"""
## GAMSSOURCE: https://www.gams.com/latest/finlib_ml/libhtml/finlib_Horizon.html
## LICENSETYPE: Demo
## MODELTYPE: LP
Portfolio horizon returns model
Horizon.gms: Portfolio horizon returns model.
Consiglio, Nielsen and Zenios.
PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 4.3.1
Last modified: Apr 2008.
"""
from __future__ import annotations
import os
import numpy as np
import pandas as pd
from gamspy import (
Alias,
Card,
Container,
Equation,
Model,
Number,
Ord,
Parameter,
Set,
Sum,
Variable,
)
def BondDataTable():
# Bond data. Prices, coupons and maturities from the Danish market
bond_data_recs = pd.DataFrame(
np.array(
[
[112.35, 2006, 8],
[105.33, 2003, 8],
[111.25, 2007, 7],
[107.30, 2004, 7],
[107.62, 2011, 6],
[106.68, 2009, 6],
[101.93, 2002, 6],
[101.30, 2005, 5],
[101.61, 2003, 5],
[100.06, 2002, 4],
]
),
columns=["Price", "Maturity", "Coupon"],
index=[
"DS-8-06",
"DS-8-03",
"DS-7-07",
"DS-7-04",
"DS-6-11",
"DS-6-09",
"DS-6-02",
"DS-5-05",
"DS-5-03",
"DS-4-02",
],
)
bond_data_recs = bond_data_recs.reset_index().melt(
id_vars="index", var_name="Category", value_name="Value"
)
return bond_data_recs
def main():
m = Container(
system_directory=os.getenv("SYSTEM_DIRECTORY", None),
)
Time = Set(
m,
name="Time",
records=[str(time) for time in range(2001, 2012)],
description="Time periods",
)
t = Alias(m, name="t", alias_with=Time)
# SCALARS #
Now = Parameter(m, name="Now", description="Current year")
Horizon = Parameter(m, name="Horizon", description="End of the Horizon")
Now[...] = 2001
Horizon[...] = Card(t) - 1
# PARAMETER #
tau = Parameter(m, name="tau", domain=t, description="Time in years")
# Note: time starts from 0
tau[t] = Ord(t) - 1
# SET
Bonds = Set(
m,
name="Bonds",
records=[
"DS-8-06",
"DS-8-03",
"DS-7-07",
"DS-7-04",
"DS-6-11",
"DS-6-09",
"DS-6-02",
"DS-5-05",
"DS-5-03",
"DS-4-02",
],
description="Bonds universe",
)
i = Alias(m, name="i", alias_with=Bonds)
# SCALARS #
spread = Parameter(
m,
name="spread",
description="Borrowing spread over the reinvestment rate",
)
Budget = Parameter(m, name="Budget", description="Initial budget")
# PARAMETERS #
Price = Parameter(m, name="Price", domain=i, description="Bond prices")
Coupon = Parameter(m, name="Coupon", domain=i, description="Coupons")
Maturity = Parameter(
m, name="Maturity", domain=i, description="Maturities"
)
Liability = Parameter(
m, name="Liability", domain=t, description="Stream of liabilities"
)
rf = Parameter(m, name="rf", domain=t, description="Reinvestment rates")
F = Parameter(m, name="F", domain=[t, i], description="Cashflows")
# Bond data. Prices, coupons and maturities from the Danish market
BondData = Parameter(
m,
name="BondData",
domain=[i, "*"],
records=BondDataTable(),
description="Bonds data",
)
# Copy/transform data. Note division by 100 to get unit data, and
# subtraction of "Now" from Maturity date (so consistent with tau):
Price[i] = BondData[i, "Price"] / 100
Coupon[i] = BondData[i, "Coupon"] / 100
Maturity[i] = BondData[i, "Maturity"] - Now
# Calculate the ex-coupon cashflow of Bond i in year t:
F[t, i] = (
Number(1).where[tau[t] == Maturity[i]]
+ Coupon[i].where[(tau[t] <= Maturity[i]) & (tau[t] > 0)]
)
# For simplicity, we set the short term rate to be 0.03 in each period
rf[t] = 0.04
spread[...] = 0.02
# Initial available budget to buy the matching portfolio
Budget[...] = 803021.814
# 803021.814
# 850000
# PARAMETER #
Liability.setRecords(
np.array(
[
0,
80000,
100000,
110000,
120000,
140000,
120000,
90000,
50000,
75000,
150000,
]
)
)
# VARIABLES #
x = Variable(
m,
name="x",
type="positive",
domain=i,
description="Face value purchased",
)
surplus = Variable(
m,
name="surplus",
type="positive",
domain=t,
description="Amount of money reinvested",
)
borrow = Variable(
m,
name="borrow",
type="positive",
domain=t,
description="Amount of money borrowed",
)
HorizonRet = Variable(m, name="HorizonRet", description="Horizon Return")
# EQUATION #
CashFlowCon = Equation(
m,
name="CashFlowCon",
type="regular",
domain=t,
description="Equations defining the cashflow balance",
)
CashFlowCon[t] = (
Sum(i, F[t, i] * x[i])
+ (Budget - Sum(i, Price[i] * x[i])).where[tau[t] == 0]
+ borrow[t].where[tau[t] < Horizon]
+ ((1 + rf[t.lag(1)]) * surplus[t.lag(1)]).where[tau[t] > 0]
== Liability[t].where[tau[t] > 0]
+ surplus[t].where[tau[t] < Horizon]
+ HorizonRet.where[tau[t] == Horizon]
+ ((1 + rf[t.lag(1)] + spread) * borrow[t.lag(1)]).where[tau[t] > 0]
)
HorizonMod = Model(
m,
name="HorizonMod",
equations=[CashFlowCon],
problem="LP",
sense="MAX",
objective=HorizonRet,
)
HorizonMod.solve()
print("HorizonRet: ", round(HorizonRet.toValue(), 3))
print("borrow: ", borrow.toDict())
print("surplus: ", surplus.toDict())
print("x: ", x.toDict())
# Simulation for different values of the initial budget
with open(
"HorizonPortfolios_new.csv", "w", encoding="UTF-8"
) as HorizonHandle:
budget = 778985.948
while budget <= 818985.948:
Budget[...] = budget
HorizonMod.solve()
for ii in i.toList():
horizon_ret = round(HorizonRet.records.level[0], 2)
bond_mat = round(BondData.pivot().loc[ii, "Maturity"], 2)
coupon = Coupon.records[Coupon.records["i"] == ii].value.array[
0
]
purchased_price = round(
x.records[x.records["i"] == ii].level.array[0]
* Price.records[Price.records["i"] == ii].value.array[0],
3,
)
HorizonHandle.write(
f'{round(budget,2)},{horizon_ret},"{ii}",{bond_mat},{coupon},{purchased_price}'
)
HorizonHandle.write("\n")
for tt in t.toList():
borrow_rec = borrow.records[borrow.records["t"] == tt]
borrow_rec = (
round(borrow_rec.level.array[0], 3)
if not borrow_rec.empty
else 0
)
HorizonHandle.write(f'"{tt}",{borrow_rec}')
HorizonHandle.write("\n")
budget += 10000
if __name__ == "__main__":
main()
