rnaba 5. mo.qenm o~ehkm ctommoctm aktmbobinsurance-institute.ru/library/burenin/burenin05.pdf ·...
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I'naea 5. Mooenu 011e11Ku cmowwocmu aKmueoe
rnABA 5. MO.QEnM O~EHKM CTOMMOCTM AKTMBOB
5.1. MoAenb ou.eHKM CTOMMOCTM aKTMBOB (CAPM)
3aAalfa 5.1. CrnsKa 6e3 pHcKa pasHa 10%, O)l(H,UaeMrui: ,n:oxo.r:1HocTb pbIHoqHoro nopTCpemr -
20%, CTaH.[lapTHOe OTKJIOHeHJfe .ZJ:OXOL(HOCTH pbIHQqHoro rropT<t>emr - 15%. Orrpe.n;eJIHTb O)l(H.ZJ:aeMyIO .n:oxo.n;HOCTb rropT<l>em1, CTaH,D;apTHOe OTKJioHemrn
.ZJ:OXO,UHOCTH KOTOporo COCTaBJUieT 30%. Peweune. O)lrn.n:aeMrui: L(OXO.ZJ:HOCTb rropT<l>emr orrpeL(emreTCH c rroMOII(blO ypasHeHlfj{ CML:
(5.1)
r.LJ;e a-i- pHCK i -ro rropT<l>emr, ,n;mr KOToporo orrpe,n;emreTCH yposeHb O)l(ll.LlaeMoli
)J;OXOL(HOCTH;
E(r;) - O)l(ll.LlaeMaH .n:oxoL(HOCTb i -ro rropT<l>emr;
a-m - pHCK pbIHOqHoro rropT<l>emr;
E(r m ) - Q)l(ll,UaeMruI .ll;OXO,UHOCTb pbIHQqHoro IIOPT<l>emr.
ComacHo ypaBHeHHIO ( 5 .1) O)l(H,llaeMaH ,n:oxo.n;HoCTh rropT<l>emr pasHa:
( ) 30% [ ] Er. =10%+-- 20%-10% =30%. l 15%
3aAalfa 5.2. CrnsKa 6e3 pHcKa paBHa 8%, O)l(ll)J;aeMaH ;::i:oxo;::i:HOCTb pbIHoqHoro rropTcpemr -
22%, CTaH,D;apTHOe OTKJIOHeHHe .ZJ:OXO.ZJ:HOCTH pbIHQqHoro rropT<l>eJIH - 14%. Orrpe,n:eJIHTb o)l(ll.LlaeMyIO .noxo.ZJ:HOCT.b nopTcpemr, cTaH,n:apTHOe OTKJioHeHHe
,UOXO,UHOCTH KOToporo COCTaBJUieT 25% . Peweune.
( 25% [ ] E rJ=8%+-- 22% - 8% =33%. 14%
Bonpoc 5.3. KaKOH IIOKa3aTeJib CJiy)l(HT .n;mr H3MepeHlfj{ pbIHQqHoro pHCKa?
0TBeT.
PbrnoqHblH pHCK H3MepHeTCH c IIOMOII(bIO K03cpcpHI(HeHTa 6eTa.
Bonpoc 5.4. qTo npe.n;crnsmreT co6oif Ko3<l>cpHI(HeHT 6ern?
0TBeT.
Ko3<l>cpHI(HeHT 6ern rrpe,n:crnsmreT co6oif ymoso.H: K03cpcpHI(HeHT HaKJioHa
JIHHHH perpeCCHH ,l(OXO,Zl;HOCTH aKnlBa Ha L(OXO).l.HOCT.b pbIHOqHoro lfH).l.eKca.
175
I'llaea 5. Mooellu 014e1-1Ku cmoUMocmu aKmueo6
Bonpoc S.S. 1ITO IlOKa.3bIBaeT K03<P<PHQHeHT 6eTa?
0TBeT.
Ko3<P<Pmu1eHT 6ern noKa.3hrnaeT 3aBHCHMOCTb Me)K,ey" .n:oxo.n:HOCThIO aKTHBa H
.llOXO.l(HOCThlO pbIHKa (phIHQqHoro HH.l(eKca). OH roBOpHT 0 TOM, B KaKOH CTeneHH
.llOXO.llHOCTb aKTHBa (H COOTBeTCTBeHHO ero QeHa) 6y.n:er pearHpOBaTb Ha .n:eiiCTBHe
pbIHOqHbJX CHJI.
3a.qaata 5.6. CTaH,Z:(apTHoe OTKJIOHeHHe ,n;oxo,n;HoCTH pbIHoqHoro HH,ZJ;eKca paBHO 25%,
KOBapHaQIDI .n:oxo.uHOCTH pbIHOqHoro 1rn,n;eKca c .noxo,n;HocThIO aKIJ;1rn KOMTiaHHH A cocraaIDieT 340. Onpe,n;eJIHTb Ko3<P<PHQHeHT 6ern aKIJ;HH A OTHOCHTeJihHO
pbrnoqHoro HH.lleKca.
Pemeune. Eera i -ro aKTHBa onpe.n:eIDieTc.si no <J.>opMYJie:
/3. = covim I 2 ' am
r.ne /3; - 6era i -ro aKTHaa; 2
O" m - .llHCTiepCIDI ,!J.OXO.llHOCTH pbIHOqHoro HH.lleKca;
(5.2)
covim - KOBapHaQHJI ,ZJ;OXO,ZJ;HOCTH pbIHOqHoro HH,ZJ;eKca c ,[J.OXO,ZJ;HOCTblO 3.KJ.Urn
i -H: KoMnamrn.
CornacHo (5.2) 6era a.KQHH KoMnaHHH A cocTaBIDieT:
3a.qa'la 5.7.
340 /3A = - 2 = 0, 544. 25
,[(oxo.n;HOCTb aKIJ;HH KOMnamm A H pbIHOqHoro nopT<l.ieIDI 3a ,n;eBJITh JieT
npe,n:cTaBJieHbI B rn6JIHQe:
[O)J.bl 1 2 3 4 5 6 7 8 9
,[(oxo,n:HoCTb A 3 -2 -1 2 6 5 8 10 12
,IJ;oxo,n;HOCTb
pbIHOqffQrQ 5 -4 -2 4 9 7 12 14 15 IIOpT<J.>eIDI
Onpe.n:eJIHTb K03<P<J.>11u;HeHT 6eTa aKIJ;HH OTHOCHTeJibHOro pbIHQqHoro rropT<PeIDI
Ha OCHOBe CMeIIJ;eHHbIX ou:eHOK. KaK MO)l(HO HHTepnpeTHpOBaTb rronyqeHHbIH
pe3yJILTaT?
Pemeune. BL16opoqHaJ1 ,[J.HcrrepcIDI ,n:oxo,n:HOCTH p1>rnoqHoro nopTcpeIDI paaHa:
176
I'llaea 5. Mooe!lu Ol{e1ll<U cmoUMocmu aKmueoe
n
~)11 -rf a-2 = i=l =39,56.
n
KmQ:>qrn:IUieHT BhI6opoqHoil Kosap1rnu;1m ,D,OXO,lJ,HOCTeii aKQHH H rropTlj:>eIDI paseH:
CornacHo (5.2) Ko31j:>l):>HIUfeHT 6era aKu;HH cocraBJUieT:
/3 = 27,93 = 0 706. A 39,56 '
Ilo.rryqeHHhIB pe3yJihTaT rosopHT 0 TOM, qTo ecm1 B CJie,n:yro:w;eM ro,D,y ,lJ,OXO,lJ,HOCTb
pbJHOqHoro nopTQ:>eJUI Bb:rpacTeT Ha 1 %, TO HHBeCTOp BIIpaBe 0)1(.H,lJ,aTb pocTa
)J.OXO,lJ,HOCTH aKQHH B cpe,lJ,HeM Ha 0,706%.
3a.qa'fa 5.8. CTaH,n:apTHoe OTKJIOHeHHe .n:oxo,D,HOCTH pbrnoqHoro HH,n:eKca paBHO 25%,
,[J;OXO,D,HOCTH aKIJ;HH KOMIIaHHH A - 20%, K031j:>lj:>Hu;HeHT KOppeJUIIJ;HH Me)K,D,y
.n:oxo,n:HOCTHMH phrnoqHoro HH)l.eKca H aKQHH A cocraaJUieT 0,68. Onpe,D,eJIHTb
K03Q:>Q:>uu;HeHT 6era aKIJ;HH A OTHOCHTeJihHO pblHOqffOrO HH,n:eKca.
PemeHHe. Eera i -ro aKTHBa orrpe,lJ,eJI51eTcH no Q:>opMYJie:
/3 CY .
