Single stock futures as a substitute
for short sales during the short sale
ban of 2008.
D.L. Heitmeijer
5956056
Finance and Organization
WG 3
Table of Content
Table of Content ... 2 1. Introduction ... 3 2. Literature review ... 4 3. Research Methodology ... 6 4. Data ... 8 4.1 Summary statistics ... 8 5. Results ... 10 5.1 Discussion ... 12 5.2 Limitations ... 14 6. Conclusion ... 15 7. Bibliography ... 16 21. Introduction
On the 21st of September 2008 the Securities and Exchange Commission (SEC) ordered the national exchanges to exclude short sales on financial institutions. The SEC was concerned that the short selling activities would have a disruptive effect on the trust in the financial institutions. Following the SEC, the Financial Serviced Authority (FSA) also imposed a ban on short sales, CEO Hector Sants said: “While short selling is still regarded as a legitimate investment technique…. We have taken decisive action, after careful consideration, to protect the fundamental integrity and quality of markets and to guard against further instability in the financial sector.” Besides the United States and the United Kingdom, other European countries and Australia took likewise actions to prevent short selling.
A short sale is performed if an investor expects the share price to decrease in the future. If the share price indeed decreased, the investor will reverse his short position and profit from the decrease in share price. An investor could short single stock futures to replicate this bearish strategy. The difference between the two strategies is that a short sale has an immediate impact on the spot price and shorting single stock futures does not necessarily immediately impact the spot price. The success of the short sale ban will depend upon the cost of circumventing it. Therefore the central question of this thesis is to which extend are futures substitutes for short sales during a short sale ban?
The purpose of this study is to test whether single stock futures have been a substitute for short sales during the short sale ban in 2008. This study will prove whether the short sale ban was successful in achieving the goal of the SEC and other agencies. It also aims to provide investors with information on bearish investment strategies. The study will use data on the companies of the S&P500, but the results will be transferable to other markets under the same conditions. This thesis is set up according to the following structure. In the second section the most important relating literature is reviewed. The third section elaborates on the research method and the hypothesis is stated. In the fourth section the data and some summary statistics are presented. The fifth section shows the results, the discussion and the limitations of this study. The sixth section contains the conclusion.
2. Literature review
Since the short sale ban of 2008 the research on alternatives for short selling has increased. The ban introduced a real situation opposed to the hypothetical situations in which until that time most theory has been formed. Therefore it seems reasonable to position this thesis among some recent research on short selling alternatives and research on the implications of a short sale ban on stock markets.
At first the relationship between short sales and the introduction of single stock futures has to be examined. If futures do not have an effect on short sales without a short sale ban introduced, then there is less reason to assume a relation when a ban is imposed. Danielsen, Van Ness and Warr (2009) investigate whether single stock future contracts serve as substitutes for short selling. They conclude that single stock futures are substitutes for short sales in a situation without a short sale ban imposed. They found that due to the introduction of single stock futures the short selling volume dropped and the costs of shorting the underlying stock decreased. According to them these results imply that there is a switch from the spot market to the futures market and that single stock futures are a low cost alternative for short selling. Ang and Cheng (2005) also concluded that stocks which were both listed at a stock exchange and had single stock futures listing, had improved efficiency and had lower trading costs, implicating that single stock futures are used as substitutes. Both papers indicate that single stock futures are used as substitutes for short sales when there is no short sale ban imposed.
It is therefore interesting to see what happens if the restrictions on short selling are introduced. Figlewski (1981) concluded that due to short sales restrictions prices would be to high, because investors with unfavorable information could not act on this information. Diamond and Verrecchia (1987) concluded in their paper that prices were not biased due to short sale constraints, but they also indicated that price discovery was slower. They reasoned that investors with bad private information are not able to trade on that information under a short sale constraint, therefore if there is less trading activity during a constraint that indicates an increased chance of informed traders with bad news. Boulton and Braga-Alves (2010) researched the effect of the ban on naked short selling of July 2008. They find that the bid-ask spreads increase by 33.6% compared to their pre ban period. This means that market makers get a higher premium which, according to them indicates that
the liquidity of the market has decreased during the ban on naked short selling. The paper of Frino, Lecce and Lepone (2011) indicate that the goal of the short sale ban of September 2008 was to prevent bearish investors to artificially drive down the share price of the financial institutions. They found that during the short sale ban the prices were artificially inflated, as shown by the positive abnormal returns. This is consistent with the overvaluation theory of Miller (1977) and suggests that the ban reaches its goal, keeping investors from artificially driving down the share prices of financial firms. Frino et al. (2011) also concluded that the market quality deteriorates in terms of abnormal returns, stock price volatility, bid-ask spreads and trading volume. According to their research the short sale ban resulted in positive abnormal returns, wider bid-ask spreads, increased price volatility and reduced trading activity. Autore, Billingsley and Kovac (2011) show that the banned stocks experience positive abnormal returns at the beginning of the short sale ban. They find that this effect is larger for stocks with less information available. This indicates that a ban on short selling has opposing effects to introducing futures. Beber and Pagano (2011) looked into the effects of the short sale ban on market performance estimated as market liquidity, price discovery and level of stock prices. In their thesis they state that especially for the stocks with small market capitalization, high volatility and no listed options the liquidity decreased. They conclude that the short sale ban increased the bid-ask spread and that these deteriorating market conditions are an unintentional effect of the ban, but they recommend not to use such a measure in the future again.
