Misapprehensions

Misapprehensions in Investment Performance Analysis

Damien Laker, CompoundingHappens.com

30th March 2008

Misapprehensions arise in many areas of human knowledge. A misapprehension is a completely wrong idea that is commonly believed even by educated people. Misapprehensions can be very difficult to eradicate, because many people have heard them repeated many times, and therefore believe with great certainty that the misapprehension is actually a fact.

For example, many people believe that one can protect oneself from lightning strikes by wearing rubber-soled shoes. This is absolutely untrue. After all, rubber is a good insulator of electricity, but air is also a good insulator. If a lightning strike is powerful enough to travel through thousands of metres of insulating air, it will not be stopped by a couple of centimetres of insulating rubber.

A fascinating aspect of misapprehensions is that they are strongly-held beliefs, and passed from one person to the next with an air of complete certainty. Because they are so often repeated, and so seldom questioned, misapprehensions can become deeply entrenched within a body of knowledge.

In our opinion, there are several common misapprehensions in the field of investment performance analysis. We think that it will be easier for the field to make substantial progress if these misapprehensions are no longer taken seriously.

Plural form of "index"

The first (and most trivial) misapprehension concerns how to spell the plural form of the noun "index" (e.g. in the phrase "stock market index"). Owing to the fact that "index" is a Latin word that English has borrowed, the traditional usage has been to use a Latin plural form "indices". The catch is that many people (most of whom probably never took Latin classes) intuitively adopt the more phonetic "indicies". To many eyes, this misapprehension is an exceptionally ugly mistake. Still, it is remarkable how often one meets people who think that "indicies" is the correct spelling. A growing number of people are deciding to avoid this whole issue by adopting the more regular plural form "indexes".

Brinson Attribution or Sector Attribution?

The second misapprehension is the idea that sector attribution (aka "Brinson attribution") was devised by Brinson et al. There are three papers by Brinson and other authors, dated 1985, 1986, and 1991 (see below for References). These papers all describe the core idea of sector attribution: comparing the returns of notional portfolios to determine how much value-added is attributable to stock selection and sector allocation.

However, sector attribution using notional portfolios was described quite explicitly in 1972 by the Society of Investment Analysts in their report "The Measurement of Portfolio Performance for Pension Funds". A revised edition appeared in 1974. He we present page 9 from the 1974 revised edition. This document clearly describes an approach to performance attribution using notional portfolios that is essentially the same as the method we see in Brinson and Fachler (1985).

The evidence is very clear-cut that the essential technique for sector attribution was well-understood and published by 1974 at the latest. Yet virtually every textbook or journal article on this topic cites Brinson and Fachler (1985) as the earliest source on sector attribution. This is plainly an historical error.

It will serve us better in the future if what we write about sector attribution is based on historical facts. The essential method was certainly published in 1974. It may even have been published earlier. It is hard to understand why most writers still labour under the misapprehension that the first publication was Brinson and Fachler (1985).

Are there Two Sector Attribution Models?

A third common misapprehension says that there are two different sector attribution models. One is called "Brinson Hood Beebower" (BHB). The other is called "Brinson Fachler" (BF). These names describe the journal articles that reputedly described the models.

As we do not wish to more deeply entrench the misapprehension, we will not describe right here what the supposed differences between these two "models" are. For a comprehensive treatment, see the section "Are there Two Sector Attribution Models?" in our guide to Arithmetic Performance Attribution.

For an example of material that is based on the faulty premise that BHB and BF are separate attribution models, see Spaulding (2003), pp. 29-51, and pp. 177-180.

For present purposes, it will suffice to present a summary of the reasons why we think that it makes no sense to speak as if there are two separate models (BHB and BF) for doing sector attribution on portfolios.

The first reason is that there is no historical basis for claiming that there are two different models. The papers by Brinson et al. were concerned with analysing the historical performance of many different portfolios at the total fund level. These papers simply did not concern sector-level attribution calculations. However, the purported differences between the models only concern the calculation of sector-level results. This lies at the heart of the misapprehension.
The second reason is that there is no sensible interpretation for the two different models. The distinctive feature of the so-called "BHB model" is that it provides a different formula for calculating asset allocation at the sector level. Calculated this way, the results show positive value-added by any decision to overweight a sector that outperforms zero, regardless of whether it outperforms the overall benchmark. However, these different sector-level numbers for asset allocation always sum to the same total-level value as in the "BF Model". The only distinctive thing about the "different model" is that it provides sector-level asset allocation results that, frankly, have no sensible interpretation. It is therefore quite a mystery that the idea of this separate model continues to persist.
The third reason is that the idea of these two different sector attribution models is no use as a guide to thinking about attribution. It is a fundamental misunderstanding to view BHB and BF as papers that propose sector-level attribution models for individual funds. It is hard to see how somebody could reach this interpretation after carefully reading the papers. Moreover, BHB and BF use formulas that sum attributes across all sectors. Subsequent interpreters have recklessly taken the inner term from these summed formulas, and expected this inner term to automatically provide a sensible sector-level attribute. This is not a sound inference. To teach people how to think clearly about attribution calculations, one should always distinguish quite clearly between sector-level attributes and total-level attributes.

