Jay's Asset Allocation Blog

Blog about my off-hours work on the problem of Asset Allocation including but not limited to Portfolio Optimization algorithms, algorithms and approaches for improved estimation of Asset Allocation inputs and other potentially related items.

Monday, November 19, 2007

Interior Points Method Entropy Objective Function

Working to get this sorted out, it will fit into my framework well and allow arbitrary linear constraints; plus I'm hoping to wrap all the quadratic constraints into a new solver that is more general purpose, but that will have to wait. I should have it done by the end of the holiday weekend, or at least that is my goal.

I've been in touch with the authors of the recent paper on this topic and they are working on a way to compute the variance to use for the constraint as well. For the moment I have settled on using a value which is a proportion of the optimal variance for the return and constraints, meaning I solve once using the regular M-V solver, essentially the same problem, then I scale the variance and stick it into the entropy solver and solve again.

Right now I have what looks like a single problem I'm hoping to solve. The constraint on variance seems only to work as a penalty term in the objective, meaning the higher I set the required variance the more distance between the M-V efficient frontier and the entropy efficient sub-frontier. I can live with this so long as I can explain it.

Sunday, November 11, 2007

Entropy paper draft finally available

Writing this paper has been harder than I expected, lots of interesting things learned along the way. Diversified Mean-Variance a first draft is finally up on the website. I ran across a new paper on Entropy objective functions, it is not freely available and I am in the process of reviewing the results shown in the paper. It seems there must be a way to introduce a reasonable constraint on the portfolio variance, my first implementation was Newton's method, but it just doesn't seem as rich as Interior Points so I'm building a better mousetrap.

I've also begun to understand why I like Black-Litterman and entropy. There is a consistent thread of information content in both methods, in Black-Litterman we have the variance of the estimates, and in entropy we have the entropy or distance between two portfolios for the results. I'm thinking it might be interesting to try and calibrate the output entropy based on the entropy of the inputs.