COMPARATIVE STUDY OF RETURNS OF STOCK WITH SECTORAL INDEX, MARKET INDEX and RISK FREE BOND January 04, 2016 Adarsh Chhajed (411) Apoorva Sharma (422) Anoop Kumar Sharma (420) Arpit Somani(423) ushi!esh Chinder!er (4"#)
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COMPARATIVE STUDY OF RETURNS OF
STOCK WITH SECTORAL INDEX, MARKET
INDEX and RISK FREE BOND
January 04, 2016
Adarsh Chhajed (411)Apoorva Sharma (422)Anoop Kumar Sharma (420)Arpit Somani(423)ushi!esh Chinder!er (4"#)
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Agenda
2
$% $ndustry overvie&
'ethodooy *i+ty $% per+ormanes - hoies o+ sto!s
'ethodooy
Correations - $n+erenes
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Overve!
*i+ty "0 The CNX Nifty is a well diversied 50 stock index accounting
for 22 sectors of the economy.
t is used for a variety of !ur!oses such as "enchmarkingfund !ortfolios# index "ased derivatives and index funds.
.overnment Seurity
$overnment security %$&'ec( means a security created andissued "y the $overnment for the !ur!ose of raising a!u"lic loan or any other !ur!ose as notied "y the$overnment in the )*cial $a+ette and having one of thefollowing forms.
o a $overnment ,romissory Note %$,N( !aya"le to or to
the order of a certain !erson- oro a "earer "ond !aya"le to a "earer- or
o a stock- oro a "ond held in a ond /edger ccount %/(.
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1
The Nifty IT index is computed using free float market capitalization
method with a base date of Jan 1, 199 indexed to a base !alue of1""" wherein the le!el of the index reflects total free float market !alue
of all the stocks in the index relati!e to a particular base market
capitalization !alue# The base !alue of the index was re!ised from
1""" to 1"" with effect from $ay %&, %""'# The method also takes into
account constituent changes in the index and importantly corporate
actions such as stock splits, rights, new issue of shares etc# withoutaffecting the index !alue#
(ffecti!e $ay %9, %"1), the index is computed with 1" companies and
weights of each company in the index are capped at %)*# +t the time
of rebalancing of shares change in index constituents change in
in!estable weight factors -I./s0, the weightage of the index
constituent -where applicable0 is capped at %)*# .eightage of such
stock may increase beyond %)* between the rebalancing periods#
Me"#$d$%$g&
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5
Company *ame /eiht ()
nfosys /td. 21.
Tata Consultancy 'ervices /td. 21.2
3C/ Technologies /td. 4.64
7i!ro /td. 42.68
Tech 9ahindra /td. 44.8
%he onstituents (sto!s) have een hosen ased on the&eihtae
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Pr$'ed(re
Step 1 .et vaue o+ sto!s, a $nde
Step 2 Cauate daiy returns +rom ompany sto!prie, *i+ty "0, *i+ty $% and .Se
Step 3 %o otain oreation et&een sto! prieand various indees(*i+ty "0, .Se)
Step 4 Cauate desriptive statistis o+ a thereturns and ompare the 5aiy, Annua and "yearmean
Step " $n+erenes &ere enerated y usinstatisti too i!e t%est
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De)'r*"ve Ana%&))
5aiy Annua " 7ears
Averae *i+ty $% &0.0: &4.2: &6.54:
Averae *i+ty "0 &0.01: &40.02: &14.2;:
Averae . se 0.04: 4.6: .81:
Averae %CS &0.06: &20.06: &62.:
Averae %eh 'ahindra 0.02: 5.20: 24.11:
Averae /ipro &0.01: &44.40: &15.6:
Averae $n+y 0.06: 4;.0: 64.28:
Averae 8C9 &0.0: &46.04: &1.2:
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-5.0000% 0.0000% 5.0000% 10.0000%
-15.0000%
-10.0000%
-5.0000%
0.0000%
5.0000%
10.0000%
15.0000%
f(x) = 0.55xR² = 0.13
