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Exam (elaborations)

Klausuraufgaben und Lösungen

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Verschiedene Aufgaben von Altklausuren zusammengestellt

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  • July 21, 2023
  • 3
  • 2022/2023
  • Exam (elaborations)
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Aufgabe 2
a) Ermitteln Sie den theoretischen Kurswert der Anleihe. RLZ = 6 Jahre, zu pari, Kupon 3,25%
risikoloser Zinssatz 2%.


I i +5 1
3,25
po =
+


1023+
+ +

107
=




b) welchen Kurswert hätte die hier betrachtete Anleihe bei einem
b1) Kapitalmarktzins von 0,00%
b2) Kapitalmarktzins von 3,25%

5,25
31253125 3,25 3,25 103125
Be Po =

+
1102
t
1103
t
1104
t
1105
t
100 119,5
=




3,25 3,25 3,25 103,25
b2 40 1+1,03252 1,03253
= +
I
1103254 153255 1,03256 100
+ +
=




c) Bestimmen Sie die laufende Rendite deren Abweichung von der Effektivverzinsung. Worin
liegt der Grund für diese Abweichung?

Laufende Rendite:
p I25 =
=
3,04%
Rückz. KUTS -
Ankaufk.
inomt
Effektivverzinslig:y
I
=



Ankalifkurs


3,25
100 6 107
+
-




y 1,9470%
=
=




107



Probe:Po
=




1 +nzz+niges nongt ringst sie
=107,31 1074 kleine Abweichling
ungenal
1194% etwas zu niedrig
=




d) Bestimmen Sie die modifizierte Duration der betrachteten Anleihe

Diod (H = -



=17. Macaulay-Dur.
Macaulay-Dut.:
1325+42 3825+++6 +




D 5,565 Jahre
=
=
107


Dmod 1102:5,565
=



5,456
=




e) Welche Restlaufzeit muss ein Zerobond haben, der dieselbe modifizierte Duration wie die
betrachtete Anleihe aufweist?
D RLZ
=




5,456 102.D
=




1:oz
5,565 D
=

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