CHAPTER IV BID ASK SPREAD FOR FUTURES MARKETS 4.1 INTRODUCTION Futures and Options (commonly denoted as F&O) was introduced in the National Stock Exchange during 2000s. Since its introduction, there has been a dramatic increase in the growth rate of Futures and Options. The turnover has increased nearly 15 times till date since inception. The launch of derivative products has significantly altered the movement of the share prices in the spot market. Futures contracts provide opportunities to hedge their risk involved with holding diversified portfolios. The spot and futures markets are linked by arbitrage (Thenmozhi). One of the most important feature of derivatives contracts is the price discovery function, where it is possible to predetermine prices thus showing the direction of price movements. Futures are contracts whose value is based on the underlying and a contract between two parties to buy or sell an asset at a future date at a predetermined price. Here, if the exercise price is favorable to the buyer of the contract, he gets a profit otherwise he gets a loss. The payoff for a futures contract holder is unlimited. He either gets a huge profit or a huge loss. Options are contracts to buy or sell the asset at a future date at a predetermined price. Either of the party, called the buyer of the option gets the right but not the obligation to exercise the contract. In case the option holder, as the term is commonly known, finds that he is likely to get a loss, he lets the contract go, unexpired. So his loss is limited to the premium he pays to buy the contract. The options holders profit is unlimited whereas his loss is limited. Futures and Options trading have three maturity cycles. They are the near month or the first month, the second month or the next month and the third month or the far month cycle. The contracts expire during the last Thursday of the particular month. On any trading day, the Futures and Options contracts usually has three contracts each per asset. As the contract matures, a new contract is formed. Thus the cycle goes on.
4.2 ANALYTICAL FRAMEWORK During March 2010, the National Stock Exchange of India had permitted trading of securities in Futures and Options for 197 securities. But very few securities which are most liquid alone are traded. As far as the futures trading are considered, in order to be eligible for inclusion in the sample, those securities which had a trading for more than 15 trading days alone were considered. This brings down the number of securities to 190. Prior research done on the related topics has considered the contracts maturing on the first month alone, as they are considered as the most liquid. (Thenmozhi, 2004).For the contracts expiring on the second month, there very few securities which had regular trading. So those securities which were traded for at least 12 trading days alone were considered. This restricted the sample securities to 100. There were extremely few securities trading which expired on the third month. It was not worth considering these securities for the study. So the securities expiring in the third month were excluded for the study. In some cases, this list excludes the securities forming the Nifty too. For the options segment, though the same number of securities was permitted for trading in the options segments, only a few of them were actively traded. So the same conditions were applied to the options segment too. For the first month contracts, the number of securities that were traded for more than 15 trading days alone were considered and for the second month, securities traded for at least 12 trading days alone were considered. Options segment had very few trading and these trading were irregular. So the number of securities was restricted to 50. The most liquid 50 companies forming the Nifty index alone were taken for the study. For the options expiring on the second month, the number of securities was restricted to 45. Jegadeesh and Subramanian (1993) 1 use bid ask spread to measure volatility.hongchio et al (1994) 2 use bid ask spread as a measure of liquidity and volatility, to measure the impact of trading on spot market 1. Jegadeesh and A. Subramanian,. Liquidity Effects of the Introduction of the S&P 500 Index Futures Contracts on the Underlying Stocks, Journal of Business, No. 66, 1993, pp 171 187. 2. Chio Hong and Avanidhar Subramanyam, Using intra-day data to test for effects of index futures on the underlying stock markets, Journal of Futures Markets, No. 14, 1994, pp 293-322.
Spread is calculated for these futures and options instruments. Roll s spread estimator is used for calculation of spread. The formula is given as: S = 2 - COV (ΔP t, ΔP t-1 ) Where P t is the transaction price at time t1, P t-1 is the transaction price at time t-1 (previous time), Δ is the change in price. COV (ΔP t, ΔP t-1 ) is the covariance between two successive price changes. The differences between the successive changes in strike price are used for calculating spread. One way analysis is variance is also used here to estimate the relationship between two variables. The formula is given as: Mean Square between samples= ( ) where (k-1) represents degrees of freedom (d.f.) between samples and Mean Square within= ( ) where (n-k) represents degrees of freedom within samples F-ratio= If the F ratio computed is less than 0.05, the results are significant. This leads to the rejection of null hypothesis, otherwise the results indicate non significance and the null hypothesis is accepted. This section analyses the overall performance of the futures segments. The analysis is carried out on a component by component basis. All the components of the futures segments are analyzed in detail. 4.3 BID ASK SPREAD FOR FUTURES SEGMENT
