Thursday, December 8, 2011

Dealing with zero weights

I got an email from a client recently, asking how one should treat the case where a manager has zero exposure to one of the sectors in the benchmark.

If you are using one of the Brinson models and simply use the formulas as written, you'll find that the interaction effect gets most of the credit (or blame) for the decision. But does this make any sense? No!

And so, you may want to shift the interaction results to one of the other effects: selection or allocation.

Now, which do you think it should be? [pause, to allow you to reflect a moment] I think allocation, since the manager made the decision to go void in the sector. Thus, I would move the entire interaction effect there.

I'll address this in greater detail in this month's newsletter.


  1. Stephen Campisi, Scourge of the Interaction EffectDecember 8, 2011 at 9:03 PM

    No! No! NO!!

    Your analysis perpetuates a persistent misperception among performance personnel, who are unfortunately afflicted with an inertia around clinging to errors that are repeated, chief among these errors being the ridiculous attribution model that includes an attribution effect. Contrary to popular opinion, interaction is simply an error in the Brinson model that arises from a lack of understanding of the investment process. It is silly to argue over where to assign the interaction effect, since there is no value in assigning an error term. Everyone's time would be better spent in correcting the error. An analysis without an interaction effect places the attribution effects into those categories that represent legitimate investment decisions, namely allocation (where to invest capital) and selection (which specific investments to make which fulfill the allocation decision that was already made.) First you allocate capital and then you select investments. You can't "un-ring a bell" and so you can't reverse the allocation decision that was already made when you calculate the selection effect. A correct interpretation of selection is the joint decision of BOTH the portfolio manager and the analyst. The only value in a specific interaction effect is to provide supplemental information to break out the manager's impact from the analyst's impact. However, BOTH participants have a role to play in the specific return attributable to both of these decisions. In fact, the sector weight is often the result of the selection decision involving HOW MUCH of each security is to be bought. In such a circumstance, the allocation decision is not so deliberate, but rather is a secondary consequence of selection. This is further proof that how much of each issue is held is part of the selection decision, and so the portfolio weight should be used in calculating the selection effect (not the benchmark weight.)

    Imagine your scenario involving the "missing" sector being the best sector of all. First, the correct interpretation of no portfolio exposure to a benchmark sector is that there is no weighting and no return, both of which should be represented by a zero in the portfolio. There are no "null" values because the sector return and weighting are relevant to the benchmark. They are relevant to the portfolio as a reference of relative exposure, and so a zero value is appropriate, and not a null value. (Again, "null" means "not relevant to the analysis;" if that were true it would be excluded, not included with a non-zero null value.) So in this example, there would appear to be a negative relative selection value between the portfolio and the benchmark, but accompanied by a zero weight, the selection effect is zero. Using the benchmark weight creates the error of having a large negative selection value, an error that is "corrected" by introducing yet another error through the interaction effect. Two wrongs don't make a right. This is another example where interaction is revealed to be nothing more than an error.

    "Where to assign interaction" is rather like: a) sweeping dirt under the rug or b) debating how many angels can dance on the head of a pin. (Of course, everyone knows that angels sing, but don't necessarily dance - hard to do with wings, I guess...) Let go of the past. Look forward to a bright and clear future without the confusion of the "interaction error." Now THAT'S a good name for it!

  2. While we (Steve and I, that is) will agree on virtually everything related to performance, we won't on this matter. Interaction DOES exist, whether we like it or not. The authors of the models that are most commonly used (both beginning with Gary Brinson) saw the wisdom of this effect. To combine it with selection (by using the portfolio weight) clouds the effect with a touch of allocation.

    There is no "perpetuation" on my part: I am holding true to the authors' intent, and am in agreement with them. The beauty of this topic is that firms can decide how they wish to treat it. I am a huge fan of selective adaption of the effect (as I wrote in my article on the "black box approach to interaction"): just add some true logic to the process, so that the effect isn't slammed into interaction without any thought.

    Sadly, though we agree on SO much, not everything (but the same fact holds with my wife and me, too, so you're in good company).

  3. Stephen Campisi, Friend of Dave and Enemy of InteractionDecember 10, 2011 at 10:37 AM

    We also agree on one thing from your initial posting: a zero portfolio weighting to a benchmark sector should be reflected as an allocation effect. That should be obvious to anyone who is paying attention to the investment process. The decision to exit a benchmark sector is by definition an allocation decision. But there still should be NO selection effect, since you haven't selected any issues.

    But even in our coincidental agreement, we have a disagreement. You're missing the fact that you have several "black swans" in your analysis which definitively REFUTE the interaction effect. (While we can't necessarily prove something, we can disprove it by showing evidence of its contradiction. So, we can't prove that all swans are white, but we can prove that they are not by simply presenting a black swan.)

    First, any attribution term that requires judgment to assign it properly to the other effects is purely subjective, and therefore not a correctly defined effect. If it were correctly defined, it would not require moving its effect to other attribution terms, where they belong.

    Second, consider the true nature of the selection effect and you will conclude that your example again refutes the interaction effect. "Selection" is meant to measure the effect of differences in return between the securities held in a portfolio and those held in the benchmark. In your example, you don't hold any securities, so you can't have a difference in return. To have a difference between two things, you have to hold both things. You should not have a selection effect when you haven't made any issue selections. That's just one flaw in the interaction effect - it measures what is not there.

