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Stock Portfolio Selection using Mathematical

Programming: An Educational Approach

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Abstract: - $4 2<98 /0/.1 W. /1.8.42 04 0//=9;02954 56 302<.3029;0= /15>103394> 7894> 1.0= 825;G 301G.2 :020I

K582 56 2<. 827:.428 <0M. 853. 6039=90192X W92< 2<. 825;G 301G.2 04: 2<.1.651. ;04 74:.18204: 2<. /15F=.3

.089=XI ".1. W. .C/=51. 2<. 8217;271. 56 2<. 825;G /51265=95 2<157>< 302<.3029;0= /15>103394> Y5/2939R02954Z

85 08 25 0;<9.M. 0 /.1651304;. <9><.1 6153 2<. 54. 56 2<. 825;G 94:.CI

Key-Words: 302<.3029;0= /15>103394>D /51265=95 8.=.;2954D 825;G8D 5/2939R02954I

1 Introduction&<. =94.01 /15>103394> 35:.= <08 F..4 0//=9.: 94 0

=01>. 473F.1 56 01.08 94;=7:94> 69404;.D 39=9201X

0//=9;029548D 21048/51202954 8;<.:7=94>D /15:7;2954

04: 94M.4251X 3040>.3.42D 2.=.;533749;029548I

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/15>103394> 85=72954 F72 94 304X ;08.8 853.

94>.4792X 98 1.[791.: 651 2<. 35:.==94>I B94.01

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0//=9;029548 94 ;53F94025190= 5/2939R02954 04:

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56 893/=.C 0=>5192<38 /15/58.: 04: :.M.=5/.: FX

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/15>103394> 3.2<5:8 <0M. 0=85 F.;53. /10;29;0=

255=8 651 ;.12094 ;=088.8 56 =94.01 /15>103394>

/15F=.38D 8.. 651 9482.0: \L]D \?]D \O]D \^]D \@]I

&<. /15F=.3 56 /51265=95 8.=.;2954 98 452 M.1X 5=:I $4

<98 W51GD "011X K01G5W92R \LA]D 8.2 2<. 6574:029548

56 35:.14 /51265=95 2<.51XI _153 2<.4 54D 304X

072<518 827:9.: 2<. /15F=.3 56 /51265=95 8.=.;2954 94

304X :91.;29548 \T]D \S]D \LV]I `92<94 2<. 35:.14

.;54539; 1.0=92XD 825;G /51265=95 3040>.3.42 98 0 /15F=.3 60;.:D 54 2<. 54. <04:D FX 304X 69404;90=

040=X828 04: 1.8.01;<.18 04:D 54 2<. 52<.1 <04:D FX

Proceedings of the 10th WSEAS Int. Conference on MATHEMATICS and COMPUTERS in BUSINESS and ECONOMICS

ISSN: 1790-5109 53 ISBN: 978-960-474-063-5

mailto:[email protected]








8/12/2019 9fcfd50f968a26c201


/10;292954.18 W<5 01. ;0==.: 7/54 25 30G.

94M.823.42 :.;989548 651 87F8204290= 94M.823.42

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8.48929M. >9M.4 2<. 67271. ;533923.42 94M5=M.:I &<.

;548217;2954 56 0 35:.= 651 .66.;29M. 3040>.3.42 94

2<. 8.48. 56 30C939R94> /52.4290= 1.27148 W9== F. 04

942.1.8294> 04: [792. 78.67= 9887.I

$4 2<. =082 X.018D [792. 0 6.W 1.8.01;<.18 <0M.

3.1>.: 87Fa.;28 6153 :966.1.42 :98;9/=94.8 9425 2<.

=.01494> /15;.88 85 08 25 0;<9.M. 0 F.22.1

;53/1.<.48954 54 2<. /012 56 2<. 827:.428 \LL]D \L?]I

$4 2<98 /0/.1 W. /1.8.42 0 2.0;<94> 35:.= 56

302<.3029;0= /15>103394> 2<157>< 825;G /51265=95

8.=.;2954I

2 Problem Formulation

$4 &0F=. LD W. /1.8.42 2<. /15a.;29548 651 2<. /.1651304;. 56 2W5 825;G8 04: 2<. %25;G $4:.C 56 0

825;G 301G.2I &<.8. 01. :020 W<9;< 0158. 6153 2<.

93/=.3.4202954 56 8937=02954 2.;<49[7.8D W<58.

