Merenje performansi portolia - ekof.bg.ac.rs · Šarpov indeks S p=(R p-R f)/σ p •R p-prosečna...
Transcript of Merenje performansi portolia - ekof.bg.ac.rs · Šarpov indeks S p=(R p-R f)/σ p •R p-prosečna...
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Merenje performansi portolia
Ekonomski fakultet Univerziteta u Beogradu
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Definisanje i izražavanje rizika
• Standardna devijacija• Beta koeficijent
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Grafik rizik/prinos
Grafik rizik/prinos
A, 21%
B, 22%
C, 23%
D, 24%
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00%
rizik
prin
os
A
B
C
D
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Metodi merenja rizikuprilagođenih performansi
• Šarpov indeks• Trejnorov indeks• Jensenov indeks• Modiljani-kvadrat• Trejnor-kvadrat• Informacioni racio
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Šarpov indeks
Sp=(Rp-Rf)/σp
• Rp- prosečna stopa prinosa portfolia
• Rf- stopa prinosa na bezrizičnu aktivu
• σ p- standardna devijacija prinosa portfolia• Šarpov indeks jeste odnos između riziko premije i
standardne devijacije prinosa portfolia.
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Šarpov indeks
standardna devijaciija
stop
a pr
inos
a
RfRp
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Utvrđivanje i prikazivanjeŠarpovog indeksa
• Stopa prinosa tržišnog portfolia 14%• Stopa prinosa na bezrizičnu aktivu 8%• Standardna devijacija stope prinosa tržišnog portfolia
20%
Portfolio Stopaprinosa
σ
D 13% 0.18E 17% 0.22F 16% 0.23
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• SIt=(0.14-0.08)/0.20=0.3• SId=(0.13-0.08)/0.18=0.278• SIe=(0.17-0.08)/0.22=0.409• SIf=(0.16-0.08)/0.23=0.348
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Pozicioniranost portfolia u odnosuna CML liniju
CML
StSd
SeSf
00.020.040.060.080.1
0.120.140.160.18
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
standardna devijacija
stop
a pr
inos
a
StSdSeSf
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Trejnorov indeks
TIp=(Rp-Rf)/βp
• Rp- prosečna stopa prinosa portfolia
• Rf- stopa prinosa na bezrizičnu aktivu
• βp- beta koeficijent portfolia• Trejnorov indeks predstavlja odnos između riziko premije i
beta koeficijenta.
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Trejnorov indeks
vrednost beta koeficijenta
stop
a pr
inos
a po
rtfol
ia
RfRp
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Primer: Utvrđivanje Trejnorovog indeksa
• Stopa prinosa tržišnog portfolia 14%• Stopa prinosa na bezrizičnu aktivu 8%
Portfolio Stopaprinosa
βkoeficijent
A 12% 0.90B 16% 1.05C 18% 1.20
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• TIt=(0.14-0.08)/1.00=0.060• TIa=(0.12-0.08)/0.90=0.044• TIb=(0.16-0.08)/1.05=0.076• TIc=(0.18-0.08)/1.20=0.083
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Pozicioniranost portfolia u odnosu naSML liniju
SML
TtTa
TbTc
0
0.04
0.08
0.12
0.16
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
beta koeficijent
stop
a pr
inos
a
TtTaTbTc
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Jensenov indeks
αp=Rp-(Rf+βp[Rm-Rf])
• Rp- prosečna stopa prinosa portfolia P• Rf- stopa prinosa na bezrizičnu aktivu• βp- sistematski rizik• Rm- prosečan prinos tržišnog portfolia
• Apsolutni pokazatelj performansi portfolia investicionih fondova• Zasniva se na CAPM i SML
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Prikaz Jensenovog modela merenjaperformansi
riziko premija trzišnog portfolia
rizik
o pr
emija
por
tfolia
p
α=0
α<0
α>0
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Grafički prikaz Jensenovog indeksa
beta portfolia
pros
ečan
prin
os p
ortfo
lia
ABC
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M2 mera performansi
• Posebna verzija Šarpovog pokazatelja• U portfolio P se dodaju zapisi trezora tako da
“korigovani” portfolio ima istu volatilnost kao i tržišni indeks
M2=Rp*-Rt• Rp*- stopa prinosa korigovanog portfolia P
• Rt- stopa prinosa tržišnog portfolia
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Grafički prikaz M2 mere
M kvadrat
8
15
8
17
20
0
5
10
15
20
25
0 10 20 30 40 50
standardna devijacija
stop
a pr
inos
a
CML
portfolio P
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T2 mera performansi
• Posebna verzija Trejnorovog indeksa• Formira se portfolio P* tako da beta
koeficijent dobijenog portfolia bude 1
T2=Rp*-Rt=Rp/βp-Rt
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Grafički prikaz Trejnor-kvadrat mere
Trejnor kvadrat
10
13
16.25
0
2
4
6
8
10
12
14
16
18
0 0.5 1 1.5 2
beta koeficijent
doda
tni p
rinos
SML
P
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Informacioni racio
e
jIRσα
=
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Kritike modela merenja performansiportfolia
• Trejnor i Jensen posmatraju samosistematski rizik i koriste SML
• Šarp koristi ukupan rizik polazeći od CML
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• Šarpov indeks se zasniva na pretpostavcida je CML prava linija
• Rol tvrdi da Jensenov i Trejnorov indekszavise od položaja tržišnog portfolia u odnosu na efikasni set
• Rol smatra da nije moguće naći pravi tržišniportfolio