Equity options during the shorting ban of 2008

Cakici, Nusret; Goswami, Gautam; Tan, Sinan Article Equity options during the shorting ban of 2008 Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Cakici, Nusret; Goswami, Gautam; Tan, Sinan (2018) : Equity options during the shorting ban of 2008, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 11, Iss. 2, pp. 1-31, https://doi.org/10.3390/jrfm11020017 This Version is available at: https://hdl.handle.net/10419/238865 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Risk and Financial Management Article Equity Options During the Shorting Ban of 2008 Nusret Cakici *,†, Gautam Goswami †and Sinan Tan Gabelli School of Business, Fordham University, New York, NY 10458, USA; [email protected] (G.G.); [email protected] (S.T.) *Correspondence: [email protected] † Current address: Fordham University GBA, 113 West 60th St, New York, NY 10023, USA. Received: 11 February 2018; Accepted: 27 March 2018; Published: 31 March 2018   Abstract: The Securities and Exchange Commission’s 2008 emergency order introduced a shorting ban of some 800 financials traded in the US. This paper provides an empirical analysis of the options market around the ban period. Using transaction level data from OPRA (The Options Price Reporting Authority), we study the options volume, spreads, pricing measures and option trade volume informativeness during the ban. We also consider the put–call parity relationship. While mostly statistically significant, economic magnitudes of our results suggest that the impact of the ban on the equity options market was likely not as dramatic as initially thought. Keywords: SEC; shorting ban; OPRA; intraday stock options 1. Introduction The Securities and Exchange Commission’s (SEC) September 2008 emergency order introduced a near complete shorting ban of some 800 financials traded in the US. The only precedent from the 1930s, the order was controversial across the board. While the proponents of the ban often cited market stability and orderly functioning, the opponents often thought of the ban as an arbitrary intervention with negative effects on the price discovery and the capital allocation process in the economy. Furthermore, while there has been some recent work considering the implications of the ban for the stock market directly (see, for example, Boehmer et al. (2013)), the effects of the shorting ban on the equity options have been much less explored in the literature. This paper provides an empirical analysis of the equity options market during the three months that include the duration of the ban. Using transaction level data from OPRA (The Options Price Reporting Authority), we study the options prices and market liquidity during the ban. Since we have data for the entire universe of optionable stocks across the exchanges, we are able to compare the options of the banned stocks and non-banned stocks to identify the effects. We have three main findings. First, during the ban period, banned stock effective and quoted option spreads increase as well as the Black and Scholes (1973) and Merton (1973) volatilities and prices relative to non banned stocks. Second, in predictive intraday regressions of future stock returns on lagged signed option trading volume, we find that option volume becomes informative during the ban for the banned stocks. Third, our measure of the violation of American stock put–call parity exhibits a significant increase during the ban period and only for banned stocks. Nevertheless, the economic magnitude and statistical insignificance of some of our findings suggest that the impact on the equity options market is likely less pronounced than initially thought. The initial ban release states the ban would be effective starting 19 September 2008 for a duration of 10 trading days with a possible extension for a total of 30 calendar days. Eventually, the ban was effective until August 10 2008 for a total of 14 trading days. To consider the impact of the ban, we identify some 199 Initial Ban List and 1998 Never Banned stocks in the OPRA database. However, a J. Risk Financial Manag. 2018,11, 17; doi:10.3390/jrfm11020017 www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2018,11, 17 2 of 31 broad inspection of data reveals that a large number of stocks have very low volume in their options, thus, to prevent the analysis being driven by these stocks, we require that the stocks have traded options for at least half of the trading days in the period that we consider. This activity measure leaves us with about 80 and 800 stocks for the Initial Ban List and Never Banned stocks. We consider a period of 42 trading days, which includes the 14-trading day ban period of from 19 September 2008 to August 10 2008 in the middle. We combine the two 14-day preand post-ban periods into one non-ban period, and contrast results for the non-ban period with during the ban period, for Never Banned stocks and Initial Ban List stocks. The restriction to have traded options on at least half of the trading days is an important constraint for stocks. If the activity measure is made more stringent requiring a trade every trading day, then the sample size is reduced further. In that case for the largest moneyness range we consider, we would have 33 and 238 (29 and 225) stocks for call (put) options in the Initial Ban List and Never Banned groups. Fortunately, the qualitative results presented in this paper exhibit a considerable degree of robustness to further constraining the activity measure this way. Boehmer et al. (2013) considered the impact of the ban on stock prices and found that the start of the shorting ban is associated with a pronounced but temporary increase in share prices for the banned stocks. 1 Moreover, they found that banned stocks suffer a severe degradation in market quality, as measured by spreads, price impacts and intraday volatility. 