Short-Sale Constraints and Option Trading: Evidence from Reg SHO

Transcription

1 Short-Sale Constraints and Option Trading: Evidence from Reg SHO Abstract Examining a set of pilot stocks experiencing releases of short-sale price tests by Regulation SHO, we find a significant decrease in put volume and price pressure of options of the pilot stocks after Regulation SHO. Violations of put-call parity and information content of option trading significantly decrease after Regulation SHO. The relaxation of short-sale constraints on equity markets allows traders to switch part of their trading demand from option markets to stock markets and hence significantly affects option market quality and spot and option market relations. Thus, it is important to consider the cross-market effects of short-sale regulations. 0

2 Purchasing a put or writing a call option is a common method for establishing a short position when traders expect a price decline. Option markets are closely related to the equity markets, and exchanges are constantly competing for order flows. Thus, any trading rule changes to one market are likely to affect the trading activity, price, and market quality of the other. The Securities and Exchange Commission (SEC) passed Regulation SHO (Reg SHO), effective on January 3, 2005, which provides a new regulatory framework governing short-selling of securities on the U.S. equity markets. Given the interconnectedness of the two markets, this regulatory change also likely affects the option markets. Among other things, Reg SHO established the Pilot Program, an experiment that temporarily suspended short-sale price tests. 1 The Pilot Program was implemented on a subset of the Russell 3000 index component stocks (pilot stocks), representing a broad cross-section of the U.S. equity markets. The Pilot Program commenced on May 2, 2005 and ended on July 6, During the period, the pilot stocks were allowed to short without regard to any price tests. The appendix provides a detailed description of the Pilot Program. Numerous studies have examined the effect of the Pilot Program on the stock market trader behavior and market quality (SEC 2007; Alexander and Peterson 2008; Diether, Lee, and Werner 2009; Boehmer and Wu 2013). SEC (2007), Alexander and Peterson (2008), and Diether et al. (2009) examine the effect of Reg SHO on the NYSE and Nasdaq, and Boehmer and Wu (2013) focus on the NYSE. Overall, these studies find that, although short trading volume increases significantly both for NYSE- and Nasdaq-listed pilot stocks, spread and volatility are not significantly affected. Also, the suspension of the price tests contributes 1 These price tests apply to short sales and are known individually as the uptick rule on the NYSE and the bid test on Nasdaq. The uptick rule states that short sales cannot be made at a lower price than the previous price (known as a minus tick) or at the same price as the preceding trade, but at a lower price than the last trade of a different price (known as a zero-minus tick). The bid test prohibits short sales at or below the current best bid when that bid is lower than the previous best bid. These two restrictions on short sale executions are collectively referred to as price tests. 2 Based on empirical analyses by SEC staff, academic researchers, and feedback from industry practitioners, the SEC voted on June 13, 2007 to remove any existing exchange-mandated short-sale price test effective for all stocks on July 6,

3 significantly to price discovery in equity markets. They conclude that the removal of price tests has no deleterious effect on trader behavior and does not lead to a decrease in market quality. We examine the effect of the Pilot Program on option markets. Although the experiment was directed at the equity market, it can significantly affect option markets in several ways. First, a trader who wants to reflect a negative view about a security can sell the security if he or she owns it, sell the security short, or buy (write) put (call) options. It seems straightforward to view option trading as a substitute for directly selling a stock short. Some studies show that, instead of selling 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). Second, short-sale constraints will likely cause price pressures on put relative to call options, because traders use strategies of buying puts or writing calls to circumvent short-sale constraints. Thus, the higher demand for a put option to circumvent short-sale constraints leads to a price increase for put options relative to call options. 3 Third, if informed traders do trade in the option markets to circumvent short-sale constraints, short-sale constraints will likely impact the dynamic price discovery processes on the equity and option markets. Miller (1977) and Damodaran and Lim (1993) find that in the presence of short-sale constraints, traders with negative information are forced to sit out of the stock market. Thus, they may trade options to circumvent the short-sale constraints. Damodaran and Lim find that following option introduction, a greater amount of information is impounded in stock prices. Overall, we conjecture that short-sale constraints on the equity market have implications for cross-market information linkage, price discovery, and hence 3 Figlewski and Webb (1993) and Lin and Lu (2015) demonstrate that the differences in the prices (implied volatilities) between puts and calls arise in the presence of short-sale constraints on the underlying stocks as well as the deviations from put-call parity (Lamont and Thaler 2003; Ofek and Richardson 2003; Ofek et al. 2004; Evans, Geczy, Musto, and Reed 2009). 2

