Tuesday, December 31, 2013

A great example of why BF is better than BHB

The late Damien Laker once opined that there was no difference between the two "Brinson models," Brinson-Fachler and Brinson-Hood-Beebower. I went out of my way to enlighten him on this subject, pointing out that the allocation effect for the latter uses only the benchmark sector return while the former uses the benchmark sector return minus the benchmark return:

As a result, there can be sizable differences in the results and, at times, even sign-switching!

The BHB model rewards investors who overweight positively performing sectors, while the BF only does so if the sector outperforms the benchmark. When discussing this in our training classes, I explain that if all the sectors are positive, BHB would want the investor to overweight them all!

The WSJ today reported that all 10 stock sectors of the S&P 500 will, in fact, have positive gains for this year ("All 10 Stock Sectors Post Gains in Big Year." Dan Strumpf Page C4).

Thus, we have such an occurrence when the investor is supposed to overweight everything; but how can they do this without borrowing money? They can't. BF, more correctly, I believe, wants the investor to only overweight those sectors that fall above the benchmark itself.

Thus, we have a perfect example to draw upon to demonstrate the superiority of the older (by only one year) model, which Gary Brinson crafted with Nimrod Fachler.


  1. Two thumbs up on this. BF is not simply "different" than "BHB." It's BETTER... much better. Like the difference between being right and being wrong.

  2. excellent comment, as usual; thanks!

  3. The differences you see between BHB and BF exist only because you evaluate properties that are not decisions. The asset allocation decision to allocate money between equities and bonds is a single distribution decision. It is not two separate decisions, one to allocate money to equities and another to allocate money to bonds. For instance, once one allocates 60 % of your money to equities it is not a separate decision to then allocate 40% of your money to bonds. Thus, I believe that Laker was correct to say that there is no difference between BHB and BF because at the level of actual decisions they do in fact give identical results. Only at the economically meaningless level where one decomposes the meaningful result to the level of the individual assets do they create the differences you describe.

  4. Thank you for your comments. I do object, however, to what you suggest. All one need do is look at the formulas in order to see there is a vast difference. And while 60/40 equities and bonds may be characterized as a single decision, you are failing to also consider other asset classes that might be considered, such as cash and cash equivalents, and so the assumption that the 40% is not a separate decision is potentially invalid. Plus, if one runs BHB or BF against such decisions, considering the benchmark equity and bond returns, they will see different results. The second decision, which you fail to consider, is selection, which is also a component of both, though the two models agree on the math for this. I would suspect that an investor does not make a single decision (let's put 60% into equities) but rather two decisions: that is, how much to put into each, taking the anticipated future results of both, vis-à-vis, the goals of the client as well as the expectations for each market. If the investor is solely thinking "how much do I put into stocks," then they are not doing justice to bonds, I would think.

  5. Laker has perhaps made varying comments on the subject. But I have heard him say that the two formulas produce identical results at the overall level (which is true and can be mathematically proven). But if you want meaningful results at a lower (e.g., sector) level, then *of course* you would want to use BF. I would agree with this position. There might be isolated situations where BHB is useful, but I suspect not to most active portfolio managers.

  6. While it is true that they sum to the same values (that is, the sum of the allocation effects of the individual components are equal), the value of the difference lies in how the divisions (be they asset classes, sectors, industries, etc.) are evaluated. Yes, we can say that overall the allocation effected yielded X% of the excess return, and this result will be identical for each; but in most cases we also wish to investigate the underlying parts of the portfolio. He made a broad statement that there isn't a difference; on this point he erred.

  7. I never met or talked to Damien Laker, but based on his writings on the subject (e.g. the paper Arithmetic Performance Attribution and many places of his former web site) he wouldn’t object that the two formulas in your post give different results for a sector’s allocation effect. In fact, he points out in some detail why the second one (BHB) shouldn’t be used at all.

    Wherever he suggests a formula for the sector allocation he uses the first one (BF). And he writes that “the outputs from the so-called BHB asset allocation calculations seem to produce numbers that can be at wild variance to what one expects based on the principles of portfolio management.” And he also states that the task of the asset allocator is to be “underweighting sectors whose benchmark return will be lower than the overall benchmark return, and overweighting sectors whose benchmark return will exceed the overall benchmark return”.

    Actually my guess is that Laker would have agreed with you that your example in the post is an excellent one to show why there is only one correct way to calculate the sector allocations. He might have objected, though, to your use of the labels BF and BHB since he argued that the latter was never intended by Brinson to be used on a sector level, only on a top level. Not because the two formulas in your post don’t give different results, but rather from the perspective that to even regard BHB as an attribution model of its own is to give it way too much credit!

    Thanks for an interesting post!

  8. Thanks for your note. I didn't realize that this post would focus so much on Damien's writings. He wrote a piece that he posted on the Internet, which specifically challenged the notion that there was a difference between the two approaches. I reached out and discussed this with him. I suspect the piece you're referring to was published after his initial "there's no difference" piece. I'd like to think that I may have been one who persuaded him of the difference. I knew Damien and actually did a consulting assignment for him around 20 years ago (evaluating his system, which he later sold to Barra). Although I didn't see him often (given the rather long distances between our respective home bases), we did meet a few times, and chatted often via the Internet.


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