. =-'corr I lm'
(Ym
r.n;e (Yi - CTaH.n;apTHoe OTKJIOHemrn ,lJ,OXO,lJ,HOCTH i -ro aKTHBa;
CY m - ,lJ,HCnepCIDI ,lJ,OXO,[(HOCTH pbIHOqHoro HH,[(eKca;
(5.3)
corrim - KOppeJUIIJ;IDI ,lJ,OXO,lJ,HOCTH pi,rnoqHoro HH,lJ,eKca c ,ll;OXO,ll;HOCTbIO aKQHH
i -H KOMIIaHHH.
Eera aKQHH KOMilaHHH A cocraBJUieT:
3aAa'la 5.9.
20 /3A =-0,68 = 0,544. 25
IlopTlj:>eJib COCTOHT H3 aKQHH KOMIIaHHH A, B H c. y ,[I;. Beca aKTHBOB B noprlj:>eJie
H 6eThI a:rru;HH OTHOCHTeJibHO pbIHOqHoro 1rn.n;eKca paBHbI: BA = 0,5, B8 = 0,3,
Be = 0,2, jJA = 0,8, /38 = 1,1 H /Jc = 1,3. Onpe.ri;eJIHTb 6ery rroprlj:>eJIH.
PemeHHe. Eera noprQ:>eJIH orrpe,IJ;eAAeTCH no Q:>opMyne:
n
/JP= °'L.B;/3;· (5.4) i=l
177
I'llaea 5. Mooe;zu OtfeHKu cmoUMocmu aKmueoB
CornacHo ( 5 .4) 6ern nopTcpeIDI paBHa:
/JP = 0,5·0,8+0,3·1,1 +0,2· l,3 = 0,99.
3a.qa'la 5.1 O. CrnBKa 6e3 pHcKa paBHa 10%, O)lrn,I(aeMaJI .n;oxoJJ;HOCTb pbIHOl:moro noprcpeIDI -
20%, 6era aKIJ;MH KOMnaHMH A OTHOCHTeJibHO pbIHQqHoro nopnpemI - 1,2. Onpe.n;eJIHTb O)l(HJJ:aeMYJO JJ:OXOJJ:HOCTb aKIJ;HH.
PemeHHe. O)l(M,ZJ;aeMaJI ,n;oxo,l(HOCTb aKIJ;HM orrpe,n;eIDieTCji c n0Momo10 ypaBHCHHjl SML:
(5.5)
r,l(e /J; - 6eTa i -H aKIJ;HH, ,l(JUI KOTOpoii orrpe,n;eJUieTCH ypoBeH.b O)l(H,l(aeMOH
,l(OXO,l(HOCTH;
E(r; ) - O)l(H,I(aeMaJI ,n;oxo,l(HOCTh i -ii aKIJ;HH;
am - pHCK pbIHoqHoro nopTcpeIDI;
E(r m ) - O)l(H,I(aeMaJI .zi;oxo,r:i;HOCTh pbIHQqHoro nopTcpeIDI.
Q)1rn,n;aeMaJ1 ,n;oxo,n;HocTh aKIJ;HH paaHa:
E(rA) = 10+1,2(20-10) = 22%.
3a.qa'la 5.11. O)l(HJJ:aeMa» ,n;oxo,n;HocTD poIHOqffOro nopT<jleIDI paaHa 20% , craaKa 6e3 pHcKa
8% ro,n;oBhlx. Ko3<jl<jlHIJ;HeHT 6era aKUHH KOMrraHHH A OTHOCHTenbHO p1>moqHoro rropr<jleJUI cocTaBJUieT 1,3. Ha aKIJ;HIO 6hIJI BbIIIJiaqeH roJJ;OBOH .l(HBM,n;eH,l( B pa3Mepe 5 py6. B rrocne,n;HHe ro,n;1.1 e)l(ero,n;Hhlii reMrr rrpHpocrn ,l(HBM,n;eH,r:i;a paBeH 4%. Onpe.n;emITh u;eHy aKIJ;Jrn.
PemeHHe. Ha ocHoBe ypaBHeHHjl SML onpe,n;eJUieM o)l(H,I(aeMYJO ,n;oxo,n;HOCTb ( crnB.KY
,l(HCKOHTHpOBaHMjl), COOTBeTCTByromyro pHCKY HHBecrnpoBaHIDI B aKIJ;Jrn KOMIIaIIHH A:
E(rA) = 8+1,3(20-8) = 23,6%.
I(eHa aKIJ;Jrn paBHa:
5(1+0,04) PA= = 26,53py6.
0,236-0,04
3a.qa'la 5.12. O)l(H.l(aeMaJI ,n;oxo,n;HOCTh p1.rnoqHoro nopT<jleIDI paBHa 20% , cTaBKa 6e3 pHcKa
10% ro,n;oBbIX. Ko3tjlcpRu;ReHT 6ern aKUHH KOMnaHHH A OTHOCHTenbHO pbIHOqHoro rroprtjleJUI cocraBIDieT 1,2, KOMnaHHH B - 1,4, KOMnamrn C- 0,8. Y.n;. aeca aKIJ;HH B
nopT<jlene COCTaBJUIIOT: e A = 0,5 ' e B = 0,3 ' e c = 0,2 . Onpe,n;eJIHTh Q)l(M,l(aeMYJO
,l(OXO,l(HOCTb IIOpT<jleJUI.
178
I'JLa6a 5. MooeJLu OtfeHKU cmoUMocmu aKmu6o6
PemeHHe. CornacHo (5.4) 6ern nopnpeIDI paBHa:
/JP = 0,5·1,2+0,3·1,4+ 0,2·0,8=1,18.
Q)l(H.u;aeMasr )J,OXO)J,HOCTb IIOpT<l_}eIDI COCTaBIDieT:
E(rp) = 10+ 1,18(20-10) = 21,8%.
3aiAa'la 5.13. O:t1n1.u;aeMM .u;oxo.n;HOCTb pbrnoqHoro nopT<l_}eIDI 20%, CTaBKa 6e3 pHcKa 10%
ro.n;oBhIX. Ko3<l_}<l_}m.lHeHT 6eTa am1rn KoMnamrn A OTHOCHTeJibHO phlHoqHoro nopT<l_}eIDI cocTaBllileT 1,2, KOMrramrn B - 0,8. D;eHa aKu;HH A paBHa 15 py6., B - 23 py6. llHBecTOp O)l(H.n;aeT, qTO qepe3 ro.u; u;eHa amMM A cocTaBHT 19 py6., amMM B -26,5 py6. ,ll,HBH,D;eH.u;bI no aKu;wrM He BbIIIJiaqMBaIOTCjl. Onpe.n;eJIHTb, KaKasr H3 amMii no MHeHHIO HHBecTopa rrepeou;eHeHa, a KaKM He.u;oo:ueHeHa.
PemeHHe. CornacHo ypaBHeHHIO SML paBHOBecm,1e O)l(H,D;aeMbie .u;oxo.n;HOCTH aKu;lill
paBHbI:
E(rA) = 10+1,2(20-10) = 22%,
E(rB) = 10+0,8(20-10) = 18%.
,ll,eiiCTBHTeJibHbie O)l(H,ll;aeMbie ,ll;OXO,D;HOCTH aKD;HH Ha OCHOBe nporH030B HHBeCTOpa CTOHMOCTH aKD;HH qepe3 ro,ri; COCTaBIDIIOT:
~ = 19
-1=26,67% , 15
- - 26,5 -1-15 2201 rB - - , ;ro. 23
,ll,e.H:crnHTeJihHasr O)l(H,ri;aeMasr ,ri;oxo,ri;HOCTb aKQHH A 6011bme paBHOBecHoii, no3TOMY
aKQHjI He.n;oou;eHeHa. ,D;eiicTBMTeJibHM O)l(H.n;aeMasr ,ri;oxo,n;HOCTb aKQHH B MeHbme paBHOBeCHOH, 1103TOMY aKu;IDI nepeou;eHeHa.
3aAa~a 5.14. O)l(H,D;aeMrui: .n;oxo.n;Hocn pbIHOqfforo 11opT<l_}eIDI 20%, CTaBKa 6e3 pHcKa 10%
ro.n;oBbIX. Ko3<1_}<1_}11u;11eHT 6eTa aKII;HH KOMIIaHHH A OTHOCHTeJibHO pbrnoqHoro nopT<l_}eIDI paBeH 1,3. D;eHa aKu;HH A l 5 py6. llHBecTop O)l(H.n;aeT, qTo qepe3 ro.n; u;eHa aKD;HH COCTaBHT 17 ,2 py6., Ii Ha aKD;HIO 6y.n;eT BbIIIJiaqeH .D;HBH,D;eH,IJ; B 1 py6.
Onpe.neJIHTI>, CTOHT mi: HHBecTopy KYIIHTI> aKu;Hro A. PemeHHe. CornacHo ypaBHeHHIO SML paBHOBecHajl O)l(H,ll;aeMasr .u;oxo,n;HOCTb aKQHH paBHa:
E(rA) = 10+ 1,3(20-10) = 23%.
