"""
## GAMSSOURCE: https://www.gams.com/latest/finlib_ml/libhtml/finlib_CVaR.html
## LICENSETYPE: Demo
## MODELTYPE: LP
## DATAFILES: WorldIndices.gdx
Conditional Value at Risk models
CVaR.gms: Conditional Value at Risk models.
Consiglio, Nielsen and Zenios.
PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 5.5
Last modified: Apr 2008.
"""
from __future__ import annotations
import os
from pathlib import Path
import numpy as np
from gamspy import (
Card,
Container,
Equation,
Model,
Number,
Parameter,
Smax,
Smin,
Sum,
Variable,
)
def index_data():
np.array(
[
1.034769211,
1.024362083,
1.005721076,
1.014359531,
1.008024402,
1.015164086,
1.011776948,
0.999367312,
1.022337255,
1.014084294,
1.002478561,
1.004830772,
1.022048865,
1.001584376,
1.014789245,
1.018465908,
1.02023507,
1.001142139,
1.028357519,
1.012274672,
1.005320247,
0.991451365,
1.007344745,
1.017165464,
0.997931432,
0.990041853,
0.9933217,
0.991912481,
1.036980768,
0.994451813,
1.007412617,
0.955150659,
0.958840232,
1.033624988,
1.018079311,
1.010736753,
1.016700717,
1.048121923,
1.015146812,
1.0074283,
1.025778693,
0.983151788,
1.022476292,
1.004850227,
1.0091122,
0.995361207,
0.992432266,
1.024212556,
1.022181138,
1.006772127,
0.990354861,
1.0067649,
1.008943286,
0.983974563,
1.000347655,
1.001230771,
1.020880921,
1.019415483,
1.008638044,
1.017173042,
1.011831605,
1.018260066,
1.014054495,
1.011841085,
0.988155751,
1.009224769,
1.010321982,
1.033008126,
0.999626315,
1.022733809,
1.00083866,
1.039925522,
1.0144168,
0.974402144,
0.971108237,
1.002198078,
1.001221179,
0.988342113,
1.01750901,
1.019968377,
0.992895551,
1.000905761,
0.997333999,
0.994982525,
0.987972315,
1.000443735,
1.01583315,
1.018338346,
1.026183302,
0.999209138,
1.018809687,
1.009775599,
1.01722367,
0.999752239,
1.015986198,
1.019400469,
1.017624299,
0.996067065,
1.00947457,
1.0164916,
0.997929107,
1.008892447,
0.990498799,
1.011843222,
1.023338977,
1.001536085,
1.023978065,
0.994238826,
1.022819962,
1.012142345,
0.989862601,
1.021050206,
1.019165002,
1.023260624,
1.027413626,
0.971346297,
1.026087902,
0.959990261,
1.008484984,
1.014365951,
1.010347985,
1.029266037,
1.01989954,
0.999383722,
0.992191473,
0.993782093,
1.010730888,
0.918149916,
1.008729179,
1.031641438,
1.032632304,
1.004115995,
1.007398109,
0.99859111,
1.032604061,
1.027883261,
0.979268923,
1.024656356,
0.989556024,
1.001926578,
0.991713793,
1.020697126,
1.022268183,
1.031273723,
0.992301368,
1.011547524,
1.02121809,
0.988701862,
0.991540642,
1.014546705,
0.997009882,
1.01168258,
0.982543898,
0.992197467,
]
)
def main():
gdx_file = str(Path(__file__).parent.absolute()) + "/WorldIndices.gdx"
m = Container(
system_directory=os.getenv("SYSTEM_DIRECTORY", None),
load_from=gdx_file,
)
# SETS #
i, l = m.getSymbols(["i", "l"])
# SCALARS #
Budget = Parameter(
m, name="Budget", description="Nominal investment budget"
)
alpha = Parameter(m, name="alpha", description="Confidence level")
MU_TARGET = Parameter(
m, name="MU_TARGET", description="Target portfolio return"
)
MU_STEP = Parameter(m, name="MU_STEP", description="Target return step")
MIN_MU = Parameter(
m, name="MIN_MU", description="Minimum return in universe"
)
MAX_MU = Parameter(
m, name="MAX_MU", description="Maximum return in universe"
)
RISK_TARGET = Parameter(
m, name="RISK_TARGET", description="Bound on CVaR (risk)"
)
LossFlag = Parameter(
m, name="LossFlag", description="Flag selecting the type of loss"
)
Budget[...] = 100.0
alpha[...] = 0.99
# PARAMETERS #
pr = Parameter(m, name="pr", domain=l, description="Scenario probability")
P = Parameter(m, name="P", domain=[i, l], description="Final values")
EP = Parameter(m, name="EP", domain=i, description="Expected final values")
AssetReturns = m.getSymbols(["AssetReturns"])[0]
pr[l] = 1.0 / Card(l)
P[i, l] = 1 + AssetReturns[i, l]
EP[i] = Sum(l, pr[l] * P[i, l])
MIN_MU[...] = Smin(i, EP[i])
MAX_MU[...] = Smax(i, EP[i])
# Assume we want 20 portfolios in the frontier
MU_STEP[...] = (MAX_MU - MIN_MU) / 20
TargetIndex = Parameter(
m, name="TargetIndex", domain=l, description="Target index returns"
)
