Y3I>EK11ctoh pecnYI>U11kac11 ou11 ba ypta

l\ Kono rapHH ceKbIO TpHK Tax,rHrH

Yw6y 6O6HHHr 4.7-YH naparpacpH)l, ai1THJlraHH)l, K, l\ TJl l\OFO3Jl H cp H)l, Jl ³⁰ ,
TeXHHK³¹Ba yJl HHr )l, HpacH)l, 6Owl\ TypJl Tax,JlHJl ycyJlJlapH MaB y)l,³².

²⁹ ep3OH H.VI. H )l,p. OH)l,OBIi1 pIHOK: YYe6.nOcO6He.-2-e H3)l,.-M.: BHTa npecc, 1999.-400 c.
³⁰ CH)l,HH KOTTJl, PO)l, ep .Moppei1, paHK E. Jl K. AHaJl 3 u,eHHIX 6yMar rp3Ma H O)l,)l,a.-M.: 0Jl Mn H3Hec, 2000.-674
c.;
³¹ ep3OH H.VI. H )l,p. OH)l,OBIi1 pIHOK: YYe6.nOcO6He.-2-e H3)l,.-M.: BHTa npecc, 1999.-400 c.
³² WOXab3aMHi1 W.W. CeKbopHMeTpHKa. apcJlHK.-T.: Y36eKHcTOH MHJlJlHi1 3Hu,HKJlOne)l,H51cH, 2005.-476 c.
X,O3Hp)l, Tax,JlHJl aMaJl HHHHr HOMJl pH ai1 6 yTHJl H ycyJlJl H y3JlyKcH3 TaKOMHJlJl wyB
apaeHH)l, eKH yJl HHr acOcH)l, 51 Jl nai1)l, 6yJl KeJl l\)l, . MacaJl , 6y apaeHHHHr O6beKTHB Max,cyJl cHcpaTH)l,a l\ TJl l\OFO3Jl H ceKbopHMeTpHK (cp HcOMeTpHK) Tax,JlHJl ycyJl KeJlTHpHw MyMKHH.
K, TJl l\OFO3 KypcaTKHYJl HH O6beKTHB 6ax,OJl yYyH yJlapHH 6a3HcH KypcaTKHYJl Hra 3KBHBaJl HTJlHJl H )l, pa acHHH (C) l\ i1H)l,arH HKKH apryMeHT cp HKu,H51 H )l,e6 l\ 6yJl l\HJl MyMKHH:
C = f(C₁, C₂), (4.8.1)
6yH)l, C₁ – l\ MaTJl l\OFO3 Ba yHHHr 6a3HcH )l, Ma)l,Jl Jl KypcaTKHYJl (peaJl Ba 6O3Op) 3KBHBaJl HTJlHJl H )l, pa acH;
C₂ – l\HMMaTJlH l\OFO3 Ba yHHHr 6a3HcH 6ax,OJlapH (6O3Op Ba peaJl Hapx,H, KypcH) 3KBHBaJl HTJlHJl H )l, pa acH.