4.3.1 Near Month Next Month Futures Near month contracts are those that mature on the last Thursday of the nearest trading month and the next month futures are those which mature on the next trading month. The futures contract on shares the strike price depends on the market price of the security. As in the case of share trading, when strike price is fixed, it is a reflection of the performance of the security in the futures market. So the bid ask spread, a concept used to measure the performance of the security and a measure of microstructure in the spot market and futures market is used here. This section compares the spread for the near month and the next month contracts. 190 companies shares were traded in the futures market during the first month. Table 4.1 gives the number of companies taken for analysis, the mean spread and the standard deviation. TABLE 4.1 Descriptive Statistics for Near month Next month contracts Particulars N Mean Std. Deviation Std. Error Near month contracts 190 1.746 1.136585.082457 Next month contracts 100 2.505 1.119606.111961 Total 290 2.1564 1.162263.068250 Table 4.1 shows that the number of companies taken for analysis is 190 and has a mean spread of 1.746 for the first month contract. The standard deviation is slightly lower than the standard deviation for the second month contracts. The spread for the second month contracts are 2.505 and the number of companies considered for analysis is 100. Thenmozhi (2004) 3 put it right, the second month futures are less liquid than the first month s contracts. The mean spread for both month contracts are 2.156. A comparison is made between the performance of the two 3. M. Thenmozhi, Futures Trading, Information and Spot Price Volatility of NSE -50 Index Futures Contract, Research Paper, National Stock Exchange of India, 2002. As
segments using One-way analysis of variance and the results of the same are presented in Table 4.2. In this regard, the null hypothesis is formulated as such: H 0 : There is no significant difference between the mean spread for the futures contracts maturing in the first and second month. TABLE 4.2 Results of ANOVA test for Near month Next month contracts Particulars Sum of Mean df Squares Square F Sig. Result Between Groups 22.144 1 22.144 17.318.000 Sig Within Groups 368.253 288 1.279 Total 390.397 289 Sig. - Significant From Table4.2, it is found that since the F value of 17.318 and p value of 0.00 are statistically significant at 5% level, the null hypothesis is rejectedthere is a difference between spread for the first month and the next month contracts. 4.3.2 Relationship between spread for first month contracts and number of share The number of shares denotes the total number of shares that are traded on a trading day. Usually, one trade represents 200 contracts of shares. In rare cases, the NSE permits odd trading. During the 20 days trading the daily average was 6,34,812entries. Out of this, the average value is found for all the shares traded on a trading day. From the daily averages, the monthly average is found. The range of the number of shares is from 14166.67(for Asian Paints Limited) to 113974796 shares (for Sterlite Industries). The number of shares traded is placed in ascending order and divided into five portfolios, each portfolio consisting of 38 companies. The first portfolio consists of companies with lowest number of shares traded and the fifth portfolio consists of companies with the highest number of shares trades. The market microstructure of the futures contract of these companies are computed using bid ask spread. A comparison is made between the number of shares trades and the spread. The results are given in Table 4.3. TABLE 4.3 Descriptive Statistics for Number of Shares and Spread
Portfolios N Mean Std. Std. Deviation Error Portfolio 1 38 2.222 1.14016.18496 Portfolio 2 38 1.991 1.06173.17224 Portfolio 3 38 1.611 1.07437.17429 Portfolio 4 38 1.528 1.15931.18806 Portfolio 5 38 1.377 1.13261.18373 Total 190 1.746 1.13659.08246 From Table4.3, it is found that the mean spread for percentile 1 is 2.222, for the percentile 2 it is 1.991,for the percentile 3, it is 1.611, for the percentile 4 it is 1.528 and for the percentile 5, the spread is 1.377.It is concluded that as the number of shares traded increases, the spread decreases.there is an inverse relationship between the number of trades and the spread. Spread is lowest in thefifth percentile. To verify this result, One-wayanalysis of variance is used and the conclusions are given in Table 4.4. In this context, the null hypothesis formulated is: H 0 : There is no significant differences in the mean spread among five portfolios and an inverse relationship between number of shares and spread for futures maturing on the first month. TABLE 4.4 Results of ANOVA test for Number of Shares and Spread for contracts maturing in the first month Particulars Sum of Mean Df Squares Square F Sig. Result Between Groups 14.447 4 3.612 2.909.023 Sig Within Groups 229.708 185 1.242 Total 244.155 189 Sig. - Significant From Table4.4, it is found that since the F value of 2.909 and p value of 0.023 are statistically significant at 5% level, the null hypothesis is rejected. There is difference between the spread at different percentiles. These five portfolioshave different spread values during the trading month. Spread has an inverse relationship with the number of shares traded.