4 market efficiency (Chakravarty, Gulen, and Mayhew 2004; Ofek, Richardson, and Whitelaw 2004). We find that after the relaxation of the equity short-sale constraints, the put option trading volume of the pilot stocks decreases significantly, relative to that of the control stocks, indicating that investors trade fewer put options after the release of short-sale price tests. 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. Furthermore, we use a two-equation structural model, which allows option volume and spreads to be simultaneously determined (George and Longstaff 1993), to show that the negative impact of the Reg SHO on put option volume is robust. To investigate the effects of the Pilot Program on option prices, we adopt two option valuation measures often used in the literature: implied volatility spread (IV spread) and implied volatility skew (IV skew) (Bollen and Whaley 2004; Cremers and Weinbaum 2010; Xing, Zhang, and Zhao 2010; Jin, Livnat, and Zhang 2012; Chan, Ge, and Lin 2013). IV spread is the difference in the implied volatility between put and call options with the same underlying stock and identical times to expiration and strike price, and IV skew is the difference in the implied volatility between the out-of-the-money (OTM) puts and the at-the-money (ATM) calls with the same underlying stock and identical times to expiration. Both measures gauge the differences in implied volatilities between puts and calls. High put implied volatilities relative to call implied volatilities (i.e., high IV spread and IV skew) suggest that puts are more expensive relative to calls, and vice versa. The excess demand for put options due to investors trying to circumvent the short-sale constraints on the stock markets likely induces the higher prices of puts than those of calls (Figlewski and Webb 1993; Lamont and Thaler 2003; Ofek et al. 2004). We find that, after the suspension of the price tests, both IV spread and IV skew significantly decrease for options of the pilot 3

5 stocks but not for those of the control stocks. These findings indicate that the relaxation of short-sale constraints decreases the demand for put options relative to that for call options, and thus put option prices decrease relative to call option prices. We further examine the upper put-call parity bound for U.S. 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 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 (Lamont and Thaler 2003; Ofek et al. 2004; Grundy, Lim, and Verwijmeren 2012). As a result, our findings support the assertion that short-sale constraints degrade market efficiency, because the probability of put-call parity violations significantly decreases when short-sale constraints are lessened. We further find that the information content of the pilot securities option trading decreases significantly after Reg SHO. We first employ the option and stock volume ratio (O/S) as a proxy for the option information content (Roll, Schwartz, and Subrahmanyam 2010; Johnson and So 2012; Hu 2014) and find a significant decrease in O/S after the suspension of the price tests. In addition, we examine the predictability of implied volatility differences (IV differences; i.e., IV spread and IV skew) on future stock returns. Because investors holding negative information tend to buy put options or sell call options and thus raise IV differences, higher IV differences are expected to be negatively associated with future stock returns (Xing et al. 2010; Jin et al. 2012; Chan et al. 2013). We find that the 4

6 predictability of IV spread on future returns significantly weakens after the suspension of price tests, indicating a decrease in the information content of the pilot securities option trading. These results show that short-sale constraints induce traders with private information to trade more actively on the option market and that 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. The effects of short-sale regulations have not been fully understood in the literature, because finding two economies that are identical except for whether they have short-sale constraints is difficult. We take advantage of the unique setting of Reg SHO, which releases short-sale constraints for a set of pilot stocks, while keeps the constraints for other stocks intact. This experiment allows us to use a set of control stocks to control for other potential confounding factors and test the effect of short-sale constraints. Our work complements earlier studies that examine the Pilot Program. 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 et al. 2009; Boehmer and Wu 2013). We instead focus on the option trading activity and price, and dynamic trading relation between the option and the stock markets. The only exception to the previous research that we are aware of is the SEC (2007), which examines the effect of Reg SHO on option trading but finds no evidence that the Pilot Program has an impact on option trading volume or open interest. The SEC, however, does not control for other factors that may affect option trading such as stock volume, stock returns, marketwide uncertainty, and option trading cost. Our analysis provides a comprehensive investigation of the effect of the Pilot Program on the option market by carefully controlling for potential confounding effects. In addition to studying option trading volume as examined by the SEC, we also examine option prices, violation of put-call parity, and information 5

