How Much Does It Cost To Short Sale A Stock Index? *

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1 How Much Does It Cost To Short Sale A Stock Index? * 1. Introduction In a comprehensive study of the borrowing/lending market for stocks, D Avolio (2002) showed that constituents of the S&P 500 are almost always general collateral. Such a result means that the rebate rate received on the collateral deposit by the borrower of a stock pertaining to the S&P 500 is very close to the prevailing market interest rates when the short is undertaken. Using a different sample, Ofek et al. (2003) also showed that more than 70% of the stocks in their sample have a null rebate rate spread, that is the difference between (i) the rebate rate and (ii) the standard rebate rate on the majority of stocks, which is known as the cold rate, is zero. Geczy et al. (2002) found that in their sample, Large and Medium general collaterals have rebate rates that are 8 bp (0.08%) and 15 bp only below the Federal Funds Effective Rate. Therefore, it may safely be concluded that the cost of shorting the S&P 500 Index is likely to be negligible. In addition to the empirical findings cited above, there exist a very liquid market for S&P 500 futures, and the market for S&P Deposit Receipt (SPDR) recorded a constant growth of activity since its launching in 1993, two facts that are likely to ease even more short selling of the S&P 500. The evidence about rebate rates relative to market interest rates have been supplemented by analyses of the short sale cost that is implicit in options prices, notably by Ofek et al. (2003), Evans et al. (2003) and Lamont and Thaler (2003). This approach builds upon the well-documented evidence that the existence of options helps short selling of the underlying stocks (see Figlewski and Webb (1993), Sorescu (2000) and * We are very grateful to Raphael Franck for extensive Editorial Assistance and especially to Patrice Poncet for very detailed comments on previous drafts of this paper. The first author acknowledges financial support from The Maurice Falk Institute for Economic Research in Israel.

2 2 Danielsen and Sorescu (2001)). The methodology used is a simple test of the Call-Put Parity (CPP) in which options prices are used to calculate the implicit stock price. The latter is then compared to the prevailing stock price. Because of short sale restrictions in the market, the average implicit stock price should be lower than the prevailing stock price in the market. The (algebraic) difference is indeed what the short seller is willing to forsake for short selling the stock through the options market. Empirical evidence in Ofek et Al. (2003) showed that the CPP disparities are asymmetric in the direction of short sale constraints. They find that on the average the implicit stock price is lower that the prevailing stock price by 30 bp (0.30%) of the stock price in their sample. Similar findings are reported in Evans et al. (2003) who show that the average disparity is 16 bp of the stock price on the average. They all use American stock options and the CPP has been adjusted accordingly for future dividend and early exercise premium. Our objective in this paper is to assess the cost of short selling a stock index using traded stock index options. However, the standard approach in the literature should be amended for the following reason: it ignores the fact that in the same way that options could be used for shorting synthetically the underlying, traders may also use options to buy synthetically the underlying through the options market. This is especially true for a stock index where CPP disparities reflect both possibilities. Thus one should disentangle these disparities to assess the cost of buying synthetically the underlying through the options market from the cost of short selling it synthetically. One may expect the latter to be higher than the former, the increment representing the additional cost for the short sale. To achieve this goal, we suggest the following approach. First, we define the spread as the difference between the stock index value implicit in options prices and the prevailing stock index value. If the buyers of the stock index on the options market are the majority, we expect the spread to be positive. If short sellers of the stock index on the options market are the majority, we expect the spread to be negative. We can thus build two sub-samples of CPP disparities, one of positive spreads and another of