The first papers conclude that the introduction of futures increased market quality and the subsequent papers all conclude that market quality decreases due to a short sale ban. These conclusions lead one to consider whether futures could be a solution for this problem. Harris (1989) concluded that the futures index market leads the price discovery of the stock index market, he credited this effect to the large autocorrelation he found. This implies that a relation between stock and futures exists. McMillan and Philip (2012) looked into the spot-futures dynamics under a short sale constraint in Europe. They concluded that spots were more valuable under a short sale constraint compared to the future holdings. This would indicate that it is not a profitable strategy to hold futures instead of stock. Furthermore research of Grundy, Lim and Vermijeren (2012) has focused on the implications of short sale restrictions on the option market. As Miller (1977) has suggested put options
may be used to replicate bearish short selling strategies, i.e. an investor could buy put options instead of short selling stock, therefore this strategy is considered in that paper. They found that trade volumes for options on banned stocks decreased during the ban. A significant part of the decrease in option trading volumes has been caused by an increase in the price spread. These results imply that the short sale ban acted as a restriction on the options market. Therefore they concluded that trading options is not a substitute for shorting stock; this indicates that the short sale ban worked. In their paper Grundy et al. (2012) also took a moderate look at single stock futures, but they did not find any prove of single stock futures being substitutes for shorting stock
3. Research Methodology
The previous literature shows that due to a short sale ban market quality is reduced, spot assets are more valuable then futures and options trading is not a substitute for short selling. However, when a short sale ban is not imposed futures trading is considered as a substitute for short selling. Therefore the hypothesis is as follows.
H0: Futures are not subsitutes for short sales during a short sale ban.
H1: Futures are substitutes for short sales during a short sale ban.
The hypothesis will be tested using an ordinary least squares regression. As stated in the literature review Grundy et al. (2012) investigate whether options could be used as substitutes for short sales during a short sale ban. Because this thesis only differs in the use of the financial instrument, the effect of the short sale ban on the total daily futures volume per stock will be examined using a similar ordinary least squares regression.
, 0 1* Voli, t 2* Reti, t 3* VIXt 4* Bannedi 5* Periodt 6* (Banned * Period )i t
i t
FVS =β +β +β +β +β +β +β +e
In which the daily futures volume per stock is denoted as FVSi,t, the daily stock volume is
denoted as Voli,t, the daily stock return is denoted as Reti,t and the VIXt represents the
closing value of the volatility index of CBOE. The variable Bannedi is a dummy variable which
is one if a stock has been banned at any time and the variable Periodt is one if the
observation date is within the period when the short sale ban is induced.. Bannedi*Periodt is
an interaction variable between de dummy variables Bannedi and Periodt, which controls for
time invariant characteristics of banned stocks.
Roll, Schwartz and Subrahmanyam (2010) have found that the ratio of options trading/stock trading was influenced by size, implied volatility and trading costs. If we extend these findings to the futures market it becomes apparent which factors should be included into the regression. Therefore changes in daily trading stock volume and stock return could influence the trading in future volume. If the regression coefficient of daily stock volume is positive and significant this indicates that the daily stock volume has a positive effect on the daily futures volume. This implies that the higher the daily volume of a specific stock is the higher the daily volume of futures on that stock is. If the coefficient of the daily stock return is positive and significant, than the daily futures volume of that stock is also higher.
