Solucion de problemas de cálculo de bonos (libro: capital markets de fabozzi y modigliani)
Página 1 de 13
Valor Nominal =
1 2
BONO X 1,000.00
3 4
Valor Nominal =
1 2
BONO Y 1,000.00
34
Valor Nominal =
1 2
BONO Z 1,000.00
3 4
N Años 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
C Cupon Anual 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00%
Tasa de Precio de N C Interés Bonos Años Cupon (TIR) Estimados Anual 1.00% 1,599.62 11 10.00% 5.00% 1,213.23 11 10.00% 9.00% 940.05 11 10.00% 13.00% 743.42 1110.00% 17.00% 599.45 11 10.00% 21.00% 492.29 11 10.00% 25.00% 411.27 11 10.00% 29.00% 349.06 11 10.00% 33.00% 300.60 11 10.00% 37.00% 262.32 11 10.00% 41.00% 231.66 11 10.00% 45.00% 206.80 11 10.00% 49.00% 186.38 11 10.00% 53.00% 169.42 11 10.00% 57.00% 155.18 11 10.00% 61.00% 143.10 11 10.00% 65.00% 132.75 11 10.00% 69.00% 123.80 11 10.00% 73.00% 116.00 11 10.00% 77.00% 109.15 11 10.00%
Tasade Precio de N C Interés Bonos Años Cupon (TIR) Estimados Anual 1.00% 1,933.09 12 11.00% 5.00% 1,415.32 12 11.00% 9.00% 1,068.05 12 11.00% 13.00% 829.39 12 11.00% 17.00% 661.45 12 11.00% 21.00% 540.54 12 11.00% 25.00% 451.54 12 11.00% 29.00% 384.63 12 11.00% 33.00% 333.29 12 11.00% 37.00% 293.14 12 11.00% 41.00% 261.17 12 11.00% 45.00% 235.28 12 11.00% 49.00% 213.99 12 11.00% 53.00% 196.22 1211.00% 57.00% 181.21 12 11.00% 61.00% 168.37 12 11.00% 65.00% 157.27 12 11.00% 69.00% 147.59 12 11.00% 73.00% 139.06 12 11.00% 77.00% 131.50 12 11.00%
Tasa de Precio de Interés Bonos (TIR) Estimados 1.00% 2,125.51 5.00% 1,531.80 9.00% 1,143.21 13.00% 881.65 17.00% 700.70 21.00% 572.16 25.00% 478.48 29.00% 408.54 33.00% 355.09 37.00% 313.37 41.00% 280.14 45.00% 253.19 49.00% 230.97 53.00% 212.3657.00% 196.58 61.00% 183.03 65.00% 171.27 69.00% 160.97 73.00% 151.87 77.00% 143.76
2,500.00
`´
2,000.00
1,500.00
1,000.00
BONO X BONO Y BONO Z
500.00
0.00
13.00% 17.00% 21.00% 25.00% 29.00% 33.00% 37.00% 41.00% 45.00% 49.00% 53.00% 57.00% 61.00% 65.00% 69.00% 73.00% 77.00% 1.00% 5.00% 9.00%
NOTA: Graficamente considerarìa que el Bono Z es más volátil.
Página 2 de 13BONO X
0 1
PRINCIPAL
2 3
100
4 5 6 7 8
r 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% SUMA Precio del Bono
t 1 2 3 4 5 6 7 8 9
CF 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 108.00
t x CF 8.00 16.00 24.00 32.00 40.00 48.00 56.00 64.00 972.00
1/(1+r)t 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 Precio del Bono
(2*4) 7.69 7.407.11 6.84 6.58 6.32 6.08 5.85 75.88 129.7413
(3*4) 7.69 14.79 21.34 27.35 32.88 37.94 42.56 46.76 682.91 914.22
t*(1+ t)*CF 16.00 48.00 96.00 160.00 240.00 336.00 448.00 576.00 9,720.00
4*7 15.38 44.38 85.34 136.77 197.26 265.55 340.44 420.88 6,829.14 8,335.15
=
129.741
multiplico x (-1)
dP / dR
=
-914.22 1.04
multiplico x (-1)
=
-879.06
Duración McD (años)
=879.06 129.741
x
1.04
=
7.05
Anual
Duración Modificada ò tambien
=
-1.00 129.741 Duración McD
x
-879.06
=
6.78
=
/
1.04
=
6.78
d2P / dR2
=
1.04
8,335.15 ^
2
elevado al cuadrado
=
7,706.31
Convexidad (años)
=
129.74
7,706.31 x
2
=
29.70
Anual
Página 3 de 13
BONO Y
0 1
PRINCIPAL
2 3
1004 5 6 7 8
r 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% 4.0000% SUMA Precio del Bono
t 1 2 3 4 5 6 7 8 9 10 11
CF 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 110.00
t x CF 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 1,210.00
1/(1+r)t 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496...
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