2 Harris et al. (2013), along similar lines of research, used the four factor model and found that, during the short ban, banned stock prices were inflated by about 10–12% on a risk adjusted basis. Barclay et al. (2008) found evidence for large order imbalances and excess volatility on triple witching days and the initiation of the ban was a triple witching day. We implement a two way fixed effects methodology similar to Boehmer et al. (2013) to understand how option volumes, spreads and pricing statistics change using some 12 variables. Focusing on call options with strike to spot ratios between 0.9 and 1.1, there were about 70 more trades, 1370 more size volume, and about half a million more dollar volume per underlying per day. These quantities are over and above the non-ban period averages of 109 (trades), 2021 (size volume) and 0.7 million dollars (dollar volume), therefore represent economically important increases in trading volume for the call options market. All three changes are statistically significant. Moreover, spreads go up by 3–5% (effective and quoted spreads). These values are over and above the 9 and 16 percent averages during the non-ban period, and therefore can be thought of as rather moderate. The prices go up by about 28 cents and implied volatilities by about 2.5 percent. All these quantities are for Initial Ban List stocks, during the ban relative to the non-ban period and Never Banned stocks. Turning to the put options, the number of trades, size and dollar volume measure changes are statistically insignificant and economically small. Spreads increase by two and three percent (effective and quoted spreads, respectively). The spread increases are over and above the 8 and 14 percent averages during the non-ban period and in this sense can be thought of as moderate. Put option prices go up by about fifty cents and implied volatilities by some six percent. The increase in the number of trades, size and dollar volumes for call options can be interpreted from the lens of Ross (1976). Ross (1976) argued that options written on existing assets can improve welfare by permitting an expansion of contingencies covered by existing securities. 3 Therefore, when shorting is prohibited, the contingencies can be argued to be covered by option trades rather than direct short sales. We also present separate sets of results for the same variables for At, In and Out of the money options. Since the hedge ratios are different across the moneyness categories, there is a direct economic channel through which effects of different 1 Hasan et al. (2010) found that during the ban financial stock shorting activity was mostly concentrated on the stocks with heavy subprime and credit risk exposures, thus can be thought of as a rational response rather than speculation. They argued therefore that the shorting ban likely obstructed the market’s disciplinary forces. 2 Jones (2012) considered the sequence of regulatory events that made shorting more difficult or impossible during the 1930s and found a positive stock price reaction to the regulatory events. 3 Cao and Huang (2007) provided recent evidence that options are not redundant by means of a spanning result for in the money options. J. Risk Financial Manag. 2018,11, 17 3 of 31 magnitudes can be expected on the options market. For example, we find that for Out of the money call options, option spreads go up by slightly less than At the money call options. One likely reason might be that delta hedging a long position in an Out of the money call position requires shorting less stock compared with an At the money option. We also consider how the informativeness of options trades for the stock market changes during the ban. We run minutely overlapping regressions of the next 10, 15 and 30 min cross section of stock returns on the last 30 min of signed relative option volume. The signed relative option volume is defined as the ratio of the buy initiated volume to the sell initiated volume where option trades are marked using the algorithm presented by Lee and Ready (1991). We find that put option relative buy volume negatively predicts future returns during the ban. We are unable to detect any predictability during the non-ban period or using the call option signed relative volumes. These predictive regressions can be interpreted as tests of Semistrong-Form market efficiency (Fama (1970); Roberts (n.d.)). Our results suggest that the Semistrong-Form market efficiency is largely intact within the frame of specifications we employ. Easley et al. (1998) and Chan et al. (2002) used similar regressions in their work. In corroborating results, Kolasinksi et al. (2009)found that during the 2008 shorting ban, the short sales informativeness increased more for optionable stocks. Lastly, we consider how the put–call parity is affected during the ban. A time series plot of the cross section of put–call parity violations suggest that the violations are most pronounced on 19 September, and drastically shrank immediately after. Measures similar to ours were constructed and studied by Ofek et al. (2004) and Cremers and Weinbaum (2010). The closest paper to our paper is Battalio and Schultz (2011). Similar to our paper, they considered the impact of the shorting ban on equity options using OPRA data and document that potential short sellers did not migrate to the options market. This result is consistent with our insignificant dollar and size volume results for put options. 4 This paper provides information on how the option spreads reacted to the ban, although does not report separate results for the moneyness categories like we do. Similar to our paper, they emphasized how the put–call parity violations likely increased during the ban for the banned stocks though their work does not include intraday predictive regressions of stock returns regressed on lagged option market volume information. The SEC Initial Ban order included a few clauses to dampen the impact on the options market. For example, a limited exception was granted to “...registered market makers, block positioners, or other market makers obligated to quote in the over-the-counter market, in each case that are selling short a publicly traded security of an Included Financial Firm as part of bona fide market making in such security...”