Tuesday, August 2, 2011

Shall we interact?

I had a conversation with a client last week, where we addressed a variety of aspects regarding performance attribution. They asked how common it is for firms to report their interaction effect. While I don't believe we've addressed this question in any of our surveys, my gut tells me that most firms avoid doing so, in order to avoid having to explain it.

What is interaction? All one need to is to look at the formula to answer this: it's the difference in weights (portfolio minus benchmark) times the difference in returns (again, portfolio minus benchmark); and these components represent allocation and selection, respectively. And so, it's the interaction of these two decisions.

Why is it needed or why does it appear? Because the individual effects (allocation and selection) are isolated from one another, so as to not allow the influence of the other to impact its results (e.g., the selection effect is the difference in returns times the BENCHMARK weight, not the portfolio, since portfolio weight would reflect allocation). But this answer fails to mean much to most folks, thus the desire to avoid it.

The topic of whether it should be included or not is often hotly debated, as there are passionate voices on both sides of this issue. I've written an article on the topic, as have others, including my friend, Steve Campisi. In the end it's up to the firm to decide how they wish to handle it.

We will include a question on this topic in our upcoming attribution survey; more details to follow. We hope you'll join in, as we want as many participants as possible, all of whom will receive a complimentary copy of the results.


  1. Stephen Campisi, Intuitive Performance SolutionsAugust 2, 2011 at 11:30 AM

    Great timing on this posting. If we combine your Interaction post with your prior posting regarding "Asking the right questions" then I think we can make some headway (finally) on deciding when an interaction effect is appropriate. I re-read the 1985 Brinson paper the other day and he mentions having an unbiased calculation of the selection effect. That is, he doesn't want the sector weighting to leverage or deleverage the impact of stock picking. That's a fair point - he wants to evaluate the analysts. He is really clarifying the question, which is "Are my analysts good at stock picking?" However, as a part of portfolio attribution, the appropriate question is this: "What was the impact of stock picking on the total portfolio?" To answer this question, you have to include the impact of the portfolio manager, who may have decided the weighting of the sector and you must use the portfolio weighting for this. So, if you want to separate out the selection effect "attributable" to the analyst, then use the traditional approach of applying the benchmark weighting in the calculation. This means that the so-called "Interaction" effect answers the other question: "What was the portfolio manager's impact on the selection result?" And, when you sum the "pure selection" effect and the "Interaction" effect, you get the right answer to the right question, which was "What was the impact of implementing the sector strategy actively instead of passively?" which is: (Portfolio weight times (Portfolio sector return minus Benchmark sector return.)) If you want to run an attribution on this active impact, then you have an amount attributable to the stock pickers (Benchmark weight times (Portfolio sector return minus Benchmark sector return)) and an amount attributable to the portfolio manager which is the so-called "interaction effect" calculated as: difference in weightings times difference in returns. (Of course, this is the same as subtracting the pure selection effect from the total selection effect.)

    So, it's not about calculations; it's about getting the question right BEFORE you start calculating.

  2. Steve, thanks for your comments. I remain unconvinced, but still very much value your insights. Thanks!

  3. Stephen Campisi, Intuitive Perfomance SolutionsAugust 2, 2011 at 4:27 PM

    Still unconvinced that Interaction has (at best) limited value? Then consider this scenario. I was teaching the basics of attribution to a colleague of mine, someone well versed in investments and the processes followed by active equity managers. She pointed out that many managers are really "bottom-up stock pickers" and that their decision to "select" a stock always includes the weighting of that stock relative to the benchmark. This weighting indicates their degree of conviction in the stock, with a higher weight allocated to stocks in which they have a higher conviction. So, she noted correctly that the weighting of a stock is a critical component of the stock selection process. In fact, the sector weighting is often nothing more than a by-product of the stocks the portfolio manager happens to like in a particular sector. In that case, the sector weighting is a result of stock selection, and not necessarily a specific and deliberate decision by the portfolio manager. When you attribute this active equity process, you see that the stock selection effect is modeled correctly by using the portfolio sector weighting (AKA the sum of the weightings deliberately chosen for each stock.) And of course, this removes the presence of the Interaction Effect. So, it's not that "pure stock selection" is calculated using the benchmark weight. Rather, you get the true selection effect when you use the portfolio sector weighting, understanding that how much of a stock you own is as important as which stocks you own.