,ll,eiiCTBHTeJibHasI O)l(H,ll;aeMasr )J,OXO.D;HOCTb aKD;HH Ha OCHOBe nporH030B HHBeCTOpa COCTaBJUieT:
179
T1iaea 5. Mooe!lu ottemcu cmoUMocmu aKmueoe
rA = 17
•2 +1
1=21,33%. 15
,L(eHCTBHTeJibHa.51 Q)l(H,D;aeMa.51 ,Il;OXO,Il;HOCTb amHH MeHbIIIe paBHOBeCHOH, Il03TOMY 6yMara rrepeo:ueHeHa. CJie,n;oBaTeJibHO, ee He CTOHT noKyrraT1>, TaK KaK :u;eHa ee ,n:oJDKHa ynacTb.
3a.qa'la 5.15. B Ta6mr:ue rrpe,n;cTaBJiem.1 .n:oxo.n;HocTH 6YMar A H B 11 pbrnoqHoro :irn,n:eKca 3a
IUITb JieT:
A 15 18 10 3 -10
B 8 11 7 4 -4
IIH,n;eKc 10 12 9 5 -6
HaIIHcan ypaBHeHHe SML ,n:m1 6yMar A H B OTHOCHTeJibHO p1>rnoqHoro 1rn,n:eKca, ecJIH CTaBKa 6e3 pHcKa paBHa 10% ro.n;oB1>1x. Orrpe,n;eJIHTb O)l(H)J;aeMI>Ie .n:oxo,l(HOCTH 6yMar B cJie.n;yroru;eM ro.n:y, ecm1 ,l(OXO.ZJ:HOCTD HH.[(eKca cocTaBHT 15%. B pacqernx HCIIOJib30BaTD B1>16opoqH1>1e ,n;Hcrrepci:rn H KOBapna:u;HH.
Pemenue. CornacHo ( 4.1) B1>16opoqHaH .uncrrepcHH .uoxo,n:HOCTH pLrnoqHoro rropT<l>eM
paaHa a; = 41,2. CornacHO (4.9) KOJcl>cl>HU:HeHTbl BLI6opoqHoR KOBapHaI(HH
.uoxo.uHocTeii amm1 A H B H pbIHoqHoro rropT<l>eM coorneTcTBeHHO paBHI>I
COY Am = 63 H COY Bm = 32,6. CornaCHO (5.2) K03<l><l>H:UlleHTbl 6eTa aK:UHH
cocTaBJIHIOT fl A= 1,529, flB = 0,791. CornacHo (5.5) ypaBHeHHH SML 6yMar AH B HMelOT BH,D;:
E(rA)= 10+ 1,529[E(rm )-10] ,
E ( rB) = 10 + 0, 791 [ E (rm )-10 J. 0)1(H)J;aeMble .UOXO.UHOCTH 6yMar B CJie,n;y10ru;eM ro.n:y JJ:1IH JJ:OXOJJ:HOCTH HH,n;eKca 15% COCTaB.HT:
3a.qa'la 5.16.
E(rJ=lO+l,529(15-10]=17,645%,
E(rB) = 10 + 0, 791[15-10] = 13,955%.
B Ta6mru:e rrpe,n;cTaBJieHhI .n;oxo,ll,HOCTH 6yMar A H B H pi,rnoqHoro HH,ll,eKca 3a IUITb JieT:
A 19 12 2 -1 -10
B 8 9 7 6 1
15 11 4 3 -4
180
Dwea 5. MooeAu Ol/eHKU cmoUMocmu aKmueoe
CTaBKa 6e3 pHCKa paBHa 8% ro,n;OBhIX. Orrpe,n;eJIHTh Ha ocHoBe ypaBHeHHH SML O)Klf,ZJ;aeMbie ,n;oxo,n;HoCTH 6yMar A H B B c11e,n;y10meM ro,n;y, ecnH ,n;oxo,n;HoCTh
HH,l(CKCa COCTaBHT 10%. B pacqernx HCIIOJib30BaTb Bb16opoqHbie ,ZJ;lfCIIepcHH H
KOBapHa.QHH. Pemeuue. YpaBHeH1u1 SML aKI.t;HH A H B HMeIOT BH,n::
E(rA) = 8+1,528[E(rm )-8] ,
E(r8 ) = 8 + 0,371[ E(rm )-8 ].
O)l(H,ZJ;aeM1>1e ,n;oxo,n;HoCTH 6yMar B cJie,n;y10meM ro,n;y .[(.JUI ,n;oxo,n;HOCTH HH,n;eKca 10% COCTaBHT:
3aAa~a 5.17.
E(rA )= 8+1,528(10-8]=11,056% ,
E(rB) = 8 + 0,371(10-8] = 8, 742%.
Ilo O.QeHKaM HHBeCTopa paBHOBeCHaH O)KH,ZJ;aeMaH ,ZJ;OXO,ZJ;HOCTb aK.QHH KOMIIaHHH A paBHa 25%, ,n;e.HcTBHTeJihHaH O)KH,n;aeMaH ,n;oxo,n;HOCTh aK.QHH - 30%. Orrpe,n;eJIHTh
aJib<PY aKUHH. 0 'lCM rosopHT aJib<pa ,n;aHHOH aKU.HH? Pemeuue. Arrhll_}a aK.QHH orrpe,n;eJIHeTcH no ll_}opMYJie:
a;=P;-E(r;), (5.6)
r,n:e E ( 'i ) - pasHosecHaH O)l(H,n:aeMaH ,n:oxo,n:HoCTh i -.H aK.QHH;
Y; - ,n:eHCTBHTeJThHaH O)l(H,ZJ;aeMaH ,ZJ;OXO,ZJ;HOCTb i -H aK.QHH.
CornacHo (5.6) an1>1l_}a aK.QHH A pasHa:
aA = 30-25 = 5.
Ilono)l(HTeJThHOe 3Haqemre an1>1l_}1>1 rosopHT o TOM, 1lTO aKUHH A He,n;oo.QeHeHa.
38Aa~a 5.18. Ilo O.QeHKaM HHBeCTOpa paBHOBeCHaH Q)K.H,l(aeMaH ,ZJ;OXO,ZJ;HOCTb aK.QHH KOMIIaHHH
A paBHa 25%, ,n;eiicTBHTeJibHaH O)KH,n;aeMaH ,n;oxo,n;HoCTb aKIJ;HH - 20%. Orrpe,n;eJIHTb
aJib<py aKIJ;HH. 0 qeM rosopHT aJib<pa ,n:aHHOH aKUIIH?
Pemeuue. CornacHo (5.6) anbll_}a aK.QHH A paBHa:
aA =20-25=-5.
0TPHUaTeJI1>Hoe 3Haqem1e anb<pb1 rosop1n o TOM, qTo aK.QHH A rrepeou,eHeHa.
38Aa~a 5.19. O)KH,n;aeMa}I ,n;oxo,n;HocTh pbrnoqHoro rropTQ_)eJIH 15%, CTaBKa 6e3 pncKa 5%.
Ko31l_}ll_}n.QHeHT 6eTa aKIJ;HH KOMIIaHHH A OTHOCHTeJibHO phrnoqHoro nopT<l>eIDI paBeH
181
I'1za6a 5. Mooenu 014eN1<u cmoUMocmu a1<mu606
1, 1. Am,Q:>a aKI.lHH paBHa 0,4. Orrpe,u:errHT.b ,u:eiicTBHTeJI.bH)'IO 0:11m.n:aeM)'IO ,U:OXO,U:HOCT.b aKI.lHH.
Pemeuue. CornacHo SML paattosecttrui O)lrn:.naeMrui .n:oxo.n:ttocT.b aKI.lHH A pasHa:
E(rA) = 5+1,1(15-5) = 16%.
Ha OCHOBaHHH (5.6) .n:eiicTBHTeJibHruI O)KH,U:aeMruI .[{OXO,U:HOCTh aKI.lHH COCTaBJUieT:
r; = E(rA)+aA = 16+0,4=16,4%.
3a,Aa'la 5.20. Y .n:. Beca rrepsoii, BTopoii 11 'I'peneii amHii B rropTQ:>ene cooTBeTCTBeHHO paBHhl
20%, 35% H 45%. An.bl}>a rrepBOH amHH 0,3, BTOpoii MHH)'C 0,15, -rpeT.beii 0,4. Orrpe.n:em:1Th ani,Q:>y rropTQ:>eIDI.
Pemeuue. AnI>Q:>a rropTQ:>eIDI orrpe.n:eIDieTC.K KaK cpe.n:HeB3BeweHHruI an.bl}> a 6yMar,
BXOMII.lHX B rropTQ:>eni,:
aP = 0,2 ·0,3 + 0,35 · (-0,15) + 0,45 · 0,4 = 0,1875.