3 3 negative spreads. The first sub-sample assesses the cost of buying the underlying synthetically and the second one assesses the cost of short selling it the underlying synthetically. Although the latter sub-sample is likely to represent a large fraction of the total sample, we expect the sample of positive spreads not to be small. Around one third of the cases analyzed by Ofek et al. (2003) had positive spreads. If our decomposition is sustainable empirically, it means that the previous measures of short selling costs through options markets used in the literature underestimated the real cost of short selling. To illustrate our argument, consider two successive observations in the options market. In the first one, the implicit stock price is lower than the prevailing stock price (negative spread) by 1.20 %. This negative spread suggests that if options have been used as substitute for direct trading in the underlying, it was for shorting it this day. In the next observation, the implicit stock price is higher by 1 % than the prevailing stock price. This positive spread indicates that the market was buying the underlying through the options market. Averaging these two observations yields an average CPP disparity of 20 bp. This is obviously far below the real cost of shorting which worth 120 bp. One possible way to assess whether our decomposition is sustainable empirically is as follows. In days when the spread is positive, the market is a net buyer and thus optimistic. One widely used market indicator for such a situation is the ratio of call trading volume over put trading volume. When this ratio is larger than one, calls are more traded than puts and thus, the market is optimistic. When it is lower than one, the market is pessimistic: puts are more traded than calls. Therefore, in days where the spread is positive, trading volume on calls should be higher than trading volume on puts whereas in days where the spread is negative, the reverse should be true. We implement our methodology in the case of a Stock Index. In addition to this methodological contribution, the database we use allows us to provide an empirical contribution to the literature. We consider Stock Index options on the TA 25, a stock index from the Tel Aviv Stock Exchange (TASE). Whereas most papers dealing with

4 4 short sale costs focused on individual stocks only, we provide evidence on the cost of short selling a stock index. We also give an estimation of the cost of buying the stock index through the options markets. As to the implicit costs of short selling in options prices, Kamara and Miller (1995) showed that deviations from the CPP are much less frequent and smaller with European options than with American options. One possible reason for this lies in the necessity to estimate the early exercise premium in the case of American options, which may affect the results. In the case of the TASE, the options are European, nevertheless it is likely that CPP deviations are significant since: i) easy and cheap substitutes to the underlying do not have a liquid market. Although Futures contract exist on the TASE, their trading volume is close to zero. Calls with an exercise price of 1 index point may also be traded but their trading volume is negligible. A security that is equivalent to the S&P Deposit Receipt has only been introduced recently and did not exist during our sample period. 1 ii) the market for short sales of individual stocks is very limited, if not inexistent. In addition, the TASE has several properties that render inference using the CPP easy to implement and probably more accurate since: i) the stock index is dividend protected. This eliminates another source of error when testing for CPP deviations. Indeed, for individual stocks, the dividend yield to be taken into account in the CPP must be estimated. The same is true for most index options. In our case, there is no need for such estimation since the index is calculated with all dividends reinvested. ii) there are no designated market makers on this market. This is a pure supply and demand market, a feature that makes the empirical findings comparable to the market for shorting stocks directly. Empirical evidence suggest that the bid and ask spreads 1 A first study by Ackert and Tian (2001) suggests that these securities may increase substantially pricing efficiency.

5 posted by market makers may have important sensitivity to market structure and thus affect inference based on the midpoint between the bid and the ask (Mayhew (2002)). 5 We show that the average CPP deviation for the buyer of the stock index through the options market is 28 bp while the average CPP deviations for the short seller of the stock index is 57 bp. Therefore, the incremental cost for short selling is 29 bp. Hence, annual deviations for the buyer and the short seller respectively amount to 5.35% and 7.01%, i.e. an incremental cost for short sale of 1.66%. 2 These numbers may seem relatively low, but they must be put into perspective: our sample is restricted to atthe-money options with moneyness of 98% to 102%, compared to the 90% to 110% usually retained. In addition, the deviations in dollars from the CPP were negligible for individual stocks. For example, in Ofek et al. (2003), the average stock price and the average CPP deviations are respectively $32 and 30 bp, thus a dollar deviation of 10 cents. The dollar deviation in our sample is around $23. Following our decomposition, it costs the buyer around $23 to buy the stock index and it costs the short seller around $44 to short sale the stock index, thus an incremental cost for short selling of $21 per contract. The remainder of the paper is planned as follows. In the next section we give the institutional background of the TA 25 options market and provide descriptive statistics. In section 3, we give two perspectives on the implicit costs in the options markets, through the spread and through the Implied Volatilities. In section 4, we isolate variables deemed to explain the spread level. The last section contains some concluding remarks. 2 One should be aware that the conversion on an annual basis should be weighted by the time to maturity of the options, details are given in section 3.

