chapter- 4 data analysis and...

107

CHAPTER- 4

DATA ANALYSIS AND INTERPRETATION

The previous chapter dealt with conceptual framework of Indian securities market,

National Stock Exchange, derivatives, futures contract, business growth of global and

Indian derivatives market and futures pricing models. The previous chapter helped to

understand the basic concepts of derivatives, futures contracts, futures terminologies,

futures trading mechanism, technology and applications of NSE, the size of global

and Indian derivatives market in terms of volume and turnover. Further, the previous

chapter helped to understand the terminologies and operations of three futures pricing

models (CCM, HLM and HWM) to test empirically on Indian markets.

This chapter deals with data analysis and interpretation of the study. The analysis and

interpretation of secondary data is broadly classified in to five parts. They are as

follows

4.1 Descriptive statistics of daily trading volume of both stock futures and

indices, underlying stocks & indices.

4.2 Testing the specification of Hemler and Longstaff Model

4.3 Testing of futures pricing models and assess the pricing performance of all

the three pricing models for both individual stock futures and indices.

4.4 Results of Independent t Test

4.5 Results of Kormogorov - Smirnov Z test

4.6 Results of regression analysis - Impact of various factors on Absolute

Pricing Errors (APE).

4.7 Construction and interpretation of Percentage Pricing Errors chart

The study uses many statistical tools to analyse and interpretation of the data.

Shapiro-Wilk test has been used to test normality. Regression analysis has been used

to test the specification of HLM and impact of various factors on Absolute Pricing

Errors (APE). Independent t test and Kormogorov- Smirnov Z test has been used to

test the hypothesis of MAPE statistics, obtained from each model are statistically

different from each other. Additionally, the study uses statistical tools like mean,

standard deviation, kurtosis and skewness for descriptive statistics.

108

4.1 Descriptive Statistics

Table 4.1: Descriptive statistics of daily trading volume of stock index futures

Index

futures N Mean Max Min Std Dev Kurtosis Skewness

CNX Nifty 1741 442492 1338598 1935 207670 0.24 0.69

Bank Nifty 1741 52007 256601 7 38064 1.33 0.88

CNX IT 1741 305 3037 1 332 19.54 3.71

(Source: Developed by Researcher)

Table 4.1 reports the descriptive statistics of daily trading volume of three stock index

futures contracts- CNX Nifty, Bank Nifty and CNX IT. Table 4.1 clearly indicates

that the average daily trading volume is substantially larger for CNX Nifty index

futures, which has highest trading history of 14 years, constitutes 50 major stocks and

66.85% of free float market capitalization of NSE than Bank Nifty futures and CNX

IT futures contract as on June 30, 2014.The average daily trading volume of CNX

Nifty futures contract 8.5 and 1449.5 times more than average daily trading volume of

Bank Nifty futures and CNX IT Futures contract during the sample period

respectively.

The average daily trading volume is higher for Bank Nifty index futures which has

trading history of 9 years, constitutes 12 stocks of banking sectors, represents 89.90%

of the free float market capitalization of the banking stocks which are listed in NSE

and finally constituents 15.55% of the free float market capitalization of all the stocks

which are listed in NSE than CNX IT index futures as on June 30, 2014. The average

daily volume of Bank Nifty futures contract 170.36 times more than CNX IT futures

contract during the sample period.

The average daily trading volume of CNXIT index futures is negligible compared to

CNX Nifty index futures and Bank Nifty index futures. CNX IT index futures trading

from last 11 years, constitutes 20 major stocks of IT sectors, represents 97.25% of the

free float market capitalization of the IT sectors and constitutes 11.27% of the free

float market capitalization of all the stocks of NSE.

Table 4.1 shows, the maximum and minimum daily trading volume for CNX Nifty

index futures during the sample period is 1338598 and 1935 respectively. Further, the

maximum and minimum daily trading volume for Bank Nifty index futures during the

sample period are 256601and 7 respectively. Additionally, the maximum and

minimum daily trading volume for CNX IT index futures during the sample period is

3037 and 1 respectively. Additionally, The CNX Nifty index futures has the highest

109

standard deviation of futures trading volume followed by Bank Nifty index futures

and CNX IT index futures.

Table 4.2: Descriptive statistics of daily trading volume of individual stock

futures

Stock Futures N Mean Max Min Std Dev Kurtosis Skewness

ACC 1741 2747.44 36486 37 2042.27 51.37 4.83

AMBUJACEM 1741 1672.28 17891 42 1267.25 23.61 3.36

AXIS BANK 1741 10210.66 98595 109 8068.38 18.87 2.84

BANK OF BARODA

1741 2637.57 20023 15 2228.71 9.95 2.55

BHARATHI

AIRTEL 1741 6793.14 67264 2 6871.62 7.12 1.91

BHEL 1741 8217.50 58695 110 6148.91 7.84 2.30

BPCL 1741 1957.94 29858 7 2134.68 54.22 5.94

CARIN INDIA 1741 12627.72 212692 139 13039.28 50.21 5.44

CIPLA 1741 2074.34 28571 35 1767.20 34.26 3.86

DRREDDY 1741 1587.11 21228 5 1478.64 34.46 4.22

GAIL 1741 1781.86 16126 29 1254.02 18.81 3.22

GRASIM 1741 1349.16 6568 11 901.36 2.63 1.45

HCLTECH 1741 2072.97 22559 0 2077.00 21.03 3.66

HDFC BANK 1741 6963.15 43293 71 3930.59 7.22 1.73

HDFC 1741 5939.10 48152 46 4007.48 13.69 2.53

HERO MOTO CORP

1741 3266.09 48152 22 3054.35 32.38 3.63

HINDALCO 1741 6515.33 2910 55 3607.87 2.68 1.22

HUL 1741 3893.00 60784 55 3766.62 92.41 7.88

ICICI BANK 1741 23134.00 131094 841 13183.67 9.35 2.34

IDFC 1741 5397.80 35689 100 3168.08 11.00 2.39

INFOSYS 1741 8152.35 174828 0 10462.31 71.39 6.17

ITC 1741 4697.12 32053 59 3005.91 11.78 2.72

JINDLAL STEEL 1741 4201.60 42569 49 2730.03 26.71 3.02

JP ASSOCIAT 1741 9324.93 57806 224 5421.49 6.68 1.76

KOTAK BANK 1741 3278.41 16571 26 1835.45 4.46 1.73

L&T 1741 13312.55 112470 194 9026.92 12.06 2.48

LUPIN 1741 1338.06 21298 1 1674.91 26.42 4.02

M&M 1741 4072.98 20114 9 2782.39 3.94 1.63

MARUTHI 1741 4596.91 65332 28 3353.08 76.82 5.99

ONGC 1741 5788.30 41951 80 4106.28 7.28 2.01

PNB 1741 3551.25 36551 38 2663.47 34.81 4.29

RANBAXY 1741 3850.98 62221 24 4173.28 53.95 5.71

RELIANCE 1741 35108.29 178201 642 29292.80 3.23 1.83

SBIN 1741 28710.38 159167 575 14673.58 12.92 2.42

SUNPHARMA 1741 1762.07 20323 3 1701.43 19.60 3.44

TATA MOTORS 1741 12483.55 91884 79 8656.70 8.34 1.92

TATA POWER 1741 2048.47 27545 15 1780.97 46.88 4.81

110

TATA STEEL 1741 17490.33 61482 441 7686.93 2.52 1.15

TCS 1741 6762.50 66646 128 4799.47 22.95 3.42

ULTRACEMCO 1741 770.56 8650 0 836.26 12.17 2.70

WIPRO 1741 2801.93 24256 51 1889.01 24.89 3.70


Table 4.2 reports the descriptive statistics of daily trading volume of all the 41

individual stock futures during the sample period. The highest average daily trading

volume of more than 10000 can be observed for eight stock futures in the descending

order - Reliance Industries futures contract (35108.29) followed by SBIN (28710.38),

ICICI Bank (23134), TATA Steel (17490.33), Larsen & Toubro (13312.55), Carin

India (12627.72), TATA Motors (12483.55) and Axis Bank (10210.66). The next

highest average daily trading volume between 5000 and 10000 can be observed for

ten stock futures in the descending order – JP Associates (9325) , BHEL (8218) ,

Infosys (8152) , HDFC Bank (6963), Bharathi Airtel (6793) , TCS ( 6763), Hindalco

Industries (6515), HDFC ( 5939), ONGC ( 5788) , IDFC ( 5398). Further, the average

daily trading volume between 2000 and 5000 can be observed for 14 stock futures in

the descending order – ITC (4697), Maruthi Suzuki India (4597), Jindal Steel (4202),

M&M ( 4073), HUL (3893), Ranbaxy Laboratories (3851), PNB (3551), Kotak Bank

( 3278), Hero Motor Corporation (3266), Wipro (2802), Bank of Baroda ( 2638),

Cipla ( 2074), HCL Technologies (2073) and Tata Power ( 2048).

Finally, the lowest average daily trading volume of less than 2000 can be observed for

8 companies in descending order - UltraTech Cement (770.56), followed by Lupin

(1338.06), Grasim Industries (1349.16), Dr. Reddy's Laboratories (1587.11), Ambuja

Cements (1672.28), Sun Pharmaceutical Industries (1762.07), GAIL (1781.86) and

BPCL (1957.94).

Table 4.3: Descriptive statistics of daily returns of underlying indices

Spot Index N Mean Std Dev Kurtosis Skewness Shapiro-

Wilk

CNX Nifty 1740 0.0003 0.0166 9.4113 0.1148 0.925 ***

Bank Nifty 1740 0.0005 0.0219 4.4587 0.1464 0.96***

CNX IT 1740 0.0003 0.0185 4.8954 -0.0943 0.939***


The Table 4.3 reports descriptive statistics of daily returns of underlying indices –

CNX Nifty, Bank Nifty and CNX IT. Table 4.3 shows, the mean return of spot Bank

Nifty index is higher than CNX Nifty index and CNX IT index. The average daily

111

standard deviations of CNX Nifty index, BANK Nifty index and CNX IT index are

1.66%, 2.19% and 1.8% respectively. Further, the highest volatility can be seen in

Bank Nifty index followed by CNX IT index and CNX Nifty index. CNX Nifty index

has the lowest volatility than the Bank Nifty and CNX IT index.

The kurtosis values of all the three spot indices are greater than the standard normal

distribution value (K>3). Thus, the daily return of all three indices are more peaked

(Lepto – kurtic). The skewness values of CNX Nifty index and Bank Nifty index are

slightly positive. Thus, the spot returns of CNX Nifty index and Bank Nifty index are

slightly skewed towards right side from the standard normal distribution.

Additionally, the skewness value of spot return of CNX IT is slightly negative. Thus,

the data is slightly skewed towards left side from the standard normal distribution.

The skewness and kurtosis values clearly indicate that all the three spot return series

are not normally distributed. Moreover, Shapiro-Wilk statistics for all the three return

series found significant at 1% level. Thus, reject the null hypothesis sates that the

return series of all the three underlying indices are normally distributed. It implies that

the return series of all the three underlying indices are not normally distributed.

Table 4.4: Descriptive statistics of daily returns of underlying individual stocks

Underlying Stock N Mean Std Dev Kurtosis Skewness Shapiro-

Wilk

ACC 1740 0.0004 0.0219 5.1862 -0.3950 0.949***

AMBUJACEM 1740 0.0004 0.0236 3.3537 0.1180 0.961***

AXIS BANK 1740 0.0007 0.0293 3.0400 0.1498 0.97***

BANK OF

BARODA 1740 0.0007 0.0262 2.6278 0.1665 0.974***

BHARATHI

AIRTEL 1740 -0.0005 0.0296 152.9159 -6.5034 0.753***

BHEL 1740 -0.0014 0.0499 680.4605 -21.6637 0.362***

BPCL 1740 0.0003 0.0305 168.3695 -6.9931 0.74***

CARIN INDIA 1740 0.0005 0.0257 6.3371 -0.4221 0.933***

CIPLA 1740 0.0003 0.0190 5.5724 -0.3082 0.949***

DRREDDY 1740 0.0007 0.0185 4.2108 -0.2131 0.961***

GAIL 1740 0.0002 0.0247 64.0376 -3.4679 0.833***

GRASIM 1740 0.0002 0.0211 12.9548 -0.6295 0.915***

HCLTECH 1740 0.0009 0.0274 4.5745 0.1485 0.946***

HDFC BANK 1740 -0.0001 0.0443 996.6824 -27.4385 0.308***

HDFC 1740 -0.0003 0.0456 826.0943 -23.7826 0.374***

HERO MOTO CORP

1740 0.0007 0.0208 7.7470 0.6577 0.946***

HINDALCO 1740 0.0007 0.0208 7.7470 0.6577 0.971***

HUL 1740 0.0006 0.0185 5.2968 0.4231 0.955***

112

ICICI BANK 1740 0.0003 0.0300 5.4216 -0.0853 0.948***

IDFC 1740 0.0003 0.0331 4.3495 0.1620 0.954***

INFOSYS 1740 0.0003 0.0214 14.4687 -0.7856 0.898***

ITC 1740 0.0005 0.0253 351.1336 -12.5124 0.616***

JINDLAL STEEL 1740 0.0004 0.0219 5.1862 -0.3950 0.949***

JP ASSOCIAT 1740 -0.0013 0.0576 420.4892 -14.6831 0.56***

KOTAK BANK 1740 0.0003 0.0336 79.2662 -4.1688 0.811***

L&T 1740 -0.0001 0.045185 253.1415 -2.3761 0.455***

LUPIN 1740 0.0002 0.0435 1077.494 -29.1365 0.279***

M&M 1740 0.0002 0.0303 139.4742 -5.8952 0.744***

MARUTHI 1740 0.0006 0.0223 2.5540 -0.1022 0.973***

ONGC 1740 -0.0005 0.0412 862.7836 -24.6408 0.361***

PNB 1740 0.0003 0.0373 171.1584 -0.5518 0.592***

RANBAXY 1740 0.0000 0.0297 21.7342 -1.1876 0.849***

RELIANCE 1740 -0.0002 0.0294 213.0845 -8.6218 0.691***

SBIN 1740 0.0004 0.0252 3.3718 0.1598 0.97***

SUNPHARMA 1740 -0.0003 0.0466 843.4410 -25.4206 0.269***

TATA MOTORS 1740 -0.0003 0.0496 708.1051 -21.2811 0.428***

TATA POWER 1740 -0.0002 0.0709 764.6155 -15.2782 0.217***

TATA STEEL 1740 0.0000 0.0312 3.2221 -0.2420 0.962***

TCS 1740 0.0003 0.0281 212.8808 -8.4454 0.69***

ULTRACEMCO 1740 0.0006 0.0216 3.1955 0.2015 0.96***

WIPRO 1740 0.0000 0.0259 82.5797 -4.3078 0.812***

Note: *** Significant at the 1 % Level. (Source: Developed by Researcher)

Table 4.4 clearly indicates that the average daily standard deviations of all the 41

individual underlying stocks vary between 1.85% and 7.09%.

The highest average daily standard deviation of more than 5 % can be observed for

two stock futures in the descending order – Tata Power (7.09%) and JP Associates

(5.76%). The next highest average daily standard deviation varies between 4 % and

5% can be observed for eight stock futures in descending order - BHEL (4.99%), Tata

Motors (4.96%), Sun Pharmaceutical Industries (4.66%) and HDFC (4.56%), Larsen

& Toubro (4.51%), HDFC Bank (4.43%), Lupin (4.35%), ONGC (4.12%).

Further, the average daily standard deviation between 3% and 4% can be observed for

seven stock futures in the descending order – PNB (3.73%) Kotak Bank (3.36%),

IDFC (3.31%), Tata Steel (3.12%), BPCL (3.05%), Mahindra & Mahindra (3.03%)

and ICICI Bank (3%).

Additionally, the average daily standard deviation between 2 % and 3% can be seen

for twenty one stock futures – Ranbaxy Laboratories (2.97%), Bharathi Airtel

(2.96%), Reliance Industries (2.94%), Axis Bank (2.93%), TCS (2.81%), HCL

Technologies (2.74%), Bank of Baroda (2.62%) ,Wipro (2.59%), Carin India (2.57%),

113

ITC (2.53%) , SBIN (2.52%), GAIL (2.47%), Ambuja Cements (2.36%), Maruthi

Suzuki India (2.23%), ACC (2.19%), Jindal Steel (2.19), UltraTech Cement (2.16%),

Infosys (2.14%), Grasim Industries (2.11%), Hero MotoCorp (2.08%) and Hindalco

industries (2.08%). Finally, the lowest average daily standard deviation can be seen

for three stock futures – Cipla (1.9%), Dr. Reddy's Laboratories (1.85%), and HUL

(1.85%).

The kurtosis values of Bank of Baroda and Maruthi Suzuki India are less than the

standard normal distribution value (K>3). Thus, the daily return of these underlying

stocks is flatter than normal curve (Platy-kurtic). Except Bank of Baroda and Maruthi

Suzuki India, the kurtosis values of all the remaining underlying stocks are more than

the standard normal distribution value (K>3). Thus, the daily return of these

underlying stocks are more peaked (lepto – kurtic).

The return series of 10 individual underlying stocks [Ambuja Cements, Axis Bank,

Bank of Baroda, HCL Technologies, Hero MotoCorp, Hindalco Industries, Hindustan

Unilever (HUL), Infrastructure Development Finance Company (IDFC), State Bank

of India (SBI) and UltraTech Cement] are positively skewed. Thus, the return series

of these underlying stocks are skewed towards right side from the standard normal

distribution. The return series of remaining 31 underlying stocks are negatively

skewed. Thus, the return series of these underlying stocks are skewed towards left

side from the standard normal distribution. The skewness and kurtosis values of all

the 41 individual stock futures clearly indicate that return series of all the underlying

stocks are not normally distributed. Moreover, Shapiro-Wilk statistics for all the 41

individual underlying stocks are found significant at 1% level. Thus, reject the null

hypothesis sates that the return series of all the 41 individual series are normally

distributed. It implies that that the return series of all the 41 individual series are not

normally distributed.

114

Table 4.5: Descriptive statistics of daily returns of stock index futures

Index

Futures N Mean

Std

Dev Kurtosis Skewness

Shapiro-

Wilk

CNX Nifty 1740 0.0004 0.0175 8.4652 0.0080 0.926***

BANK Nifty 1740 0.0005 0.0225 4.5559 0.1231 0.959***

CNX IT 1740 0.0004 0.0186 4.2812 -0.1505 0.938***


The Table 4.5 reports descriptive statistics of daily returns of stock index futures –

CNX Nifty, Bank Nifty and CNX IT. Table.4.5 shows, the mean return of Bank Nifty

index is higher than CNX Nifty index and CNX IT index. The daily standard

deviations of CNX Nifty index, BANK Nifty index and CNX IT index are 1.75%,

2.25% and 1.86 % respectively. Further, the highest volatility can be seen in Bank

Nifty index followed by CNX IT index and CNX Nifty index. CNX Nifty index has

lowest volatility than Bank Nifty and CNX IT index.

The kurtosis values of all the three stock index futures are greater than the standard

normal distribution value (K>3). Thus, the daily returns of all three stock index

futures are more peaked. The CNX Nifty index futures and Bank Nifty index futures

are slightly positively skewed. Thus, the futures returns of CNX Nifty index and Bank

Nifty index are slightly skewed towards right side from the standard normal

distribution. Additionally, the futures return of CNX IT is slightly negatively skewed.

Thus, the data is slightly skewed towards left side from the standard normal

distribution. The skewness and kurtosis values clearly indicate that all the three

futures return series are not normally distributed.

Moreover, Shapiro-Wilk statistics for all the three futures return series are found

significant at 1% level. Thus, reject the null hypothesis sates that the return series of

all three indices are normally distributed. It implies that the return series of all three

indices are not normally distributed.