. Option market makers on the other hand were only given a single trading day exception with the purpose of allowing them to hedge for 20 September which is an equity option expiration day. However, with a follow up release on Sunday 21 September, SEC extended the option market maker shorting for the duration of the ban. We think that this extension of the exemption likely reduced the impact of the ban on the option market prices, liquidity, and efficiency to a very significant extent. In fact, in figures depicting the volume, spread and price statistics, we can see that 19 September is quite distinct from all the other days in our sample period. A second feature of the initial release was that SEC provided “...an exception to allow short sales that occur as a result of automatic exercise or assignment of an equity option held prior to effectiveness of this order due to expiration of the option...”, which is a clause that also likely dampened the impact of the ban on the options market. However, another reason why the ban had a dampened effect on the options market is possibly because investment banks can simply reduce their existing long equity positions to hedge their options activities rather than short. In this sense, they do not strictly need to short to cover their options trading.5 4 Grundy et al. (2012), using daily closing options data, provided corroborating results and argued that options spreads increased and put volumes did not increase. 5We are grateful to the referee for making this point. J. Risk Financial Manag. 2018,11, 17 4 of 31 The paper is organized as follows: Section 2describes our data source, OPRA. Section 3presents the methodology. Section 4details the results. Section 5provides the robustness results when we work with a smaller universe of stocks. Section 6concludes the paper. 2. The Data We use intraday data available from the OPRA (Options Price Reporting Authority). OPRA data are the quotes and trades disseminated by all U.S. options exchanges. The participating exchanges include AMEX (American Stock Exchange), BSE (Boston Stock Exchange), CBOE (Chicago Board of Options Exchange), ISE (International Securities Exchange), NASDAQ, NYSE, Arca and PHLX (Philadelphia Stock Exchange). OPRA also provides a consolidated list for the underlying securities for every month which includes the underlying names and tickers for which options were traded or quoted during that month. For September 2008, OPRA reports 3239 underlying securities for which an option was traded or quoted. These underlying securities include stocks, ETFs of stock indices and commodities and treasury indices. We try to identify all the underlying names and tickers in the CRSP to determine the precise type of the underlying securities. In Table 1A, we report that 2248 of OPRA underlying securities are stocks (based on CRSP share codes 10 and 11), 865 of OPRA underlying securities are Non-stocks (certificates, ADRs, shares of beneficial interest, units, companies incorporated outside the U.S., Americus Trust components, closed-end funds, preferred stocks and REITS). We are unable to identify the remaining 126 securities since they are not present in CRSP. Table 1. OPRA underlying stocks and short sales ban status. Panel A: OPRA Underlying Securities Ban Status Stocks Non-Stocks Non-Present in CRSP Initial Ban List 199 39 0 Later 51 33 4 Never Banned 1998 793 122 Total 2248 865 126 Panel B: OPRA Stocks after the Filters Call Options Put Options Moneyness Initial Ban List Never Banned Initial Ban List Never Banned All 83 834 81 748 At 34 227 33 223 Out 55 500 50 431 In 44 324 40 335 The list of banned stocks is available from the SEC (release 34-58592). A few days after the start of the ban, the SEC delegated to the exchanges all decisions about the ban of a listed firm and allowed them to add or remove stocks into the ban list. Using the NYSE EuroNext’s website, we are able to identify a total of 134 additions to and 10 removals from the ban list by the exchanges during the period of the ban. We exclude these later banned securities from our analysis, focusing on the Initial Ban List stocks and stocks that were Never Banned. In Table 1A, out of a total of 2248, we identify 199 stocks that are in the Initial Ban List and 1998 stocks that were Never Banned. After a broad inspection of the data, we found that many of the options of this set of stocks trade very thinly. Following the empirical equity option literature, we impose some restrictions on the data before we proceed with our analysis. In particular, we provide the restrictions that moneyness (strike to spot ratios) are between 0.9 and 1.1, maturities are between 15 days and 360 days and Black and Scholes (1973) and Merton (1973) volatilities are less than 200%. We implement an activity measure where we require that stocks have at least one option traded in at least half of the trading days in our sample period. This brings our sample size to about 80 and 800 stocks J. Risk Financial Manag. 2018,11, 17 5 of 31 for the Initial Ban List and Never Banned stocks, respectively. In particular, in Table 1B, for All options, we have 83 and 834 (81 and 748) for call (put) options for Initial Ban List and Never Banned stocks. We also consider At the money call options with strike to spot ratios of between 0.98 and 1.02. In the money call options have strike to spot ratios of between 0.90 to 0.98. Out of the money call options have strike to spot ratios of between 1.02 to 1.10. The same cutoff values are used to determine the moneyness of the put options. Since the moneyness range in these cases is more limited, the sample universe of stocks shrinks. For example, for At the money options, we have 34 and 227 (33 and 223) for call (put) options for Initial Ban List and Never Banned stocks, respectively. For Out of the money options, we have 55 and 550 (50 and 431) for call (put) options for Initial Ban List and Never Banned stocks, respectively. Finally, for In the money options, we have 44 and 324 (40 and 335) for call (put) options for Initial Ban List and Never Banned stocks, respectively. These numbers indicate that the sample universe is slightly larger for call options, and is largest for Out of the money, then In the money and finally At the money. The data periods used in the tables is the 42 trading days which include the ban period in the middle. The ban period covers the 14 trading days from 19 September 2008 to 10 August 2008. Following Boehmer et al. (2013) , we consider the before and after the ban periods jointly, and so the non-ban period consists of the immediate 14 trading days before and after the ban. In particular, the non-ban period covers all the 28 trading days from 29 August 2008 to 18 September 2008 and 9 October 2008 to 28 October 2008. In the figures, however, for sake of completeness, we plot data obtained from all the 65 trading days in August, September and October 2008. 