M0190F9=92X 2<57>< :5.8 452 :966.1 37;< 6153 2<.

.[79M0=.42 /.1651304;. 56 87;< 94:.C.8 94 0 1.0=

825;G 301G.2I &<. /15a.;29548 94 &0F=. L 1.6.1 25 2<.

X.01 ?AAb 04: 01. 54 0 3542<=X F0898I

J71 208G 98 25 729=9R. 2<.8. /15a.;29548 04: 25 3040>.

825;G /51265=958 W92< 2W5 825;G8 <0M94> 08 571 30a51

;53/.29251 2<. %25;G $4:.C 56 2<. %25;G +C;<04>.

651 2<. X.01 ?AAbI $4 .88.4;. W. 01. 20;G=94> 2<.

/51265=95 /15F=.3 6153 0 >03. 2<.51X /5942 56 M9.W\b]D \LO]I

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`. ;57=: F19.6=X 87//58. 2<02 2<. 3040>.3.42 56 0

825;G /51265=95 94;=7:.8 2<. 65==5W94> /<08.8c

Phase 1 %25;G /51265=95 8.=.;2954I _153 2<. :020 56

2<. .C.1;98.D 825;G /51265=95 8.=.;2954 98 0 >9M.4 60;2I&<.1. 01. 2W5 825;G8 04: 2<. 30a51 ;53/.29251 98 2<.

%25;G $4:.C 56 2<. %25;G +C;<04>.I

Phase 2 J/29373 %25;G /51265=95 %217;271.I &<.

825;G /51265=95 8217;271. 1.6.18 3094=X 25 2<.

/.1;.420>.8 56 .0;< 825;Gd8 /0129;9/02954 94 2<. 825;G

/51265=95I &<. 5/29373 825;G /51265=95 8217;271. W9==

0198. 6153 2<. 8.=.;2954 56 2<. /.1;.420>. 56 .0;<

825;Gd8 /0129;9/02954 94 2<. 825;G /51265=95I

$4 2<. ;08. 56 2<. 3040>.3.42 56 2<. 2W5 825;G8 94

&0F=. LD 2<. 3040>.1d8 82102.>X 651 2<. 69182 2<1..

3542<8 56 ?AAb 98 /1.8.42.: 94 &0F=. ?I "98

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W92< W<9;< .0;< 825;G /0129;9/02.8 94 2<. 825;G

/51265=95I $2 >5.8 W92<572 80X94> 2<02

L x ? x

LeLAA?L x x I

%25;G $4:.C

January February March

&FGHI / L x L x L x K040>.1

&FGHI 0 ? x ? x ? x&0F=. ?. &<. $4M.823.42 %2102.>X 56 2<. K040>.1IP.1;.420>.8 56 2<. %25;G8d P0129;9/02954 94 2<. %25;G /51265=95

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L x ? x

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%25;G $4:.C

January February March

K040>.1 &FGHI / LL K ?L K OL K

&FGHI 0 L? K ?? K O? K

&0F=. OI &0F=. 56 K040>.1d8 P156928

$6 2<. 3040>.1 93/=.3.428 2<. 82102.>X 56 &0F=. ?D

2<.4 .M.1X 3542<D F08.: 54 &0F=. OD <98 /156928 6153

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fhO 94 293. /.195: 2fOIO??OLL K x K x

$6 h 98 2<. /156928 6153 2<. K040>.1d8 94M.823.42


ISSN: 1790-5109 54 ISBN: 978-960-474-063-5

8/12/2019 9fcfd50f968a26c201


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V K x

it

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.1 Stock portfolio management with two

&<. 54 56 2<. 94M.823.42 82102.>X 651 2<.

Ja uary March

2

stocks /1.8.42029

69182 2193.82.1 Y651 2<. 3542<8 56 i04701XD _.F1701X

04: K01;<Z 98 /1.8.42.: 94 &0F=. VI%25;G $4:.C

nuary Febr

K040>.1 25;G L% ADV^?T NAD@L?b NADTV^

%25;G ? AD@V@V AD^@TO LDS@AS

&0F=. . 56 >. 2

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*08.: 54 2<. 0F5M.D 2<. 1.87=294> 5/29373 825;G

:.C

ay June

VI &0F= 2<. K040 1d8 P1569 8I

%571;.c -020 6153 &0F=. LI

94 2<. 6513 56 0 =94.01 /15>103394> /15>103 98 0865==5W8c V 30C 87Fa.;2 25 2<. 65==5W94> 1.8219;29548c

AD

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W9== F.c AL x D L? x W92< /15692 hfAI^@TOI &<.

