Tuesday, December 21, 2010

Rethinking equality...

You may recall that the only major controversy regarding the AIMR Performance Presentation Standards (AIMR-PPS(R)) was the use of asset-weighted returns, rather than equal-weighted. Two groups in particular, the Investment Management Consultant's Association (IMCA) and the Investment Counsel Association of America (ICAA) (now the Investment Adviser Association), opposed asset-weighting, partly because they felt that larger accounts would have greater influence on the return, which could cause "special handling" of these accounts. The reason for the asset-weighted approach was to have the composite look like an account. Not surprisingly the GIPS(R) standards adopted asset-weighting, too. Until today I hadn't given this much thought.

However, I recently did a GIPS (Global Investment Performance Standards) verification for a client who has a couple composites which are dominated by very large mutual funds. For example, one has a fund of roughly $250 million and individual accounts of around $500,000; suffice it to say, the composite return usually approximates or equals the fund return, even though the individual accounts may differ by several basis points (e.g., -2.38 vs. -2.11, the composite matches the fund (-2.38); 8.46 vs. 6.56; the composite matches the fund (6.56)). Granted, this is a very extreme example, but it does cause me to wonder if the asset-weighted approach truly is better.

What is the composite return supposed to represent? Clearly some sort of average, right? And so we have asset-weighting, but does this always make sense? While I understand the idea of the composite looking like a portfolio, in reality no one is managing the composite; the accounts are being managed. Something to ponder, perhaps?


  1. The measure of dispersion could provide some insight into such a composite (where one or a few portfolios dominate because of size), although a size-weighted standard deviation could still mask the issue...

  2. This also raises questions for the verifier:

    - should the verifier (perhaps strongly) suggest that the equal-weighted composite return also be included in the presentation?

    - should the verifier try to discourage the firm from using an asset-weighted measure of dispersion in such a situation, or, alternatively, encourage the firm to show an additional measure of dispersion that treats portfolios "equally" (assuming the firm wants to stick with an asset-weighed dispersion)?

    - should the verifier encourage the firm to use size as a criterion for composite construction, resulting in additional composites?

    I prefer the asset-weighed return measure... but this definitely seems like a case where a firm has a choice between showing the bare minimum to be compliant, or, alternatively, including more information to make the firm's track record more understandable.

  3. Stephen Campisi, Intuitive Performance SolutionsDecember 21, 2010 at 11:25 PM

    I have always favored equal weighting of composites rather than size weighting, because equal weighting serves prospective clients better. Why? Because equal weighting answers the relevant questions that clients are asking: "What is the return on the average portfolio?" and "What is the likelihood that I will get the same return as advertised in the composite?" (Notice that they are not asking some abstract question about the return on the "average dollar/Euro/etc." invested.)

    So, in your "worst case scenario" of a large account getting special treatment, an equal weighted composite will report something closer to the return that the majority of clients actually received, and will convey the information that prospective clients need to make an informed decision in their own best interest. And THAT'S what GIPS are supposed to be about; we call it "fair representation."

  4. Steve, thanks for your insightful comments. I hadn't really given it much thought until recently, figuring that the FAF and AIMR probably got it right 20+ years ago, but now am questioning it, and so am pleased to see that you, too, (though a longer time) feel that equal-weighting is better. Of course, the likelihood of this changing is quite slim.

  5. Interesting points, John. I like the idea of recommending the use of equal-weighted composite returns, to supplement the asset-weighted; and, as a critic of equal-weighted standard deviation, this would only add more support for my views. Thanks!

  6. Stephen Campisi, CFADecember 22, 2010 at 12:48 PM

    In the discussion of size weighted vs equal weighted composites, the issue of risk is perhaps even more important than the issue of return, since we are using the composite return to help the client understand the risk that they may not achieve the return of the composite. It is clear that a size weighted composite dampens the volatility of return across the individual portfolios since the large portfolio acts as an anchor and the dispersion of return from the smaller portfolios is underweighted. This artificially lowers the composite's risk and will inflate the value of various risk adjusted statistics such as the Sharpe ratio.

