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AN APPLICATION ON THE METHODS OF MEASUREMENT OF MARKET RISKS OF INSURANCE COMPANIES FINANCIAL INVESTMENTS
ABSTRACT
In emerging markets, to be able to provide sustainable competitive advantages and assets of the insurance companies are required to follow effective risk management policies. These developments increase the necessity of effective risk management for insurance companies. This study focuses on market risks, which are important elements of effective risk management. Also, the concept of value at risk (VaR), commonly used in the market risk measurement methods for financial investments that have the most impact of market risks, the more successful and measurable approach, has been used in this study. Value at risk calculated by the standard method is compared with value at risk calculated by the variance- covariance method in terms of cost and risk analysis.
Keywords: Insurance, Risk Management, Market Risk Mnagement, Value at Risk(VaR)
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ULVNH PDUX] GH÷HU KHVDSODPDVÕQGD NXOODQÕODFDN RODQ 9DU\DQV-Kovaryans Yönteminin YRODWLOLWHVLQLQKHVDSODQPDVÕQGDNXOODQÕOPÕúWÕU
Bu formül,
Burada ; ı 9RODWLOLWH\L
%HNOHQHQJHWLULRUDQÕQÕ
(5 1DNLWDNÕúODUÕQÕQEHNOHQHQGH÷HULQL
+HUQDNLWDNÕúÕQÕQJHUoHNOHúPHRUDQÕQÕJ|VWHULU
Tablo 2. Beklenen Getiriye Göre Hesaplanan Portfoyün Volatilitesi
$÷ÕUOÕN Standart Sapma
Devlet Tahvili (DT) 40% 0,0074
Hisse Senedi (HS) 5% 0,0727
9DGHOL0HYGXDW+HVDEÕ9+ 50% 0,0127
Hazine Bonosu (HB) 5% 0,0018
Portföy 100% 0,0076031
dDOÕúPDGDSRUWI|\ROXúWXUDQILQDQVDO YDUOÕNODUÕQSL\DVDGDNLGH÷LúNHQOHUH J|UHED]
DOÕQDQ ]DPDQ VHULOHULQGH ULVN-getiri ikilisine ek olarak portföyün durumunu ortaya NR\XS PDNVLPXP ND\ÕS KHVDSODQPÕú YH EX ND\ED J|UH SRUWI|\Q YRODWLOLWHVL
KHVDSODQPÕúWÕU (Bkz Tablo 2)
Varyans-.RYDU\DQV \|QWHPLQH J|UH ULVNH PDUX] GH÷HU KHVDSODQÕUNHQ JHWLUL
VHULOHULQH DLW GD÷ÕOÕPODUÕQ QRUPDO GD÷ÕOÕPD X\XS-X\PDGÕ÷Õ -DJXH %HUUD 7HVWL16
\DSÕOPÕúWÕU3RUWI|\QEDVÕNOÕNGH÷HULoDUSÕNOÕNGH÷HUL-0,3532311 olarak hesaplaQPÕú GD÷ÕOÕPÕQ VD÷D H÷LN KDILI oDUSÕN ROGX÷X DQODúÕOPDNWD YH -% GH÷HUL
RODUDNKHVDSODQPÕúJHWLULOHULQWDPRODUDNQRUPDOGD÷ÕOÕPDX\PDGÕ÷ÕWHVSLW
HGLOPLúDQFDNQRUPDOGD÷ÕOÕPDH÷ULVLQHVDKLSROGX÷XYDUVD\ÕPÕ\DSÕOPDNWDGÕU*HWLUL
RUDQODUÕ ) IRUPOLOH KHVDSODQÕU /RJDULWPLN JHWLULVL KHVDSODQDQ
SRUWI|\ YDUOÕNODUÕQÕQ EHOLUOL ELU JYHQ DUDOÕ÷ÕQGD SRUWI|\ YRODWLOLWHVL LOH oDUSÕOPDVÕ
VRQXFXZGH÷HULKHVDSODQPÕúWÕU%N]7DEOR
)
<XNDUÕGDWDQÕPODQDQ5W]DPDQÕQGD\DWÕUÕP\DSÕOPÕúRODQYDUOÕ÷ÕQIL\DWÕQÕYH3LVH
\DWÕUÕPÕQWYHW-]DPDQGLOLPOHULDUDVÕQGDNLJHWLULVLQLLIDGHHWPHNWHGLU
Bu formül : Burada;
Z $÷ÕUOÕNYHNW|UQ
ı 9RODWLOLWH\L
= Güvenilirlik (%99,5),
= Logaritmik getiriyi gösterir.
