically, it requires a temporarily suspending from the provisions of Rule 10a-1 under the Securities Exchange Act of 1934 and any short-sale price tests of any exchange or national securities association for short sales of certain securities for certain time periods to evaluate the overall effectiveness and necessity of such restrictions (a Pilot Program pursuant to Rule 202T). 2 The Pilot Program commenced on May 2, 2005 and was set to end on August 6, 1 Damodaran and Lim (1993) find that following option introduction, a greater amount of information related to earnings announcement shocks is impounded in stock prices and that prices adjust more quickly to negative earnings shocks. 2 Detailed descriptions of the Pilot Program are in the Appendix. 5

6 During the period, approximately a third of the stocks in the Russell 3000 Index, i.e., the pilot stocks, were allowed to short without regard to any price tests. The pilot stocks were selected by the SEC to represent a broad cross-section of the U.S. equity markets. As the SEC pointed out, the Pilot Program will allow the investigation of trading behavior in the absence of short-sale price tests through empirical analysis. We examine the differences in option trading of stocks subject to the Pilot Program with those not subject to the program. For option trading volume, our analysis shows that after the relaxation of the short-sale constraints, the put option trading volumes of the pilot stocks decrease significantly, relative to those of the control stocks. Investors appear to buy put options as an alternative for selling a stock short. The decrease in put volume is not caused by increases in trading costs, as we do not find significant changes in option bid-ask spreads surrounding the event. The negative impact of short-sale constraints on put option volume is robust by using a two-equation structural model, which allows option volume and spreads to be simultaneously determined (George and Longstaff, 1993). To investigate the effects of the Pilot Program on option prices, we adopt two option measures often used in the recent literature: Implied Volatility (IV) Spread and IV Skew (Figlewski and Webb, 1993; Jin, Livnat, and Zhang, 2012; Chan, Ge, and Lin, 2013). IV Spared is the difference in the implied volatility between put and call options with the same underlying stock, identical times to expiration and strike price and IV Skew is the difference in the implied volatility between the out-of-the-money puts and the 3 The Pilot Program effectively ended on July 6, Based on empirical analyses by SEC staff, academic researchers, and feedback from industry practitioners, the SEC voted on June 13, 2007 to adopt amendments to Rule 10a-1 (17 CFR a-1) and Regulation SHO (17 CFR et. seq.) that removed Rule 10a-1 as well as any existing exchange-mandated short-sale price test effective July 6, 2007 for all stocks. The price tests, however, was reintroduced in 2009 by SEC to help promote market stability and restore investor confidence after the 2008 financial crisis, which is widely debated. A modified form of the rule was adopted on February 24,

7 at-the-money calls with the same underlying stock and identical times to expiration. IV Skew is used to measure the demand of investors holding negative information for the out-of-the-money puts, because these options offer traders the greatest leverage (Chakravarty, Gulen, and Mayhen, 2004; Chen, Lung, and Tay, 2005). Both measures gauge the differences in implied volatility between puts and calls. High put implied volatilities relative to call implied volatilities suggest that puts are more expensive relative to calls, and vice versa. The higher prices of puts than those of calls are likely induced by the excess demand for put options relative to that of call options due to investors trying to alleviate the short-sale constraints on the stock markets (Figlewski and Webb, 1993; Lamont and Thaler, 2003; Ofek et al., 2004). We document that, after the suspension of the price tests, both IV Spread and IV Skew significantly decrease for options of the pilot stocks, but not for those of the control stocks. These findings indicate that the relaxation of short-sale constraints decreases the demand of put options relative to that of call options and thus put option prices decrease relative to call prices. When short selling is restrictive, investors may use options as a substitute, especially put options, which would make them overpriced and hence induce put-call parity violations. We examine the upper put-call parity bound for American options: the sum of the prices of a stock and a put should not exceed the sum of the price of a call (with equivalent strike and maturity), strike price and the present value of the dividends to be paid prior to maturity. Violation of put-call parity occurs when the package of the stock and a put appears overpriced relative to the package of the call, strike price, and dividend rights. We show that the suspension of the price tests significantly reduces the probability of put-call parity violations, which is in line with both theoretical predictions and previous 7