6 6 2. Data Stocks included into the TA 25 Stock Index are those with the highest market capitalization and are among the 75 shares with the highest average daily turnover. The Index is updated twice a year, on January and July. The stock index is dividend protected, so that its value is obtained assuming the reinvestment of any dividend into the stock distributing the dividend. European options on the stock index started to be traded on August Until 2000, options were traded with expiration date every two months. Since 2000, a new serie of options is introduced each month with three months to expiration so that each month one traded serie expires. The average daily number of contracts traded has known a constant growth for the past years, reaching more than contracts per day. In terms of the underlying (weighted by the deltas), options trading represents more than 800% of the turnover in the TA 25 shares. Futures contracts on the stock index have been introduced on October 1995 with three months to maturity. There are no official market makers on the TASE and this could explain the lack of trading in those futures contracts. 3 Following Evans et al. (2003) and Ofek et al. (2003), we use closing prices for TA 25 options. Our sample covers 6 years of data, from January 1, 1996 to December 31, Our data set, provided by the TASE, include daily options closing price, trading volume, open interest, number of transactions. Based on this information, we filtered the data according to the following steps. We first dropped all the options for which trading volume was zero. Since there are no market makers, we cannot afford to keep options within a wide range of moneyness. Therefore, we limited ourselves to options with moneyness (exercise price over index value) ranging from 98% to 102%. For the sake of comparison, Ofek et al. (2003) used moneyness that ranged from 90% to 110%. For each option, we calculated the implied volatility by inverting the standard 3 On June 17, 2003, TASE announced the introduction of market makers on both derivatives markets and primitive asset markets.

7 7 Black and Scholes formula. The risk free interest rate used in this study has also been provided by the TASE. It is based on the average of the yield of the Treasury Bills with maturity from 60 to 120 days. The mean risk free rate for the period was 10% with a standard deviation of 3%. Following previous studies, all options with implied volatility of more than 100% have been dropped. Options with the same exercise price and the same maturity were organized by pairs. At the end of this filtering process, we were left with 4350 pairs of options. For each day, we had between 1 to 4 pairs. Time to maturity range from 1 day to 120 days. Since options with maturity inferior to 7 days (which represents 7% of the data) have characteristics which are very close to the other options, we did not drop them. Table I. Summary Statistics for the TA 25 daily return from 1/1/96 to 31/12/01. Mean 0.03 % Median 0.05 % Standard Deviation 1.19 % Kurtosis 5.97 Skewness Minimum % Maximum 7.40 % Number of Observations 1,423 In Table I, we report the summary statistics of the TA 25 for our sample period. The daily average return for the TA 25 was 0.03%, that is 12.41% on an annual basis, with a daily standard deviation of 1.19%. Thus, the index was very volatile during this period which was characterized by an asymmetric return distribution towards positive daily returns.

8 8 In addition, on the average, calls were more expensive than puts as shown in the following table. Table II Summary Statistics for the Options Prices as a fraction of the stock index value from 1/1/96 to 31/12/01. The figures are for options with moneyness (exercise price over underlying value) between 98% and 102%. Call Put Mean 3.7 % 2.7 % Median 3.7 % 2.7 % Standard Deviation 1.9 % 1.2 % Kurtosis Skewness Minimum 0.0 % 0.0 % Maximum 10.5 % 7.6 % Number of Observations 4,350 4,350 While the value of calls was on the average 3.7 % of the underlying, it was only 2.7% for puts for the same period. These numbers should be kept in mind when assessing the economic (quantitative) significance of the short sale cost implied in option prices computed in the next section. Calls were also more traded than puts during this period.

9 9 Table III Summary Statistics for TA 25 Calls and Puts Trading Volume in number of contracts traded and in dollars (turnover). The sample period ranges from 1/1/96 to 31/12/01. The options have a moneyness (exercise price over the underlying value) between 98% and 102%. The exchange rate used for converting NIS turnover in dollars is 4.5 NIS per dollar. Trading Volume in Number of Contracts Trading Volume in Dollar (Turnover) Call Put Call Put Mean 3,705 3, , ,452 Median 1,560 1, , ,137 Maximum 54,992 37,906 6,405,767 6,665,878 Minimum Standard Deviation 5, , , ,105.8 Skewness Kurtosis Number of Observations 4,350 4,350 4,350 4,350 For our moneyness between 98% and 102%, the average daily trading volume was of 3705 calls and of 3067 puts per serie of options. Given that we have 1 to 4 series per day, the total daily trading volume for the options with moneyness between 98% and 102% is from 3705 to contracts for calls, on the average, and for puts, the figures are from 3067 to contracts. An interesting feature of the data concerns the high correlations between call and put trading volume and call and put number of transactions, which respectively amount to 0.80 and This feature of the data stems from the behavior of some market participants, usually large institutions who can trade heavily on the underlying, and act unofficially as market makers. They have two strategies at their disposal: They may sell the underlying on the options market by selling expensive calls, buy the corresponding puts, and hedge themselves by buying the underlying on the spot market. Alternatively, they may sell expensive puts, buy the