The entire distinction that is drawn between BHB and BF has virtually nothing to do with the original papers by Brinson et al. Rather, it is a misapprehension -- developed by subsequent commentators -- that has strengthened over time. But surely, some people say, even if this is a misapprehension, what harm does it do? Aren't people entitled to develop their own misinterpretations, and then to adopt them or not according to whether they find them useful in practice?

This "Freedom of Speech" argument has some merit. However, the opposing "Freedom of Truth" argument carries more weight, since this is supposed to be a professional body of knowledge. Many people who set out to learn about performance attribution quickly become brainwashed that the supposed distinction between BHB and BF is a meaningful and important one. This weakens their grasp of performance attribution concepts. They then proceed to issue requirements documents for new performance attribution systems. If there are supposedly two important attribution models (BF and BHB), then surely the best systems must definitely cater for "both models"? A system that doesn't support "both models" may be eliminated from the selection process at an early stage. At this point, commercial pressure falls on software vendors to provide BF and BHB regardless of whether it makes sense. In other words, stupidity becomes almost compulsory.

The final outcome of this misapprehension is that it is very market-distorting. People who need attribution software waste a lot of time checking whether software systems provide "both models". People providing the software are commercially penalised if they have the audacity not to provide "both models". The misapprehension becomes more deeply entrenched, and resources that could have productively been directed to innovation are instead misdirected into providing support for "both models". This is a potent example of the way that misapprehensions are holding back progress in the investment performance measurement & attribution profession.

Short Returns: Positive or Negative?

The last misapprehension concerns how to calculate returns on short positions. If an asset's price moves from $10 to $8, one can see that the return is minus 20%. If the price then moves from $8 to $6, one can see that the return for this second period is minus 25%, and the cumulative return is (1-20%) x (1-25%)-1 = minus 40%. It is easy to see that a compound return of minus 40% reconciles with a change in price from $10 to $6. What could be simpler or more fundamental?

Well, in actual fact, it has been suggested more than once that the signs on these returns should be reversed when the security is held short. One suggestion was in Ryan, Timothy P. "Separating the Impact of Portfolio Management Decisions" Journal of Performance Measurement Fall 2001, pp. 29-40. We describe on the Measurement Basics page how we published a letter in the Journal of Performance Measurement showing why reversing the signs would lead to several kinds of trouble. However, misapprehensions die hard. Even after our letter appeared, the Spaulding Group published an "Investment Performance Tidbit", advocating (just as Ryan did) that one should take the absolute value of the denominator in the return calculation for a short position, thereby changing the sign of the return for a position held short.

There are several ramifications if one takes the absolute value of the denominator in return calculations for short positions. For example, when the share price for a short position goes from $10 to $8, the calculated return becomes plus 20%. And when the price goes to $8 from $6, the calculated return becomes plus 25%. These returns compound out to plus 50%. Neither Ryan nor Spaulding has yet explained how this plus 50% return corresponds back to the total price movement from $10 to $6.

Moreover, it is easy to show that arbitrarily reversing the signs of the returns for short positions will lead to some difficulties when doing contribution and attribution calculations.

While it may initially seem appealing to arbitrarily reverse the signs of returns for short positions, the result is that one obtains returns that do not compound sensibly, and which do not work in attribution or contribution calculations. Yet this very same idea continues to raise its head from time to time.

Summary

There are many common misapprehensions in the field of investment performance analysis. This document only identifies some of the most egregious and persistent ones. Misapprehensions are not simply inadvertent mistakes (like typographic errors). Rather, they are fundamental misunderstandings that have the double disadvantage of seeming plausible, and being repeated over and over by apparently knowledgeable people.

In mature bodies of scientific knowledge, like physics, one does not hear experts presenting urban myths (such as the story of rubber-soled shoes as lighting protectors) as if they were scientifically plausible. Yet, in the field of investment performance analysis, urban myths are considered to be publishable.

It will be very hard for the body of knowledge in the field of investment performance analysis to consistently move forwards when incorrect ideas are so often repeated, and so infrequently corrected.

References

Brinson, Gary P., and Nimrod Fachler, "Measuring Non-US Equity Portfolio Performance," Journal of Portfolio Management, Spring 1985, pp. 73-76.

Brinson, Gary P., L. Randolph Hood, and Gilbert L. Beebower, "Determinants of Portfolio Performance," Financial Analysts Journal, July-August 1986, pp. 39-44.

Brinson, Gary P., Singer, Brian D., and Gilbert L. Beebower, "Determinants of Portfolio Performance II: An Update," Financial Analysts Journal, May-June 1991, pp. 40-48.

Spaulding, David, Investment Performance Attribution: A Guide to What it is, How to Calculate it, and How to Use it, New York: McGraw-Hill, 2003.

(Working Group of) The Society of Investment Analysts (UK), The Measurement of Portfolio Performance for Pension Funds (1972, Revised 1974).