“w´GH÷HULQLELUGHQoRNHQVWUPDQÕbulunan portföye uygulanabilmesi için ;
IRUPONXOODQÕOÕU
16Jaque Berra Testi, HOGHNLJ|]OHPOHULQQRUPDOGD÷ÕOÕPDX\XSX\PDGÕ÷ÕQÕQEHOLUOHQPHVLQGHNXOODQÕODQ HQ\D\JÕQWHVWWLU
7DEOR%HNOHQHQ*HWLUL\H*|UH+HVDSODQDQ$÷ÕUOÕN9HNW|U
DT HS VM HB
w
0,002950 0,003634 0,006370 0,000090
w'
0,002950336 0,003633863 0,0063703 9,023E-05
Varyans-Kovaryans \|QWHPL\OHKHVDSODPD\DSÕOÕUNHQYRODWLOLWHQLQELOLQPHVLJHUHNLU
9RODWLOLWHLVHJHWLULVHULOHULQLQVDELWVWDQGDUWVDSPDQÕQKHVDSODQPDVÕ\ODEXOXQXU%X
VWDQGDUW VDSPDODU YH SRUWI|\ ROXúWXUDQ \DWÕUÕP DUDoODUÕQÕQ D÷ÕUOÕNODUÕ LOH ELUOLNWH
%99,5 güven düzeyinLQ GH÷HUL oDUSÕODUDN w YHNW|U KHVDSODQPÕúWÕU %X \|QWHPOH
KHVDSODPD \DSÕOÕUNHQ GH KHU ELU \DWÕUÕP DUDFÕQÕQ SRUWI|\GHNL D÷ÕUOÕ÷ÕQD J|UH
\DSÕOPÕúWÕU w YHNW|U KHVDSODQGÕNWDQ VRQUD SRUWI|\Q NROHUDV\RQ NDWVD\ÕVÕ17 KHVDSODQPÕúWÕU%N] 7DEOR3RUWI|\QWRSODPGH÷HUL7/¶GLUZ
YHNW|U YH NRUHODV\RQ NDWVD\ÕVÕ DUDFÕOÕ÷Õ LOH 9DU\DQV-Kovaryans yöntemine göre ULVNHPDUX]GH÷HUKHVDSODQPÕúWÕU
7DEOR3RUWI|\2OXúWXUDQ'H÷LúNHQOHUHøOLúNLQ.RUHODV\RQ.DWVD\ÕODUÕ
DT HS VW HB
DT 1 -0,0504 -0,0365 -0,3323
HS -0,0504 1 -0,0448 -0,0482
VM -0,0365 -0,0448 1 0,03716
HB -0,3323 -0,0482 0,03716 1
.RUHODV\RQNDWVD\ÕVÕKHVDSODQDQSRUWI|\QYRODWLOLWHVLKHVDSODQÕU
'DKDVRQUDDúD÷ÕGDNLIRUPOLOHSRUWI|\Q50'¶L KHVDSODQPÕúWÕU
17.ROHUDV\RQNDWVD\ÕVÕ YDUOÕNODUÕQDUDVÕQGDNL LOLúNL\L J|VWHULU%X LOLúNL - LOH DUDVÕQGD\HU DOÕU
PozitLIGH÷HUOHUGLUHN\|QOGR÷UXVDOLOLúNL\LQHJDWLIGH÷HUOHULVHWHUV\|QOELUGR÷UXVDOLOLúNL\LEHOLUWLU
.RUHODV\RQNDWVD\ÕVÕLVHV|]NRQXVXGH÷LúNHQOHUDUDVÕQGDGR÷UXVDOELULOLúNL\RNWXU
gQFHNL E|OPOHUGH GH DQODWÕOGÕ÷Õ ]HUH,w \DWÕUÕP DUDoODUÕQÕQ ULVNH PDUX] GH÷HULQL
LoHUHQD÷ÕUOÕNYHNW|U w vektörünün transpozesi, korelasyon matrisidir.