10 10 corresponding calls, and hedge themselves by selling the underlying on the spot market. Since trades are not simultaneous, there exists a residual risk, which is probably less severe than the residual risk of a market maker who dynamically hedges his position. There is no dynamic hedging on the TASE market and this may explain the significant lack of liquidity for the futures contract. Even for a small market like the TASE, the turnover in the options segment is significant. The average daily turnover is $732,777 for calls and $530,452 for puts. Parts of these amounts are related to frictions in the market, and it will be interesting to assess their economic importance. With this background in mind, we turn now to the issue of the level of short sale costs for the TA 25 stock index implicit in the sample we have described. 3. The Cost of Short Selling the TA 25 Index In this section, we report the results on the CPP deviations. As explained in the introduction, we follow a standard methodology in the literature that consists in comparing the stock index value implied in the options prices to the prevailing index value in the market. When markets are arbitrage free and frictionless, European call and put options on a stock index with the same exercise price (K) and the same time to maturity (T-t) should satisfy at each time t until the maturity of the options the following relation: C(t) P(t) = S(t) Ke -R(T-t) (1) where S(t) is the stock index value at time t and R is the risk free rate prevailing in the economy. This relation holds when the underlying does not distribute dividend or alternatively, when it is dividend protected. Since this is the case for the TA 25, we need not estimate future dividends which is very valuable for the robustness of our results.

11 11 Table IV Summary Statistics for Call-Put Parity deviations. Column I gives the implied index obtained from the Call Put parity minus the closing index; Column II gives the implied index obtained from the Call Put parity minus the closing index in percentage of the Closing Index and Column III gives the implied index obtained from the Call Put parity minus the closing index in percentage of the Closing Index on an annual basis. The annualisation is obtained by multiplying the deviation in percentage by 365 and then dividing by the time to maturity of the options. The exchange rate used to convert NIS into dollars is 4.5 NIS per dollar. Panel A contains all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains option pairs for which the implied index is less than the closing index (negative spread). I (in $) II (in %) III (in %) Panel A Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Number of Observations 4,350 4,350 4,350 Panel B Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Number of Observations 1,304 1,304 1,304 Panel C Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum Number of Observations 3,046 3,046 3,046

12 12 Table IV reports the CPP deviations in our sample. Panel A is the outcome for the whole sample, where no distinction is made between a positive spread and a negative spread. On the average, the implicit stock index is less than the prevailing stock index by 109 NIS (New Israeli Shekels) that represents around $23.6. Relative to the stock index value, it represents a cost of 32 bp and on an annual basis this cost is 3.30%. Caution is required when converting the daily result to an annual basis. Indeed, the options offer the possibility to short sale or to buy the underlying up to the options maturity. The cost is incurred at the time the trader enters the market up to the options maturity. Therefore the right way to convert the cost on an annual basis is by weighting the daily cost by the time to maturity, that is: Annual Spread = Daily Spread 365 Time to Maturity The standard interpretation of this finding is that a short seller of the stock index through the options market incurs a cost of $23.6 per contract. Indeed, looking at the data at this aggregate level leads us to lose important information and eventually to under- estimate the real cost of short selling the underlying through options. In Panel B, we report all the cases in which the spread was positive while Panel C reports all the cases in which it was negative. Panel B is intended to provide information on the convenience yield paid by the trader who uses options as a device for trading the stock index. This convenience yield is to be incurred by a short seller who also pays for the short sell possibility offered by the options. The difference between the two spreads informs us on this incremental cost for short selling. As shown by table IV, when the spread is positive, the implied index is larger than the prevailing index by NIS, thus around $24. Hence for each contract traded through the option market, the convenience cost is $24. It represents 0.3% of the underlying or an annual cost of 5.35%. Compared to the average call and put prices for our sample period, this cost is still high. As to the cost incurred by the short seller, it

