PROJECT REPORT
ON
OPTIMIZATION OF PORTFOLIO RISK AND RETURN
In Partial fulfillment for the award of Requirements for the award of the degree of
Master of Business Ad inistration
DECLARATION
I here by declare that the project report titled !OPTIMIZATION OF PORTFOLIO RISK AND RETURN” prepared under the guidance """" (finance department) of """" towards partial fulfillment for the requirement of award of M#B#A#
!he Project report has not been submitted to any other "ni#ersity for the $ward of any %egree or %iploma&
"""
ACKNO$LED%EMENT
!he presentation of this project has gi#en me an opportunity to e'press my profound gratitude to all concern in guiding me& (oremost I would li)e to than) """" the %irector of our *ollege+ """"" for pro#iding an opportunity to "ndergo a project study program& I would li)e to than) """" (finance department) for guiding me to complete the Project ,or)&
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""""
CONTENTS
C&APTER ' I . . . . C&APTER ' II . / / / / / Introduction Objecti#e of 1tudy 3ethodology 5imitations Portfolio and 7olding period returns 8 1harpe9s Performance 3easure !reynor9s Performance 3easure C&APTER ' III . / $nalysis and Interpretations 244 4: 0 2 4 6 0
2
Con()usion * Su++estions Bi,)io+ra-./
64 66
4
C&APTER 0 I
INTRODUCTION
*ombination of indi#idual assets or securities is a portfolio& Portfolio includes in#estment in different types of mar)etable securities or in#estment papers li)e shares+ debentures stoc) and bonds etc&+ from different companies or institution held by indi#iduals firms or corporate units and portfolio management refers to managing securities& Portfolio management is a comple' process and has the following se#en broad phases&
6
& 1pecification of in#estment objecti#es and constraints& -& *hoice of asset mi'& 2& (ormulation of portfolio strategy& 4& 1election of securities& 6& Portfolio e'ecution& 0& Portfolio rebalancing& ;& Portfolio performance&
Portfo)io Di1ersifi(ation2
$n important way to reduce the ris) of in#esting is to di#ersify your in#estments& %i#ersification is a)in to <not putting all your eggs in one bas)et”& (or e'ample+ if your portfolio only consisted of stoc)s of technology companies& It would li)ely face a substantial loss in #alue if a major e#ent ad#ersely affected the technology industry& !here are different ways to di#ersify a portfolio whose holding are concentrated in one industry& =ou might in#est in the stoc)s of companies
0
belonging to other industry groups& =ou might allocate to different categories of stoc)s+ such as growth+ #alue+ or income stoc)s& =ou might include bonds and cash in#estments in your asset allocation decisions& Potential bond categories include go#ernment+ agency municipal and corporate bonds& =ou might also di#ersity by in#esting in foreign stoc)s and bonds& %i#ersification requires you to in#est din securities whose in#estment returns do not mo#e together& In other words+ their in#estment returns ha#e a low correlation& !he correlation coefficient is used to measure the degree that returns of two securities are related& (or e'ample+ two stoc)s whose returns mo#e in loc)step ha#e a coefficient of > &?& !wo stoc)s whose returns mo#e in e'actly the opposite direction ha#e a correlation of @ &?& !o effecti#ely di#ersity+ you should aim to find in#estments that ha#e a low or negati#e correlation& $s you increase the number of securities in your portfolio+ you reach a point where you9#e li)ely di#ersified as much as reasonably possible& (inancial planners #ary in their #iews on how many securities you need to ha#e a fully di#ersified portfolio& 1ome say it is ? to -? securities& Others say it is closer to 2? securities& 3utual funds offer di#ersification at a lower cost& =ou can buy no@load mutual funds from an online bro)er& Often+ you can buy shares fund directly from the mutual fund+ a#oiding a commission altogether&
Asset a))o(ation2
$sset allocation is the process of spreading your in#estment across the three major asset classes of stoc)s+ bonds and cash&
;
$sset allocation is a #ery important part of your in#estment decision@ ma)ing& Professional financial planner frequently point out that asset allocation decisions are responsible for must of your in#estment return& $sset allocation begins with setting up an initial allocation& (irst+ you should determine your in#estment profile& 1pecially+ this requires you to assess you in#estment horiAon+ ris) tolerance+ and financial goals. In#estment horiAon+ $lso called time horiAon your in#estment horiAon is the number of years you to sa#e for a financial goal& 1ince you9re li)ely to ha#e more than goal+ this means you will ha#e more than one in#estment horiAon& (or e'ample+ sa#ing for your gi#e@year@daughter9s college has an in#estment horiAon of - years& 1a#ing for your retirement in 2? tears has an in#estment horiAon of 2? years& ,hen you retire+ you will want to ha#e sa#ed a lump sum that is large enough to generate earnings e#ery year until you die ris) tolerance& =our ris) tolerance is a measure of your willingness to accept a higher degree of ris) in e'change for the chance to earn a higher rate or return& !his is called the ris)@return trade@off& 1ome of us+ naturally+ are conse#atyi:#e in#estor+ while other are aggressi#e in#estors& $s a general rule+ the younger your are+ the higher your ris) tolerance and the more aggressi#e you can be& $s a result+ you can afford to allocate a higher percentage of your in#estment to securities with more ris)& !hese include aggressi#e growth stoc)s and the mutual funds that in#est ion them& $ more aggressi#e allocation is #iable because you ha#e more time to reco#er form a poor year of in#est0ment returns& (inancial goal+ younger and aggressi#e in#estor9s allocation+ as a general rule+ younger and aggressi#e in#estors allocate ;?B to ??B of their
C
portfolios to stoc)s+ with the remainder in bonds and cash& *onser#ati#e in#estors allocate 4?B to 0?B in bonds+ and the remainder in cash& 3oderate in#estors allocate somewhere between the allocation of aggressi#e and conser#ati#e+ to ma)e an initial allocation+ you need to build a portfolio of indi#idual securities+ mutual funds+ or both& In general+ mutual funds pro#ide more di#ersification benefit for the buc)& 7ow you choose to precisely allocate among the major asset classes depends+ in part+ on other factors& (or e'ample+ if e'ample+ if interest rates are e'pected to rise+ you might allocate a greater percentage to money mar)et mutual funds+ *%s+ or other ban) deposits& If rates are headed lower+ you may choose to allocate more to stoc)s or bonds& (inancial planners suggest that you rebalance+ or reallocate+ your portfolio from time to time& !hey differ in their #iews on how often you should reallocate& It may be once a year or it may be e#ery three to si' months& $t a minimum+ reallocation lets you up date any changes in your in#estment profile+ or to ta)e ad#antage of a change in interest rates& Rebalancing often in#ol#es nothing more than a <fine@tuning” of your current0 allocations& (or e'ample+ a conser#ati#e in#estor may decide to shift 6B of her portfolio form stoc)s to cash to ta)e ad#antage of higher rates that money mar)et funds may be offering&
&
:
?