8 empirical findings that short-sale constraints induce mispricing and prevent arbitragers from implementing the put-call parity arbitrage strategy that involves short selling the stock. Our results support the assertion that short-sale constraints negatively affect market efficiency, because when short-sale constraints are lessened, the probability of put-call parity violations is significantly decreased. Finally, we find that the information content of the pilot securities option trading decreased significantly after Reg SHO, using the option and stock volume ratio (O/S) as a proxy for the option information content (Roll et al., 2010; Johnson and So, 2012; Hu, 2014). Our finding of decreased O/S after the suspension of the price tests supports the argument that short-sale constraints induce traders with private information to trade more actively on the option market; thus the short-sale constraints relaxation for the pilot stocks allows traders with negative information to switch part of their trading demand to the stock market. Our paper is most closely related to Grundy et al. (2012), who find that trading volume in the option market does not increase significantly during the 2008 financial crisis short-sale ban on the stock market and conclude that derivative strategies are not effective substitutes for short sales. We contribute to the literature by examining the impact of stock short-sale constraints on option trading through the Pilot Program, which we believe better delineates the effect. Our paper differs significantly from Grundy et al. (2012) and the related literature in the following ways. First, since the SEC imposed short-sale bans on financial stocks only during the 2008 financial crisis, studies using the financial crisis samples are left with financial stocks in the treatment group and non-financial firms in the control group. The systematic 8

9 differences between these two groups of stocks might introduce other confounding effects that potentially interfere with those of the short-sale ban (Fama and French, 1992; Foerster and Sapp, 2005) 4. range of industries. In contrast, the pilot securities selection process spans a much wider In the Pilot Program, the pilot stocks and the control stocks are similar in terms of the distributions of the NYSE, Amex, and Nasdaq securities, as well as the distributions of securities for which there are associated options and single stock futures. 5,6 We also show that if only financial firms in the pilot stocks are selected as the treatment samples and non-financial firms are selected as the control samples, similar to the sample setup of Grundy et al. (2012), then we fail to find evidence showing option trading being a substitute for short sales. Second, the 2008 short-sale ban was implemented as a response to unusual market conditions, while the Pilot Program was commenced when the market is relatively stable. Hoffmann, Post, and Pennings (2013) show that individual investors perceptions about risk exhibit significant fluctuations during different market conditions. We expect that the volatile market fluctuations during the financial crisis are likely interfering with investors risk tolerance and risk perceptions and this in turn would affect their trading behaviors. The changes in trading behaviors and the implementation of short-sale ban are likely to simultaneously change the dynamic trading and informational relations between the stock and the option markets. Third, traders experienced extreme funding liquidity risk during the 2008 financial crisis. Since banks are short on capital, they need to scale back their trading that requires 4 It is a common practice for many finance empirical studies to exclude financial services firms from the samples to avoid the effect of capital structures dictated by regulatory considerations. Fama and French (1992) point out that, for example, because high leverage is normal for financial firms, it probably does not have the same meaning as for non-financial firms, where high leverage more likely indicates distress. 5 Securities Exchange Act Release No (July 28, 2004). 6 Our sample naturally includes only firms in these two groups with listed options. 9

10 capital and also scale back the amount of capital they lend to other traders such as hedge funds. Brunnermeier and Pedersen (2009) find that traders become reluctant to take on positions when funding liquidity is tight. In particular, a decrease in funding liquidity (either due to the change in trader s wealth or the change in margin interest rates) is likely to reduce the trading volume and raise the bid-ask spreads. Thus, the decrease in option market liquidity as founded in Grundy et al. (2012) is likely to be at least partially driven by the lack of funding liquidity during the 2008 financial crisis. Forth, some studies (e.g., Figlewski and Webb, 1993; Danielsen and Sorescu, 2001) test whether the introduction of traded options represents a relaxation of short-sale constraints by providing an alternative device for short seller. However, the decision to introduce exchange-traded options on a stock may result in a selection bias if short interest happens to be related to the characteristics of a stock that make it a good candidate for options trading, for example, excellent past performance, and/or large market capitalization. Our sample pilot stocks and control stocks include firms that already have listed options and are thus less likely to be subject to such sample selection biases. Finally, our work differs from previous studies which also examine the Pilot Program. We focus on the dynamic trading relation between the stock and the option markets, while most of the prior studies only examine the effect of the Pilot Program on the stock market quality. Previous literature of the Pilot program focuses on its impact on the stock market short activity, liquidity, volatility, market efficiency, and price impact (Alexander and Peterson, 2008; Diether, Lee and Werner, 2009b). Exchanges, however, are constantly competing for order flows and any trading rule changes in one market are likely to affect the other. Thus, it is important to know how regulation changes in the short-sale constraints on the stock market would impact the trading of option market. Our research will shed light on the impact of short-sale 10