Danielsen et al. (2009) found that single stock futures are a low cost substitute for stock. An increase in risk could therefore induce an increase in the use of futures. By using the VIX in the regression it takes into account the possibility that the volume of futures trading per stock could be influenced by market risk. If the coefficient of the volatility index is positive and significant the higher the implied volatility of the market and the higher the daily volume of futures is. This would imply that when the market risk is higher the use of futures would rise.
The regression uses dummy variables to indicate whether a stock is banned and whether the period is before the ban and during the ban. The dummy variable Bannedi is
one if the stock is banned by the SEC through their emergency order and the second dummy variable Periodt is one if the observation date is during the short sale ban and zero if the
observation date is in the period before the ban. The short sale ban was imposed on the 18th
of September 2008 and ended at the 9th of October 2008. The period before the ban will be
defined as 3 months prior to the ban untill the date before the ban, this constitutes to the 18th of June 2008 untill the 17th of September. If the coefficient of Bannedi is positive and
significant, the daily volume of futures is increased for the banned stock in all periods. If the coefficient of Periodt is positive and significant, the daily volume of futures is higher during
the ban for that stock. The interaction term Bannedi*Periodt has been added to allow for
interaction between the stock being banned and the observation date being during the short
sale ban, which controls for time invariant characteristics of the banned stock. If the coefficient of the interaction term is positive and significant, the daily volume of the futures of the banned stocks has increased more than the daily volume of futures of unbanned stocks during the banperiod. Therefore the null hypothesis is rejected when the coefficient on the interaction variable Bannedi*Periodt is positive and significant, because this indicates
a significant increase in the use of futures.
4. Data
For this research a sample is needed with a good representation of the financial sector for the banned stocks, furthermore it has to be broad enough to have a benchmark of non-banned stocks. Therefore the sample consists of companies listed on the S&P500 index. The data have been collected from the Center of Research of Security Prices (CRSP), the Chicago Boards Options Exchange (CBOE) and the OneChicago exchange. OneChicago is an equity finance exchange providing a marketplace for security futures including single stock futures.
The list of the companies included in the S&P500 index is retrieved from the official website of Standard & Poors. The banned firms have been selected using the SEC emergency order 34-58592. The stocks without a single stock futures listing at the OneChicago exchange during the observation period have been removed. The stocks without a listing at the S&P500-index or the OneChicago exchange during the complete observation period have also been removed. This leaves 422 firms of which 54 stocks are banned for short sales and 368 stocks are not banned for short sales. The data are checked for outliers. The stock return did not exceed 72% and was not below -62%. The largest values of the single stock futures volume recorded were divided between a few firms, therefore it is reasonable to assume that these firms had multiple days with large sales of single stock futures. The stock volumes were also proportionally rational to each other and their firm sizes.
4.1 Summary statistics
Table 1 shows the number of firms, the average stock return and the average stock volume in millions. It shows the summary statistics for the complete observation period, the time period before the short sale ban and during the short sale ban.
It shows that the average stock return of the firms during the observation period was -0.42% for the banned stocks and -0.49% for the unbanned stocks. The average stock volume of the banned stock is 15.1 million and the unbanned stock 7.44 million. In the period before the short sale ban the average stock return of the banned stock was 0% and the unbanned stock -0.13%. During the short sale ban the average stock return of banned stock was -2.24% and unbanned stock -2.04%. The average stock volume of banned stocks before the ban was 14.6 million and unbanned stock 7.03 million. During the short sale ban the average stock volume of banned stock was 17.6 million and of unbanned stock the average stock volume was 9.20 million.
Table 1. Number of firms, average stock return and average stock volume during the observation period.
Complete Period All Stock Banned stock Unbanned stock
Number of firms 422 54 368
Average stock return -0.48% -0.42% -0.49%
Average stock volume 8.42 15.1 7.44
Before the ban All Stock Banned stock Unbanned stock
Average stock return -0.11% 0.00% -0.13%
Average stock volume 8.00 14.6 7.03
During the ban
Average stock return -2.07% -2.24% -2.04%
Average stock volume 10.3 17.6 9.20
Table 2 shows the average single stock futures volume and standard deviation. Single stock future contract are written on 100 futures. Therefore the average volume of single stock futures of the banned stock during the complete period is 9.27 contracts of 100 futures with standard deviation 67.74. The average volume of single stock futures of unbanned stock during the complete period is 19.47 contracts of 100 futures with standard deviation 267.75. The average single stock futures volume of banned stock before the ban was 7.33 with standard deviation 57.30 and of unbanned stock it was 20.36 with standard deviation 288.40. During the ban the average single stock futures volume of the banned stock was 17.68 with standard deviation 100.86 and of the unbanned stock the average single stock futures volume was 15.62 with standard deviation 147.78.