13 13 amounts to NIS on the average or around $44. This represents an additional cost for shorting of around $20 per contract. Relative to the underlying, it amounts to an annual cost of 7% and thus, an additional cost of 1.65% for short selling. Indeed, several discussions with the professionals in the TASE confirmed this figure which is evaluated to be around 1.5%. To sum up, the total cost of short selling the TA 25 Index through the options is 7%, which is more than twice as much as the 3.3% obtained by simply averaging the whole sample. An important remark is in order at this stage. Standard tests applied to Panel B and C would have led to a difference which is not statistically significantly different from 0. This would have made further analysis irrelevant. However, this would be the wrong way to test the significance of our results, especially since the data are highly skewed. This is why we performed a bootstrap simulation of our data and the results are given in the following Table.

14 14 Table V Bootstrap tests for the mean deviations of the call-put parity. The bootstrap simulations were performed with replacement and the basis sample was simulated 1000 times. Column I gives the implied index obtained from the Call Put parity minus the closing index; Column II gives the implied index obtained from the Call Put parity minus the closing index in percentage of the Closing Index and Column III gives the implied index obtained from the Call Put parity minus the closing index in percentage of the Closing Index on an annual basis. The annualisation is obtained by multiplying the deviation in percentage by 365 and then dividing by the time to maturity of the options. The exchange rate used to convert NIS into dollars is 4.5 NIS per Dollar. Panel A contains all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains option pairs for which the implied index is less than the closing index (negative spread). Panel A I II III Simulated Mean - $ % -3.30% t Statistic % Conf. Int. - $24.9; - $ %; -0.3% -3.73%; -2.88% Panel B I II III Simulated Mean $ % 5.35% t Statistic % Conf. Int. $22.8; $ %; 0.3% 4.68%; 6.02% Panel C I II III Simulated Mean - $ % -7% t Statistic % Conf. Int. - $45.2; - $ %; -0.55% -7.46%; -6.55% This Table reports results from a bootstrap simulation of our sample data with replacement to compute the distribution of our mean estimates. We performed the simulation 1000 times for each Panel. The simulated means are almost equal to the means of our sample appearing in Table IV and statistically significant at almost any

15 15 level. Therefore, the means in Panels B and C are statistically different from zero, and their differences represent the additional cost for short selling. Overall, the average short sell cost of the TA 25 Index is $20. Given that the average put daily trading volume is less than the average call daily trading volume, we take this number as an approximation of the number of contracts synthetically traded in the market. The average put daily trading volume is 3067 times $20, that is $61,340 per option series. Since for our moneyness range, we had 1 to 4 options pairs, it turns out that the total short sell cost was from $61,340 to $245,360. The average turnover of the put was $530,452 per option serie and per day. Therefore, as a fraction of the turnover, the short sell cost in the market represents around 12 % of this turnover! Thus, market frictions do matter for asset pricing in general, and derivatives pricing in particular. An equivalent perspective on the short sale cost implicit in options prices may be obtained by looking at the implied volatilities in the options. This is probably a more accurate way than the implied stock index value although the later approach is the one retained by the literature. It is well documented, notably by Figlewski and Green (1999), that traders mark up the implied volatility to account for market imperfections. Therefore, since market participants are aware that options are used as a substitute to direct trading in the underlying, they will charge some premium in the options prices through a mark up of the implied volatilities. When the spread is positive, the market is buyer and thus the implied volatility of a call will be higher than the corresponding put s implied volatility. In days where the spread was negative, the implied volatility of a put will be higher than the implied volatility of the corresponding call.