11 constraints on the dynamic relations between the stock market and the option market, and hence provide important policy implications for the influence of short sale constraints on price formation and order follow competitions in closely related markets. The remainder of the paper is organized as follows. Section 2 briefly reviews the relevant literature and develops testable hypotheses. Section 3 describes the data and summary statistics. Section 4 presents the empirical results of changes in option volume, option prices, put-call parity violations, and information content of the option market due to the Pilot Program. Section 5 reports robustness tests. Section 6 concludes the paper. 2. Literature Review and Testable Hypotheses The empirical results of the relation between option trading and stock market short selling are rather mixed. Some studies show that the introduction of traded options represents a relaxation of short-sale constraints (Figlewski and Webb, 1993; Danielsen and Sorescu, 2001). The argument is that, by buying put options or writing call options, options facilitate short selling by enabling investors with negative information to take synthetic short positions on the option market. Danielsen and Sorescu (2001) show that the documented negative abnormal returns and changes in short interest around option listings are consistent with the mitigation of short-sale constraints resulting from the option introduction. Beber and Pagano (2013), studying the 2008 short-sale ban around the world due to financial crisis, find that bans were detrimental to liquidity, but the effects of short selling restrictions on the bid-ask spreads are stronger for stocks without a listed option than for those with a listed option. 7 They conclude that for stocks with 7 Most stock exchange regulators around the world imposed some sorts of bans or constraints on short sales in response to the financial crisis, which include Australia, Austria, Belgium, Canada, Denmark, France, Germany, Greece, Ireland, Italy, Japan, Luxembourg, Netherlands, Norway, Portugal, South Korea, Spain, Switzerland, UK and USA. 11

12 listed options, investors could use the option market to gain short exposure during the short-sale ban period. Other studies, however, do not find evidence on the substitutability of short sale and option trading. Battalio and Schultz (2011) investigate the ratio of option-to-stock volume for U.S. markets during the 2008 financial crisis short-sale ban period and find no evidence that investors seeking short exposures in banned stocks (financial stocks) migrated to the options market during the short-sale ban period. Similarly, Grundy et al. (2012) find a significant diminution in option volumes for banned stocks relative to unbanned stocks during the ban period. Thus, under the short-sale ban, stocks with traded options do not seem to experience significant migration of trading from the stock market to the option market. Grundy et al. (2012) conclude that option trading does not seem to be a substitute for short-sale demand during the ban period. Diether et al. (2009b), examining the effect of the Pilot Program on the stock market, show that the short-sale volume increases significantly for pilot stocks relative to that of control stocks, which shows that the suspension of the price tests makes it easier to execute short sales. In this study, we utilize the Pilot Program to investigate whether option volume decreases after the suspension of the price tests. If option trading is indeed a substitute to stock trading and traders attempt to circumvent short-sale constraints through trading in the option market, then, compared to control stocks, there will be a significant decline in the option volume of pilot stocks after the relaxation of short-sale constraints during the Pilot Program period. We thus propose the first hypothesis as follows: Hypothesis 1: Option volume will decrease after the suspension of the price tests due to Reg SHO. 12