4.3.3 Relationship between spread for first month and number of trades Shares are traded in lots and this lot is called number of trades. The lots for the Futures and Options segments are in the multiples of 200. A minimum of 200 contracts make one trade. An increase in the number of trades is an indication of a bullish market. The buyers are on an increase and large volumes are bought.the number of trades is placed in ascending order and is divided into five portfolios. The first portfolio consists of shares with the lowest number of trades and the fifth portfolio consists of the highest number of trades. Spread,the concept used to study the microstructure and a measure of performance of strike prices of the security is found and is compared between these five portfolio and the results are given in Table 4.5 TABLE 4.5 Descriptive Statistics for number of trades and Spread for contracts maturing in the first month Portfolios N Mean Std. Std. Deviation Error Portfolio1 38 2.169 1.16222.18854 Portfolio2 38 1.784 1.18330.19196 Portfolio 3 38 1.692 1.18283.19188 Portfolio 4 38 1.48 1.31278.21296 Portfolio 5 38 1.605.78244.12693 Total 190 1.746 1.13659.08246 It is found from Table 4.5 that spread is highest for thefirst portfolio at 2.169 and lowest for the fourth portfolio at 1.48. However, the spread for the fifth portfolio where the number of trades are highest is 1.605, which is the second lowest value. For the third portfolio the spread is moderate at 1.692. Therefore it is concluded that the spread and number of trade are related to a certain extent. This is verified using One-wayanalysis of variance, in Table4.6. TABLE 4.6 Results of ANOVA test for Number of Trades and Spread for contracts maturing in the first month
Particulars Sum of Squares Df Mean Square Between Groups Within Groups 239.969 185 1.297 Total 244.155 189 F Sig. Result 4.186 4 1.047 3.807.052 Sig The results from Table4.6 indicate that since the F value of3.807 and p value of 0.052 are statistically significant at 5% level, the null hypothesis here is rejected. There is a difference in the spread value of these five different portfolios. Spread varies based on the number of trades, showing an inverse relationship. 4.3.4 Relationship between spread for first month and open interest Open interest is the total number of futures contracts that are not closed on a particular day. Open interest are better measure than the number of trades and number of shares traded. The open interest ranges from 15850 (for Asian Paints Limited) to 72123396 (for IFCI Limited). The data is placed in the ascending order based on the open interest. This is divided into five portfolios, each consisting of 38 companies. Portfolio 1 consists of shares with the lowest open interest and portfolio 5 consists of shares with the highest open interest. The performance of the company s strike price is measured by spread. Spread is then compared with these portfolio and the following conclusions are drawn. The results are given in Table 4.7. TABLE 4.7 Descriptive Statistics for Open Interest and Spread for contracts maturing in the first month Std. Std. Portfolios N Mean Deviation Error Portfolio 1 38 2.099 1.19942.19457
Portfolio 2 38 1.817 1.09870.17823 Portfolio 3 38 1.765.93514.15170 Portfolio 4 38 1.714 1.18280.19188 Portfolio 5 38 1.335.90726.14718 Total 190 1.746 1.13659.08246 From Table4.7, it is found that the spread is highest for the first portfolio, at 2.099 and lowest for the last portfolio at 1.335. As the open interest increases, value of spread decreases. So it is concluded that spread and open interest are inversely related to each other. One-wayanalysis of variance is used here to support this result. In this context the null hypothesis is given as: H 0 : there is no significant difference between the spread in different portfolios and has a direct relationship with spread. The results of the ANOVA test are shown in Table 4.8. TABLE 4.8 Results of ANOVA test for Open Interest and Spread for contracts maturing in the first month Particulars Sum of Squares Df Mean Square F Sig. Result Between Groups 31.687 4 7.922 6.898.000 Within Groups 212.468 185 1.148 Total 244.155 189 Sig. - Significant Sig From Table 4.8, it is found that since the F value of 6.898 and p value of 0 are statistically significant at 5% level, the null hypothesis is rejected. There exists a difference between the spread in each portfolio. The spread values are not the same. Spread and open interest are inversely related. 4.3.5 Relationship between spread for first month and strike price Strike price denotes the price which is fixed in advance and on which the trade must be executed. It is the price which are negotiated by the traders and fixed in advance, to be exercised later. Also known as exercise price, this is the most important aspect in futures
trading. Profit or loss on futures trading depends on the strike price.if the strike price is greater than the spot price, a long position on the futures contracts would result in profit and vice versa. Strike price ranges from Rs.19.483 (for ISPAT industries) to Rs. 4809.61 (for Bosch Limited). Bid ask spread is used to ensure the performance of the strike price. A comparison is made between the strike price and the spread and the results are presented in Table 4.9. TABLE 4.9 Descriptive Statistics for Strike Price andspread for contracts maturing in the first month Portfolios N Mean Std. Std. Deviation Error Portfolio 1 38 1.817.97424.15804 Portfolio 2 38 1.765.90931.14751 Portfolio 3 38 2.099.99854.16198 Portfolio 4 38 1.714 1.17023.18984 Portfolio 5 38 1.335 1.19464.19380 Total 190 1.746 1.13659.08246 Table4.9 shows that the spread for the fifth portfolio is lowest at 1.335. The highest spread is for the third portfolio at 2.099. It is also found that as the market price increases, there is a decrease in the spread. So spread and strike price are inversely related. To find if there is difference between the spread in different portfolios, One-wayanalysis of variance is used and the results are given in Table 4.10 obtained. The null hypothesis is formulated as thus: H 0: There is no significant relationship between the mean spread among the five portfolios and direct relationship between strike price and spread. TABLE 4.10 Results of the ANOVA test forstrike Price and Spread for contracts maturing in the first month Particulars Sum of Squares Df Mean Square F Sig. Result Between Sig 38.076 4 9.519 8.545.000 Groups Within Groups 206.079 185 1.114 Total 244.155 189