y cpyHKu, 51 (4.8.1) MHl\)l,OpHi1 6ax,OJl yYyH MaTeMaTHKa)l, MabJlyM 6yJl aH KOMnJl y3rapyBYHJl p Ha3apH51 HHH l\ JlJl w MyMKHH. YHra acOcaH KOMnJl c cOH (y3apyBYH) HKKH l\ M)l, H H6OpaT, 51 H peaJl Ba MaBx,yM cOH)l,aH TapKH6 TOnraH 6yJl )l,H. WyHra MOc paBHw)l,a l\HMMaTJl l\OFO3HHHr 3KBHBaJl JlHJlHK )l, HH (51 4.8.1-YH cp pMyJl ) MaTeMaTHK waKJl)l, KOMnJl y3rapyBYH (cOH) KypHHHwH)l, HcpO)l,aJl w MyMKHH. eMaK, 6y HcpO)l, HH l\ TJl l\ FO3HHHr O6beKTHB cHcpaT KypcaTKHYH )l, 6 l\ 6yJl l\HJlHw MyMKHH 6yJla)l,H. yH)l, KOMnJl c cOHHHHr peaJl Ba MaBx, M l\ MJl H MOc paBHw)l, l\ TJl l\OFO3HHHr peaJl Ba 6O3Op KypcaTKHYJlapHHH HcpO)l, Jl i1)l,H. 51 HH:
C₆ = r₆ + jm₆, (4.8.2)
Z_o = r_o + jm_o, (4.8.3)
6yH)l, : C₆ , C₆ – l\ MMaTJl l\ FO3HHHr O6beKTHB 6ax,OcH (Hapx,H, KypcH) Ba )l,apOMa)l,JlHJl rH; r₆ , r_o – peaJl Hapx, Ba )l, Ma)l,Jl Jl ; jm₆ , jm_o – 6O3Op Hapx, Ba )l, Ma)l,Jl Jl ; cp pMyJlaJlap)l,arH + 6eJl cH l\ywHw aMaJlHHH aHrJl ai1)l, .
OpMyJl (4.8.2) Ba (4.8.3) ep)l,aMH)l,a r Ba m y3rapyBYHJl pHHHr MabJl M l\Hi1MaTJlapH)l,a C₆ Ba (eKH)
C_o KypcaTKHYJl HH x,HcO6Jl w acOcH)l, l\ MaTJl l\OFO3HHHr y3 6a3HcHra (eKH 6a3HcHH l\ MaTJl
l\ FO3ra) HHc6aTaH KypcH Ba (eKH) )l, Ma)l,Jl JlHrHHH KaM eKH OpTHl\ 6ax,OJl aHJl H )l, HH aHHl\Jlaw MyMKHH.
WyH)l,ai1 l\HJl 6, ol\ pH)l, H cpOpMyJl ep)l, )l, r Ba m l\Hi1MaTJl acOcH)l, C napaMeTpHHHr y3rapHw )l, MHKacHHH rpacpHK KypHHHw)l,a Tax,JlHJl l\HJl w MyMKHH. yHH reOMeTpHK HHTepnpeTau,H51)l,a l\ i1H)l,arHYa HcpO)l,aJlaw MyMKHH.
yHHHr yYyH 4.8.1-YH pacM)l, KypcaTHJlraHH)l,eK TeKHcJl )l, rH TyFpH 6ypYaKJlH KOOp)l,HHaTa cHcTeMacH)l,a ol\OpH)l,arH cp HKu,H51Jl HH HcpO)l, Jlai1 .