13 In addition to the effect of the short-sale constraints on option volume, another strand of the finance literature has focused on the relation between option prices and short-sales constraints. Figlewski and Webb (1993) argue that because of the price tests and other impediments to short selling, put prices will be high relative to call prices with a large investor demand for short positions. Specifically, if pessimistic investors buy puts or write calls as substitutes for selling short, either to hedge against future price drop or to speculate on the potential returns, then put prices are raised and call prices are depressed. Therefore, puts become unusually expensive and the implied volatilities of puts will be greater than those of calls. Figlewski and Webb (1993) show that stock market short interest is correlated with the option price patterns and put implied volatilities are found to be high relative to call implied volatilities. Furthermore, recent literature points out the inflated put price patterns will especially significant for the out-of-money puts. Chakravarty, Gulen, and Mayhen (2004), and Chen, Lung, and Tay (2005) document that investors holding negative information tend to buy out-of-the-money puts because out-of-the-money options offer informed traders the greatest leverage. 8 Due to the pessimistic investors preference for out-of-the-money puts, IV Skew (Xing, Zhang, and Zhao, 2010), defined as the difference in implied volatility between out-of-the-money puts and at-the-money calls, is considered to be a proxy for negative price pressures on the options market and can significantly predict future equity returns (Bollen and Whaley, 2004; Xing, Zhang, and Zhao, 2010; Jin, Livnat, and Zhang, 2012). The results are consistent with the notion that informed traders with negative information prefer to trade out-of-the-money put options, and that the equity 8 Theory suggests several factors that might influence investors choice of strike price. Out-of-the-money options offer the greatest leverage. On the other hand, bid-ask spreads and commissions tend to be the largest for out-of-the-money options. Bid-ask spreads tend to be the lowest for at-the-money options, while commissions tend to be the lowest for in-the-money options. However, the relative importance of these competing factors is an empirical question and has not yet been adequately resolved (Jong, Koedijk, and Schnitzlein, 2006; Anand and Chakravarty, 2007; and Chakravarty, Gulen, and Mayhen, 2004). 13

14 market is slow in incorporating the information embedded in IV Skew. If short-sale constraints help raise put prices relative to call prices, then suspending them would result in a decrease in the differences between the prices of puts and calls for pilot stocks relative to those for control stocks. Hence, we propose the second hypothesis as follows: Hypothesis 2: The difference between put prices and call prices will decrease after the suspension of the price tests due to Reg SHO. One of the most commonly mentioned no-arbitrage relations between stocks and options is put-call parity, which defines an arbitrage free relation between the prices of put and call options of the same underlying stocks, strike prices and expiration dates. The short-sale constraints of the underlying stocks are likely to cause violation of put-call parity because short-sale constraints increase the demand for puts, which bids up put prices relative to call prices, and lead to stock price overvaluation (Lamont and Thaler, 2003; Ofek et al., 2004). How short-sale constraints will increase the demand for put options and thus increase put prices has been discussed previously. As for the relation between short-sale constraints and stock price overvaluation, Miller (1977) presents a theoretical model showing that dispersion of investor opinion in the presence of short-sale constraints leads to stock price overvaluation. Short-sale constraints, combined with investors heterogeneous beliefs and information about the security s value, force pessimistic investors to sit out of the market. Thus, in the presence of short-sales constraints, security prices tend to reflect a more optimistic valuation than the average opinion of potential investors and tend to be upward biased. There is a large body of empirical work finding that stocks are sometimes expensive to short, and short-sale constraints induce overpricing of constrained stocks (Figlewski and Webb, 1993; Dechow, Hutton, 14

15 Meulbroek and Sloan, 2001; Asquith, Pathak, and Ritter, 2005; Chang, Cheng, and Yu, 2007; and Diether, Lee, and Werner, 2009a). 9 Lamont and Thaler (2003) document severe violations of put-call parity for a small sample of three stocks that have gone through an equity carve-out, and the parent sells for less than its ownership stake in the carve-out. Lamont and Thaler (2003) view this evidence as consistent with there being high costs to short these stocks. Ofek et al. (2004) investigate put-call parity in conjunction with short-sales restrictions as measured by the rebate rates from the stock short lending market. They find that, due to short-sale constraints, as stocks market values rise above those implied by the options markets, there is no arbitrage mechanism that forces convergence. On the other hand, if stock prices fall below their implied value, one can arbitrage by buying shares and taking the appropriate option positions. Evans et al. (2009) also document violations of put-call parity for hard-to-borrow stocks. Based on the prior literature, our third hypothesis is as follows: Hypothesis 3: The likelihood of put-call parity violation will become smaller after the suspension of the price tests due to Reg SHO. Another interesting issue of the relation between option and stock markets is where informed traders trade. Whether option markets lead equity markets or vice versa 9 For example, Chang et al. (2007) use Hong Kong market data to show that stocks included in an official short-sales list (allowed for selling short) experience a decline in stock prices and thus negative abnormal returns. In contrast, the 2008 ban on U.S. short sales of financial stocks increases the price of these banned stocks and cause positive abnormal returns for these stocks; the overpricing and positive abnormal returns are reversed when the ban is lifted (Gagnon and Witmer, 2009; Autore, Billingsley, and Kovacs, 2011). Diether et al. (2009b) show that the suspension of the price tests during the Pilot Program causes lower returns for pilot stocks relative to those of control stocks on the announcement day and the effective day. 15