Sig Significant It is inferred from Table 4.10 that since the F value of 8.545 and the p value of 0.00are statistically significant at 5% level, the null hypothesis is rejected. It is concluded that there exists a significant difference between the spread in each of the five portfolios. 4.3.6 Relationship between spread for first month and total traded value Total traded value denotes the total of the strike price multiplied by the number of shares traded. It is a rupee value of the number of shares traded. The total traded value ranges from Rs 10769079.58 (for BOSCH Limited) to Rs 10182497891 (for TATA motors). Based on the total traded value, the data is placed in ascending order and divided into five portfolios, each portfolio consisting of 38 companies. Spread is used a measure of the performance of the contract in the stock exchange. The spread for these categories are found and the conclusions drawn are presented in Table 4.11. TABLE 4.11 Descriptive Statistics for Open Interest and Spread for contracts maturing in the first month Portfolios N Mean Std. Deviation Std. Error portfolio 1 38 2.015 1.20585.19562 portfolio 2 38 1.947 1.27011.20604 portfolio 3 38 1.803.96749.15695 portfolio 4 38 1.794 1.15542.18743 portfolio 5 38 1.171 1.04187.16901 Total 190 1.746 1.13659.08246 As the total traded values increases, the spreadshows a decreasing trend.spread is highest for the first percentile at 2.015 where the total traded value is lowest and spread islowest for the fifth percentile at 1.171, where the total traded values are highest. So there is an inverse relationship between spread and total traded value. As the total traded values increases, spread decreases and vice versa. This result is verified using One-wayanalysis test and presented in Table 4.12. The null hypothesis is formulated as: H 0: There is no significant relationship among the mean spread in five portfolios and direct relationship between total traded value and spread. TABLE 4.12
Results of ANOVA testfor Total Traded Value and Spread for contracts maturing in the first month Particulars Sum of Mean Df Squares Square F Sig. Result Between Groups 6.474 4 1.619 3.260.0287 Sig Within Groups 237.681 185 1.285 Total 244.155 189 Sig. - Significant The analysis of variance test given in Table 4.12 indicates that since F value of 3.260 and p value of0.0287 are statistically significant at 5% level, the null hypothesis is rejected. There is a significant difference between the spread in different portfolios as the total traded values increase, spread decreases. 4.2.7 Relationship between spread for second month and number of shares Thenumber of futures contracts on shares maturing on the second month is 100. The second month contracts are less liquid compared to the first month contracts. So only those companies which had a trading of at least 12 days are considered. 100 companies come in this list. Thenumber of shares for these companies is placed in the ascending order and is divided into four segments called quartiles. The first quartile consists of 25 shares with the lowest number of shares and the fourth quartile consists of 25 companies with the highest number of shares. The spread, which measures the performance of the instrument, is found. A comparison is done for the spread and the number of shares, and the results are given in Table 4.13. TABLE 4.13 Descriptive Statistics for Number of Shares traded for second month and Spread Quartiles N Mean Std. Std. Deviation Error Quartile 1 25 2.864.82381.16476 Quartile 2 25 2.583 1.03052.20610 Quartile 3 25 2.221 1.41696.28339 Quartile 4 25 2.355 1.01775.20355 Total 100 2.505 1.11961.11196 From Table4.13, it is concluded that as the number of shares increases, there is a
reduction in spread.spread is highest for the first quartile at 2.864 and lowest for the fourth quartile at 2.355, with a mean standard deviation of 1.11 and.111 as the standard error. Thoughthe mean spread is quite high compared to the first month contracts, the standard deviation for all five segments are very low, indicating that there are not much fluctuations in spread. There is uniformity in spread. To verify the results further, One-wayanalysis of variance is applied to the data and the results obtained are given in Table 4.14. In this context, the null hypothesis is formulated as: H 0 : There is no significant difference in spread among the four quartiles and a direct relationship between spread and number of shares traded during the second month. TABLE 4.14 Results of ANOVA testfor number of shares traded and Spread for contracts maturing in the second month Particulars Sum of Mean Df Squares Square F Sig. Result Between Groups 9.276 3 3.092 2.585.05 Sig Within Groups 114.822 96 1.196 Total 124.098 99 Sig - Significant Table4.14 indicates that since the F value of 2.585 and p value of 0.05 are statistically significant at 5% level, the null hypothesis is rejected. There is a difference between spread among the different quartiles. It is also seen that as the number of shares traded increases, there is a decrease in spread, showing an inverse relationship. 4.2.8 Relationship between spread for second month and number of trades Number of trades denotes the number of lots that are traded. Each lot consists of 200 contracts. Number of trades is also a sign of increasing volumes. Number of trades is placed in ascending order and isdivided into four segments called quartiles. Each quartile consists of 25 companies shares. The first quartile consists of shares whosenumber of trades is lowest and the last quartile consists of shares whosenumber of trades is highest. Spread, a measure of the performance of the instrument in the stock exchange is found. A comparison of spread is done for the four quarters of the number of trades and the results obtained are shown in Table 4.15. TABLE 4.15
Descriptive Statistics for number of trades for second month and Spread Quartiles N Mean Std. Std. Deviation Error Quartile 1 25 2.715 1.06602.21320 Quartile 2 25 2.644 1.06753.21351 Quartile 3 25 2.318 1.04145.20829 Quartile 4 25 2.346 1.27813.25563 Total 100 2.505 1.11961.11196 From Table4.15, it is found that spread is lowest at 2.318 for the third quartile and spread is highest at 2.715 for the first quartile, with a total standard deviation of 1.12 and a standard error of.111.it is seen that as the Number of trades increase, there is a decrease in spread, except in the fourth quartile. For three of the four quartiles, spread shows an inverse relationship with number of trades. So it is concluded that spread is inversely related to number of trades, even for the contracts maturing in the second month. To support this finding, a One-wayanalysis is used and the results are obtained and presented in Table 4.16. The null hypothesis is given as: H 0 : There is no significant difference in spread among the four quartiles and a direct relationship between the spread and number of trades for futures contracts maturing in the second month. TABLE 4.16 Results of ANOVA test for number of trades and Spread for contracts maturing in the second month Particulars Sum of Squares Df Mean Square F Sig. Result Between Groups 4.236 3 1.412 1.131.034 Sig Within Groups 119.862 96 1.249 Total 124.098 99 Sig. - Significant From Table 4.16, it is found that since the F value of 1.131 and p value of 0.034 are statistically significant at 5% level, the null hypothesis is rejected. There are differences among spread belonging to the different quartiles. The spread are dependent on the number of trades and has an inverse relationship. 4.2.9 Relationship between spread for second month and strike price