3. Methodology There are three types of analysis we implement using our data source. First, we explore how volumes, spreads and pricing statistics change using 12 variable definitions, using a similar methodology to Boehmer et al. (2013). Second, we explore how the informativeness of options trading volume change by exploring intraday predictive regressions similar to Easley et al. (1998) and Chan et al. (2002). Third, we consider how the put–call parity relationship is affected by calculating violation measures similar to Ofek et al. (2004) and Cremers and Weinbaum (2010). For each one of the stocks presented in Table 1, we construct twelve summary statistics for each trading day using transaction level data for that day. We are interested in three broad categories of summary measures: volume, spreads and pricing. For volume measures, we consider four statistics: First, the number of types of contacts traded, which means that we simply count the unique maturity and strike price pairs across all the trades of the underlying stock during the trading day. Second, we simply count the number of trades regardless of the size of the trade or the dollar amount. Third, we calculate the size volume, which is the number of options contracts traded. Fourth, we calculate the dollar option trading volume for that underlying. For spread measures, we focus on effective and quoted spreads, size volume and dollar volume weighted for a total of four measures. Quoted spread for a given trade is calculated using, Quoted Spread =Ask −Bid (Ask +Bid)/2, (1) where Bid and Ask are the prevailing quotes at the time of the trade.6 The effective spread is calculated using, Effective Spread =2×|Trade −(Ask +Bid)/2| (Ask +Bid)/2 , (2) 6 Following Easley et al. (1998), we directly use the live quote rather than quote prevailing five seconds before the transaction (see, for example, Lee and Ready (1991)), since quote revisions in the CBOE is less than five seconds. J. Risk Financial Manag. 2018,11, 17 6 of 31 where the numerator stands for the distance between the trade price and quote midpoint. Once Quoted and Effective spreads are calculated, to arrive a daily value for each stock and each trading day, we calculate weighted spreads by the size volume or the dollar volume of the trade. Turning finally to the pricing measures, we consider prices directly and Black and Scholes (1973) and Merton (1973) volatilities, again prices can be equal weighted across trades or by size volume and Black and Scholes (1973) and Merton (1973) volatilities can be weighted by dollar or size volume for a total of four measures. Our choice for implied volatility calculations is driven by simplicity. Implied volatilities that come from alternative options pricing models which explicitly incorporate stock borrowing fees would have been more appropriate (see, for example, papers by Avellaneda and Lipkin (2009) and Ma and Zhu (2017)). For each stock the daily values for each of the 12 variables are equally weighted across trading days for that stock in the ban and the no ban periods to arrive at the average values for the ban and the non-ban periods. The resulting cross sectional average values for the variables for the ban and the non-ban periods can be used to construct a t-statistic for testing if the cross sectional means are the same. If a stock does not have an option that satisfies the implied volatility, moneyness and maturity criteria, the ban or the non-ban period average is calculated across the days for which that stock actually had an option that satisfies the criteria. In particular, the following regressions are run: yi,ban period −yi,non ban period =αInitial Ban list +ei,f or i ∈Initial Ban list Stocks (3) yi,ban period −yi,non ban period =αNever Banned +ei,f or i ∈Never Banned Stocks (4) yi,ban period −yi,non ban period =αAll Stocks +βAll Stocks ×bandummyi+ei, (5) f or i ∈Never Banned Stocks ∪Initial Ban list Stocks In the above equations, yi,ban period and yi,non ban period mean the variable value for the ith stock for the ban period and the non-ban period, respectively, and bandummyi is a stock specific dummy value which assumes the value of unity, if the stock is in the Initial Ban List and zero otherwise. Equations (3) and (4) allow us to focus on the difference the ban period makes for the Initial Ban List stocks and Never Banned stocks. Equation (5) allows us to focus on the difference the ban makes for the Initial Ban List stocks over and above the change in the Never Banned stocks. By construction, Equation (5) implies that the OLS estimate of βAll Stocks is equal to EInitial Ban list hyi,banperiod −yi,ban periodi−ENever Banned hyi,banperiod −yi,banperiodi , where EInitial Ban list and ENever Banned stand for the cross sectional expectations taken over the Initial Ban List stocks and Never Banned stocks. Therefore, while Equation (5) is a difference-in-difference construct, Equations (3) and (4) focus on the within group differences between the non-ban period and during the ban. We also employ a two-way fixed effect regression to explore how the same 12 variables change during the ban period. In particular, yit =αi+γt+η×bandummyit +eit. (6) In addition to a firm fixed effect αi , the specification has calendar dummies for each trading day, γt and bandummyit is a variable set equal to one if and only if the shorting ban is in effect for stock i on day t. The specification allows us to identify the effect of a particular quantity, y , using the cross sectional information, by comparing ban and non-banned stocks on the same trading day, removing any differences between Initial Ban List stocks and Never Banned stocks that might exist when there is no ban on short sales. Second, to explore the informativeness of options trading volume, we run intraday predictive regressions similar to Easley et al. (1998) and Chan et al. (2002). In particular, we consider a linear specification, J. Risk Financial Manag. 