Tablo 5. KovaryansMatrisi Kovaryans Matrisi
DT 0,000054 -0,000027 -0,000003 -0,000004
HS -0,000027 0,005282 -0,000041 -0,000006
VM -0,000003 -0,000041 0,000162 0,000001
HB -0,000004 -0,000006 0,000001 0,000003
.RYDU\DQV PDWULVL \DUGÕPÕ\OD JHUoHNOHVHQ GH÷HUOHU NXOODQÕODUDN RSWLPDO SRUWI|\
YDU\DQVÕ YH VWDQGDUW VDSPDVÕ KHVDSODQPÕúWÕU %N] 7DEOR 9DU\DQV-Kovaryans
<|QWHPLLOH \DSÕODQLúOHPOHU JYHQLOLUOLNWH18SRUWI|\QYHKHUELUYDUOÕ÷ÕQ
JQONJQONYHLúJQONULVNHPDUX]GH÷HULKHVDSODQPÕúWÕU
Tablo 6. Varyans-Kovaryans Yöntemi øOH+HVDSODQDQ3RUWI|\Q50'¶VL Portfoy RMD
PD 1.357.037.718,46
Standart Sapma 0,007603131
*YHQ$UDOÕ÷Õ 99,50%
='H÷HUL 2,330
RMD (1 gün) 24.040.323,42 RMD (10 gün) 76.022.177,68 RMD (252 gün) 381.628.303,17
.DWVD\Õ 3
RMD/PD %2
6LJRUWD úLUNHWOHULQLQ VRQ EHú \ÕOOÕN PDOL \DWÕUÕPODUÕ ED] DOÕQDUDN ROXúWXUXODQ
SRUWI|\QGH÷HUL\ÕOÕPDOL\DWÕUÕPODUDJ|UHEHOLUOHQPLúWLU7/
SRUWI|\ GH÷HUL ELU \DWÕUÕPÕQ JQON 50'¶VL 7/ JQON
RMD’si76.022.177,68 7/ YH \ÕOOÕN 50'¶ VL LVH RODUDN
KHVDSODQPÕú YH PDOL \DWÕUÕPODU LoLQ D\UÕOPDVÕ JHUHNHQ VHUPD\H WXWDUÕ +D]LQH
0VWHúDUOÕ÷Õ WDUDIÕQGDQ EHOLUOHQHQ NDWVD\Õ RUDQÕ LOH oDUSÕOGÕ÷ÕQGD
18JYHQLOLUOLNG]H\LLoLQVWDQGDUWQRUPDOGD÷ÕOÕPGH÷HUL 2,33’tür.
