Sharpe model

Sharpe.py Sharpe.gdx

"""
## GAMSSOURCE: https://www.gams.com/latest/finlib_ml/libhtml/finlib_Sharpe.html
## LICENSETYPE: Demo
## MODELTYPE: NLP
## DATAFILES: Sharpe.gdx


Sharpe model

Sharpe.gms: Sharpe model.
Consiglio, Nielsen and Zenios.
PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 3.3
Last modified: Apr 2008.
"""

from __future__ import annotations

import os
from pathlib import Path

import gamspy.math as gams_math
import numpy as np
import pandas as pd
from gamspy import (
    Alias,
    Container,
    Equation,
    Model,
    Problem,
    Sense,
    Sum,
    Variable,
)


def main():
    m = Container(
        system_directory=os.getenv("SYSTEM_DIRECTORY", None),
        load_from=str(Path(__file__).parent.absolute()) + "/Sharpe.gdx",
    )

    # SETS #
    Assets = m.getSymbols(["subset"])[0]
    ii = Alias(m, name="ii", alias_with=Assets)
    j = Alias(m, name="j", alias_with=Assets)

    # PARAMETERS #
    RiskFreeRate, ExExpectedReturns, ExVarCov = m.getSymbols(
        ["MeanRiskFreeReturn", "MeanExcessRet", "ExcessCov"]
    )

    # VARIABLES #
    x = Variable(
        m,
        name="x",
        type="positive",
        domain=ii,
        description="Holdings of assets",
    )
    PortVariance = Variable(
        m, name="PortVariance", description="Portfolio variance"
    )
    d_bar = Variable(
        m, name="d_bar", description="Portfolio expected excess return"
    )

    # EQUATIONS #
    ReturnDef = Equation(
        m,
        name="ReturnDef",
        description="Equation defining the portfolio excess return",
    )
    VarDef = Equation(
        m,
        name="VarDef",
        description="Equation defining the portfolio excess variance",
    )
    NormalCon = Equation(
        m,
        name="NormalCon",
        description="Equation defining the normalization contraint",
    )

    ReturnDef[...] = d_bar == Sum(ii, ExExpectedReturns[ii] * x[ii])

    VarDef[...] = PortVariance == Sum([ii, j], x[ii] * ExVarCov[ii, j] * x[j])

    NormalCon[...] = Sum(ii, x[ii]) == 1

    # Objective Function
    ObjDef = d_bar / gams_math.sqrt(PortVariance)

    # Put strictly positive bound on Variance to keep the model out of trouble:
    PortVariance.lo[...] = 0.001

    Sharpe = Model(
        m,
        name="Sharpe",
        equations=[ReturnDef, VarDef, NormalCon],
        problem=Problem.NLP,
        sense=Sense.MAX,
        objective=ObjDef,
    )
    Sharpe.solve()

    print("Objective Function Variable: ", round(Sharpe.objective_value, 3))

    current_port_variance = 0
    results = []
    while current_port_variance <= 1:
        theta = np.sqrt(current_port_variance / PortVariance.records.level[0])
        current_port_return = (
            RiskFreeRate.records.value[0] + theta * d_bar.records.level[0]
        )
        results.append(
            [np.sqrt(current_port_variance), current_port_return, theta]
        )
        current_port_variance += 0.1

    # Also plot the tangent portfolio
    theta = 1
    results.append(
        [
            np.sqrt(PortVariance.records.level[0]),
            RiskFreeRate.records.value[0] + theta * d_bar.records.level[0],
            theta,
        ]
    )
    SharpeFrontier = pd.DataFrame(
        results, columns=["Standard Deviations", "Expected Return", "Theta"]
    )
    SharpeFrontier.to_csv("SharpeFrontier.csv")


if __name__ == "__main__":
    main()