7 content of option trading after Reg SHO, which yields important implications for the effect of short-sale constraints on the cross-market price efficiency and price discovery. In light of the recent global financial crisis and the extensive use of short-sale constraints around the world, our paper provides important evidence for the ongoing debates regarding the effectiveness of short selling regulations. We also show that it is important to consider the cross-market effects of short-sale regulations. Our paper is also closely related to studies that examine whether option strategies are substitutes for short sales (Figlewski and Webb 1993; Danielsen and Sorescu 2001; Battalio and Schultz 2011; Grundy et al. 2012) but differs significantly from the previous literature in many ways. Figlewski and Webb (1993) and Danielsen and Sorescu (2001) find that the introduction of traded options provides an alternative device for short sellers and thus represents a relaxation of short-sale constraints. Although we also find that the short sales and derivatives appear to be substitutes, we address this issue by the control sample approach that controls for other confounding factors such as stock characteristics. Figlewski and Webb (1993) and Danielsen and Sorescu (2001) find empirical evidence that option trading is substitute for equity short sales. They compare stocks with exchange-traded options and stocks with no options, but 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 or large market capitalization. Our sample of pilot stocks and control stocks include firms that have already listed options and are thus less likely to be subject to such sample selection biases. Recent papers by Battalio and Schultz (2011) and Grundy et al. (2012) investigate the substitutability of short-sale and derivatives for the U.S. market during the 2008 financial crisis short-sale ban period. They find that derivative strategies are not substitutes for short 6

8 sales because trading volume on the option market does not increase significantly during that period. However, short-sale bans during the crisis period only apply to financial firms, and the financial crisis period experiences extreme market turmoil, which likely interferes with the effect of short sale bans. Because the SEC imposed short-sale bans only on financial stocks, their conclusion on the debate about the substitutability of short sales and derivatives may be distorted by the systematic differences between the treatment group (financial firms) and the control group (non-financial firms), which may potentially interfere with the short-sale ban (Fama and French 1992; Foerster and Sapp 2005). In contrast, the pilot securities span a much wider range of industries. In the Pilot Program, the pilot stocks and the control stocks are similar in terms of the distributions of the NYSE and Nasdaq securities as well as the distributions of securities with associated options. 4 To show the effects of this potential sample selection bias, we repeat our tests using financial firms in the pilot stocks as the treatment samples and non-financial firms as the control samples, similar to the sample setup of Battalio and Schultz (2011) and Grundy et al. (2012). Interestingly, we fail to find evidence showing that option trading is a substitute for equity short sales. The 2008 short-sale ban was implemented as a response to unusual market conditions, while the Pilot Program was undertaken when the market was 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 likely interfere with investors risk tolerance and risk perceptions, which, in turn, affect their trading behaviors. The changes in trading behaviors and the implementation of short-sale ban are likely to change simultaneously the dynamic trading and informational relations between the stock and the option markets. 4 See Securities Exchange Act Release No (July 28, 2004). Our sample naturally includes only firms with listed options. 7

9 The remainder of the paper is organized as follows. Section 1 briefly reviews the relevant literature and develops testable hypotheses. Section 2 describes the data and summary statistics. Section 3 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 4 reports robustness tests, and Section 5 concludes the paper. 1. 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 effectively facilitate short selling by enabling investors to take synthetic equity 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. They conclude that for stocks with listed options investors can use the option market to gain short exposure during the short-sale ban period. Other studies, however, do not find evidence on the relation between equity short-sale constraints 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 option market during the short-sale ban period. Similarly, Grundy et al. (2012) 8