PacM.4.8.1. HaTH aBHi1 C BeKTOpHHHHr reOMeTpHK TaJll\HHH MO)l,eJl

K, i1H)l, rHJl wapTJl pHH l\ 6yJl l\HJlaMH3: C napaMeTpHH BeKTOp )l, 6 OJl , yHHHr TeKcHJl )l, rH i1yHaJlHwH (r,m) l\Hi1 TJl pHHHHr KecHwyB Hyl\ 6OpH6 Tal\aJl )l, (51 0, C₁); Y – MaBx, M cOHJl yl\H (l\ MaTJl l\OFO3HHHr 6O3Op Hapx,H eKH )l, pOMa)l,JlHJl rH KypcaTKHYJl H yl\H), X – peaJl cOHJlap yl\H (l\ MMaTJl l\OFO3HHHr peaJl Hapx,H eKH )l,apOMa)l,JlHJlHrH KypcaTKHYJlapH yl\H).

a3 l\HJlai1Jl , 4.8.1-pacM)l, H TeKHcJlHK)l, r₁, m₁ Ba r₂, m₂ KOOp)l, aJl HKKH HaTH aBHi1 C₁
Ba C₂ BeKTOpJl MaB y)l, 6yJl , yJl OA YH3HFHHHHr (6ypYarH 45 rpa)l, c 6yJl ) HKKH TapacpH)l,
Oi1Jl raH. y YH3Hl\HH 6a3HcJl l\ TJlH l\ HHHr (l\OFO3Jl Hr) BeKTOpJlap)l,a HcpO)l, Jl H TeKHcJl )l, rH 3KBHBaJl HTJlHJl nOTeHu,HaJlHHH (nOTeHu,HaJlJlapHH) a paTyBYH wapTJl Yerapa )l, 6 l\ 6yJl l\HJlHw MyMKHH. 51 TeKHcJl )l, 6y YH3Hl\HHHr ycTHra TyFpH KeJl (ycTMa ycT TywraH)
BeKTOp l\ MaTJl l\OFO3HHHr y3 6a3HcHra MOc 3KaHJlHrH)l,aH (BeKTOp 6yi1 6a3Hc Ba yHHHr l\ TJl l\ FO3H nOTeHu,HaJlJlapH ai1 3KBHBaJl JlHrH)l,aH) )l,aJl Jl 6epa)l, . Arap BeKTOp yw6y TeKHcJlHK)l,
TyFpH YH3Hl\)l,aH nacT)l,a Oi1Jl raH 6yJl , 6a3HcHHHr peaJl 6ax,OcH ()l, pOMa)l,JlHJl ) nOTeHu,HaJl 6O3Op 6ax, cH nOTeHu,HaJl )l, ol\ pH x,HcO6JlaHa)l, , aKc x,OJl)l, 3ca l\ MaTJl l\OFO3HHHr 6O3Op 6ax,OcH ()l, pOMa)l,JlHJl rH) nOTeHu,HaJl 6a3HcHHHr peaJl 6ax,OcH nOTeHu,HaJlH)l,aH ol\OpHJl HH aHrJlaTa)l, . BeKTOpHHHr YH3Hl\l\a HHc6aTaH 6ypYaK y3rapHwJl pHra l\ pa6 3KBHBaJl HTJlHJl nOTeHu,HaJl KypcaTKHYHHH (wy 6HJlaH 6Hpra pHcKJlHJl )l, pa acHHH x,aM) MHl\)l,OpHi1 yJl aw MyMKHHJl 51l\l\OJl KypHHH6 TypH6)l,H.
a3HcHHHr 3KBHBaJl HTJl Jl nOTeHu,HaJl 3MHTeHTHHHr x,aTTH x,apaKaTHra, l\ TJl l\OFO3HHHr 3KBHBaJl HTJlHJl nOTeHu,HaJl 3ca HHBecTOpHHHr 6O3Op)l, x,aTTH x,apaKaTH, HMKOHH51 H Ba x,Ox, 6OFJlHl\. KynHHYa 3MHTeHT Ba HHBecTOpHHHr Bal\THHYaJl x,Ox, OHH51TJlapH Tycp i1Jl x,aTTH- x,apaKaTJl 6Hp 6HpHra MOc KeJlMacJlHrH ca6aJl l\ MaTJl l\ 3HHHr 6O3Op KypcH, HaTH a)l, 3KBHBaJl HTJlHJl nOTeHu,HaJl x,aM, wapTJlH YerapaBHi1 YH3Hl\ aTpOcpH)l, Te6paHH6 TypHwHHH Ky3aTHw MyMKHH (1.6 naparpacpra l\ paJlcHH). MabJl MKH, 6yH)l, i1 Te6paHHwJl pHHHr 3Hr ol\OpH aMnJl )l,
6O3Op cp3)l, acOcH)l, eKH MyBO3aHaTJl BYH MeXaHH3M ep)l, )l, (1.7 naparpacp a l\apaJl H) YerapaJl 6 Typa)l,H.
reOMeTpHK MO)l, Jl)l,aH (4.8.1-YH pacM) l\ i1H)l, x,OJlaTJlapHH KypHw MyMKHH.