0Need 0O,3e(ti1e 0Met.odo)o+/
SPECIFIC IN4ESTMENT OBJECTI4E AND CONSTRAINS
!he first step in the portfolio management process is to specify the one9s in#estment objecti#es and constraints& !he commonly stated in#estment goals are.@ INCOME @ !o pro#ide a steady income through the regular interest or di#ided payment& %RO$T& @!o increase the #alue of the principal amount through capital appreciation& STABILIT5 D 1ince income and growth represent two ways by which return is generated and in#estment objecti#es may be e'pressed in terms of
return and ris)& $n in#estor will be interested in higher return and lower le#el ris)& 7owe#er the ris) and return go hand to hand+ so an in#estor has to bear a higher le#el of ris) in order to earn a higher return& CONSTRAINTS D $n in#estor should bear in mind the constraints arising our of the following factor& @5iquidity @!a'es @!ime horiAon @"nique preferences and circumstances
OBJECTI4ES
!o construct three portfolios of public sector units+ public limited companies and foreign collaboration and fine their e'@post returns and ris) for the period of three year&
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!o ma)e a comparati#e study of the ris)@adjusted measure of portfolio performance using the shapre9s and !reynor9s performance indeed under total ris) and mar)et ris) and mar)et ris) situations+ by ta)ing e'@post returns for a period of three years&
MET&ODOLO%5 "sing a model consisting of two modules has carried out the wor)& !he first module in#ol#es the section of portfolio and the second module in#ol#ed e#aluation of portfolio9s performance& MODULE06 1ecurities selection and portfolio construction has been made by ta)ing scripts Public 1ector "nits+ public limited companies and foreign
2
collaboration units& Equal weigtage has been gi#en to industries li)e shipping+ oilFgas and power growth oriented industries li)e pharmaceuticals+ ban)ing and (3*G and technology oriented industries li)e software and telecommunications&
MODULE ' 7 Portfolio performance was e#aluated by ran)ing holding period9s returns under total ris) and mar)et ris) situation (measured by standard de#iation and Heta coefficient) for the period of three years&
LIMITATIONS
T.e 8or9 .as ,een (arried out under t.e fo))o8in+ )i itations2
? !he all portfolio consist of ris)ly assets there no ris)@free assets& ? Ris)ly assets consist of equity shares and where as ris)@free assets consists of in#estments in the sa#ing ban) account+ deposits+ treasury bills+ bonds etc&
4
? !he holding period for ris)y assets was for I yr i&e& shares were assumed to be purchased at the first day and sold at the second consecuti#e day and a#erage return for I yr is considered& ? $n equal no of shares i&e& I (one) share of each script is assumed to be purchased form the secondary mar)et& ? Return on the sa#ing ban) account is considered as benchmar) rate of return& ? $ll the portfolio has been held constant for the whole period of the three years&
C&APTER 0 II
6
PORTFOLIOS
PORTFOLIOS I
NSE CODE H$NI O( IN%$ H7E5 H$NIIN%I$ 7E5
0
755 3F3 1*I 1$!=$3 *O3P"!ER J1N5 G5$KO IHP 1$I5
7IN%5EJER 3F3 1*I 1$!=$3*O3P"!ER J1N5 G5$KO IHP 1$I5
PORTFOLIO II
NSE CODE "!I H$NI !$!$ PO,ER I!* E1*OR!1 "!IH$NI !$!$PO,ER I!* E1*OR!1
;
J$R"N17IPING ,IPRO H7R$!I %RRE%%=1 IP*5 !I1*5
J$R"N17IP ,IPRO H7R$!I %RRE%%= IP*5 !I1*O
PORTFOLIO III
NSE CODE ING J=1=$ $HH *$%I5$ J=1=$ H$NI $HH *$%I5$
C
3I*O HO17 GE17IPPING 7"G7E1 1O(!,$RE !$!$ !E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5
3I*O GE17IP 7"G7E11O(! !$!$ !E5E*O3 NI*O5$1PIR ONG* E11$RG"L
&OLDIN% PERIODS RETURNS2
:
$ll the in#estment is made at a certain period of time& 7olding period returns enables an in#estor to )now his returns during that period of time& It can be computed by using the formula.@ 7olding period returns (7PR) M !oday9s closing price D =esterday9s closing price =esterday9s closing price 7olding period returns are used for comparati#e criterion& 7olding period returns can be compared for ma)ing an assessment of relati#e returns&
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MODULE I
&OLDIN% PERIOD RETURNS
Portfo)io I for 7::;0:<
-
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1iden d de()are d
Di1iden d a ount
Mar9et -ri(e 8.en -ur(.ase d ?&6 -C&; ---&:&2?&? -42&; -C0&4 ;&C
=Return on di1idend
=Return on se(urit/
Tota) return
H$NI O( IN%I$ H7E5 755 3F3 1*I 1$!=$3 *O3P J1N5 G5$KO IHP 1$I5 -
? ?
? 4? 2??
? 4 2 ? ? ? ? ; ?? ? ?
? 2& &26 ?&?? ?&?? ?&?? ?&?? &0C 2&4? ?&??
@ ;&44?&06&C4 C& :C& 4 &-4 @-?&-; @2& C :&:6 @2&:C
@ ;&442&;-: ;& :? C& :C& 4 &-4 @-?&-; @ &6?4 -2&26 @2&:C
? ?
? ? ?
? ? ? ?
? ?
-:4&2 6&;
?
Return
-;&C66
Portfo)io I for 7::<0:>
--
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend &2-&&24&CC 0&?? ?&C0 4&6 -&?4 &6; ?&??
=Return on se(urit/
Tota) return
H$NI O( IN%I$ H7E5 755 3F3 1*I 1$!=$3 *O3P J1N5 G5$KO IHP 1$I5 -
? ?
2? 4? 2??
2 4 2 6&6 ? ? -&C&6 ; 4 ?
-0&6 C?&C --;&-6 -&C ;-&66 -6; CC&6 24&; C: &26 6&06
C:&2-4&:: @2:&4; @0&6@-?&: @-C&66 @CC&0 @0&6 @ 2&:6 ; &;4
??&0 -;&@2C& 4 @ &044 @-?&: @-;&0: @C4& @4&46; @ -&2C ; &;4
? ?
66 ?
? ? ? ?
C6 ;? 4? ?
Return
&?-0
Portfro)io I for 7::>0:?
-2
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend -&64 &24 -&? :&?C?&??? &0 0&?6; 2&2:2 ?&??? ?&???
=Return on se(urit/
Tota) return
H$NI O( IN%I$ H7E5 755 3F3 1*I 1$!=$3 *O3P J1N5 G5$KO IHP 1$I5 -
? ?
? 2? 2?? 2 2 : ? 4? -&C 46&6 ? ? ?
2:&26 --2&06 4:& 6 ::& 6 &-6 ;2&06 ;4&2 -:4&; ::&C :&?6
4:&?0 ?;& C&42 04&-2 ?:&6 0;&-: 6:&6 ;;&?-2&C 62&?0
6 &0? ?C&44 ?&44 ;2&2 ?:&6 0C&:?06&60; C?&4 2 -2&C 62&?
? ?
:? ?
? ? ? ?
46 ?? ? ?
Return :4&6?6
PORTFOLIO II FOR 7::;0:<
-4
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend ?&??? ?&??? ?&??? &-:; ?&??? ?&?;: ?&??? ?&??? ?&??? ?&???
=Return on se(urit/
Tota) return
"!IH$NI !$!$PO,ER I!* E1OR!1 J$R"N17IPING ,IPRO H7$R!I %RRE%%= IP*I !I1*O 6 -
? ? ? ? ?
? ? ? ? ? 6?
? ? ?
-2&; ?2& 0-6 ;;&
02&CC&
?& : @ ?& ; 0&02 6C&; @ 2& --&-4 6-&-0 @;&C
02&CC& ?& : @C&C;2 0&02 6C&;C: @ 2& --&-4 6-&-0 @;&C
?
&66 -0C&46
?
? ?
? ? ? ?
44&26 : 4&:6 64& 6 6&;6
? ?
? ?
Return
C&-0C
PORTFOLIO II FOR 7::<0:>
-6
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend 6&4?64 6&0::-6 ? &0262? ?&?6: ; 6& 4 2: ?&460 0 -&6; 42 C& ;6;C
=Return on se(urit/
Tota) return
"!IH$NI !$!$PO,ER I!* E1OR!1 J$R"N17IPING ,IPRO H7$R!I %RRE%%= IP*I !I1*O 6 -
? ? ? ? ?
-06 ? ? ? 6?
-&0&6 ?
4?&; 4&?6 ;?0&2 0 & 6
-&-2 -&-; @C&0 @4C&;4 @- &4 @--&6C @-2&?4 @ 2&6 C&4; 26&:
;&0264 ;&:0:2 @C&0 @4;& ?6 @- &4 @--&6@ ;&C:: @ 2&?44 &?4 44&?;0
?
&; 0:?
?
-? ??
6 -&-6 C
2C&: ?:0& C;&6 :;&C6
? ?
--&6 C?
Return
@6&:C60
PORTFOLIO II FOR 7::>0:?
-0
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend 0&-0600 0& 24:; 2& :64 ? 0&6- ;4 ?&2-4C: -?&0 C0 ?&6404C -&:C 6 ;&4? :-
=Return on se(urit/
Tota) return
"!IH$NI !$!$PO,ER I!* E1OR!1 J$R"N17IPING ,IPRO H7$R!I %RRE%%= IP*I !I1*O 6 -
? ? ? ? ?
-6 ;? -?? ? 0 -??
-&6 ; -? ? ?&0 4 0 6 -&6 ?
2:&: 4& 0-6&: 26&-6 :&-2 &-:& : 4&:6 C2&C6 26&
6?&0 -C& 64&0C ;0&64 ?6&4: - &26 C2&20 4&:C:&-&C-
60&C2 24&-4 6;&C;6 ;0&64 -&? - &0;6 -?2&:C 6&400 :-& C-?&--
?
0? ??
? ?
-6 ??
Return ::& ?-
PORT>FOLIO III FOR 7::;0:<
-;
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend 2& ? ? ? ? ?&22; 2 ? ? & 4? :42
=Return on se(urit/
Tota) return
ING J=1$ $HH *$%I5$ 3I*OHO17 GE17IPPING 7"G7E1 !$!$!E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5 6 6
? ?
26 ? ?
2&6 ? ? ? ? ? ?
-&-2C&: -4 -;?: -6&2 6:2&-6 60&4 -:6&;6
C:&:6 0&;&-C@4&?0 --&46 @4?&46 2:& @?&?4; C;&:; C;&:;
:2&?0: 0&;&-C @4&?0 --&46 @4?& 2:& @?&?4; ::& C;&:; 2
?? ?
? ? 4?
? ? ? ?
? ? 4? ?
4 ?
-6&06 -6&06
Return 4-&64C
PORTFOLIO III FOR 7::<0:>
-C
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend &4 66; -&-;26: -&;? 00 &0;66 2&??C ?&;-?&46422 2&C;2C2&:44 ; ?
=Return on se(urit/
Tota) return
ING J=1$ $HH *$%I5$ 3I*OHO17 GE17IPPING 7"G7E1 !$!$!E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5 6 6
? ?
4? 0? ;?
2&6 0 2&6 4? 4 -&6 ?&6 2 ?