115

Table 4.6: Descriptive statistics of daily returns of individual stock futures

Stock Futures N Mean Std

Dev Kurtosis Skewness Shapiro-Wilk

ACC 1740 0.0004 0.0222 5.4122 -0.3949 0.948***

AMBUJACEM 1740 0.0004 0.0236 3.7385 0.1141 0.959***

AXIS BANK 1740 0.0007 0.0294 3.6744 0.1587 0.966***

BANK OF BARODA 1740 0.0007 0.0266 3.8190 0.2254 0.967***

BHARATHI AIRTEL 1740 -0.0005 0.0295 158.7387 -6.7240 0.749***

BHEL 1740 -0.0014 0.0498 671.6072 -21.4537 0..364***

BPCL 1740 0.0003 0.0301 163.4192 -6.8326 0.744***

CARIN INDIA 1740 0.0005 0.0255 6.8485 -0.4275 0.925***

CIPLA 1740 0.0003 0.0188 5.3481 -0.2608 0.949***

DRREDDY 1740 0.0007 0.0183 5.6500 -0.3986 0.95***

GAIL 1740 0.0002 0.0250 62.8758 -3.4204 0.83***

GRASIM 1740 0.0002 0.0219 11.3579 -0.4924 0.922***

HCLTECH 1740 0.0009 0.0278 4.7114 0.1822 0.942***

HDFC BANK 1740 -0.0001 0.0443 997.0697 -27.4402 0.306***

HDFC 1740 -0.0003 0.0011 840.8143 -24.0959 0.367***

HERO MOTO CORP 1740 0.0007 0.0204 6.8933 0.5291 0.949***

HINDALCO 1740 0.0001 0.0315 2.7606 -0.0116 0.972***

HUL 1740 0.0007 0.0181 5.6889 0.4196 0.952***

ICICI BANK 1740 0.0003 0.0300 6.0705 -0.0346 0.944***

IDFC 1740 0.0003 0.0334 4.1150 0.1330 0.955***

INFOSYS 1740 0.0003 0.0208 14.0718 -0.7259 0.899***

ITC 1740 0.0005 0.0251 357.6917 -12.7032 0.612***

JINDLAL STEEL 1740 -0.0012 0.0715 541.0934 -20.5494 0.296***

JP ASSOCIAT 1740 -0.0013 0.0581 414.8549 -14.5385 0.563***

KOTAK BANK 1740 0.0003 0.0339 80.4372 -4.1653 0.806***

L&T 1740 -0.0001 0.0319 139.5650 -6.5326 0.72***

LUPIN 1740 0.0003 0.0435 1072.1021 -29.0419 0.278***

M&M 1740 0.0002 0.0302 148.4754 -6.4641 0.746***

MARUTHI 1740 0.0006 0.0224 3.0124 -0.1391 0.969***

ONGC 1740 -0.0005 0.0414 835.9116 -24.0187 0.369***

PNB 1740 0.0003 0.0258 3.0836 0.0704 0.969***

RANBAXY 1740 0.0000 0.0302 22.9688 -1.4754 0.836***

RELIANCE 1740 -0.0002 0.0294 212.9884 -8.6172 0.69***

SBIN 1740 0.0004 0.0258 3.7136 0.1142 0.966***

SUNPHARMA 1740 -0.0003 0.0464 859.2640 -25.8219 0.266***

TATA MOTORS 1740 -0.0003 0.0497 718.8620 -21.5357 0.422***

TATA POWER 1740 -0.0002 0.0710 761.6933 -15.1981 0.219***

TATA STEEL 1740 0.0000 0.0315 3.1196 -0.2380 0.963***

TCS 1740 0.0003 0.0279 216.4574 -8.5953 0.683***

ULTRACEMCO 1740 0.0006 0.0212 2.8681 0.1646 0.963***

WIPRO 1740 0.0000 0.0262 73.9630 -3.9595 0.817***


The Table 4.6 reports descriptive statistics of daily returns of all the 41individual

stock futures. Table 4.6 clearly indicates that the average daily standard deviation of

116

all the 41 individual stock futures varies between 1.1% and 7.15%. The highest

average daily standard deviation of more than 5 % can be observed for three stock

futures in the descending order – Jindal Steel (7.15%), Tata Power (7.1%) and JP

Associates (5.81%). The next highest average daily standard deviation between 4 %

and 5% can be observed for six stock futures in descending order - BHEL (4.98%),

Tata Motors (4.97%), Sun Pharmaceutical Industries (4.64%), HDFC Bank (4.43%),

Lupin (4.35%) and ONGC (4.14%). Further, the average daily standard deviation

between 3% and 4% can be observed for nine stock futures in the descending order –

Kotak Bank (3.39%), Infrastructure Development Finance Company (3.34%), Larsen

& Toubro (3.19%), Hindalco Industries (3.15%), Tata Steel (3.15%), M&M (3.02%),

Ranbaxy Laboratories (3.02%), BPCL (3.01%) and ICICI Bank (3%). Additionally,

the average daily standard deviation between 2 % and 3% can be seen for nineteen

stock futures - Bharathi Airtel (2.95%), Axis Bank (2.94%), Reliance Industries Ltd

(2.94%), TCS (2.79%), HCL Technologies (2.78%), Bank of Baroda (2.66%) , Wipro

(2.62%), PNB (2.58%), SBIN (2.58%), Carin India (2.55%), ITC (2.51%), GAIL

(2.5%), Ambuja Cements (2.36%), Maruthi Suzuki India (2.24%), ACC (2.22%),

Grasim Industries (2.19%), UltraTech Cement (2.12%), Infosys (2.08%) and Hero

MotoCorp (2.04%). Finally, the lowest average daily standard deviation can be seen

for four stock futures – Cipla (1.88%), Dr. Reddy's Laboratories (1.83%), HUL

(1.81%) and HDFC (0.11%).

The kurtosis values of UltraTech Cement, ITC and Hindalco are less than the standard

normal distribution value (K>3). Thus, the daily returns of these stock futures are

flatter than normal curve (Platy-kurtic).

Except UltraTech Cement, ITC and Hindalco Industries, the kurtosis values of all the

remaining stock futures are greater than the standard normal distribution value (K>3).

Thus, the daily return of these stock futures are more peaked (lepto – kurtic)

The return series of 12 individual stock futures [Ambuja Cements, Axis Bank, Bank

of Baroda, Bharat Heavy Electricals (BHEL), HCL Technologies, Hero MotoCorp

Hindalco Industries, Hindustan Unilever (HUL), Infrastructure Development Finance

Company (IDFC), Punjab National Bank (PNB), State Bank of India (SBI) and

UltraTech Cement] are positively skewed .Thus, the return series of these stock

futures are slightly skewed towards right side from the standard normal distribution.

The return series of remaining 29 stock futures are negatively skewed. Thus, the

return series of these stock futures are skewed towards left side from the standard

117

normal distribution. The skewness and kurtosis values of all the 41 individual stock

futures clearly indicate that return series are not normally distributed. Moreover,

Shapiro-Wilk statistics for all the 41 individual futures are found significant at 1%

level. Thus, reject the null hypothesis sates that the return series of all the 41

individual stock futures returns are normally distributed. It implies that the return

series of all the 41 individual stock futures are not normally distributed.

Table 4.7: Descriptive statistics of daily basis for stock index futures

Index

Futures N

BASIS

Negative Basis Positive Basis

Number Percentage Number Percentage

CNX Nifty 1741 550 31.59 1191 68.41

Bank Nifty 1741 599 34.4 1142 65.6

CNX IT 1741 640 36.76 1101 63.24


Table 4.8: Descriptive statistics of daily basis for individual stock futures

Stock futures N

BASIS

Negative Basis Positive Basis

Number Percentage Number Percentage

ACC 1741 767 44.06 974 55.94

AMBUJACEM 1741 680 39.06 1061 60.94

AXIS BANK 1741 604 34.69 1137 65.31

BANK OF BARODA 1741 609 34.98 1132 65.02

BHARATHI AIRTEL 1741 368 21.14 1373 78.86

BHEL 1741 712 40.9 1029 59.1

BPCL 1741 406 23.32 1335 76.68

CARIN INDIA 1741 422 24.24 1319 75.76

CIPLA 1741 310 17.81 1431 82.19

DRREDDY 1741 465 26.71 1276 73.29

GAIL 1741 550 31.59 1191 68.41

GRASIM 1741 516 29.64 1225 70.36

HCLTECH 1741 529 30.38 1212 69.62

HDFC BANK 1741 554 31.82 1187 68.18

HDFC 1741 488 28.03 1253 71.97

HERO MOTO CORP 1741 1008 57.9 733 42.1

HINDALCO 1741 320 18.38 1421 81.62

HUL 1741 630 36.19 1111 63.81

ICICI BANK 1741 549 31.53 1192 68.47

IDFC 1741 321 18.44 1420 81.56

INFOSYS 1741 526 30.21 1215 69.79

118

ITC 1741 404 23.21 1337 76.79

JINDLAL STEEL 1741 303 17.4 1438 82.6

JP ASSOCIAT 1741 292 16.77 1449 83.23

KOTAK BANK 1741 449 25.79 1292 74.21

L&T 1741 540 31.02 1201 68.98

LUPIN 1741 496 28.49 1245 71.51

M&M 1741 543 31.19 1198 68.81

MARUTHI 1741 673 38.66 1068 61.34

ONGC 1741 589 33.83 1152 66.17

PNB 1741 578 33.2 1163 66.8

RANBAXY 1741 326 18.72 1415 81.28

RELIANCE 1741 315 18.09 1426 81.91

SBIN 1741 601 34.52 1140 65.48

SUNPHARMA 1741 442 25.39 1299 74.61

TATA MOTORS 1741 797 45.78 944 54.22

TATA POWER 1741 603 34.64 1138 65.36

TATA STEEL 1741 614 35.27 1127 64.73

TCS 1741 544 31.25 1197 68.75

ULTRACEMCO 1741 581 33.37 1160 66.63

WIPRO 1741 541 31.07 1200 68.93


The difference between actual futures price and underlying spot price is known as

“Basis”. Closure to maturity of futures contract, the basis, will trend towards zero.

This also known as convergence of spot and futures price on maturity. On account of

CCM always basis should be positive. According to this model, theoretical index

futures and stock futures price predicted by CCM must be greater than underlying

spot index and stock price respectively. The CCM equals to the cost of holding

underlying index or stock (Risk free interest rate) less the income received (Cash

dividend). It states that index and stock futures prices always exceeds underlying

stock prices by the cost of carry. Persistent negative basis (actual futures price less

than spot price) indicates that the standard CCM is not able to reasonably explain the

behaviour of stock and index futures prices.

Table 4.7 shows, the average frequency of negative basis is relatively small in all

cases both Index futures and stock futures contracts. The mean daily negative basis is

relatively lower for the CNX Nifty index futures. The percentage of negative basis for

CNX Nifty index futures is (31.9%) which is lower than the Bank Nifty futures

contract (34.40%) and CNX IT futures contract (36.76%). Further Table 4.8 shows

the lowest average daily negative basis observed for J P Associates (16.77%) and

largest average daily negative basis observed for Hero MotoCorp (57.9%). Table 4.7

119

clearly indicates that the mean percentage of negative basis relatively small in all

cases. Finally, the average frequency of negative basis for seven companies is in the

range of 15% - 19%, for ten companies is in the range of 21-29%, eleven companies

is in the range of 33%- 39 % and four companies is in the range of 40- 57%

respectively.

120

4.2 Testing the specifications of HLM and CCM using Hemler & Longstaff

regression equation

The specifications of HLM & CCM can be tested using Hemler & Long staff

model regression equation (Equation (2)). The (Equation (2)) is as follows

Lt = α+β1 rt+ β2 vt +εt

Where Lt = ln (Fteqτ /St ) is the logarithm of the dividend adjusted futures / Spot

price ratio, Ft is the theoretical futures price, St is the underlying spot index, τ is

the time to maturity ( T-t) , rt is the risk free interest rate, Vt is the market

volatility, α,β1& β2 are the regression coefficients. ε is the error part assumed to be

normally distributed with mean zero.

The Equation (2) indicates that, logarithm of the dividend adjusted futures / Spot

price ratio (Lt) has a linear relationship with risk free interest rate and market

volatility of spot index returns. Further, if we substitute α = 0, β1= T-t, β2 = 0 in

the above equation (2) then it becomes Lt = rt (T-t). Then Equation (2) can be

rearranged to explain CCM (Equation (1)). Thus, the CCM can be represented as a

special case of the HLM or CCM may be nested with in the Hemler & Longstaff

regression model. Thus, we can test the specifications of CCM and HLM using

Hemler & Longstaff regression framework.

According to the H&L equilibrium pricing model, the regression coefficients of

Equation (2) would be α≠ 0, β1>0, and β2≠ 0. In contrast, if the CCM holds the

coefficients of the Equation (2) would be α= 0, β1= T-t and β2= 0.

Table 4.9: Testing the specifications of HLM and CCM for stock index futures

Note: ** & *** Significant at 5% and 1 % Level respectively.


Index futures N α β1 β2 R2 F DW

CNX Nifty 1703 -0.001*** (0.005)

-.005*** (0.000)

0.044*** (0.000)

0.057 51.793*** (0.000)

0.536

Bank Nifty 1703 -0.003***

(0.000)

0.064***

(0.000)

-0.014 **

(0.026) 0.059

53.108***

(0.000) 0.557

CNXIT 1703 0.000 (0.897)

0.024 *** (0.001)

-0.05*** (0.000)

0.024 21.28*** (0.000)

0.897

121

Table 4.9.1: Number of stock index futures are significant and insignificant

Particulars

Number of Indices

Statistically

Significant

Number of Indices

Statistically

Insignificant

Total

α 2 1 3

β1 3 0 3

β2 3 0 3

F 3 0 3

(Source: Table 4.9)

Table 4.10: Testing the specifications of HLM and CCM for individual stock

futures

Stock Futures N α β1 β2 R2 F DW

ACC 1703 -0.010*** (0.000)

0.136*** (0.000)

0.005*** (0.001)

0.061 55.555*** (0.000)

0.464

AMBUJACEM 1703 -0.003***

(0.009)

0.042***

(0.001)

-0.001

(0.287) 0.008

6.888 ***

(0.001) 0.633

AXIS BANK 1703 0.002** (0.013)

0.003 (0.744)

-0.004*** (0.000)

0.021 18 *** (0.000)

0.729

BANK OF BARODA

1703 -0.008*** (0.000)

0.124*** (0.000)

-0.001 (0.311)

0.046 41.227 *** (0.000)

0.495

BHARATHI

AIRTEL 1703

-0.011 ***

(0.000)

0.216***

(0.000)

0.000

(0.127) 0.234

259.224***

(0.000) 0.413

BHEL 1703 0.006 ***

(0.000)

-0.074***

(0.000)

0.000

(0.183) 0.024

20.540 ***

(0.000) 0.558

BPCL 1703 0.000 (0.896)

0.038*** (0.001)

0.000 (0.827)

0.007 5.810 *** (0.003)

0.734

CARIN INDIA 1703 0.001 (0.141)

0.022** (0.017)

-0.002*** (0.000)

0.015 12.843*** (0.000)

0.640

CIPLA 1703 0.001*

(0.077)

0.033***

(0.000)

-0.004**

(0.016) 0.018

15.230***

(0.000) 1.006

DRREDDY 1703 0.001

(0.115)

0.025 ***

(0.003)

-0.010***

(0.000) 0.044

0.939 ***

(0.000) 39.038

GAIL 1703 0.027*** (0.0000)

-0.042*** (0.000)

-0.002*** (0.000)

0.017 14.53*** (0.000)

0.023

GRASIM 1703 -0.001* (0.081)

0.052*** (0.000)

-0.003 *** (0.008)

0.024 21.183 *** (0.000)

0.523

HCLTECH 1703 0.003***

(0.002) )

-0.005***

(0.000) )

-0.007***

(0.000) 0.037

32.57***

(0.000) ) 0.490

HDFC 1703 -0.001

(0.162)

0.042***

(0.000)

0.000

(0.252) 0.018

15.407***

(0.000) 0.638

HDFC BANK

1703 -0.002*** (0.000)

0.056 *** (0.000)

0.000 (0.659)

0.024 20.930*** (0.000)

0.670

HERO MOTO CORP

1703 -0.007*** (0.000)

0.074*** (0.000)

-0.002 (0.505)

0.013 11.158*** (0.000)

0.483

HUL 1703 -0.002 ***

(0.007)

0.063***

(0.000)

-0.016***

(0.000) 0.075

68.815***

(0.000) 0.587

ICICI BANK 1703 -0.003***

(0.000)

0.063***

(0.000)

0.000

(0.873) 0.028

24.334***

(0.000) 0.517

IDFC 1703 0.002*** (0.003)

0.018** (0.033)

0.000 (0.455)

0.003 2.836 (0.455)

0.589

122

Note: *, **, and *** Significant at the 10%, 5% and 1 % levels respectively.

(Source: Developed by Researcher).

INDALCO 1703 -0.002*** (0.001)

0.071*** (0.000)

-0.001 (0.051)

0.047 41.559*** (0.000)

0.859

INFOSYS 1703 0.002 ** (0.037)

0.025** (0.035)

-0.009 *** (0.000)

0.029 25.373*** (0.000)

0.671

ITC 1703 -0.001 (0.121)

0.052*** (0.000)

0.000 (0.444)

0.014 12.118*** (0.000)

0.516

JINDLAL

STEEL 1703

0.001*

(0.09)

0.033 ***

(0.000)

-0.002**

(0.012) 0.019

16.9***

(0.000) 0.533

JP ASSOCIAT 1703 0.02 *** (0.000)

0.017* (0.097)

0.0000*** (0.000)

0.023 20.016*** (0.001)

0.821

KOTAK BANK 1703 0.000

(0.509)

0.034 ***

(0.000)

0.000**

(0.011) 0.018

15.543***

(0.000) 0.920

L&T 1703 -0.003*** (0.003)

0.070 (0.152)

0.001*** (0.001)

0.011 9.334*** (0.000)

1.974

LUPIN 1703 -0.012*** (0.000)

0.182*** (0.000)

0.000*** (0.003)

0.1333 130.833 *** (0.000)

0.728

M&M 1703 -0.004*** (0.000)

0.078 *** (0.000)

0.000 (0.808)

0.035 30.558*** (0.000)

0.877

MARUTHI 1703 -0.001* (0.071)

0.038*** (0.000)

-0.008*** (0.000)

0.029 24.943 *** (0.000)

0.709

ONGC 1703 0.000

(0.785)

0.017

(0.19)

0.000

(0.171) 0.002

1.7

(0.178) 0.444

PNB 1703 -0.001 (0.696)

0.037 (0.330)

0.002 *** (0.000)

0.014 12.003*** (0.000)

1.788

RANBAXY 1703 -0.001 (0.637)

0.034 (0.162)

0.001 (0.214)

0.002 1.757 (0.173)

0.356

RELIANCE 1703 0.000 (0.865)

0.043*** (0.000)

0.000 (0.889)

0.027 23.714*** (0.000)

0.672

SBIN 1703 0.000

(0.886)

0.028***

(0.003)

-0.004***

(0.000) 0.020

17.37***

(0.000) 0.614

SUNPHARMA 1703 -0.002 *** (0.000)

0.066 *** (0.000)

0.000*** (0.003)

0.035 30.755*** (0.000)

1.025

TATA MOTORS 1703 -0.016*** (0.000)

0.204*** (0.000)

0.000*** (0.002)

0.114 109.46*** (0.000)

0.556

TATA POWER 1703 -0.006*** (0.000)

0.096*** (0.000)

0.000 (0.333)

0.052 46.47*** (0.000)

0.668

TATA STEEL 1703 -0.002 **

(0.011)

0.057***

(0.000)

-0.002 ***

(0.004) 0.024

21.228***

(0.000) 0.540

TCS 1703 0.002** (0.016)

0.007 (0.377)

0.000 (0.831)

0.001

0.502 (0.606)

0.675

ULTRACEMCO 1703 -0.001 (0.3013)

0.026** (0.017)

0.006*** (0.000)

0.011 9.16 (0.000)

1.341

WIPRO 1703 0.001

(0.273)

0.006

(0.551)

0.001

(0.155) 0.001

1.107***

(0.000) 0.552

123

Table 4.10.1 Number of individual stock futures are significant and insignificant

Particulars

Number of Scrips

Statistically

Significant

Number of Scrips

Statistically

Insignificant

Total

α 29 12 41

β1 34 7 41

β2 22 19 41

F 37 4 41

(Source: Table 4.10)

The Tables 4.9 and 4.10 summarize the results of the linear regression model, given in

expression (2) and also tested the specifications of two pricing models CCM and

HLM for index futures and individual stock futures respectively. If the HLM holds,

then the constant coefficient (α) should not be equal to zero. As shown in the Tables

4.9 & 4.10 the coefficients (α) of Nifty futures and Bank Nifty index futures and 36

individual stock futures are statistically different from zero. This findings support

HLM and contrary to CCM but the constant coefficients (α) of CNX IT index futures

and five individual stock futures (BPCL, Kotak Bank, ONGC, Reliance Industries and

SBI) are not statistically different from zero. This finding supports the CCM and

contrary to the HLM.