3a,Aa'la 5.21. IlopTQ:>eJih COCTOHT H3 'I'peX amHii. Ani,Q:>a rrepsoii amHH paBHa 2, BTOpoii- 0,3,
ani,Q:>a rropTQ:>eIDI pasHa 0,69. Y.n:. Bee rrepsoii aKI.lHH B rropTQ:>ene 50%, BTopoii 30%. CTaBKa 6e3 pHcKa cocrnsmreT 10%, m1rn:.n:aeMa.K .n:oxo.n:HoCT.b pI>rno~rnoro rropTQ:>eID:I 20%, 6ern rrepsoii aKI.lHH 1,5, BTopoii 1,2, -rpeT.beii 0,8. Orrpe.n:emfTL .n;eliCTBl:ITeJibHYIO m1m.n;aeM)'IO ,Il;OXO,Il;HOCTb rpeTbeH aKr(Hl:I.
Pemeuue. PaBHOBecttrui mK1:1.n:aeMrui .n:oxo,L(HOCT.b -rpeTheii aKI.ll:IH pasHa:
E ( r3 ) = 10 + 0, 8 ( 20 -10) = 18%.
Anbl}>a 'I'peT.beii 6yMarn COCTaBIDieT:
a = 0,69-0,5·2-0,3·0,3 =-2. 3 0 2
' ,n:eliCTBl:ITeJibHruI oxm.uaeMruI ,UOXO,UHOCTb rpeTbeii aKI.lHH paBHa:
r; = 18-2=16%.
IlpHMe11auue. ~ pemeHIDI 3a,n;aqH He -rpe6oBaJIOCb 3HaHJie 3Haqemlii 6eThl rrepBOH H BTOpoii aKu;1:1li. 0HH 6bIJIH rrp1rne.n;eH1>1 .n;IDI ycrrm1rneHID1 ycrroBMH 3a.n;aqH.
182
Diaea 5. MooeJlu OZJe"flKU cmoUMocmu aKmueoe
5.2. PblHO'IHaa MOAeni.
3aAa'la 5.22. B Ta6mn.1,e npe.n;crnsrrem.1 .noxo.l(HOCTM 6yMan1 A M pbrnoqHoro MH,LleKca 3a
IDITb rreT:
l~e•cl 13 20 14 7 5
10 12 9 5 -6
HanMcaTb ypasHeHMe pI>rnoqHoli Mo.nerrM B npe.ncrnsrremm TpeliHopa .nm1 6yMarM A OTHOCMTeJibHO pbIHOqHoro MH.l(eKca. B pacqeTax MCnOJih30BaTb Bbl6opoqHble .n;ncnepcm:r, CTaH.l(apTHbie OTKJIOHeHIUI, KOBapIIaIJ,MM II KOppemIIJ,IIII.
PemeHHe. PI>rnoqmur Mo.nerrb B npe.ncTasrremrn: TpeliHopa MMeeT BH.l(:
~ = Y; + /3;rm + &; ,
r.n;e rm - )J;OXO)J;HOCTb pnIH01IHOro IIH)J;eKca;
/3; - K03cpqmuHeHT 6eTa i -ro aKTIIBa.
(5.7)
ri - Q)J<M.l(aeMruI .l(OXO.l(HOCTb i -rO aKTHBa npH OTCYTCTBMH BJIIDIHIDI Ha Hero
pbIHOqHbIX cpaKTOpoB, OHa HBIDICTCH KOHCTaHTOM;
&; - crryqaliHrui: BeJIH1IJ1Ha ( onm6Ka ), ee cpe.n;Hee 3Ha1IeHIIe paBHO eymo,
.LIIICnepcIDI noCTOHHHa, KOBapHaUHH c .LIOXO.LIHOCTblO pbrnoqHoro HH.l(eKca paBHa eyrrro; KOBapHaUIDI c HepbrnoqHbIM KOMnOHeHTOM JJ;OXOJJ;HOCTM .z:i;pyrHx aKTMBOB
paBHa eynro.
EeTa i -ii 6YMarn: orrpe,ri:em1eTCH no cpopMYnaM (5.2) MITH (5.3). EeTa 6yMarH A paBHa flA =0,7136.
f aMMa i -li 6YMarn orrpe,ri:em1eTc.a no cpopMYrre:
(5.8)
r.ri:e ~ - cpe.ri:wrn .ri:oxo.D:HOCTb i -ro aKTHBa 3a npe,ri:bl,11:ymne nepHO.D:hl BpeMeHn;
rm - cpe,LUIIDI .D:OXO.D:HOCTb pbIH01IHOro IIH,ri:CKCa 3a IIpC.D:bmymIIC nepHO.D:bl BpCMCHII.
Cpe.n;wrn .n;oxo,n;HOCTb 6YMarM A H pbrnoqHoro HH,n;eKca 3a npe.n;nI,IzyIIJ,He nepMO.l(bl BpeMeHM COCTaBJIHIOT:
_ _ 13 + 20 + 14 + 7 - 5 _ l l go/ rA - - /O
5 ' '
- _ 10+12+9+5-6 -601 rm - - /0.
5
faMMa 6yMarn cornacHo cpopMyne (5.8) pasHa:
YA= 11,8-0,7136·6 = 7,5184%.
YpaBHCHHe pbrnoqHOM MO)J;CJIH 6yMarHA HMeeT BH,ri::
rA = 7,5184+ 0,7136r711 + c: A.
183
I'!laea 5. ModeJLu OIJeH.Ku cmoUMocmu aKmueoe
3aAa'la 5.23. B Ta6mn:i;e rrpe.n;cTaaJieHbI .n:oxo;:i;HocTH 6yMarH A H pbrnoqHoro HH;:I;eKca 3a
IUITb JieT:
A 12 18 12 6 4
9 11 7 4 -3
Ha1mcaTb ypaaHeHHe pbIHoqHo:H Mo.n;eJIH ;:I;llil 6yMarH A OTHOCHTeJI1>Ho pbrnoqHoro irn;:i;eKca. B pacqeTax HCIIOJI1>3oaan, Bb16opoqHb1e ;:i;HcrrepcHH, cTaH.n;apTHbie OTKJIOHeHIDI H KOBapHaUHH.
PeweHue. Eern 6yMarn A cornacHo <j_}opMYne ( 5 .2) paaHa /3 A = 0, 929 5.
raMMa i -H 6yMarn COrJiaCHO <j_}opMyJie (5.8) COCTaBllileT YA= 5,195. YpaaHeHHe p1>rnoqHoii Mo.n;eJIH 6YMarH A HMeeT am:i::
rA = 5,195 +0,9295rm +&A.
3~a'la 5.24. Ha ocHoae ycJioBHii 3a,n;aqH 5 .23 orrpe.n;e.JilITb o)l(H)J;aeMYJO .n:oxo.z:i;Hocn 6YMarn A B
cne.zzyromeM nepHo;:i;e, ecJilf O)KH,)];aeMrui: .n;oxo.n:ttocn pbrno~oro HH,n;eKca paima 15%. PeweHue. Ha OCHOBe pbIHOqHoH MO)J;eJIH O)Kll)J;aeMruI .LJ:OXO.lJ;HOCTb i -H 6yMarH orrpe.z:i;e
llileTC» KaK:
(5.9)
CornacHo (5.9) O)KH,)];aeMrui: .z:i;oxo.n;HocTb 6yMarnA B cJie.ny10meM rrepHo.z:i;e paaHa:
E(rA) = 5,195+0,9295 ·15=19,14%.
3aAa11a 5.25. Ha OCHOBe pbIHOqHoii MO,lJ;eJIH pa3,n;eJIHTb BeCb pHCK aKTHBa Ha pbIHOqHbIH H
HepbrnoqHbIH. Peweuue. Ha ocHoae Mo;:i;en11:
)J,HCIIepCIDI .lJ;OXO.lJ;HOCTH i -ro aKTJrna paBHa:
ai2
= var(r;) = var(r; + /3; rm + E;) = /3/ a; + 2 /3; cov &,m + a;, , r.z:i;e var(.) - .z:i;HcrrepcH».
TaK KaK cov &,m = 0, TO MO)J(HO 3a1rn:caTb:
;T 2 = /32;T2 + 2 v i iv m er&; '
184
(5.10)
I'Jtaea 5. MooeJtu 014e1tKu cmoUMocmu aKmueoe
3a.qa1.1a 5.26. Bera aKUHH A pasHa 1,5, cTaH)J.apTHoe oTKJioHeHHe cneumlmqecKoro pHcKa
aKuHH - 5%, CTaH.[(apTHOe OTKJIOHemi:e .[(OXO.[(HOCTH pi.rnoqHoro nopTcpeIDI - 10%. Onpe.[(eJIHTh seci. pHcK aKTHBa, H3MepeHHbIH CTaH)1,apTHhIM OTKJIOHeHHeM.
PemeHHe. CornacHo ( 5 .10) ,ll;HCnepcIDI )1,0X0)1,HOCTH aK.QHH A paBHa:
0-~ = 1, 52 • 102 + 52 = 250.
CTaH.ZJ;apTHoe OTKJIOHeHHe .[(OXO.[(HOCTH cocTaBIDieT: J250 = 15, 81 %.