16 remains an open question. 10 We use the O/S ratio, defined as the ratio of the total option volume to the total stock volume, as a proxy for the information content of option and equity volumes (Roll et al., 2010; Johnson and So, 2012; Hu, 2014). Roll et al. (2010) suggest that the cross-sectional and time-series variations in O/S could be driven by informed trade. As an extension of Roll et al. (2010), Johnson and So (2012) examine the relation between O/S and future returns and find that low O/S firms outperform the market while high O/S firms underperform. Johnson and So (2012) point out that equity short-sale costs result in a negative relation between relative option volume and future firm value. If short-sale constraints induce traders with negative information to trade more actively on the option market, then we expect that after Reg SHO, the short-sale constraints relaxation for the pilot stocks allows traders to switch part of their trading demand to the stock market, which would reduce the information content in the pilot stocks option trading. Thus, our forth hypothesis is as follows: Hypothesis 4: The O/S will decrease after the suspension of the price tests due to Reg SHO. 10 For example, Easley, O Hara, and Srinivas (1998) and Pan and Poteshman (2006) show that options order flows can predict the underlying stock returns. Anthony (1988) examines the interrelation of stock and option volumes and finds that call-option activity predicts volume in the underlying equity with a one-day lag. Similar findings are reported in Manaster and Rendleman (1982). In contrast, Stephan and Whaley (1990) find no evidence that options lead equities. Furthermore, Hao, Lee and Piqueira (2013) find a leading informational role of short sales by showing that short sales predict subsequent stock and put option returns, while put option imbalance only predicts its own future returns. Hao et al. (2013) suggest that short sales contain more information than option trading. 16

17 3. Data Our sample includes firms in the Russell 3000 Index as of June 2004 listed on the NYSE and on Nasdaq with listed options. 11 We partition these stocks into two categories: pilot stocks and control stocks. We obtain the list of 986 pilot stocks, where 525 of them with listed options, from the initial SEC order (Securities Exchange Act Release No (July 28, 2004), and 69 FR (August 6, 2004)), and the remaining securities in Russell 3000 index with listed options are included as control stocks. 12 To eliminate the potential confounding influence of index inclusions and exclusions, we require that sample stocks be part of the Russell 3000 index in the period between June 2004 and December Firms that change listing venue, go private, are involved in a merger or an acquisition, or for some reasons stop issuing options during the sample period are excluded. The final sample is summarized in Table 1. After applying our filters, 525 pilot stocks and 1,064 control stocks are left. For the pilot stocks, there are 283 (53.9%) NYSE-listed and 242 (46.1%) Nasdaq-listed stocks, whereas for the control stocks, there are 566 (53.2%) NYSE-listed and 498 (46.8%) Nasdaq-listed stocks. [Table 1 to be inserted here] Our sample period spans twelve months sounding the effective date of the Pilot Program, from November 1, 2004 to October 31, The sample period before the effective date of the Pilot Program, May 2, 2005, is defined as the Pre Reg SHO period, 11 Following Diether et al. (2009b), we exclude stocks that were listed on the AMEX due to the small sample size for this market. However, our results remain similar with the AMEX samples included. 12 Not all stocks in the Russell 3000 Index are treated as initial samples for the Pilot Program. See the Appendix for more details on the selection process. 13 We thank Russell Investments for providing access to the data of Russell 3000 holdings. 17

