Portfolio Optimization

PortfolioProblem

Description

Defines the portfolio optimization problem.

Fields

• returns::Matrix{<:Real}: A matrix of historical returns for the assets.
• thresholdreturn::Real: The minimum expected return required for the portfolio.

PortfolioResult

Description

A structure to hold the result of the portfolio optimization problem.

Fields

• weights::Vector{Float64}: The optimal weights for the assets in the portfolio.
• expectedreturn::Float64: The expected return of the optimal portfolio.
• model::JuMP.Model: The JuMP model used to solve the problem.

solve(problem)

Description

Solves a portfolio optimization problem given by an object of in type PortfolioProblem. The optimization problem is formulated as a quadratic programming problem where the objective is to minimize the portfolio variance (risk) subject to constraints on the expected return and the weights.

Mathematically, the problem can be stated as:

Minimize: w' * Covmat * w Subject to:

• sum(w) == 1 (the weights must sum to 1)
• sum(w[i] * means[i] for i in 1:m) >= thresholdreturn
• 0 <= w[i] <= 1 for all i (weights must be between 0 and 1)

Where:

• w is the vector of asset weights
• Covmat is the covariance matrix of asset returns
• means is the vector of expected returns for each asset
• thresholdreturn is the minimum expected return required for the portfolio

Arguments

• problem::PortfolioProblem: The problem in type of PortfolioProblem

Returns

• PortfolioResult: The result of the portfolio optimization problem, containing the optimal weights, expected return, and the JuMP model used to solve the problem.

Example

using OperationsResearchModels

problem = PortfolioProblem(rand(100, 5), 0.01)
result = solve(problem)
println("Optimal Weights: ", result.weights)
println("Expected Return: ", result.expectedreturn)