1. 
   BeKTOpHH (Y,-X) TeKHcJlHrH)l,a (2-YH OKTaHT)l, ) Oi1Jl x,OJl H l\ TJlH l\ FO3HHHr 3KBHBaJl HTJlHJl nOTeHu,HaJl 6O3Op TOMOHH)l,aH x,a)l,)l,aH Tawl\ H ol\OpH 6ax,OJlaHraHJlHrHHH 6HJl)l,Hpa)l,H, 6yH)l, “nycp K l\HJlH6 HwHpHJl ” l\ TJlH l\OFO3Jl p 6ax,OcH, HaTH a)l, 3MHTeHTHHHr 6aHKpOTJl x,OJl H By y)l,ra KeJla)l,H.
   
2. 
   BeKTOpHH (-Y,-X) TeKHcJlHrH)l, (3-YH OKTaHT)l, ) Oi1Jl aH x,OJl l\ Jl l\OFO3HHHr 3KBHBaJl HTJlHJl nOTeHu,HaJl yMyMaH i1yl\Jl )l, H )l, JlOJl 6epa)l,H, 6yH)l, 6aHKpOT 6yJl 3MHTeHT 6apYa aKTHBJl HHH cOTraHH)l,aH cyHr acOcHi1 Kpe)l,HTOpJl MaHcpaaTJl pHHH l\OH)l, raH)l,aH Kei1
   

l\ TJl l\ FO3Jl 6yi1 HHBecTOpJl OJl)l,H)l,arH Ma 6ypH51 yMyMaH 6a apa OJl i1)l, ,
HaTH a)l,a 6aHKpOTJl 6HJl H 6OFJlHl\ )l, cpOJl By y)l,ra KeJla)l, .

3. 
   BeKTOpHH (-Y, X) TeKHcJlHrH)l, (4-YH OKTaHT)l, ) Oi1Jl aH x,OJl l\ Jl l\OFO3HHHr 3KBHBaJl HTJlHJl nOTeHu,HaJl 6O3Op TOMOHH)l,aH x,a)l,)l,aH Tawl\apH nacT 6ax,OJlaHraHJl HHH 6HJl)l,Hpa)l,H, 6yH)l, “Ha3ap)l,aH i1HpOl\”, “51 nOTeHu,HaJlJl ”, Jl HH nOTeHu,HaJl KeJl K)l,a 3MHTeHTHHHr H O6Hi1 x,aTTH x,apaKTJl H 3Ba3Hra HaMOeH 6yJl MyMKHHJlHrH)l,aH )l, JlOJl 6epa)l,H. yH)l, caHau,H51
   

apaeHHHH H O6Hi1 yTHwH x,OJl H x,aM yw6y TeKHcJl )l, Oi1Jlawa)l,H.

4. 
   BeKTOpHH (Y, X) TeKHcJl H)l, (1-YH OKTaHT)l,a) Oi1Jl raH x,OJl l\ MMaTJl l\OFO3HHHr 3KBHBaJl HTJlHJl nOTeHu,HaJl 6O3Op TOMOHH)l,aH O6beKTHB 6ax,OJlaHraHJl rHHH 6HJl)l, a)l,H, 6yH)l, l\ TJl l\OFO3Jl HHHr 3BHBaJl HTJlHJlHK nOTeHu,HaJl ol\OpH x,OJl By y)l, KeJl , HwOHYJl , cneKyJl51THB, Te6paHyBYaH, Jl BH)l, 6ax,OcH x,yKMpOH 6yJla)l,H.
   

