Choices, Opportunities, and Solutions

To date I’ve invested approximately 800 hours developing and testing the heuristics and algorithms behind HALO. Finding exact solutions (with respect to expected-return assumptions) to certain real-world portfolio-optimization problems can be solved. Finding approximate solutions to other real-world portfolio-optimization problems is relatively easy, but finding provably optimal solutions is currently “impossible”. The current advanced science and art of portfolio optimization involves developing methods to efficiently find nearly optimal solutions.

I believe that HALO represents a significant step forward in finding nearly-optimal solutions to generalized risk models for investment portfolios. The primary strengths of HALO are in flexibility and dimensionality of financial risk modeling. While HALO currently finds solutions that are almost identical to exact solutions for convex optimization problems; the true advantage of HALO is in the quality of solutions for non-convex portfolio-optimization problems

Do you know if your particular optimization metric can be articulated in canonical convex notation? I argue that HALO does not care.  If it can be, HALO will find a near-optimal solution virtually identical to the ideal convex optimization solution.  If it cannot be, and is indeed non-convex, HALO will find solutions competitive with other non-convex optimization methods.

It could be argued that “over-fitting” is a potential danger of optimal and near-optimal solutions. However, I argue that given a sufficiently diverse and under-constrained optimization task, over-fitting is less worrisome.   In other words, the quality of the inputs greatly influences the quality of the outputs.  One secret is to supply high-quality (e.g. asset expected return) estimates to the optimization problem.