18 and the period during the program is defined as the Reg SHO period. The temporary suspension of short-sale price tests on pilot stocks ended on July 6, The first data set comes from OptionMetrics, which provide daily option prices, option volume, open interest, implied volatilities, delta, and stock trading volume. It computes implied volatilities for all listed options using the binomial tree model. 15 Daily stock closing prices and bid-ask quotes are obtained from CRSP. We use the closing value of the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) as a proxy for the market-wide volatility. Company accounting data and earnings forecast data are retrieved from Compustat and I/B/E/S, respectively. Similar to Ofek et al. (2004) and Grundy et al. (2012), we apply a set of data filters to minimize data errors and ensure option liquidity as follows: (1) We eliminate options that are either deep in- or out-of-the-money with an absolute moneyness greater than 4. Moneyness is defined as:, (1) where S i,t is the stock price of the underlying stock i on day t, K j is the exercise price for option j, ATM is the implied volatility of the firm s closest-to-the-money call (put) option in the call (put) option chain with the same expiration and observation date, and j,t is time to expiration for option j on day t. 16 (2) Options with the offer prices less than the bid prices are eliminated. 14 Securities Exchange Act Release No (June 28, 2007). 15 For calculating implied volatilities, according to the OptionMetrics, the theoretical option price is set equal to the midpoint of the best closing bid price and best closing offer price for the option. The Black-Scholes formula is then inverted using a numerical search technique to calculate the implied volatility for the option. 16 Following Grundy et al. (2012), we use a single implied volatility across all similarly specified options, instead of the implied volatility of each option, to abstract from the effects of volatility smiles. The reason is that since at-the-money options are generally the most liquid, their implied volatility might be the most reflective of the market s belief of the true volatility of the underlying security. However, the results are qualitatively similar if we repeat the analysis by using the implied volatility of each option. 18

19 (3) We focus on intermediate maturity options to ensure liquidity, thus options with a time to expiration less than 30 days or greater than one year are deleted. (4) Observations with zero open interest are dropped, since these options tend to be the least liquid. Table 2 provides a summary of the stocks and their listed options in our sample. Panel A reports the summary statistics for stocks, including returns and volume. Pilot stocks have an average daily return of 0.03%, while control stocks have an average daily return of 0.01%. The average daily trading volumes are 1.38 million and 1.34 million shares for the pilot and the control stocks, respectively. [Table 2 to be inserted here] Panel B of Table 2 reports the average daily option volume, open interest and the average days to expiration for puts and calls. Daily option volume (daily open interest) is the trading volume (open interest) of all options of a stock on a specific day. The average daily volume for puts is less than two-third of calls volume, while the trading volume of the pilot and the control stocks are similar. There are and contracts traded for puts on the pilot and the control stocks, respectively. There are and contracts traded for calls on the pilot and the control stocks, respectively. The daily open interest of the call options also tends to be larger than that of the put options and they are similar for the pilot and the control stocks. The open interest is 9,819 and 10,424 contracts for puts on the pilot and the control stocks, respectively. The open interest is 13,760 and 13,941 contracts for calls on the pilot and the control stocks, respectively. The prior literature (Ofek et al., 2004; Grundy et al., 2012) find similar results that calls trading volumes and open interests are usually larger than those of the put options. 19

20 The average number of days to expiration is around 120 days for both put and call options on all stocks. Panel C of Table 2 reports summary statics for options by moneyness. Most of the volume and open interest are concentrated in the at-the-money options, indicating that at-the-money options are the most liquid contracts. 4. Empirical Results 4.1 The effect of Reg SHO on option volume In this section, we test whether option trading volume decreases for the pilot stocks relative to the control stocks, after the short-sale price tests are suspended after Reg SHO. Section investigates the overall option volume and open interest, section focuses on subsamples by moneyness, and section examines a two-equation structural model considering the simultaneity of volume and spreads Overall option volume and open interest It has been shown by Diether et al. (2009) that short selling activity increases for both the NYSE- and Nasdaq-listed pilot stocks after Reg SHO. 17 To examine the effect of Reg SHO on option volume, we first aggregate the volume of all options on the same stock (daily total option volume; ) and, following Grundy et al. (2012), estimate an ordinary least squares (OLS) regression to examine the effect of Reg SHO on : (2) where OVS i,t is the put (call) option volume for a given stock i on day t. Each unit of volume corresponds to a single contract written on 100 shares. Stock volume i,t is the total 17 From our preliminary analyses, we also find that short-sale volume increases significantly after Reg SHO. 20

