alastairparagas · September 16, 2022 15:06
diff --git a/bonds.py b/bonds.py
 import numpy as np
 import matplotlib.pyplot as plt
 np.seterr(all="ignore")
 import matplotlib.ticker as ticker
 import numpy_financial

 # Treasury, TIPS and I-bonds - these are all bonds, which allows you to lend 
 # a $ amount (principal) to the US government. The US government promises to pay 
 # you back in time (years). 

 # They also give you interest payments every so often to compensate you for 
 # lending the US government money. Every year, this $ in interest payment profit 
 # amounts to principal*coupon rate.

 # The government in turn uses investors paying for bonds, to fund projects like 
 # build infrastructure and grow the US economy by allocating capital to industries 
 # that may not be as profitable but the government has an incentive 
 # to direct American society to. For ex: renewable energy, state-side semiconductor 
 # manufacturing, etc (industries where companies have relatively small profit 
 # margins, but the US government wants to keep them afloat until they mature)

 # In turn, US taxpayers are the ones essentially paying the principal + coupons 
 # (interest payments) owed to investors, who lent money to the US government.

 def calculate_tbond_return(years, principal, coupon_rate):
  return numpy_financial.fv(0, np.arange(years+1), -1*principal*coupon_rate, -1*principal)

 def calculate_ibond_return(years, principal, inflation):
  return numpy_financial.fv(inflation, np.arange(years+1), 0, -1*principal)

 def calculate_tips_return(years, principal, coupon_rate, inflation):
  # TIPS guarantees principal/par stays constant - even in deflation
  inflation = max(inflation, 0)
  tips_bond_principal = numpy_financial.fv(inflation, np.arange(years+1), 0, -1*principal)
  tips_bond_coupons = tips_bond_principal * coupon_rate
  return tips_bond_principal + tips_bond_coupons

 # These calculations assume you hold to maturity (you don't sell for the duration 
 # of the bond, which is 10 years in this example)

 principal = 1000
 # Treasury bonds selling at discount - $97.25~ for $100 of debt, repayment in 10 years
 # In essence, you are lending the US government $100 using only $97.25. 
 # In 10 years, they will pay you back the $100. 
 # To add, they will make annual fixed interest payments of 1.0282% of $100 (aka coupon rate)
 # or roughly $1.02 a year, to compensate you lending out $100 to them.
 tbond_initial_value = principal*1.0282

 # TIPS selling at premium - $111.18~ for $100 of debt, repayment in 10 years
 # In essence, you are lending the US government $100 for $111.18!
 # In 10 years, they will pay you back $100 OR the inflation adjusted equivalent of $100 in 
 # 10 years - whichever is higher - your $100 will grow to match inflation!
 # To add, they will make annual fixed interest payments of 0.125% of $100 (aka coupon rate)
 # or roughly $0.125 a year, to compensate you lending out $100 to them
 tips_initial_value = principal*0.8994

 # In the real world, the "yield" of a Treasury or TIPS bond combines the coupon rate 
 # and the premium/discount pricing of bonds. The difference in yield between the 
 # 10-year Treasury bond and the TIPS bond is the CURRENT (for the given day) 
 # market's estimate for the average annual inflation for the next 10 years. 
 # Currently (Sept 12 2022), 10 year Treasury yield is at 3.343% and 10 year TIPS yield 
 # is at 0.942%. As such market is assuming a 10 year average inflation rate of 2.401%.

 # If 10 years into the future, the average inflation is above 2.401%, investing 
 # into TIPS would have made more money. If the average inflation is below 2.401%, 
 # investing into a 10-year Treasury would have made more money.

 # US government bond yields also bleed into the stock market. The higher yields 
 # go, the more investors are likely to choose investing a "safe" US government 
 # bond over stocks (less risk, more assured profit). The lower bond yields go, the 
 # more investors are likely to choose investing into stocks (as there are not much 
 # profit to be made from bonds, investors flock to riskier assets)

 # In the real world, when interest rates go up, companies find it harder to 
 # borrow money. Companies that depend on borrowing money to grow and increase their 
 # net profit (growth companies) will typically see their valuations (stock price)
 # re-adjusted by the market. Mature companies that depend less on borrowed money 
 # (but may also not have the capability to increase net profits), see more stable 
 # valuations (stock price) as they can better weather the environment.