Further CCM implies that the interest rate coefficients (β1) should be equivalent to the

average contract maturity during the sample period of 0.04182 years for all three

stock index futures and all the forty one individual stock futures. The Tables 4.9 &

4.10 present that all the interest rate coefficients (β1) are not exactly equal to the

0.04182 years. This finding supports equilibrium model and contrary to the CCM.

In addition to this, if the HLM holds then interest rate coefficient should greater than

zero (β1>0). As shown in the Tables 4.10 & 4.10.1 all the interest rate coefficients (β1)

are positive and significant except seven individual stock futures (Axis, Larsen

&Toubro, ONGC, PNB, Ranbaxy Laboratories, TCS and Wipro) whose coefficients

are positive but insignificant. This finding supports HLM and contrary to CCM.

Further Nifty index futures, BHEL, GAIL & HCL Technologies whose interest rate

coefficients are negative and significant. So this finding supports CCM and contrary

to HLM.

Further, CCM implies that market volatility should not have explanatory power for Lt

i.e β2= 0. In contrast, HLM implies that the logarithm of the futures / spot ratio (Lt)

can be represented a linear regression on risk free interest rate and market volatility

(Eq-2). The Tables 4.9 & 4.10 reveal that market volatility coefficient (β2) of sixteen

124

individual stock futures are exactly zero, this finding supports the CCM and contrary

to the HLM. In addition to this market volatility coefficients (β2) of three index

futures and remaining twenty one individual stock futures are negative and

significant. Further, β2 value of four individual stock futures (Indalco, Hero

MotoCorp, Bank of Baroda & Ambuja Cements) is negative but insignificant. This

finding strongly supports H &L model and contrary to CCM.

To summarize, the Tables 4.9, 4.9.1, 4.10 & 4.10.1 clearly indicate that the regression

results of two stock index futures (CNX Nifty and CNX IT ) and eighteen individual

stock futures (Bharathi Airtel, BHEL, BPCL, GAIL, HCL Technologies, HDFC,

HDFC Bank, ICICI Bank , JP Associates, Kotak Bank, Lupin, Mahindra & Mahindra,

ONGC, Reliance Industries , Sun Pharmaceutical Industries, Tata Motors, Tata power

and TCS ) clearly support neither the specifications of the CCM or nor the Hemler&

Longstaff equilibrium model. These results are consistent with Gay and Jung (1999)

study on Korean Stock Exchange (KSE). They found that regression results neither

supports CCM nor HLM. Further they explain futures prices do not follow strictly

CCM, but at the same it is difficult to conclude that they instead follow the HLM.

Further, the regression results of Bank Nifty index futures and remaining twenty three

individual stock futures [ACC , Ambuja Cements , Axis Bank , Bank of Baroda ,

Cairn India , Cipla , Dr. Reddy's Laboratories , Grasim Industries , Hero MotoCorp ,

Hindalco Industries , Hindustan Unilever Ltd (HUL), Infrastructure Development

Finance Company , Infosys , ITC , Jindal Steel & Power , Larsen & Toubro, Maruthi

Suzuki India Limited, Punjab National Bank (PNB), Ranbaxy Laboratories , State

Bank of India (SBI), Tata Steel , UltraTech Cement, WIPRO ] are support the

empirical implications of the H & L equilibrium model. Janchung Wang (2009) found

that regression results support the specification of the Hemler- Long staff model for

both the TAIFEX and SGX futures contracts.

125

4.3 Pricing performance of futures pricing models

Table 4.11: Pricing performance of futures pricing models for stock index

futures


Table 4.11.1 summarizes the number of indices, each model outperform than

other model based on lower MAPE

Number of

Index

Futures

CCM vs HLM HWM vs CCM HWM vs HLM

CCM HLM Total HWM CCM Total HWM HLM Total

1 2 3 3 0 3 3 0 3


Table 4.11.2 summarizes the number of indices, each model Over Prices and

Under Prices

Number of

Index Futures

CCM HLM HWM

OP UP Total OP UP Total OP UP Total

3 0 3 2 1 3 0 3 3

OP - Over Price (ε = -ve; Ft > AF), UP - Under Price, (ε = +ve; Ft < AF)


Table 4.11 presents summary statistics of futures pricing model’s error for three stock

index futures. Each model pricing performance is measured by calculating Mean

Absolute Error (MAE), Mean Percentage Error (MPE) and Mean Absolute Percentage

Error (MAPE).

Index

Futures

Pricing

Models N

Absolute Error Percentage error Absolute

Percentage error

Mean

(%)

SD

( %)

Mean

( %)

SD

( %)

Mean

(%)

SD

( %)

CNX Nifty

CCM

HLM

HWM

1741

1703

1740

12.0680

12.0092

7.9264

11.7802

10.3505

7.70143

-0.1484

-0.0243

0.0093

0.3441

0.3316

0.2262

0.2530

0.2440

0.1611

0.2765

0.2258

0.1589

Bank Nifty

CCM

HLM

HWM

1741

1703

1740

23.77

25.0662

15.8919

24.0362

23.3729

15.2893

-0.1460

0.0054

0.0088

0.3605

0.3620

0.2505

0.2731

0.2701

0.1811

0.2768

0.2410

0.1733

CNX IT

CCM HLM

HWM

1741 1703

1740

15.34 67.0291

10.6948

15.7949 64.4995

11.4074

-0.1620 -0.0298

0.0075

0.3960

1.8954

0.3357

0.2896

1.3148

0.2032

0.3149 1.3652

0.2673

126

Pricing performance of all the three futures pricing models for all the three stock

index futures.

Tables 4.11 & 4.12 show the percentage error, over price and underprices statistics.

The CCM overprices all the thee stock index futures – Nifty, Bank Nifty and IT

contract by an average of -0.1484% , -0.1460% and -0.1620% respectively. The

largest overpricing of CCM is an average of -0.1620% found in CNXIT index futures.

HLM overprices two stock index futures – Nifty index futures and IT index futures by

an average of -0.0243% & -0.0298% respectively. Additionally, HLM under-prices

Bank Nifty futures by an average of 0.0054%. Further, HWM under-prices all the

three stock index futures- Nifty futures, Bank Nifty futures and IT index futures by an

average of 0.0093%, 0.0088% & 0.0075% respectively.

On the basis of percentage error it is found that, the MPE of CCM is the highest for IT

index futures by an average of -0.1620%.

Table 4.11 shows the MAPE of CCM for CNX Nifty index futures, Bank Nifty index

futures and CNX IT index futures is 0.250%, 0.2731% and 0.2896% respectively.

Further, the MAPE of HLM for CNX Nifty index futures, Bank Nifty index futures

and CNX IT index futures is 0.2440%, 0.2701% and 1.3148% respectively. It clearly

indicates that the MAPE of CCM is the highest for Nifty & Bank Nifty index futures

and the lowest for IT index futures compares to HLM. For two indices – Nifty &

Bank Nifty index futures, HLM is preferred over CCM. Additionally, the Table 4.11

present that MAPE of HLM is highest for CNX IT index futures compared to MAPE

of CCM and HWM for Nifty and Bank Nifty index futures.

The MAPE of HWM for three stock index futures CNX Nifty, Bank Nifty & CNX IT

is 0.1611%, 0.1811%, & 0.2032% respectively. Further it is found that, the MAPE of

HWM provides the best pricing performance than the CCM & HLM for all the three

stock index futures – Nifty, Bank & IT futures. The absolute pricing errors of HWM

are the lowest than MAPE of CCM and HLM for the three stock index futures - Nifty,

Bank & IT respectively.

Overall, on the basis of Mean Percentage Error (MPE) & Mean Absolute Percentage

Error (MAPE), the best pricing model preferred is HWM, followed by HLM and

finally CCM.

127

Table 4.11.1 summarizes the number of indices each model outperforms than other

model on the basis of lowest MAPE. It illustrates that, MAPE of HLM outperforms

CCM for 2 stock index futures. The MAPE of CCM outperforms HLM for only one

stock index futures (CNX IT). Further, MAPE of HWM outperforms CCM & HLM

for all the three stock index futures – Nifty, Bank Nifty & XNXIT.

MAPE for Indices

CNX Nifty index futures contract has been trading from last 14 years. Average daily

trading volume during the sample period is 442492 and the percentage of negative

basis is 31.59%. Further, CNX Bank Nifty futures contract has been trading from last

7 years, average daily trading volume during the sample period is 52007 and the

percentage of negative basis is 34.40%. Additionally, CNX IT futures contract has

been trading from last 11 years. Average daily trading volume during the sample

period is only 305 and the percentage of negative basis is 36.76%.

Table 4.11 reports pricing performance statistics of all the three pricing models. It

clearly indicates that the CNX Nifty index futures has lowest MAPE statistics than

other two stock index futures. CNX Nifty index futures has highest average trading

volume during the sample period (4, 42,492), followed by Bank Nifty index futures

which has the next highest average trading volume after Nifty index futures (52,007).

Finally, CNXIT index futures has highest MAPE statistics than CNX Nifty and Bank

Nifty index futures respectively.

Additionally Hsu- Wang (2004) and Janchung Wang (2005) state that CCM cannot

reasonably explain the negative basis (Difference between actual futures price and the

underlying value). According to CCM the basis should reflect the carrying cost and

this carrying cost must be positive (actual futures price > Spot price). Unless the

dividend yield is higher than the risk free interest rate this seldom occurs. Thus, it

clearly indicates that there is a relationship between frequency of negative basis and

as well as pricing performance of CCM.

As shown in the Table 4.11, the MAPE of CCM is lowest for Nifty index futures

which has lowest frequency of negative basis (31.59%) during the sample period,

followed by, Bank Nifty index futures which has next lowest frequency of negative

basis (34.40%) after Nifty futures. CNXIT index futures has witnessed highest MAPE

statistics and frequency of negative basis (36.76%).

128

Hsu & Wang (2006) demonstrated that stock index futures with high trading history

and higher average trading volume have better pricing performance than indices with

low trading history and low average trading volume. In the present study it is found

that stock index futures with higher average trading volume have better pricing

performance.

Table 4.12: Pricing performance of futures pricing models for individual stock

futures.

Stock

Futures

Pricing

Models N

Absolute Error Percentage error

Absolute

Percentage

error

Mean

(%)

SD

(%)

Mean

(%)

SD

(%)

Mean

(%)

SD

(%)