Table 2. Daily trading volume of single stock futures.
Complete period Av. SSF Volume St. dev. Min Max
All Stock 18.16 251.20 0 20020 Banned Stock 9.27 67.74 0 2064 Unbanned stock 19.47 267.75 0 20020 Before ban All Stock 18.69 270.10 0 20020 Banned Stock 7.33 57.30 0 2064 Unbanned stock 20.36 288.40 0 20020 During ban All Stock 15.88 142.62 0 6611 Banned Stock 17.68 100.86 0 2037 Unbanned stock 15.62 147.78 0 6611
One future contract is denominated as 100 contracts of single stock futures.
5. Results
The results of the regressions are tabulated in table 3 en table 4. Table 3 contains the results of the pooled ordinary least squares regression and table 4 contains the results of the fixed effects model. The coefficients of the regression are represented with a * if it is significant at a level of 10%, ** at a significance level of 5% and *** at a significance level of 1%. The standard deviation is presented in brackets below each coefficient.
Table 3 panel A contains the results of the pooled ordinary least squares regression, panel B shows the results of the regression when the logarithm of futures volume and the stock volume is used. Both the regressions include robustness.
Panel A contains the results of the regression including the logarithms. The stock return has an insignificant positive effect on the average single stock futures trading volume. The average stock volume has a significant positive effect on the single stock futures volume, if the stock volume increases with 1 the number of contracts increases with 0.000000665. The average single stock futures volume is negatively effected by the VIX, if the VIX rises by 1 the number of single stock futures contracts traded decrease with 0.36 contracts. Furthermore the coefficient of the variable Banned is negative and significant. This means that at any time the banned stocks have a lower trading volume in single stock futures than the unbanned stocks. The coefficient on the variable Period is not significant. The coefficient on the variable Banned*Period is positive and significant, this means that during the short sale ban the average single stock futures trading volume on banned stocks increases with 14.60 contracts.
Panel B shows that the pooled ordinary least squares regression which uses the logarithms of the single stock futures volume and the stock volume. The results show an insignificant influence of the stock return on the average single stock futures volume. The stock volume shows a positive significant influence, this means that if the average stock volume increases by 1% the average single stock futures volume increases with 24%. The VIX has a significant negative effect on the average futures volume, if the VIX increases with 1 the average futures volume decreases with 0.99%. The negative and significant coefficient of the variable banned shows that a banned stock during the entire period has a lower average single stock futures volume of 26%. The positive and significant coefficient of the variable period shows that during the short sale ban the average single stock futures volume is 43% higher than before the short sale ban for all stocks. The coefficient on the interaction variable banned * period shows that for banned stocks during the short sale ban the average single stock futures volume is 28% higher and this result is significant at a significance level of 5%.
Table 3. Average single stock futures trading volumes.
A. SSF trading volume B. LN SSF trad. volume
Constant 24.19*** (4.34) -1.47*** (0.27) Stock return 14.26 (25.95) (0.37) 0.20 Stock volume 0.000000665*** (0.0000000941) 0.24*** (0.017) VIX -0.36** (0.16) -.0099*** (0.0033) Banned -18.07*** (2.43) -0.26*** (0.051) Period 1.30 (3.51) 0.43*** (0.081) Banned * Period 14.60*** (4.62) 0.28** (0.13)
Part A consists of the pooled ordinary least squares regression and part B contains the regression including the logarithms on futures volume and stock volume. * Significant at a 10% significance level, ** significant at a level of 5% and *** significant at a level of 1%.
Table 4 panel A contains the results of the fixed effects model, panel B shows the results of this model when the logarithms of the futures volume and the stock volume is used, both models include robustness.
The results of the fixed effects model including robustness in panel A show significant results on variables average stock volume and VIX. The coefficient on the average stock volume is positive and significant. If the average stock volume increases with one than the average single stock futures trading volume increases with 0.000000508 contracts. The VIX is negative and significant, if the VIX increases with 1 than the average single stock futures volume decreases by 0.33 contracts. The dummy variable Period and the variable average stock return do not show a significant results.