-4;&-6 -02&: -:&66 -2C;&26 2?&;6 -;;&; ; &: -; &?6 2-:&0 2-:&0
4&;; -&;; @2&2 4;&46 -6&:: @-C&-4;&46 @-4&CC 2&42 2&42
0& C60 6&?44 @?&0?C2 4:& -6 2C&::C @-;&6 4C&:?4 @- &??0 ;&2;4 2&42
?? ?
4? 4? 4?
? ? ? ?
-6 ?6 2? ?
Return
2&::6
PORTFOLIO III FOR 7::>0:?
-:
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend &4 66; -&-;26: -&;? 00 &0;66 2&??C ?&;-?&46422 2&C;2C2&:44 ; ?
=Return on se(urit/
Tota) return
ING J=1$ $HH *$%I5$ 3I*OHO17 GE17IPPING 7"G7E1 !$!$!E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5 6 6
? ?
4? 0? ;?
2&6 0 2&6 4? 4 -&6 ?&6 2 ?
-4;&-6 -02&: -:&66 -2C;&26 2?&;6 -;;&; ; &: -; &?6 2-:&0 2-:&0
;0&-C ?0&0; 44&?: 2C&20 26&0 ;&06 :0&2; @-4&CC :6&-0 :6&-0
;;&0:0 ?C&:4 40&?4 4?&?4 4C&0 C&2; :;&C-4 @- &??0 ::&-?4 :6&-0
?? ?
4? 4? 4?
? ? ? ?
-6 ?6 2? ?
Return
? & ;-;
E"0POST PORTFOLIO RETURNS
2?
5EAR -??6 -??0 -??; Ri
PORTFOLIO PORTFOLIO PORTFOLIO I II III -;&C6 C&-0 4-&64 &?@6&:C 2&:: :4&6 ::& ? & ; 4 & -22222 2;& -00000; 6-&60;
2
MODULE ' II
RISK ADJUSTED MEASUREMENT OF PORTFOLIO PERFORMANCE S&ARPE@S PERFORMANCE MEASURE CALCULATIONS OF STANDARD DE4IATION
Ris9
Ris) in holding securities is generally associated with the possibility that realiAed return will be less than returns were e'pected& !he source of such disappointment is the failure of di#idends or the fail in security9s prices& (orces that contribute to #ariation in return+ price or di#idend
2-
const0itures elements of ris)& 1ome influences that are e'ternal to the firm+ cannot be controlled and affect large number of securities& Other influences are internal to the firm are controllable to all large degree&
S/ste ati( Ris9
!he systematic ris) affects the entire mar)et& !hose forces that are uncontrollable e'ternal and board in the effect are called sources of systematic ris)& Economic+ political and sociological changes are sources of systematic ris)&
S/ste ati( ris9 furt.er di1ided into
@3ar)et Ris) @Interest @Purchasing power Ris)
Mar9et Ris9
L&*& (rancis defined 3ar)et ris) as that portion of total #ariability of returned caused by the alternating farces of bull and bear mar)et& ,hen the security inde' mo#es upwards haltingly for a significant period of time+ it is )nown as bull mar)et& In the bull mar)et the indeed mo#es form a low le#el to the pea)& Hear mar)et is just re#erse to the bull mar)et& %uring the bull
22
and bear mar)et more than C? percent of the securities prices rise or fall along with the stoc) mar)et indices&
Interest Rate Ris9
!he rise or fall in the interest rate affects the cost borrowing& ,hen the call money mar)et rate changes& Interest rates not only affect the security traders but also corporate bodies who carry their business on borrowed funds& !he cost of borrowing would& Increase and a hea#y out flow of profit would ta)e place in the form of interest to the capital borrowed& !his lead a reduction in earning per share and a consequent fall in the price of share&
Pur(.asin+ -o8er Ris9
Jariations in the returns are caused also by the loss of purchasing power of currency& Inflation is the reason behind the loss of purchasing power the rise in price penaliAes the returns to the in#estors+ and e#ery potential rise in price a ris) to the in#estor&
Uns/ste ati( Ris9
"nsystematic ris) is the unique ris)+ which will be different to different firms& "nsystematic ris) stems form managerial inefficiency+ technological change in production process+ a#ailability of raw material mentioned factors differ form industry to industry+ and company to company& !hey ha#e to be analyAed separately for each industry and firm&
24
Hroadly "nsystematic ris) can be classified into. @Husiness ris) @(inancial ris)
Business Ris9
It is the portion of the unsystematic ris) caused by the operat0in en#ironment of the business&
Finan(ia) Ris9
(inancial ris) in a company is associated with the capital structure the company& It refers to the #ariability of the income to the equity capital to debt capital&
Measure ent of Ris9
!he ris) of a portfolio can be measured by using the following measure of ris)&
4aria,i)it/
In#estment ris) is associated with the #ariability of rates of return& !he more #ariable is the return+ the more ris)y the in#estment& !he total #ariance is the rate of return on a stoc) around the e'pected a#erage+ which includes both systematic and unsystematic ris)&
26
!he total ris) can be calculated by using the standard de#iation& !he standard de#iation of a set of numbers is the squares root of the square of de#iation around the arithmetic a#erage& =mbolically+ the standard de#iation can be e'pressed as@ N M O (rit@ri) n@ ,here+ ri is the mean return of the portfolio and rit is the return form the portfolio for a particular year
S&ARPE@S PERFORMANCE INDE"20
,illiam 1harpe9s of portfolio performance is also )nown as reward to #ariability ratio (RJ$R)& It is simply the ratio of reward+ which defined as
20
realiAed portfolio returns in e'cess of the ris) free rate+ to the #ariability of return measured by the standard de#iation relation to total ris) assumed by the in#estor& !he measure can be defined follows.@ RJ$R M rp@rf N ,here+ rpM the a#erage return for the portfolio (P) during it 7PR rfM ris) free rate of return during L7PR N M the standard de#iation of the portfolio (P) during 7PR
CAPITAL MARKET LINE
2;
*apital mar)et shows the conditions pre#ailing in the capital mar)et in terms of e'pected return and ris)& It depicts the equilibrium condition that pre#ails in the mar)et for efficient portfolio9s consisting of the portfolio of ris)y asset or ris) free asset or both& $ll combination of ris)y and ris) free portfolio are bounded by the capital mar)et line+ and all in#estors will end up with portfolio somewhere on the capital mar)et line& !he capital mar)et is usually deri#ed under the assumptions that there e'ists a ris) a ris)@less asset a#ailable for in#estment& It is further assumed that0 in#estor can borrow or lend as much as desired at the ris) free assets with a portfolio or ris)y assets to obtain the desired ris) return combination& "sing the capital mar)et line can graphically represent 1harpe9s measure for portfolios& !he #ertical a'is represents the return on the portfolios and the the horiAontal a'is represents the standard de#iation for returns& !he #ertical intercept is rf& RJ$R measures the slope of the line form rf to the portfolio being e#aluated& !he steeper the line+ the higher the slope (RJ$R) and the better performance&
TRE5NOR@S PERFORMANCE INDE"
!he measure is also referred to as reward to #olatility ratios (RJO5)& !reynor sough to relate return on a portfolio to its ris)& 7e distinguished between total ris) and systematic ris) assuming that0 the portfolio is well di#ersified& In measuring the portfolio performance !reynor introduced the
2C
concept of characteristic line& !he slope of the characteristics measures the relati#e #olatility of the portfolio9s returns& !he slope of this line is the beta co@efficient which is measure of the #olatility (or responsi#eness) of the portfolio9s returns in relation to those of the mar)et inde'& !reynors9s ratio is the realiAed portfolio9s return in e'cess of the ris)@free to the #olatility of return as measured by the portfolio beta& RJO! M rp@rf Hp M $#erage e'cess return of portfolio (P) 1ystematic ris) for portfolio
SECURIT5 MAEKET LINE
!he security mar)et line indicates the ris)@return trade@off for portfolio and indi#idual securities& !reynor e'tended his analysis to identify the component of ris) that will be compensated by the mar)et& It is )nown as systematic ris) and is commonly measured by the beta& Heta is a
2:
measure of ris) that applies to all assets and portfolio whether efficient or inefficient& 1ecurity mar)et line specifies the relationship between e'pected return and ris) for all assets and portfolios whether efficient or inefficient& !he security mar)et is obtained by ta)ing the ris) (beta) on the horiAontal a'is and portfolio return on the #ertical a'is& !he 1ecurity mar)et line can be graphically&
E (rm)
135
rf Heta &??
Beta
Heta is a mar)et ris) measure employed primarily in the equity& It measures the systematic ris) of a single instrument or an entire portfolio& ,illiam 1harp ( :04) used the notion in his landmar) paper introducing the capital asset pricing model (*$P3)& !he name <beta” was applied later&
4?
