Corporate bond indexation model

Corporate.py Corporate.gdx

"""
Corporate bond indexation model

Corporate.gms: Corporate bond indexation model
Consiglio, Nielsen and Zenios.
PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 8.3
Last modified: May 2008.
"""
from pathlib import Path

import gamspy.math as gams_math
from gamspy import Card
from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Parameter
from gamspy import Sense
from gamspy import Sum
from gamspy import Variable


def main():
    # Define container
    m = Container(
        delayed_execution=True,
        load_from=str(Path(__file__).parent.absolute()) + "/Corporate.gdx",
    )

    # SETS #
    BroadAssetClassOne, BroadAssetClassTwo, BroadAssetClassThree, ACTIVE = (
        m.getSymbols(
            [
                "BroadAssetClassOne",
                "BroadAssetClassTwo",
                "BroadAssetClassThree",
                "ACTIVE",
            ]
        )
    )

    # ALIASES
    i, l, j, m1, m2, m3, a = m.getSymbols(
        ["i", "l", "j", "m1", "m2", "m3", "a"]
    )

    # PARAMETERS #
    AssetReturns = m.getSymbols(["AssetReturns"])[0]
    BroadWeights = Parameter(
        m,
        name="BroadWeights",
        domain=[j],
        description="Weights of the broad asset classes",
    )
    AssetWeights = Parameter(
        m,
        name="AssetWeights",
        domain=[i],
        description="Weights of each asset in the index",
    )

    # Assign weights randomly

    AssetWeights[i] = gams_math.uniform(1, 10)

    # DISPLAY  AssetWeights

    # Normalize the random weights
    WeightsSum = Parameter(m, name="WeightsSum")

    WeightsSum[...] = Sum(i, AssetWeights[i])

    AssetWeights[i] = AssetWeights[i] / WeightsSum

    BroadWeights["BA_1"] = Sum(m1, AssetWeights[m1])
    BroadWeights["BA_2"] = Sum(m2, AssetWeights[m2])
    BroadWeights["BA_3"] = Sum(m3, AssetWeights[m3])

    IndexReturns = Parameter(
        m,
        name="IndexReturns",
        domain=[l],
        description="Index return scenarios",
    )
    BroadAssetReturns = Parameter(
        m,
        name="BroadAssetReturns",
        domain=[j, l],
        description="Broad asset class return scenarios",
    )
    Benchmark = Parameter(
        m,
        name="Benchmark",
        domain=[l],
        description="Current benchmark scenario returns",
    )

    BroadAssetReturns["BA_1", l] = Sum(
        m1, AssetWeights[m1] * AssetReturns[m1, l]
    )
    BroadAssetReturns["BA_2", l] = Sum(
        m2, AssetWeights[m2] * AssetReturns[m2, l]
    )
    BroadAssetReturns["BA_3", l] = Sum(
        m3, AssetWeights[m3] * AssetReturns[m3, l]
    )

    IndexReturns[l] = Sum(j, BroadWeights[j] * BroadAssetReturns[j, l])

    CurrentWeight = Parameter(
        m,
        name="CurrentWeight",
        description="Current weight for tactcal allocation",
    )
    EpsTolerance = Parameter(m, name="EpsTolerance", description="Tolerance")
    pr = Parameter(
        m, name="pr", domain=[l], description="Scenario probability"
    )

    pr[l] = 1.0 / Card(l)

    # VARIABLES #
    x = Variable(
        m,
        name="x",
        type="positive",
        domain=[i],
        description="Percentage invested in each security",
    )
    z = Variable(
        m,
        name="z",
        type="positive",
        domain=[j],
        description="Percentages invested in each broad asset class",
    )
    PortRet = Variable(
        m, name="PortRet", domain=[l], description="Portfolio returns"
    )
    ObjValue = Variable(
        m, name="ObjValue", description="Objective function value"
    )