3a.qa'la 5.27 mm YCJIOBHH 3a,[(aqff 5.15 onpe;:i;eJIHTh K03cpqm1U1eHThI )1.eTepMHHarorn: aKUHiiA H B. PemeHHe. K03<l><}mIJ;i-1eHT .[(eTepMHHau1rn: i -:H: 6YMarH onpe.ZJ;eIDieTCH no q,opMyne:
2 2 R. =corr. z zm, (5.11)
r)J,e corrim - K03<l><l>HUHeHT KOppeIDIUHH )1,0XO.[(HOCTH i -:H: 6yMarn: c .[(OXO.[(HOCTblO
pbIHoqHoro HH.ZJ;eKca.
K03<l><}mu;HeHThI KoppeIDIUHH aKQHH A H B coornercrneHHo paBHhI:
corr Am = 0,983 , corr Em = 0,993.
Ko3<l><l>RuHeHTbl ,n;erepMHHau;m-1 aKUHH COCTaBIDIIOT:
R~ = 0,966, R~ = 0,986.
3a.qa1.1a 5.28. Ha OCHOBe ,n;aHHhIX 3a)J,aq11 5 .16 onpe,n;emni. K03<l><l>11u11eHThl .[(eTepMll:Hauu:u:
6YMarA u:B. 0TBeT.
Ko:J<l><l>u:uu:eHThI )1,erepMHHau;u:u: 6yMar paBHIJ: R~ = 0,9959, R~ = 0,7767 .
3a.qa'la 5.29. Pi.rnoK Haxo,n;HTCH B paBHOBeCHH. Cpe,ll;~ )1,0XO.ZJ;HOCTh aKQHH A paBHa 10%
r0)1,0BbIX, cpe.[(~ )1,0X0)1,HOCTh pi.rnoqHoro nopTcpeIDI COCTaBJUieT 12% r0)1,0BbIX.
CrnH,n;apTHOe OTKJIOHeHHe ,n;oxo~OCTH amHH A 8%, PIJHOqHoro IIOPT<PeIDI I 0%, K03<l><l>u:uHeHT Koppemru;HH )1,0XO)J,HOCTeH aKUHH H p1:.rnoqHoro nopTcpeIDI 0,85. Onpe;:i;eJIHTb senu:q1rny CTaBKH 6e3 pu:cKa.
PemeHue. Onpe,n;eIDleM KO:J<i><l>HuHeHTbl /3 H r aKIJ;HJI )1,IDI ypaBHeHHH pi.rnoqHoH MO)J,eJIH:
185
I'Jzaea 5. MoiJe;zu 014e1tKU cmoUMocmu aKmueoe
8 /JA = -0,85 = 0,68, YA= 10-0,68· 12=1,84. 10
O)l(H,l(aeMaH ,l(OXO,l(HOCTb aKTHBa Ha OCHOBe pbrnoqHOH MO,l(eJIH pasHa:
E(lf) = Y; + /J;E(rm ), Ha ocHoae Mo.uemf CAPM oHa cocrnamieT:
E ( 1i ) = r1 + /J; [ E (rm )- r1 J. Ilp:apaamrn ypaaHeHne Mo,n;errH IIIaprra n CAPM H rrpeo6pa3oaaa, rrorryqttM:
r =_Ji_= 1•84 = 5 75%.
I l - /J; 1- 0, 85 '
3aAa'la 5.30. CrnH.uapTHoe OTKJIOHeHHe pbIHOqfforo rropT<pemI paaHo 15%, CTaH.l(apTHoe
OTKnOHeHHe mHpoKo .UHBepcmpuu;HpoaaHHoro rropTQ:>emI A - 12%, 6eTa nopTQ:>eJUI A 0,8. Orrpe,n:eJIHTb, SIBJUieTCSI JIH rropTQ:>eJib A 3Q:>Q:>eKTHBHhlM?
Peweuue. Beeb pHCK rropTQ:>eJUI aHaJIOrHqHo Q:>opMJJie ( 5 .10) MO)l(HO p33.UeJIHTh Ha
phlHOqHblH H He p1>rnoqHwii:
ECJIH rropTQ:>eJib 3Q:>Q:>eKTHBHbIH, TO He p:r,rnoqHbIH pHCK y Hero OTCYTCTByeT.
2 2 2 - (J'p Il03TOMY MO)l(HO 3aIIHCaTb: (J'p = /Jp(J'm. 0TCIO,l(a: pp - -.
(J'm
12 ,l(JUI rropTQ:>eJUI A rrorryqaeM: PA = - = 0,8. Cne.uoBaTeJibHO, rropTQ:>eJib A
15 SIBJUieTCSI 3Q:>Q:>eKTHBHhlM.
5.3. Ap6MTpa>KHaJI MOAen1a (APT)
Bonpoc 5.31. Ilepeq1:1cJI1:1Te 06m;1:1e rroJIO)l(eHHSI .l(JUI Mo.ueneii CAPM H APT? 0TBeT.
1) HHBeCTOpbI npe.urroqHTalOT 6oJibIIIee KOJIHqeCTBO 6oraTCTBa MeHbIIIeMy;
2) HHBeCTOpbI He CKnOHHbl K pHcey;
3) HHBeCTOpbl HMeIOT O,l(HHaKOBbie 0)1(1:1,l(aHHSI OTHOCHTeJibHO pHCKa H
,l(OXO,l(HOCTH aKTHBOB;
4) Q:>HHaHCOBbIH pbIHOK SIBJISieTCSI 3Q:>Q:>eKTHBHbIM;
Bonpoc 5.32. KaK1:1e rrorro)Kemrn or111:1qa10T Mo.ri:em. APT or CAPM?
186
I'llaea 5. Mooe.nu 071e1-1Ku cmoUMocmu aKmueoe
0TBeT.
APT He rrpe~onaracr ofoI3aTeJihHo:
1) O.IJ:HOro apeMeHHoro rrepHo,IJ;a;
2) HOpMaJibHOe pacrrpe,IJ;enem-1e .IJ:OXO.IJ:HOCTH aKUIBOB;
3) onpe,ll;eJieHHblH BH,ll; <PYHKUHH IIOJie3HOCTH;
4) HaJIIflIHe pbrnoqHoro rropT<j:lem1;
5) B03MO)l(HOCTb 3aHHMaTb H rrpe,IJ;OCTaBIDITh cpe,Il;CTBa IIO,ll; CTaBKY 6e3 pHCKa.
3CIACl'la 5.33. O)l(lf,D;aeMbie AOXOAHOCTH amHii KOMrraHHii A H B cooTBeTCTBYIOT paaHoBeCHbIM
H cocTaBIDIIOT 25% H 20%. Ko3<j:l<j:IHUHeHT qyacTBHTeJibHOCTH aKIJ;HH A K
pbIHOqffOMY HHAeKcy paaeH 1,3, aKIJ;HH B - 0,8. HarrHcan ypaBHem1e O.IJ:HO
<j:laKTOpHOH Mo,IJ;eJIH APT, ecnH crren;H<j:IHqecKHM pHCKOM MO)KHO rrpeHe6peqh.
PemeHHe. 0,D;Ho<j:laKTOpHasi MO,D;e1Ib APT HMeeT BH,D;:
E(7:) = A0 + AJ3i , (5.12)
r,D;e E(':) - OlKH,ZlaeMaSI .IJ:OXO,D;HOCTb i -ro aKTHaa;
A0 - .IJ:OXO.IJ:HOCTh aKnrna rrpH OTCYTCTBHH BJIIDIHIDI Ha Hero pbIHoqHoro <j:la.KTopa
(.IJ:oxo,D;Hocn aKTHBa c 6cro:H: paaHoii: HYJIIO );
A, - rrpeMIDI 3a pHCK .D:JUI pbIHQqHoro HH.D:eKca (<j:laKTOpa pHCKa);
/3; - K03<j:l<j:IHIJ;HeHT qyBCTBHTeJibHOCTH i -ro aKTHBa K pbIHOtIHOM)' HH,D;eKcy
(<j:laKTopy pHCKa).
Ha ocHoae ypaBHeHIDI (5.12) 3amm1eM ypaBHeHIDI APT cooTBeTCTBeHHO .D:JUI aKl.l;HH A H B:
25 = A0 + 1,3A1 ,
20 =Ao +0,8Ai.
Ilo.JI)"IHJIH CHCTeM)' ypaBHeHHii:. Ee y,D;o6Ho pemHTb B MarpiflIHOH <j:lopMe. B MaTpHtI
HOH <j:lopMe CHCTeMY MO)l(HO 3an11can KaK:
AA.=B.
Ee pemeHHe HMeeT BH.IJ:;
A.= A-'B
r.n:e A-1 o6paTHaSI MaTpm:J;a K MaTpHn:e A.