Heta describes the sensiti#ity of an instrument or portfolio to broad mar)et mo#ements& !he stoc) mar)et (represented by an inde' such s the 1FP 6?? or ??) is assigned a beta of &?& Hy comparison+ a portfolio (or instrument) with a beta of -&? will tend to benefit or suffer form broad mar)et mo#es twice as much as the mar)et o#erall& !he formula for beta is O"50AOK=) (O=) NOK@(OK) ,here K is the mar)et return $nd = is the security return Hoth quantities are calculated using simple returns& Heta is generally estimated form historical price time series& (or e'ample+ 0? trading of simple returns might be used with sample estimators for co#ariance and #ariance& It is possible to construct negati#e beta portfolio beta portfolios& $pproaches include& Heta is sometimes used as a measure of a portfolio9s mar) ris)& !his can be misleading because beta does not capture specific ris)& Hecause of specific ris)& $ portfolio can ha#e a low beta+ but still be highly #olatile& !i price fluctuations would simply ha#e a low correlation with those of the o#erall mar)et& It is said that a security or portfolio ha#ing higher beta will perform well pro#ided mar)et has to go up i&e&+ mar)et indeed&
4
Ca)(u)ation of standard de1iation of returns
PORTFOLIO I
5ear -??6 -??0 -??; RiM Return -;&C6 &?:4&6 4 & -2 DiBr0ri @ 2&-;2 @4?& ?2 62&2;; DiCDi ;0& C 0?C&2 -C4:& 4022&6 S#D 4C& 22
PORTFOLIO II
5ear
-??6 -??0 -??; RiM
Return
C&-0 @6&:C ::& 2;& -;
DiBr0ri
@ C&C0; @42&:;2
DiCDi
266&:6 C6C&2C4?&; 0?64&C
S#D
66&?--
PORTFOLIO III
5ear -??6 -??0 -??; RiM Return 46&64 2&:: ? & ; 62&60; DiBr0ri @C&?-0; @2:&6;; 4;&0?2 DiCDi 04&4-; 600&2 --00& 2C:0&C S#D 44& 4
4-
S&ARPE PERFORMANCE MEASURE
A1+ -ortfo)io Portfo)ios I II III Return AD-E in = 4 & -C 2;& -C 6-&6; Ris9 free Rate AnE= 6&-6 6&-6 6&-6 EF(ess return Ar-0riE 26&C;C 2 &C;C 4;&2Standard De1iation 4C& 2 66&?44& 4 S.ar-e@s Ratio r-0 rtG ?&;46 ?&6;: &?;Ran9in+ 2
42
TRE5NOR@S PERFORMANCE MEASURE CALCULATION OF BETA
Beta for -ortfo)io I
5ear A1+ Mar9et Return " "7 A1+ Sto(9 Return 5 "5
44
-??4@?6 -??6@?0 -??0@?;
6&0C2 @C&C-; ;-&CC0
2-&-:0 ;;&: 0 6C:?&C
-;&C66 &?-6 -2&2C
6C&2 @:&?4;; ;224&4
Heta M &?6-0
Beta -ortfo)io II
5ear A1+ A1+
46
Mar9et Return "
"7
Sto(9 Return 5
"5
-??4@?6 -??6@?0 -??0@?;
6&0C2 @C&C-; ;0&?2 ;-&CC0
2-&-:0 ;;&: 0 6;C?&0 6C:?&C
C&-0; @6&:C6 ::& ?&2C
?2&C 6-&C2 ;624&; ;0: &4
Heta M &- ?? C
Beta for -ortfo)io III
40
5ear
A1+ Mar9et Return " "7
A1+ Sto(9 Return 5 "5
-??4@?6 -??6@?0 -??0@?;
6&0C2 @C&C-; ;0&?2 ;-&CC0
2-&-:0 ;;&: 0 6;C?&0 6C:?&C
4-&64C 2&:: ? & ; 6;&;
Heta M?&:06;2-
-4 &C @ -2&4: ;0:-& ;C ?&4
TRE5NORS PERFOMANCE INDED"
Portfo)io Portfo)ios A1+ Return Ar-E Ris9 free Rate ArfE Beta Ris9 Pre i u Tn R-0rf H Ran9in+
I
4 & -C
6&-6
&?6-
26&C;C
24& ?40
-
4;
II III
2;& -C 6-&6;
6&-6 6&-6
&?&:06
2 &C;C 4;&2-
-0&2466 4:&?202
2
C&APTER 0 III
4C
ANAL5SIS
AND
INTERPRETATIONS
&OLDIN% PERIOD RETURNS
In !7E =E$R -??4 N1E IN%EK gained 6&6CB returns during the same year portfolio I+ II and III has registered a growth of -;&C6+ :4&6? respecti#ely& Return wise portfolio III emerges as best portfolio subsequently PI and PII %uring the year -??6 the N1E IN%EK registered a negati#e growth rate of @C&C- during the same year portfolio I II and III has registered return
4:
of C&-0+ @6&:C and ::& ? respecti#ely& Return wise portfolio III performs well and portfolio I and II occupying subsequent position& In the year -??0 he N1E IN%EK shows a fabulous growth rate of ;0&CC and portfolio I+ II and III performed by 4-&64+ 2&-: and ? & ; and portfolio III emerged as best portfolio subsequently portfolio I and II
O4ERALL PERFOMANCE * !he o#erall performance of the mar)et and the portfolios can be shown by ta)ing the arithmetic a#erage of return& (or the pre#iously said of three years mar)et has registered growth rate of -4&6C& $rithmetic of portfolio I II and III are 4 & -C+ 2;& - and 6-&6; respecti#ely& Portfolio III emerges as best performer&
S&ARPE@S PERFORMANCE MEASURE 1harpe9s performance measure gi#es the appropriate return per unit of ris) as measured by standard de#iation& !he reward of #ariability ratios computed has shown the e'@post return of per unit of ris) for the three portfolio9s for the period of three years& !he rate of ris) of portfolio II is high de#iation by 66&?- by an a#erage return of 2;& -+ similarly the portfolio I has a de#iation of 4C& 2
6?
with a return or 4 & -C and portfolio III with a de#iation of 44& 4 with an a#erage return of 66&6;& "sing 6&-6 as return on sa#ing ban) account as a pro'y for the ris) free rate and substuting there #alue in 1harpe9s e#aluation portfolio I gi#es a slope of ?&;46+ in portfolio I gi#es a reward of 26&C;(4 & -C@4&-6) for bearing a ris) of 4C& 2 ma)ing the sharpe9s ratio to ?&;46& (or e#ery additional B ris) and in#estor has as additional pf ?&;46 returns for abo#e portfolio& Portfolio II gi#es a return or 2;& - while the standard de#iation was 66&?- using 6B return on the sa#ing account as pro'y mar)et shares ratios to ?&6;:& !herefore for e#ery additional B ris) in#estor will earn an additional ?&6;: of return& $nd portfolio II with a return of 6-&6; with an standard de#iation ma)ing 1harpes ratios to &?;- as additional return&
O4ERALLPERFORMANCE
O#erall performances of the portfolios are 4 & -+ 2;+ - and 6-&6; respecti#ely& !he ris) free rate was 6&-6& In#esting in three portfolios during the same period pro#ide an ris) premium of 26&C;+ 2 &C;+ one 4;&2respecti#ely& (or e#ery B of additional ris) an in#estor will earn ?&;46+
6
?&6;: and &?; of return& Portfolio III outperformed by &?;- compared with other two portfolios& !he in#estor will earn on return per unit of beta of 24& -?+ -0&24 and 4:&?20 by ran)ing the portfolio shows that portfolio III performs well as compared with other two portfolios&
TRE5NOR@S PERFORMANCE MEASURE
!reynor9s performance measure gi#es appropriate return per unit or firs) as measured by the beta coefficient& Portfolio I+II and II pro#ided a return of 4 & -B 2;& -B and 6-&6;B with &?6B &- B and ?&:06B as beta coefficient respecti#ely& !reynor9s
6-
ratios for the three portfolios abo#e the ris) free rate of 6&-6B were 24& 0B-0&24B+ 4:&?20B respecti#ely& In#esting in portfolio I II and III pro#ides ris) premium of 26&C;+ 2 &C; and4;&2- for bearing a ris) of beta of &?6-B &- B and ?&:06B recepti#ely& !hus an in#estor will earn a return per unit of beta of 24& 0B -0&24B and 4:&?2B recepti#ely& Portfolio III emerging as the best performer+ portfolio I and II was occupying the subsequent position&
CONCLUSIONS AND SU%%ESTIONS
& $mong the three portfolios I II and III+ portfolio III gi#es a highest return with a proportionate ris) ( ) of 44B with a return of 6-&6;B& -& Portfolio III has outperformed in both sharpe9s and !reynor9s measure&
62
2& It is ad#isable to in#est in portfolio III i&e& foreign collaboration securities in long run and portfolio II i&e& public limited companies in short run because the later is more correlated with the mar)et inde'& 4& %i#ersification of portfolios in #arious projects or securities may reduce high ris) and it pro#ides the high wealth to the shareholders& 6& Heta is used to e#aluate the ris) proper measurement of beta may reduce the high ris) and it gi#es the high ris) premium&
Bi,)io+ra-o./
? Prasanna *handra 3anagement) (1ecurity $nalysis and Portfolio
64
? $#adhani 3anagement) ? (rancis and !aylor
(1ecurity $nalysis and Portfolio
(In#estment 3anagement)
? Graham and %odd 1ecurity $nalysis+ 3cGraw 7ill
INTERNET SITES2 www&nseindia&com www&wi)ipedia&com www&bseindia&com SEARC& EN%INES2 www&google&com
66
doc_814459145.doc
ON
OPTIMIZATION OF PORTFOLIO RISK AND RETURN
In Partial fulfillment for the award of Requirements for the award of the degree of
Master of Business Ad inistration
DECLARATION
I here by declare that the project report titled !OPTIMIZATION OF PORTFOLIO RISK AND RETURN” prepared under the guidance """" (finance department) of """" towards partial fulfillment for the requirement of award of M#B#A#
!he Project report has not been submitted to any other "ni#ersity for the $ward of any %egree or %iploma&
"""
ACKNO$LED%EMENT
!he presentation of this project has gi#en me an opportunity to e'press my profound gratitude to all concern in guiding me& (oremost I would li)e to than) """" the %irector of our *ollege+ """"" for pro#iding an opportunity to "ndergo a project study program& I would li)e to than) """" (finance department) for guiding me to complete the Project ,or)&
-
""""
CONTENTS
C&APTER ' I . . . . C&APTER ' II . / / / / / Introduction Objecti#e of 1tudy 3ethodology 5imitations Portfolio and 7olding period returns 8 1harpe9s Performance 3easure !reynor9s Performance 3easure C&APTER ' III . / $nalysis and Interpretations 244 4: 0 2 4 6 0
2
Con()usion * Su++estions Bi,)io+ra-./
64 66
4
C&APTER 0 I
INTRODUCTION
*ombination of indi#idual assets or securities is a portfolio& Portfolio includes in#estment in different types of mar)etable securities or in#estment papers li)e shares+ debentures stoc) and bonds etc&+ from different companies or institution held by indi#iduals firms or corporate units and portfolio management refers to managing securities& Portfolio management is a comple' process and has the following se#en broad phases&
6
& 1pecification of in#estment objecti#es and constraints& -& *hoice of asset mi'& 2& (ormulation of portfolio strategy& 4& 1election of securities& 6& Portfolio e'ecution& 0& Portfolio rebalancing& ;& Portfolio performance&