Return TCS- Nifty 50
-10.0000% -5.0000% 0.0000% 5.0000% 10.0000%
-15.0000%
-10.0000%
-5.0000%
0.0000%
5.0000%
10.0000%
15.0000%
f(x) = - 0.08xR² = 0
Return TCS- G sec
TCS
:artiuars :vaue $n+erene
*i+ty "0 0;406<100<" %he is no sini=ant di>erene et&eenmean o+ returns o+ *$?%7 "0 and %CS
*i+ty $% 0;6#2##@2#" %he is no sini=ant di>erene et&eenmean o+ returns o+ *$?%7 "0 and %CS
.Se 0;10#<30<@" %he mean o+ returns o+ *$?%7 $% and %CSare eua
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TCS Return Nifty IT Return TCS
9ean &0.0005;121 &0.000;8
<ariance 0.00045146 0.00021;48
)"servations 408 408df 408 408
= 0.025;;6
= Critical one&tail
0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there isnt any signicant di?erence
"etween the variances on returns in Nifty T and TC' returns
Return Nifty 50 Return TCS
9ean &0.0008;18 &0.000;8
<ariance 0.00040;1 0.00021;48
)"servations 408 408
df 408 408
= 0.1865128;
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty 50 and TC'returns
?%est
t %est
Return Nifty IT Return TCS
)"servations 408 408
,ooled <ariance 0.000242545
df 202
t 'tat 0.241821144
,%T@At( one&tail 0.1454556
t Critical one&tail 4.1556;86,%T@At( two&tail 0.68084542
t Critical two&tail 4.;440;54
! value is 0.68 which is greater than al!ha 0.05 sonull hy!othesis acce!ted which im!lies that "oth
mean are eBual
Return Nifty 50 Return TCS
)"servations 408 408
,ooled <ariance 0.0004;58;
df 202
t 'tat 0.68;6018
,%T@At( one&tail 0.216;558
t Critical one&tail 4.1556;86,%T@At( two&tail 0.1;5;540
t Critical two&tail 4.;440;54
aily returns of "oth N=TD 50 and TC' are eBualwhich means whether we invest in N=TD 50 or TC'
for a day the returns are same or similar.
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-10.0000% -5.0000% 0.0000% 5.0000% 10.0000%
-20.0000%
0.0000%
20.0000%
0.0000%
!0.0000%
80.0000%
100.0000%
120.0000%
10.0000%
1!0.0000%
f(x) = 0.12xR² = 0
Return Tec" #$"inr$- G sec
-5.0000% 0.0000% 5.0000% 10.0000%
-20.0000%
0.0000%
20.0000%
0.0000%
!0.0000%
80.0000%
100.0000%
120.0000%
10.0000%
1!0.0000%
f(x) = 0.58xR² = 0.02
Return Tec" #$"inr$- Nifty 50
Te'# Ma#ndra
:artiuars :vaue $n+erene
*i+ty "0 0;6#1064##1 %he mean o+ returns o+ eturn *i+ty "0 and%eh 'ahindra are eua
*i+ty $% 0;""324#32# %he mean o+ returns o+ *$?%7 $% and %eh'ahindra are eua
.Se 0;@2<24#4"1 %he mean o+ returns o+ eturn . Se and%eh 'ahindra are eua
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Te'# Ma#ndra Return Nifty IT
Return TechMahindra
9ean &0.0005;121 0.00020854
<ariance 0.00045146 0.0022554;4)"servations 408 408
df 408 408
= 0.068;
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty T and Tech
9ahindra returns
Return Nifty IT Return Tech Mahindra
)"servations 408 408
,ooled <ariance 0.004245805
df 202
t 'tat &0.5550542
,%T@At( one&tail 0.2656;588
t Critical one&tail 4.1556;86
,%T@At( two&tail 0.54;41
t Critical two&tail 4.;440;54
! value is 0.5 which is greater than al!ha 0.05 so nullhy!othesis acce!ted which im!lies that "oth mean are
eBual
Return Nifty 50 Return HCL
9ean &0.0008;18 &0.0004164
<ariance 0.00040;1 0.0006165
)"servations 408 408
df 408 408
= 0.426;05;4
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty 50 and
3C/ returns
Return Nifty 50Return Tech
Mahindra
)"servations 408 408
,ooled <ariance 0.00446282;
df 202
t 'tat &0.8;;6126
,%T@At( one&tail 0.8115606t Critical one&tail 4.1556;86
,%T@At( two&tail 0.6;8484
t Critical two&tail 4.;440;54
aily returns of "oth N=TD 50 and Tech 9ah are eBualwhich means whether we invest in N=TD 50 or T9 for a
day the returns are same or similar.