21 number of shares of stock i traded on day t; Stock return i,t is the daily return of the stock (%); VIX t is the closing value of the CBOE Volatility Index on day t. Equation (2) allows for links between option volume and both the stock volume and stock returns. The effect of the market-wide uncertainty is captured by the level of VIX. Pilot i is a dummy variable that equals one if a given stock is a pilot stock, and zero otherwise. Reg SHO t is a dummy variable that equals one if the observation is between May 2, 2005 and October 31, 2005 when Reg SHO authorizing the Pilot Program is in effect, and zero otherwise. The industry dummies are included to control for the industry-level fixed effects. As a robustness check, we replace the option volume by the option open interest and repeat the above analyses. A significantly negative (positive) coefficient on the interaction dummy, Pilot i Reg SHO t, indicates that the pilot stock options experience a significant decrease (increase) in option volumes during the Reg SHO period, compared to those of the control stocks. Panels A and B of Table 3 present the regression results of option volume and option open interest, respectively. Panel A shows that the coefficients on the pilot dummy, Pilot i, for both put and call options are significantly negative. This indicates that the pilot stock options generally have lower trading volumes. The significant positive coefficient on Reg SHO dummy indicates a general increase in option volume after the suspension of the price tests, possibly due to the increased trading interest on both the stock and the option markets through time. More importantly, we find that the interaction dummy, Pilot i Reg SHO t, is significantly negative for put options, which indicates that the pilot stock put options experience a decrease in volume relative to the control stock put options after Reg SHO. Further, the differences between the pilot stock call volume and the control stock call volume are not significant. Although theoretically writing a call option is another 21

22 strategy to take advantage of an expected drop in stock price and might be a substitute for short sale, buying a put option is superior due to the chance of a larger profit and lower risk. More specifically, buying put options as an alternative to short sales offers potential profit limited only by stock prices declining to zero and predetermined financial risk versus predetermined profit and unlimited upside risk from writing call options (Figlewski and Webb, 1993; Chen and Singal, 2003; and Diether et al., 2009b). Thus, the decline in option volume after the suspension of the price tests is especially significant for put options. These results support our Hypothesis 1 and indicate that after the relaxation of short-sale constraints, traders seem to transfer their short selling demand from put options to stock trading, which induces a significant drop in put volume, while call volume remains roughly the same. Traders use put options as a substitute for short sales. [Table 3 to be inserted here] Stock volume has a positive and significant effect on option volume. The coefficient on stock returns on call (put) volume is positively (negatively) significant. Positive stock returns generate more trading interests in call options, while the opposite is true for put options. It is generally argued that higher market-wide uncertainty leads to more option trading. However, we find that VIX has a negative impact on option volume, which is consistent with Grundy et al. (2012), who point out it is possible that a contemporaneous increase in market-maker inventory costs and/or an increase in spreads could dampen the positive relation between market-wide uncertainty and option trading. Panel B of Table 3 reports the OLS results of the effects of Reg SHO on open interest. The coefficient on the interaction term between Pilot i and Reg SHO t for put option is again significantly negative, indicating that after Reg SHO the open interest of pilot stock put 22

23 options are significant decreased. All the coefficients on other control variables are similar to those of the volume regressions. Overall, results from Table 3 show that Reg SHO leads to a significant decrease in the trading activity and open interest of the pilot stock put options, compared to those of the control stock put options. These results support our Hypothesis 1 that investors trade put options as a substitute for selling a stock short. To test the impact of control stock choices, we re-estimated the effect of the relaxation of short-sale constrains on volume (Equation (2)) with a sample setup similar to that of Grundy et al. (2012). For the pilot stock options, we keep financial firms only, and for the control stock options, we keep non-financial firms only. With these samples, we find that the effect of Reg SHO on the pilot stock option trading volume relative to the control stock option trading volume becomes statistically insignificant. Thus, we conjecture that the insignificant findings of the 2008 short-sale ban on option trading volume in Grundy et al. (2012) may be partially due to the mismatch in their sample firms and control firms Subsample analysis We next examine option trading by different option moneyness to allow for the possibility that some option traders are more likely to turn instead to the stock market after short-sale constraints are relaxed. If short-sellers seek to replicate the dollar price sensitively of a short position in stock, establishing long positions in the in-the-money puts might be the best substitute trading strategy for short sale, in which case we expect to see a significant decline in the in-the-money put volume after the suspension of the price 18 Grundy et al. (2012) recognize that their samples differ in a range of firm characteristics and match their sample financial firms with other non-financial firms with a set of firm characteristics. However, in the end, the matching firm method is not able to alleviate the problem of comparing financial with non-financial firms. 23