2018,11, 17 7 of 31 ri t,t+δ=αt+βtyt−τ,t+et−τ,t+δ, (7) where ri t,t+δ is the return on the underlying stock i from time t to t+δ (holding period) and yt−τ,t is the log of the ratio of the buyer to seller initiated dollar option trade volume from time t−τ to t (estimation period), using transaction level option trade data from OPRA. Buyer and seller initiated option trades are defined using the algorithm described in Lee and Ready (1991). yt−τ,t is calculated for call and put option trades of the underlying stocks provided in Table 1when they happen to trade in the estimation period. The cross-sectional regression is run on a rolling minutely basis for various holding periods δ and an estimation period τ of 30 min. The minutely cross-sectional regression coefficients βt ’s are calculated for each of the trading days during the ban and the non-ban periods. Parameter estimates and standard errors come from the Fama and MacBeth (1973) procedure, with aNewey and West (1987) correction where we use as many lags as the sum of the minutes in the estimation and holding periods. Third, we consider how the put–call parity relationship is affected by considering a violation measure of the put–call parity. In particular, it is well known that, for American options on dividend paying stocks where the dividend is paid continuously, an arbitrage relationship is (C−P)≥(S×e−qT −K). (8) As usual C is the call price, P is the put price, S is the stock price, q is the continuous dividend yield, T is the time to maturity, and K is the strike price. Notice that to arbitrage away any violation of the inequality, investors would short the stock. Thus, larger negative values of the quantity (C−P)−(S×e−qT −K)would likely indicate shorting difficulties. To explore the extent to which this inequality holds, we calculate the quantity (C−P)−(S×e−qT −K) for matched trades for call and puts for Initial Ban List and Never Banned stocks and during the ban period and the non-ban period. 4. Results We next report results of the regression Equations (3)–(5) for understanding how volumes, spreads and pricing statistics change for our moneyness categories: first, All options taken together, and then for each of At, Out and In the money options. All options have strike to spot ratios between 0.9 and 1.1. We further define At the money call options with strike to spot ratios of between 0.98 and 1.02. In the money call options have strike to spot ratios of between 0.90 to 0.98. Out of money call options have strike to spot ratios of between 1.02 to 1.10. The same cutoff values are used to determine the moneyness of the put options. Focusing on Table 2, the first three columns report the results for the Initial Ban List stocks and the second three columns report for the Never Banned stocks. For each category of stocks, we report the non-ban period and during the ban period means and the t-statistic for the regression intercept, α in the regression Equation (3) or Equation (4). The two last columns of the table reports the coefficient estimates and the t-statistics for the regression intercept β in the regression Equation (5). Notice that the first two specifications are equivalent to a usual t-test for same means of the matched sample of stocks. The third specification is a difference in difference methodology with one implicit time dummy and one explicit ban dummy. Later, we also use a two way fixed effect methodology, allowing for firm level and trading day fixed effects. All errors are ordinary OLS errors. Table 2A reports the All call options and Table 2B reports the All put options results. J. Risk Financial Manag. 2018,11, 17 8 of 31 Table 2. Cross sectional means and t-statistics for option trade summary statistics: All options. Initial Ban List Never Banned All Means Means Period Non Ban Period During t-stat Non Ban Period During t-Stat βt-Stat Panel A: Call Options types of contracts 5.73 6.65 5.03 4.41 4.72 10.16 0.62 5.56 trades 109 183 3.02 55 61 3.67 67 6.96 size volume 2021 3342 2.43 1008 1016 0.26 1313 6.69 dollar volume 0.69 1.14 2.72 0.31 0.32 0.54 0.45 7.04 dollar volume weighted quoted 15.66 23.79 10.84 14.71 17.33 14.08 5.51 8.65 size volume weighted quoted 16.63 25.17 10.52 15.88 18.84 14.70 5.58 8.11 dollar volume weighted effective 8.65 13.92 11.04 8.42 10.18 12.94 3.51 7.69 size volume weighted effective 9.12 14.93 10.47 9.08 11.08 13.86 3.81 7.77 size volume weighted price 3.54 3.75 3.68 2.78 2.71 −4.92 0.28 5.76 equal weighted price 3.55 3.77 3.89 2.81 2.74 −5.12 0.28 6.06 dollar volume weighted implied vol 74.17 72.71 −1.09 63.98 59.91 −21.39 2.62 3.56 size volume weighted implied vol 74.19 72.59 −1.21 63.96 59.92 −21.02 2.44 3.31 Panel B: Put Options types of contracts 5.54 6.05 2.91 4.47 4.77 9.35 0.21 1.91 trades 111 118 0.74 50 55 2.95 1 0.22 size volume 2544 2706 0.60 1047 1114 2.03 96 0.71 dollar volume 1.03 1.11 0.56 0.37 0.43 2.40 0.02 0.17 dollar volume weighted quoted 13.72 19.35 9.10 12.24 14.70 17.04 3.18 6.59 size volume weighted quoted 14.49 20.08 9.14 13.13 15.70 16.58 3.02 5.89 dollar volume weighted effective 7.92 11.83 8.16 7.06 8.49 9.47 2.48 5.13 size volume weighted effective 8.39 12.32 8.20 7.49 9.06 10.77 2.37 5.05 size volume weighted price 3.86 4.37 4.15 3.07 3.09 0.96 0.49 6.89 equal weighted price 3.87 4.32 3.92 3.08 3.10 1.12 0.43 6.78 dollar volume weighted implied vol 79.31 81.65 1.66 66.89 62.94 −18.95 6.28 8.02 size volume weighted implied vol 79.83 82.00 1.53 67.27 63.26 −18.96 6.18 7.79 J. Risk Financial Manag. 2018,11, 17 15 of 31 For At the money put options, size volume, spreads, prices and implied volatilities go up and these changes are statistically significant. Though the size of the economic magnitudes can be thought of as moderate. For example, size volume goes up by 329 on top of a non-ban period average of 1463. Spreads go up by about 3.5% and 2% (quoted and effective) on top of non-ban period averages of about 8.5% and 4.5%. Prices and implied volatilities go up by about sixty cents and 8% on top of non-ban period averages of five dollars and 83%. Figures 3and 4plot the associated cross sectional means and the 20th, 50th and 80th percentile values of dollar volume, percent effective spread and percent implied volatilities through August, September and October 2008 for calls and puts. Comparing Figure 3A,B help us understand the positive relative dollar volume change for at the money Call options (some three hundred and twenty thousand dollars per underlying per day as reported in Table 3A). The volume after the ban period is particularly low for Initial Ban List stocks, with little change for either of the two groups of stocks