Setting Up Portfolio Optimization with a CVaR Constraint

Summary

The document addresses portfolio optimization where conditional value at risk must stay below a specified portfolio-wide limit. Its central setup is to choose variance as the objective while imposing CVaR as a constraint, alongside a budget constraint and bounds on the portfolio variables. It identifies scenario returns, expected returns, and functions for CVaR, linear constraints, and standard deviation as inputs to the optimization problem.

The response presents this as a way to formulate a constrained portfolio problem rather than minimizing CVaR itself. It points to a specialized commercial optimization product and briefly lists the data and problem components needed to use it. No complete solver implementation, mathematical derivation, or empirical example is provided; the response says a fuller illustration would come later. As a result, the material is a high-level formulation outline, and it does not establish that the suggested setup is suitable for every portfolio or solver.

Key ideas

• A portfolio-wide CVaR limit can be imposed as a constraint in an optimization problem.
• The response proposes variance as the objective and CVaR as a risk constraint.
• The listed setup also includes a budget constraint and box bounds on portfolio variables.
• Scenario returns and expected returns are among the required input data.
• The document gives a software-oriented outline rather than a derivation or worked implementation.

Tags

# Portfolio optimization with Portfolio CVaR Constraint


# 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 by Markus (score 0, accepted)

https://quant.stackexchange.com/a/11035

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.