24 tests. If instead short-sellers emphasize on maximizing profits with a stock price decline, they would buy the out-of-the-money puts as a substitution for short sale. Finally, the at-the-money puts are usually the most liquid options, as is also true in our samples (see Panel C of Table 2). If would-be short-sellers care more about liquidity, then they tend to buy the at-the-money puts (Jong, Koedijk, and Schnitzlein, 2006; Anand and Chakravarty, 2007; and Chakravarty, Gulen, and Mayhen, 2004). Thus, it is an empirical question as to which moneyness of options is going to be most sensitive to changes in short-sale rules. Moneyness is defined in Equation (1). We partition our sample options by three ranges of moneyness: 1. at-the-money (ATM): for both calls and puts; 2. in-the-money (ITM): for calls and for puts; and 3. out-of-the-money (OTM): for calls and for puts. Table 4 presents the effect of Reg SHO on option volumes by moneyness. For put options, the coefficients on the interaction dummy, Pilot i Reg SHO t, are negative for all moneyness subsamples, but only those for the ATM and ITM options are significant. Furthermore, the coefficient on the interaction dummy of the ATM options exhibits much more economic significance compared to that of the ITM options. This result implies that the ATM put option traders seem to be most affected by Reg SHO and appear to be the ones that switch their short-sale demand from the option market to the stock market after Reg SHO. For the call options, the coefficients on the interaction dummies are all insignificant. Thus, it is found again that the substitution of short sales by options is mainly concentrated in put options, especially the ATM put options. [Table 4 to be inserted here] 24

25 Two-equation structural model George and Longstaff (1993) show that changes in option volume negatively influence option bid-ask spreads and vice versa. Considering the simultaneity between option volume and option spread, a potential concern of our approach in Section is that the found effect of Reg SHO on option volume might be through its effect on the bid-ask spreads. For example, the decrease in option volume might be due to the increase in the option bid-ask spread after Reg SHO. To control for the problem, we first investigate the effect of the suspension of the price tests on option bid-ask spreads and then use a two-equation structural model to delineate the net impact of Reg SHO on option volume. We use a new measure of relative spreads, the spread relative to optionality (SRO) introduced by Grundy et al. (2012), which focuses on the cost of trade relative to the interesting component of an option s value. As pointed out by Grundy et al. (2012), the traditional relative spread measure will mechanically increase as an option become out of money, because the denominator will be larger for ITM options than for OTM options. 19 Since the option spreads are reflection of information asymmetries and inventory holding costs linked to price uncertainty, the traditional spread measure which has an asymmetric effect induced by moneyness is less appropriate. The SRO measure scales the spread by only the uncertainty-related portion of the premium, i.e., the interesting component, defined as the option price minus the maximum of the option s intrinsic value (a lower bound based on the ability to exercise immediately) and the present value of a forward contract with the same maturity and strike as the option (a lower bound based on the ability to commit to exercise at maturity). Due to the 19 The traditional relative spread measure is. 25

26 adjustment in the denominator relative to the traditional relative spread measure, SRO will tend to be lower for ATM options and higher for both the deep ITM and the deep OTM options. Following Grundy et al. (2012), SRO is defined as follows: ; (3) { [ ] for calls [ ] for puts (4) { for calls for puts (5) where Best offer j,t and Best bid j,t refer to the lowest closing ask price and the highest closing bid price for option j on day t, respectively. S i,t is the stock price of the underlying stock i on day t, K j is the exercise price for option j, and j,t is the time to expiration of that option. PV i,t (div) is the present value of the set of dividends with ex-dates prior to the option s maturity as reported by CRSP. We obtain Treasury bill rate data from the Federal Reserve Bank at St. Louis as the dividend discount rate. Following Grundy et al. (2012), we eliminate options (1) with a bid price that is less than the maximum of the intrinsic value and PV(forward), and (2) with a spread that is more than 50% of the excess of the midpoint price over and above the maximum of the intrinsic value and PV(forward). These filters naturally exclude all observations in which the denominator of the SRO is zero or negative. Panel A of Table 5 reports summary statistic of SRO. Over the entire sample period, the average SRO is 19.53% for puts and 19.71% for calls, which are slightly higher than the SRO in Grundy et al. (2012) using the 26