# To test the model with a market index, uncomment the following two lines.
# Note that, this index can be used only with WorldIndexes.inc.
# Index = Parameter(m, name="Index", domain=l, records=index_data(), description="Index returns")
# TargetIndex[l] = Index[l]
# VARIABLES #
x = Variable(
m,
name="x",
type="positive",
domain=i,
description="Holdings of assets in monetary units (not proportions)",
)
VaRDev = Variable(
m,
name="VaRDev",
type="positive",
domain=l,
description="Measures of the deviations from the VaR",
)
VaR = Variable(m, name="VaR", description="Value-at-Risk")
Losses = Variable(
m, name="Losses", domain=l, description="Measures of the losses"
)
# EQUATIONS #
BudgetCon = Equation(
m,
name="BudgetCon",
type="regular",
description="Equation defining the budget contraint",
)
ReturnCon = Equation(
m,
name="ReturnCon",
type="regular",
description="Equation defining the portfolio return constraint",
)
CVaRCon = Equation(
m,
name="CVaRCon",
type="regular",
description="Equation defining the CVaR allowed",
)
LossDef = Equation(
m,
name="LossDef",
type="regular",
domain=l,
description="Equations defining the losses",
)
VaRDevCon = Equation(
m,
name="VaRDevCon",
type="regular",
domain=l,
description="Equations defining the VaR deviation constraints",
)
BudgetCon[...] = Sum(i, x[i]) == Budget
ReturnCon[...] = Sum(i, EP[i] * x[i]) >= MU_TARGET * Budget
CVaRCon[...] = VaR + Sum(l, pr[l] * VaRDev[l]) / (1 - alpha) <= RISK_TARGET
VaRDevCon[l] = VaRDev[l] >= Losses[l] - VaR
LossDef[l] = (
Losses[l]
== (Budget - Sum(i, P[i, l] * x[i])).where[LossFlag == 1]
+ (TargetIndex[l] * Budget - Sum(i, P[i, l] * x[i])).where[
LossFlag == Number(2)
]
+ (Sum(i, EP[i] * x[i]) - Sum(i, P[i, l] * x[i])).where[
LossFlag == Number(3)
]
)
z = VaR + Sum(l, pr[l] * VaRDev[l]) / (1 - alpha)
MinCVaR = Model(
m,
name="MinCVaR",
equations=[BudgetCon, ReturnCon, LossDef, VaRDevCon],
problem="LP",
sense="MIN",
objective=z,
)
output_csv = '"Status","VaR","CVaR","Mean",'
i_recs = [f'"{i_rec}"' for i_rec in i.records.uni.tolist()]
output_csv += ",".join(i_recs) + "\n"
LossFlag[...] = 2
# Comment the following line if you want to track the market index.
TargetIndex[l] = 1.01
mu_target = MIN_MU.records.value[0]
while mu_target <= MAX_MU.records.value[0]:
MU_TARGET[...] = mu_target
MinCVaR.solve()
output_csv += f"{str(MinCVaR.status).split('.')[-1]},{VaR.records.level.round(3)[0]},{round(MinCVaR.objective_value, 3)},{round(MU_TARGET.records.value[0] * Budget.records.value[0],3)},"
x_recs = [str(x_rec) for x_rec in x.records.level.round(2).tolist()]
output_csv += ",".join(x_recs) + "\n"
mu_target += MU_STEP.records.value[0]
with open("CVaRFrontiers.csv", "w", encoding="UTF-8") as FrontierHandle:
FrontierHandle.write(output_csv)
if __name__ == "__main__":
main()