10 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 experience significant migration of trading from the stock market to the option market. Grundy et al. conclude that option trading is not a substitute for short-sale demand during the ban period. Alexander and Peterson (2008) and Diether et al. (2009), 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 indicates that the suspension of the price tests makes it easier to execute short sales. We conjecture that if traders attempt to circumvent short-sale constraints by trading on the option market, then the option volume of pilot stocks, compared to that of control stocks, will decline significantly after the relaxation of short-sale constraints due to Reg SHO. In addition to the effect of the short-sale constraints on option volume, another strand of literature focuses on the relation between option prices and short-sale constraints. Figlewski and Webb (1993) and Cremers and Weinbaum (2010) 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. Empirically, Figlewski and Webb show that stock market short interest is correlated with the option price patterns and put implied volatilities are high relative to call implied volatilities. Furthermore, recent literature points out the inflated put price patterns are especially significant for out-of-money puts because investors holding negative information tend to buy 9

11 OTM puts due to the higher leverage offered by these options (Chakravarty et al. 2004; Chen, Lung, and Tay 2005). 5 Due to pessimistic investors preference for OTM puts, IV skew, defined as the difference in implied volatility between OTM puts and ATM calls, is positive and is a proxy for negative price pressures on future equity returns (Bollen and Whaley 2004; Xing et al. 2010; Jin et al. 2012; Chan et al. 2013). If short-sale constraints raise put prices relative to call prices, then suspending them would result in a decrease in the price differences between put and call options after 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 they increase the demand for puts, which bids up put prices relative to call prices (Lamont and Thaler 2003; Ofek et al. 2004). 6 Lamont and Thaler (2003) find 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 view this evidence as consistent with the high costs of short selling these stocks. Ofek et al. (2004) investigate put-call parity in conjunction with short-sale 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, no arbitrage mechanism exists that forces convergence. On the other hand, if stock prices fall below their implied value, one can 5 Theory suggests several factors that may influence investors choice of strike price. OTM options offer the greatest leverage. On the other hand, bid-ask spreads and commissions tend to be the largest for OTM options. Bid-ask spreads tend to be the lowest for ATM options, whereas commissions tend to be the lowest for ITM options. The relative importance of these competing factors is, however, an empirical question and has not yet been adequately resolved (Chakravarty et al. 2004; Jong, Koedijk, and Schnitzlein 2006; Anand and Chakravarty 2007). 6 Stock price overvaluation may be another reason for the equity short-sale constraints causing violation of put-call parity. However, Alexander and Peterson (2008) and Diether et al. (2009) provide no evidence that the Pilot Program had a material effect on equity price levels. 10

12 arbitrage by buying shares and taking the appropriate option positions. Evans et al. (2009) also report violations of put-call parity for hard-to-borrow stocks. Based on the prior literature, we expect that 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. Studies find that informed traders tend to trade on option markets (Easley, O Hara, and Srinivas 1998; Pan and Poteshman 2006; Roll et al. 2010; Xing et al. 2010). Easley et al. (1998) and Pan and Poteshman (2006) show that options order flows can predict the underlying stock returns. Further, Easley et al. indicate that, due to the rules limiting short sales on the equity market, option markets are more attractive venues for traders acting on negative information. 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. suggest that short sales contain more information than option trading. Our study sheds further light on this debate by examining the information content of option trading during the Pilot Program. If short-sale constraints induce traders with negative information to trade more actively on the option market, then the relaxation of short-sale constraints allows informed traders to switch part of their trading demand to the stock market, which leads to a reduction in the information content of option trading. 11

13 2. Data Our samples include firms in the Russell 3000 Index as of June 2004 listed on the NYSE and on Nasdaq with listed options. 7 We partition these stocks into two categories: pilot stocks and control stocks. We obtain the list of 986 pilot stocks; 609 of them have listed options from the initial SEC order (Securities Exchange Act Release No , July 28, 2004, and 69 FR 48032, August 6, 2004). We include as control stock the remaining securities in the Russell 3000 index with listed options. 8 To eliminate the potential confounding influences 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 stop issuing options during the sample period are excluded. Table 1 provides a summary of the final sample. After applying these filters, 525 pilot stocks and 1,064 control stocks remain. The pilot stocks comprise 283 (53.9%) NYSE-listed and 242 (46.1%) Nasdaq-listed stocks, and the control stocks comprise 566 (53.2%) NYSE-listed and 498 (46.8%) Nasdaq-listed stocks. [Table 1 to be inserted here] Our sample period spans the 12 months surrounding 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, and the period during the program is defined as the Reg SHO period. We obtain daily option prices, option volume, open interest, implied volatilities, and delta from the OptionMetrics database. OptionMetrics computes implied volatilities for all 7 Following Diether et al. (2009), we exclude stocks that are listed on the AMEX due to the small sample size for this market. However, our results remain similar with the AMEX samples included. 8 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. 9 We thank Russell Investments for providing the history of the Russell 3000 index component stocks. 12