Strike price is the price at which the futures contracts are traded upon expiry or upon exercising. Strike price is the tool used for price discovery. Strike price tells about the future movements of the assets. The strike prices are placed in ascending order and are divided into four parts called quartiles. Each quartile consists of 25 shares. The first quartile consists of 25 securities with the lowest strike price and the fourth quartile consists of securities with the highest strike price. Spread is used here to find the performance of the instrument. An attempt is made to study the relationship between the strike price and the spread. The results are given in Table4.17. TABLE 4.17 Descriptive Statistics for Strike Price and Spread for contracts maturing in the second month Quartiles N Mean Std. Deviation Std. Error Quartile 1 25 2.594.90451.18090 Quartile 2 25 2.035.94995.18999 Quartile 3 25 2.918 1.34480.26896 Quartile 4 25 2.476.83800.16760 Total 100 2.505 1.11961.11196 From Table 4.17, it is found that the spread is lowest for the shares belonging to quartile 2 and spread is highest for the contracts belonging to quartile 3. The average spread is 2.505 and the quartile 3 has the highest standard deviation. It is difficult to formulate a relationship between the strike price and the spread. To verify the relationship, Onewayanalysis is used and the results drawn are presented in Table 4.18.In this regard, the null hypothesis is formulated as H 0 : There is no significant difference among spread in the four quartiles and no relationship between the open interest for the futures contracts maturing in the second month and spread. TABLE 4.18 Results of ANOVAtest for Open Interest and Spread for contracts maturing in the second month Particulars Sum of Mean Df Squares Square F Sig. Result Between Groups 5.546 3 1.849 1.497.220 N.S Within Groups 118.552 96 1.235 Total 124.098 99
N.S Not Significant From Table 4.18, it is concluded that since the F value of 1.497 and the p value of 0.220, which are statistically insignificant at 5% level, the null hypothesis is accepted. It is concluded that the spread is independent of the strike prices. Spread is not dependent on the strike price. It is difficult to draw conclusions based on the above data. 4.2.10 Relationship between spread for second month and total traded value The total traded value is the rupee value of total number of shares that are traded. It is measured in rupees. The second month futures are divided into four parts called quartiles and each quartile consists of 25 shares. The first quartile consists of shares with the lowest traded value and the fourth quartile consists of shares with the highest traded value. Bid ask spread is used here as a measure of the performance of the company. The quartiles, their spread and the standard deviation are given in Table 4.19. TABLE 4.19 Descriptive Statistics for Total Traded Value and Spread for contracts maturing in the second month Quartiles N Mean Std. Std. Deviation Error Quartile 1 25 2.798 1.02315.20463 Quartile 2 25 2.511 1.13548.22710 Quartile 3 25 2.071.89541.17908 Quartile 4 25 2.643 1.38323.27665 Total 100 2.505 1.11961.11196 Table 4.19 shows that Quartile 3 has the lowest spread at 2.071 and quartile 1 consists of shares with highest spread at 2.798. The standard deviation is lowest for the quartile 3.It indicates that the fluctuations in the spread are minimum. There is no relationship between the total traded value and the spread. This result is supported by using One-wayanalysis and the results obtained are given in Table 4.20.The null hypothesis is formulated as: H 0 : there is no significant difference in the mean spread among the four quartiles and no relationship between spread and the total traded value for the futures contract maturing in the second month.
TABLE 4.20 Results of ANOVA test fortotal traded value and Spread for contracts maturing in the second month Particulars Between Groups Sum of Squares Df Mean Square F Sig. Result 2.868 3.956.757.521 Within Groups 121.230 96 1.263 Total 124.098 99 N.S Not Significant From Table4.20, it is concluded that since the F value of 0.757 and the p value of 0.521 are statistically insignificant at 5% level, the null hypothesis is accepted. There is no difference in spread for the companies belonging to different percentiles. The companies spread isirrespective of the total traded values. The spread and total traded values do not follow any pattern. 4.2.11 Relationship between spread for second month and open interest day. Open interest is defined as the number of positions that are not closed on a particular Open interest are a better measure than volume. Based on the open interest, spread is divided into four parts called quartiles. The open interest are placed in ascending order and divided into quartiles. The first quartile consists of 25 shares with the lowest open interest and the last quartile consists of shares whose open interest is the highest. The performance of the futures contracts measured by spread in each quarter is compared among themselves. The results are presented in Table 4.21. TABLE 4.21 Descriptive Statistics for Open Interest and Spread for contracts maturing in the second month Quartiles N Mean Std. Std. Deviation Error Quartile 1 25 2.918.78103.15621 Quartile 2 25 2.346 1.09481.21896 Quartile 3 25 2.644 1.54066.30813 Quartile 4 25 2.318.87030.17406 Total 100 2.505 1.11961.11196 N.S