RODUDN EHOLUOHQPLúWLU %X VHUPD\H WXWDUÕ SRUWI|\Q LIODV ULVNLQH NDUúÕOÕN D\UÕOPDVÕ
JHUHNHQ VHUPD\H WXWDUÕ RODUDN EHOLUOHQPLú YH WRSODPGD SRUWI|\Q PDOL\HWL RODUDN
NDUúÕPÕ]DoÕNPDNWDGÕU7/RODQPDOL\DWÕUÕPODULoLQJQGHLIODV
HWPHRODVÕOÕ÷ÕRODUDNKHVDSODQPÕúWÕU
Bu uygulamadDLoLQPDOL\DWÕUÕPODUÕQWRSODPGH÷HULQHJ|UHHQID]ODND\ÕSJQON
RODUDNKHVDSODQÕUNHQJQONYH\ÕOOÕNND\ÕSLVHKHVDSODQPÕúWÕU
6WDQGDUW<|QWHPLOH+HVDSODQDQ5LVNH0DUX]'H÷HU$QDOL]L
6WDQGDUW\|QWHPGHSRUWI|\ROXúWXUDQYDUOÕNODUWHNLORODUDNGH÷HUOHQGLULOLU%|\OHFH
KDQJL YDUOÕ÷ÕQ GDKD ULVNOL ROGX÷X QHW ELU úHNLOGH J|UOU dDOÕúPDGD ROXúWXUXODQ
SRUWI|\Q ULVNH PDUX] GH÷HUL VWDQGDUW \|QWHP LOH KHVDSODQPDVÕ KDOLQGH SRUWI|\
ROXúWXUDQ KHU ELU YDUOÕN LoLQ JHoPLú ]DPDQ GH÷HUOerine göre belirlenen standart VDSPD LOH ULVNH PDUX] GH÷HU KHVDSODPDVÕ \DSÕOGÕNWDQ VRQUD EX GH÷HUOHULQ WRSODPÕ
DOÕQDUDNSRUWI|\QULVNHPDUX]GH÷HULEHOLUOHQLU
50' 3' ı Į 3'3RUWI|\'H÷HUL
ı: Risk faktörlerinin volatilitesi : Elde tutma süresinin karekökü Į: Güvenilirlik (%99,5)
<XNDUÕGDNLIRUPOLOHYDUOÕNODUÕQ50'KHVDSODPDVÕ\DSÕOGÕNWDQVRQUD
IRUPO\OHKHVDSODQÕU
Tablo 7. Standart Yöntem ile Hesaplanan PortföyRMD’si DEVLET
7$+9ø/ø
+ø66(
6(1('ø
+$=ø1(
BONOSU
9$'(/ø
MEVDUAT Portfolio VaR
PD 542.815.087,38 67.851.885,92 67.851.885,92 678.518.859,23 Standart
Sapma 0,0074 0,0727 0,0018 0,0127
Güvenilirlik 99,50% 99,50% 99,50% 99,50%
='H÷HUL 2,330 2,330 2,330 2,330
RMD (1
gün) 9.328.662,35 11.489.903,05 285.304,93 20.142.217,35 RMD (10
gün) 29.499.820,55 36.334.263,72 902.213,39 63.695.283,95 RMD (1
\ÕOOÕN 148.087.923,87 182.396.556,27 4.529.075,29 319.747.787,78
.DW6D\Õ 3 3 3 3
Sermaye
<HWHUOLOL÷L 444.263.771,60 547.189.668,82 13.587.225,88 959.243.363,35 RMD/PD 0,017185709 0,169338006 0,004204819 0,029685567 4.4. Varyans-.RYDU\DQV<|QWHPLLOH6WDQGDUW<|QWHPL.DUúÕODúWÕUÕOPDVÕ
