Black-Litterman Weights Don't Change for Assets Without Views

Question

I am using Idzorek 2002 (https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Idzorek_onBL.pdf) as a reference to implement the BL model in R.

I have specified the model in its standard form, but I find BL does not alter weights for assets classes where views are not specified. This is addressed briefly by Idzorek in footnote 11 of the above paper:

The fact that only the weights of the assets that are subjects of views change from the original market capitalization weights is a criticism of the Black-Litterman Model. Critics argue that the weight of assets that are highly (negatively or positively) correlated with the asset(s) of the view should change. I believe that the factors which lead to one’s view would also lead to a view for the other highly (negatively or positively) correlated assets and that it is better to make these views explicit.

Idzorek makes the reasonable argument that assets highly correlated to those for which you have views should therefore themselves have views. However, the trouble with this is that it assumes you have a grasp on cross-correlations between asset classes a priori. What if you have a portfolio with 100 assets? I thought the whole point of the BL model was to take full advantage of the covariance matrix such that if I want to overweight asset A it will tell me how to size the overweight and what to underweight to "finance" the overweight position in A (presumably an asset negatively correlated to A).

Without this ability, it is hard for me to see why BL is so useful. Is there a way to specify BL such that asset classes without views have flexible weights?

Thank you.

Answer 1

So, in short, you've told BL that Exxon sucks, but you haven't specified the same for Chevron or Conoco! So the model sells XOM, but maintains the longs in the others given the more attractive pairs-trades given their correlations ;-)

Mathematically, it makes perfect sense... the question is how much (and how) to attribute to "oil stocks" versus to Exxon specifically. You could BL-penalise stocks pro-rata to their beta of market-relative returns to XOM-relative. You could penalise stocks based on their principal-component loadings to XOM. Either would punish "things that look like XOM" in general, rather than XOM specifically. They create "views" for things like Exxon.

Answer 2

Is there a way to specify BL such that asset classes without views have flexible weights?

Black-Litterman has uncertainties on its views as well, so if you increase uncertainties for some highly correlated assets, the weights will be more "flexible". You probably also want to increase uncertainty in your "picked" assets where you have nontrivial views.

Of course, the hoped-for outcome is that assets highly correlated with your outperformer will get extra weight after you set all this up. That will not necessarily happen since the high correlations simultaneously make those correlates look good as hedges for your picked assets.

As an alternative, you could use your covariance matrix and initial picks to set up a maximum likelihood estimate of the altered set of means. Warning: this implicitly involves matrix inversion and might be a touch unstable.