14 listed options using the binomial tree model. 10 Stock trading volume, daily stock closing prices, and bid-ask quotes are obtained from University of Chicago s Center for Research in Securities Prices (CRSP). We use the closing value of the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) as a proxy for marketwide volatility. Company accounting data and earnings forecasts data are retrieved from Compustat and I/B/E/S, respectively. Following 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 ITM or OTM with an absolute moneyness greater than 4. Moneyness is defined as Moneyness,, ln,,, (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 Options with the offer prices less than the bid prices are eliminated. 3. Options with a time to expiration less than 30 days or greater than one year are deleted to ensure liquidity. 4. Observations with zero open interest are dropped, because these options tend to be the least liquid. Table 2 provides a summary of the sample stocks and their listed options. Panel A reports the summary statistics for stocks, including returns and volume. Pilot stocks have an 10 For calculating implied volatilities, according to 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. 11 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 because ATM options are generally the most liquid, their implied volatility may 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 using the implied volatility of each option. 13

15 average daily return of 0.03%, whereas 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 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; the trading volume of the pilot and control stocks are similar. The average daily open interest of the calls also tends to be larger than that of the puts, while it is similar between the pilot and the control stocks. The prior literature (Ofek et al. 2004; Grundy et al. 2012) finds similar results that calls trading volumes and open interests are usually larger than those of put options. The average number of days to expiration is around 120 days for both put and call options. Panel C of Table 2 reports summary statistics for options by moneyness. Most of the volume and open interest are concentrated in the ATM options, indicating that ATM options are the most liquid contracts. 3. Empirical Results 3.1 The effect of Reg SHO on option volume In this section, we test the impact of Reg SHO on option trading volume and open interest. Section investigates the overall impact of Reg SHO, Section focuses on subsamples by moneyness, and Section presents results controlling for the simultaneity of volume and spreads with a two-equation structural model. 14

16 3.1.1 Overall option volume and open interest 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; OVS) and, following Grundy et al. (2012), estimate an ordinary least squares (OLS) regression to examine the effect of Reg SHO on OVS. The regression equation is, α,,,, (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 number of shares of stock i traded on day t, Stock return i,t is the daily return of stock i on day t, and 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 marketwide uncertainty is captured by VIX. Pilot i is a dummy variable that equals 1 if a given stock is a pilot stock, and zero otherwise. Reg SHO t is a dummy variable that equals 1 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. µ k represents unobserved industry-specific heterogeneity or, in other words, industry fixed effects. A significantly negative (positive) coefficient on the interaction dummy, Pilot i Reg SHO t, in equation (2) indicates that the pilot stock options experience a significant decrease (increase) in option volumes after Reg SHO, compared to those of the control stocks. As a robustness check, we repeat the above analyses with the option volume replaced by the option open interest. Panels A and B of Table 3 present the regression results of option volume and option open interest, respectively. [Table 3 to be inserted here] 15