6WDQGDUW \|QWHPGH SRUWI|\Q ULVNH PDUX] GH÷HUL GDKD \NVHN SRUWI|\ LoLQ
D\UÕOPDVÕ JHUHNHQ HNRQRPLN VHUPD\HGH ID]OD oÕNPÕúWÕU 9DU\DQV-Kovaryans
\|QWHPLQGH NRUHODV\RQ HWNLVL LOH ULVNH PDUX] GH÷HU GúN oÕNPÕúWÕU %X GXUXP
SRUWI|\ YDUOÕNODUÕQÕQ DUDVÕQGD GR÷UXVDO LOLúNL ROPDVÕ YH SRUWI|\Q QHJDWLI
NRUHODV\RQDVDKLSROPDVÕQGDQND\QDNODQÕU
7DEORøNL$\UÕ<|QWHPOH+HVDSODQDQ50')DUNÕQÕ*|VWHULU7DEOR TOPLAM
PORTFÖY RMD VARYANS-
KOVARYANS
RMD FARK
Portföy
'H÷HUL 1.357.037.718,46 TL
RMD (1 gün) 65.286.411 TL 24.040.323 TL -41.246.087 TL RMD (10 gün) 206.453.759 TL 76.022.177 TL -130.431.581 TL 50'\ÕOOÕN 1.036.389.646 TL 381.628.303 TL -654.761.343 TL
RMD/PV % 3,03 % 2
<XNDUÕGDNLWDEOR\DJ|UHVWDQGDUW\|QWHPLOHvaryans-NRYDU\DQV\|QWHPLDUDVÕQGDNL
IDUN DoÕNoD J|UOPHNWHGLU %X IDUN JQON 50'¶GH-41.246.087 TL, 10 günlük RMD’de 130.431.581 7/ \ÕOOÕN 50'¶GH LVH-654.761.343 7/ KHVDSODQPÕúWÕU
$\UÕFDVWDQGDUW\|QWHPLOH\DSÕODQDQDOL]GHSRUWI|\QWRSODPJQONND\EÕ
seviyelerindeyken, varyans-NRYDU\DQV \|QWHPLQGH LVH JQON ND\ÕS
VHYL\HOHULQHLQPLúWLU
6218dYH'(ö(5/(1'ø50(
6LJRUWD úLUNHWOHUL GH PDOL NDUOÕOÕNODUÕQÕ DUWÕUPDN YH NDUOÕOÕ÷Õ VUGUOHELOLU KDOH
getirmek için finansal piyasalarda süreNOLJHOLúPHND\GHGHUHNVD÷ODPELUPDOL\DSÕ
LOH XOXVODUDUDVÕ ]HPLQGH JYHQ LVWLNUDU YH úHIIDIOÕN DUD\ÕúÕ LoLQGH ROPDNWDGÕU %X
ED÷ODPGD SL\DVD ULVNOHUL \|QHWLPL oHUoHYHVLQGH ULVNOHUL WDQÕPDNWD GR÷UX ELOJLOHUOH
manipüle olmadan piyasa gözetimini daha etkLQ NÕOPD\D LoVHO RODUDN SL\DVD
GLVLSOLQLQL ROXúWXUPD\D GHYDP HWPHNWHGLU %XQXQ LoLQ VLJRUWD úLUNHWOHUL HWNLQ ELU
SL\DVD ULVNL \|QHWLPL LOH PDUX] NDOGÕNODUÕ ULVNOHUL WDQÕPODPDNWD ULVN \|QHWLP
VLVWHPLQL NXUPDNWD YH NDUDU DOPD PHNDQL]PDVÕQÕ EX VLVWHPH J|UH oDOÕúWÕUPDVÕ
gerekmektedir.