B HameM IIpHMepe:
A=(: ~!} B=G~} Ilo3TOM)' CHCTeMy ypaBHeHHH MO)KHO rrpe.IJ:CTaBHTb KaK:
(1 l,3J(AoJ = (25J· 1 0,8 Ai 20
187
I'Jia6a 5. MooeJlu oi,eHKU cmoUMocmu aKmu606
Ero pernem1e paBHo:
(~)=(1 1,3)-1
(25)=(12)· Ai 1 0,8 20 10
0,n;Ho<j)aKTOpHoe ypaBHemrn APT HMeeT BR.[(:
E(r;)=12+10/J;·
3aAa1.1a 5.34. O)l(tt,n;aeMble ,n;oxo,n;HOCTH a.KJJ;HH KOMrraHHH A H B cooTBeTCTBYIOT paBHOBeCHbIM
H cocTaBJUIIOT 24% H 18%. Ko3<l_}<l_}imtteHT IJYBCTBHTerr1>HOCTH aKIJ;HH A K pDIHOqHOMY HH,n;eKcy paBeH 1,2, aKIJ;HH B - 0,4. Hanttcan ypaBHeHHe o,n;Ho<l_}aKTOpHoH: Mo,n;errH APT.
PemeHHe. Ha ocHoBe ypaBHeHIDI (5.12) 3amnneM ypaBHeHIDI APT cooTBeTcTBeHHO ,[(JUI
aKu;ttH: A H B:
24 = ~ +1,2Ai
18 = ~ +0,4Ai.
3arrHIIIeM CHCTeMY ypaBHeHHH (5.13) B MarpnqHQM BR,[(e:
G ~~)(~)=G:J. Pernrui: cttcTeMY, norryqaeM:
(~)=(: 1,2J-l (24J ( 15 J 0,4 18 - 7,5 .
0,n;Ho<j)aKTopHoe ypaBHeHne APT HMeeT BH,n;:
E(r;)=l5+7,5/J;·
3aAaLla 5.35.
(5.13)
CoxpamnoTc.SI ycrroBIDI 3a,n:aqn 5.34. llMeeTCSI TaK)l(e aKIJ;HSI KOMITaHHH C. Ee O)l(II.n;aeMasi: ,ll;OXO,ll;HOCTh paBHa 21 %, KO'.)<PqmrweHT qyBCTBIITeJibHOCTH K IIlI)J;eKcy COCTaB
JISleT 0,8. Onpe,n;errHTh, MO)l(HO JIH norryqnn ap6ttrp~ nptt61>1Jlb 3a cqer <l_}opMHpoBaHHSI ap6Hrpa)l(HOro nopT<j)eJISI, ecJIH He pbIHOqH:E>IM pHCKOM MO)l(HO npeHe6peTh.
PemeHHe. B 3a,n;aqe 5 .34 o,n;Ho<l>aKTopHoe ypaBHeHHe APT HMeeT BH,n;:
E(r;) = 15 + 7,5/J;·
Ha ero OCHOBe paBHOBecHaSI Q)l(H,[(aeMrui: ,ll,OXO,D;HOCTb aKD;HH c COCTaBJISieT:
E (re) = 15 + 7, 5 · 0, 8 = 21 %.
188
I';wea 5. Mooe;zu OlfeHKU cmowwocmu aKmueoe
Ap6IrrpIDK He B03MO)l(eH, TaK KaK .n:oxo,n:HOCTH Bcex 6y:~rnr HMeIOT paBHOBeCHhle
ou:eHKH.
3a.qa11a 5.36. CoxpaIDIIOTCJI ycJIOBHJI 3a.n;aqH 5.34. llMeeTCJI TaK)l(e aKu:HJI KOMilaHHH C. Ee
Q)l(H,IJ;aeMaJI ,Il;OXO,ll;HOCTb paBHa 22%, K03cl><l>HU:HeHT qyBCTBHTeJihHOCTH K HH,n:eKcy
cocrnsJIJieT 0,8. Orrpe.nemITh, MO)l(HO JIM norryqHT1> ap6HTpIDKHy:IO nptt61>m1> 3a cqeT
q,opMHposaHHJI ap6HTpa)l(HOro rropT<l>eJIJI . EcJIH rrpH6hIJI1> B03MO)l(Ha, To
rrepequcJIHTh ,n:elicTBHJI ap6HTpaiKepa.
PeweHHe. B 3a,naqe 5 .34 o,nHo<PaKTopttoe ypaBHeHHe APT HMeeT BH,n:
E(r;) = 15 + 7,5P;·
Ha ero OCHOBe paBHOBecHaH O)l(H,n:aeMaJI ,n:oxo,n:HocTh aKU:HH C cocTaBAAeT:
E (re) = 15 + 7, 5 · 0, 8 = 21 %.
Ap6HTpa)I( B03MO)l(eH, TaK KaK .nelicTBHTe111>HaJI o)l(HJJ:aeMaJI .D.OXO.D.HOCTh 6y:MarH C He pasHa paBHOBecHoif. Ap6HTpIDKepy c11e.nyeT ocymecTBHTh KopoTKy:IO rrpo,n;IDKy
nopTcl>eJIJI H3 amuif A H B H KyrrHTh 6onee .n;oxo.n;eyro (He,n:oou:eHeHeyro) aKu:HIO C.
3aAa'ta 5.37. CoxpaIDIIOTCJI yc110BHJ1 3a,naqH 5.36. llHsecrnp HMeeT B03MOiKHOCTh
ocymecTBHTb KOpOTKYIO rrpo,n;IDKy rropT<l>eAA, COCTOJIIUero H3 aKIJ:HH KOMIIaHHH A H
B Ha 10 TblC. py6. H Ky:IIHTb Ha HHX amim KOMIIaHHH c. Orrpe.neJIHTh BeJIHqHey
ap6HTpa)l(HOH rrpu61>um. AKu:HH MO)l(HO 3aHHMaTh 6e3 rrpou:eHTOB.
PeweHHe. Hali.n;eM y.n;. Beca aKU:HH A H B B rrpo,n;aBaeMoM rropTcpene. PHCK .n;aHHOro
rropT<l>eJIJI .D.OJiiKeH COOTBeTCTBOBaTb pHCKY aKIJ:HH c. 0TCIO,n:a rroJiyqHM rrepsoe
ypasHeHne:
BAPA + B0 P0 ='=Pc, (5.14)
r.n:e BA, B0 - y.n;. seca aKU:Hif A H BB rrpo,n:aBaeMOM rropTcpe11e;
/3 A ' /3 B' /3 c - K03cpcpmi;neHTbl qyBCTBHTeJihHOCTH amnH: K HH)J;eKcy.
CyMMa y,n:. secoB aKU:HH A H B s rropTcperre ,n;orr)l(Ha paBIDIThCJI e.n;HHHu;e:
f}A+fJB=l. (5.15)
Bb1pa3HM BA H3 paseHcTBa (5.15) n rro.n;cTaBHM B (5.14):
BAPA +(1-BA)PB =Pc- (5.16)
ll3 (5.16) norryqaeM:
() =/Jc - /ls A .
/JA - /Js (5.17)
CorrracHO (5.17) y,n. sec aKI(HH KOMrramm A B rrpo,n;asaeMOM rropTcpene paseH:
189
I'JZaBa 5. MoiJeJZu 014eHKU cmoUMocmu aKmUB06
(} = 0,8-0,4 = 0 5. A 12-04 '
' ' y .ll,. Bee aKJUIH KOMIIamrn B COCTaBIDieT:
(}8 = 1-0,5 = 0,5.
lIHsecTop 3aHHMaeT H rrpo.LJ.aeT aKU.HH A Ha 5 TI>IC. py6. H aKIJ;HH B Ha 5 TbIC. py6. H
noeyrraeT aKIJ;HH C Ha 10 TbIC. py6.
B KOHUe HHBeCTHUHOHHoro rrepHO.LJ.a no aKIJ;HH C HHBecTOp rro~aeT CYMMY:
10000 py6.(1+0,22) = 12200 py6.
3a aKU,HH A H B OH ymiaqHsaeT:
5000py6.(1+0,24)+ 5000py6.(1+0,18)= 12100py6.
H B03Bpam;aeT HX Kpe,n:HTOpy.
Ap6irrpIDKHaJI rrpH6brn1> pasHa:
12200 -12100 = 100 py6.
3a,Aa'la 5.38. Ha pnIHKe TopryroTc~ aKIJ;HH mHpoKo ,n:Haepcmpm~HpOBaHHLIX
HHBeCTHU.HOHHbIX cpoH,n:oB A, B H C. 0)l(HJJ:aeMI>Ie .LJ.OXOJJ:HOCTH aKIJ;HH cpoH,n:OB A H B COOTBeTCTBYIOT paBHOBeCHbIM H COCTaBJUIIOT 14 % H 1 7%. Km$cpHUHeHT
qyBCTBHTeJII>HOCTH aKIJ;HH AK p:r,rnoqHoMy HH,neKcy paaeH 1,1, aKU.HH B- 1,4, aKIJ;HH
c - 1,35. ,l(eiiCTBHTeilbHaJI Q)J<H.n;aeMaJI )lOXO.n;HOCTb aKJUIH <PoH,n:a c paBHa 16%. lIHBecTOp MO)J(eT 3aHHMaTb aKIJ;HH <PoH.D:OB .n:mI KopoTKOii rrpo,n:a)l(H Ha CYMMY 100 TbIC. py6. Orrpe.n:enHTb, MO)J(HO IlH IIO~HTb ap6HTpa)l(Hyro npH6bIIlb Ha OCHOBe
Mo,uenH APT H aem1qHHY rrpH6nrnH, rrepe1rncnHTb .n;eiicTB~ ap6HTpIDKepa. AKIJ;HH
MO)J(HO 3aHHMaTb 6e3 rrpou;eHTOB.