16 16 Table VI Summary Statistics for TA 25 Calls and Puts implied volatilities and their ratio. The sample period ranges from 1/1/96 to 31/12/01. The options have a moneyness (exercise price over the underlying value) between 98% and 102%. Panel A contains all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains option pairs for which the implied index is less than the closing index (negative spread). Call Put Ratio Panel A Mean 22 % 24.5 % 1.15 Median 21.8 % 24.3 % 1.09 Standard Deviation 5 % 5.3 % 0.33 Kurtosis Skewness Minimum 3.1 % 1.3 % 0.27 Maximum 73.3 % 81.7 % 6.45 Number of Observations 4,350 4,350 4,350 Panel B Mean 24.7 % 22 % 0.89 Median 24.7 % 21.9 % 0.92 Standard Deviation 4.9 % 4.7 % 0.11 Kurtosis Skewness Minimum 3.1 % 1.3 % 0.22 Maximum 73.3 % 48.2 % 1.05 Number of Observations 1,304 1,304 1,304 Panel C Mean 20.9 % 25.6 % 1.27 Median 20.6 % 25.2 % 1.16 Standard Deviation 4.6 % 5.1 % 0.33 Kurtosis Skewness Minimum 3.8 % 5.9 % 0.41 Maximum 3.82 % 81.7 % 6.45 Number of Observations 3,046 3,046 3,046

17 17 Table VI provides evidence as to the implied volatilities of call and puts and their ratio according to the spread sign. When the spread is positive, puts volatilities are less than their corresponding calls implied volatility by almost 12%. However, when the spread is negative, put volatilities are higher than their corresponding calls volatility by 26.5%. These numbers may seem excessive given the standard findings in the empirical literature that when options are at the money, call and put implied volatilities are very close to each other. To check the robustness of the findings, we performed a bootstrap simulation of our data. Results are reported in Table VII. Table VII Bootstrap tests for the mean of the implied volatility of TA 25 Calls and Puts, and their ratio. The bootstrap simulations were performed with replacement and the basis sample was simulated 1000 times. The sample period ranges from 1/1/96 to 31/12/01. The figures are for options with moneyness (exercise price over underlying value) between 98% and 102%. Panel A contains all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains option pairs for which the implied index is less than the closing index (negative spread). Call Put Ratio Panel A Simulated Mean % % 1.15 t Statistic % Conf. Int % ; % % ; % 1.14 ; 1.16 Panel B Simulated Mean % % 0.89 t Statistic % Conf. Int % ; % % ; % 0.89 ; 0.9 Panel C Simulated Mean % % 1.27 t Statistic % Conf. Int % ; % % ; % 1.25 ;1.28 These results show that differences between the call and put implied volatilities are significant at almost any level. A natural question is whether volatility differences are

18 18 function of the moneyness, in other words, whether there is a smile or a smirk in this short range. Figure 1 We report the call and put implied volatilities of the TA 25 as a function of their moneyness. Panel A contain all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains option pairs for which the implied index is less than the closing index (negative spread). Panel A Implied Volatility Moneyness Panel B Call Put 0.27 Implied Volatility Moneyness Call Put

19 19 Panel C Implied Volatility As shown in Figure 1, implied volatilities are almost flat for calls and puts relative to options moneyness meaning that there is no smile effect. Some empirical support for our decomposition can be found in the behavior of the ratio of call trading volume (in units or dollars) to the corresponding put trading activity. This is a widely used indicator on financial markets which assesses market optimism. When markets are optimistic, this ratio is greater than one. When the market is pessimistic, it is below one Moneyness Call Put

20 20 Table VIII Summary Statistics for the trading volume in units and the turnover of TA 25 Calls and Puts. The sample period ranges from 1/1/96 to 31/12/01. The options have a moneyness (exercise price over the underlying value) between 98% and 102%. The ratio is the trading volume of the call over the trading volume of the put. Panel A contains all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains option pairs for which the implied index is less than the closing index (negative index). Ratio of Trading volume in number of contracts Ratio of Trading Volume in dollars (Turnover) Panel A Panel B Panel C Panel A Panel B Panel C Mean Median Standard Deviation Kurtosis Skewness Minimum Maximum 1,862 1, , , Number of Observations 4,350 1,304 3,046 4,350 1,304 3,046 Evidence on the relative trading volume of the call and its corresponding put is given in Table VIII. Before interpreting the data in table VIII, it must be remembered that in the period covered by our sample, and on the average, calls were always traded more than puts. As shown in Panel A, the trading volume of the call was 214% more important than the trading volume of the put in terms of the number of traded contracts, and 284% more important than the turnover of the put. However, when the spread was positive calls trading volume was respectively 227% and 389% the corresponding trading volume of the put. When the spread was negative, calls were traded more than the corresponding puts by only 208% and 239%. Such evidence about the market activity lead to the conclusion that positive spreads usually appear when the market is optimistic