    While many performance analysts remain unconvinced, we still find that equity managers understand that they have a stock selection return advantage, along with a weighting to that advantage, and that this represents and explains their active management process. We also continue to find that these managers don't "get" the Interaction effect, no matter how hard you try to explain and to justify it. Why? Because it doesn't represent how they invest and it doesn't represent their decision process. Turns out that you really "can't fight City Hall."

  4. By taking into consideration the weighting of the stock, as well as the selection, we lose the value of each individually (perhaps they got the weighting right, but the selection wrong?). Thus, the need to separate them into the ALLOCATION and SELECTION effects, without blurring the formulas. Your example provides support for the occasional need to use the full attribution model at the security level, which I believe often loses value. But this example doesn't say that we ignore interaction. If you were a "drinking man" I'd suggest we discuss this over a beer or two, but I'm fine doing it over something less potent!

  5. Dave:

    Maybe you're right. It just might be that Interaction is truly the "Drinking man's performance statistic." I can just picture a table of boozed-up investment performance managers hotly debating the value of Interaction, much to the envy of the boys at the other tables who have no recourse but to debate politics, sports and the like. Reminds of the phrase that only "Mad Dogs and Englishmen" might go for the Interaction effect, but then I recall that our friend Carl Bacon is BOTH a Brit and a notorious hater and debunker of the interaction myth.

    So, you and your Interaction buddies are left trying to explain to an equity manager that his decision to buy Microsoft is one decision and his decision about how much to buy is yet another decision. The fact that he considers them both to be part of the same decision is of no consequence ("Barkeeper: Another round for my friends!") And when this equity managers explains his under performance to his client, he should start out by saying that "I picked the right stock" ("Buy me a beer!") but he underweighted it ("Hold that beer!") Or better yet, he should explain the Interaction Alpha that resulted from the fact that he overweighted the worst sector in the benchmark, and then bought all of the underperforming stocks in that sector. And when the client tells him that "Two wrongs don't make a right" he can just say: "Hey, that's the Interaction Effect for you... have another round on me!"

    Good luck with that.
    (I'll have a ginger ale - straight up.)

  6. The flexibility of attribution is that one can adapt it to the way the firm manages. If, as you point out, the manager sees the selection and weighting of the asset as a single decision, then including the interaction effect with selection (by using the portfolio weight) would be fine; I have no problem with this. But I would think that even in this case, the manager would benefit by splitting the decisions (since they're clearly two, are they not?) so that they can grasp how each contributed.

    Oh, and you don't like ice w/your ginger ale?

  7. Perhaps it's the hazy fog induced by the "demon rum" that has kept you from the truth of my last statement, so let me be clear: selecting a stock is essentially a single allocation decision - it does not involve two decisions. The "selection" decision is essentially this: "How much of this stock should I buy? None? A benchmark neutral amount? Less? More?" Every selection decision is essentially an allocation decision. Remember that you cannot buy a stock without allocating money to it.

    In terms of the investment process, it's more likely that the sector allocation effect is a byproduct of stock selection rather than a "macro first" decision implied (but not stated) in the sacred attribution model. (Get the sarcasm there? I really don't consider the Brinson model to be sacred. And let's not forget that attribution was first developed in England, regardless of what everyone else things.) It's a curious yet unstated rule that one calculates the allocation effect first. Why? If you want to speak of "the way the firm manages" then you should recognize that managers essentially allocate money to individual stocks based on their degree of conviction, and this produces a byproduct of sector weights. Why not consider the allocation effect to be the residual of the stock selection process rather than a primary decision? That is more consistent with the investment process than simply assuming that stock pickers first express a view of the attractiveness of sectors and then go about picking stocks. Their main emphasis is on stock selection - or rather allocating money to stocks they expect to outperform the general market.

    With this approach, you are free to enjoy the "flexibility" of the attribution process by considering sector allocation as a deliberate first decision followed by an allocation to individual stocks, or to consider allocation to be nothing more than an unintended consequence or a residual effect. One can make a case for either approach as representative of the investment process, but nowhere in the investment process do you find any mention of an "interaction" effect.