Ai1 OH3KH, wapTJlH YerapaBHi1 YH3Hl\l\ HHc6aTaH 6ypYaKHHHr y eKH 6y Tapcp y3rapHwH MHl\)l,OpHra l\ pa6 l\ TJl l\OFO3HHHr pHcKJlHJl )l, pa acH 2-3 OKTaHJl p HYH)l,a 3Hr ol\OpH x,HcO6JlaHa)l, , 4-YH OKTaHT)l, 3ca 6y )l, 2-3 OKTaHJlap)l, )l, Kyn 6yJl ai1)l, , Jl 1-YH OKTaHT)l,arH)l,aH ol\OpH.
Hp 3MHTeHTHHHr l\ MaTJl l\OFO3H 3KBHBaJl HTJlHJl nOTeHu,HaJl )l, pa acHHH )l, MHKa)l, TeH)l,eHu,H51 HHH Tax,JlHJl l\HJlHw yYyH TeKHcJl )l, (acOcaH 1-YH OKTaHT)l,a) BeKTOpJl ycTH)l,a KOMnJl c cOHJl Ha3apH51 ra 6HHOaH MabJl M apHcp eTHK aMaJlJl 6a apHw Ba x,OcHJl 6yJla)l, aH HaTH aBHi1 BeKTOpra l\ pa6 l\ TJl l\ 3 Ba yHHHr 6a3HcHra yJl HHHr 3KBHBaJl HTJlHJl nOTeHu,HaJl Hyl\ H Ha3ap)l, 6ax,O 6epHw Tal\ 3THJla)l, .
VI)l,eaJl x,OJlaT)l, HaTH aBHi1 BeKTOpHHHr 3KBHBaJl HTJlHJl nOTeHu,HaJlH )l, pa acH (Y, X) TeKHcJlHrH)l,a MyKaMMaJl x,HcO6Jl Ha)l,H l\ YOHKH l\ TJlH l\OFO3HHHr r Ba m l\Hi1MaTJlapH y3apO MyTaHOcH6Jl )l, OwH6 6Opca, 51 H r :: m wapTH wapTJlH YerapaBHi1 YH3Hl\l\a 51l\HH cnp3)l, OpaJlHFH)l, 6a apHJl . Cnp3)l,)l, Tawl\apH)l, l\ MaTJl l\ 3Jl acOcaH 6Hp a)l, Tawl\ 6O3OpH)l, MyOMaJla)l, 6yJl MyMKHH, yHHHr HYH)l,arH l\ FO3Jl 3ca O)l,aT)l,a “MOBHi1 cp wKaJlap” l\ TOpH)l, H ypHH OJla)l, )l, 6 ai1 Hw MyMKHH.
CeKbopHMeTpHK Tax,JlHJl rpacpHK ycyJlH (MO)l,eJl ) l\ i1H)l, KeJlTHpHJlraH MacaJl Jl HH eYHwra ep)l,aM 6epa)l,H: l\ TJl l\OFO3Jl p 6O3OpH)l,a 6ax,OJl (KypcJlap) )l, pa acHHH Tax,JlHJl l\HJlH6 npOrHO3HHH aMaJl OwHpHwra; l\ TJl l\ FO3HH cOTHw eKH cOTH6 OJl r OnTHMaJl Bal\THHH aHHl\Jlawra; cp H)l, MeHTaJl Tax,JlHJl HaTH aJl HHHHr TyFpHJl rH Ba TyJlHl\Jl rHHH TeKwHpHwra Ba aKcHHYa TeXHHK Tax,JlHJl HaTH aJl HHHHr TyJlHl\Jl rH Ba TyFpHJl HHH TeKwHpHwra; l\ TJl l\OFO3 Ba yHHHr 6a3HcHHH 3KBHBaJl JlHJlHK nOTeHu,HaJl )l, HH 6ax,OJl ra; yMyMaH OJlraH)l, l\ Jl l\ 3Jl 6O3OpH Ba peaJl Hl\ cO)l, HHr y3apO 3KBHBaJl TJl JlHK )l, HH 6ax,OJl ra; l\ MaTJl l\OFO3Jl nOpTcpeJlJlapHHH 3KBHBaJl HTJlHJl nOTeHu,HaJl Hyl\ H Ha3apH)l,aH acOcHi1 KypcaTKHYJlapHHH ()l, pOMa)l,JlHJl rHHH, 6ax,OcHHH, pHcKJlHJl , HwOHYJlHJlHK Ba Jl BH)l,JlHJl )l, pa acHJl pHHH) 6ax,OJl
acOcJl Tap3)l, waKJlJl HpHw Ba 6Owl\ Hwra (6yH)l, OnTHMaJlJl pHw MacaJlaJl r.MapKOBHu,³³,