21 and thus, is a buyer of the index through the options market. Negative spreads appear when the market is a seller of the stock index Factors that explain the Spread level We now focus on the relevant variables explaining the level of CPP deviations. For individual stocks, the natural candidate is the rebate rate as discussed by Ofek et al. (2003). However, in the case of a stock index, such a variable does not exist and other explanations must be given. Natural candidates for explaining CPP deviations are: - Stock Index Return: If the market is optimistic, it is legitimate to expect the return on to be positive. And the reverse if the market is pessimistic. Therefore, the stock index return may be expected to have a positive impact on the spread; - Time To Maturity: Options offer the possibility to trade the underlying but by their own nature, this possibility is limited in time. Therefore, the longer the time to maturity, the higher the expected spread should be; - Risk Free Rate: the options offer, in addition to a convenient way to trade the underlying, a leverage that allows buying the stock index by paying a small amount of cash. Therefore, the higher the risk free rate is, the more valuable the service and the larger the spread; - Implied Standard Deviation: it is the standard measure of expensiveness or cheapness on a given day. It is hard to predict the impact of this variable of the options prices. On the one hand, a high standard deviation implies high options prices and therefore, investors may be reluctant to pay some additional premia. This implies a negative impact on the spread. On the other hand, high uncertainty leads the market to charge high implied volatility. This requires a high spread to make people accept to trade the derivatives.

22 22 We do not expect liquidity variables to have any impact on the spread for the simple reason that we restricted ourselves to very liquid options. Nevertheless, we tested such a conjecture. We thus performed the following regressions for each of our three panels: Spread ti = λ 0 +λ +λ 1 4 Index Re turn t + λ Time To Maturity Im plieds tan dard Deviation 2 ti + λ 3 Risk Free Rate t and Spread ti =β 0 +β +β +β Index Re turn t + β Time To Maturity Im plieds tan dard Deviation + β Ln(TRading VolumeIn Dollars) 2 5 ti + β 3 Risk Free Rate Ln(Trading Volume In Units) t In the first regression, Regression 1, no liquidity variable has been introduced. In the second regression, Regression 2, we introduced variables related to trading activity in the options market. For the Implied Standard Deviation of each option pair, we took the average of the call and the put implied standard deviation. As to the trading volume variables, we also took the average of the call and the put trading volume both for the units and the turnover. The main motivation for this choice is the high correlations between call and put data. The implied standard deviation of the call and the put have a positive correlation of 0.6, trading volume in units of 0.8 and turnover of Therefore, to avoid multicolinearities when using data for each option, we took for each pair the mid point between put and call data. Since the spread is in percentage and the trading volume in different units of measure, we took the logarithm of the trading volume for the coefficients of the regression to be meaningful. The results from these regressions is given in Table IX.

23 23 Table IX We report the results of two regressions where the dependent variable is the spread (, i.e., the implicit stock index obtained from option prices using the call put parity and the closing index. In Regression 1, the explanatory variables are the stock index return, the time to maturity, the risk free rate and the implied standard deviation (which is the average of the implied volatility of the call and of the implied volatility of the corresponding put). In Regression 2, in addition to the explanatory variables in Regression 1, we added the traded volume in number of contracts and in dollars (turnover). The sample period ranges from 1/1/96 to 31/12/01. The figures are for options with moneyness (exercise price over underlying value) between 98% and 102%. Panel A contains all the option pairs in our sample, Panel B contains option pairs for which the implied index is higher than the closing index (positive spread) and Panel C contains options pairs for which the implied index is less than the closing index (negative spread). Constant Stock Index Return Time To Maturity Risk Free Rate Implied Standard Deviation Regression 1 Regression 2 Panel A Panel B Panel C Panel A Panel B Panel C (9.56) (-2.62) (13.52) (0.83) (0.63) (-1.35) (-1.87) (-12.46) (-13.09) (-6.23) (-0.9) (4.11) 1.84 (7.4) 0.73 (4.58) (-0.42) (-15.74) -5.7 (-19) (-11.8) (-2.18) (-6.16) (-8.69) (-6.28) Turnover (2.17) Trading Volume (Contracts) (-1.63) (-0.95) (5.57) 1.13 (3.6) 1.12 (5.57) (-3.1) 0.08 (3.66) (-1.15) (-12.47) (-8.75) (-13.9) 0.24 (7.33) (-7.2) Adj. R Before interpreting the findings, some caveats are in order. An important property of the options prices is that they have non linear relations with several of the variables used in the regressions. As a consequence, all OLS may not be an adequate estimation