17 Panel A of Table 3 shows that the coefficients on the pilot dummy, Pilot i, for both put and call options are significantly negative. This result indicates that in general the pilot stock options have lower trading volumes. The significant positive coefficient on the 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 option markets through time. The coefficient on Pilot i Reg SHO t is for put options and significant at the 1% level, indicating that the pilot stock put options experience a significant decrease in volume relative to the control stock put options after Reg SHO. In contrast, the differences between the pilot stock call volume and the control stock call volume are not significant. Although theoretically writing a call option is an alternative strategy to buying a put option, buying a put may be preferred. 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, whereas writing call options offers predetermined profit and unlimited upside risk (Figlewski and Webb 1993; Chen and Singal 2003; Diether et al. 2009). Thus, the decline in option volume after the suspension of the price tests is especially significant for put options. These results indicate that after the relaxation of short-sale constraints, traders 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. 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 whereas the opposite is true for put options. We find that VIX has a negative impact on option volume, which is consistent with Grundy et al. (2012), who point out that a contemporaneous increase in market-maker inventory costs or an increase in spreads can possibly dampen the positive relation between marketwide uncertainty and option trading. 16

18 Panel B of Table 3 reports the effects of Reg SHO on open interest. The coefficient on the interaction term of 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 options is significantly decreased. All the coefficients on other control variables are similar to those of the volume regressions. Overall, the results from Table 3 show that Reg SHO leads to a significant decrease in the trading activity of the pilot stock put options. These results support the argument that investors buy put options as an alternative to selling a stock short. To test the impact of control stock choices, we reestimated the effect of the relaxation of short-sale constrains on volume (equation (2)) with a sample setup similar to that of Battalio and Schultz (2011) and Grundy et al. (2012). Specifically, we use financial firms in the pilot stock as samples only and nonfinancial firms as the control stock samples only. With these samples, we find that the effect of Reg SHO on the pilot 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 Battalio and Schultz and Grundy et al. may be partially due to the mismatch of 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 to the stock market after short-sale constraints are relaxed. If short sellers attempt to replicate the dollar price sensitivity of a short position in stock, establishing long positions in the in-the-money (ITM) puts may be the best substitute trading strategy for short sale, in which case we expect to see a significant decline in the ITM put volume after the suspension of the price tests. If instead short sellers emphasize maximizing profits with a stock price decline, they would buy the OTM puts. However, the ATM puts are usually the most liquid options, as is also true in our samples 12 Grundy et al. (2012) recognize that their samples differ in a range of firm characteristics and match their sample financial firms with nonfinancial firms with a set of firm characteristics. However, they are still not able to account for the fundamental differences between financial and nonfinancial firms. 17

19 (see Panel C of Table 2). If would-be short sellers care more about liquidity, they tend to buy the ATM puts (Chakravarty et al. 2004; Jong et al. 2006; Anand and Chakravarty 2007). Thus, which moneyness of options is most sensitive to changes in equity short-sale rules is an empirical question. Moneyness is defined in equation (1). We partition our sample options by three ranges of moneyness: (i) ATM, 1 Moneyness,, 1 for both calls and puts; (ii) ITM, 4 Moneyness,, 1 for calls and 4 Moneyness,, 1 for puts; and (iii) OTM, 4 Moneyness,, 1 for calls and 4 Moneyness,, 1 for puts. Table 4 presents the effect of Reg SHO on option volume by moneyness. [Table 4 to be inserted here] 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 magnitude of the coefficient on the interaction dummy of the ATM options is much higher than that of the ITM options. 13 This result implies that the ATM put option traders are most affected by Reg SHO and appear to be the ones that switch more of their short-sale demand from the option market to the stock market after Reg SHO. The embedded leverage provided by options is an important motive for option trading, except for the ability of options to circumvent short-sale constraints (Black 1975; Chakravarty et al. 2004; Chen et al. 2005). OTM option traders do not seem to migrate significantly from option trading to stock trading after the relaxation of short-sale constraints, possibly because they trade OTM options mainly due to their high embedded leverage, instead of circumventing short-sale constraints. For the call options, the coefficients on the interaction dummies are all 13 We run the pool regression for ATM and ITM put volume: OVS i,t = α + β 1 Stock volume i,t + β 2 Stock return i,t + β 3 VIX t + β 4 Pilot i + β 5 Reg SHO t + β 6 (Pilot i Reg SHO t ) + β 7 AT + β 8 (AT Stock volume i,t ) + β 9 (AT Stock return i,t ) + β 10 (AT VIX t ) + β 11 (AT Pilot i ) + β 12 (AT Reg SHO t ) + β 13 (AT Pilot i Reg SHO t ) + µ k + ε i,t. where AT is a dummy variable that equals 1 if the observation is ATM put, and zero if the observation is ITM put. The coefficient on AT Pilot i Reg SHO t is and significant at the 5% level, indicating that the decrease in the ATM put volume is significantly higher than that of the ITM put volume. 18