Portfo)io Di1ersifi(ation2
$n important way to reduce the ris) of in#esting is to di#ersify your in#estments& %i#ersification is a)in to <not putting all your eggs in one bas)et”& (or e'ample+ if your portfolio only consisted of stoc)s of technology companies& It would li)ely face a substantial loss in #alue if a major e#ent ad#ersely affected the technology industry& !here are different ways to di#ersify a portfolio whose holding are concentrated in one industry& =ou might in#est in the stoc)s of companies
0
belonging to other industry groups& =ou might allocate to different categories of stoc)s+ such as growth+ #alue+ or income stoc)s& =ou might include bonds and cash in#estments in your asset allocation decisions& Potential bond categories include go#ernment+ agency municipal and corporate bonds& =ou might also di#ersity by in#esting in foreign stoc)s and bonds& %i#ersification requires you to in#est din securities whose in#estment returns do not mo#e together& In other words+ their in#estment returns ha#e a low correlation& !he correlation coefficient is used to measure the degree that returns of two securities are related& (or e'ample+ two stoc)s whose returns mo#e in loc)step ha#e a coefficient of > &?& !wo stoc)s whose returns mo#e in e'actly the opposite direction ha#e a correlation of @ &?& !o effecti#ely di#ersity+ you should aim to find in#estments that ha#e a low or negati#e correlation& $s you increase the number of securities in your portfolio+ you reach a point where you9#e li)ely di#ersified as much as reasonably possible& (inancial planners #ary in their #iews on how many securities you need to ha#e a fully di#ersified portfolio& 1ome say it is ? to -? securities& Others say it is closer to 2? securities& 3utual funds offer di#ersification at a lower cost& =ou can buy no@load mutual funds from an online bro)er& Often+ you can buy shares fund directly from the mutual fund+ a#oiding a commission altogether&
Asset a))o(ation2
$sset allocation is the process of spreading your in#estment across the three major asset classes of stoc)s+ bonds and cash&
;
$sset allocation is a #ery important part of your in#estment decision@ ma)ing& Professional financial planner frequently point out that asset allocation decisions are responsible for must of your in#estment return& $sset allocation begins with setting up an initial allocation& (irst+ you should determine your in#estment profile& 1pecially+ this requires you to assess you in#estment horiAon+ ris) tolerance+ and financial goals. In#estment horiAon+ $lso called time horiAon your in#estment horiAon is the number of years you to sa#e for a financial goal& 1ince you9re li)ely to ha#e more than goal+ this means you will ha#e more than one in#estment horiAon& (or e'ample+ sa#ing for your gi#e@year@daughter9s college has an in#estment horiAon of - years& 1a#ing for your retirement in 2? tears has an in#estment horiAon of 2? years& ,hen you retire+ you will want to ha#e sa#ed a lump sum that is large enough to generate earnings e#ery year until you die ris) tolerance& =our ris) tolerance is a measure of your willingness to accept a higher degree of ris) in e'change for the chance to earn a higher rate or return& !his is called the ris)@return trade@off& 1ome of us+ naturally+ are conse#atyi:#e in#estor+ while other are aggressi#e in#estors& $s a general rule+ the younger your are+ the higher your ris) tolerance and the more aggressi#e you can be& $s a result+ you can afford to allocate a higher percentage of your in#estment to securities with more ris)& !hese include aggressi#e growth stoc)s and the mutual funds that in#est ion them& $ more aggressi#e allocation is #iable because you ha#e more time to reco#er form a poor year of in#est0ment returns& (inancial goal+ younger and aggressi#e in#estor9s allocation+ as a general rule+ younger and aggressi#e in#estors allocate ;?B to ??B of their
C
portfolios to stoc)s+ with the remainder in bonds and cash& *onser#ati#e in#estors allocate 4?B to 0?B in bonds+ and the remainder in cash& 3oderate in#estors allocate somewhere between the allocation of aggressi#e and conser#ati#e+ to ma)e an initial allocation+ you need to build a portfolio of indi#idual securities+ mutual funds+ or both& In general+ mutual funds pro#ide more di#ersification benefit for the buc)& 7ow you choose to precisely allocate among the major asset classes depends+ in part+ on other factors& (or e'ample+ if e'ample+ if interest rates are e'pected to rise+ you might allocate a greater percentage to money mar)et mutual funds+ *%s+ or other ban) deposits& If rates are headed lower+ you may choose to allocate more to stoc)s or bonds& (inancial planners suggest that you rebalance+ or reallocate+ your portfolio from time to time& !hey differ in their #iews on how often you should reallocate& It may be once a year or it may be e#ery three to si' months& $t a minimum+ reallocation lets you up date any changes in your in#estment profile+ or to ta)e ad#antage of a change in interest rates& Rebalancing often in#ol#es nothing more than a <fine@tuning” of your current0 allocations& (or e'ample+ a conser#ati#e in#estor may decide to shift 6B of her portfolio form stoc)s to cash to ta)e ad#antage of higher rates that money mar)et funds may be offering&
&
:
?
0Need 0O,3e(ti1e 0Met.odo)o+/
SPECIFIC IN4ESTMENT OBJECTI4E AND CONSTRAINS
!he first step in the portfolio management process is to specify the one9s in#estment objecti#es and constraints& !he commonly stated in#estment goals are.@ INCOME @ !o pro#ide a steady income through the regular interest or di#ided payment& %RO$T& @!o increase the #alue of the principal amount through capital appreciation& STABILIT5 D 1ince income and growth represent two ways by which return is generated and in#estment objecti#es may be e'pressed in terms of
return and ris)& $n in#estor will be interested in higher return and lower le#el ris)& 7owe#er the ris) and return go hand to hand+ so an in#estor has to bear a higher le#el of ris) in order to earn a higher return& CONSTRAINTS D $n in#estor should bear in mind the constraints arising our of the following factor& @5iquidity @!a'es @!ime horiAon @"nique preferences and circumstances
OBJECTI4ES
!o construct three portfolios of public sector units+ public limited companies and foreign collaboration and fine their e'@post returns and ris) for the period of three year&
-
!o ma)e a comparati#e study of the ris)@adjusted measure of portfolio performance using the shapre9s and !reynor9s performance indeed under total ris) and mar)et ris) and mar)et ris) situations+ by ta)ing e'@post returns for a period of three years&
MET&ODOLO%5 "sing a model consisting of two modules has carried out the wor)& !he first module in#ol#es the section of portfolio and the second module in#ol#ed e#aluation of portfolio9s performance& MODULE06 1ecurities selection and portfolio construction has been made by ta)ing scripts Public 1ector "nits+ public limited companies and foreign
2
collaboration units& Equal weigtage has been gi#en to industries li)e shipping+ oilFgas and power growth oriented industries li)e pharmaceuticals+ ban)ing and (3*G and technology oriented industries li)e software and telecommunications&
MODULE ' 7 Portfolio performance was e#aluated by ran)ing holding period9s returns under total ris) and mar)et ris) situation (measured by standard de#iation and Heta coefficient) for the period of three years&
LIMITATIONS
T.e 8or9 .as ,een (arried out under t.e fo))o8in+ )i itations2
? !he all portfolio consist of ris)ly assets there no ris)@free assets& ? Ris)ly assets consist of equity shares and where as ris)@free assets consists of in#estments in the sa#ing ban) account+ deposits+ treasury bills+ bonds etc&
4
? !he holding period for ris)y assets was for I yr i&e& shares were assumed to be purchased at the first day and sold at the second consecuti#e day and a#erage return for I yr is considered& ? $n equal no of shares i&e& I (one) share of each script is assumed to be purchased form the secondary mar)et& ? Return on the sa#ing ban) account is considered as benchmar) rate of return& ? $ll the portfolio has been held constant for the whole period of the three years&
C&APTER 0 II
6
PORTFOLIOS
PORTFOLIOS I
NSE CODE H$NI O( IN%$ H7E5 H$NIIN%I$ 7E5
0
755 3F3 1*I 1$!=$3 *O3P"!ER J1N5 G5$KO IHP 1$I5
7IN%5EJER 3F3 1*I 1$!=$3*O3P"!ER J1N5 G5$KO IHP 1$I5
PORTFOLIO II
NSE CODE "!I H$NI !$!$ PO,ER I!* E1*OR!1 "!IH$NI !$!$PO,ER I!* E1*OR!1
;
J$R"N17IPING ,IPRO H7R$!I %RRE%%=1 IP*5 !I1*5
J$R"N17IP ,IPRO H7R$!I %RRE%%= IP*5 !I1*O
PORTFOLIO III
NSE CODE ING J=1=$ $HH *$%I5$ J=1=$ H$NI $HH *$%I5$
C
3I*O HO17 GE17IPPING 7"G7E1 1O(!,$RE !$!$ !E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5
3I*O GE17IP 7"G7E11O(! !$!$ !E5E*O3 NI*O5$1PIR ONG* E11$RG"L
&OLDIN% PERIODS RETURNS2
:
$ll the in#estment is made at a certain period of time& 7olding period returns enables an in#estor to )now his returns during that period of time& It can be computed by using the formula.@ 7olding period returns (7PR) M !oday9s closing price D =esterday9s closing price =esterday9s closing price 7olding period returns are used for comparati#e criterion& 7olding period returns can be compared for ma)ing an assessment of relati#e returns&
-?