    Consider a composite that has 75% of its assets in a single portfolio that earned 8% while the remaining assets are distributed equally among 5 portfolios earning returns from 7% - 8% in 25 bps increments. The size weighted composite return is 30 bps higher than the equal weighted composite return (7.88 vs 7.58) the risk is proportionately about 25% lower (28 bps vs 37 bps) and the Sharpe ratio is dramatically higher (17.5 vs 12.3). Clearly the impact of size weighting is more pronounced when we bring the effects on return and risk together.

    Which method truly helps a prospective client understand the return that is representative of the strategy and the manager's ability to deliver that strategy across the entire client segment? Clearly, it's the equal weighted method.

    Weight Return
    75% 8.00
    5% 7.00
    5% 7.25
    5% 7.50
    5% 7.75
    5% 8.00

    Return Risk Sharpe
    Size Weighted 7.88 0.28 17.53
    Equal Weighted 7.58 0.37 12.30

  7. Steve, excellent insights. Perhaps we can get the GIPS EC to give this some thought. Thanks!

  8. In defense of asset-weighting:

    1) What if the very large portfolio is the worst performing one? Under equal-weighting the smaller portfolios would inflate the average return. This would in turn increase the Sharpe.

    2) Couldnt the argument be made that equal-weighting would encourage managers managing to give their best effort to smaller portfolios?

    Smaller portfolios are easier to manage. They can be more nimble than large portfolios with more efficient timing on trades leading to higher returns.

    3) Equal-weighting would also encourage managers to artifically segment the portfolios to "game the system". Surely they could take there best portfolio and divide it in two, doubling its weight in their composite. Equal weighting currently renders this exercise pointless.

    If you go for equal weighting you would need to have a much larger section specifying rules around what is and isnt a portfolio.

    4) Why are you assuming the risk of the larger portfolio is lower than the smaller ones? What if the risk of the large portfolio was higher than the smaller ones? That would affect the Sharpe in the opposite way to that offered.

  9. Hang on a second.

    Are you using the dispersion of the portfolios as your risk in calculating the Sharpe ratio?

    You should be using the standard deviation of the composite, no?

  10. Kimble, interesting points. You're right that with equal weighting the smaller clients' performance would have the same impact as the larger. My point is a simple question: what is the composite return supposed to represent? If a firm is managing ten accounts, and one is humongous; SO large that its performance carries the day, and in the end the composite return is really only reflecting the performance of that one account, how representative is that? Should the composite return be reporting how the underlying accounts performed "on average," or report (as it does today) how the COMPOSITE did, as if someone is managing the composite?

  11. Kimble, dispersion and risk are two different things. Dispersion is a reflection on how each account that was present for the full year did, relative to one another; it shows how spread out the returns are. From a risk perspective, when we use standard deviation, we're showing how volatile the composite return was over the period. If we're speaking of Sharpe ratio we would be using standard deviation across the period (e.g., the 36 month standard deviation), not dispersion.

  12. Hello,

    On the dispersion issue, the only reason I ask is because the Risk figures Stephen is using looked like the standard deviation (population) of the figures. (How many investments return 8% at such a low stdev?) I checked and saw that the 0.37 was in fact the StDevP of the group and that 0.28 matched a weighted standard deviation.

  13. Imagine a composite with a small number of portfolios, lets say 4. One is very very large, and another is very very very small. If that very small portfolio has either absolutely fantastic or spectacularly bad performance, equal weighted composite performance would be badly skewed. Imagine if the fund lost 85%, while the others lost only 10%. The composite loss would be -28.75%. Is that a fair representation?

    For every anecdote that makes equal weighting look good, I can come up with one that makes it look bad. The choice between equal and dollar weighting will always come down to which option is least bad.

    I think the affect of outliers and the opening of a loophole to allow gaming by managers are two very important problems that arise from equal weighting. And that they put the problems with asset weighting into perspective.

    A further point I just considered, the dispersion statistic is calculated on an equal weighted basis. As such it gives the analyst an idea of the range of returns within the composite even if the composite is constructed using asset weighting.

    If the composite was a simple average, there would need to be an additional statistic that gives the analyst an idea of the concentration of money within the composite. That statistic is very hard (I think impossible) to construct well.


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