20 insignificant. Thus, again the substitution of short sales by options is mainly concentrated in put options, especially the ATM put options, because traders circumventing short-sale constraints seem to value the better liquidity of ATM options 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 OLS approach is that the found effect of Reg SHO on option volume may be influenced by its effect on the bid-ask spreads. For example, the decrease in option volume may 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, 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. The interesting component of an option s value is its value in excess of the lower bound on its value given both the ability to exercise immediately and the ability to commit to exercise at maturity. Thus, 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). As pointed out by Grundy et al., the traditional relative spread measure mechanically increases as an option becomes out of money, because the denominator is larger for ITM options than for OTM options. Because the option spreads are a reflection of information asymmetries and inventory holding costs 19

21 linked to price uncertainty, the traditional spread measure, which has an asymmetric effect induced by moneyness, is less appropriate. 14 Following Grundy et al. (2012), SRO is defined as,,,, 100; (3),, /,,,,,,, max 0,, for calls max 0,, 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. PV i,t (div) is the present value of dividends with ex-dates prior to the option s maturity as reported by CRSP. We calculate the dividend discount rates by interpolating from the curve of the Treasury bill rate and matching the maturities of the zero curve with the time to the dividend payments. Treasury bill rates are obtained from the Federal Reserve Bank of St. Louis. Following Grundy et al. (2012), we eliminate options (i) with a bid price that is less than the maximum of the intrinsic value and PV j,i,t (forward) and (ii) 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 j,i,t (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 statistics for SRO. Over the entire sample period, the average SRO is 19.53% for puts and 19.71% for calls, which are close to the SROs in Grundy et al. using the sample period of January, The SRO for calls is higher than the SRO for puts, which is also found in Grundy et al. 14 The traditional relative spread measure is {(Best offer j,t Best bid j,t )/ (Best offer j,t + Best bid j,t )/2} 100. Although the new measure, SRO, is a preferable measure of option trading costs comparing to the traditional relative spread as suggested by Grundy et al. (2012), we reestimate our regression with the traditional relative spread measure, and the signs and significance of the estimated coefficients are qualitatively unchanged. 20

22 [Table 5 to be inserted here] Following Grundy et al. (2012), the structural model is specified as 15,,,,,,,,, (6),,,,,,,,,, 1,,,, 1,,,,,,,,,. (7) Equation (6) is the option volume equation. The dependent variable, OV j,i,t, is the daily volume for option j on day t. In the two-equation structural model, we use the individual option volume instead of the aggregated OVS as in equation (2), because the bid-ask spreads are calculated for each individual option. The bid-ask spread represents a major component of the transaction cost, which is expected to impact volume adversely. The control variables included in the trading volume equation are the total number of shares of the underlying stock i traded on date t (, ), the daily return on the underlying stock (, ), and the closing value of the CBOE Volatility Index ( ). We use all exogenous variables as instruments to obtain the estimated spreads,,,, and use them in estimating equation (6). Equation (7) is the option spread equation. The dependent variable, SRO j,i,t, is as defined previously. D j,t is a dummy variable that equals 1 if, >, and zero otherwise. Recall that Moneyness,, ln,,., is the inverse of the option s time to maturity. is the closing value of the CBOE Volatility Index on day t. and 15 As a preliminary test, we examine the effect of Reg SHO on SRO and find that SRO is not significantly related to Reg SHO, which suggests that the decrease in put volume for the pilot stocks cannot be explained by changes in option spreads. 21

