4.13

(2004-5-23)

With Python

code

Pythonで解くcode を下に示す。
discount factor は、年複利とした。
連立方程式は、numpy.linalg.solve()で解いた。

# 4.13.py
# created on 2016-12-09

import numpy
import matplotlib.pyplot as plt

# input
s_percent = numpy.array([7.67, 8.27, 8.81, 9.31, 9.75, 10.16, 10.52, 10.85])
x = numpy.array([ 500,  900,  600,  500,  100,   100,   100,    50])
t = numpy.arange(len(x)) + 1
p1 =  65.95
d1 =   7.07
p2 = 101.66
d2 =   3.80

# calculate
s  = s_percent / 100 # in decimal form
st = s * t
df  = 1/(1+s)**t
df2 = 1/(1+s)**(t+1)
dx = df * x
pv = sum(dx)
txd = t * x * df2
sumtxd = sum(txd)
duration = sumtxd / pv

a = numpy.array([[p1,             p2], \
                 [p1*d1,       p2*d2]])
b = numpy.array( [pv,    pv*duration] )
x1, x2 = numpy.linalg.solve(a, b)

# output
print('4.13.py')
fmt1='{:>10}{:>10}{:>10}{:>10}{:>10}{:>10}'
fmt2='{:10}{:10.4f}{:10.3f}{:10.0f}{:10.2f}{:10.2f}'
print(fmt1.format('t', 's', 'd', 'x', 'x*d', '-PV\''))
print(60 * '-')
for i in range(len(s)):
  print(fmt2.format(t[i], s[i], df[i], x[i], dx[i], txd[i]))
print(60 * '-')
print('{:40}{:3}{:7.2f}{:10.2f}'.format('','PV=', pv, sumtxd))
print(60 * '-')
print('{:50}{:>5}{:5.2f}'.format('', 'D=', duration))
print()
print('P1 x1    + P2 x2    = PV')
print('P1 D1 x1 + P2 D2 x2 = PV D')
print('-> x1 = {:.2f}, x2 = {:.2f}'.format(x1, x2))

# plot
x  = numpy.array([-30, 40])
y1 = (pv - p1 * x ) / p2
y2 = (pv * duration - p1 * d1 * x) / p2 / d2

plt.plot(x, y1, label='P1x1+P2x2=PV')
plt.plot(x, y2, label='P1D1x1+P2D2x2=PV*D')
w  = 1.5
hw = 7
fc = 'black'
plt.annotate('(-14.04, 31.13)', xy = (x1, x2), xytext = (-15, 5), \
             arrowprops=dict(width=w, headwidth=hw, facecolor=fc, shrink=0.05))
plt.title('Fig. 4.13.py')
plt.xlabel('x1')
plt.ylabel('x2')
plt.legend()
plt.grid()
plt.show()
# end of code

output

4.13.py
         t         s         d         x       x*d      -PV'
------------------------------------------------------------
         1    0.0767     0.929       500    464.38    431.30
         2    0.0827     0.853       900    767.76   1418.23
         3    0.0881     0.776       600    465.74   1284.10
         4    0.0931     0.700       500    350.21   1281.54
         5    0.0975     0.628       100     62.80    286.12
         6    0.1016     0.560       100     55.96    304.78
         7    0.1052     0.496       100     49.65    314.46
         8    0.1085     0.439        50     21.93    158.28
------------------------------------------------------------
                                        PV=2238.44   5478.81
------------------------------------------------------------
                                                     D= 2.45

P1 x1    + P2 x2    = PV
P1 D1 x1 + P2 D2 x2 = PV D
-> x1 = -14.04, x2 = 31.13

graph

上のcodeで書いた図を下に示す。

Hand calculation

価格P₁=65.95、デュレーションD₁=7.07、 単位数x₁
価格P₂=101.66、デュレーションD₂=3.80、 単位数x₂
上記は、次の連立方程式を満たす。
P₁x₁+P₂x₂=PV
P₁D₁x₁+P₂D₂x₂ =PV*D
∴ x₁=-14.14、x₂=31.23

上記の連立方程式のグラフをFig. 4.13に示す。(2005-2-15)

図化コマンドを次のリンクに示す。(2011-10-26)

• Fig.4.13

Julia

Juliaのコードを次のリンクに示す。

2023-05-03 4.13.jl

JavaScript

2024-11-02 4.13.js

Fortran

2024-11-02 4.13.f90

history

2004-05-23 create.
2005-02-15 revise.
2011-10-26 revise.
2016-12-10 add a Python code.
2021-02-17 change XHTML to html5, change shift-jis to utf-8, add viewport.
2023-05-03 add a Julia code.
2024-11-02 add a JavaScript code and a Fortran code.