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166 | from datetime import date
from math import exp, log
# Program by Jim Shapiro, Ph.D.
# 2021-07-29
# Boulder, CO 80301-5013
#
# If you copy this file, please include this header. If you modify the code, please
# note the modifications.
Iterations, Epsilon = 20, 1.0e-5
# Requires amounts and times already converted from dates
class Transactions:
def __init__(self):
self.amounts, self.times = [], []
def add(self, amount, time):
self.amounts.append(amount)
self.times.append(time)
# Requires amounts and dates. Dates then get converted to times, i.e. days
class Date_Transactions:
def __init__(self):
self.amounts, self.times, self.the_dates = [], [], []
def add_amount_and_date(self, amount, a_date):
self.amounts.append(amount)
self.the_dates.append(a_date)
# dates_2_times requires a second parameter, the separator in the dates.
def dates_2_times(self, sep):
ds = []
for a_date in self.the_dates:
y, m, d =[int(x) for x in a_date.split(sep)]
ds.append(date(y, m, d))
for a_date in ds:
# Note that self.times[0] is always 0. We calculate it
# anyway for no good reason.
self.times.append((a_date - ds[0]).days / 365.25)
# print('{0:.2f}'.format(self.times[-1]))
# Uses a Date_Transactions class which needs conversion to times
# irrcc requires a second parameter, the separator in the dates.
def irrcc(date_transactions, sep):
global Iterations, Epsilon
have_pos, have_neg = False, False
# Dates haved been entered. Convert to times, i.e., days after
# first date.
date_transactions.dates_2_times(sep)
for amount in date_transactions.amounts:
if amount > 0.0:
have_pos = True
if have_neg:
break
elif amount < 0.0:
have_neg = True
if have_pos:
break
if have_neg and have_pos:
u, converged = 0.0, False
for i in range(Iterations):
pos, d_pos, neg, d_neg = 0.0, 0.0, 0.0, 0.0
# dd_pos, dd_neg = 0.0, 0.0
# print(i)
for j in range(len(date_transactions.amounts)):
an_amount, a_time = date_transactions.amounts[j], date_transactions.times[j]
tmp = an_amount * exp(u * a_time)
if an_amount > 0.0:
pos += tmp
d_pos += tmp * a_time
# dd_pos += tmp * a_time * a_time
else:
neg -= tmp;
d_neg -= tmp * a_time
# dd_neg -= tmp * a_time * a_time
# Haley's 2nd order Newton's method
f = log(neg / pos)
fp = (d_neg / neg) - (d_pos / pos)
# tmp = (neg * dd_neg - d_neg * d_neg) / neg / neg
# fpp = tmp - ((pos * dd_pos - d_pos * d_pos) / pos /pos)
# h_inv = -fp / f + fpp / (2 * fp)
# delta = -1 / h_inv
# First order Newton's method
# delta = log(neg / pos) / (d_neg / neg - d_pos / pos)
delta = f / fp
u -= delta
if abs(delta) < Epsilon:
converged = True
break
if converged:
result = -u
else:
result = 'No convergence'
else:
result = 'Bad Data!'
return result
# Uses a Transactions class which already has times
def jns_irr(transactions):
global Iterations, Epsilon
have_pos, have_neg = False, False
for amount in transactions.amounts:
if amount > 0.0:
have_pos = True
if have_neg:
break
elif amount < 0.0:
have_neg = True
if have_pos:
break
if have_neg and have_pos:
u, converged = 0.0, False
for i in range(Iterations):
pos, d_pos, neg, d_neg = 0.0, 0.0, 0.0, 0.0
# print(i)
for j in range(len(transactions.amounts)):
an_amount, a_time = transactions.amounts[j], transactions.times[j]
tmp = an_amount * exp(u * a_time)
if an_amount > 0.0:
pos += tmp
d_pos += tmp * a_time
else:
neg -= tmp;
d_neg -= tmp * a_time
delta = log(neg / pos) / (d_neg / neg - d_pos / pos)
u -= delta
if abs(delta) < Epsilon:
converged = True
break
if converged:
result = -u
else:
result = 'No convergence'
else:
result = 'Bad Data!'
return result
if __name__ == "__main__":
amounts = [-1000.00, 500.00, -2000.00, -2000.00, 1500.00, 4000.00]
dates = ['2016-03-16', '2017-09-26', '2018-01-15', '2020-04-05', '2019-05-1', '2021-01-01']
dts = Date_Transactions()
for i in range(len(amounts)):
dts.add_amount_and_date(amounts[i], dates[i])
# irrcc requires a second parameter, the separator in the dates.
irr = irrcc(dts, '-')
print('The internal rate of return with continuous compounding is {0:.2f}%.'.format(100 * irr))
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