def bond_convexity(price, par, T, coup, freq, dy=0.01):
ytm = bond_ytm(price, par, T, coup, freq)
ytm_minus = ytm - dy
price_minus = bond_price(par, T, ytm_minus, coup, freq)
ytm_plus = ytm + dy
price_plus = bond_price(par, T, ytm_plus, coup, freq)
convexity = (price_minus + price_plus - 2 * price) / (price * dy**2)
return convexity
def bond_mod_duration(price, par, T, coup, freq, dy=0.01):
ytm = bond_ytm(price, par, T, coup, freq)
ytm_minus = ytm - dy
price_minus = bond_price(par, T, ytm_minus, coup, freq)
ytm_plus = ytm + dy
price_plus = bond_price(par, T, ytm_plus, coup, freq)
mduration = (price_minus-price_plus)/(2.*price*dy)
return mduration
def bond_mod_duration(price, par, T, coup, freq, dy=0.01):
ytm = bond_ytm(price, par, T, coup, freq)
ytm_minus = ytm - dy
price_minus = bond_price(par, T, ytm_minus, coup, freq)
ytm_plus = ytm + dy
price_plus = bond_price(par, T, ytm_plus, coup, freq)
mduration = (price_minus - price_plus) / (2. * price * dy)
return mduration
def bond_convexity(price, par, T, coup, freq, dy=0.01):
ytm = bond_ytm(price, par, T, coup, freq)
ytm_minus = ytm - dy
price_minus = bond_price(par, T, ytm_minus, coup, freq)
ytm_plus = ytm + dy
price_plus = bond_price(par, T, ytm_plus, coup, freq)
convexity = (price_minus+price_plus-2*price)/(price*dy**2)
return convexity
def bond_mod_duration(price, par, T, coup, freq, dy=0.01):
ytm = bond_ytm(price, par, T, coup, freq)
ytm_minus = ytm - dy
price_minus = bond_price(par, T, ytm_minus, coup, freq)
ytm_plus = ytm + dy
price_plus = bond_price(par, T, ytm_plus, coup, freq)
# calculate the difference in price when bond moves up and down
# for a given change in yield
mduration = (price_minus - price_plus) / (2. * price * dy)
return mduration
def bond_convexity(price, par, T, coup, freq, dy=0.01):
"""
Measures the change in duration due to a change in yield
a convexity of 300 means a 1% change in yield will lead to a 3% (0.03) change in price resulting from convexity
"""
ytm = bond_ytm(price, par, T, coup, freq)
ytm_minus = ytm - dy
price_minus = bond_price(par, T, ytm_minus, coup, freq)
ytm_plus = ytm + dy
price_plus = bond_price(par, T, ytm_plus, coup, freq)
convexity = (price_minus+price_plus-2*price)/(price*dy**2)
return convexity
p0 = 100.0
## the actual principal, the initial investment in dollars
invest = 1e2
## time to maturity of each note/bond you want to calculate
t10 = 10
t7 = 7
texp = 10
## daily rebalance?
## initialize arrays for all desired note/bond prices
price10 = np.zeros((len(bond_yield)))
price7 = np.zeros((len(bond_yield)))
for i in range(len(bond_yield)):
price7[i] = bond_price(r=r, y=bond_yield.y7[i] / 100, n=t7, p0=p0)
price10[i] = bond_price(r=r, y=bond_yield.y10[i] / 100, n=t10, p0=p0)
## add the price to the dataframe
price7_df = pd.DataFrame(price7, index=bond_yield.index)
price10_df = pd.DataFrame(price10, index=bond_yield.index)
bond_yield.insert(2, "price7", price7_df)
bond_yield.insert(3, "price10", price10_df)
## okay, now ready to do backtesting with the following strategy:
## we start rolling from the date:
#prev_year='1981'
date_array = pd.date_range('1/2/1981', '1/2/2019', freq='BAS-oct')
## divide our initial investment into 3 ten year notes, starting with 1981,
# -*- coding: utf-8 -*-
"""
Created on Sun Aug 25 22:22:04 2019
yield_plotter.py
This script plots bond price as a function of yield
@author: jeffreywalker
"""
import numpy as np
from bond_price import bond_price
y = np.linspace(-0.1, 0.1, 1e3)
p = np.zeros((len(y)))
## rate=0 for zero coupon bonds
rate = 0
texp = 30
par = 100
for i in range(0, len(y)):
p[i] = bond_price(rate, y[i], texp, par)
plt.figure()
plt.title('Bond Price as Function of Yield')
plt.plot(y, p, '-k', label='Bond Price')
plt.legend()
plt.xlabel('Yield')
plt.ylabel('Bond Price')