ACC

CCM 1741 4.4754 5.1486 -0.2856 0.7372 0.4922 0.6186

HLM 1703 4.5477 4.3291 -0.0288 0.7116 0.4868 0.5196

HWM 1740 2.8096 2.9093 -0.0061 0.4616 0.3054 0.3461

AMBUJA

CEMENTS

CCM 1741 0.6173 0.7218 -0.2576 0.7154 0.4829 0.5873

HLM 1703 0.6647 0.6181 0.0485 0.6967 0.5062 0.481

HWM 1740 0.4455 0.5061 -0.0012 0.5232 0.3471 0.3914

AXIS BANK

CCM 1741 3.3681 4.0043 -0.1766 0.5299 0.3516 0.4339

HLM 1703 3.5753 3.5861 -0.0118 0.5186 0.3566 0.3765

HWM 1740 2.6991 2.6429 0.0023 0.4121 0.2808 0.3016

BANK OF BARODA

CCM 1741 2.5979 3.6044 -0.1816 0.793 0.4772 0.6588

HLM 1703 2.8971 3.2184 0.0301 0.7778 0.5197 0.5794

HWM 1740 1.6977 2.0972 0.0038 0.5125 0.3199 0.4003

BHARATHI

AIRTEL

CCM 1741 1.61 2.3007 -0.0758 0.4034 0.2927 0.2876

HLM 1703 2.0973 2.4166 0.0205 0.5212 0.4087 0.3238

HWM 1740 1.3317 1.6897 0.0456 0.3261 0.2466 0.2181

BHEL

CCM 1741 4.6176 5.7932 -0.2701 0.6969 0.4346 0.608

HLM 1703 4.6463 5.5027 -0.0384 0.6523 0.419 0.5013

HWM 1740 3.7306 5.2134 -0.0017 0.4776 0.2978 0.3733

BPCL

CCM 1741 1.617 2.3703 -0.0308 0.6183 0.3563 0.5062

HLM 1703 1.8167 2.3147 -0.0044 0.6285 0.3968 0.4872

HWM 1740 1.3081 2.2329 0.0144 0.5087 0.2877 0.4198

CARIN INDIA

CCM 1741 0.9599 1.1281 -0.0673 0.506 0.3464 0.3748

HLM 1703 1.0228 1.0982 0.002 0.5142 0.3637 0.3634

HWM 1740 0.675 0.7422 0.0136 0.3727 0.2538 0.2731

CIPLA

CCM 1741 0.7288 0.8883 0.0138 0.403 0.2589 0.309

HLM 1703 0.8268 0.9509 0.0122 0.4263 0.2853 0.317

HWM 1740 0.6678 1.0989 0.0218 0.4065 0.2335 0.3334

129

DRREDDY

CCM 1741 3.3935 3.2923 -0.0934 0.4335 0.2941 0.3318

HLM 1703 3.9578 3.7803 0.0057 0.4418 0.3178 0.3068

HWM 1740 2.9079 3.0768 0.0116 0.4022 0.2565 0.3099

GAIL

CCM 1741 1.4575 1.8043 -0.133 0.6672 0.4077 0.5445

HLM 1703 1.5666 1.6269 0.0252 0.6391 0.4281 0.475

HWM 1740 1.05381 1.1766 0.0067 0.4388 0.2889 0.3302

GRASIM

CCM 1741 8.8914 9.0949 -0.1033 0.5509 0.3726 0.4186

HLM 1703 9.4893 8.7543 -0.0366 0.5485 0.3922 0.3851

HWM 1740 6.4543 6.9135 0.0128 0.3804 0.2626 0.2754

HCLTECH

CCM 1741 1.47 1.8208 -0.1602 0.7242 0.401 0.6239

HLM 1703 1.7233 1.9407 0.0205 0.7211 0.4388 0.5725

HWM 1740 1.1978 1.3977 0.0075 0.4771 0.2998 0.3711

HDFC

BANK

CCM 1741 4.0288 5.2211 -0.1507 0.4905 0.3337 0.3898

HLM 1703 4.0474 4.6191 -0.0467 0.4861 0.343 0.3475

HWM 1740 3.2009 3.7367 0.0078 0.379 0.2629 0.273

HDFC

CCM 1741 4.3326 5.7247 -0.0881 0.4249 0.2879 0.3246

HLM 1703 4.4481 5.1856 0.0199 0.4365 0.3131

3 0.3047

HWM 1740 3.7677 4.9926 0.0126 0.3248 0.2326

8 0.2269

HERO

MOTO CORP

CCM 1741 8.7862 11.9424 -0.5135 0.9962 0.6605 0.9054

HLM 1703 8.8273 9.7932 0.001 0.936 0.6094 0.7103

HWM 1740 5.26 7.0828 -0.0235 0.6363 0.39 0.5032

HINDALCO

CCM 1741 0.3711 0.4259 -0.0175 0.4439 0.2741 0.3494

HLM 1703 0.4188 0.4392 0.0023 0.473 0.3127 0.3549

HWM 1740 0.3454 0.3888 0.01523 0.40554 0.2587 0.3125

HUL

CCM 1741 1.2535 1.4325 -0.1947 0.6238 0.4174 0.5027

HLM 1703 1.3898 1.4964 -0.0073 0.5782 0.4121 0.4055

HWM 1740 0.8676 1.008 0.0023 0.4247 0.2825 0.317

ICICI BANK

CCM 1741 3.0584 3.7676 -0.1187 0.5184 0.3369 0.4114

HLM 1703 3.3094 3.4451 0.0383 0.5075 0.3591 0.3605

HWM 1740 2.2219 2.2613 0.0102 0.348 0.2491 0.2431

IDFC

CCM 1741 0.3965 0.4509 0.0069 0.4421 0.2923 0.3316

HLM 1703 2.5011 0.9093 -1.836 0.4762 1.8368 0.4762

HWM 1740 0.3259 0.3357 0.0188 0.3328 0.2396 0.2317

INFOSYS

CCM 1741 11.0979 14.6354 -0.2437 0.6674 0.4605 0.5409

HLM 1703 11.2505 14.6563 0.1564 0.6706 0.4528 0.5187

HWM 1740 7.7066 11.6184 0.0171 0.5155 0.313 0.4099

ITC

CCM 1741 0.7263 1.0532 -0.0497 0.6063 0.3379 0.5058

HLM 1703 0.8399 1.0334 -0.0186 0.6053 0.3797 0.4716

HWM 1740 0.5586 0.6779 0.0142 0.4126 0.2581 0.3222

130

JINDAL

STEEL

CCM 1741 5.7608 17.5857 0.0164 0.3787 0.2378 0.2952

HLM 1703 8.7269 25.9365 0.2082 0.4559 0.3575 0.3512

HWM 1740 4.6981 13.464 0.0214 0.3864 0.2459 0.2987

JP

ASSOCIAT

CCM 1741 0.6511 1.5865 0.02331 0.3757 0.2707 0.2614

HLM 1703 0.6767 1.7129 -1.8196 1.8196 0.298 0.2703

HWM 1740 0.5802 1.2195 0.024 0.3429 0.254 0.2315

KOTAK

BANK

CCM 1741 1.8627 2.097 -0.1036 0.4136 0.2961 0.3068

HLM 1703 1.9539 2.1808 -0.0502 0.4142 0.3017 0.2881

HWM 1740 1.7404 2.1409 0.0153 0.3979 0.2739 0.2889

L&T

CCM 1741 5.5088 23.2638 -0.0658 1.532 0.3274 1.498

HLM 1703 5.7027 7.192 -0.0556 0.5335 0.3394 0.4152

HWM 1740 4.4479 6.5628 0.0097 0.4652 0.2557 0.3887

LUPIN

CCM 1741 2.8336 3.9896 -0.1352 0.6564 0.3877 0.5466

HLM 1703 3.3091 3.7984 0.0422 0.6381 0.4313 0.472

HWM 1740 2.186 2.8357 0.0085 0.5088 0.3071 0.4057

M&M

CCM 1741 2.3299 2.8466 -0.136 0.5724 0.3466 0.4754

HLM 1703 2.6173 2.6917 -0.002 0.5699 0.3743 0.4296

HWM 1740 1.984 2.522 0.0088 0.4994 0.2893 0.4071

MARUTHI

CCM 1741 4.5005 4.7388 -0.2699 0.6033 0.4291 0.5027

HLM 1703 4.5555 4.1355 -0.0468 0.5786 0.4092 0.4115

HWM 1740 3.2391 3.4005 0.0016 0.459 0.3014 0.346

ONGC

CCM 1741 3.4765 5.525 -0.1611 0.7493 0.4616 0.6117

HLM 1703 3.5061 4.8129 0.0227 0.7234 0.4918 0.5307

HWM 1740 2.1452 3.443 0.0033 0.4625 0.281 0.3673

PNB

CCM 1741 4.2373 12.996 -0.0915 1.6477 0.5317 1.5622

HLM 1703 4.6692 12.8824 -0.029 1.6673 0.5964 1.5572

HWM 1740 2.3522 3.42546 0.00465 0.513 0.3066 0.4113

RANBAXY

CCM 1741 1.4748 5.8318 -0.1249 1.4956 0.3546 1.4583

HLM 1703 1.7304 5.7859 0.0122 1.504 0.4111 1.4468

HWM 1740 1.082 3.2766 0.0133 0.8632 0.2629 0.8222

RELIANCE

CCM 1741 3.1534 3.7299 0.0146 0.3155 0.231 0.2153

HLM 1703 3.59 3.9653 0.0022 0.3518 0.2703 0.2251

HWM 1740 2.7838 3.4852 0.021 0.2698 0.1972 0.1853

SBIN

CCM 1741 6.665 7.5512 -0.1603 0.5053 0.3479 0.3999

HLM 1703 7.06 6.834 -0.0066 0.5017 0.3612 0.3481

HWM 1740 4.8618 5.0384 0.0058 0.3699 0.2543 0.2686

SUNPHAR

MA

CCM 1741 3.3511 5.1474 -0.0849 0.5068 0.3158 0.4053

HLM 1703 3.4106 4.9124 -0.0446 0.5041 0.331 0.3827

HWM 1740 2.8975 5.1522 0.015 0.479 0.2765 0.3913

TATA

MOTORS

CCM 1741 2.9075 4.2496 -0.4033 0.8312 0.5511 0.7414

HLM 1703 2.8659 3.4073 0.0132 0.7836 0.5355 0.572

HWM 1740 1.8483 2.4915 -0.0128 0.5579 0.353 0.4321

131

TATA

POWER

CCM 1741 3.0448 4.4882 -0.17 0.5715 0.3763 0.4624

HLM 1703 0.026 4.8061 0.0488 0.5591 0.3882 0.4051

HWM 1740 2.3841 3.3757 0.0078 0.4376 0.2954 0.3228

TATA STEEL

CCM 1741 1.9558 2.8241 -0.1512 0.652 0.395 0.5403

HLM 1703 2.0132 2.5675 -0.0171 0.6395 0.413 0.4884

HSM 1740 1.4147 2.1271 0.0058 0.4475 0.2825 0.347

TCS

CCM 1741 3.3579 3.8519 -0.0991 0.4486 0.3122 0.337

HLM 1703 3.7192 3.5525 0.0458 0.4515 0.3414 0.2989

HWM 1740 2.4652 2.7774 0.0102 0.3477 0.2333 0.2579

ULTRACEMCO

CCM 1741 4.2286 5.1942 -0.129 0.6083 0.3835 0.4894

HLM 1703 4.2169 4.6321 0.0115 0.6002 0.3826 0.4625

HWM 1740 3.4851 4.2978 0.0099 0.6493 0.3456 0.5497

WIPRO

CCM 1741 1.5754 2.1924 -0.1579 0.5967 0.3594 0.5017

HLM 1703 1.6594 2.0301 -0.0139 0.6006 0.3811 0.4643

HWM 1740 1.1955 1.426 0.0059 0.4205 0.2705 0.3219


Table 4.12.1 summarizes the number of individual stock futures, each model

outperform than other model based on lower MAPE

Individual

stock futures

CCM vs HLM HWM vs CCM HWM vs HLM

CCM HLM Total HWM CCM Total HWM HLM Total

39 2 41 41 0 41 40 1 41


Table 4.12.2 summarizes the number of individual stock futures, each model

over prices and under prices

Individual stock

futures

CCM HLM HWM

OP UP Total OP UP Total OP UP Total

36 5 41 19 22 41 05 36 41

OP - Over Price (ε = -ve; Ft > AF), UP - Under Price, (ε = +ve; Ft < AF)


Table 4.12 presents summary statistics of futures pricing model’s error for 41

individual stock futures. Each pricing model performance is measured by calculating

Mean Absolute Error (MAE), Mean Percentage Error (MPE) and Mean Absolute

Percentage Error (MAPE).

132

Pricing performance of all the three pricing models for 41 individual stock

futures

Tables 4.12 & 4.12.2 present the pricing performance of all the three models – CCM,

HLM & HWM for 41 individual stock futures. More closely examining the empirical

results, suggests, the pricing performance is relatively better in all the cases. The

largest MAPE of CCM (0.6605%) is observed for Hero MotoCorp & the lowest

MAPE of CCM (0.2310%) is observed for Reliance Industries. Further, the largest

MAPE error of HLM (0.6094%) is observed in Hero MotoCorp after Infrastructure

Development Finance Company (IDFC) (1.8368%) & the lowest MAPE error of

HLM (0.2703%) is observed in Reliance Industries. Finally, the largest MAPE of

HWM (0.3900%) in Hero Motor Corporation and the lowest MAPE of HWM

(0.1972%) are observed in Reliance Industries.

Table 4.12 shows the largest and lowest MAPE are 0.6605% and 0.19% of CCM for

Hero MotoCorp and HWM for Reliance Respectively. The MAPE statistics obtained

from all the three models indicate that the MAPE is not exceeded 0.7% except in one

case (HLM for IDFC).

Tables 4.12 & 4.12.2 present percentage pricing errors. The CCM overprices for 36

Individual Stock Futures (ISF) and under prices for 5 individual stock futures. HLM

overprices for 19 ISF and under prices for 22 ISF. HWM overprices for 5 ISF &

under-prices 36 ISF. Overall it indicates that majority of individual stock futures are

trade at the discount for CCM, ISF are trade at the premium for HWM and in case of

HLM , individual stock futures trade at the both discount and as well as premium.

Table 4.12.1 summarizes the number of stocks each model outperforms than other

model based on lower MAPE. It shows that for 34 individual stock futures the MAPE

of CCM is significantly lower than HLM and only in 7 cases the MAPE of HLM is

better than CCM.

Further, the MAPE of HWM is significantly lower than CCM for 40 individual stock

futures out of 41 ISF and only in one case the MAPE of CCM is better than HWM.

Finally, the MAPE of HWM is significantly lower than HLM for all the 41 individual

stock futures.

Finally the Tables 4.12 & 4.12.1 summarize that HWM which incorporates price

expectation, assume that capital markets are imperfect and an argument of incomplete

arbitrage mechanism provides the best and more accurate pricing performance than

the CCM and HLM for all the three stock index futures and 40 individual stock

133

futures. The absolute pricing errors of HWM with implied method of price

expectation for both individual stock futures and stock index futures are the lowest

compared to CCM and HWM. Therefore, in order to select futures pricing model to

predict theoretical futures prices for individual stocks and stock index futures, the

investors should determine the DOMI for the markets they would like to participate.

The CCM with an assumption of capital markets are perfect and no arbitrage

argument provides slightly better pricing performance than the HLM for 39 individual

stock futures and one index futures (CNX IT).

CCM does not provide better pricing performance in two stock index futures – CNX

Nifty, Bank Nifty. The absolute pricing errors of CCM for these two indices are

slightly lower than the HLM. Further, CCM provides no improvements over the

HWM for all the three stock index futures and 41 individual stock futures.

The HLM with an assumption of capital markets are perfect and incorporates market

volatility and risk free interest rate provides marginally better pricing performance

than CCM for two stock index futures (CNX Nifty and Bank Nifty). Overall, it

provides worst pricing performance than HWM and CCM for individual stock futures.

The absolute pricing errors of HLM marginally lower and the lowest compared to the

performance of CCM and HWM respectively. Further, Tables 4.11 & 4.12 clearly

indicate that the percentage pricing errors of HLM for CNX IT index futures, Grasim

Industries , GAIL and Infrastructure Development Finance Company (IDFC) are

higher in magnitude compare to CCM and HWM.

Generally, HLM provides better pricing performance in market has higher volatilities.

It provides no improvement over HWM and CCM for Indian futures market. The

Tables 4.4 & 4.6 show the descriptive statistics of spot and futures returns of all the

individual stock futures. Further, we can observe stocks which have highest volatility.

These are as follows. Jindal steel ( 7.15%), Tata power ( 7.1%) , JP Associates (

5.81%) , BHEL ( 4.98%), Tata Motor ( 4.97%) , Sun Pharmaceutical Industries

(4.64%) , HDFC ( 4.56%) HDFC Bank (4.43%), Lupin (4.35%), ONGC (3.39%),

Kotak Bank (3.39%) and Infrastructure Development Finance Company (IDFC)

(3.34%). Though these stocks have the highest volatility in spot and futures return,

HLM unable to provide better pricing performance in any of these stocks compared

HWM & CCM

Additionally, Table 4.10 reports regression results of Bank Nifty index futures and 23

individual stock futures. The results support the empirical implications of the HLM.

134

Though, these 23 stocks support the specification of HLM, the pricing performance of

HLM is significantly lower than the CCM and HWM.

Finally, this findings imply that consideration of equally weighted moving average of

market volatility in to futures pricing models is not beneficial for estimating

theoretical futures values for individual stock futures. Therefore, when selecting

futures pricing models to predict theoretical values of individual stock futures,

investors need not to identify stock volatility for the markets they would like to

participate. But investors can consider market volatility when they would like to

predict theoretical values of CNX Nifty and Bank Nifty index futures.

135

4.4 Results of Independent t test

Independent t test (parametric test) is used to test whether the MAPE statistics are

obtained from each model for all the three stock index futures – CNX Nifty, Bank

Nifty and CNX IT and for all the forty one individual stock futures are statistically

different. Test has been carried out between MAPE statistics of two pricing models –

CCM & HLM, CCM & HWM and HLM & HWM.

Table 4.13: Results of independent t test for stock index futures

Index Futures Pricing Models N t Sig (2- tailed)

CNX Nifty

CCM vs HLM 1741 - 1703 18.242*** 0.000

CCM vs HWM 1741 - 1740 59.839*** 0.000

HLM vs HWM 1703 - 1740 57.018*** 0.000

BANK Nifty

CCM vs HLM 1741 - 1703 28.641*** 0.000

CCM vs HWM 1741 - 1740 107.064*** 0.000

HLM vs HWM 1703 - 1740 89.049*** 0.000

CNX IT

CCM vs HLM 1741 - 1703 -188.230*** 0.000

CCM vs HWM 1741 - 1740 96.998*** 0.000

HLM vs HWM 1703 - 1740 217.247*** 0.000 Note: *** Significant at the 1 % level. (Source: Developed by Researcher).

Table 4.13.1 Number of stock index futures are significant and insignificant

Pricing Models Number of Scrips are

statistically significant

Number of scrips are

statistically insignificant Total

CCM vs HLM 3 0 3

CCM vs HWM 3 0 3

HLM vs HWM 3 0 3


The Table 4.13 clearly shows, the independent t test results for all the three stock

index futures - CNX Nifty, Bank Nifty and CNX IT. Further Table 4.13.1 reports

number of indices statistically significant and insignificant. Tables 4.13 and 4.13.1

clearly indicate that the MAPE statistics obtained from each model (CCM & HLM,

CCM & HWM and HLM& HWM) are statistically significant at 1% level for all the

three stock index futures. Thus, reject the null hypothesis which states that the MAPE

values obtained from CCM & HLM, CCM & HWM and HLM & HWM are

statistically equal for all the three stock index futures. Thus, it implies that the mean

pricing error ascertained from each model is statistically not equal.

136

Table 4.14: Results of Independent t test for individual stock futures

Stock Futures Pricing Models N t Sig

(2- tailed )

ACC

CCM vs HLM 1741 - 1703 -2.396*** 0.000

CCM vs HWM 1741 - 1740 84.142*** 0.000

HLM vs HWM 1703 - 1740 121.942*** 0.000

AMBUJA

CEMENTS

CCM vs HLM 1741 - 1703 -17.161*** 0.000

CCM vs HWM 1741 - 1740 56.541*** 0.000

HLM vs HWM 1703 - 1740 105.322*** 0.000

AXIS BANK

CCM vs HLM 1741 - 1703 12.902*** 0.000

CCM vs HWM 1741 - 1740 42.442*** 0.000

HLM vs HWM 1703 - 1740 39.561*** 0.000

ANK OF

BARODA

CCM vs HLM 1741 - 1703 -26.872*** 0.000

CCM vs HWM 1741 - 1740 70.317*** 0.000

HLM vs HWM 1703 - 1740 122.070*** 0.000

BHARATHI AIRTEL

CCM vs HLM 1741 - 1703 -15.821*** 0.000

CCM vs HWM 1741 - 1740 24.159*** 0.000

HLM vs HWM 1703 - 1740 48.899*** 0.000

BHEL

CCM vs HLM 1741 - 1703 0.669 0.504

CCM vs HWM 1741 - 1740 71.251*** 0.000

HLM vs HWM 1703 - 1740 78.710*** 0.000

BPCL

CCM vs HLM 1741 - 1703 -8.208*** 0.000

CCM vs HWM 1741 - 1740 32.991*** 0.000

HLM vs HWM 1703 - 1740 40.666*** 0.000

CARIN INDIA

CCM vs HLM 1741 - 1703 -6.195*** 0.000

CCM vs HWM 1741 - 1740 28.247*** 0.000

HLM vs HWM 1703 - 1740 36.140*** 0.000

CIPLA

CCM vs HLM 1741 - 1703 -4.988*** 0.000

CCM vs HWM 1741 - 1740 28.401*** 0.000

HLM vs HWM 1703 - 1740 398.661*** 0.000

DRREDDY

CCM vs HLM 1741 - 1703 -4.450*** 0.000

CCM vs HWM 1741 - 1740 18.957*** 0.000

HLM vs HWM 1703 - 1740 25.968*** 0.000

GAIL

CCM vs HLM 1741 - 1703 3.434*** 0.000

CCM vs HWM 1741 - 1740 30.556*** 0.000

HLM vs HWM 1703 - 1740 26.9598*** 0.000

GRASIM

CCM vs HLM 1741 - 1703 3.905*** 0.000

CCM vs HWM 1741 - 1740 58.236*** 0.000

HLM vs HWM 1703 - 1740 68.386*** 0.000

HCLTECH

CCM vs HLM 1741 - 1703 -1.650* 0.099

CCM vs HWM 1741 - 1740 42.867*** 0.000

HLM vs HWM 1703 - 1740 47.913*** 0.000

HDFC BANK

CCM vs HLM 1741 - 1703 9.683*** 0.000

CCM vs HWM 1741 - 1740 38.409*** 0.000

HLM vs HWM 1703 - 1740 30.236*** 0.000

HDFC

CCM vs HLM 1741 - 1703 -1.115 0.265

CCM vs HWM 1741 - 1740 32.441*** 0.000

HLM vs HWM 1703 - 1740 28.895*** 0.000

137

HERO MOTO

CORP

CCM vs HLM 1741 - 1703 33.405*** 0.000

CCM vs HWM 1741 - 1740 63.858*** 0.000

HLM vs HWM 1703 - 1740 56.901*** 0.000

HINDALCO

CCM vs HLM 1741 - 1703 -21.782*** 0.000

CCM vs HWM 1741 - 1740 10.615*** 0.000

HLM vs HWM 1703 - 1740 31.507*** 0.000

HUL

CCM vs HLM 1741 - 1703 22.220*** 0.000

CCM vs HWM 1741 - 1740 47.042*** 0.000

HLM vs HWM 1703 - 1740 41.796*** 0.000

ICICI BANK

CCM vs HLM 1741 - 1703 14.047*** 0.000

CCM vs HWM 1741 - 1740 33.035*** 0.000

HLM vs HWM 1703 - 1740 55.563*** 0.000

IDFC

CCM vs HLM 1741 - 1703 -987.546*** 0.000

CCM vs HWM 1741 - 1740 27.017*** 0.000

HLM vs HWM 1703 - 1740 1006.030**

* 0.000

INFOSYS

CCM vs HLM 1741 - 1703 19.339*** 0.000

CCM vs HWM 1741 - 1740 88.131*** 0.000

HLM vs HWM 1703 - 1740 70.655*** 0.000

ITC

CCM vs HLM 1741 - 1703 -14.380*** 0.000

CCM vs HWM 1741 - 1740 48.460*** 0.000

HLM vs HWM 1703 - 1740 57.595*** 0.000

JINDLAL STEE

CCM vs HLM 1741 - 1703 -30.581*** 0.000

CCM vs HWM 1741 - 1740 -8.852*** 0.000

HLM vs HWM 1703 - 1740 64.464*** 0.000

JP ASSOCIAT

CCM vs HLM 1741 - 1703 -19.975*** 0.000

CCM vs HWM 1741 - 1740 -3.271*** 0.000

HLM vs HWM 1703 - 1740 17.871*** 0.000

KOTAK BANK

CCM vs HLM 1741 - 1703 -14.646*** 0.000

CCM vs HWM 1741 - 1740 3.733*** 0.000

HLM vs HWM 1703 - 1740 18.218*** 0.000

L&T

CCM vs HLM 1741 - 1703 -12.430*** 0.000

CCM vs HWM 1741 - 1740 47.078*** 0.000

HLM vs HWM 1703 - 1740 55.572*** 0.000

LUPIN

CCM vs HLM 1741 - 1703 -0.403 0.687

CCM vs HWM 1741 - 1740 33.891*** 0.000

HLM vs HWM 1703 - 1740 41.063*** 0.000

M&M

CCM vs HLM 1741 - 1703 -14.918*** 0.000

CCM vs HWM 1741 - 1740 20.915*** 0.000

HLM vs HWM 1703 - 1740 42.935*** 0.000

MARUTHI

CCM vs HLM 1741 - 1703 12.637*** 0.000

CCM vs HWM 1741 - 1740 84.466*** 0.000

HLM vs HWM 1703 - 1740 61.327*** 0.000

ONGC

CCM vs HLM 1741 - 1703 6.383*** 0.000

CCM vs HWM 1741 - 1740 45.638*** 0.000

HLM vs HWM 1703 - 1740 47.023*** 0.000

PNB CCM vs HLM 1741 - 1703 -22.999*** 0.000

CCM vs HWM 1741 - 1740 56.755*** 0.000

138

HLM vs HWM 1703 - 1740 105.515*** 0.000

RANBAXY

CCM vs HLM 1741 - 1703 -9.050*** 0.000

CCM vs HWM 1741 - 1740 38.007*** 0.000

HLM vs HWM 1703 - 1740 51.204*** 0.000

RELIANCE

CCM vs HLM 1741 - 1703 -35.607*** 0.000

CCM vs HWM 1741 - 1740 26.986*** 0.000

HLM vs HWM 1703 - 1740 58.502*** 0.000

SBIN

CCM vs HLM 1741 - 1703 -22.970*** 0.000

CCM vs HWM 1741 - 1740 52.855*** 0.000

HLM vs HWM 1703 - 1740 86.631*** 0.000

SUNPHARMA

CCM vs HLM 1741 - 1703 5.809*** 0.000

CCM vs HWM 1741 - 1740 23.348*** 0.000

HLM vs HWM 1703 - 1740 21.738*** 0.000

TATA POWER

CCM vs HLM 1741 - 1703 5.154*** 0.000

CCM vs HWM 1741 - 1740 32.554*** 0.000

HLM vs HWM 1703 - 1740 23.564*** 0.000

TATA STEEL

CCM vs HLM 1741 - 1703 -11.941*** 0.000

CCM vs HWM 1741 - 1740 84.268*** 0.000

HLM vs HWM 1703 - 1740 74.419*** 0.000

TCS

CCM vs HLM 1741 - 1703 -7.664*** 0.000

CCM vs HWM 1741 - 1740 59.344*** 0.000

HLM vs HWM 1703 - 1740 78.440*** 0.000

WIPRO

CCM vs HLM 1741 - 1703 6.181*** 0.000

CCM vs HWM 1741 - 1740 36.362*** 0.000

HLM vs HWM 1703 - 1740 32.364*** 0.000

TATA MOTORS

CCM vs HLM 1741 - 1703 6.445*** 0.000

CCM vs HWM 1741 - 1740 55.395*** 0.000

HLM vs HWM 1703 - 1740 71.767*** 0.000

ULTRACEMCO

CCM vs HLM 1741 - 1703 -30.070*** 0.000

CCM vs HWM 1741 - 1740 -10.763*** 0.000

HLM vs HWM 1703 - 1740 10.994*** 0.000 Note: * and *** Significant at the 10% and 1 % levels respectively. (Source: Developed by

Researcher).