3L\DVDULVNOHULVLJRUWDúLUNHWOHULQLQNDUúÕNDUúÕ\DNDOGÕNODUÕHQ|QHPOLULVNWUOHULQLQ
EDúÕQGD JHOPHNWHGLU 3L\DVD ULVNOHULQLQ DUWPDVÕ SL\DVD GH÷LúNHQOHULQH G|YL] NXUX
R\QDNOÕ÷Õ IDL] RUDQODUÕQGDNL GH÷LúLNOLNOHU KLVVH VHQHGL IL\DWODUÕQGDNL GH÷LúLNOLNOHU
JD\ULPHQNXO GH÷HULQGHNL GH÷LúLNOLNOHU ED÷OÕ NDOPDNWDGÕU %X ED÷ODPGD VLJRUWD
úLUNHWOHULQLQSL\DVDGH÷LúNHQOHULQHJ|UH\DWÕUÕPVWUDWHMLOHULQLEHOLUOHPHOLGLU
6LJRUWD úLUNHWOHULQLQ - \ÕOÕ ELODQoR G|QHPL LQFHOHQGL÷LQGe, piyasa ULVNOHULQLQ PDOL NDUOÕOÕ÷ÕQD HWNLVLQL SL\DVD GH÷LúNHQOHULQH ED÷OÕ RODUDN PDOL
\DWÕUÕPODUÕLOHELUOLNWHGH÷HUOHQGLULOPLúWLUøQFHOHQHQG|QHPGHVLJRUWDúLUNHWOHUL
RUDQÕQGDYDGHOLPHYGXDW\DWÕUÕPODUÕLOHHQoRNIDL]ULVNLQGHQHWNLOHQPHNWH\DEDQFÕ
SDUD FLQVLQGHQ DoÕN SR]LV\RQODUÕQÕQ E\N ELU NÕVPÕ UHDVUDQV DQODúPDODUÕQGDQ YH
G|YL]H ED]OÕ SROLoHOHUGHQ ND\QDNODQGÕ÷ÕQGDQ GROD\Õ RUDQÕQGD NXU ULVNLQGHQ
HWNLOHQPHNWHGLU +LVVH VHQHGL ULVNLQGHQ \DWÕUÕP oRN GúN RUDQODUGD \DSÕOGÕ÷Õ LoLQ
PDOLNDUOÕOÕ÷DoRNE\NHWNLVLEXOXQPDPDNWDGÕU
8\JXODPDGDVLJRUWDúLUNHWOHULQLQHúLWJHWLUL\LVD÷OD\DFDNPLQLPXPULVNHVDKLSRODQ
YHID\GDIRQNVL\RQXGR÷UXOWXVXQGDEHOLUOHQPLúRODQSRUWI|\DGHWVHUPD\HDUDFÕQÕ
(devlet tahvili, hisse senedi, hazine bonosu ve vadeli mevduat) içermektedir.
3RUWI|\ ROXúWXUDQ ILQDQVDO YDUOÕNODUÕQ SL\DVDGDNL GH÷LúNHQOHUH J|UH ED] DOÕQDQ
zaman serilerinde risk-JHWLUL LNLOLVLQH J|UH DUDODUÕQGDNL NRUHODV\RQ ED] DOÕQDUDN
hesaplanan RMD ile (Varyans-.RYDU\DQV <|QWHPL NRUHODV\RQ LOLúNLVL dikkate DOÕQPDGDQ KHVDSODQDQ 6WDQGDUW <|QWHP SRUWI|\ DUDVÕQGD 1 günlük RMD’ de - 41.246.087,67 TL, 10 günlük RMD’ de 130.431.581,62 7/\ÕOOÕN50'¶GHLVH- 654.761.343,22 7/ KHVDSODQPÕúWÕU $\UÕFD VWDQGDUW \|QWHP LOH \DSÕODQ DQDOL]GH
portföyün toplam 1 JQON ND\EÕ VHYL\HOHULQGH\NHQ YDU\DQV-kovaryans
\|QWHPLQGHLVHJQONND\ÕSVHYL\HOHULQHLQPLúWLU
$\UÕFD SRUWI|\ ROXúWXUDQ YDUOÕNODUÕQ ULVN D÷ÕUOÕNODUÕ vadeli mevduat portföy içerisinde % 50¶OLN D÷ÕUOÕ÷D VDKLSNHQ JQON ND\ÕS-kazanç noktDVÕ % 0,03 KHVDSODQPÕúdevlet tahvili portföy içerisinde % 40¶OÕND÷ÕUOÕ÷DVDKLSNHQJQON
ND\ÕS-ND]DQo QRNWDVÕ % 0,017 RODUDN KHVDSODQPÕú hisse senedi portföy içerisinde
% 5¶OLN D÷ÕUOÕ÷D VDKLSNHQ JQON ND\ÕS-ND]DQo QRNWDVÕ % 0,17 olarak KHVDSODQPÕúhazine bonosu portföy içerisinde % 5¶OLND÷ÕUOÕ÷DVDKLSNHQJQON
ND\ÕS-ND]DQo QRNWDVÕ % 0,004 RODUDN KHVDSODQPÕúWÕU %X GXUXPD J|UH YDGHOL
PHYGXDWYHGHYOHWWDKYLOOHULHQJYHQLOLU\DWÕUÕPDUDoODUÕROXúWXUXODQSRUWI|\QULVN
LúWDKÕQDHQX\JXQYDUOÕNNRQXPXQGDGÕUODU6LJRUWDúLUNHWOHULQLQQHGHQHQoRNYDGHOL
PHYGXDW YH GHYOHW WDKYLOLQLQ \DWÕUÕP DUDFÕ RODUDN NXOODQGÕNODUÕQÕQ NÕVPL J|VWHUJHVL
olarak gösterilebilir.