    You didn't hold these securities at the weight of the benchmark, but you pretend that you did so that you can evaluate the effect of the analyst who made the stock recommendations. Well intentioned, but wrong. You see, we're supposed to be measuring the effect of selection ON THE PORTFOLIO - we're not running a "one off" evaluation of the skill of your analysts. You've got to get the question right BEFORE you start calculating things.

    So, we can end with agreement on this: the interaction effect does have usefulness in breaking out the impact that the analyst and portfolio manager have in producing a selection effect in the portfolio. They both play a role: the analyst selects names and the managers approves the selections and decides how much to buy. Both parts are relevant and could be measured. So, the interaction effect is (at best) a useful sub-component of selection but NOT a portfolio effect.

    Of course, the third "black swan" that you've never acknowledged is the erroneous and ridiculous result that it produces when a manager makes two wrong decisions: under-weighting the best sector while purchasing the worst securities in that sector. It's obvious that BOTH of these decisions produced a NEGATIVE relative return. Yet when you multiply the two negative differences, you get a POSITIVE relative return effect. Now, how can the "interaction" of two bad decisions produce a good result? How can two decisions that subtract alpha somehow add alpha? Now, I would expect a skillful debater and interaction enthusiast like you to quip that "since you picked bad stocks, it's better that you didn't hold a lot of them, so it's not as bad as it might have been." But let's be honest and say that this is not the same as a positive outcome. "It could be worse" is little comfort when your decisions lose money. Even if you had that handy comeback, you would still have to justify the other side of it: "Since you held too little of the best sector to invest in, it's good that you bought the worst stocks." Sorry, "that dog just won't hunt!"

  4. Thanks Steve for your note.

    To your first point, you don't need to have judgment; you can continue to show it separately. I happen to feel that one CAN assign it, if they wish. One needs to interpret it, just as one would interpret any effect; interaction is a bit more challenging, but still do-able.

    I believe the true nature of the selection effect is to focus on one thing: selection, without carrying along the manager's allocation decision, too (via the portfolio weight). If one wants to really isolate the selection, one must use benchmark weight, which results in the interaction effect. Weighting and selection are two different decisions: don't mix them.

    I have acknowledged the third point (I am pretty sure it's addressed in my article, too). Your characterization of them being "two wrong decisions" may not be correct: "underweighting" is a "wrong decision" (Wp-Wb)? How's that? Granted, underperforming (Rp-Rb) would reflect poor performance, but perhaps the underweighting is then a good thing, yes (one wouldn't want to overweight when they didn't do too well picking the stocks, would one?)

  5. OK, two things:

    First, let me be as gracious as you were in your response by acknowledging your point that the evaluation of selection skill should not always be influenced by the prior allocation decision. I have seen an instance where this makes perfect sense, but it was in the context of total portfolio attribution, not the analysis of a single asset fund, which is your example. I was evaluating the three sources of excess return in a multi-asset portfolio - these were a) tactical asset allocation b) tactical sector allocation and c) manager selection. We informed the client that the performance impact from hiring active managers within each asset sector (i.e. large growth, small value, etc.) produced a certain amount of excess return BUT the amount of excess return was influenced by the weighting of their sectors. IN THIS INSTANCE it made sense to separate the decision to hire the manager from the decision to overweight that manager's active effect. In this exceptional case, the interaction effect would have been helpful in isolating the excess return attributable to each manager's investment skill.

    HOWEVER, in the case of a "stock picker" within a mandate, both the decision to hold a certain stock and the decision of how much to hold are BOTH part of the process of SELECTING a stock. You can't hold a stock unless you allocate a certain amount of money to it, and as noted before, the sector decision is often simply the result of the amounts held in each stock and not the other way around.

    Now as to your first and third points: Sorry, no sale. "Just because you can, doesn't mean you should." Or should I say "YES WE CAN" assign the interaction effect, but this is simply proof that a) no one really gets it, even after all these years and countless less-than-helpful explanations, and b) if it had been correctly defined, there would be no need to assign it to those attribution effects that do make sense.

    Your third point is simply wrong. Under weighting the best sector IS a "wrong decision." Or can you justify putting more money into sectors with returns below the average? As its name implies, the "interaction" effect is explained as the interaction of TWO DECISIONS (allocation and selection) and in my Black Swan example, BOTH of these decisions produced relative under performance, and so I've classified them as "wrong decisions." In fact, these were already assigned to the "naughty list" in their allocation and selection effects.

    So, let's agree that you've convinced me that interaction has usefulness as a supplemental analysis for separating the effect of the analysts' selection decisions from the manager's allocation decisions. However, it seems I've still "got some wood to chop" in convincing you of the error of your ways with regard to the value of interaction as a portfolio effect... and that "two wrongs don't make a right..." and that just because something was published in an article by a famous guy, it doesn't make it right.

    When we're done with this, we'll hash out our differences on BHB, yet another error by Mr. B.

  6. (Interesting choice of names!) Thanks! I'll be touching on this a bit more in this month's newsletter.


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