 # 10-year Treasury coupon rate of 1.125%
 treasury_bond = calculate_tbond_return(
  years=10, principal=tbond_initial_value, coupon_rate=0.0125
 )
 # 10-year TIPS coupon rate of 0.125%
 # TIPS 1% annual deflation, TIPS guarantees principal never dips even with deflation if held to maturity
 tips_bond_1pctdeflation = calculate_tips_return(
  years=10, principal=tips_initial_value, coupon_rate=0.00125, 
  inflation=-0.01
 )
 # TIPS 1% annual inflation
 tips_bond_1pctinflation = calculate_tips_return(
  years=10, principal=tips_initial_value, coupon_rate=0.00125, 
  inflation=0.01
 )
 # TIPS 2% annual inflation
 tips_bond_2pctinflation = calculate_tips_return(
  years=10, principal=tips_initial_value, coupon_rate=0.00125, 
  inflation=0.02
 )
 # TIPS 4% annual inflation
 tips_bond_4pctinflation = calculate_tips_return(
  years=10, principal=tips_initial_value, coupon_rate=0.00125, 
  inflation=0.04
 )
 # I-bond, 4% annual inflation
 ibond_4pctinflation = calculate_ibond_return(
  years=10, principal=principal, 
  inflation=0.04
 )

 fig3, fig3_ax1 = plt.subplots()
 fig3_ax1.plot(treasury_bond, label='Treasury Bond')
 fig3_ax1.plot(tips_bond_1pctdeflation, label='TIPS, 1% deflation')
 fig3_ax1.plot(tips_bond_1pctinflation, label='TIPS, 1% inflation')
 fig3_ax1.plot(tips_bond_2pctinflation, label='TIPS, 2% inflation')
 fig3_ax1.plot(tips_bond_4pctinflation, label='TIPS, 4% inflation')
 fig3_ax1.plot(ibond_4pctinflation, label='I-bond, 4% inflation')
 fig3_ax1.set_xlabel('Years')
 fig3_ax1.set_ylabel('Total Return, $')
 fig3_ax1.set_title('10-year Treasury Bonds vs TIPS, Bought at $1k \n(TIPS at premium, Treasury at discount), Held to Maturity')
 fig3_ax1.legend()
 fig3_ax1.yaxis.set_major_formatter(ticker.FormatStrFormatter('$%.0f'))
	import numpy as np
	import matplotlib.pyplot as plt
	np.seterr(all="ignore")
	import matplotlib.ticker as ticker
	import numpy_financial

	# Treasury, TIPS and I-bonds - these are all bonds, which allows you to lend
	# a $ amount (principal) to the US government. The US government promises to pay
	# you back in time (years).

	# They also give you interest payments every so often to compensate you for
	# lending the US government money. Every year, this $ in interest payment profit
	# amounts to principal*coupon rate.

	# The government in turn uses investors paying for bonds, to fund projects like
	# build infrastructure and grow the US economy by allocating capital to industries
	# that may not be as profitable but the government has an incentive
	# to direct American society to. For ex: renewable energy, state-side semiconductor
	# manufacturing, etc (industries where companies have relatively small profit
	# margins, but the US government wants to keep them afloat until they mature)

	# In turn, US taxpayers are the ones essentially paying the principal + coupons
	# (interest payments) owed to investors, who lent money to the US government.

	def calculate_tbond_return(years, principal, coupon_rate):
	return numpy_financial.fv(0, np.arange(years+1), -1principalcoupon_rate, -1*principal)

	def calculate_ibond_return(years, principal, inflation):
	return numpy_financial.fv(inflation, np.arange(years+1), 0, -1*principal)

	def calculate_tips_return(years, principal, coupon_rate, inflation):
	# TIPS guarantees principal/par stays constant - even in deflation
	inflation = max(inflation, 0)
	tips_bond_principal = numpy_financial.fv(inflation, np.arange(years+1), 0, -1*principal)
	tips_bond_coupons = tips_bond_principal * coupon_rate
	return tips_bond_principal + tips_bond_coupons

	# These calculations assume you hold to maturity (you don't sell for the duration
	# of the bond, which is 10 years in this example)

	principal = 1000
	# Treasury bonds selling at discount - $97.25~ for $100 of debt, repayment in 10 years
	# In essence, you are lending the US government $100 using only $97.25.
	# In 10 years, they will pay you back the $100.
	# To add, they will make annual fixed interest payments of 1.0282% of $100 (aka coupon rate)
	# or roughly $1.02 a year, to compensate you lending out $100 to them.
	tbond_initial_value = principal*1.0282

