CHAPTER- 4 DATA ANALYSIS AND...
Transcript of 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
(Source: Developed by Researcher)
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***
(Source: Developed by Researcher)
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***
Note: *** Significant at the 1 % Level. (Source: Developed by Researcher)
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***
Note: *** Significant at the 1 % Level. (Source: Developed by Researcher)
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
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
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.
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
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
(Source: Table 4.11)
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)
(Source: Table 4.11)
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
(Source: Developed by Researcher)
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
(Source: Table 4.12)
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)
(Source: Table 4.12)
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
(Source: Table 4.13)
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).
Table 4.14.1 Number of individual stock futures are significant and insignificant
Pricing
Models
Number of Scrips are
statistically significant
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
(Source: Table 4.14)
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).
Table 4.15.1 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
(Source: Table 4.15)
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).
Table 4.16.1 Number of individual stock futures are significant and insignificant
Pricing Models
Number of Scrips
are statistically
significant
Number of scrips are
statistically insignificant
Total
scrips
CCM vs HLM 41 0 41
CCM vs HWM 41 0 41
HLM vs HWM 41 0 41
(Source: Table 4.16)
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
Table 4.17.1 Number of stock index futures are significant and insignificant
(Source: Table 4.17)
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).
Table 4.18.1 Number of individual stock futures are significant and insignificant
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
(Source: Table 4.18)
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
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
-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
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
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
(Source: Developed by Researcher)
Fig.4.3 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
-8
-3
2
7
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 IT index futures
CCM HLM HWM
-4.5
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
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
ACC
CCM HLM HWM
167
Fig.4.4 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
-5
-4
-3
-2
-1
0
1
2
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
Ambuja Cements
CCM HLM HWM
-6
-5
-4
-3
-2
-1
0
1
2
3
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
Bank of Baroda
CCM HLM HWM
168
Fig.4.6 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
Fig.4.7 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
Fig.4.8 clearly shows that percentage errors of the HLM much higher than the CCM
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
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
Axis Bank
CCM HLM HWM
-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
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
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
-4 -3.5
-3 -2.5
-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
BHEL
CCM HLM HWM
-4 -3.5
-3 -2.5
-2 -1.5
-1 -0.5
0 0.5
1 1.5
2
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
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
(Source: Developed by Researcher)
Fig.4.11 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
-2.5 -2
-1.5 -1
-0.5 0
0.5 1
1.5 2
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
Carin India
CCM HLM HWM
-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
Cipla
CCM HLM HWM
171
Fig.4.12 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
Fig.4.13 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
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
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
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
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
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
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
Fig.4.16 clearly shows that percentage errors of the HLM much higher than the CCM
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
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
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
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
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
(Source: Developed by Researcher)
Fig.4.17 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
Fig.4.18 clearly shows that percentage errors of the HLM much higher than the CCM
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
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
HDFC Bank
CCM HLM HWM
-2.5
-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
HDFC
CCM HLM HWM
174
Figure: 4.19 Percentage pricing errors of CCM, HLM & HWM for Hero
MotoCorp
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
Fig.4.20 clearly shows that percentage errors of the HLM much higher than the CCM
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
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
Hero MotoCorp
CCM HLM HWM
-4 -3.5
-3 -2.5
-2 -1.5
-1 -0.5
0 0.5
1 1.5
2
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
Hindalco
CCM HLM HWM
175
Figure: 4.21 Percentage pricing errors of CCM, HLM & HWM for HUL
(Source: Developed by Researcher)
Fig.4.21 clearly shows that percentage errors of the HLM are much higher than the
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
(Source: Developed by Researcher)
Fig.4.22 clearly shows that percentage errors of the HLM much higher than the CCM
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
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 HUL
CCM HLM HWM
-3 -2.5
-2 -1.5
-1 -0.5
0 0.5
1 1.5
2
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
ICICI Bank
CCM HLM HWM
176
Figure: 4.23 Percentage pricing errors of CCM, HLM & HWM for IDFC
(Source: Developed by Researcher)
Fig.4.23 clearly shows that percentage errors of the HLM are much higher than the
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
(Source: Developed by Researcher)
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
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
IDFC
CCM HLM HWM
-4
-3
-2
-1
0
1
2
3
4
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
Infosys
CCM HLM HWM
177
Figure: 4.25 Percentage pricing errors of CCM, HLM & HWM for ITC
(Source: Developed by Researcher)
Fig.4.25 clearly shows that percentage errors of the HLM are much higher than the
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
(Source: Developed by Researcher)
Fig.4.26 clearly shows that percentage errors of the HLM are much higher than the
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
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 ITC
CCM HLM HWM
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
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
Jindal Steel
CCM HLM HWM
178
Figure: 4.27 Percentage pricing errors of CCM, HLM & HWM for Jaiprakash
Associates
(Source: Developed by Researcher)
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)
Fig.4.28 clearly shows that percentage errors of the HLM are much higher than the
CCM and HWM for Kotak Bank. It also observed from the Fig.28 that the Percentage
errors of HWM are lowest compared to other two models.