/1.8.4202954 56 2<. 94M.823.42 82102.>X 651 2<.

8.;54: 2193.82.1 Y651 2<. 3542<8 56 (/19=D K0X 04:

i74.Z 98 /1.8.42.: 94 &0F=. Î

%25;G $4

April M K040>.1 GHI / 76:9<<9 7608:9 067::/&F

&FGHI 0 76<@?0 /699?: 76780/

& 0F=. 5 .1d8

08.: 54 2<. :020 6153 &0F=. ^D 2<. 3040>.1d8

0F=. ^. & 6 K040> P156928%571;.c -020 6153 &0F=. L

*

/15F=.3 94 2<. 6513 56 0 =94.01 /15>103394>

/15>103 98 08 65==5W8c V 30C 87Fa.;2 25 2<.

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W9== F.c ^TbÎAL x 04: VOASIAL L? x x I

2.2 The Outcomes of the management as a

`. 1./.02.: 2<. 0F5M. /15;.:71. 56 2<.whole

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/1.8.42.: 94 &0F=. TI &<. 69182 04: 8.;54: ;5=7348

56 &0F=. T /1.8.42 2<. /.1;.420>.8 56 571 825;G

/51265=95 W92< 2<. 2W5 825;G8I &<. 2<91: ;5=734 56

2<. &0F=. /1.8.428 2<. .M5=72954 56 2<. /.1651304;.

56 2<. 825;G /51265=95 2<157>< 293. 08 92 0198.8 F08.:

54 2<. 65==5W94> 674;2954c

t t t xmet x port d L j j ?L t met ? j YP.1651304;. 56

2<. %25;G P51265=95Z

t xL J/29373 P.1;.420>. 56 825;G L 94 2<. /51265=95

t x? J/29373 P.1;.420>. 56 825;G ? 94 2<. /51265=95

t L j P.1651304;. 56 %25;G Lmet

t ? j met P.1651304;. 56 %25;G ?

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ISSN: 1790-5109 55 ISBN: 978-960-474-063-5

8/12/2019 9fcfd50f968a26c201


&0F=. TI K040>.3.42 J72;53.8D P.1;.420>.8 942<. 825;G /51265=95 8217;271.I %571;.c &0F=. L-020 P15;.88.:

k&<98 ;5=734 .C/1.88.8 2<. ;737=029M. /.1651304;.

56 2<. 825;G /51265=95 04: 98 ;0=;7=02.: F08.: 54 2<.

:020 94 ;5=734 V 08 65==5W8c

D W92<t t t port d port s port s j j j L

L j j

t o port d port s

$4 &0F=. SD W. /1.8.42 2<. ;737=029M. /.1651304;. 56

2<. %25;G $4:.CD 56 2<. %25;G /51265=95 04: 56 825;G8 L

04: ? 1.8/.;29M.=XI &<. /1.:539404;. 56 2<. /52.4290=

56 825;G /51265=95 3040>.3.42 94 1.=02954 25 F52< 2<.

%25;G $4:.C 04: 2<. >15W2< 56 2<. 2W5 /0129;7=01

825;G8 98 5FM9578 04: ;546913.: FX 2<. >10/<9;

1./1.8.4202954 56 _9>71. LI

!"#$%&

%&J!,$'-+U

%&J!,PJ#&_JB$J

%&J!,L

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12#3245 100,00 100,00 100,00 100,00

=,>43245 102,03 102,62 101,22 102,62

!24(% 104,79 107,23 103,31 107,23

2A4*B 105,19 108,47 104,67 108,24

!25 107,11 111,31 106,88 111,78

13#, 105,18 110,65 107,19 109,85

13B5 106,18 112,44 108,04 112,03

23D3&$ 103,98 110,85 108,16 109,68

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"($">,4 99,79 108,73 108,18 107,02

#"E,!>,4 102,75 113,16 109,63 111,38

+,(,!>,4 106,45 118,61 113,49 116,75

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:7R77

:<R77

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BD,#

BA"4$

B!,$/

B!,$0STOCK INDEX

PORTFOLIO

STOCK 1

STOCK 2

_9>I LI !53/019854 56 2<. !737=029M. P.1651304;. 56 2<.