It is found from Table4.21 that the spread for the first quartile is 2.918, while for the second quartile, the mean spread is 2.346. For the third quartile the spread is 2.644 and for the fourth quartile, and the spread is 2.318. It is seen that as the open interest increases, the spread decreases. The standard deviation is highest at 1.54 for the third quartile and lowest for the first quartile. Third quartile has the highest variations in spread. The results are verified in Table4.22, using One-way analysis of variance test. The null hypothesis in this regard is given as H 0 : There is no significant difference in the mean spread among the four quartiles and no relationship between the open interest for futures contracts maturing in the second month and spread. TABLE 4.22 Results of ANOVAtest for Open Interest and Spread for contracts maturing in the second month Partiuclars Sum of Mean Df Squares Square F Sig. Result Between Groups 22.548 3 7.516 7.105.000 sig Within Groups 101.550 96 1.058 Total 124.098 99 Sig - Significant From Table4.22, it is concluded that since the F value of 7.105 and p value of 0.00 are statistically significant at 5% level, the null hypothesis is rejected. It is concluded that there are difference among the spread in different quartiles. The spread varies and shows an inverse relationship with open interest. 4.4 BID ASK SPREAD FOR THEOPTIONS SEGMENT The National Stock Exchange of India has permitted 197 shares to trade on the options segment on March 2010. But options contracts are highly illiquid. Very few shares are traded in the options segment. The strike price for the options contracts are fixed in steps of 10. So options are not like the futures market where the futures prices are random. Options trading took place in very few securities. To create uniformity of data, the companies whose
shares were traded in the options segment for at least 12 trading days alone are considered. So the number of securities is limited to 50, which are the Nifty forming securities. The market microstructure of the options contract are found by computing the bid ask spread. Spread is found for options on these secutiries. The options that give the holder the right to buy the contracts are called Call Options and the options that gives the holder the right to sell the contract are called Put Options. Options which can be exercised any time till maturity are termed as American Options and those contracts which can be exercised only during expiry are termed as European options. The combinations of these contracts are denoted as CA and PA. Usually options on index are European and options on stock are American options. As in the case of futures contracts, most actively traded contracts are those on the near month. The next month and far month contracts are very rarely traded. So, the Nifty forming 50 companies contracts alone are taken here. The spread for options contract are found and a step by step analysis is carried out to find the relationship between spread and the other variables. 4.4.1 Spread for call options for the first month and capitalization The spread for 50 companies forming the Nifty are found. Based on the capitalization, the companies are divided into five portfolios, each portfolio consisting of 10 companies. These portfolios are placed in ascending order. The first portfolio consists of 10 companies with the lowest capitalization and fifth portfolio consists of 10 high capitalization companies. Bid ask spread is calculated for these options contracts. The performance of these categories of companies is analyzed and the results including spread are foundand presented in Table 4.23. TABLE 4.23 Descriptive Statistics for first month call option maturing in the first month and capitalization Divisions N Mean Std. Std. Deviation Error Division1 10 2.4000.88819.28087 Division2 10 2.7940.79800.25235 Division3 10 2.4770.88679.28043 Division4 10 2.4300.76456.24178 Division5 10 2.1100.54457.17221
Total 50 2.4422.78521.11105 Table4.23shows the mean spread for the five portfolios is 2.44. It is found that the lowest spread at 2.11 is for the last division, whose market capitalization is the highest. The second portfolio of companies has the highest spread of 2.79. The standard deviation is lowest and below 1 for all the categories. The fluctuations in spread are minimum. Spread has an inverse relationship for the last four portfolios. One-way variance test is used to find the level of significance and the results are presented in Table 4.24. The null hypothesis is formulated as H 0 : There is no significant difference in spread in five portfolios and does not show any relationship between the spread for options maturing in the first month and capitalization. TABLE 4.24 Results of ANOVA test for first call options maturing in the first month and capitalization Particulars Sum of Squares df Mean Square F Sig. Result Between Groups 2.373 4.593.959.439 N.S Within Groups 27.839 45.619 Total 30.211 49 N.S Not Significant From Table 4.24, it is inferred thatsince the F value of 0.959 and p value of 0.439 are statistically insignificant at 5% level, the null hypothesis is accepted. It is difficult to draw conclusions as the spread is lowest for the last portfolio. Through the results obtained from the analysisof variance, it is found that there is no significant relationship; it is difficult to draw conclusions here. 4.4.2 Relationship between call for first month and open interest Open interest is the total number of contracts that are not closed on a particular day. Open interest are a better measure then volume. Spread, a measure of performance of the instrument is found for different portfolios and is presented in Table 4.25. TABLE 4.25 Descriptive Statistics for spread for Call options maturing in the first
month and open interest Divisions N Mean Std. Deviation Std. Error Division1 10 2.4100.71562.22630 Division2 10 2.9540.81884.25894 Division3 10 2.3400.68020.21510 Division4 10 2.3270.76257.24115 Division5 10 2.1800.85739.27113 Total 50 2.4422.78521.11105 From Table 4.25, it is seen that spread shows a decreasing trend except for the first division. The second division has the highest spread. From the second portfolio onwards, spread shows a decreasing trend, which can be concluded that as the open interest increases, spread decrease. For the other cases, spread is inversely related to open interest. The results are verified using One-way analysis test and the results are given in Table 4.26.In this regard, the null hypothesis is formulated as: H 0 : There is no significant differences in the mean spread among the five portfolios and no relationship between spread for call options contracts maturing in the first month and spread. TABLE 4.26 Results of ANOVA test for call options maturing in the first month call and open interest Partiuclars Sum of Squares df Mean Square F Sig. Result Between Groups 3.554 4.889 5.500.021 Sig Within Groups 26.657 45.592 Total 30.211 49 Sig Significant The results given in Table 4.26 indicates that since the F value of 5.5 and p value of 0.021 are statistically significant at 5% level, the hypothesis is rejected. There are differences between spread among different divisions. Spread is influenced by open interest.