6LJRUWDúLUNHWOHULLoLQ-\ÕOÕG|QHPLQGH\DWÕUÕP\DSÕODQVHUPD\HDUDoODUÕQÕQ
QRUPDO GD÷ÕOÕPÕ J|UH ROXúWXUXODQ SRUWI|\Q JQON JHWLUL IL\DW VHULOHULQH J|UH
KHVDSODQDQ YRODWLOLWHQLQ QRUPDO GD÷ÕOÕPD X\JXQ VRQXo YHUGL÷L J|UOPHNWHGLU (OGH
HGLOHQ YRODWLOLWH LOH \DSÕODQ 50' KHVDSODPDVÕ VRQXFX VHUPD\H DUDoODUÕ DUDVÕQGaki LOLúNLND\QDNOÕNROHUDV\RQHWNLVLYHNRYDU\DQVVHULOHULQGHQGROD\ÕYDU\DQV-kovaryans
\|QWHPLQLQ VWDQGDUW \|QWHPGHQ JYHQLOLUOL÷LQGH Lú JQON HOGH
EXOXQGXUPD VUHVLQH J|UH GDKD D] PDOL\HWOL ROGX÷X YH GDKD D] SL\DVD ULVNL
EDUÕQGÕUGÕ÷Õ J|UOPúWU %X GD \DWÕUÕPODUÕQ ULVNLQL D]DOPDN LoLQ \DWÕUÕPODUÕ NHQGL
LoHULVLQGH GH÷HUOHQGLULOPHVLQLQ ULVNL GúUPHGL÷LQL YH NXUXODQ RSWLPDO SRUWI|\Q
ULVNLGúUPHDPDFÕQDKL]PHWHWWL÷LQLJ|VWHUPHNWHGLU
6RQXo RODUDN \DWÕUÕP \DSÕODQ VHUPD\H DUDoODUÕQÕQ JHoPLú tarihlerdeki piyasa GH÷LúNHQOHULQGHQ QDVÕO HWNLOHQGL÷L J|]OHPOHQHUHN ROXúWXUXODQ YRODWLOLWH\H J|UH
ELODQoR \ÕOÕLoHULVLQGHSL\DVD ULVNLQLQ PDOL\HWLQL YHVHUPD\HDUDoODUÕQÕQHQID]OD QH
NDGDU]DUDUHGHELOHFH÷LNRQXVXQGDILNLUHOGHHGLOPLúWLU$UDúWÕUPDGD\DWÕUÕP\DSÕODQ
VHUPD\H DUDoODUÕQÕQ KHU ELULQLQ NHQGL YRODWLOLWHOHUL GLNNDWH DOÕQGÕ÷ÕQGD WRSODP
50'¶QLQ GDKD ID]OD YH PDOL\HWOL ROGX÷X J|]OHPOHQPLúWLU $QFDN \DWÕUÕP \DSÕODQ
VHUPD\H DUDoODUÕQÕQ PHYFXW SRUWI|\H J|UH YDU\DQV-kovaryans yöntemi ile KHVDSODQGÕ÷ÕQGD NRUHODV\RQ HWNLVLQGHQ GROD\Õ 50'¶ QLQ GDKD D] PDOL\HWOL ROGX÷X
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