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, December 27, 2007

Two-Factor Black-Litterman Model

So being done with Qian and Gorman has left me free to noodle with Krishnan and Mains 2005 paper on a two-factor Black-Litterman model. I'd like to try and replicate their results from the beginning, but that requires a lot of data. I've been able to take what data is in their paper and their equations and reproduce their results which I think is a good start.

The last bit of Black-Litterman that has piqued my interest is the fact that one should be able to back out the implied views from a return estimate vs the equilibrium values. Black and Litterman show this in their paper, but don't cover the math at all so it'd give me some room to run working on it. I expect it might be interesting to see the results as well.

Once this is done I think my Black-Litterman work will be on hiatus for a while so I can focus on some other things, my Entropy Diversification paper is calling out to really be finished as it's been suffering in a draft format for some time. A big apology to anybody who's downloaded it expecting it to be polished. Ouch!

Wednesday, December 26, 2007

Black Litterman insights

So I've been pondering Qian and Gorman's paper for the last week and finally made some progress tying it all back to the same Bayesian equations. I also came across an interesting note in their paper about the weights of assets not changing under certain circumstances. Sure enough, working back with the He and Litterman data I found that updating the posterior variance means that only assets with a view have their weights change. If you don't use an updated posterior variance as is more commonly done, the weights of all assets might change. It isn't always a large change, but it's easy enough to see it.

So now I am going to back track and read all the papers to see if any of the Black-Litterman specific papers observed this weight change or not change.

Over the weekend I also found what I think is the original Black-Litterman paper in the Journal of Fixed Income, September 1991. I'm hoping reading it might provide a few more insights into what they were thinking about when they came up with this model.

Wednesday, December 12, 2007

Updated Black-Litterman content

I'm slowly getting more of the Black-Litterman content from my paper converted over into webpages and putting it up on the site. Just added two more pages, cookbook which describes exactly what one needs to do to implement Black-Litterman in terms of variables and formulas, and methods which describes the differences between the papers I've worked on.

I still chase the holy grail of reproducing the results from the original paper. I've tried several approaches to the reverse optimization and just can't get crank the weights from the returns or vice versa. I guess next I need to figure out what values are off a bit in the covariance matrix, or in the weights or returns.

Sunday, December 9, 2007

Black-Litterman update pushed

I get a little manic the last few days of working on these papers (which explains why I'm not sleeping now I guess). I just pushed some new content to the site, mostly in the form of an update to my Black-Litterman paper. I've added derivations for the BL master equation in the Bayesian space, but it's not too much work to plug in the B-L expressions, or just re-work them with the Black-Litterman variables as desired.

I've been reading an interesting book, "Advances in Portfolio Construction and Implementation" edited by Satchell and Scowcroft. For me the interesting chapters have been looking at State Preference theory and how by using ranking rather than absolute values you get more robust optimization results. I've built a bunch of code to do this, but still have the problem in the end of how to get back from rank space to show the results. Anyways, interesting book and has some chapters I didn't expect to see in it which was a pleasant surprise.

Monday, December 3, 2007

Back to Black-Litterman

I pushed the draft of the Entropy paper to the website, but it is very rough. It's also a little discouraging as I was hoping for more statistically significant results. I did build an Interior Point solver with the KLIC measure as the objective and a quadratic constraint on the variance, but it seems there are some problems with the code or the math as the results are strange.

In the meantime, I am in the process of revising the Black-Litterman paper and adding some more content. I've decoded the Fusai-Meucci paper, "Assessing Views" given their MATLAB implementation. Now if only I could reproduce the original Black-Litterman results.