Pricing

Models

Number of Scrips are



statistically insignificant

Total

scrips

CCM vs HLM 38 3 41

CCM vs HWM 41 0 41

HLM vs HWM 41 0 41


The Table 4.14 clearly shows, the independent t test results for all the forty one stock

futures. Further Table 4.14.1 reports number of individual stock futures are

statistically significant and insignificant. Tables 4.14 and 4.14.1 clearly indicate that

the MAPE statistics, obtained from each model (HLM & HWM and CCM & HWM)

139

are statistically significant at 1% level for all the forty-one individual stock futures.

Thus, reject the null hypothesis which states that the MAPE values obtained from

CCM & HWM and HLM & HWM are statistically equal for all the 41 individual

stock futures. Thus, it implies that the mean pricing error ascertained from each model

is statistically not equal.

Further Tables 4.14 & 4.14.1 present, the MAPE statistics, obtained from CCM &

HLM are significant at 1% for 37 individual stock futures and 10% significant for one

stock futures (HCL). So from these results, it can be concluded that the researcher

unable to accept the null hypothesis. Thus, there is a statistically significant difference

in MAPE values between pricing models. Additionally, MAPE statistics obtained

from CCM & HLM are statistically insignificant for three individual stock futures

(HDFC, LUPIN and BHEL). So the Mean pricing error ascertained from CCM is

equal to mean pricing errors ascertained from HLM for these three individual stock

futures.

140

4.5 Results of Kormogorov- Smirnov Z test

The results of Shapiro-Wilk test from the Tables 4.3, 4.4, 4.5 and 4.6 clearly indicate

that the spot and futures return series for both indices and individual stocks are not

normally distributed. Thus, the study used Kormogorov- Smirnov Z test (Non

parametric test) to test whether the MAPE statistics, obtained from each model for all

the three stock index futures – CNX Nifty, Bank Nifty and CNX IT and for all the

forty one individual stock futures are statistically different. Test has been used

between MAPE statistics of two pricing models – CCM & HLM, CCM & HWM and

HLM & HWM.

Table 4.15: Results of Kormogorov- Smirnov Z test for Stock index futures

Index Futures Pricing Models N Z Sig (2- tailed)

CNX Nifty CCM vs HLM 1741 – 1703 10.736*** 0.000

CCM vs HWM 1741 – 1740 29.500*** 0.000

HLM vs HWM 1703 – 1740 25.895*** 0.000

Bank Nifty CCM vs HLM 1741 – 1703 17.345*** 0.000

CCM vs HWM 1741 – 1740 28.619*** 0.000

HLM vs HWM 1703 – 1740 27.736*** 0.000

CNX IT CCM vs HLM 1741 – 1703 29.341*** 0.000

CCM vs HWM 1741 – 1740 29.483*** 0.000

HLM vs HWM 1703 – 1740 29.337*** 0.000 Note: *** Significant at the 1 % level. (Source: Developed by Researcher).


Pricing Models Number of Scrips are



statistically insignificant Total

CCM vs HLM 3 0 3

CCM vs HWM 3 0 3

HLM vs HWM 3 0 3


The Table 4.15 clearly shows the Kormogorov- Smirnov Z test results for all the three

stock index futures CNX Nifty, Bank Nifty and CNX IT. Further Table 4.15.1 reports

number of indices statistically significant and insignificant. Tables 4.15 and 4.15.1

clearly indicate that the MAPE statistics, obtained from each model (CCM and HLM,

CCM and HWM and HLM and HWM) are statistically significant at 1% level for all

the three stock index futures. Thus, reject the null hypothesis which states that the

MAPE values obtained from CCM & HLM, CCM & HWM and HLM & HWM are

statistically equal for all the three stock index futures. Thus, it implies that the mean

absolute pricing error ascertained from each model is statistically not equal.

141

Table 4.16: Results of Kormogorov- Smirnov Z test for individual stock futures

Stock Futures Pricing

Models N Z Sig (2- tailed )

ACC

CCM vs HLM 1741 - 1703 6.074*** 0.000

CCM vs HWM 1741 - 1740 28.085*** 0.000

HLM vs HWM 1703 - 1740 28.942*** 0.000

AMBUJA

CEMENTS

CCM vs HLM 1741 - 1703 10.492*** 0.000

CCM vs HWM 1741 - 1740 25.838*** 0.000

HLM vs HWM 1703 - 1740 28.585*** 0.000

AXIS BANK

CCM vs HLM 1741 - 1703 10.129*** 0.000

CCM vs HWM 1741 - 1740 18.706*** 0.000

HLM vs HWM 1703 - 1740 18.207*** 0.000

ANK OF

BARODA

CCM vs HLM 1741 - 1703 11.463*** 0.000

CCM vs HWM 1741 - 1740 24.176*** 0.000

HLM vs HWM 1703 - 1740 29.028*** 0.000

BHARATHI AIRTEL

CCM vs HLM 1741 - 1703 18.673*** 0.000

CCM vs HWM 1741 - 1740 16.835*** 0.000

HLM vs HWM 1703 - 1740 25.274*** 0.000

BHEL

CCM vs HLM 1741 - 1703 4.256*** 0.000

CCM vs HWM 1741 - 1740 27.348*** 0.000

HLM vs HWM 1703 - 1740 28.206*** 0.000

BPCL

CCM vs HLM 1741 - 1703 8.805*** 0.000

CCM vs HWM 1741 - 1740 17.225*** 0.000

HLM vs HWM 1703 - 1740 29.302*** 0.000

CARIN INDIA

CCM vs HLM 1741 - 1703 3.769*** 0.000

CCM vs HWM 1741 - 1740 14.768*** 0.000

HLM vs HWM 1703 - 1740 17.191*** 0.000

CIPLA

CCM vs HLM 1741 - 1703 7.363*** 0.000

CCM vs HWM 1741 - 1740 11.922*** 0.000

HLM vs HWM 1703 - 1740 18.433*** 0.000

DRREDDY

CCM vs HLM 1741 - 1703 7.191*** 0.000

CCM vs HWM 1741 - 1740 28.144*** 0.000

HLM vs HWM 1703 - 1740 16.096*** 0.000

GAIL

CCM vs HLM 1741 - 1703 4.213*** 0.000

CCM vs HWM 1741 - 1740 19.226*** 0.000

HLM vs HWM 1703 - 1740 19.845*** 0.000

GRASIM

CCM vs HLM 1741 - 1703 6.904*** 0.000

CCM vs HWM 1741 - 1740 22.007*** 0.000

HLM vs HWM 1703 - 1740 25.774*** 0.000

HCLTECH

CCM vs HLM 1741 - 1703 5.235*** 0.000

CCM vs HWM 1741 - 1740 15.937*** 0.000

HLM vs HWM 1703 - 1740 19.518*** 0.000

HDFC BANK

CCM vs HLM 1741 - 1703 4.954*** 0.000

CCM vs HWM 1741 - 1740 15.598*** 0.000

HLM vs HWM 1703 - 1740 16.369*** 0.000

HDFC CCM vs HLM 1741 - 1703 2.921*** 0.000

142

CCM vs HWM 1741 - 1740 17.666*** 0.000

HLM vs HWM 1703 - 1740 17.803*** 0.000

HERO MOTO

CORP

CCM vs HLM 1741 - 1703 16.947*** 0.000

CCM vs HWM 1741 - 1740 27.974*** 0.000

HLM vs HWM 1703 - 1740 22.252*** 0.000

HINDALCO

CCM vs HLM 1741 - 1703 13.786*** 0.000

CCM vs HWM 1741 - 1740 28.534*** 0.000

HLM vs HWM 1703 - 1740 16.567*** 0.000

HUL

CCM vs HLM 1741 - 1703 22.142*** 0.000

CCM vs HWM 1741 - 1740 1.364*** 0.048

HLM vs HWM 1703 - 1740 19.919*** 0.000

ICICI

BANK

CCM vs HLM 1741 - 1703 7.165*** 0.000

CCM vs HWM 1741 - 1740 26.245*** 0.000

HLM vs HWM 1703 - 1740 22.364*** 0.000

IDFC

CCM vs HLM 1741 - 1703 29.324*** 0.000

CCM vs HWM 1741 - 1740 16.531*** 0.000

HLM vs HWM 1703 - 1740 29.320*** 0.000

INFOSYS

CCM vs HLM 1741 - 1703 8.324*** 0.000

CCM vs HWM 1741 - 1740 26.569*** 0.000

HLM vs HWM 1703 - 1740 21.770*** 0.000

ITC

CCM vs HLM 1741 - 1703 9.185*** 0.000

CCM vs HWM 1741 - 1740 18.633*** 0.000

HLM vs HWM 1703 - 1740 22.522*** 0.000

JINDAL STEEL

CCM vs HLM 1741 - 1703 23.644*** 0.000

CCM vs HWM 1741 - 1740 18.673*** 0.000

HLM vs HWM 1703 - 1740 25.220*** 0.000

JP ASSOCIAT

CCM vs HLM 1741 - 1703 13.210*** 0.000

CCM vs HWM 1741 - 1740 3.216*** 0.000

HLM vs HWM 1703 - 1740 13.309*** 0.000

KOTAK BANK

CCM vs HLM 1741 - 1703 6.465*** 0.000

CCM vs HWM 1741 - 1740 9.462*** 0.000

HLM vs HWM 1703 - 1740 12.271*** 0.000

L&T

CCM vs HLM 1741 - 1703 7.713*** 0.000

CCM vs HWM 1741 - 1740 17.074*** 0.000

HLM vs HWM 1703 - 1740 22.095*** 0.000

LUPIN

CCM vs HLM 1741 - 1703 6.108*** 0.000

CCM vs HWM 1741 - 1740 14.453*** 0.000

HLM vs HWM 1703 - 1740 16.502*** 0.000

M&M

CCM vs HLM 1741 - 1703 9.918*** 0.000

CCM vs HWM 1741 - 1740 10.395*** 0.000

HLM vs HWM 1703 - 1740 17.892*** 0.000

MARUTHI

CCM vs HLM 1741 - 1703 10.887*** 0.000

CCM vs HWM 1741 - 1740 27.484*** 0.000

HLM vs HWM 1703 - 1740 24.076*** 0.000

ONGC

CCM vs HLM 1741 - 1703 6.336*** 0.000

CCM vs HWM 1741 - 1740 23.346*** 0.000

HLM vs HWM 1703 - 1740 24.295*** 0.000

PNB CCM vs HLM 1741 - 1703 14.927*** 0.000

143

CCM vs HWM 1741 - 1740 25.027*** 0.000

HLM vs HWM 1703 - 1740 28.441*** 0.000

RANBAXY

CCM vs HLM 1741 - 1703 9.365*** 0.000

CCM vs HWM 1741 - 1740 19.126*** 0.000

HLM vs HWM 1703 - 1740 22.758*** 0.000

RELIANCE

CCM vs HLM 1741 - 1703 18.898*** 0.000

CCM vs HWM 1741 - 1740 16.002*** 0.000

HLM vs HWM 1703 - 1740 21.958*** 0.000

SBIN

CCM vs HLM 1741 - 1703 10.864*** 0.000

CCM vs HWM 1741 - 1740 24.620*** 0.000

HLM vs HWM 1703 - 1740 27.741*** 0.000

SUNPHARMA

CCM vs HLM 1741 - 1703 3.552*** 0.000

CCM vs HWM 1741 - 1740 8.77*** 0.000

HLM vs HWM 1703 - 1740 10.745*** 0.000

TATA POWER

CCM vs HLM 1741 - 1703 6.531*** 0.000

CCM vs HWM 1741 - 1740 16.784*** 0.000

HLM vs HWM 1703 - 1740 17.703*** 0.000

TATA STEEL

CCM vs HLM 1741 - 1703 5.439*** 0.000

CCM vs HWM 1741 - 1740 28.432*** 0.000

HLM vs HWM 1703 - 1740 29.015*** 0.000

TCS

CCM vs HLM 1741 - 1703 13.155*** 0.000

CCM vs HWM 1741 - 1740 20.997*** 0.000

HLM vs HWM 1703 - 1740 29.044*** 0.000

WIPRO

CCM vs HLM 1741 - 1703 4.669*** 0.000

CCM vs HWM 1741 - 1740 18.395*** 0.000

HLM vs HWM 1703 - 1740 18.786*** 0.000

TATA MOTORS

CCM vs HLM 1741 - 1703 7.253*** 0.000

CCM vs HWM 1741 - 1740 24.434*** 0.000

HLM vs HWM 1703 - 1740 24.709*** 0.000

ULTRACEMCO

CCM vs HLM 1741 - 1703 13.502*** 0.000

CCM vs HWM 1741 - 1740 9.343*** 0.000

HLM vs HWM 1703 - 1740 10.511*** 0.000 Note: *** Significant at the 1 % level. (Source: Developed by Researcher).


Pricing Models

Number of Scrips

are statistically

significant


statistically insignificant

Total

scrips

CCM vs HLM 41 0 41

CCM vs HWM 41 0 41

HLM vs HWM 41 0 41


The Table 4.16 clearly shows, the Kormogorov- Smirnov Z test results for all the

forty one individual stock futures. Further table 4.16.1 reports number of individual

stock futures are statistically significant and insignificant. Tables 4.16 and 4.16.1

144

clearly indicate that the MAPE statistics obtained from each model (HLM & HWM

and CCM & HLM) are statistically significant at 1% level for all the forty-one

individual stock futures. Further Table 4.16 shows, the MAPE statistics obtained from

CCM & HWM is significant at 1% for 40 individual stock futures and 5% significant

for one stock futures (HUL). Thus, reject the null hypothesis which states that the

MAPE values obtained from CCM & HWM, HLM & HWM and CCM & HLM are

statistically equal for all the 41 individual stock futures. Thus, it implies that the mean

pricing error ascertained from each model is statistically not equal.

145

4.6 Impact of various factors on Absolute Percentage Errors of futures pricing

models

The study followed Hsu &Wang (2009) and examined the impact of four explanatory

factors and the absolute pricing errors for the three futures pricing models as defined

in the equation (13)

The first two explanatory factors considered are the absolute percentage errors of the

1 day & 2 day lags. Many previous studies Hsu &Wang (2009), Panayiotis and

Pierides (April 2008), Darren Butterworth & Phil Holmes (2000), Gay & Jung (1999),

Wolfgang Buhler &Alexander Kemp (1995), Brenner, Menachem; Subrahmanyam,

Marti G;Uno, Jun ( 1990), Cornell & French (1983), documented persistent under-

pricing in the futures market. Thus the actual futures price was persistently below the

theoretical price determined by the CCM.

Followed Hsu &Wang (2008), Gay & Jung (1999), regression framework and

examined the persistence mispricing over the sample period by including the absolute

percentage errors of the 1 day & 2 day lags for all the three futures pricing models of

the study.

The third explanatory factor is time to maturity. Many previous studies, Hsu &Wang

(2009), Panayiotis and Pierides (April 2008), Fung & Draper (1999), Gay & Jung

(1999), Braisford and Cusack (1997), Swati Bhatt & Nuset Cackici (1990), Yadav &

Pope (1990) found that the pricing errors are positive and significantly related to time

to maturity. This explanatory factor is examined in the present study also.

The fourth explanatory factor is futures trading volume. It is based on the argument

that suppose if any deviation of actual price from the theoretical price determined

CCM then there is a possibility of arbitrage opportunity. So this arbitrage process may

impact futures trading volume. Thus a positive relationship can be expected between

futures trading volume and absolute percentage errors (APE).

Conversely Bessem binder and Seguin (1992) clearly explained that futures market

with high treading volume improves liquidity and indicates an efficient market in

which there no possibility of profitable arbitrage opportunities. Thus a negative

relationship can be expected between futures trading volume and absolute pricing

error.

The following regression equation (Equation (13)) is estimated based on the daily

absolute percentage errors of all the three futures pricing models.

146

APE = α + β1 APE t-1 + β2 APE t-2 + β3 MAT t + β4 VOL t + ε t

Where APE is the absolute percentage errors of three futures pricing models – CCM,

HLM & HWM as defined in the Eq (13). APE t-1 and APE t-2 are the absolute

percentage errors of 1 day and 2 day lags respectively. MAT t is the time to maturity

(T-t). VOL t is the futures trading volume. α is the constant coefficient. β1, β2, β3 and

β4 are the regression coefficient of the absolute percentage errors of 1 day lags, the

absolute percentage errors of 2 day lags, time to maturity and futures trading volume

respectively.

147

Table 4.17: Impact of various factors on Absolute Percentage Errors of futures pricing models for stock index futures.

Index Futures Pricing Models N α β1 β2 β3 β4 R2 F

CNX Nifty

CCM 1739 0.048*** (0.001)

0.496*** (0.000)

0.198*** (0.000)

2.026*** (0.000)

-1.3E-07*** (0.000)

0.558

546.651*** (0.000)

HLM 1701 0.064***

(0.000)

0.477***

(0.000)

0.195***

(0.000)

0.999***

(0.000)

-5.8E-08***

(0.005) 0.439

332.234***

(0.000)

HWM 1738 0.157***

(0.000)

0.141***

(0.000)

0.013

(0.568)

1.211***

(0.000)

-1.6E-07***

(0.000) 0.125

61.695***

(0.000)

Bank Nifty

CCM 1739 0.004

(0.741)

0.477***

(0.000)

0.194***

(0.000

2.253***

(0.000)

-16E-07

(0.192) 0.481

403.924***

(0.000)

HLM 1701 0.031***

(0.006)

0.430***

(0.000

0.218***

(0.000

1.456***

(0.000

5.42E-08

(0.650) 0.410

294.062***

(0.000)

HWM 1738 0.111***

(0.000)

0.150***

(0.000)

0.021

(0.384)

1.350***

(0.000)

-3.149***

(0.002) 0.080

37.690***

(0.000)

CNX IT

CCM 1739 0.014

(0.299)

0.444***

(0.000)

0.142***

(0.000)

2.006***

(0.000)

7.07E-05***

(0.000) 0.355

238.134***

(0.000)

HLM 1701 0.679***

(0.000)

0.224***

(0.000)

0.222***

(0.000)

1.018

(0.423)

9.80E-05

(0.347) 0.133

65.159***

(0.000)

HWM 1738 0.001**

(0.027)

1.111***

(0.000)

-0.117***

(0.000)

0.004**

(0.015)

131E-07

(0.316) 0.993

63060***

(0.000)

Note: ** and *** Significant at the 5 % and 1 % levels respectively. (Source: Developed by Researcher).

148



Statistically significant Statistically insignificant

CCM HLM HWM TOTAL CCM HLM HWM TOTAL

+VE -VE +VE -VE +VE -VE +VE -VE +VE -VE +VE -VE +VE -VE +VE -VE

α 1 0 3 0 3 0 7 0 2 0 0 0 0 0 2 0

β1 3 0 3 0 3 0 9 0 0 0 0 0 0 0 0 0

β2 3 0 3 0 1 0 7 0 0 0 0 0 2 0 2 0

β 3 3 0 2 0 3 0 8 0 0 0 1 0 0 0 3 1

β4 1 1 0 1 0 2 1 4 0 1 2 0 1 0 3 1

F 3 3 3 9 0 0 0 0

149

Table 4.17 reports the results of regression Eq (13) for all the three stock index

futures. Table 4.17.1 summarizes number of stock index futures are statically

significant (positive & negative), and statistically insignificant (positive & negative)

for all the three futures pricing models respectively.

The Table 14.17 shows all the values of F are statistically significant at 1 % level.

Thus, it indicating that the given regression model explains major proportions of

variations in Absolute Percentage Error of pricing models for all the three stock index

futures.

