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# !/usr/bin/python
# -*- encoding: utf-8 -*-
"""
Codes for Kinyu HW
URL: https://github.com/myuuuuun/various/kinyu
"""
%matplotlib inline
from __future__ import division, print_function
import math
from random import uniform, normalvariate, shuffle
import numpy as np
import matplotlib.pyplot as plt
np.set_printoptions(threshold=np.nan)
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def average(probability, asset):
return np.sum(probability * asset)
def variance(probability, asset):
ave = average(probability, asset)
return np.sum(probability * pow(asset - ave, 2))
def std(probability, asset):
return np.sqrt(variance(probability, asset))
# 資産A, B, Cがあり、状態1〜5がある
# [state1, state2, ..., state5]
probability = np.array([0.2, 0.5, 0.1, 0.15, 0.05])
assetA = np.array([2.56, 1.79, 1.02, 0.26, 0.00])
assetB = np.array([4.73, 1.18, 0.47, 0.47, 0.00])
assetC = np.array([0.00, 0.22, 1.10, 4.39, 0.00])
# 問題2(1) 資産A〜Cの平均と標準偏差
def pro2_1():
print("Average of assetA: " + str( average(probability, assetA) ))
print("Average of assetB: " + str( average(probability, assetB) ))
print("Average of assetC: " + str( average(probability, assetC) ))
print("SD of assetA: " + str( std(probability, assetA) ))
print("SD of assetB: " + str( std(probability, assetB) ))
print("SD of assetC: " + str( std(probability, assetC) ))
pro2_1()
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# 問題2(2) 資産A, Bの組み合わせで達成可能なポートフォリオを図示（横軸標準偏差、縦軸平均）
# p*assetA + (1-p)*assetB とする(0<=p<=1)
def pro2_2():
aves = []
stds = []
for p in np.linspace(0, 1, 21):
portfolio = p * assetA + (1-p) * assetB
aves.append(average(probability, portfolio))
stds.append(std(probability, portfolio))
print(aves)
print(stds)
fig, ax = plt.subplots(figsize=(10, 8))
plt.title("oppotunity curve of portfolio of asset A & B")
plt.xlabel("sigma: standard deviation")
plt.ylabel("mu: average")
plt.plot(stds, aves, color='b', linewidth=2, label='p*assetA + (1-p)*assetB (0<=p<=1)')
plt.legend()
ax.set_ylim(0.8, 2.0)
ax.set_xlim(0.3, 2.0)
plt.text(1.57, 1.64, '(1.58, 1.65)\n(p=0. only assetB)', ha = 'left', va = 'top')
plt.text(0.79, 1.55, '(0.79, 1.55)\n(p=1. only assetA)', ha = 'right', va = 'bottom')
plt.show()
pro2_2()
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# 問題2(3) 資産A, Bの組み合わせで達成可能なポートフォリオを図示（横軸標準偏差、縦軸平均）
# p*assetA + q*assetB + (1-p-q)*assetC とする(0<=p, q<=p+q<=1)
def pro2_3():
fig, ax = plt.subplots(figsize=(10, 8))
plt.title("oppotunity curve of portfolio of asset A & B & C")
plt.xlabel("sigma: standard deviation")
plt.ylabel("mu: average")
# p=(一定)の時のAとBとCの組み合わせで書ける曲線
plt.plot(0, 0, color='c', label='p*A + q*B + (1-p-q)*C (p=const)')
for p in np.arange(0, 1.01, 0.02):
aves = []
stds = []
for q in np.arange(0, 1.01-p, 0.02):
portfolio = p * assetA + q * assetB + (1-p-q) * assetC
aves.append(average(probability, portfolio))
stds.append(std(probability, portfolio))
if p == 0:
plt.plot(stds, aves, color='r', linewidth=2, label='q*B + (1-q)*C (p=0)')
else:
plt.plot(stds, aves, color='#88ffff')
#print(aves)
#print(stds)
# q=0の時のAとCの組み合わせで書ける曲線
aves = []
stds = []
q = 0
for p in np.arange(0, 1.02, 0.02):
portfolio = p * assetA + q * assetB + (1-p-q) * assetC
aves.append(average(probability, portfolio))
stds.append(std(probability, portfolio))
plt.plot(stds, aves, color='g', linewidth=2, label='p*A + (1-q)*C (q=0)')
# p+q=1の時のAとBの組み合わせで書ける曲線
aves = []
stds = []
for p in np.arange(0, 1.02, 0.02):
q = 1 - p
portfolio = p * assetA + q * assetB + (1-p-q) * assetC
aves.append(average(probability, portfolio))
stds.append(std(probability, portfolio))
plt.plot(stds, aves, color='b', linewidth=2, label='p*A + q*B (p+q=1)')
plt.legend()
ax.set_ylim(0.8, 2.0)
ax.set_xlim(0.3, 2.0)
plt.text(0.79, 1.56, '(0.79, 1.55)\n(p=1, q=0. only assetA)', ha = 'right', va = 'bottom')
plt.text(1.57, 1.64, '(1.58, 1.65)\n(p=0, q=1. only assetB)', ha = 'left', va = 'top')
plt.text(1.50, 0.88, '(1.50, 0.88)\n(p, q=0. only assetC)', ha = 'left', va = 'bottom')
plt.show()
pro2_3()
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