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.

Thursday, May 28, 2009

Robustification of Black-Litterman

I'm reading a paper, "Comparison and robustification of Bayes and
Black-Litterman models", by Schottle, Werner and Zagst
. It is interesting in how they build up a Bayesian framework to get uncertainty in the variance of the distribution. Usually in Black-Litterman, the only uncertainty in the variance comes from the uncertainty in the estimate of the mean, so this is a way to add another degree of freedom to the problem. I'd like to build up the MATLAB code to work on this and see how it goes.

Of course, I've also come across some interesting papers on factor models with Black-Litterman and need to digest those. So many things to do. I'm adding links and quick descriptions of all the papers to my RSS feed, so you can pick the papers up from there if you are interested.

Saturday, May 23, 2009

Qian and Gorman

I've been working on understanding paper for oh so long, and finally figured it out. Not sure if it's a testament to other than my follow through on the task, but it feels nice.

It seems they came up with a posterior variance formula different from the Black-Litterman model's posterior variance, and with some less than optimal characteristics. It doesn't include mixing, and it doesn't generally decrease because of the mixing, it can increase. They describe it as allowing the investor to specify views on covariance, but I am stuck on the math. It is not so obvious how the investors view mixes (at least to me), for example any non-zero investors view on variance will increase the posterior variance.

I need to read a bit more on how it should be used in order to really understand what they've done.

I've added a new section to the paper covering this analysis, but in the end it's just tying up a loose end and not really adding anything new to the puzzle.

I've also come across some more new papers, including a few out of Lehman in 2007 which cover some intriguing ways of handling factor models. Factor models and Black-Litterman is definitely an area that I am interested in.