24 24 procedure. We performed some GMM estimations of the preceding equations in lieu of the OLS and the parameters estimate was very close to those obtained in the case of the OLS. A general word of caution is that, while sometimes the liquidity variables (turnover and trading volume) are statistically significant, they only add marginally to the explanatory power of our results. Therefore, our restriction of the moneyness to 2% mitigated the potential impact of market liquidity that may be crucial due to the lack of market makers. We first focus on the findings of Regression 1. In this regression, we employed standard variables deemed to impact options prices and tested their effect on the spread. In Panels B and C, it turns out that these variables have the same impact on the spread whether it is negative or positive. The stock index return impact is not statistically significant. This is a desirable property of the market since it is likely that the rebate rate for individual stocks is only marginally, if at all, affected by the stock return. Concerning the Time to Maturity, the risk free rate and the Implied Standard Deviation, they have the expected impact. The higher the time to maturity is, the higher the cost both for the buyer and the seller. It must be remembered that a negative impact on a negative variable (negative spread in Panel C) is equivalent to a positive impact. The same is true when the risk free rate is changing. Negative spread is however much more sensitive to the above variables than positive spreads reflecting the additional impact of short sale constraints. Regression 2 provides additional insights as to the parameters affecting the spread. The additional explanatory power of liquidity variables is marginal. This means that our findings are not likely to result from some liquidity premium in the market. The moneyness range used here is certainly at the origin of this result. The impact of the other variables is not changed compared to Regression 1.

25 25 5. Concluding Remarks Market frictions have long been a concern to practitioners and academicians as to their impact on primitive and derivatives assets pricing. No less worrisome was the perception by the market of such imperfections. While theoretical analysis of such questions is well advanced, only few opportunities to assess these costs empirically are available. In the TASE market where there are no market makers, and where European options are written on a dividend protected index, we have an interesting opportunity to quantify the importance of such market frictions. Our findings show that these frictions are quantitatively economically significant, thereby justifying the researchers concern.

26 26 References Ackert, L. and Y. Tian, 2001, Efficiency in index options markets and trading in stock baskets, Journal of Banking and Finance 25, Danielsen, B. and S. Sorescu, 2001, Why do option introductions depress stock prices? A study of diminishing short sales constraints, Journal of Financial and Quantitative Analysis 36(4), D`Avolio, G., 2002, The Market for Borrowing Stock, Journal of Financial Economics 66(2-3), Figlewski, S. and G. Webb, 1993, Options, short sales and market completeness, Journal of Finance 48(2), Figlewski, S. and T. Green, 1999, Market risk and model risk for a financial institution writing options, Journal of Finance 54(4), Geczy, C., D. Musto and A. Reed, 2002, Stocks are special too: an analysis of the equity lending market, Journal of Financial Economics 66(2-3), Evans, R., Geczy, C., D. Musto and A. Reed, 2003, Failure is an option: Impediments to short selling and options prices, Working Paper. Kamara. A. and T. Miller, 1995, Daily and Intra daily tests of European Put-Call Parity, Journal of Financial and Quantitative Analysis 30(4), Lamont, O. and R. Thaler, 2003, Can the Market Add and Subtract? Mispricing in Tech Stock Carve-outs, Journal of Political Economy 111(2), Mayhew, S., 2002, Competition, Market Structure, and Bid Ask Spreads in Stock Option Markets, Journal of Finance 57(2), Ofek, E., M. Richardson and R. Whitelaw, 2003, Limited arbitrage and short sales restrictions: evidence from options markets, Journal of Financial Economics, forthcoming. Sorescu, S., 2000, The effects of options on stock prices: 1973 to 1995, Journal of Finance 55(1),

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