MODULE I
&OLDIN% PERIOD RETURNS
Portfo)io I for 7::;0:<
-
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1iden d de()are d
Di1iden d a ount
Mar9et -ri(e 8.en -ur(.ase d ?&6 -C&; ---&:&2?&? -42&; -C0&4 ;&C
=Return on di1idend
=Return on se(urit/
Tota) return
H$NI O( IN%I$ H7E5 755 3F3 1*I 1$!=$3 *O3P J1N5 G5$KO IHP 1$I5 -
? ?
? 4? 2??
? 4 2 ? ? ? ? ; ?? ? ?
? 2& &26 ?&?? ?&?? ?&?? ?&?? &0C 2&4? ?&??
@ ;&44?&06&C4 C& :C& 4 &-4 @-?&-; @2& C :&:6 @2&:C
@ ;&442&;-: ;& :? C& :C& 4 &-4 @-?&-; @ &6?4 -2&26 @2&:C
? ?
? ? ?
? ? ? ?
? ?
-:4&2 6&;
?
Return
-;&C66
Portfo)io I for 7::<0:>
--
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend &2-&&24&CC 0&?? ?&C0 4&6 -&?4 &6; ?&??
=Return on se(urit/
Tota) return
H$NI O( IN%I$ H7E5 755 3F3 1*I 1$!=$3 *O3P J1N5 G5$KO IHP 1$I5 -
? ?
2? 4? 2??
2 4 2 6&6 ? ? -&C&6 ; 4 ?
-0&6 C?&C --;&-6 -&C ;-&66 -6; CC&6 24&; C: &26 6&06
C:&2-4&:: @2:&4; @0&6@-?&: @-C&66 @CC&0 @0&6 @ 2&:6 ; &;4
??&0 -;&@2C& 4 @ &044 @-?&: @-;&0: @C4& @4&46; @ -&2C ; &;4
? ?
66 ?
? ? ? ?
C6 ;? 4? ?
Return
&?-0
Portfro)io I for 7::>0:?
-2
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend -&64 &24 -&? :&?C?&??? &0 0&?6; 2&2:2 ?&??? ?&???
=Return on se(urit/
Tota) return
H$NI O( IN%I$ H7E5 755 3F3 1*I 1$!=$3 *O3P J1N5 G5$KO IHP 1$I5 -
? ?
? 2? 2?? 2 2 : ? 4? -&C 46&6 ? ? ?
2:&26 --2&06 4:& 6 ::& 6 &-6 ;2&06 ;4&2 -:4&; ::&C :&?6
4:&?0 ?;& C&42 04&-2 ?:&6 0;&-: 6:&6 ;;&?-2&C 62&?0
6 &0? ?C&44 ?&44 ;2&2 ?:&6 0C&:?06&60; C?&4 2 -2&C 62&?
? ?
:? ?
? ? ? ?
46 ?? ? ?
Return :4&6?6
PORTFOLIO II FOR 7::;0:<
-4
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend ?&??? ?&??? ?&??? &-:; ?&??? ?&?;: ?&??? ?&??? ?&??? ?&???
=Return on se(urit/
Tota) return
"!IH$NI !$!$PO,ER I!* E1OR!1 J$R"N17IPING ,IPRO H7$R!I %RRE%%= IP*I !I1*O 6 -
? ? ? ? ?
? ? ? ? ? 6?
? ? ?
-2&; ?2& 0-6 ;;&
02&CC&
?& : @ ?& ; 0&02 6C&; @ 2& --&-4 6-&-0 @;&C02&CC&
?& : @C&C;2 0&02 6C&;C: @ 2& --&-4 6-&-0 @;&C?
&66 -0C&46
?
? ?
? ? ? ?
44&26 : 4&:6 64& 6 6&;6
? ?
? ?
Return
C&-0C
PORTFOLIO II FOR 7::<0:>
-6
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend 6&4?64 6&0::-6 ? &0262? ?&?6: ; 6& 4 2: ?&460 0 -&6; 42 C& ;6;C
=Return on se(urit/
Tota) return
"!IH$NI !$!$PO,ER I!* E1OR!1 J$R"N17IPING ,IPRO H7$R!I %RRE%%= IP*I !I1*O 6 -
? ? ? ? ?
-06 ? ? ? 6?
-&0&6 ?
4?&; 4&?6 ;?0&2 0 & 6
-&-2 -&-; @C&0 @4C&;4 @- &4 @--&6C @-2&?4 @ 2&6 C&4; 26&:
;&0264 ;&:0:2 @C&0 @4;& ?6 @- &4 @--&6@ ;&C:: @ 2&?44 &?4 44&?;0
?
&; 0:?
?
-? ??
6 -&-6 C
2C&: ?:0& C;&6 :;&C6
? ?
--&6 C?
Return
@6&:C60
PORTFOLIO II FOR 7::>0:?
-0
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend 0&-0600 0& 24:; 2& :64 ? 0&6- ;4 ?&2-4C: -?&0 C0 ?&6404C -&:C 6 ;&4? :-
=Return on se(urit/
Tota) return
"!IH$NI !$!$PO,ER I!* E1OR!1 J$R"N17IPING ,IPRO H7$R!I %RRE%%= IP*I !I1*O 6 -
? ? ? ? ?
-6 ;? -?? ? 0 -??
-&6 ; -? ? ?&0 4 0 6 -&6 ?
2:&: 4& 0-6&: 26&-6 :&-2 &-:& : 4&:6 C2&C6 26&
6?&0 -C& 64&0C ;0&64 ?6&4: - &26 C2&20 4&:C:&-&C-
60&C2 24&-4 6;&C;6 ;0&64 -&? - &0;6 -?2&:C 6&400 :-& C-?&--
?
0? ??
? ?
-6 ??
Return ::& ?-
PORT>FOLIO III FOR 7::;0:<
-;
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend 2& ? ? ? ? ?&22; 2 ? ? & 4? :42
=Return on se(urit/
Tota) return
ING J=1$ $HH *$%I5$ 3I*OHO17 GE17IPPING 7"G7E1 !$!$!E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5 6 6
? ?
26 ? ?
2&6 ? ? ? ? ? ?
-&-2C&: -4 -;?: -6&2 6:2&-6 60&4 -:6&;6
C:&:6 0&;&-C@4&?0 --&46 @4?&46 2:& @?&?4; C;&:; C;&:;
:2&?0: 0&;&-C @4&?0 --&46 @4?& 2:& @?&?4; ::& C;&:; 2
?? ?
? ? 4?
? ? ? ?
? ? 4? ?
4 ?
-6&06 -6&06
Return 4-&64C
PORTFOLIO III FOR 7::<0:>
-C
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend &4 66; -&-;26: -&;? 00 &0;66 2&??C ?&;-?&46422 2&C;2C2&:44 ; ?
=Return on se(urit/
Tota) return
ING J=1$ $HH *$%I5$ 3I*OHO17 GE17IPPING 7"G7E1 !$!$!E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5 6 6
? ?
4? 0? ;?
2&6 0 2&6 4? 4 -&6 ?&6 2 ?