PemenHe. Ha ocHoBe ypasHeHIUI (5.12) 3anmueM ypaBHeH~ APT cooTBeTCTBeHHO JlmI
aKIJ;Hii <PoH.n;oB A H B:
14=-10 +1,lAi
17=-1u+l,4Ai.
3arrmneM CHCTeMY ypaBHemrii ( 5 .18) B Ma'IpHqHoM BH,n:e:
( 1 1,1J(AuJ=(14J· 1 1, 4 Ai 17
PeIIIWI cHcTeMy, nonyqaeM:
(AuJ (1 1,1)- l (14) ( 3) Ai - 1 1, 4 17 - 10 .
0,nHocpaKTOpHoe ypaBHeHHe Mo.n;enH APT HMeeT BH,n:
E(r;)=3+IOP;·
190
(5.18)
(5.19)
I'llaea 5. Mooe;zu 011eHKU cmoUMocmu aKmueoe
Ha octtoBe ( 5 .19) paBHOBeCHaJl O:>KH,D:aeMrui: ,n:oxo,n:HOCT.b aKQHH <Pott,n:a C paBHa:
E(r;) = 3+10·1,35=16,5%.
Ap6HTPa:>K B03MO:>KeH, TaK KaK .n:eM:cTBHTen1>HaR o:>KH,D:aeMrui: ,n:oxo~ocn 6)'Marn C He paBHa pasHoaecHoH. Ap6RTPa:>Kepy cne.n:yeT ocyw:ecTBHTb KopOTKyro rrpo.na:>KY aKQHH C, rrocKOJI.bKY otta rrepeou;eHeHa H KYIIHTb rropT<Pen1> H3 aKQHH AH B.
IIocTPOHM H3 aKQHH <PoH,D;oB A H B rropT<l>eJib P , 6ern KOToporo pasHa 6eTe aKQHH <PoH.D:a C.
BA/3A + BB/3B = f3c· (5.20)
CyMMa y.n;. aecoa a:c<IJ;IIH A H B B nopT<l>ene P .n;oJDKHa paBHRTbCH e,n:HHHQe:
BA+ OB = 1. (5.21)
Bn1pa3HM BA m paseHCTBa (5.21) 11 no.n;crnBHM B (5.20):
BA/3A +(1-BA)/3B =Pc· (5.22)
113 (5.22) rrony~meM:
BA = Pc - /3B . PA - PB
(5.23)
CornacHo (5.23) y.n;. Bee aKQHli <PoH,D;aA B nopT<flene P paaeH:
B = 1,35-1,4 =0 167. A 11-14 '
' ' y ,n:. Bee aKQHH <PoH.D:a B B IIOPT<Pene COCTaBJIHeT:
OB =1-0,167=0,833.
O:>KH.n;aeMrui: .n;oxo~ocT.b rropT<l>eJIH P pasHa:
E(rP) = 0,167·14%+0,833·17=16,5%,
T.e. paBHOBeCHOH O:>KH,IJ;aeMOH ,IJ;OXO.D:HOCTH aKD;HH <PoH.ri;a c. l'.IHsecmp 3aHHMaeT H ocyw:ecTBJIHeT KopoTKyro rrpo.n:~ aKQH:H: <PoH,D;a C Ha
100 TbIC. py6. H rroKyrraeT Ha HHX aKD;HH <PoH,D;OB AH B COOTBeTCTBeHHO Ha C)'MM.bl:
1OOmbzc.·0, 167 = 16, 7 mbzc.py6. ,
1OOmbzc.·0, 833 = 83, 3mbzc.py6.
O:>KH,n:aeMbIH .ri;oxo.ri; no rropT<flemo P cocTaBHT:
16, 7·l,14+83,3·1,17=l16,5mblC.py6.
AKaUHH <PoH.n;a C cornacHo HX .n;elicTBHTeJ11>Holi o:>K.11,n:aeMoli ,n:oxo,n:HocTH 6y.n:yT BnIKyrrneHbI 3a:
1OOmbzc.·1, 16 = 1 l 6mbzc.py6.
Ap611TPa:>K.Has rrpn6bmb paBHa:
l 16,5mbzc. - 116mbzc. = 500py6.
191
I'1iaea 5. ModeJZu OtfeHKU cmoUM.ocmu aKmueoe
3a"a11a 5.39. lhmecrop IDimrnpyer KYffiITb aKTHB A. OH rroJiaraer, 'ITO qepe3 ro.ri; no aKTHBY 6y.ri;er
BbllIJiaqeHa C)'MMa 1000 py6. Orrpe,n:e.JilfTh u;eey aKTHBa A, ecmI ero 6era ornocmeJI:bHO p:r,moqfforo mmeKca paBHa 1,5, 11 o,n:HocpaicropHIDI Mo,n:eJI:b APT HMeer BM,rr
E(r;)=3+10/J;·
PemeHue. O:>KH,ri;aeMrui: .ri;oxo,ri;HocTb aKTHBa paBHa:
E(rA) = 3+10·1,5=18%.
AKTRB ,lJ;OJI)l(eH CTOHTh:
lOOOpy5. = 847 46 6. 1+0,18 ' PY
3a"a11a 5.40. PaBHOBeCHbie m1rn,n:aeML1e .ri;oxo.r:i:HocTH aKU:HH KOMIIaHHH A, B M C
COOTBe'l'CTBeHHO COCTaBIDIIOT 18,6% M 22,8% H 19,5%. EeTbl aKIJ;HH OTHOCHTeJibHO
pbIHOqHhIX HH,lJ;eKCOB 11 H 12 paBHbI: /JAi = 0, 7 ' /JA2 = 1, 1, /JBI = 1, 1 ' fls2 = 1, 3'
flc1 = 1, 15 ' flc2 = 0, 9 .
Harr11caTh ypaBHeHHe ,n;Byx<PaKTOpHoii Mo,n;enM APT. Pemeuue. ,[(Byx<i>aKTopHIDI Mo,n;eJib APT 1rneer BH,n::
E ( 1i) = Au + A,Pil + A:z/Ji2 '
r,n:e E('i) - o:>KH,n;aeMIDI ,n:oxo,n:HOCTh i -ro aKTHBa;
(5.24)
Ao - ,ll;OXOJJ:HOCTh aKnrna npH OTCYTCTBHH B.JIIDIHIDI Ha Hero p1>rnoqHoro <t>aKTopa
(,n:oxo,n:HOCTh aKTHBa c 6eroif paBHOH HynIO );
Ai, Ai - rrpeMHH 3a p11cK .LJ:JUI HH,n:eKCOB 11 H 12 ;
/Ji!, Pi2 - K03<l><l>Hn:HeHThI qyBcTBHTerr1>HOCTH i -ro aKTRBa K HH,n:eKcaM 11 11 12 •
Ha ocHoBe ypaBHemUI (5.24) 3arrmneM ypaBHeHIDI APT cooTBeTCTBeHHO ,n:JUI a:rmHii: A, B 11 C:
18, 6 = Au + 0, 7 A, + 1, lA:z '
22, 8 = A-0 + 1, lAi + 1, 3Ai , 19,5 =Au+ l,15Ai + 0, 9A:z.
IIorryq11rrn CHCTeMY H3 TPeX ypaBHeHHH. 3anmneM ee B MaTPJlqHOM BH,n:e:
[ ~1 1,15
1, 1 1,lJ[AuJ [18,6] 1,3 A, = 22,8 . 0,9 Ai 19,5
0,7
Pemrui cwcTeMy, nonyqaeM:
192
I'Jza6a 5. MooeJlu OlfeHKU cmoUMocmu aKmueoe
[AuJ-[1 o, 7 1,1 J-
1
(1s,6J-[4,5J Ai - 1 1, 1 1, 3 22, 8 - 6 .