entering the ban period. Figure 4A,B for put options seems to show that, entering the ban period, there is little change in either groups’ dollar volume though, exiting the ban period the dollar volumes seem to fall for both. The relative effect for dollar volume reported for put options in Table 3B is statistically insignificant. Comparing Figure 3C,D with Figure 1C,D for All call options, we understand that spreads are in general smaller and had a smaller spike on 19 September. Comparing Figure 4C,D with Figure 2C,D for All put options reveals a similar result. Focusing on implied volatilities of put options, Figure 4E shows that the ban has the effect of stopping the upward trend for the Initial Ban List stocks. For Never Banned Stocks, on the other hand, Figure 4F shows that implied volatilities continued to trend up during the ban period and stabilize and start falling only after the ban period. Figure 3E,F portray a slightly different picture for calls. As Figure 3E shows for the Initial Ban List stocks, the ban had the effect of reducing the implied volatilities especially early in the ban, although the implied volatilities have an up trend during the ban similar to the implied volatilities of the Never Banned stocks, as Figure 3F shows. Table 4reports the results for Out of the money options. Focusing on the relative effects reported in the last two columns of Table 4A for call options, all 12 variables increase and exhibit statistical significance. Spreads go up by slightly less than At the money call options. One reason might be that delta hedging a long position in an out of the money call position requires shorting less stock compared with an at the money option. Turning to the put option results reported in Table 4B, spreads, prices and implied volatilities go up and are statistically significant. Dollar volume is statistically insignificant. Spreads go up by about 3% and 2% (quoted and effective, respectively), prices by slightly less than 50 cents and implied volatilities by about 6%. When compared to the averages in the non-ban period, these magnitudes appear modest. Figures 5and 6are the supporting figures for Out of the money calls and puts. It is hard to find a large difference in the way the ban affected the Out of the money call dollar volumes by considering Figure 5A,B. Figure 6A,B portrays a similar picture for the puts. Focusing on spreads, Figure 5C shows that on 19 September spreads skyrocketed for calls of the Initial Ban List stocks. Figure 5D shows that the spreads of the Never Banned Stocks were also affected in a similar way but the magnitudes are much smaller. Figure 6C,D reports the spreads for the put options. Comparing Figures 5C and 6C, the size of the 19 September effect and the overall effect appears slightly smaller for puts than calls. Turning to the implied volatilities, Figures 5E,F and 6E,F show that the impact is fairly similar to the impact for the At the money options (compare the same plots across Figures 3and 4with Figures 5and 6). In particular, the Never Banned Stock option implied volatilities has an upward trend during the ban for calls and puts. For the Initial Ban List stocks, the upward trend flattens for the put options with the ban and drops initially then continues to increase for calls. J. Risk Financial Manag. 2018,11, 17 16 of 31 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Initial Ban List, At the Money Calls Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel A. 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Never Banned, At the Money Calls Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel B. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Initial Ban List, At the Money Calls Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel C. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Never Banned, At the Money Calls Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel D. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Initial Ban List, At the Money Calls Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel E. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Never Banned, At the Money Calls Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel F. Figure 3. Time series of cross sectional options summary statistics: At the money call options of Initial Ban List and Never Banned Stocks during the ban and non-ban periods: ( A , C , E ) results for the three variables for Initial Ban List Stocks; and ( B , D , F ) results for the three variables for Never Banned Stocks. J. Risk Financial Manag. 2018,11, 17 17 of 31 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Initial Ban List, At the Money Puts Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel A. 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Never Banned, At the Money Puts Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel B. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Initial Ban List, At the Money Puts Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel C. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Never Banned, At the Money Puts Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel D. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Initial Ban List, At the Money Puts Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel E. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Never Banned, At the Money Puts Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel F. Figure 4. Time series of cross sectional options summary statistics. At the money put options of Initial Ban List and Never Banned Stocks during the ban and non-ban periods: ( A , C , E ) results for the three variables for Initial Ban List Stocks; and ( B , D , F ) results for the three variables for Never Banned Stocks. J. Risk Financial Manag. 