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O;f"V vFkZ'kkL=k osQ fl¼kar
uksV fuos'kd visf{kr izkfIr;ksa dks ^^vPNk** rFkk tksf[ke (σ) dks ^^cqjk** ekurk gS] fofoèk iksVZiQksfy;ks esa ls
mlosQ vfèkeku] mnklhurk oØksa }kjk iznf'kZr gksrs gSaA ,d fuos'kd osQ mnklhurk oØ visf{kr izkfIr rFkk
tksf[ke osQ chp mlosQ fofu;e (tradeoff) djus dh bPNk izdV djrs gSaA n{k lhek osQ lkFk&lkFk] ;s
mnklhurk oØ ;g fuèkkZfjr djrs gSa fd dkSu lk fo'ks"k n{k iksVZiQksfy;ks og pqurk gSA ;g loksZÙke ;k
b"Vre iksVZiQksfy;ks gSA
fp=k 29-6 rhu mnklhurk oØ I ] I rFkk I n'kkZrk gSA mudh mQij dh vksj] ck,¡ ls nk,¡ <yku tksf[ke
1 2 3
izkfIr fofue; iznf'kZr djrh gSA oØ I oØ I ls vfèkd vfèkeku rFkk oØ I oØ I ls vfèkd vfèkeku
2 1 3 2
iznf'kZr djrk gSA EF n{k lhek gSA P b"Vre iksVZiQksfy;ks dk fcanq gS ftlesa oØ EF oØ I dks Nwrk
2
gSA fcanq A Hkh I oØ ij gSA foaQrq ;g loksZÙke iksVZiQksfy;ks dk fcanq ugha gS D;ksafd ;g n{k lhek ls ckgj
2
gSA iqu%] I oØ ij fcanq B b"Vre iksVZiQksfy;ks ugha gS D;ksafd ;g fuos'kd dks fuEurj tksf[ke izkfIr
1
vfèkeku iznku djrk gSA bl izdkj P b"Vre iksVZiQksfy;ks gS D;ksafd ;g fuos'kd osQ fy, mPpre tksf[ke
izkfIr vfèkeku okys I oØ rFkk n{k lhek EF osQ chp Li'kZ fcanq ij iM+rk gSA
2
fp=k 29-6
Expected rate of return Optimal B I P 3 I 2 I 1 F
Protfolio
A
E
O
Standard Deviation (Risk)
iksVZiQksfy;ks fofoèkhdj.k }kjk tksf[ke esa deh
(Risk Reduction through Portfolio Diversification)
,d fuos'kd] LVkWd cktkj esa vius fuos'k dk tksf[ke fofoèkhdj.k }kjk de dj ldrk gSA fofoèkhdj.k dk
vFkZ gS vius fuos'k dks nks ;k vfèkd ifjlaifÙk;ksa ;k 'ks;jksa esa iSQykukA ;g fcYoqQy ^^,d gh Vksdjh esa lkjs
vaMs u j[kus** osQ leku gksrk gSA tksf[ke dks de djus osQ fy, fuos'kd vius iksVZiQksfy;ks p;u esa
fofoèkhdj.k dks ,d funZs'kd fl¼kar cukrk gSA og vius iksVZiQksfy;ks ij vkSlr izkfIr de fd, fcuk
tksf[ke de djus osQ ;ksX; gksrk gSA iksVZiQksfy;ks fofoèkhdj.k dks le>us osQ fy,] eku yks fd ,d fuos'kd
osQ ikl nks tksf[ke okyh ifjlaifÙk;k¡ BP (Hkkjr isVªksfy;e) 'ks;jksa rFkk SAIL (LVhy vFkkWfjVh vkWiQ
bafM;k fyfeVsM) 'ks;jksa ij fuos'k djus osQ fy, 100 #- gSaA izR;sd 'ks;j dh dher 1 #- gSA izR;sd oaQiuh
osQ 'ks;j ls rsth (boom) esa ykHk ikus dh 50 izfr'kr laHkkouk gS rFkk eanh esa Hkh ykHk dh 50 izfr'kr
laHkkouk gSA
vc ekuks fd og vius iwjs 100 #- BP osQ 'ks;j [kjhnus esa fuosf'kr dj nsrk gSA rsy m|ksx dh ,d rsth
esa] ;g fuos'k mls 10 #- dh izkfIr rFkk eanh esa 2 #- dh izkfIr nsrk gSA rsth rFkk eanh osQ 50&50 izfr'kr
volj fn, tkus ij] bl 'ks;j ls mldh visf{kr vkSlr izkfIr gksxh]
E = -5 (10 #-) + -4 (2 #-) = 6 #-
R
2
2
2
bldk izlj.k (Variance) (σ) = -5 (10 μ 6) + -5 (2 μ6) = 16 #-
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