Portfolio Optimization with Tracking Error Constraints

An article in May 2010 Financial Analysts Journal revisits Portfolio Optimization with Tracking Error Constraints. The author provides a good discussion of some geometric concepts for visualizing constant tracking error efficient frontiers and constant information ratio frontiers. New ideas for visualizing financial data are something I'm interested in right now, either in the charting or the mathematics.

Visualization and Other Ideas

I am on a bit of kick on visualization of data now. It ranges from clipping interesting art work on asset allocation, performance or risk data; as well as geometric approaches to working with this type of data. I am thinking I'll try and put together a bit of a gallery at some point. I am hoping to include a lecture on this topic for the Financial Informatics class at BU, it seems a pretty natural fit.

Speaking about the class, this semester I think we'll be more hands on with some excel plugins, I'm putting one together from my java analytics using ikvmc and excel-dna, both excellent open source projects, together they make it a piece of cake to put together a really easy to use Excel add-in. When I get it packaged I'll put it up on sourceforge with the rest of my code.

Max Golts has a paper at ssrn, and he's done a few presentations on the topic for the Boston and New York QWAFAFEW groups which have been interesting. One of his thrusts is that if you look at the eigenvectors of the covariance matrix you want to align your asset weights with the more significant ones, rather than the least significant ones. If you're asset allocation lines up with the least significant eigenvectors you are working with the noise. It has taken me far longer than I hoped to understand what he's doing, but I am on track to eventually have some code to implement his approach.

More insight on Diversification or Lack There of

I recently came across this paper from the folks at PIMCO on diversification and how market regimes. Their thrust is that most assets have significant exposures to global equity factors. During low volatility regimes the returns due to this factor exposure get chalked up to manager expertise, but in fact it's just the unexpected equity factor. During stress regimes the exposure to this global equity factor causes correlations between assets to rise and diversification to fall just when it's needed most. I need some more time to parse it out a bit more, but it seems an interesting approach to the problem of increasing correlations between assets during stress regimes.

Custom Benchmarks

Went to an interesting talk at the Boston QWAFAFEW meeting by David Kane. It was based on this paper.
The basic thrust was that if you construct random benchmark portfolios with all aspects of the portfolio save for those where the manager claims skill the same, and those aspects where the manager claims skill are randomized across the universe you can see what the manager is really doing.
Of course this requires position level transparency to carry out as just described, but it seems like a powerful technique. If you are going to work with a portfolio where you don't have position level transparency, you could apply a factor model and potentially get similar results.

Updated the paper on tau

Ok, my focus is much clearer in the updated version of the document. Definitely quantified the impact of the various reference models and tried to make the concept of tau more clearly defined.

Will publish this to ssrn in the next few days.

New paper on Black-Litterman tau parameter

Finally got this paper put together enough to post for some feedback.

The crux of the paper is either to use tau properly or just drop it altogether, but no sense messing around with tau when you don't even need to. Most authors would do better to drop tau from their model and use what I call the Alternative Reference Model. I think Atillio Meucci uses the same name for it, we have some agreement that it is a different animal and can be clearly defined.

I expect to make a small set of edits/updates to this paper over the next week and then get it posted up on ssrn with my other paper on Black-Litterman. Mean while the big paper will also be shortly getting some edits. I've had many people tell me over the past year or areas which are not clear, mistakes or ways to simplify the paper and I am going to start making those edits. Also came upon some interesting new metrics during the research for the tau paper. I'll leave that for another time when I get the edits made to the paper.

William Sharpe's Adaptive Asset Allocation

Just read William Sharpe's article in the latest FAJ and it seems like an interesting idea, Adaptive Asset Allocation or the concept of adapting a static asset allocation to the current market conditions based on the conditions in place when the allocation policy was determined. It frees the investor from having to rebalance as the market moves, though it seems like the literature has a lot to say about the value of rebalancing. Sharpe calls that a contrarian strategy, buying losers and selling winners and that certainly seems correct. He makes some good arguments that it cannot be an equilibrium strategy, if everybody tried to sell the latest winners or buy the loser it the market wouldn't clear. There needs to be a mix of momentum investors in order to keep the market liquid. Being an equilibrium type this argument is appealing to me on some level.

Didn't see any historical results in the paper, so I guess that has been left up to somebody else to run the analysis and see how the Adaptive Asset Allocation process works over time in order to really judge it.

I am still digesting MarkKritzman's article in the March/April FAJ which told us about the 1/N fallacy. He did lots of historical analysis and showed several portfolios beating the market portfolio and I expect that they made use of rebalancing, but he didn't spend a lot of time on simple 60/40 type portfolios.