Portfolio optimization with Portfolio CVaR Constraint

I wanted to optimize a portfolio based on a portfolio-wide CVaR constraint (i.e. $CVaR_p \leq 0.08$). Unfortunately, I only find solution that minimizes the entire CVaR of the Portfolio.

Do you mind telling me if I need to add a restriction or how to change the utility function?

Here, you find the initial data and optimization Link

Edit

I removed some stupid elements. I will give a full answer once I finished the semester at the university.

Links

Paper Portfolio Optimization with Conditional Value-at-Risk Objective and Constraints

Answer

Writing a linear solver with a CVaR-Constraint is time-consuming. "Portfolio Safeguard" of "American Optimal Decision Inc." is optimized for such kind of problems.

In order to get it work, you must add the following elements:

Data

• matrix_scenarios (a matrix of all your returns)


• matrix_returns (a vector containing the expected returns)

Function

• CVaR (cvar_risk)


• linear (linear)


• standard deviation (st_risk)

Problem

• variance as objective


• CVaR as constraint


• budget as constraint


• Box variables

Optimization

• you can run the optimization by pressing CTRL + o

Later I will illustrate the process.