?%est
t %est
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-5.0000% 0.0000% 5.0000% 10.0000%
-10.0000%
-5.0000%
0.0000%
5.0000%
10.0000%
15.0000%
f(x) = 0.5xR² = 0.1
Return &i'r- Nifty 50
-10.0000% -5.0000% 0.0000% 5.0000% 10.0000%
-10.0000%
-5.0000%
0.0000%
5.0000%
10.0000%
15.0000%
f(x) = 0.02x
R² = 0
Return &i'r- G Sec
W*r$
:artiuars :vaue $n+erene
*i+ty "0 0;@33"##<"6 %he mean o+ returns o+ eturn *i+ty "0 and
/ipro are eua
*i+ty $% 0;60@0431<< %he mean o+ returns o+ *$?%7 $% and /iproare eua
.Se 0;3"@3#<0<3 %he mean o+ returns o+ eturn . Se and/ipro are eua
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W*r$
Return NiftyIT
Return Wipro
9ean &0.0005;121 &0.00011056
<ariance 0.00045146 0.0002682)"servations 408 408
df 408 408
= 0.2;814828
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty T and 7i!roreturns
Return Nifty 50 Return Wipro
9ean &0.0008;18 &0.00011056
<ariance 0.00040;1 0.0002682
)"servations 408 408
df 408 408
= 0.8;22028
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty 50 and
7i!ro returns
Return Nifty IT Return Wipro
)"servations 408 408
,ooled <ariance 0.0002205
df 202
t 'tat &0.880;41;
,%T@At( one&tail 0.80155168
t Critical one&tail 4.1556;86,%T@At( two&tail 0.10;40;
t Critical two&tail 4.;440;54
! value is 0.1 which is greater than al!ha 0.05 sonull hy!othesis acce!ted which im!lies that "oth
mean are eBual
Return Nifty
50 Return Wipro
)"servations 408 408
,ooled <ariance 0.0004;10;;
df 202
t 'tat 0.0054542
,%T@At( one&tail 0.146;5245
t Critical one&tail 4.1556;86
,%T@At( two&tail 0.;18;018
t Critical two&tail 4.;440;54
aily returns of "oth N=TD 50 and 7i!ro areeBual which means whether we invest in N=TD50 or 7i!ro for a day the returns are same or
similar.