-4;&-6 -02&: -:&66 -2C;&26 2?&;6 -;;&; ; &: -; &?6 2-:&0 2-:&0
4&;; -&;; @2&2 4;&46 -6&:: @-C&-4;&46 @-4&CC 2&42 2&42
0& C60 6&?44 @?&0?C2 4:& -6 2C&::C @-;&6 4C&:?4 @- &??0 ;&2;4 2&42
?? ?
4? 4? 4?
? ? ? ?
-6 ?6 2? ?
Return
2&::6
PORTFOLIO III FOR 7::>0:?
-:
Na e of t.e s(ri-t
Fa(e 1a)ue
Di1idend de()ared
Di1idend a ount
Mar9et -ri(e 8.en -ur(.ased
=Return on di1idend &4 66; -&-;26: -&;? 00 &0;66 2&??C ?&;-?&46422 2&C;2C2&:44 ; ?
=Return on se(urit/
Tota) return
ING J=1$ $HH *$%I5$ 3I*OHO17 GE17IPPING 7"G7E1 !$!$!E5E*O3 NI*O5$1 P7$R3$ ONG* E11$R 1!EE5 6 6
? ?
4? 0? ;?
2&6 0 2&6 4? 4 -&6 ?&6 2 ?
-4;&-6 -02&: -:&66 -2C;&26 2?&;6 -;;&; ; &: -; &?6 2-:&0 2-:&0
;0&-C ?0&0; 44&?: 2C&20 26&0 ;&06 :0&2; @-4&CC :6&-0 :6&-0
;;&0:0 ?C&:4 40&?4 4?&?4 4C&0 C&2; :;&C-4 @- &??0 ::&-?4 :6&-0
?? ?
4? 4? 4?
? ? ? ?
-6 ?6 2? ?
Return
? & ;-;
E"0POST PORTFOLIO RETURNS
2?
5EAR -??6 -??0 -??; Ri
PORTFOLIO PORTFOLIO PORTFOLIO I II III -;&C6 C&-0 4-&64 &?@6&:C 2&:: :4&6 ::& ? & ; 4 & -22222 2;& -00000; 6-&60;
2
MODULE ' II
RISK ADJUSTED MEASUREMENT OF PORTFOLIO PERFORMANCE S&ARPE@S PERFORMANCE MEASURE CALCULATIONS OF STANDARD DE4IATION
Ris9
Ris) in holding securities is generally associated with the possibility that realiAed return will be less than returns were e'pected& !he source of such disappointment is the failure of di#idends or the fail in security9s prices& (orces that contribute to #ariation in return+ price or di#idend
2-
const0itures elements of ris)& 1ome influences that are e'ternal to the firm+ cannot be controlled and affect large number of securities& Other influences are internal to the firm are controllable to all large degree&
S/ste ati( Ris9
!he systematic ris) affects the entire mar)et& !hose forces that are uncontrollable e'ternal and board in the effect are called sources of systematic ris)& Economic+ political and sociological changes are sources of systematic ris)&
S/ste ati( ris9 furt.er di1ided into
@3ar)et Ris) @Interest @Purchasing power Ris)
Mar9et Ris9
L&*& (rancis defined 3ar)et ris) as that portion of total #ariability of returned caused by the alternating farces of bull and bear mar)et& ,hen the security inde' mo#es upwards haltingly for a significant period of time+ it is )nown as bull mar)et& In the bull mar)et the indeed mo#es form a low le#el to the pea)& Hear mar)et is just re#erse to the bull mar)et& %uring the bull
22
and bear mar)et more than C? percent of the securities prices rise or fall along with the stoc) mar)et indices&
Interest Rate Ris9
!he rise or fall in the interest rate affects the cost borrowing& ,hen the call money mar)et rate changes& Interest rates not only affect the security traders but also corporate bodies who carry their business on borrowed funds& !he cost of borrowing would& Increase and a hea#y out flow of profit would ta)e place in the form of interest to the capital borrowed& !his lead a reduction in earning per share and a consequent fall in the price of share&
Pur(.asin+ -o8er Ris9
Jariations in the returns are caused also by the loss of purchasing power of currency& Inflation is the reason behind the loss of purchasing power the rise in price penaliAes the returns to the in#estors+ and e#ery potential rise in price a ris) to the in#estor&
Uns/ste ati( Ris9
"nsystematic ris) is the unique ris)+ which will be different to different firms& "nsystematic ris) stems form managerial inefficiency+ technological change in production process+ a#ailability of raw material mentioned factors differ form industry to industry+ and company to company& !hey ha#e to be analyAed separately for each industry and firm&
24
Hroadly "nsystematic ris) can be classified into. @Husiness ris) @(inancial ris)
Business Ris9
It is the portion of the unsystematic ris) caused by the operat0in en#ironment of the business&
Finan(ia) Ris9
(inancial ris) in a company is associated with the capital structure the company& It refers to the #ariability of the income to the equity capital to debt capital&
Measure ent of Ris9
!he ris) of a portfolio can be measured by using the following measure of ris)&
4aria,i)it/
In#estment ris) is associated with the #ariability of rates of return& !he more #ariable is the return+ the more ris)y the in#estment& !he total #ariance is the rate of return on a stoc) around the e'pected a#erage+ which includes both systematic and unsystematic ris)&
26
!he total ris) can be calculated by using the standard de#iation& !he standard de#iation of a set of numbers is the squares root of the square of de#iation around the arithmetic a#erage& =mbolically+ the standard de#iation can be e'pressed as@ N M O (rit@ri) n@ ,here+ ri is the mean return of the portfolio and rit is the return form the portfolio for a particular year
S&ARPE@S PERFORMANCE INDE"20
,illiam 1harpe9s of portfolio performance is also )nown as reward to #ariability ratio (RJ$R)& It is simply the ratio of reward+ which defined as
20
realiAed portfolio returns in e'cess of the ris) free rate+ to the #ariability of return measured by the standard de#iation relation to total ris) assumed by the in#estor& !he measure can be defined follows.@ RJ$R M rp@rf N ,here+ rpM the a#erage return for the portfolio (P) during it 7PR rfM ris) free rate of return during L7PR N M the standard de#iation of the portfolio (P) during 7PR
CAPITAL MARKET LINE
2;
*apital mar)et shows the conditions pre#ailing in the capital mar)et in terms of e'pected return and ris)& It depicts the equilibrium condition that pre#ails in the mar)et for efficient portfolio9s consisting of the portfolio of ris)y asset or ris) free asset or both& $ll combination of ris)y and ris) free portfolio are bounded by the capital mar)et line+ and all in#estors will end up with portfolio somewhere on the capital mar)et line& !he capital mar)et is usually deri#ed under the assumptions that there e'ists a ris) a ris)@less asset a#ailable for in#estment& It is further assumed that0 in#estor can borrow or lend as much as desired at the ris) free assets with a portfolio or ris)y assets to obtain the desired ris) return combination& "sing the capital mar)et line can graphically represent 1harpe9s measure for portfolios& !he #ertical a'is represents the return on the portfolios and the the horiAontal a'is represents the standard de#iation for returns& !he #ertical intercept is rf& RJ$R measures the slope of the line form rf to the portfolio being e#aluated& !he steeper the line+ the higher the slope (RJ$R) and the better performance&
TRE5NOR@S PERFORMANCE INDE"
!he measure is also referred to as reward to #olatility ratios (RJO5)& !reynor sough to relate return on a portfolio to its ris)& 7e distinguished between total ris) and systematic ris) assuming that0 the portfolio is well di#ersified& In measuring the portfolio performance !reynor introduced the
2C
concept of characteristic line& !he slope of the characteristics measures the relati#e #olatility of the portfolio9s returns& !he slope of this line is the beta co@efficient which is measure of the #olatility (or responsi#eness) of the portfolio9s returns in relation to those of the mar)et inde'& !reynors9s ratio is the realiAed portfolio9s return in e'cess of the ris)@free to the #olatility of return as measured by the portfolio beta& RJO! M rp@rf Hp M $#erage e'cess return of portfolio (P) 1ystematic ris) for portfolio
SECURIT5 MAEKET LINE
!he security mar)et line indicates the ris)@return trade@off for portfolio and indi#idual securities& !reynor e'tended his analysis to identify the component of ris) that will be compensated by the mar)et& It is )nown as systematic ris) and is commonly measured by the beta& Heta is a
2:
measure of ris) that applies to all assets and portfolio whether efficient or inefficient& 1ecurity mar)et line specifies the relationship between e'pected return and ris) for all assets and portfolios whether efficient or inefficient& !he security mar)et is obtained by ta)ing the ris) (beta) on the horiAontal a'is and portfolio return on the #ertical a'is& !he 1ecurity mar)et line can be graphically&
E (rm)
135
rf Heta &??
Beta
Heta is a mar)et ris) measure employed primarily in the equity& It measures the systematic ris) of a single instrument or an entire portfolio& ,illiam 1harp ( :04) used the notion in his landmar) paper introducing the capital asset pricing model (*$P3)& !he name <beta” was applied later&
4?