4.4.3 Spread for put option for the first month and capitalization The spread, a measure of the performance of the instrument in the stock exchange is computed for the put options of the Nifty companies. Put option gives the Holder the right but not the obligation to exercise the right to sell the option. Based on capitalization, the spread is divided into five portfolios, each consisting of 10 companies. Their mean and standard deviation are given in Table 4.27. TABLE 4.27 Descriptive Statistics for put options maturing in first month and capitalization Divisions N Mean Std. Deviation Std. Error Division1 10 4.8100 4.51059 1.42637 Division 2 10 4.7300 4.01858 1.27079 Division 3 10 3.2400.36271.11470 Division 4 10 2.040.93238.29484 Division 5 10 2.4900.98708.31214 Total 50 3.4620 2.89489.40940 From Table4.27, it is found that the mean spread is 3.462. It is found from Table 4.27 that the spread for companies in the first portfolio is 4.81 and spread reduces as the Capitalization increases. For the fifth portfolio, the spread is low at 2.49. The spread is lowest at 2.04 for the shares in the fourth portfolio. Except for the fourth and fifth portfolios, there is an inverse relationship between spread and capitalization. One-way analysis of variance is used to verify the results and presented in Table 4.28.In this regard, the null hypothesis is formulated as H 0 : There is no significant difference in mean spread among the five portfolios and no relationship between put options maturing in the first month and spread. TABLE 4.28 ANOVA TEST for first month put option and capitalization Particulars Sum of Squares df Mean Square F Sig. Result Between Groups 64.411 4 16.103 5.093.049 N.S
Within Groups 346.227 45 7.694 Total 410.638 49 N.S Not Significant It is shown from Table 4.28 that the F value of 5.093 and p value of 0.049are statistically significant at 5% level, the null hypothesis is rejected. There are differences in spread for the different portfolios. It is also concluded that as the capitalization increases, the spread for put options decreases, which means an inverse relationship exists between capitalization and spread. 4.4.4 Relationship between put for first month and open interest The relationship is found between the put options and the open interest. The open interest is divided into 5 segments, based on their value. Segment 1 consists of put options with the lowest open interest whereas segment 5 consists of put options with highest open interest. Spread is used as a measure of performance of the instrument. An analysis is done to find the relationship between put options maturing on the second month and the open interest. The conclusions drawn are presented in Table 4.29. TABLE 4.29 Descriptive Statistics for put options maturing in the first month and open interest Divisions N Mean Std. Deviation Std. Error Division1 10 5.9300 5.53395 1.74999 Division 2 10 3.1700 1.42910.45192 Division 3 10 2.7900 1.16376.36801 Division 4 10 3.0200 1.29855.41064 Division 5 10 2.4000 1.04137.32931 Total 50 3.4620 2.89489.40940 Table4.29 presents the spread for five different portfolios. It is seen that the spread is highest for the first portfolio, where the open interest is very low. Portfolio 5 consists of companies with the lowest spread, and highest open interest. It is seen that the spread for the companies belonging to the first portfolio is the highest at 5.93 and the spread for the companies belonging to the fifth portfolio are the lowest at 2.4. Spread shows a decreasing trend except for portfolio 2 and 3. It is concluded that as the open interest increases, spread decreases. This result is supported by analyzing the variance. The null hypothesis formulated is as such:
H 0 : There is no significant difference in mean spread among the five portfolios and no relationship between put options maturing in the first month and spread. TABLE 4.30 Results of ANOVAtest for spread for put options maturing in the first month and open interest. Particularts Sum of Squares df Mean Square F Sig. Result Between Groups 79.511 4 19.878 2.701.042 Sig Within Groups 331.127 45 7.358 Total 410.638 49 Sig. - Significant It is known from Table 4.30 that since the F value of 2.701 and the p value of 0.042 are statistically significant at 5% level, the null hypothesis is rejected. There are differences between spread among these different values of open interest. Spread for the first month put options depends on open interest, showing an inverse relationship. 4.4.5 Relationship between call for the second month and capitalization Second month or the next month contracts are those which expire in the second month. For example, a second month call option on 3 March contract would expire in April. A next month contract traded on 29 March 2010 would expire on May 27, 2010, the last Thursday, which are the expiry days for derivatives. Capitalization is divided into five segments after placing them in ascending order. Segment 1 consists of lowest capitalization companies and segment 5 consists of highest capitalization companies. Bid Ask spread is used here to measure the performance of the contract in the derivatives segment of the stock exchange. relationship between capitalization and spread and given in Table 4.31. It is analyzed to find the
TABLE 4.31 Descriptive Statistics for call options maturing in the second month and capitalization Divisions N Mean Std. Deviation Std. Error Division1 10 11.7850 5.98194 1.89165 Division2 10 11.3140 3.46785 1.09663 Division3 10 10.8300 2.48429.78560 Division4 10 11.1150 3.02088.95529 Division5 10 6.6100 3.37233 1.06642 Total 50 10.3308 4.16059.58840 From Table 4.31, it is found that since the trading for the second month contracts are very low, the mean spread is high. The mean spread is 10.33. The total standard deviation is high at 4.160. Spread is highest for the first segment at 11.785, where the standard deviation is high at 5.98. A high standard deviation indicates high fluctuations in the spread. Spread is lowest at 6.61 in the last segment where capitalization is highest. There is an inverse relation between capitalization and spread, except in the third and fourth segments. It is concluded that as the capitalization increases, there is a reduction in spread. The results are given in Table 4.32. The null hypothesis here is given as H 0 : There is no significant difference in mean spread among the five portfolios and no relationship between the call options maturing in the second month and spread. TABLE 4.32 Results of ANOVA test for spread for call options maturing in the second month and capitalization Particulars Sum of Squares df Mean Square F Sig. Result Between Groups 177.899 4 44.475 2.986.029 Sig Within Groups 670.316 45 14.896 Total 848.215 49