2018,11, 17 18 of 31 Table 4. Cross sectional means and t-statistics for option trade summary statistics: Out of the money options. Initial Ban List Never Banned All Means Means Period Non Ban Period During t-Stat Non Ban Period During t-Stat βt-Stat Panel A: Call Options types of contracts 4.46 5.20 5.22 3.41 3.66 8.82 0.49 5.06 trades 84 128 3.06 48 56 3.69 36 4.57 size volume 1621 2364 2.38 931 940 0.31 734 5.36 dollar volume 0.45 0.63 2.48 0.22 0.23 0.11 0.18 4.83 dollar volume weighted quoted 14.04 21.70 9.23 14.06 16.88 12.62 4.84 6.65 size volume weighted quoted 14.87 22.41 9.01 15.11 18.19 12.54 4.46 5.65 dollar volume weighted effective 7.55 12.82 9.57 8.05 9.82 9.89 3.50 6.16 size volume weighted effective 7.95 13.30 9.26 8.58 10.53 10.68 3.40 5.84 size volume weighted price 3.03 3.16 2.39 2.51 2.41 −5.08 0.23 3.77 equal weighted price 3.02 3.12 1.85 2.50 2.41 −4.96 0.19 3.33 dollar volume weighted implied vol 70.77 68.90 −1.37 61.57 58.13 −14.93 1.57 1.90 size volume weighted implied vol 71.04 69.04 −1.46 61.75 58.30 −14.86 1.45 1.74 Panel B: Put Options types of contracts 4.22 4.58 1.99 3.26 3.39 4.46 0.24 2.25 trades 81 84 0.49 38 43 2.65 −3−0.41 size volume 2063 1874 −0.89 826 861 1.07 −224 −1.88 dollar volume 0.66 0.65 −0.07 0.22 0.25 1.74 −0.03 −0.61 dollar volume weighted quoted 13.13 18.57 9.57 11.98 14.25 10.69 3.17 4.86 size volume weighted quoted 13.67 19.09 9.71 12.80 15.05 10.31 3.16 4.73 dollar volume weighted effective 7.82 11.46 10.83 6.77 8.17 6.49 2.24 3.49 size volume weighted effective 8.15 11.75 10.63 7.12 8.53 8.22 2.20 4.26 size volume weighted price 3.43 3.85 4.09 2.68 2.63 −2.44 0.47 6.46 equal weighted price 3.39 3.76 3.70 2.67 2.62 −2.57 0.42 6.12 dollar volume weighted implied vol 78.60 81.15 1.35 66.12 62.77 −12.21 5.89 5.74 size volume weighted implied vol 79.04 81.45 1.26 66.41 63.00 −12.28 5.81 5.60 J. Risk Financial Manag. 2018,11, 17 19 of 31 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Initial Ban List, Out of the Money Calls Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel A. 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Never Banned, Out of the Money Calls Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel B. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Initial Ban List, Out of the Money Calls Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel C. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Never Banned, Out of the Money Calls Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel D. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Initial Ban List, Out of the Money Calls Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel E. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Never Banned, Out of the Money Calls Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel F. Figure 5. Time series of cross sectional options summary statistics: Out of the money call options of Initial Ban List and Never Banned Stocks during the ban and non-ban periods: ( A , C , E ) results for the three variables for Initial Ban List Stocks; and ( B , D , F ) results for the three variables for Never Banned Stocks. J. Risk Financial Manag. 2018,11, 17 20 of 31 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Initial Ban List, Out of the Money Puts Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel A. 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Never Banned, Out of the Money Puts Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel B. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Initial Ban List, Out of the Money Puts Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel C. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Never Banned, Out of the Money Puts Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel D. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Initial Ban List, Out of the Money Puts Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel E. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Never Banned, Out of the Money Puts Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel F. Figure 6. Time series of cross sectional options summary statistics: Out of the money put options of Initial Ban List and Never Banned Stocks during the ban and non-ban periods: ( A , C , E ) results for the three variables for Initial Ban List Stocks; and ( B , D , F ) results for the three variables for Never Banned Stocks. J. Risk Financial Manag. 2018,11, 17 21 of 31 Table 5focuses on In the money options. Focusing on the relative effects reported in the last two columns of Table 5A for call options, 11 out of the 12 variables (except for the size volume weighted implied volatility) increase and exhibit statistical and economic significance. Spreads go up by slightly more than At the money or Out of the money call options. One reason might be that delta hedging a long position in an In the money call position requires shorting more stock compared with Out or At the money calls. Turning to the results for put options in Table 5B, only the spreads, prices and implied volatilities go up and exhibit statistical significance, while size volume or dollar volume does not. Figures 7and 8 are the supporting figures. Figure 7C,D and Figure 8C,D show that spreads increased dramatically for the Initial Ban List stocks, more so for calls and also increased but in a much smaller way for the Never Banned Stocks. The drastic affect fast disappears after 19 September. We next turn to the results that explore how the same twelve variables change during the ban period by means of a two way fixed effects specification introduced in Equation (6). The results are given in Table 6and are very similar to the OLS regression results in Equation (5). In particular, the β coefficient estimates in the regression Equation (5) are very similar to the η coefficients in the regression Equation (6) (compare the β estimates in Tables 2–5to the η estimates reported in Table 6). For each of the twelve variables introduced earlier, coefficient estimates, η , of the ban dummy, and the associated t-statistics are reported for All, At the money, Out of the money and In the money options. Standard errors are the usual OLS errors and the specification is estimated directly as a pooled OLS regression. Table 6A reports for calls and Table 6B reports for puts. Focusing on All call options, strike-to-spot ratios between 0.9 and 1.1, 70 more trades happen and size volume goes up by 1370, dollar volume goes up by about half a million per day, spreads go up around 5.3% and 3.5% for quoted and effective spreads respectively. Whether the spread values are size volume weighted or dollar volume weighted makes little difference. Prices go up by about 28 cents and implied volatilities go up by 2.5%. All of these numbers can be interpreted as difference in difference values, relative values for the Initial Ban List stocks in relation to the Never banned and during