~ 1 1,15 0,9 19,5 9
.[(ayx<PaKTOpHoe ypaaHeHHe APT HMeeT BM):{:
E(r;)=4,5+6/Jil +9/J;z·
3aAa'la 5.41. Pa:BHOBeCHhle O)l{H,JJ;aeMMe ,JJ;oxo.z:i;HocTH a.KU:HH KOMITaHHii A, B H C
COOTBeTCTBeHHO COCTaBmnot 13,2% H 16,95% H 20,45%. EeTbI a~HH OTHOCHTeJibHO
pbIHO'llibIX HH,neKcos 11 H 12 paBHhI: jJA1 = 0, 6, /3A2 = 0, 9, /JBI = 0, 95, /382 = 1, 15,
/3c1 = 1, 25 , /3c2 = 1, 4. O:J1rn.z:i;aeM<UI .z:i;oxo.z:i;HoCTb aKl(HH KOMrraHHH D cocTaBmreT
23%, 6eTbI amHH OTHOCHTeJibHO pbIHoqHbIX irn,neKcoa 11 H 12 paBHbI: Pm= 1,3 H
/3D2 = 1, 45 . Orrpe,neJIHTb m1rn.naeM)'JO ,noxo,nHocTb aKUHH D Ha ocHoBe
,JJ;Byx<l>aKTOpHOH Mo.z:i;enH APT. Pemeuue. Ha ocHoae ypaBHeHWI ( 5 .24) 3arrmneM ypaaHeHIDI APT cooTBeTcTBeHHO .nmr
amHii A, B H C:
13,2 =Au+ 0,6Ai +0,9~' 16,95 =Au +0,95~ +1,15~' 20,45=Au+1,25~ + 1,4~.
Ilo.nyqHJIH CHCTeMY H3 rpex ypaBHeHHH. 3anmneM ee B MarpH'IHOM BH,ne:
[
1 0,6
1 0,95
1 1,25
0,9J[AuJ ( 13,2 J 1,15 A, ~ 16,95 .
1,4 ~ · 20,45
0,6
0,95
1,25 J-1 ( J ( J
0,9 13,2 3 1,15 16,95 = 5 .
1,4 20,45 8
.[(ayx<PaKTopHoe ypaBHeHHe APT HMeeT BH,n:
E ( 1i) = 3 + 5 /Ji! + 8 /J;2 •
PaBHOBecHaji mKH):{aeM<UI ,noxo.z:i;HOCTb aKTHBa D paaHa:
E(rn) = 3+ 5·1,3+ 8 ·1,45 = 21,1%.
193
I'llaBa 5. Mooe;zu oi,emcu cmoUMocmu aKmu6o6
3a"a11a 5.42. 1
PaBHOBeCHI>Ie O)J{R,D;aeMble .n;oxo.n;HOCTH aKUHH HHBeCTHU:HOHHl>IX <PoH,n;oB A, B H
c COOTBeTCTBeHHO COCTaBJUHOT 21,8%, 26,46% H 27,4%. EeTl>I aKUHH OTHOCHTeJibHO
p1>rnoqHl>IX HH,D;eKCOB 11 H 12 paBHl>I: PAi =0,8, PAz =1,12, PBI =1,18, p02 =l,32,
Pei = 1, 2 • Pc2 = 1, 4 · ,[.I;elicTBHTeJihHaJI O)J{R,D;aeMaJI .uoxo.UHOCTI> aKUHH 1rnBeCTHU:HOHHoro <J?oH.[la D
COCTaBIDleT 25%, 6eTbl aKn;HH OTHOCHTeJibHO pI>moqHbIX HH,n;eKCOB II H 12 paBHbI:
Pm = 1, 1 H PD2 = 1, 35. Orrpe.n;eJIHTI>, MO)J{HO JIH IIO.rrytIIITb ap6HrpaJKHY10 rrpH6I>mh
Ha ocHoBe MO.lleJIH APT H MaKCHMaJibH)'IO BeJIHqHey rrpH6bmH, rrepeqHCJIHTI>
.n;e:H:CTBIDI ap6Hrpa)J{epa. ,[.I;IDI KOpOTKOH rrpo.n;a)J{H ap6Hrpa)J{ep MO)J{eT 3aHJrMaTb
aKI.l;HH Ka)J{.llOro <PoH.n;a Ha 100 Tl>IC. py6. IlopT<i>eJIH HHBeCTHU:HOHHblX cPOH,D;OB
nrnpOKO .llHBepCHcPHU:HPOBaHI>I, II03TOM)' rrpe.n;rronaraeTCH, ~o He pbIH0111IbIH pHCK
oTcyTCTByeT. AKn:HH MO:>KHO 3aHHMaTI> 6e3 npon;eHToB.
PeweHHe. Ha ocHose ypaBHeHIDI (5.24) 3a1rnmeM ypaBHeHIDI APT cooTBeTCTBeHHO .llIDI
aKUHH A, B H C:
21, 8 = ~ + 0, 8Ai + 1, 12Ai '
26,46 = ~ + l,18Ai + l,32Ai'
27,4 = ~ + l,2Ai + l,4Ai.
IlO.rrytIHJIH CHCTeM)' H3 Tpex ypaBHeHHH. 3arrHmeM ee B MaTpHqffOM BR,D;e:
( 1~ PemaJI CHCTeM)r, rrorryqaeM:
0,8
1,18 1,12](~] ( 21,8 J 1,32 Ai = 26,46 .
1,4 Ai 27,4 1,2
0,8
1, 18
1,2 J-1 ( J [ J
1,12 21,8 5
1,32 26,46 = . 7 .
1,4 27,4 10
,lJ;Byxcl>aKTopHoe ypaBHeHHe APT HMeeT BH.ll:
E(r;)=5+7Pn +10pi2.
CorrracHo ypaBHeHHro APT paBHOBeCHaJI O)J{H.UaeMaJI .uoxo.uHoCTb aKTHBa D pasHa:
E(rn) = 5+7·1,1+10·1,35 = 26,2%.
IIocKOJibKY .ue:HcTBHTeJibHaJI O:>KR,D;aeMaH .llOXOJlHOCTb aKTHBa D cocTaBIDleT 25%, TO
ap6HTpa:>K B03MO:>KeH.
1 3a,qaya Om1Mnl4a.Qbt no pbtHKY 4eHHb1x 6yMar l4 npot.13BO.QHblX cpt.1HaHcOBblX l4HCTpyMeHTOB. Onl4Mnl4a.Qa npowna B Mn.1MO(Y) Mlt1A P¢ Ha Kacpe,Qpe ¢oH.QOBoro pbtHKa 18.05.06. OpraHl43aropbt Onl4Mnl4a,Qbt: Kacpe,Qpa ¢OHAOBoro pbtHKa Mrl-1MO, ¢OHAOBaR 6t.1plKa PTC l4 Ha~Ho-TeXHl449CKoe 0611\ecreo l4M. aKa.Q. CJ.1.BaBl4IlOBa. V1HcpopMa4l40HHyio nop,qeplKKY om'IMnl4a.Qbl OCYIJ.lSCTBilRn lKYPHan BanlOTHbtVI cneKYnRHT.
194
I'!ia6a 5. MooeJ1u 014eHKU cmoUMocmu aKmueoe
CocTaBJIM Jl3 aKIJ;nii A, B JI C rropT<iJeJI1> P, 6en1. KOToporo oTHOCJ1TeJI1>HO
HH,n;eKCOB 11 II 12 paBH1>1 6eraM aKTJIBa D. Y,n;. Beca aKTJIBOB B rropT<iJene Haii.n;eM H3
cne,rzyromeli CJICTeMbl ypaBHeHJIH:
eA +eB +ec =1
0,8BA +l,18t9B +l,2Bc =1,1
l,12BA +l,32BB +l,4Bc =1,35.
3airnmeM no.rryqemzyIO CHCTeMY ypaBHeHHH B MarpHqHQM BH,n;e:
( o'.8 1,~8 1\j(i.J=(1'.1J. 1,12 1,32 1,4 Be 1,35
Pemrui: cHcTeMy, rronyqaeM:
1
1,18
1,32
1 J-I ( 1 J ( 0, 265 J 1,2 1,1 = -0,303 .
1,4 1,35 1,038
lhrnecTop 3aHHMaeT H ocymecTBIDieT KopoTKyro npo.zi;aJKY aKUHH <PoH,n;a B Ha 100 r1>1c. py6. JI aKIJ;JIH ¢oH,n;a D Ha 100 T1>1c. py6. lfa rronyqeHHhIX 200 Thie. py6. HHBecTop noKynaeT aKIJ;HH ¢oH.ri;OB A H C. Ilporrop:u;WI aK:QHli A B ,n;aHHo:H: C)'MMe paBHa:
0,265 = 0 203 0, 265 + 1, 03 8 ' '
aKIJ;Hli C:
1,038 =0 797. 1 303 ' . '
HHBecmp rroeyrraeT aKIJ;HH A Ha CYMMY
200000. 0, 203 = 40600 py6. '
200000. 0, 797 = 159400 py6.
1Iepe3 ro,n; ,n;oxo,n; no noPT<Pemo P ,n;oJDKeH coCTaBHT1>:
40600·1, 218+159400·1, 274-100000·1, 2646=126066,4py6.
Ilo BDIKyny aK:QHH D HHBecTop HeceT pacxo,n;1>1 B cyMMe:
100000 · l, 25=125000 py6.
Ap611rpa)l(HblH .n;oxo.n; cocTaBIDieT:
126066, 4-125000=1066, 4 py6.
195