Heta describes the sensiti#ity of an instrument or portfolio to broad mar)et mo#ements& !he stoc) mar)et (represented by an inde' such s the 1FP 6?? or ??) is assigned a beta of &?& Hy comparison+ a portfolio (or instrument) with a beta of -&? will tend to benefit or suffer form broad mar)et mo#es twice as much as the mar)et o#erall& !he formula for beta is O"50AOK=) (O=) NOK@(OK) ,here K is the mar)et return $nd = is the security return Hoth quantities are calculated using simple returns& Heta is generally estimated form historical price time series& (or e'ample+ 0? trading of simple returns might be used with sample estimators for co#ariance and #ariance& It is possible to construct negati#e beta portfolio beta portfolios& $pproaches include& Heta is sometimes used as a measure of a portfolio9s mar) ris)& !his can be misleading because beta does not capture specific ris)& Hecause of specific ris)& $ portfolio can ha#e a low beta+ but still be highly #olatile& !i price fluctuations would simply ha#e a low correlation with those of the o#erall mar)et& It is said that a security or portfolio ha#ing higher beta will perform well pro#ided mar)et has to go up i&e&+ mar)et indeed&
4
Ca)(u)ation of standard de1iation of returns
PORTFOLIO I
5ear -??6 -??0 -??; RiM Return -;&C6 &?:4&6 4 & -2 DiBr0ri @ 2&-;2 @4?& ?2 62&2;; DiCDi ;0& C 0?C&2 -C4:& 4022&6 S#D 4C& 22
PORTFOLIO II
5ear
-??6 -??0 -??; RiM
Return
C&-0 @6&:C ::& 2;& -;
DiBr0ri
@ C&C0; @42&:;2
DiCDi
266&:6 C6C&2C4?&; 0?64&C
S#D
66&?--
PORTFOLIO III
5ear -??6 -??0 -??; RiM Return 46&64 2&:: ? & ; 62&60; DiBr0ri @C&?-0; @2:&6;; 4;&0?2 DiCDi 04&4-; 600&2 --00& 2C:0&C S#D 44& 4
4-
S&ARPE PERFORMANCE MEASURE
A1+ -ortfo)io Portfo)ios I II III Return AD-E in = 4 & -C 2;& -C 6-&6; Ris9 free Rate AnE= 6&-6 6&-6 6&-6 EF(ess return Ar-0riE 26&C;C 2 &C;C 4;&2Standard De1iation 4C& 2 66&?44& 4 S.ar-e@s Ratio r-0 rtG ?&;46 ?&6;: &?;Ran9in+ 2
42
TRE5NOR@S PERFORMANCE MEASURE CALCULATION OF BETA
Beta for -ortfo)io I
5ear A1+ Mar9et Return " "7 A1+ Sto(9 Return 5 "5
44
-??4@?6 -??6@?0 -??0@?;
6&0C2 @C&C-; ;-&CC0
2-&-:0 ;;&: 0 6C:?&C
-;&C66 &?-6 -2&2C
6C&2 @:&?4;; ;224&4
Heta M &?6-0
Beta -ortfo)io II
5ear A1+ A1+
46
Mar9et Return "
"7
Sto(9 Return 5
"5
-??4@?6 -??6@?0 -??0@?;
6&0C2 @C&C-; ;0&?2 ;-&CC0
2-&-:0 ;;&: 0 6;C?&0 6C:?&C
C&-0; @6&:C6 ::& ?&2C
?2&C 6-&C2 ;624&; ;0: &4
Heta M &- ?? C
Beta for -ortfo)io III
40
5ear
A1+ Mar9et Return " "7
A1+ Sto(9 Return 5 "5
-??4@?6 -??6@?0 -??0@?;
6&0C2 @C&C-; ;0&?2 ;-&CC0
2-&-:0 ;;&: 0 6;C?&0 6C:?&C
4-&64C 2&:: ? & ; 6;&;
Heta M?&:06;2-
-4 &C @ -2&4: ;0:-& ;C ?&4
TRE5NORS PERFOMANCE INDED"
Portfo)io Portfo)ios A1+ Return Ar-E Ris9 free Rate ArfE Beta Ris9 Pre i u Tn R-0rf H Ran9in+
I
4 & -C
6&-6
&?6-
26&C;C
24& ?40
-
4;
II III
2;& -C 6-&6;
6&-6 6&-6
&?&:06
2 &C;C 4;&2-
-0&2466 4:&?202
2
C&APTER 0 III
4C
ANAL5SIS
AND
INTERPRETATIONS
&OLDIN% PERIOD RETURNS
In !7E =E$R -??4 N1E IN%EK gained 6&6CB returns during the same year portfolio I+ II and III has registered a growth of -;&C6+ :4&6? respecti#ely& Return wise portfolio III emerges as best portfolio subsequently PI and PII %uring the year -??6 the N1E IN%EK registered a negati#e growth rate of @C&C- during the same year portfolio I II and III has registered return
4:
of C&-0+ @6&:C and ::& ? respecti#ely& Return wise portfolio III performs well and portfolio I and II occupying subsequent position& In the year -??0 he N1E IN%EK shows a fabulous growth rate of ;0&CC and portfolio I+ II and III performed by 4-&64+ 2&-: and ? & ; and portfolio III emerged as best portfolio subsequently portfolio I and II
O4ERALL PERFOMANCE * !he o#erall performance of the mar)et and the portfolios can be shown by ta)ing the arithmetic a#erage of return& (or the pre#iously said of three years mar)et has registered growth rate of -4&6C& $rithmetic of portfolio I II and III are 4 & -C+ 2;& - and 6-&6; respecti#ely& Portfolio III emerges as best performer&
S&ARPE@S PERFORMANCE MEASURE 1harpe9s performance measure gi#es the appropriate return per unit of ris) as measured by standard de#iation& !he reward of #ariability ratios computed has shown the e'@post return of per unit of ris) for the three portfolio9s for the period of three years& !he rate of ris) of portfolio II is high de#iation by 66&?- by an a#erage return of 2;& -+ similarly the portfolio I has a de#iation of 4C& 2
6?
with a return or 4 & -C and portfolio III with a de#iation of 44& 4 with an a#erage return of 66&6;& "sing 6&-6 as return on sa#ing ban) account as a pro'y for the ris) free rate and substuting there #alue in 1harpe9s e#aluation portfolio I gi#es a slope of ?&;46+ in portfolio I gi#es a reward of 26&C;(4 & -C@4&-6) for bearing a ris) of 4C& 2 ma)ing the sharpe9s ratio to ?&;46& (or e#ery additional B ris) and in#estor has as additional pf ?&;46 returns for abo#e portfolio& Portfolio II gi#es a return or 2;& - while the standard de#iation was 66&?- using 6B return on the sa#ing account as pro'y mar)et shares ratios to ?&6;:& !herefore for e#ery additional B ris) in#estor will earn an additional ?&6;: of return& $nd portfolio II with a return of 6-&6; with an standard de#iation ma)ing 1harpes ratios to &?;- as additional return&
O4ERALLPERFORMANCE
O#erall performances of the portfolios are 4 & -+ 2;+ - and 6-&6; respecti#ely& !he ris) free rate was 6&-6& In#esting in three portfolios during the same period pro#ide an ris) premium of 26&C;+ 2 &C;+ one 4;&2respecti#ely& (or e#ery B of additional ris) an in#estor will earn ?&;46+
6
?&6;: and &?; of return& Portfolio III outperformed by &?;- compared with other two portfolios& !he in#estor will earn on return per unit of beta of 24& -?+ -0&24 and 4:&?20 by ran)ing the portfolio shows that portfolio III performs well as compared with other two portfolios&
TRE5NOR@S PERFORMANCE MEASURE
!reynor9s performance measure gi#es appropriate return per unit or firs) as measured by the beta coefficient& Portfolio I+II and II pro#ided a return of 4 & -B 2;& -B and 6-&6;B with &?6B &- B and ?&:06B as beta coefficient respecti#ely& !reynor9s
6-
ratios for the three portfolios abo#e the ris) free rate of 6&-6B were 24& 0B-0&24B+ 4:&?20B respecti#ely& In#esting in portfolio I II and III pro#ides ris) premium of 26&C;+ 2 &C; and4;&2- for bearing a ris) of beta of &?6-B &- B and ?&:06B recepti#ely& !hus an in#estor will earn a return per unit of beta of 24& 0B -0&24B and 4:&?2B recepti#ely& Portfolio III emerging as the best performer+ portfolio I and II was occupying the subsequent position&
CONCLUSIONS AND SU%%ESTIONS
& $mong the three portfolios I II and III+ portfolio III gi#es a highest return with a proportionate ris) ( ) of 44B with a return of 6-&6;B& -& Portfolio III has outperformed in both sharpe9s and !reynor9s measure&
62
2& It is ad#isable to in#est in portfolio III i&e& foreign collaboration securities in long run and portfolio II i&e& public limited companies in short run because the later is more correlated with the mar)et inde'& 4& %i#ersification of portfolios in #arious projects or securities may reduce high ris) and it pro#ides the high wealth to the shareholders& 6& Heta is used to e#aluate the ris) proper measurement of beta may reduce the high ris) and it gi#es the high ris) premium&
Bi,)io+ra-o./
? Prasanna *handra 3anagement) (1ecurity $nalysis and Portfolio
64
? $#adhani 3anagement) ? (rancis and !aylor
(1ecurity $nalysis and Portfolio
(In#estment 3anagement)
? Graham and %odd 1ecurity $nalysis+ 3cGraw 7ill
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doc_814459145.doc