## variables
r = 0.01625
r = 0.0
## principal; but actually the par value here.
p0 = 100.0
## the actual principal, the initial investment in dollars
invest = 1e2
## time to maturity of the bond
texp = 10
## daily rebalance?
price = np.zeros((len(bond_yield)))
for i in range(len(bond_yield)):
price[i] = bond_price(r=r, y=bond_yield.y[i] / 100, n=texp, p0=p0)
## add the price to the dataframe
price_df = pd.DataFrame(price, index=bond_yield.index)
bond_yield.insert(1, "price", price_df)
## use this loop to calculate the return?
prev_year = '1981'
date_array = pd.date_range('1/2/1981', '1/2/2019', freq='BAS-oct')
purchase_date = date_array[0]
return_rate = np.zeros((len(date_array)))
## the number of bonds corresponding to the investment.
nbonds = np.zeros((len(date_array)))
sell_price = np.zeros((len(date_array)))
purchase_price = np.zeros((len(date_array)))
tot_return = np.zeros((len(date_array)))
## Make an animation?
## use this loop to calculate the return?
prev_year = '1981'
date_array = pd.date_range('1/2/1981', '1/2/2019', freq='BAS-oct')
## the number of bonds corresponding to the investment.
nbonds = np.zeros((len(date_array)))
d = {'value': np.zeros((len(date_array)))}
portfolio = pd.DataFrame(data=d, index=date_array)
purchase_date = date_array[0]
return_rate = np.zeros((len(date_array)))
## the number of bonds corresponding to the investment.
nbonds = np.zeros((len(date_array)))
## the number of bonds at the begining
nbonds[0] = invest / bond_price(
r=r, y=bond_yield.y10[date_array[0]] / 100, n=10, p0=p0)
nb = nbonds[0]
sell_price = np.zeros((len(date_array)))
purchase_price = np.zeros((len(date_array)))
tot_return = np.zeros((len(date_array)))
tot_return[0] = 0
return_factor = np.zeros((len(date_array)))
index = 0
for date in date_array[1:]:
## sell the bond from last year
p = nb * (bond_price(
r=r,
y=bond_yield.y9.values[bond_yield.index == date][0] / 100,
n=9,
p0=p0))
p0=100.0
## the actual principal, the initial investment in dollars
invest=1e2
## time to maturity of each note/bond you want to calculate
t10=10
t7=7
texp=10
## Can we try a monthly rebalance?
## initialize arrays for all desired note/bond prices
price10=np.zeros((len(bond_yield)))
price7=np.zeros((len(bond_yield)))
for i in range(len(bond_yield)):
price7[i]=bond_price(r=r,y=bond_yield['7'][i]/100,n=t7,p0=p0)
price10[i]=bond_price(r=r,y=bond_yield['10'][i]/100,n=t10,p0=p0)
## add the price to the dataframe
price7_df=pd.DataFrame(price7,index=bond_yield.index)
price10_df=pd.DataFrame(price10,index=bond_yield.index)
bond_yield.insert(2, "price7", price7_df)
bond_yield.insert(3, "price10", price10_df)
## okay, now ready to do backtesting with the following strategy:
## we start rolling from the date:
date_array=pd.date_range('1/2/1981','1/2/2020',freq='BAS-oct')
## divide our initial investment into 3 ten year notes, starting with 1981,
## then 1982, then 1983.