23. 
    apna³⁴ H 6Owl\aJl MO)l,eJlJl acOcH)l, eYHJla)l, ).
    

CeKbopHMeTpHK Tax,JlHJl ep)l,aMH)l,a 6O3Op)l, rH l\ MMaTJl l\OFO3Jl pHHHr 3KBHBaJl HTJlHJlHK nOTeHu,HaJl )l, pa aJl H acOcH)l, cp H)l, 6O3OpHHHHr nOTeHu,HaJl H 6ax,OJl MyMKHH. yH)l, 3KBHBaJl HTJlHJl nOTeHu,HaJl HH HaTH aBHi1 BeKTOpHHHr MHl\)l,OpHra (HaTH aBHi1 i1yHaJlTHpHJl aH KyY

³³ Markowitz H.M. Mean Variance Analysis in Portfolio Choise and Capital Markets, Basil, Blackwell, 1990.

³⁴ Wapn Y., AJl KcaH)l,ep r., 3i1Jl . VIHBecTHu,HH: nep.c aHrJl.-M.: VIHPA M, 1999.-XII, 1028 c.
cHcpaTH)l,a) Kynai1 cH l\ TJlH l\ FO3HHHr l\ BBaTH KyYHHH, 6y l\ BBaTJl pHHHr i1HFHH)l, H 3ca l\ MMaTJlH l\OFO3Jl 6O3OpH Myx,HTHHHHr l\ BBaTH KyYHHH 6HJl)l,Hpa)l,H (1.1 naparpacpra l\apaJlcHH).

Caao!l!lap

1. 
   CeKbopHMeTpHK Tax,JlHJl ycyJl HHMa)l,aH H6OpaT?
   
2. 
   CeKbopHMeTpHK Tax,JlHJl 6Owl\ Tax,JlHJl ycyJlJl p)l, HHMaJlap 6HJl cpapl\Jl a)l, ?
   
3. 
   3KBHBaJleHTJlHJl K nOTeHu,HaJlH HHMa?
   
4. 
   CeKbopHMeTpHK Tax,JlHJlHHHr reOMeTpHK TaJll\ MO)l,eJl HHMara ep)l, 6epa)l, ?
   
5. 
   KOHKpeT TaHJl OJl l\ MaTJl l\OFO3HHHr C npaMeTpH l\ H)l, i1 6ax,OJlaHa)l,H?
   

Tonmupu !l

1. 
   CeKbopHMeTpHK Tax,JlHJl ycyJl TaBcHcpJl Hr.
   
2. 
   CeKbopHMeTpHK Tax,JlHJl r reOMeTpHK MO)l,eJl ep)l,aMH)l,a KOHKpeT 3MHTeHTJl p aKu,H51Jl pHHH 6ax, Jl Hr.
   
3. 
   TepMHHJl p Jl FaTHHH Ty3HHr.
   

1. I>OI>. MOU11I I>O3OP11 3M11TEHTUAP11 BA 11HBECTOPUAP11, YUAPH11Hf' C11ECAT11 BA POU11

3MHTeHTJl Ba HHBecTOpJl HHr MOJlH51 6O3OpH)l, H Ba yMyMaH Hl\ cO)l,HeT)l, H pOJl Ba cp JlH51T caMapaJlapHHH 1-YH, 2-YH Ba 3-YH HJl BaJlap)l, KeJl pHJlraH aHaJl K MabJl MOTJl )l, KypHw MyMKHH.