23 are dummy variables indicating the Reg SHO period and the pilot stocks, respectively, as defined previously. We use all exogenous variables as instruments to obtain the estimated volume,,,, and use them in estimating equation (7). Panel B of Table 5 shows the results of the two-stage least squares model. We first focus on the volume equation of put options. After considering the effect of option spreads, stock volume, stock returns, and various other control variables, the coefficient on the interaction term, Pilot i Reg SHO t, is significantly negative ( 1.306). That is, the pilot stock put volume significantly decreases relative to the control stock put volume after Reg SHO. The put spread equation shows that Reg SHO does not have a significant effect on the spread of the pilot stock puts. The evidence again is consistent with the view that put option trading is significantly related to equity short-selling rules. For the call options, the coefficients on the interaction term, Pilot i Reg SHO t, are both significantly positive: and for the volume and spread equation, respectively. The increases in the volume and spread for the pilot stock call options after Reg SHO are likely due to the increase demand for hedging activities of short sellers. Diether et al. (2009) find that the short sales activity significantly increases for pilot stocks after Reg SHO. Thus, consistent with Figlewski and Webb (1993), investors may utilize call options as a hedging device for stock market short sales. 3.2 The effect of Reg SHO on option prices We next examine the impact of Reg SHO on option prices. Studies show that the differences in the call and put prices (implied volatilities) can arise in the presence of short-sale constraints on the underlying stocks (e.g., Figlewski and Webb 1993; Lin and Lu 2015). In the presence of short-sale constraints, informed traders with negative information may instead buy put options. Thus, due to lower demand for put options following the suspension of the 22

24 price tests after Reg SHO, we expect significant decreases in the pilot stock put prices relative to the pilot stock call prices. We employ two call and put price difference measures adopted in recent literature. The first one is IV spread (Figlewski and Webb 1993; Cremers and Weinbaum 2010), which measures the relative price pressures on ATM put and call options with differences in their implied volatilities. Specifically, we first define a put-call option pair as a call and a put on the same stock with identical times to expiration and strike prices. We then compute IV spread for each option pair j for stock i on day t, as,,,,, (8) where j is the index of put and call option pairs and thus indexes both strike prices and maturities. To limit the analysis to the most actively traded option classes, which are less prone to distortions associated with market thinness, we select ATM pairs of puts and calls with the same strike price and expiration. 16 The other call and put price difference measure is IV skew. Following Xing et al. (2010), IV skew is the difference in the implied volatilities of the OTM put and the ATM call, defined as,,,, (9) where, and, are the implied volatilities of the OTM put and the ATM call options, respectively. Recall that a put option is defined as OTM when the Moneyness,, ln,, is greater than 1, and a call option is defined as ATM when the Moneyness, is between 1 and 1. When multiple ATM and OTM options exist for a stock on a particular day, we use the average implied volatilities of the multiple ATM calls and 16 Following Figlewski and Webb (1993), we reestimate our regressions by requiring both put and call options with 10 to 150 days to expiration, which are more liquid. The results are unchanged. 23

25 OTM puts in the equation. 17 ATM call is used as the benchmark because it is the most liquid option and thus is more likely to reflect investors consensus about the stock price uncertainty of the firm. Panel A of Table 6 summarizes the implied volatilities, IV spread, and IV skew. IV spread is positive, on average, with a sample mean of 0.01 and a standard deviation of IV skew is also positive, on average, with a sample mean of 0.07 and a standard deviation of If option trading and short sales are substitutes, we expect a significant decline in IV spread and IV skew after Reg SHO. Such findings would indicate that temporarily suspending the stock market short-sale constraints induces pessimistic investors to migrate from option trading to stock trading and alleviates the price pressures on put options. [Table 6 to be inserted here] We estimate the following OLS regression to control for possible effects associated with stock volume, stock return, VIX, and industry fixed effects and examine the effect of Reg SHO on IV spread and IV skew:,, α,,,,, (10), α,,,. (11) Panel B of Table 6 presents the effect of Reg SHO on IV spread and IV skew. Models (1) and (3) show that the coefficients on the interaction term between the pilot and Reg SHO dummies are significantly negative, indicating that IV spread and IV skew of pilot stock options significantly decrease after Reg SHO. These results show that the relaxation of short-sale constraints of the pilot stocks alleviates the demand for put options as traders with 17 The results are robust to various ATM and OTM option selection procedures. For example, the results are qualitatively similar if we choose the ATM call option with moneyness closest to zero, and the OTM put option with moneyness closest to 1, or if we choose the ATM call and OTM put that are the most actively traded. 24