    That said, I throw down the gauntlet: find a prospectus or a manager presentation where the Interaction Effect is showcased as part of the investment process and I will (shudder) buy you a beer (or other nefarious alcoholic elixir of your choosing.) And maybe I'll take you up on that ice in my ginger ale...

  8. Thank you for the additional clarity. In which case, why bother with the "allocation" effect at all? Since we have a single decision, contribution is the way to go. I have advocated this for a long time at the security level, as I see little benefit in slicing up the allocation and selection (and for that matter, interaction) effects: contribution is the answer.

    And so why are we arguing? Oh, perhaps because at higher levels (e.g., sector) there are different and distinct decisions occurring, and one shouldn't blur them. However, if again the firm sees them as a single decision, there seems to be no point in breaking them up!

    Glad you asked for ice; as you may know, "straight up" means "no ice." And so, I'll make sure I ask the barkeep to include it. As for me, I'm ready for a Bourbon Manhattan on the rocks (Makers Mark will be fine).

  9. Stephen Campisi, A man with tenacious faith in his friendsAugust 4, 2011 at 8:04 AM

    Agreed... Makers Mark is highly esteemed among you "hooch hounds." But to the more important point, and to your question "And so why are we still arguing?" It seems you are ready to throw out the Allocation effect rather than give up your Interaction effect. In the face of such indisputable logic regarding the spurious results that Interaction provides and its lack of representativeness regarding the actual investment process, your devotion to it seems rather Chauvinistic (in the classic, historical sense rather than the popular use of the word for boorish men.) Why cling to such a debunked idea? Especially one that is calculated but never used? (Remembering that everyone hates it because it makes no sense.)

    And so, why does this matter? Two reasons. First, because for some managers, sector weightings are a deliberate decision in the investment process and the allocation effect is relevant. And, for those for whom allocation is a byproduct of selection, it is still meaningful to note the impact of the macro allocation of capital, even as an unintended consequence - it's still a consequence. If it matters, it should be measured. Second, because selection is appropriately calculated using portfolio sector weighting, even though this may be considered a byproduct of security selection.

    But wait... there's more. Also consider that in its most basic and intuitive sense, attribution describes the impact of "opportunities" and the portfolio's "weighting" to those opportunities. In the Brinson model, there are two opportunities. The first is to the return a sector provides relative to the average return of the benchmark. The second opportunity is to the return provided by a set of issues relative to the respective sector within the benchmark. The impact of these opportunities is properly weighted using the portfolio weighting: for allocation, this means the portfolio weighting relative to the benchmark, and for selection this means the portfolio weighting. The question is really about impact on the portfolio. If a manager said he had a big relative return, your next question would be "how much exposure did you have?" You answer that question with the portfolio's weight, not the benchmark weight.

    In a nutshell, the impact of issue selection effect is managed and understood by the manager's opportunity and his/her weighting to that opportunity. That's how it works and that's how it should be measured.

  10. I don't know if anyone else is paying attention, but you and I are surely (don't call me Shirley) interacting a lot here. Okay, so first things first: yes, Makers Mark is quite esteemed and valued among us uppity Bourbon drinkers, though there are several others which are of equal (or perhaps greater) value; just don't give me Old Granddad or even Jim Beam, thank you very much (and yes, after this long back-and-forth, I'm ready for one).

    It seems that you, my dear and highly esteemed friend, are wanting to "have your cake and eat it too." At one point you say "it's one decision; allocation and selection are combined." And where I argue that blurring the selection effect with a dash of allocation (via interaction) would distort its true contribution to the excess return, you say "no problem; it's one decision anyway," which I accept, and say "then skip any of this stuff, and bring it all together via 'contribution.'"

    Your response however surprises me a bit, because you see value in splitting them up! But I heard "they're one decision." "They are, but only when we talk about interaction; when we talk from a macro perspective, I want to see how each contributes."

    Where I maintain consistency, you, the wearer of expensive suits like to twist and turn. Will we ever be able to come to an agreement? Highly doubtful, but again I suggest we take this up in person, sitting at a bar, me with my Manhattan, you with your ginger ale (w/ice)! I'll buy.


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