As shown in the Tables 4.17 & 4.17.1, all the three stock index futures for CCM,

HLM & HWM, the coefficient of absolute percentage errors of 1 day lags (β1) is

positive and statistically significant at 1% level. This implies that there is a strong

impact of previous day’s mispricing on present day’s mispricing and suggests

persistent mispricing during the sample period for all the three futures markets. The

results of CCM and HLM are consistent with Hsu & Wang (2008)

As shown in the Tables 4.17 & 4.17.1, all the three stock index futures for CCM &

HLM, the coefficient of absolute percentage errors of 2 day lags (β2) is positive and

statistically significant. This evidence shows that there is a strong impact of previous

two day’s mispricing of CCM and HLM on present day’s mispricing of the same

models respectively. This evidence suggests persistent mispricing during the sample

period for all the three futures markets. This result consistent with Hsu & Wang

(2008).

Further, one index futures (CNX IT) for HWM, the coefficient of absolute percentage

errors of 2 day lags (β2) is negative and statistically significant at 1% level. It implies

that there is a strong negative impact of previous two day’s mispricing of HWM on

present day’s mispricing of the same model. Additionally, two stock index futures

(CNX Nifty & CNX IT) for HWM, the coefficient of absolute percentage errors of 2

day lags (β2) is positive and statistically insignificant. Overall, it implies that there is

no impact of previous two day’s mispricing of HWM on present day’s mispricing of

the same model.

150

The third explanatory factor is time to maturity. Tables 4.17 & 4.17.1 present that for

three stock index futures for CCM & HWM, two stock index futures for HLM (CNX

Nifty & Bank Nifty), the coefficient of time to maturity (β3) is positive and significant

at 1 % level. Altogether from all the three pricing models 8 out of 9 stock index

futures, β3 is found positive and significant. Thus, there is an impact of time to

maturity on absolute percentage error (APE) of stock index futures. This implies that

the absolute percentage error (APE) of stock index futures for all three pricing models

increases with time to expiry. Additionally the positive relationship indicates the time

to expiry of index & stocks futures contracts is strongly contribute pricing errors.

These results consistent with many previous studies Swati Bhatt & Nuset Cackici

(1990), Panayiotis and Pierides (April 2008), Fung & Draper (1999), Braisford and

Cusack (1997), Hsu &Wang (2009), Gay & Jung (1999), Yadav & Pope (1990).

Further, one index futures (CNX IT) for HLM, the coefficient of time to maturity (β3)

is positive and insignificant. It implies that there is no impact of time to maturity of

CNX IT index futures on Absolute Percentage Error of same model.

The fourth factor is index futures trading volume. Tables 4.17 & 4.17.1 present the

regression results of absolute percentage error and futures trading volume. The

coefficient of futures trading volume (β4) is positive and statistically significant at 1%

level for 1 index futures (CNX Nifty) for all the three futures pricing models (CCM,

HLM and HWM). It implies that there is an impact of futures trading volume on

Absolute Pricing Errors of all the three futures pricing models for same index.

Positive relationship indicates higher the trading volume of stock index futures, higher

will be the absolute pricing error.

Further, one index futures (CNX Nifty) for CCM, one index futures (CNX Nifty) for

HLM and two stock index futures (CNX Nifty & Bank Nifty) for HWM ,the

coefficient of futures trading volume (β4) is negative and significant at 1 % level. It

implies that there is a negative impact of futures trading volume of CNX Nifty index

futures on absolute percentage errors of CCM and HLM for the same index.

Similarly, there is a negative impact of futures trading volume of Bank Nifty index

futures on absolute percentage errors of HLM for the same index. The negative

relationship indicates higher the trading volume of stock index futures, lower will be

the absolute pricing errors.

151

Two stock index futures (Bank Nifty and CNX IT) for HLM and one index futures

(CNX IT) for HWM, the β4 is positive and insignificant. Additionally, one index

futures for CCM, the β4 is negative and insignificant. It implies that there is no impact

of trading volume of stock index futures on absolute percentage errors of pricing

models for respective stock index futures.

Overall, it implies that there are conflicting argument with respect to the nature of

relationship between trading volume and absolute percentage errors. The sign of the

coefficient of futures trading volume (β4) in the overall sample for stock index futures

gives the mixed results. These results are consistent across CCM, HLM & HWM for

stock index futures and difficult to interpret and conclude the nature of relationship

between trading volume and absolute percentage error. These results are consistent

with the previous studies Braisford and Cusack (1997), Hsu &Wang (2009).

152

Table 4.18: Impact of various factors on Absolute Percentage Errors of futures pricing models for individual stock futures.

Stock Futures Pricing

Models N Α β1 β2 β3 β4 R2 F

ACC

CCM 1739 -0.069*** (0.005)

0.612*** (0.000)

0.144*** (0.000)

3.754*** (0.000)

1.19E-05** (0.012)

0.582 604.206*** (0.000)

HLM 1701 -0.013

(0.587)

0.555***

(0.000)

0.143***

(0.000)

3.276***

(0.000)

8.67E-06*

(0.067) 0.501

426.531***

(0.000)

HWM 1738 0.071***

(0.001)

0.174***

(0.000)

0.141***

(0.000)

2.042***

(0.000)

1.92E-05***

(0.000)

0.103

49.820***

(0.000)

AMBUJA

CEMENTS

CCM 1739 -0.036 (0.210)

0.478***

(0.000)

0.198***

(0.000)

3.731***

(0.000)

2.20E-05**

(0.010) 0.440

340.541***

(0.000)

HLM 1701 0.031

(0.240)

0.396***

(0.000)

0.174***

(0.000)

3.989***

(0.000)

1.17E-05

(0.143) 0.338

216.125***

(0.000)

HWM 1738 0.093***

(0.000)

0.279***

(0.000)

0.058**

(0.014)

2.421***

(0.000)

2.15E-05***

(0.003) 0.125

61.612***

(0.000)

AXIS BANK

CCM 1739 -0.005

(0.822)

0.452***

(0.000)

0.216***

(0.000)

2.338***

(0.000)

2.37E-06**

(0.018) 0.404

294.026***

(0.000)

HLM 1701 0.032*

(0.089)

0.404***

(0.000)

0.206***

(0.000)

1.936***

(0.000)

2.47E-06***

(0.008) 0.335

213.694***

(0.000)

HWM 1738 0.120***

(0.000)

0.265***

(0.000)

0.104***

(0.000)

0.986***

(0.000)

1.60E-06*

(0.061) 0.107

51.807***

(0.000)

BANK OF

BARODA

CCM 1739 -0.014

(0.549)

0.614***

(0.000)

0.175***

(0.000)

3.060***

(0.000)

-4.8E-06

(0.281) 0.617

699.718***

(0.000)

HLM 1701 0.015

(0.529)

0.569***

(0.000)

0.172***

(0.000)

3.243***

(0.000)

-5.9E-06

(0.157) 0.565

549.664***

(0.000)

HWM 1738 0.157***

(0.000)

0.261***

(0.000)

0.060**

(0.011)

2.096***

(0.000)

-1.0E-05**

(0.012) 0.116 56.849***

(0.000)

BHARATHI

AIRTEL

CCM 1739 0.028** (0.037)

0.383*** (0.000)

0.235*** (0.000)

1.718*** (0.000)

1.56E-06* (0.055)

0.342 225.687*** (0.000)

HLM 1701 0.082***

(0.000)

0.473***

(0.000)

0.216***

(0.000)

1.156***

(0.000)

-5.5E-07

(0.527) 0.422

309.812***

(0.000)

153

HWM 1738 0.122***

(0.000)

0.156***

(0.000)

0.092***

(0.000)

1.054***

(0.000)

2.78E-06***

(0.000) 0.069

31.908***

(0.000)

BHEL

CCM 1739 -0.047* (0.075)

0.571*** (0.000)

0.156*** (0.000)

3.305*** (0.000)

3.54E-06** (0.036)

0.507 446.510*** (0.000)

HLM 1701 0.008

(0.734)

0.528***

(0.000)

0.132***

(0.000)

2.706***

(0.000)

2.6E-06*

(0.078) 0.415

300.781***

(0.000)

HWM 1738 0.085*** (0.000)

0.233*** (0.000)

0.038 (0.119)

2.191*** (0.000)

5.0E-06*** (0.000)

0.094 45.148*** (0.000)

BPCL

CCM 1739 0.023

(0.298)

0.456***

(0.000)

0.151***

(0.000)

2.699***

(0.000)

2.26E-06

(0.623) 0.350

233.221***

(0.000)

HLM 1701 0.052** (0.015)

0.423*** (0.000)

0.143*** (0.000)

2.752*** (0.000)

2.37E-06 (0.601)

0.324 203.660*** (0.000)

HWM 1738 0.086***

(0.000)

0.325***

(0.000)

0.034

(0.160)

2.355***

(0.000)

1.17E-07

(0.979) 0.148

75.358***

(0.000)

CARIN INDIA

CCM 1739 -0.005

(0.757)

0.449***

(0.000)

0.177***

(0.000)

2.708***

(0.000)

5.87E-06***

(0.004) 0.398

286.921***

(0.000)

HLM 1701 0.037**

(0.029)

0.437***

(0.000)

0.189***

(0.000)

2.065***

(0.000)

3.37E-06*

(0.095) 0.378

257.565***

(0.000)

HWM 1738 0.072***

(0.000)

0.242***

(0.000)

0.086***

(0.000)

1.519***

(0.000)

9.51E-06***

(0.000) 0.123

60.605***

(0.000)

CIPLA

CCM 1739 0.113***

(0.000)

0.296***

(0.000)

0.099***

(0.000)

1.2181***

(0.000)

-4.8E-06

(0.226) 0.134

66.992***

(0.000)

HLM 1701 0.140***

(0.000)

0.302***

(0.000)

0.096***

(0.000)

0.765***

(0.009)

2.20E-07

0.957 0.130

63.427***

(0.000)

HWM 1738 0.080***

(0.000)

0.410 ***

(0.000)

-0.068***

(0.004)

1.330***

(0.000)

8.81E-06**

(0.034) 0.167

86.856***

(0.000)

DRREDDY

CCM 1739 0.091***

(0.000)

0.318***

(0.000)

0.184***

(0.000)

1.644***

(0.000)

-8.6E-06***

(0.000) 0.211

116.171***

(0.000)

HLM 1701 0.129*** (0.000)

0.298*** (0.000)

0.160*** (0.000)

1.154*** (0.000)

-3.1E-06 (0.518)

0.170 86.663*** (0.000)

HWM 1738 0.126***

(0.000)

0.317***

(0.000)

0.034

(0.149)

1.351***

(0.000)

-1.0E-05**

(0.029) 0.135

67.532***

(0.000)

154

GAIL

CCM 1739 -0.024

(0.277)

0.515***

(0.000)

0.249***

(0.000)

2.673***

(0.000)

3.68E-06

(0.532) 0.556

542.724***

(0.000)

HLM 1701 -0.002 (0.720)

0.945*** (0.000)

0.032 (0.181)

-0.079 (0.329)

8.82E-06*** (0.000)

0.969 13420*** (0.000)

HWM 1738 0.057***

(0.002)

0.313***

(0.000)

0.103***

(0.000)

2.012***

(0.000)

1.56E-05***

(0.007) 0.178

93.596***

(0.000)

GRASIM

CCM 1739 -0.048** (0.022)

0.503*** (0.000)

0.203*** (0.000)

2.677*** (0.000)

3.34E-05*** (0.000)

0.490 415.692*** (0.000)

HLM 1701 -0.016

(0.437)

0.492***

(0.000)

0.185***

(0.000)

2.372***

(0.000)

3.19E-05***

(0.000) 0.460

361.371***

(0.000)

HWM 1738 0.414*** (0.000)

0.005 (0.892)

0.027 (0.439)

-0.749* (0.057)

-1.5E06 (0.886)

0.002 1.076 (0.367)

HCL

CCM 1739 0.003

(0.908)

0.627***

(0.000)

0.139***

(0.000)

2.209***

(0.000)

-5.9E07

(0.902) 0.561

554.194***

(0.000)

HLM 1701 0.042*

(0.077)

0.589***

(0.000)

0.134***

(0.000)

2.123***

(0.000)

-4.7E-06

(0.27) 0.505

432.144***

(0.000)

HWM 1738 0.119***

(0.000)

0.226***

(0.000)

0.186***

(0.000)

1.689***

(0.000)

-6.3E-06

(0.118) 0.135

68.894***

(0.000)

HDFC

CCM 1739 0.014

(0.399)

0.478 ***

(0.000)

0.210***

(0.000)

1.6829***

(0.000)

8.98E-07

(0.546) 0.428

324.645***

(0.000)

HLM 1701 0.053***

(0.000)

0.475***

(0.000)

0.199***

(0.000)

1.141***

(0.000)

2.73E-07

(0.850) 0.405

288.044***

(0.000)

HWM 1738 0.132***

(0.000)

0.217***

(0.000)

0.001

(0.963)

0.996***

(0.001)

1.36E-06

(0.308) 0.062

28.423***

(0.000)

HDFC BANK

CCM 1739 0.052**

(0.024)

0.453***

(0.000)

0.194***

(0.000)

-2.7E-

06***

(0.000)

-2.7E-06

(0.157) 0.393

280.167***

(0.000)

HLM 1701 0.088***

(0.000)

0.414***

(0.000)

0.181***

(0.000)

1.590***

(0.000)

-2.1E-06

(0.250) 0.325

204.027***

(0.000)

HWM 1738 0.132***

(0.000)

0.250***

(0.000)

0.107***

(0.000)

1.401***

(0.000)

-3.1E-06*

(0.053) 0.128 63.439***

(0.000)

155

HERO MOTOCORP

CCM 1739 -0.093***

(0.007)

0.675***

(0.000)

0.063***

(0.007)

5.655***

(0.000)

8.45E-06*

(0.069) 0.589

622.060***

(0.000)

HLM 1701 -0.021 (0.492)

0.638*** (0.000)

0.039 (0.104)

4.425*** (0.000)

9.81E-06** (0.015)

0.504 430.736*** (0.000)

HWM 1738 0.055*

(0.052)

0.250***

(0.000)

0.158***

(0.000)

3.397***

(0.000)

1.02E-05***

(0.000)

0.155

79.243***

(0.000)

HUL

CCM 1739 -0.020 (0.352)

0.541*** (0.000)

0.140*** (0.000)

3.307*** (0.000)

3.30E-06 (0.155)

0.480 400.732*** (0.000)

HLM 1701 0.013

(0.489)

0.452***

(0.000)

0.123***

(0.000)

3.242***

(0.000)

6.56E-06***

(0.002) 0.372

250.753***

(0.000)

HWM 1738 0.088*** (0.000)

0.231*** (0.000)

0.110*** (0.000)

1.981*** (0.000)

3.72E-06** (0.052)

0.117 57.319 (0.000)***

ICICI BANK

CCM 1739 -0.019

(0.287)

0.549***

(0.000)

0.225***

(0.000)

1.964***

(0.000)

5.17E-07

(0.289) 0.573

582.657***

(0.000)

HLM 1701 0.014

(0.391)

0.510***

(0.000)

0.230***

(0.000)

1.957***

(0.000)

-1.1E-07

(0.800) 0.541

489.919***

(0.000)

HWM 1738 0.098***

(0.000)

0.180***

(0.000)

0.004

(0.856)

1.641***

(0.000)

1.57E-06***

(0.000) 0.077

36.145***

(0.000)

IDFC

CCM 1739 -0.005

(0.725)

0.04***

(0.000)

0.265***

(0.000)

1.355***

(0.000)

2.98E-06***

(0.000) 0.537

503.370***

(0.000)

HLM 1701 0.635***

(0.000)

0.497***

(0.000)

0.243***

(0.000)

-3.667***

(0.000)

-9.5E-07

(0.695) 0.563

546.359***

(0.000)

HWM 1738 0.085*** (0.000)

0.168***

(0.000)

-0.007

(0.755)

1.751***

(0.000)

7.91E-06***

(0.000) 0.087 41.460***

(0.000)

INDALCO

CCM 1739 0.041**

(0.043)

0.401***

(0.000)

0.200***

(0.000)

1.244***

(0.000)

2.49E

(0.204) 0.296

181.949***

(0.000)

HLM 1701 0.094***

(0.000)

0.383***

(0.000)

0.194***

(0.000)

0.766**

(0.011)

1.04E-06

(0.611) 0.267

154.182***

(0.000)

HWM 1738 0.089***

(0.000)

0.333***

(0.000)

0.050**

(0.035)

1.210***

(0.000)

3.05E-06

(0.117) 0.140 70.671***

(0.000)

156

INFOSYS

CCM 1739 0.050**

(0.028)

0.480***

(0.000)

0.223***

(0.000)

2.465***

(0.000)

-2.0E-06**

(0.033) 0.464

375.740***

(0.000)

HLM 1701 0.041* (0.063)

0.461*** (0.000)

0.232*** (0.000)

2.492*** (0.000)

-7.3E-07 (0.425)

0.446 341.126*** (0.000)

HWM 1738 0.124***

(0.000)

0.342***

(0.000)

0.124***

(0.000)

1.568***

(0.000)

-2.7E-06***

(0.002) 0.204

110.968***

(0.000)

ITC

CCM 1739 -0.038* (0.077)

0.596*** (0.000)

0.173*** (0.000)

2.386*** (0.000)

3.31E-06 (0.209)

0.582 604.613*** (0.000)

HLM 1701 -0.008

(0.718)

0.545***

(0.000)

0.192***

(0.000)

2.072***

(0.000)

4.44E-06*

(0.090) 0.536

488.852***

(0.000)

HWM 1738 0.067*** (0.001)

0.233*** (0.000)

0.062*** (0.000)

2.146*** (0.009)

5.47E-06*** (0.027)

0.103 49.785*** (0.000)

JINDAL STEEL

CCM 1739 0.085***

(0.000)

0.378***

(0.000)

0.103***

(0.000)

0.749***

(0.004)

1.69E-06

(0.470) 0.190

101.651***

(0.000)

HLM 1701 0.066***

(0.000)

0.440***

(0.000)

0.164***

(0.000)

1.849***

(0.000)

-5.3E-07

(0.8360 0.345

223.008***

(0.000)

HWM 1738 0.091***

(0.000)

0.380***

(0.000)

0.020

(0.410)

1.3112***

(0.000)

5.12E-07

(0.832) 0.170

89.040***

(0.000)

JP ASSOCIAT

CCM 1739 0.054*

(0.000)

0.374***

(0.000)

0.223***

(0.000)

1.143***

(0.000)

7.83E-07***

(0.000) 0.293

179.764

(0.422)

HLM 1701 0.801***

(0.000)

0.402***

(0.000)

0.234***

(0.000)

-3.910***

(0.000)

2.69E-06***

(0.048) 0.445

339.490***

(0.000)

HWM 1738 0.101***

(0.000)

0.170***

(0.000)

0.020

(0.394)

1.869***

(0.000)

2.84E-06***

(0.004) 0.089 42.274***

(0.000)

KOTAK BANK

CCM 1739 0.042**

(0.025)

0.261***

(0.000)

0.156***

(0.000)

2.051***

(0.000)

4.55E-06***

(0.000) 0.174

91.113***

(0.000)

HLM 1701 0.087***

(0.000)

0.223***

(0.000)

0.127***

(0.000)

1.299***

(0.000)

5.51E-06***

(0.000) 0.125

60.708***

(0.000)

HWM 1738 0.60*** (0.001)

0.285***

(0.000)

0.025

(0.297)

1.705***

(0.000)

5.77E-06***

(0.000) 0.135

67.888***

(0.000)

157

L & T

CCM 1739 0.094

(0.308)

0.010

(0.682)

0.004

(0.864)

4.472***

(0.002)

3.17E-06

(0.428) 0.006

2.544**

(0.038)

HLM 1701 0.064*** (0.005)

0.346*** (0.000)

0.233*** (0.000)

1.389*** (0.000)

1.46E-06 (0.131)

0.268 154.870 (0.000)***

HWM 1738 0.066***

(0.003)

0.414***

(0.000)

-0.120***

(0.000)