Sig. - Significant From Table4.32, it is found that since the F value of 2.986 and p value of 0.029 are statistically insignificant at 5% level, the null hypothesis is rejected. There are differences between spread in each segment. Spread varies according to market capitalization. 4.4.6 Relationship between call for second month and open interest Call options, which gives the Holder the right but not the obligation to buy the asset is taken for the second month maturity contracts. The spread for the call options maturing in the second month are divided into five portfolios and classified according to their value. The lowest 10 companies with the lowest open interest are placed in the first portfolio and the 10 companies with the highest open interest are placed in the fifth portfolio, along with their spread. Spread for these portfolios are compared. The following results are obtained and presented in Table 4.33. TABLE 4.33 Descriptive Statistics for call options maturing in the second month and open interest Divisions N Mean Std. Deviation Std. Error Division 1 10 6.1720 5.38713 1.70356 Division 2 10 11.2430 2.26249.71546 Division 3 10 12.5710 3.41054 1.07851 Division 4 10 11.9610 2.35531.74481 Division 5 10 9.7070 3.71801 1.17574 Total 50 10.3308 4.16059.58840 From Table 4.33, it is found that the spread is lowest for the first portfolio and has the highest standard deviation. The highest spread is for the third portfolio. The mean spread is 10.33. In the last portfolio, the spread is 9.70. It is difficult to draw conclusions about the spread and open interest. Spread does not form any pattern. This result is supported from by using one way analysis. In this regard, the null hypothesis is formulated as H 0 : there is no significant difference in spread among the five portfolios and no relationship between spread for call options maturing in the second month and open interest. Table 4.34 presents the results of the ANOVA test.
TABLE 4.34 Results of ANOVA test for call options maturing in the second month and open interest Particulars Sum of Squares df Mean Square F Sig. Result Between Groups 42.745 4 10.686 1.275.296 N.S Within Groups 335.341 40 8.384 Total 378.085 44 N.S Not Significant It is found from Table 4.34 that since the F value of 1.275 and p value of 0.296 are not significant at 5% level, the null hypothesis is accepted. It is concluded that there is no significant relationship between spread and open interest. No patterns are formed from Tables 4.34. It is difficult to form conclusions about the results. 4.4.7 Relationship between put for the second month and capitalization A study is undertaken to find the relationship between spread for the put options maturing on the second month. Here, the second month contracts are those which expire on 29 April 2010. Capitalization is placed in ascending order and divided into five portfolios where the first portfolio represents contracts with lowest capitalization and fifth portfolio representing contracts with highest capitalization. Since there was no trading in five companies, these companies are excluding from the list. So there are 45 companies which had a trading record during the month of study. Spread, the measure of the performance of the instrument is computed. The spread for this classification of portfolio are given in Table 4.35. TABLE 4. 35 Descriptive Statistics for put options maturing in the second monthand capitalization Segments N Mean Std. Deviation Std. Error Part 1 9 10.9111 3.07893 1.02631 Part 2 9 10.1556 3.35700 1.11900 Part3 9 10.4389 2.88312.96104 Part 4 9 8.9378 3.23428 1.07809 Part 5 9 8.3000 1.54768.51589 Total 45 9.7487 2.93136.43698
From Table4.35, it is inferred that spread is lowest for the fifth portfolio at 8.3 and highest for the first portfolio at 10.91. The mean standard deviation is 2.93, which is quite high. This indicates a high fluctuation is spread among these categories. Spread shows a constantly decreasing trend for these portfolios. So it is concluded that as the volume increases, spread decreases. Volume and spread have an inverse relationship. This result is verified by using One-way analysis of variance and the results are presented in Table 4.36.Here the null hypothesis is formulated as H 0 : There is no significant difference in the mean spread among the five portfolios and no relationship between put options maturing in the second month and market capitalization. TABLE 4.36 Results of ANOVA test for put options maturing in the second month and capitalization Particulars Sum of Squares df Mean Square F Sig. Result Between Groups 261.929 4 65.482 5.026.002 N.S Within Groups 586.286 45 13.029 Total 848.215 49 From Table4.36 it is revealed that since the F value of 5.026 and p value of 0.002 are statistically significant at 5% level, the null hypothesis is rejected. There is a relationship between the spread and capitalization. capitalization increases, there is a decrease in spread. Spread is inversely related to capitalization.as 4.4.8Relationship between put for the second month and open interest Spread on put options that are maturing in the second month are compared with the open interest for the second month. The open interest is placed in ascending order and is divided into five segments. The first segment consists of shares with the lowest open interest and the fifth segment consists of companies with the highest open interest. Spread is used here to compute the performance of the instrument. A comparison is done between these