In panel B the results of the fixed effects model including the logarithms of futures volume and stock volume are displayed. They show an insignificant influence of the stock return. The logarithm of stock volume shows a significant effect, if the stock volume rises by 1% the average single stock futures volume increases with 31%. The VIX shows a negative coefficient, if the VIX increases with 1 the average single stock futures volume decreases with 0.76%. The dummy variable period shows a positive coefficient. This means that during the short sale ban the average single stock futures volume was 41% higher than before the short sale ban.
Table 4. Effect of the short sale ban on average single stock futures volume.
A. SSF trading volume B. LN SSF trad. volume
Constant 22.31*** (4.39) -2.71*** (0.49) Stock return 7.70 (25.74) (0.33) 0.21 Stock volume 0.000000508*** (0.000000165) 0.31*** (0.033) VIX -0.33** (0.15) -0.0076** (0.0034) Period 2.71 (3.81) 0.41*** (0.082)
Part A shows the results of the fixed effects model and part B contains the results of the model including the logarithms on futures volume and stock volume. * Significant at a 10% significance level, ** significant at a 5% significance level and *** significant at a 1% significance level.
5.1 Discussion
Both regression models show more significant results when the logarithms are included. Frino et al (2011) and Autore et al (2011) both concluded that during the short sale ban the stocks experienced positive abnormal returns. The pooled OLS and the fixed effects model show that the stock return does not have a significant effect on the average trading volume of single stock futures. Both regressions do not result in a negative relation between stock
return and futures volume, in contrast to Grundy et al (2012) who found a negative relation between stock return and put options volume. This result indicates that the stock return of banned and unbanned stocks did not significantly influence the average single stock futures volume.
The average stock volume positively influences the average single stock futures volume. This could imply that a stock with a more liquid stock market has a more liquid market for single stock futures. This paper is not able to draw such a conclusion, because from this regression the causal relation between liquidity of the stock market and liquidity of the single stock future market cannot be conclusive. This paper does not incorporate the bid-ask spreads of stocks and single stock futures, therefore the relation between the liquidity of the stock market measured by the bid-ask spreads and the use of single stock futures is an issue to research in a future paper. The more extensive definition of liquidity which uses bid-ask spreads is used by Beber and Pagano (2009) their paper. They, inter alia, examined the effect of the short sale ban on the bid-ask spreads and found that these spreads increased. From this result they concluded that the liquidity of the market during a short sale ban decreased.
Single stock futures volume is negatively effected by the uncertainty measured as VIX. This could indicate that investors evaluate single stock futures as risky investments when uncertainty in the market increases. This should be evaluated on a more relative basis, because it could also be that the negative relationship between the uncertainty and the single stock futures volume is smaller than the negative relationship between uncertainty and stock volume.
The average single stock futures volume is higher during a short sale ban as indicated by the dummy variable period. This could indicate that investors try to profit from their private information using futures instead of using short sales for any firm. This conclusion is not comprehensive because investors could still short sale the unbannen stocks. Therefore the interaction variable banned*period provides a more distinct picture.
The banned stock consists of stocks of financial firms. The negative coefficient on the dummy variable banned therefore indicates that single stock futures volumes on the banned financial stock are lower in general. These results imply a lower use of single stock futures
for financial firms. One reason for this result could be that investors are less informed about the performance of financial firms than on the performance of non-financial firms. But the positive coefficient on the interaction variable banned*period shows that this difference in average single stock futures volume between banned financial stock and the benchmark, the unbanned stock of the S&P500, decreases at the time of the ban. This implies that during the short sale ban the average single stock futures volume for banned stocks with respect to unbanned stocks increased. Grundy et al (2012) found the opposite result for option volumes for the interaction variable banned*period. They found a significant decrease in the average option volumes for the banned stocks during the short sale ban.
Another conclusion from these results is that during a short sale ban the use of single stock futures for financial firms relatively increases compared to that of non-financial firms. This result implies that informed investors now try to benefit from there information on financial firms using single stock futures.
Conclusively the results of the regression imply that the null hypothesis that futures are not used as a substitute for short sales during a short sale ban should be rejected. The results show an increase in the use of single stock futures of banned stock during a short sale ban.