-3.5
-2.5
-1.5
-0.5
0.5
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 Jaiprakash Associates
CCM HLM HWM
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
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
Kotak Bank
CCM HLM HWM
179
Figure: 4.29 Percentage pricing errors of CCM, HLM & HWM for L& T
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
Fig.4.30 clearly shows that percentage errors of the HLM are much higher than the
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
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 L&T
CCM HLM HWM
-4 -3.5
-3 -2.5
-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
Lupin
CCM HLM HWM
180
Figure: 4.31 Percentage pricing errors of CCM, HLM & HWM for M&M
(Source: Developed by Researcher)
Fig.4.31 clearly shows that percentage errors of the HLM are much higher than the
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
(Source: Developed by Researcher)
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
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 M&M
CCM HLM HWM
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
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
Maruthi Suzuki India
CCM HLM HWM
181
Figure: 4.33 Percentage pricing errors of CCM, HLM & HWM for ONGC
(Source: Developed by Researcher)
Fig.4.33 clearly shows that percentage errors of the HLM are much higher than the
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
(Source: Developed by Researcher)
Fig.4.34 clearly shows that percentage errors of the HLM much higher than the CCM
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
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
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
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
PNB
CCM HLM HWM
182
Figure: 4.35 Percentage pricing errors of CCM, HLM & HWM for Ranbaxy
Laboratories
(Source: Developed by Researcher)
Fig.4.35 clearly shows that percentage errors of the HLM are much higher than the
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
(Source: Developed by Researcher)
Fig.4.36 clearly shows that percentage errors of the HLM are much higher than the
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
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 Ranbaxy Laboratories
CCM HLM HWM
-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
Reliance
CCM HLM HWM
183
Figure: 4.37 Percentage pricing errors of CCM, HLM & HWM for SBIN
(Source: Developed by Researcher)
Fig.4.37 clearly shows that percentage errors of the HLM much higher than the CCM
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
(Source: Developed by Researcher)
Fig.4.38 clearly shows that percentage errors of the HLM are much higher than the
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
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 SBIN
CCM HLM HWM
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
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
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
(Source: Developed by Researcher)
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
(Source: Developed by Researcher)
Fig.4.40 clearly shows that percentage errors of the CCM & HLM are much higher
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
errors of HWM are lowest compared to other two models.
-6
-4
-2
0
2
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
Tata Motors
CCM HLM HWM
-4
-3
-2
-1
0
1
2
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
Tata Power
CCM HLM HWM
185
Figure: 4.41 Percentage pricing errors of CCM, HLM & HWM for Tata Steel
(Source: Developed by Researcher)
Fig.4.41 clearly shows that percentage errors of the CCM & HLM are much higher
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
(Source: Developed by Researcher)
Fig.4.42 clearly shows that percentage errors of the HLM are much higher than the
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
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 Tata Steel
CCM HLM HWM
-2.5
-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
TCS
CCM HLM HWM
186
Figure: 4.43 Percentage pricing errors of CCM, HLM & HWM for UltraTech
Cement
(Source: Developed by Researcher)
Fig.4.43 clearly shows that percentage errors of the CCM & HLM are much higher
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
(Source: Developed by Researcher)
Fig.4.44 clearly shows that percentage errors of the HLM are much higher than the
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
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 UltraTech Cement
CCM HLM HWM
-4.5
-3.5
-2.5
-1.5
-0.5
0.5
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
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.