	# TIPS selling at premium - $111.18~ for $100 of debt, repayment in 10 years
	# In essence, you are lending the US government $100 for $111.18!
	# In 10 years, they will pay you back $100 OR the inflation adjusted equivalent of $100 in
	# 10 years - whichever is higher - your $100 will grow to match inflation!
	# To add, they will make annual fixed interest payments of 0.125% of $100 (aka coupon rate)
	# or roughly $0.125 a year, to compensate you lending out $100 to them
	tips_initial_value = principal*0.8994

	# In the real world, the "yield" of a Treasury or TIPS bond combines the coupon rate
	# and the premium/discount pricing of bonds. The difference in yield between the
	# 10-year Treasury bond and the TIPS bond is the CURRENT (for the given day)
	# market's estimate for the average annual inflation for the next 10 years.
	# Currently (Sept 12 2022), 10 year Treasury yield is at 3.343% and 10 year TIPS yield
	# is at 0.942%. As such market is assuming a 10 year average inflation rate of 2.401%.

	# If 10 years into the future, the average inflation is above 2.401%, investing
	# into TIPS would have made more money. If the average inflation is below 2.401%,
	# investing into a 10-year Treasury would have made more money.

	# US government bond yields also bleed into the stock market. The higher yields
	# go, the more investors are likely to choose investing a "safe" US government
	# bond over stocks (less risk, more assured profit). The lower bond yields go, the
	# more investors are likely to choose investing into stocks (as there are not much
	# profit to be made from bonds, investors flock to riskier assets)

	# In the real world, when interest rates go up, companies find it harder to
	# borrow money. Companies that depend on borrowing money to grow and increase their
	# net profit (growth companies) will typically see their valuations (stock price)
	# re-adjusted by the market. Mature companies that depend less on borrowed money
	# (but may also not have the capability to increase net profits), see more stable
	# valuations (stock price) as they can better weather the environment.

	# 10-year Treasury coupon rate of 1.125%
	treasury_bond = calculate_tbond_return(
	years=10, principal=tbond_initial_value, coupon_rate=0.0125
	)
	# 10-year TIPS coupon rate of 0.125%
	# TIPS 1% annual deflation, TIPS guarantees principal never dips even with deflation if held to maturity
	tips_bond_1pctdeflation = calculate_tips_return(
	years=10, principal=tips_initial_value, coupon_rate=0.00125,
	inflation=-0.01
	)
	# TIPS 1% annual inflation
	tips_bond_1pctinflation = calculate_tips_return(
	years=10, principal=tips_initial_value, coupon_rate=0.00125,
	inflation=0.01
	)
	# TIPS 2% annual inflation
	tips_bond_2pctinflation = calculate_tips_return(
	years=10, principal=tips_initial_value, coupon_rate=0.00125,
	inflation=0.02
	)
	# TIPS 4% annual inflation
	tips_bond_4pctinflation = calculate_tips_return(
	years=10, principal=tips_initial_value, coupon_rate=0.00125,
	inflation=0.04
	)
	# I-bond, 4% annual inflation
	ibond_4pctinflation = calculate_ibond_return(
	years=10, principal=principal,
	inflation=0.04
	)

	fig3, fig3_ax1 = plt.subplots()
	fig3_ax1.plot(treasury_bond, label='Treasury Bond')
	fig3_ax1.plot(tips_bond_1pctdeflation, label='TIPS, 1% deflation')
	fig3_ax1.plot(tips_bond_1pctinflation, label='TIPS, 1% inflation')
	fig3_ax1.plot(tips_bond_2pctinflation, label='TIPS, 2% inflation')
	fig3_ax1.plot(tips_bond_4pctinflation, label='TIPS, 4% inflation')
	fig3_ax1.plot(ibond_4pctinflation, label='I-bond, 4% inflation')
	fig3_ax1.set_xlabel('Years')
	fig3_ax1.set_ylabel('Total Return, $')
	fig3_ax1.set_title('10-year Treasury Bonds vs TIPS, Bought at $1k \n(TIPS at premium, Treasury at discount), Held to Maturity')
	fig3_ax1.legend()
	fig3_ax1.yaxis.set_major_formatter(ticker.FormatStrFormatter('$%.0f'))