    # EQUATIONS #
    ObjDef = Equation(
        m,
        name="ObjDef",
        description=(
            "Objective function for the strategic model (Expected return)"
        ),
    )
    BroadPortRetDef = Equation(
        m,
        name="BroadPortRetDef",
        domain=[l],
        description="Portfolio return definition for broad asset classes",
    )
    PortRetDef = Equation(
        m,
        name="PortRetDef",
        domain=[l],
        description="Portfolio return definition",
    )
    BroadNormalCon = Equation(
        m,
        name="BroadNormalCon",
        description=(
            "Equation defining the normalization contraint for broad asset"
            " classes"
        ),
    )
    NormalCon = Equation(
        m,
        name="NormalCon",
        description="Equation defining the normalization contraint",
    )
    MADCon = Equation(
        m,
        name="MADCon",
        domain=[l],
        description="MAD constraints",
    )

    ObjDef[...] = ObjValue == Sum(l, pr[l] * PortRet[l])

    BroadPortRetDef[l] = PortRet[l] == Sum(j, z[j] * BroadAssetReturns[j, l])

    PortRetDef[l] = PortRet[l] == Sum(a, x[a] * AssetReturns[a, l])

    MADCon[l] = PortRet[l] >= Benchmark[l] - EpsTolerance

    BroadNormalCon[...] = Sum(j, z[j]) == 1.0

    NormalCon[...] = Sum(a, x[a]) == CurrentWeight

    # MODELS #
    StrategicModel = Model(
        m,
        name="StrategicModel",
        equations=[ObjDef, BroadPortRetDef, MADCon, BroadNormalCon],
        problem="LP",
        sense=Sense.MAX,
        objective=ObjValue,
    )
    TacticalModel = Model(
        m,
        name="TacticalModel",
        equations=[ObjDef, PortRetDef, MADCon, NormalCon],
        problem="LP",
        sense=Sense.MAX,
        objective=ObjValue,
    )

    # Solve strategic model

    Benchmark[l] = IndexReturns[l]

    EpsTolerance[...] = 0.02

    StrategicModel.solve()

    print("## Strategic Asset Allocation ##")
    print("z: \n", z.records.level.to_list())

    # Solve tactical model for Broad Asset 1 (BA_1)

    CurrentWeight[...] = z.l["BA_1"]

    Benchmark[l] = BroadAssetReturns["BA_1", l]

    EpsTolerance[...] = 0.02

    ACTIVE[i] = BroadAssetClassOne[i]

    if CurrentWeight.records.value[0] > 0.05:
        TacticalModel.solve()

        print("\n## Model BA_1 ##")
        print("\nx: \n", x.records.level.tolist())

    # Solve tactical model for Broad Asset 2 (BA_2)

    CurrentWeight[...] = z.l["BA_2"]

    ACTIVE[i] = BroadAssetClassTwo[i]

    Benchmark[l] = BroadAssetReturns["BA_2", l]

    EpsTolerance[...] = 0.03

    if CurrentWeight.records.value[0] > 0.05:
        TacticalModel.solve()

        print("\n## Model BA_2 ##")
        print("\nx: \n", x.records.level.tolist())

    # Solve tactical model for Broad Asset 3 (BA_3)

    CurrentWeight[...] = z.l["BA_3"]

    ACTIVE[i] = BroadAssetClassThree[i]

    Benchmark[l] = BroadAssetReturns["BA_3", l]

    EpsTolerance[...] = 0.02

    if CurrentWeight.records.value[0] > 0.05:
        TacticalModel.solve()

        print("\n## Model BA_3 ##")
        print("\nx: \n", x.records.level.tolist())

    # Solve integrated model

    CurrentWeight[...] = 1.0

    Benchmark[l] = IndexReturns[l]

    EpsTolerance[...] = 0.02

    ACTIVE[i] = True

    TacticalModel.solve()
    print("\n## Model Integrated ##")
    print("x: \n", x.records.level.tolist())

    print("\nObjective Function Value: ", round(ObjValue.records.level[0], 3))


if __name__ == "__main__":
    main()