1.454***

(0.000)

4.03E-06***

(0.000) 0.171

89.163***

(0.000)

LUPIN

CCM 1739 0.031 (0.182)

0.455*** (0.000)

0.253*** (0.000)

2.300*** (0.000)

-1.1E-05* (0.069)

0.445 348.210 (0.000)***

HLM 1701 0.090***

(0.000)

0.400***

(0.000)

0.203***

(0.000)

2.313***

(0.000)

-1.2E-05**

(0.042) 0.334

213.055

(0.000)***

HWM 1738 0.116*** (0.000)

0.333*** (0.000)

0.121*** (0.000)

1.578*** (0.000)

-1.1E-05*** (0.035)

0.428 97.387 (0.000)***

M&M

CCM 1739 0.042*

(0.092)

0.384***

(0.000)

0.223***

(0.000)

2.733***

(0.000)

-4.8E-06

(0.156) 0.332

215.596

(0.000)***

HLM 1701 0.84***

(0.000)

0.327***

(0.000)

0.185***

(0.000)

2.929***

(0.000)

-5.9E-06*

(0.069) 0.260

149.349

(0.000)***

HWM 1738 0.171***

(0.000)

0.364***

(0.000)

-0.069***

(0.004)

1.763***

(0.000)

-1.0E-05***

(0.002) 0.147

74.644)***

(0.000

MARUTHI

CCM 1739 -0.011

(0.666)

0.439***

(0.000)

0.209***

(0.000)

3.443***

(0.000)

3.89E-06

(0.168) 0.401

290.770

(0.000)***

HLM 1701 0.054**

(0.020)

0.360***

(0.000)

0.185***

(0.000)

2.892***

(0.000)

2.4E-06

(0.344) 0.281

166.117

(0.000)***

HWM 1738 0.119*** (0.000)

0.302***

(0.000)

0.092***

(0.000)

1.366***

(0.000)

1.45E-06

(0.537) 0.132 65.838

(0.000)***

ONGC

CCM 1739

-0.077***

(0.001)

0.574***

(0.000)

0.172***

(0.000)

3.564***

(0.000)

7.55E-06***

(0.001) 0.575

586.618

(0.000)***

HLM 1701 -0.061***

(0.007)

0.506***

(0.000)

0.178***

(0.000)

4.244***

(0.000)

6.75E-06***

(0.002)

0.525

467.705

(0.000)***

HWM 1738 0.024

(0.242)

0.208***

(0.000)

0.019

(0.433)

2.467***

(0.000)

1.55E-05***

(0.000) 0.122 60.379

(0.000)***

158

PNB

CCM 1739 0.162*

(0.071)

0.091***

(0.000)

0.074***

(0.002)

7.198***

(0.000)

-5.4E-06

(0.699) 0.032

14.163

(0.000)***

HLM 1701 0.156* (0.084)

0.101*** (0.000)

0.080*** (0.001)

7.531*** (0.000)

4.66E-06 (0.737)

0.037 16.411 (0.000)***

HWM 1738 0.103***

(0.000)

0.244***

(0.000)

0.043*

(0.071)

2.607***

(0.000)

1.72E-06

(0.626) 0.105

51.095

(0.000)***

RANBAXY

CCM 1739 -0.008 (0.859)

0.851*** (0.000)

-0.049** (0.040)

0.034** (0.016)

-0.004 (0.779)

0.662 849.441 (0.000)***

HLM 1701 0.003

(0.949)

0.849***

(0.000)

-0.050**

(0.038)

2.180***

(0.008)

-3.0E-06

(0.543) 0.661

825.631

(0.000)***

HWM 1738 0.086**

(0.043)

0.037 (0.118)

0.180*** (0.000)

2.827*** (0.000)

9.88E-08 (0.983) 0.044

20.086 (0.000)***

RELIANCE

CCM 1739 0.010

(0.298)

0.423***

(0.000)

0.240***

(0.000)

1.398***

(0.000)

2.53E-07

(0.063) 0.411

302.586

(0.000)***

HLM 1701 0.068***

(0.000)

0.446***

(0.000)

0.207***

(0.000)

0.511***

(0.005)

1.17E-07

(0.427) 0.372

250.849

(0.000)***

HWM 1738 0.074***

(0.000)

0.041*

(0.080)

-0.058**

(0.013)

1.967***

(0.000)

1.28E-06***

(0.000) 0.113 55.053

(0.000)***

SBI

CCM 1739 -0.016 (0.463)

0.472*** (0.000)

0.208*** (0.000)

2.642*** (0.000)

5.78E-07 (0.239)

0.445 347.463 (0.000)***

HLM 1701 0.009

(0.644)

0.433***

(0.000)

0.166***

(0.000)

2.684***

(0.000)

8.09E-07*

(0.075) 0.379

258.677

(0.000)***

HWM 1738 0.059*** (0.002)

0.210*** (0.000)

0.055** (0.020)

2.143*** (0.000)

1.34E-06*** (0.001) 0.108

52.249 (0.000)***

SUNPHARMA

CCM 1739 0.089***

(0.000)

0.322***

(0.000)

0.224***

(0.000)

1.677***

(0.000)

-1.0E-05***

(0.040) 0.247

141.978

(0.000)***

HLM 1701 0.137***

(0.000)

0.306***

(0.000)

0.192***

(0.000)

1.039***

(0.002)

-8.2E-06

(0.100) 0.193

101.483

(0.000)***

HWM 1738 0.140***

(0.000)

0.396***

(0.000)

-0.018

(0.452)

1.130***

(0.001)

-8.5E-06*

(0.098) 0.164 85.032

(0.000)***

159

TATA MOTORS

CCM 1739 0.015

(0.625)

0.577***

(0.000)

0.156***

(0.000)

4.287***

(0.000)

-3.8E-06***

(0.007) 0.556

543.141

(0.000)***

HLM 1701 0.110*** (0.000)

0.476*** (0.000)

0.164*** (0.000)

3.168*** (0.000)

-4.0E-06*** (0.001)

0.412 297.240 (0.000)***

HWM 1738 0.130***

(0.000)

0.237***

(0.000)

0.160***

(0.000)

2.585***

(0.000)

-2.0E-06*

(0.079) 0.147 74.852

(0.000)***

TATA POWER

CCM 1739 0.061***

(0.002)

0.464***

(0.000)

0.251***

(0.000)

0.440

(0.201)

1.31E-05***

(0.005) 0.444

346.317

(0.000)***

HLM 1701 0.081***

(0.000)

0.445***

(0.000)

0.210***

(0.000)

0.839**

(0.011)

8.26E-06*

(0.059) 0.376

254.967

(0.000)***

HWM 1738 0.079***

(0.000)

0.251*** (0.000)

0.062*** (0.009)

1.515*** (0.000)

2.98E-05*** (0.000) 0.132

65.709 (0.000)***

TATA STEEL

CCM 1739 -0.073***

(0.009)

0.522***

(0.000)

0.207***

(0.000)

3.222***

(0.000)

2.60E-06***

(0.026) 0.526

481.494

(0.000)***

HLM 1701 0.10

(0.723)

0.497***

(0.000)

0.203***

(0.000)

3.126***

(0.000)

-3.4E-05

(0.482) 0.504

430.917

(0.000)***

HWM 1738 0.112***

(0.000)

0.224***

(0.000)

-0.031

(0.198)

2.383***

(0.000)

3.2E-05

(0.485) 0.086 40.932

(0.000)***

TCS

CCM 1739 0.013

(0.466)

0.436***

(0.000)

0.205***

(0.000)

2.153***

(0.000)

1.2E-06

(0.363) 0.382

267.993

(0.000)***

HLM 1701 0.082***

(0.000)

0.405***

(0.000)

0.188***

(0.000)

1.318***

(0.000)

-3.0E-08

(0.982) 0.311

191.712

(0.000)***

HWM 1738 0.102***

(0.000)

0.260***

(0.000)

-0.022

(0.346)

1.660***

(0.000)

9.05E-07

(0.473) 0.098 47.228

(0.000)***

ULTRACEMCO

CCM 1739 0.153***

(0.000)

0.232***

(0.000)

0.121***

(0.000)

2.298***

(0.000)

-1.4E-06

(0.917) 0.104

50.157

(0.000)***

HLM 1701 0.208***

(0.000)

0.177***

(0.000)

0.093***

(0.000)

1.857***

(0.000)

-8.5E-06

(0.524) 0.062

28.104

(0.000)***

HWM 1738 0.200***

(0.000)

0.528***

(0.000)

-0.153***

(0.000)

0.770

(0.110)

-2.0E-05

(0.159) 0.234

132.004

(0.000)***

160

WIPRO

CCM 1739 0.019

(0.392)

0.580***

(0.000)

0.171***

(0.000)

1.681***

(0.000)

-2.7E-07

(0.952) 0.523

474.604

(0.000)***

HLM 1701 0.038* (0.093)

0.536*** (0.000)

0.171*** (0.000)

1.722*** (0.000)

8.78E-07 (0.842)

0.462 364.248 (0.000)***

HWM 1738 0.079***

(0.000)

0.300***

(0.000)

0.123***

(0.000)

1.537***

(0.000)

4.44E-06

(0.244) 0.157

80.807

(0.000)***

Note: *, **, and *** Significant at the 10%, 5% and 1 % levels respectively. (Source: Developed by Researcher).


Statistically significant Statistically insignificant

CCM HLM HWM TOTAL CCM HLM HWM TOTAL

+VE -VE +VE -VE +VE -VE +VE -VE +VE -VE +VE -VE +VE -VE +VE -VE

Α 14 7 27 1 40 0 81 8 9 11 8 5 1 0 18 16

β1 40 0 41 0 39 0 120 0 1 0 0 0 2 0 3 0

β2 39 1 38 1 23 04 101 06 1 0 2 0 10 4 13 4

β3 39 1 38 2 39 1 116 4 1 0 0 1 1 0 2 1

β4 14 05 16 03 20 08 50 16 13 09 8 14 10 3 31 26

F 40 41 40 121 01 00 01 02


161

Table 4.18 reports the results of regression Eq (13) for all the 41 individual stock

futures. Table 4.18.1 summarizes the number of individual stocks, which are statically

significant (positive & negative), and statistically insignificant (positive & negative)

for all the three futures pricing models respectively.

The Table 14.18 shows, all the values of ‘F’ are statistically significant at 1 % level.

Thus, it indicates that the given regression model explains major proportions of

variations in Absolute Percentage Error of pricing models for all the 41individual

stock futures.

As shown in the Tables 4.18 and 4.18.1, 40 individual stock futures for CCM , all the

41 individual stock futures for HLM and 39 individual stock futures for HWM, the

coefficient of absolute percentage errors of 1 day lags (β1) is positive and statistically

significant. This implies that there is a strong impact of previous day’s mispricing on

present day’s mispricing and indicates persistent mispricing during the sample period

for respective individual stock futures.

Further one stock futures (L&T) for CCM & two stock futures (Ranbaxy

Laboratories and Grasim Industries) for HWM, the coefficient of absolute percentage

errors of 1 day lags (β1) is positive and statistically insignificant. This implies that

there is no impact of previous day’s mispricing on present day’s mispricing of

respective individual stock futures and pricing models.

To summarize, From all the three pricing models altogether 120 out of 123 stock

futures, the coefficient of absolute percentage errors of 1 day lags (β1) is found

positive and significant. This implies that there is a strong impact of previous day’s

mispricing on present day’s mispricing and indicates persistent mispricing during the

sample period for stock futures.

As shown in the Tables 4.18 and 4.18.1, 39 stock futures for CCM, 38 stock futures

for HLM, and 18 stock futures for HWM, the coefficient of absolute percentage errors

of 2 day lags (β2) is positive and statistically significant at 1% level. Additionally,

four stock futures (Ambuja Cements, Bank of Baroda, Indalco Industries and SBI)

and one stock futures (PNB) for HWM, the coefficient of absolute percentage errors

of 2 day lags (β2) is positive and statistically significant at 5% and 10% level

respectively. This implies that there is a strong impact of previous day’s mispricing on

162

present day’s mispricing and indicates persistent mispricing during the sample period

for respective individual stock futures.

Further, 1 stock futures (Ranbaxy Laboratories) for CCM, one stock futures (Ranbaxy

Laboratories) for HLM and 4 stock futures (Cipla, Larsen & Toubro, M&M and

UltraTech Cement ) for HWM, the coefficient of absolute percentage errors of 2 day

lags (β2) is negative and statistically significant at 1% level . Additionally, one stock

futures (Reliance Industries) for HWM the coefficient of absolute percentage errors of

2 day lags (β2) positive and significant at 5% level. It implies negative impact of

previous two day’s mispricing on present day’s mispricing of the respective models

and stock futures.

One stock futures (Larsen & Toubro) for CCM , 2 stock futures for HLM (GAIL &

Hero MotoCorp) and 10 stock futures( BHEL, BPCL, Dr. Reddy's Laboratories,

Grasim Industries, HDFC, ICICI, Jindal Steel, J P Associates, Kotak Bank and

ONGC, for HWM, the coefficient of absolute percentage errors of 2 day lags (β2) is

positive and statistically insignificant. Additionally, four stock futures (IDFC, Sun

Pharmaceutical Industries, Tata steel and TCS), the coefficient of absolute percentage

errors of 2 day lags (β2) is negative and statistically insignificant. This implies that

there is no impact of previous day’s mispricing on present day’s mispricing of

respective individual stock futures and pricing models.

To summarize, from two pricing models (CCM & HLM) altogether 77 out of 82 stock

futures, β2 is found positive and significant. It implies that there is a strong impact of

previous two day’s mispricing of CCM and HLM on present day’s mispricing of

stock futures. This evidence suggests persistent mispricing during the sample period

for individual stock futures. Further, for the HWM which has developed under the

assumption of imperfect market and provides the best pricing performance, β2 is

found positively significant for 23 stock futures, negatively significant for 4 stocks

and insignificant for 14 stocks. Overall, it implies that there are conflicting argument

with respect to the nature of relationship between absolute percentage errors of 2 day

lags and absolute percentage errors. The sign of the coefficient of absolute percentage

errors of 2 day lags (β2) in the overall sample of HWM gives the mixed result and

difficult to interpret and conclude whether previous two day’s mispricing of HWM

impact on present day’s mispricing of stock futures.

The third explanatory factor is time to maturity. As shown in the Tables 4.18 and

4.18.1, 38 stock futures for CCM, 37 stock futures for HLM and 39 stock futures for

163

HWM, the coefficient of time to maturity (β3) is positive and significant at 1 % level.

Additionally, one stock futures (Ranbaxy Laboratories) and one stock futures (Indalco

Industries), the coefficient of time to maturity (β3) is positive and significant at 5 %

level. This implies that the Absolute Percentage Errors (APE) of individual stock

futures for all three pricing models increases with time to expiry. Additionally the

positive relationship indicates that time to expiry of stocks futures contracts is

strongly contribute pricing errors.

Further 1 stock futures (HDFC) for CCM and 2 stock futures (IDFC & JP Associates)

for HLM, the coefficient of time to maturity (β3) is negative and significant at 1 %

level. Additionally, one stock futures (Grasim Industries) for HWM, the coefficient of

time to maturity (β3) is negative and significant at 10 % level. It implies that there is a

negative impact of time to maturity on Absolute Percentage Error (APE) of stock

futures. Additionally, negative relationship indicates longer the time to expiry of stock

futures lesser the absolute percentage errors of the future stocks.

Further, one stock futures (Tata Power) for CCM and one stock futures (UltraTech

Cement) for HWM, the coefficient of time to maturity (β3) is positive and

insignificant. Additionally only one stock futures (GAIL), the coefficient of time to

maturity (β3) is negative and insignificant. It implies that, there is no impact of time to

maturity of these stock futures on Absolute Percentage Errors (APE) of the stock

futures.

To summarize, altogether from all the three pricing models 116 out of 123 individual

stock futures , the coefficient of time to maturity (β3) is found positive and significant.

Thus, there is an impact of time to maturity on absolute percentage error (APE) of

individual stock futures. Due to uncertainty in dividend payment, market volatility

and arbitrage opportunity, absolute percentage errors (APE) increase with the time to

maturity.

The fourth factor is futures trading volume. As shown in the above table 4.18 and

4.18.1, the regression results of Absolute Percentage Errors (APE) and futures trading

volume. The coefficient of futures trading volume (β4) is positive and statistically

significant at 1% level for 14 stock futures for CCM, 16 stock futures for HLM and

20 stock futures for HWM. It implies that there is an impact of futures trading volume

on Absolute pricing Errors individual stock futures. Positive relationship indicates

164

higher the trading volume of individual stock futures, higher will be the absolute

pricing error.

The coefficient of futures trading volume (β4) is negative and significant for 5 stock

futures for CCM, 3 stock futures for HLM and 8 stock futures for HWM. It implies

that there is a negative impact of futures trading volume of these individual stock

futures and absolute percentage errors of three models. The negative relationship

indicates higher the trading volume of individual stock futures, lower will be the

Absolute Percentage Errors (APE).

β4 is positive and insignificant for 13 stock futures for CCM , 8 stock futures for HLM

and 10 stock futures for HWM. Additionally, β4 is negative and insignificant for 9

stock futures for CCM, 14 stock futures for HLM and 3 stock futures for HWM. It

implies that there is no significant impact of trading volume of individual stock

futures and absolute percentage errors of pricing models for the respective stock

futures.

To summarize, altogether from all the pricing models 50 out of 123 stock futures β4 is

found positive and significant. Further, altogether 16 out of 123 stock futures, (β4) is

found negative and insignificant. Additionally, 57 out of 123 stock futures, β4 is found

insignificant. Overall the results imply that there are conflicting argument with respect

to the nature of relationship between trading volume and absolute percentage errors.

The sign of the coefficient of futures trading volume (β4) in the overall sample for

stock futures gives the mixed results and difficult to interpret and conclude the nature

of relationship between trading volume and absolute percentage error.

`

165

4.7 Percentage Pricing Errors Charts

Figures plot the percentage errors of Cost of Carry Model, Hemler & Longstaff Model

and Hsu & Wang Model for CNX Nifty index futures, Bank Nifty index futures and

CNX IT index futures respectively.

4.7.1 Percentage Pricing Errors Charts for all the three stock index futures

Figure: 4.1 Percentage pricing errors of CCM, HLM & HWM for CNX Nifty

Index futures


Fig .4.1 clearly shows that percentage errors of the Hemler and Longstaff model much

higher than the cost of carry model and Hsu & Wang model for CNX Nifty futures

index. Additionally, it shows that percentage errors of CCM slightly higher than the

Hsu & Wang model. Further, it can be observed from the Fig.4.1 that the pricing

errors are higher during the beginning of the sample period compared to rest of the

sampling period.

Figure: 4.2 Percentage pricing errors of CCM, HLM & HWM for Bank Nifty

Index futures


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2-Apr-07 25-Aug-08 18-Jan-10 13-Jun-11 5-Nov-12 31-Mar-14

Pe

rce

nta

ge E

rro

r

CNX Nifty Index futures

CCM HLM HWM

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

Bank Nifty Index futures

CCM HLM HWM

166

Fig.4.2 clearly shows that percentage errors of the HLM much higher than the CCM

and HWM for Bank Nifty futures index. Additionally, it shows that percentage errors

of CCM slightly higher than the HWM. Further, it can be observed from the Fig.4.2

that the pricing errors of CCM and HLM are overpriced and HWM under-priced.

Percentage errors of HLM are higher in magnitude than other two models and lightly

cyclical in nature.

Figure: 4.3 Percentage pricing errors of CCM, HLM & HWM for CNX IT index

futures



and HWM for CNX IT futures index. Additionally, Fig.4.3 shows that percentage

errors of HLM for CNX IT futures market during 2008-09 are higher in magnitude

than other two models.