5.2 Limitations
Some complications could exist that could induce the results to be inaccurate. The sample consists of the firms in the S&P500 index which have a single stock futures listing at the OneChicago exchange. The results of this paper could be inaccurate because for some of firms the single stock futures are not traded during the observation period. This could have a number of reasons, but the lack of liquidity in the sample could have influenced the results of this paper. To solve this a next research could use another sample or specify a larger observation date. The time period concerned could pose another problem. The short sale ban lasted for three weeks, this means that the period in which stocks were banned for short sales was small. This could imply that the single stock futures trading volume was not normally distributed. Besides that in the period before the short sale ban the markets allready experienced turmoil, so it could be that the pre ban period does not provide a good benchmark for the analyses.
6. Conclusion
This paper examines the effect of a short sale ban on the average trading volume of single stock futures of the firms listed on the S&P500. The intented effect of the short sale ban is to stop bearish investors to artificially drive down the prices of financial firms during the start of the credit crisis. The succes of the short sale ban depends on the ability of investors to circumvent this measure.
The analyses of the paper show that there is a significant increase in the use of single stock futures of the banned stocks during the short sale ban. Therefore the hypothesis that futures are not used as substitutes for short sales during a short sale ban is rejected. The results imply that single stock futures to some extend are used as subsitutes for short sales during a short sale ban.
Nevertheless further research in this area is needed, preferably when a new and longer short sale ban occurs. But this would mean that another time period of financial turmoil should have to happen which is not something one should wish for. Subsequent research could also consider the implications on the bid-ask spread of the single stock futures to evaluate the effect of the short sale ban on the liquidity of the futures market.
This study has an important implication for future policy. According to this study the short sale ban is circumvented by investors using single stock futures. A characteristic of shorting futures is that it does not directly influence the share price, but has to be taken into consideration when policy makers have to take a decision on a short sale ban in the future.
7. Bibliography
Ang, J., Cheng, Y. (2005). Financial innovations and market efficiency: The case for single stock futures. Journal of Applied Finance, Vol. 15, 38-53.
Autore, D.M., Billingsley, R.S., Kovacs, T. (2011). The 2008 short sale ban: Liquidity,
dispersion of opinion, and the cross-section of returns of US financial stocks. Journal
of Banking & Finance, Vol. 35, pp. 2252-2266.
Beber, A., Pagano, M. (2011). Short selling bans around the world: Evidence from the 2007-2009 crisis. Journal of Finance, Vol. 68, pp. 343-381.
Boulton, T.J., Braga-Alves, M.V., (2010). The skinny on the 2008 short sale restricitions.
Journal of Financial Markets. Vol.13, pp. 397-421.
Danielsen, B.R., Van Ness, R.A., Warr, R.S., (2009). Single stock futures as a substitute for short sales: evidence from microstructure data. Journal of Business Finance &
Accounting, Vol. 36, pp.1273-1293.
Diamond, D.W., Verrecchia, R.E., (1987). Constraints on short selling and asset price adjustment to private information. Journal of Financial Economics, Vol. 18, pp.
277-311.
Grundy, B.D., Lim, B., Verwijmeren, P. (2012). Do option markets undo restrictions on short sales? Evidence from the 2008 short-sale ban. Journal of Financial Economics, Vol.
106, pp. 331-348.
Figlewski, S., (1981). The informational effects of restrictions on short sales: some empirical evidence. Journal of financial and quantitative analysis. Vol. 16, pp. 463-476.
Frino, A., Lecce, S., Lepone, A. (2011). Short-sales constraints and market quality: Evidence from the 2008 short-sales bans. International Review of Financial Analysis, Vol. 20,
pp. 225-236.
Harris, L., (1989) The October 1987 S&P 500 stock-futures basis. Journal of Finance. Vol.44,
pp. 77-99.
Hong, H., Stein, J. C. (2003). Differences of opinion, short-sales constraints, and market crashes. Review of Financial Studies, Vol. 16, pp. 487–525.
Lim, B.Y., (2011). Short-sale constraints and price bubbles. Journal of Banking & Finance, Vol.
35, pp. 2443-2453.
McMillan, D.G., Philip, D., (2012) Short-sale constraint and efficiency of the spot-futures dynamics. International review of financial analysis, Vol. 24, pp. 129-136.
Ofek, E., Richardson, M., Whitelaw, R.F. (2004). Limited arbitrage and short sales predictions: evidence from the options markets. Journal of Financial Economics, Vol. 74, pp.
305-342.
Roll, R., Schwartz, E., Subrahmanyam, A., (2010). O/S: The relative trading activity in options and stock. Journal of Financial Economics, Vol. 96, pp 1-17.
