0
$\begingroup$

In their paper titled "Trend-Following meets Risk-Parity" UBS proposed an optimization algorithm for performing risk budgeting for long short portfolios. The formulation was as follows:

$$ Maximize \sum |\mu_i| \log(|w_i|) $$ Subject to:

  • $\sqrt(w^T \Sigma w) \leq \sigma_{max}$
  • $w_i \gt 0, if \mu_i \gt 0$
  • $w_i \lt 0, if \mu_i \lt 0$
  • $\sum |w_i| =1$

The optimization problem is not convex. What is the best way to solve it? Any code suggestions?

Improve this question
$\endgroup$
2
  • 2
    $\begingroup$ Without knowing the properties of the problem, I guess grid search is the best you can do. Do they mention anything on the paper? $\endgroup$ Commented Jan 28 at 19:34
  • $\begingroup$ Why is the problem not convex? You are given the $\omega_i$ and $\mu_i$ and you can just create a new weight $\gamma_i = | \omega_i |$ and this transformation just carries a few sign changes through everything, or am I missing something? $\endgroup$ Commented Jan 31 at 22:12

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.