%25;G /51265=95 W92< 2<. P.1651304;. 56 2<. %25;G $4:.C 04:2<. !737=029M. P.1651304;. 56 2<. 2W5 825;G8

3 Conclusion

%25;G /51265=95 8.=.;2954 ;04 F. /.16513.: 7894>

255=8 87;< 08 302<.3029;0= /15>103394> W<9;< 01.

.089=X :9>.82.: 04: 74:.18255: FX 2<. 827:.428I $4

2<98 W0X 2<.X ;04 452 54=X 0//1.;902. 2<. 933.:902.

78. 56 302<.3029;8 25 2<. /10;29;0= F72 93/512042 /15F=.38D F72 0=85 82012 25 F. .C/58.: 25 2<.

/15F=.38 56 35:.14 69404;.I

References:

\L] !<7G5M0D %ID B09D !I -I 04: `04>D -I mD J4 2<.

1.=029548<9/ F.2W..4 1.>1.88954 040=X898 04:

302<.3029;0= /15>103394>D Journal of Applied

Mathematics and Decision SciencesD h5=I@D '5I?D

?AAVD //I LOLNLVLI

\?] !=01G854D ,IBID B08 h.>08 0=>5192<38 651 =94.01

04: 942.>.1 /15>103394> W<.4 2<. :93.48954 98

830==D Proceedings of the 29th Annual IEEESymposium on Foundations of Computer ScienceD

Lb@@D //I V^?NV^TI

\O] !5<.4D +ID 04: K.>9::5D 'ID $3/15M.:

0=>5192<38 651 =94.01 94.[70=929.8 W92< 2W5 M0190F=.8

/.1 94.[70=92XD Proceedings of the 23st Annual ACM

Symposium on Theory of Computing ACM D LbbLD

'.W l51GD //I LV^NL^VI

\V] -042R9>D EI*ID Linear Programming and

ExtensionsD P194;.254 Q49M.1892X P1.88D P194;.254D

'IiID LbTOI

\^] +0148<0WD %I#ID 04: -.44.22, %IBID

$42.>.1nB94.01 K02<.3029;0= P15>103394> K5:.=8c( &55= 651 (==5;0294> ".0=2<;01. #.8571;.8I

PharmacoEconomicsD h5=I?LD '5IL?D ?AAOD //I @ObN

@^LI

\T] +=254D +ID E17F.1D KID P0:F.1>D KID %93/=. #7=.8

651 J/2930= P51265=95 %.=.;2954c &<. K7=29 E157/

!08.I The Journal of Financial and Quantitative

AnalysisD h5=IL?D '5IOD LbSSD //I O?bNOVÎ

\S] +=254D +I D E17F.1D KI D *15W4D %I D E5.2R3044D

ÌD Modern Portfolio Theory and Investment

AnalysisD `9=.XD 89C2< .:92954D ?AAOI

\@] "9==.1D _I%D B9F.1304 EIiD Introduction to

Operations ResearchD 89C2< .:92954D K;E10W "9==D

$4;ID LbbÎ

\b] B.3091.D iID (4 (//=9;02954 56 E03. &<.51Xc

!582 (==5;02954D (%&$' *7==.294 h5=ILVD '5ILD

Lb@VD //I TLg@LI

\LA] K01G5W92RD "ID Portfolio SelectionI &<. i57140=

56 _9404;.D $887. LD Lb^?D //I SSNbLI

\LL] K0M15330298D EID B0R0G9:57D (ID %908890G58D

,ID B0R0G9:57N,06.2R9 EID B.01494> P15;.88.8 651

!19898 K040>.3.42D WSEAS Transactions on

Advances in Engineering Education Journal D h5=IOD

'5ISD ?AATD $%%' LSbANLbSbD //I T^SNTTLI\L?] %908890G58D ,ID B01958D lID 04: P0/082.6040258D

%ID (4 9445M029M. 8X82.3 651 2<. 2.0;<.1N;.42.1.:

(QEQ%& ADOL ADTb NLDVL L?DOS

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ISSN: 1790-5109 56 ISBN: 978-960-474-063-5

http://econpapers.repec.org/article/wkhphecon/

http://econpapers.repec.org/article/wkhphecon/

8/12/2019 9fcfd50f968a26c201


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ISSN: 1790-5109 57 ISBN: 978-960-474-063-5

9fcfd50f968a26c201

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