the ban period relative to in the non-ban period. All the t-statistics are significant. Moreover, the t-statistic significance and the signs of the ban dummy coefficients remain the same turning to the At the money calls, Out of the money calls and In the money calls. Turning to All put options (Table 6B), the results are similar in sign and in terms of statistical significance with the call options, although the number of trades, size volume and dollar volume coefficients are insignificant. Spreads go up around 3.05% and 2.28% for quoted and effective spreads respectively. Put prices go up by around fifty cents and implied volatilities by about 6%. The increase in implied volatility is much higher for puts than calls, indicative of the fact the put pricing for banned stocks were more effected by the ban. Similar to the call options, for the subset of variables that are significant for All put options, significances and coefficient magnitudes carry over to At, Out or In the money options. A notable aspect of the results is that the implied volatilities for Out of the money puts increase more than In the money puts (6.02% and 5.66% for dollar volume weighted implied volatilities, respectively, for Out and In the money), reinforcing the volatility skew in the market. A second notable aspect is how the dollar volume declines by about 0.110 million dollars per day for in the money puts. Since prices go up, this effect is linked to the lower size volume (negative but insignificant by itself). J. Risk Financial Manag. 2018,11, 17 22 of 31 Table 5. Cross sectional means and t-statistics for option trade summary statistics: In the money options. Initial Ban List Never Banned All Means Means Period Non Ban Period During t-Stat Non Ban Period During t-Stat βt-Stat Panel A: Call Options types of contracts 4.11 4.79 3.19 3.21 3.28 2.06 0.60 5.03 trades 47 84 2.97 26 27 1.01 36 6.83 size volume 786 1416 2.78 432 419 −0.48 643 5.85 dollar volume 0.38 0.72 2.90 0.21 0.21 −0.01 0.35 6.78 dollar volume weighted quoted 9.43 15.07 8.56 8.21 9.63 10.61 4.22 9.67 size volume weighted quoted 9.48 15.26 8.69 8.29 9.77 10.86 4.30 9.74 dollar volume weighted effective 5.21 7.97 9.12 4.42 5.21 5.87 1.97 5.15 size volume weighted effective 5.23 8.13 8.85 4.48 5.30 5.93 2.07 5.27 size volume weighted price 5.85 6.11 2.37 5.15 5.21 1.75 0.20 2.17 equal weighted price 5.80 6.06 2.56 5.14 5.22 2.24 0.19 2.01 dollar volume weighted implied vol 76.11 74.55 −0.79 65.59 62.06 −11.42 1.96 1.77 size volume weighted implied vol 76.42 74.68 −0.87 65.76 62.19 −11.47 1.83 1.64 Panel B: Put Options types of contracts 4.50 4.65 0.96 3.28 3.47 5.92 −0.04 −0.40 trades 64 61 −0.64 28 29 0.79 −5−1.10 size volume 1327 1379 0.46 548 600 1.66 1 0.01 dollar volume 0.74 0.69 −0.40 0.30 0.36 2.07 −0.11 −1.13 dollar volume weighted quoted 7.37 11.49 9.48 7.11 8.53 10.52 2.70 6.46 size volume weighted quoted 7.46 11.62 9.39 7.20 8.65 10.63 2.71 6.40 dollar volume weighted effective 3.84 6.37 10.26 4.02 4.88 6.84 1.67 4.47 size volume weighted effective 3.88 6.45 10.13 4.06 4.93 6.57 1.69 4.29 size volume weighted price 6.29 6.89 4.61 5.35 5.46 3.03 0.49 4.23 equal weighted price 6.23 6.81 5.18 5.30 5.41 3.12 0.48 4.51 dollar volume weighted implied vol 78.66 81.00 1.26 64.29 61.09 −11.17 5.54 5.29 size volume weighted implied vol 78.90 81.23 1.24 64.44 61.23 −11.09 5.55 5.25 J. Risk Financial Manag. 2018,11, 17 23 of 31 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Initial Ban List, In the Money Calls Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel A. 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Never Banned, In the Money Calls Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel B. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Initial Ban List, In the Money Calls Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel C. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Never Banned, In the Money Calls Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel D. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Initial Ban List, In the Money Calls Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel E. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Never Banned, In the Money Calls Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel F. Figure 7. Time series of cross sectional options summary statistics: In the money call options of Initial Ban List and Never Banned Stocks during the ban and non-ban periods: ( A , C , E ) results for the three variables for Initial Ban List Stocks; and ( B , D , F ) results for the three variables for Never Banned Stocks. J. Risk Financial Manag. 2018,11, 17 24 of 31 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Initial Ban List, In the Money Puts Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel A. 0801 0919 1008 1031 −7 −6 −5 −4 −3 −2 −1 0 1 Month/Date Dollar Volume: Never Banned, In the Money Puts Million Dollars in Log Scale 20 percentile 50 percentile 80 percentile Average Panel B. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Initial Ban List, In the Money Puts Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel C. 0801 0919 1008 1031 0 10 20 30 40 50 Month/Date Effective Spread: Never Banned, In the Money Puts Percent Effective Spread 20 percentile 50 percentile 80 percentile Average Panel D. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Initial Ban List, In the Money Puts Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel E. 0801 0919 1008 1031 20 40 60 80 100 120 140 160 Month/Date Implied Volatility: Never Banned, In the Money Puts Percent Implied Volatility 20 percentile 50 percentile 80 percentile Average Panel F. Figure 8. Time series of cross sectional options summary statistics: In the money put options of Initial Ban List and Never Banned Stocks during the ban and non-ban periods: ( A , C , E ) results for the three variables for Initial Ban List Stocks; and ( B , D , F ) results for the three variables for Never Banned Stocks. J. Risk Financial Manag. 2018,11, 17 31 of 31 Ross, Stephen A. 1976. Options and efficiency. Quarterly Journal of Economics 90: 75–89. Roberts, H. Statistical Versus Clinical Predication of the Stock Market. Unpublished Working Paper, Center for Research in Security Prices, University of Chicago, Chicago, IL, USA. c 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).