4.7.2 Percentage pricing errors of CCM, HLM & HWM for Individual stock

futures

Figure: 4.4 Percentage pricing errors of CCM, HLM & HWM for ACC


-8

-3

2

7


Pe

rce

nta

ge E

rro

r

CNX IT index futures

CCM HLM HWM

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5


Pe

rce

nta

ge E

rro

r

ACC

CCM HLM HWM

167


and HWM for ACC. Additionally, it shows that percentage errors of CCM are slightly

higher than the HWM. Further, it can be observed from the Fig.4.4 that the pricing

errors of all the three pricing models are overpriced.

Figure: 4.5 Percentage pricing errors of CCM, HLM & HWM for Ambuja

Cements


Fig 4.5 clearly shows that percentage errors of the HLM are much higher than the

CCM and HWM for Ambuja Cements. Additionally, it shows that percentage errors

of CCM are slightly higher than the HWM. Further, it can be observed from the

Fig.4.5 that the pricing errors of CCM & HWM are overpriced and the pricing errors

of HLM are under-priced.

Figure: 4.6 Percentage pricing errors of CCM, HLM & HWM for Bank of

Baroda


-5

-4

-3

-2

-1

0

1

2


Pe

rce

nta

ge E

rro

r

Ambuja Cements

CCM HLM HWM

-6

-5

-4

-3

-2

-1

0

1

2

3


Pe

rce

nta

ge E

rro

r

Bank of Baroda

CCM HLM HWM

168


and HWM for Bank of Baroda. Further, it can be observed from the Fig.4.6 that the

pricing errors of HLM & HWM are overpriced and the pricing errors of CCM are

under-priced.

Figure: 4.7 Percentage pricing errors of CCM, HLM & HWM for Axis Bank



and HWM for Axis Bank. Further, it can be observed from the Fig.4.7 that the pricing

errors of CCM & HLM are overpriced and the pricing errors of HWM are under-

priced

Figure: 4.8 Percentage pricing errors of CCM, HLM & HWM for Bharathi

Airtel



and HWM for Bharathi Airtel. Additionally, it shows that percentage errors of CCM

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

Axis Bank

CCM HLM HWM

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

Bharathi Airtel

CCM HLM HWM

169

are slightly higher than the HWM. Further, it can be observed from the Fig.4.8 that

the percentage errors of HLM are higher in magnitude than other two models and

cyclical in nature.

Figure: 4. 9 Percentage pricing errors of CCM, HLM & HWM for BHEL


Fig .4.9 clearly shows that percentage errors of the HLM much higher than the CCM

and HWM for BHEL. Further, it can be observed from the Fig.4.9 that the pricing

errors of all the three pricing models are overpriced. The pricing errors are higher

during end of the sample period compared to rest of the sampling period.

Figure: 4.10 Percentage pricing errors of CCM, HLM & HWM for BPCL


-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5


Pe

rce

nta

ge E

rro

r

BHEL

CCM HLM HWM

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r

BPCL

CCM HLM HWM

170

Fig .4.10 clearly shows that percentage errors of the HLM much higher than CCM

and HWM for BPCL. The pricing errors are higher during the beginning of the

sample period compared to rest of the sampling period. Further, it can be observed

from the Fig.4.10 that the pricing errors of CCM & HLM are overpriced and the

pricing errors of HWM are under-priced.

Figure: 4.11 Percentage pricing errors of CCM, HLM & HWM for Carin India



and HWM for Carin India. The pricing errors are lower during the middle of the

sample period compared to rest of the sampling period. Further, it can be observed

from the Fig.4.11 that the pricing errors of HLM & HWM are overpriced and the

pricing errors of HWM are under-priced.

Figure: 4.12 Percentage pricing errors of CCM, HLM & HWM for Cipla


-2.5 -2

-1.5 -1

-0.5 0

0.5 1

1.5 2


Pe

rce

nta

ge E

rro

r

Carin India

CCM HLM HWM

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

Cipla

CCM HLM HWM

171


and HWM for Cipla. Further, it can be observed from the Fig.4.12 that pricing errors

of all the pricing models are lower in magnitude and under-priced.

Figure: 4.13 Percentage pricing errors of CCM, HLM & HWM for Dr. Reddy's

Laboratories



and HWM for Dr. Reddy’s Laboratories. Further, it can be observed from the Fig.4.13

that pricing errors of all the pricing models are lower in magnitude.

Figure: 4.14 Percentage pricing errors of CCM, HLM & HWM for GAIL


Fig.4.14 clearly shows that percentage errors of the HLM much higher than CCM and

HWM for GAIL. Additionally, it shows that percentage errors of CCM are higher

than HWM. Further, it can be observed from the Fig.4.14 that the percentage errors of

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Pe

rce

nta

ge E

rro

r

Dr. Reddy's Laboratories

CCM HLM HWM

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2 2.5

3


Pe

rce

nta

ge E

rro

r

GAIL

CCM HLM HWM

172

HLM are higher in magnitude than other two models and cyclical in nature. The

pricing errors of HWM are in lower magnitude compared to other two models.

Figure: 4.15 Percentage pricing errors of CCM, HLM & HWM for Grasim

Industries


Fig.4.15 clearly shows that percentage errors of the HLM are much higher than the

CCM and HWM for Grasim Industries. Further, it can be observed from the Fig.4.15

that pricing errors of HLM are overpriced and pricing errors of HWM are under-

priced. The pricing errors of HWM are in lower magnitude compared to other two

models.

Figure: 4.16 Percentage pricing errors of CCM, HLM & HWM for HCL

Technologies



and HWM for HCL Technologies. Additionally, it shows that percentage errors of

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5


Pe

rce

nta

ge E

rro

r

Grasim Industries

CCM HLM HWM

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2 2.5


Pe

rce

nta

ge E

rro

r

HCL Technologies

CCM HLM HWM

173

CCM higher than the HWM. Further, it can be observed from the Fig.4.16 that the

percentage errors of HLM & HWM under-prices and percentage errors of CCM

overprices. The pricing errors are higher during the beginning of the sample period

compared to rest of the sampling period.

Figure: 4.17 Percentage pricing errors of CCM, HLM & HWM for HDFC Bank



and HWM for HDFC Bank. Further, it can be observed from the Fig.4.17 that the

percentage errors of HWM are in lower magnitude compared to other two models.

Figure: 4.18 Percentage pricing errors of CCM, HLM & HWM for HDFC



and HWM for HDFC. Further, it can be observed from the Fig.4.18 that the

percentage errors of HWM are in lower magnitude compared to other two models.

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r

HDFC Bank

CCM HLM HWM

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

HDFC

CCM HLM HWM

174

Figure: 4.19 Percentage pricing errors of CCM, HLM & HWM for Hero

MotoCorp


Fig.4.19 clearly shows that percentage errors of the CCM much higher than the HLM

& HWM for Hero MotoCorp. Additionally, it shows that percentage errors of HLM

higher than the HWM. Further, it can be observed from the Fig.4.19 that the

percentage errors of HLM and CCM are very higher in magnitude compared to

pricing errors of HWM and the pricing errors of HWM are lowest compared to other

two models. Pricing errors of HLM are under-priced.

Figure: 4.20 Percentage pricing errors of CCM, HLM & HWM for Hindalco



and HWM for Hindalco Industries. Further, it can be observed from the Fig.4.20 that

the percentage errors of HWM are lowest compared to other two models. Pricing

errors of HLM are under-priced.

-6 -5.5

-5 -4.5

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2 2.5

3


Pe

rce

nta

ge E

rro

r

Hero MotoCorp

CCM HLM HWM

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r

Hindalco

CCM HLM HWM

175

Figure: 4.21 Percentage pricing errors of CCM, HLM & HWM for HUL



CCM and HWM for HUL. Further, it can be observed from the Fig.4.21 that the

percentage errors of HWM are lowest compared to other two models, pricing errors of

HLM are under-priced.

Figure: 4.22 Percentage pricing errors of CCM, HLM & HWM for ICICI Bank



and HLM for ICICI Bank. Further, it can be observed from the Fig.4.22 that the

percentage errors of all the pricing models are in lower magnitude and the percentage

errors of HWM are lowest compared to other two models.

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r HUL

CCM HLM HWM

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r

ICICI Bank

CCM HLM HWM

176

Figure: 4.23 Percentage pricing errors of CCM, HLM & HWM for IDFC



CCM and HWM for IDFC. Further, it can be observed from the Fig.4.23 that the

percentage errors of HLM are higher in magnitude and completely overpriced. The

pricing errors of HLM are much deviates compared to pricing errors of CCM and

HWM and can be seen separate layer in Fig. 4.23

Figure: 4.24 Percentage pricing errors of CCM, HLM & HWM for Infosys


Fig.4.24 clearly shows that percentage errors of the HLM and CCM are much higher

than the HWM for Infosys. Fig.4.24 shows the percentage errors of HLM & HWM

are under-priced and percentage errors of CCM are overpriced. It also observed from

the fig that percentage pricing errors are higher in magnitude during the year 2010-11

compared to rest of the sample period and the percentage errors of HWM are lowest

compared to other two models.

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r

IDFC

CCM HLM HWM

-4

-3

-2

-1

0

1

2

3

4


Pe

rce

nta

ge E

rro

r

Infosys

CCM HLM HWM

177

Figure: 4.25 Percentage pricing errors of CCM, HLM & HWM for ITC



CCM and HWM for ITC. It also observed from the Fig.4.25 that the percentage errors

of HWM are lowest compared to other two models.

Figure: 4.26 Percentage pricing errors of CCM, HLM & HWM for Jindal Steel



CCM and HWM for Jindal Steel. Further, the percentage pricing errors of all the

models are under-priced. It also observed from the Fig.4.26 that the percentage errors

of HWM are lowest compared to other two models. Additionally, it can be observed

from the Fig.4.26 that pricing errors of all the pricing models are lower in magnitude.

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2 2.5

3


Pe

rce

nta

ge E

rro

r ITC

CCM HLM HWM

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Pe

rce

nta

ge E

rro

r

Jindal Steel

CCM HLM HWM

178

Figure: 4.27 Percentage pricing errors of CCM, HLM & HWM for Jaiprakash

Associates


Fig.4.27 clearly shows that percentage errors of the HLM are much higher the than

CCM and HWM for Jaiprakash Associates. Further, it can be observed from the

Fig.4.27 that the percentage errors of HLM are higher in magnitude and completely

overpriced. The pricing errors of HLM are much deviates compared to pricing errors

of CCM and HWM and can be seen separate layer in Fig.4.27.

Figure: 4.28 Percentage pricing errors of CCM, HLM & HWM for Kotak Bank

(Source Developed by Researcher)


CCM and HWM for Kotak Bank. It also observed from the Fig.28 that the Percentage


-3.5

-2.5

-1.5

-0.5

0.5

1.5


Pe

rce

nta

ge E

rro

r Jaiprakash Associates

CCM HLM HWM

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Pe

rce

nta

ge E

rro

r

Kotak Bank

CCM HLM HWM

179

Figure: 4.29 Percentage pricing errors of CCM, HLM & HWM for L& T


Fig.4.29 clearly shows that percentage errors of the HLM are much higher than CCM

and HWM for L&T. It also observed from the Fig.4.29 that the percentage errors

HWM are lowest compared to other two models. Additionally, it can be observed

from the Fig.4.29 that pricing errors of all the pricing models are lower in magnitude.

Figure: 4.30 Percentage pricing errors of CCM, HLM & HWM for Lupin



HWM and CCM for Lupin. Fig.4.30 shows the percentage errors of HLM & HWM

are under - priced and percentage errors of CCM are overpriced. It also observed from

the Fig.4.30 that percentage pricing errors are higher in magnitude during the years

2007-08 to 2009-10 compared to rest of the sample period and the percentage errors

of HWM are lowest compared to other two models.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5


Pe

rce

nta

ge E

rro

r L&T

CCM HLM HWM

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5


Pe

rce

nta

ge E

rro

r

Lupin

CCM HLM HWM

180

Figure: 4.31 Percentage pricing errors of CCM, HLM & HWM for M&M



CCM and HWM for M&M. It also observed from the Fig.4.31 that the percentage

pricing errors of CCM & HLM overprices and pricing errors of HWM are under-

priced. Additionally, pricing errors of HWM are lowest compared to other two

models.

Figure: 4.32 Percentage pricing errors of CCM, HLM & HWM for Maruthi

Suzuki India


Fig.4.32 clearly shows that percentage errors of the HLM and CCM much higher than

the HWM for Maruthi Suzuki India. It also observed from the Fig.4.32 that the

percentage pricing errors of CCM & HLM overprices and pricing errors of HWM are

under-priced. Additionally, pricing errors of HWM are lowest compared to other two

models.

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r M&M

CCM HLM HWM

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5


Pe

rce

nta

ge E

rro

r

Maruthi Suzuki India

CCM HLM HWM

181

Figure: 4.33 Percentage pricing errors of CCM, HLM & HWM for ONGC



CCM and HWM for ONGC. It also observed from the Fig.4.33 that the percentage

pricing errors of CCM are overprices and pricing errors of HWM & HLM are under-

priced. Additionally, pricing errors of HWM are lowest compared to other two

models.

Figure: 4.34 Percentage pricing errors of CCM, HLM & HWM for Punjab

National Bank



and HLM for PNB. Additionally, it shows that percentage errors of CCM are slightly

higher than the HWM. It also observed from the Fig.4.34 that the percentage pricing

errors of CCM & HLM overprices and pricing errors of HWM are slightly under-

priced. Further, pricing errors of HWM are lowest compared to other two models.

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2


Pe

rce

nta

ge E

rro

r

ONGC

CCM HLM HWM

-4 -3.5

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2 2.5

3


Pe

rce

nta

ge E

rro

r

PNB

CCM HLM HWM

182

Figure: 4.35 Percentage pricing errors of CCM, HLM & HWM for Ranbaxy

Laboratories



CCM and HWM for Ranbaxy Laboratories. It also observed from the Fig.4.35 that the

percentage errors of HWM are lowest compared to other two models. Additionally, it

can be observed from the Fig.4.35 that pricing errors of all the pricing models are

lower in magnitude.

Figure: 4.36 Percentage pricing errors of CCM, HLM & HWM for Reliance

Industries



CCM and HWM for Reliance. It also observed from the Fig.4.36 that the percentage

errors of HWM are lowest compared to other two models. Additionally, it can be

observed from the Fig.4.36 that pricing errors of all the pricing models are lower in

magnitude in the range of ± 1.5.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Pe

rce

nta

ge E

rro

r Ranbaxy Laboratories

CCM HLM HWM

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

Reliance

CCM HLM HWM

183

Figure: 4.37 Percentage pricing errors of CCM, HLM & HWM for SBIN



and HWM for SBIN. Additionally, it shows that percentage errors of CCM are

slightly lower than HLM. It also observed from the Fig.4.37 that the percentage

pricing errors of CCM & HLM overprices and pricing errors of HWM are slightly

under-priced. Further, pricing errors of HWM are lowest compared to other two

models.

Figure: 4.38 Percentage pricing errors of CCM, HLM & HWM for Sun

Pharmaceutical Industries



CCM and HWM for Sun Pharmaceutical Industries. Additionally, it shows that

percentage errors of CCM are slightly lower than the HLM. It also observed from the

Fig.4.38 that the percentage pricing errors of CCM & HLM are overpriced and

-2.5

-1.5

-0.5

0.5

1.5


Pe

rce

nta

ge E

rro

r SBIN

CCM HLM HWM

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Pe

rce

nta

ge E

rro

r

Sun Pharmaceutical Industries

CCM HLM HWM

184

pricing errors of HWM are slightly under-priced. Further, pricing errors of HWM are

lowest compared to other two models. Further, the pricing errors are higher during the

beginning of the sample period compared to rest of the sampling period.

Figure: 4.39 Percentage pricing errors of CCM, HLM & HWM for Tata Motors


Fig.4.39 clearly shows that percentage errors of the CCM & HLM are much higher

than the HWM for Tata Motors. Further, pricing errors of HWM are lowest compared

to other two models.

Figure: 4.40 Percentage pricing errors of CCM, HLM & HWM for Tata Power



than the HWM for Tata Power. Further, the pricing errors are higher during the

beginning of the sample period compared to rest of the sampling period and pricing


-6

-4

-2

0

2


Pe

rce

nta

ge E

rro

r

Tata Motors

CCM HLM HWM

-4

-3

-2

-1

0

1

2


Pe

rce

nta

ge E

rro

r

Tata Power

CCM HLM HWM

185

Figure: 4.41 Percentage pricing errors of CCM, HLM & HWM for Tata Steel



than the HWM for Tata Steel. Further, the pricing errors are higher during the

beginning of the sample period compared to rest of the sampling period and pricing

errors of HWM are lowest compared to other two models. Further, the pricing errors

of all the models are fluctuating throughout the sample period.

Figure: 4.42 Percentage pricing errors of CCM, HLM & HWM for TCS



CCM and HLM for TCS. It also observed from the Fig.4.42 that the percentage errors

of HWM are lowest compared to other two models. Additionally, it can be observed

from the Fig .4.42 that pricing errors of all the pricing models are lower in magnitude.

-4

-3

-2

-1

0

1

2


Pe

rce

nta

ge E

rro

r Tata Steel

CCM HLM HWM

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5


Pe

rce

nta

ge E

rro

r

TCS

CCM HLM HWM

186

Figure: 4.43 Percentage pricing errors of CCM, HLM & HWM for UltraTech

Cement



than the HWM for UltraTech Cement. It also observed from the Fig.4.43 that the

percentage pricing errors of HWM & HLM overprices and pricing errors of HWM are

slightly under-priced. Further, pricing errors of HWM are lowest compared to other

two models.

Figure: 4.44 Percentage pricing errors of CCM, HLM & HWM for Wipro



CCM and HWM for Wipro. It also observed from the Fig.4.44 that the percentage

pricing errors are lower in magnitude throughout the sample period except during year

2008-09. Further, pricing errors of HWM are lowest compared to other two models.

-3 -2.5

-2 -1.5

-1 -0.5

0 0.5

1 1.5

2 2.5

3


Pe

rce

nta

ge E

rro

r UltraTech Cement

CCM HLM HWM

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5


Pe

rce

nta

ge E

rro

r

Wipro

CCM HLM HWM

187

Summary results of percentage pricing errors

In summary, figures 4.1 to 4.3 plot the percentage errors of CCM, HLM and HWM

for CNX Nifty index futures, Bank Nifty index futures and CNX IT index futures

respectively. It clearly shows that percentage errors of the HLM much higher than the

CCM and HWM for all the three futures markets. Further, Figures 4.1 to 4.3 show

that percentage errors of CCM are slightly higher than HWM.

Additionally, Fig 4.3, shows that percentage errors of HLM for CNX IT futures

market are higher in magnitude than other two models.

Finally, the plots 4.1, 4.2 and 4.3 are consistent with the results of table 4.11. HWM

underprices all the three futures markets. CCM overprices all the three futures

markets. HLM underprices Bank Nifty futures market and overprices other two

markets.

Figures 4.4 to 4.44 plot the percentage errors of CCM, HLM and HWM for all the 41

individual stock futures. It clearly shows that percentage errors of the HWM lower

than CCM and HLM. HLM much higher than the CCM and HWM for all the 41

individual stock futures. Further, Figures 4.4 to 4.44 show that percentage errors of

CCM are slightly higher than HWM.

Additionally, Fig.4.14, shows that percentage errors of HLM for GAIL are higher in

magnitude than other two models and cyclical in nature. Similarly Fig 4.15 &

Fig.4.23 show that percentage errors of HLM for Grasim Industries and Infrastructure

Development Finance Company are much higher in magnitude than CCM and HWM.

Finally, the plots 4.4 to 4.44 are consistent with the results of table 4.12. HWM

overprices for 5 ISF & under-prices 36 ISF. CCM overprices for 36 Individual Stock

futures (ISF) and under prices for 5 individual stock futures. HLM overprices for 19

ISF and under prices for 22 ISF. Majority of individual stock futures are trade at

premium for HWM, discount for CCM and in case of HLM, trade at both discount

and as well as premium. Overall it indicates that percentage errors of HWM are lower

than CCM and HLM for both stock index futures and as well as individual stock

futures.

chapter- 4 data analysis and...

Documents