?%est
t %est
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-10.0000% -5.0000% 0.0000% 5.0000% 10.0000%
-20.0000%
-10.0000%
0.0000%
10.0000%
20.0000%
30.0000%
0.0000%
50.0000%
!0.0000%0.0000%
80.0000%
f(x) = 0.15x
R² = 0
Return *nfy- G sec
-5.0000% 0.0000% 5.0000% 10.0000%
-20.0000%
-10.0000%
0.0000%
10.0000%
20.0000%
30.0000%
0.0000%
50.0000%
!0.0000%0.0000%
80.0000%
f(x) = 0.!3x
R² = 0.03
Return *nfy- Nifty 50
In+$)&)
:artiuars :vaue $n+erene
*i+ty "0 0;2##010""" %he mean o+ returns o+ *$?%7 "0 and $n+osys areeua
*i+ty $% 0;14<"23"3# %he mean o+ returns o+ *$?%7 $% and $n+osys are
eua.Se 0;"313<#012 %he mean o+ returns o+ *$?%7 $% and $n+osys are
eua
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$n+osys Return Nifty IT Return Infy
9ean &0.0005;121 0.0006461
<ariance 0.00045146 0.0048051)"servations 408 408
df 408 408
= 0.481858214
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty T and nfy
returns
Return Nifty 50 Return Infy
9ean &0.0008;18 0.0006461
<ariance 0.00040;1 0.0048051)"servations 408 408
df 408 408
= 0.06861028
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty 50 and
nfy returns
Return Nifty IT Return Infy
)"servations 408 408
,ooled <ariance 0.00010582
df 202
t 'tat &4.205;1;24
,%T@At( one&tail 0.448;686t Critical one&tail 4.1556;86
,%T@At( two&tail 0.22;15;
t Critical two&tail 4.;440;54
! value is 0.226 which is greater than al!ha 0.05 sonull hy!othesis acce!ted which im!lies that "oth mean
are eBual
Return Nifty 50 Return Infy
)"servations 408 408
,ooled <ariance 0.000055
df 202
t 'tat &4.00;15;565
,%T@At( one&tail 0.45180
t Critical one&tail 4.1556;86
,%T@At( two&tail 0.84262414
t Critical two&tail 4.;440;54
aily returns of "oth N=TD 50 and nfy are eBualwhich means whether we invest in N=TD 50 or nfy
for a day the returns are same or similar.
?%est
t %est
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-5.0000% 0.0000% 5.0000% 10.0000%
-20.0000%
-10.0000%
0.0000%
10.0000%
20.0000%
30.0000%
0.0000%
50.0000%
!0.0000%
0.0000%
80.0000%
f(x) = 0.!xR² = 0.05
Return +C, Nifty 50
-10.0000% -5.0000% 0.0000% 5.0000% 10.0000%
-20.0000%
-10.0000%
0.0000%
10.0000%
20.0000%
30.0000%
0.0000%
50.0000%
!0.0000%
0.0000%
80.0000%
f(x) = 0.11x
R² = 0
Return +C, G sec
HCL
:artiuars :vaue $n+erene
*i+ty "0 0;<2103#<<4 %he mean o+ returns o+ *$?%7 "0 and 8C9 are eua
*i+ty $% 0;@4<311@01 %he mean o+ returns o+ *$?%7 $% and 8C9 are eua
.Se 0;3@"123164 %he mean o+ returns o+ *$?%7 $% and 8C9 are eua
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4
HCL Return Nifty IT Return HCL
9ean &0.0005;121 &0.0004164
<ariance 0.00045146 0.0006165
)"servations 408 408
df 408 408
= 0.20141
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty T and 3C/
returns
Return Nifty
50 Return HCL
9ean &0.0008;18 &0.0004164
<ariance 0.00040;1 0.0006165)"servations 408 408
df 408 408
= 0.426;05;4
= Critical one&tail 0.;02600;
= value is less than = critical so null hy!othesis isacce!ted# there is not any signicant di?erence
"etween the variances on returns in Nifty 50 and
3C/ returns
Return Nifty IT Return HCL
)"servations 408 408
,ooled <ariance 0.0005420;4
df 202
t 'tat 0.05585
,%T@At( one&tail 0.16428t Critical one&tail 4.1556;86
,%T@At( two&tail 0.;555521
t Critical two&tail 4.;440;54
! value is 0.;5 which is greater than al!ha 0.05 sonull hy!othesis acce!ted which im!lies that "oth
mean are eBual
Return Nifty
50Return HCL
)"servations 408 408
,ooled <ariance0.0001;44
5
df 202
t 'tat 0.8804165
,%T@At( one&tail0.8058
8
t Critical one&tail4.1556;8
6
,%T@At( two&tail0.148051
t Critical two&tail
4.;440;5
4 aily returns of "oth N=TD 50 and 3C/ are eBual
?%est
t %est