Index Rex

September 09, 2003

From the Journal of Indexes - The author unveils a methodology that seeks to incorporate the collective decisions of fund mangers into investable benchmarks in an article that was originally published in the Journal of Indexes in Q2 of 2002.

The author unveils a methodology that seeks to incorporate the collective decisions of fund mangers into investable benchmarks. This article originally appeared in the Q2 2005 edition of the Journal of Indexes.

In 1896, Charles Dow created the Dow Jones Industrial Average, establishing the first measure of stock market performance and the first benchmark for portfolio performance. Limited by the technology of its times, the Dow painted a skeletal picture of the U.S. stock market. It initially consisted of just 12 stocks, weighted by their prices. As the original index, the Dow became the yardstick for relative performance.

Over the ensuing century, new technologies made it possible to create indexes that more accurately captured the performance of the U.S. stock market: for example, the Standard & Poor's 500 Index, the Russell 3000 Index, and the Wilshire 5000 Total Market Index (in ascending order of comprehensiveness). These indexes are weighted not by prices but by the market value of their constituents, and thus better represent the universe of securities available to U.S. investors.

In the mid- to late-1970s, however, a burgeoning industry of investment consultants recognized that these broad market indexes were inappropriate benchmarks for professional money managers. Most managers oversee portfolios that track not the broad market, but discrete sectors of it—stocks of a particular size, for example, or stocks with pronounced growth or value characteristics.

The consultants addressed the mismatch between managers and benchmarks by creating indexes of stocks in various capitalization ranges and of different investment styles. Since then, the industry has created multiple indexes to track every sector, industry, and sub-industry. The same has happened with bonds. There are few sectors of the financial markets that are not being sliced, diced, and tortured by an ever-growing list of index creators.

Despite the proliferation of indexes, these benchmarks have generally failed to reflect the way managers actually invest. On balance, they measure the wrong set of securities¾or, if not that, then the wrong way of managing those securities. As evidence, our research shows that the correlation between the performance of growth and value managers is much higher than the correlation between growth and value indexes. In other words, the growth and value indexes reflect a degree of difference in investment styles that doesn't exist in the real world. The same problems exist with indexes that represent other subsectors of the broad market.

It is indeed puzzling that two different indexes designed to provide insight into the same sector of the marketlarge-cap value stocks, for examplecan provide very different results. The discrepancies arise, of course, because of differences in the methodologies used to create the indexes. Over long periods, different value and growth indexes generally, though not always, provide similar results. In the short run, however, their differences cause confusion and limit their usefulness as benchmarks.

A New Approach

It is possible to create indexes that are meaningful benchmarks for managers who follow growth or value investment styles, focus on large- or small-cap stocks, or look for some combination of those characteristics. The starting point is this cardinal rule: An index must reflect the way that money managers actually invest.

This may sound like circular reasoning-defining value as what people call value. The reality, however, is that growth and value, and small-cap and large-cap, are what investment managers deem them to be. Modern portfolio theory doesn't define any of those terms. Managers do. The indexes that track these sectors should incorporate the thought processes of these managers. The best index isn't necessarily the one that provides the highest return; it's the one that most accurately measures the performance of the style it's designed to track.

This article proposes guidelines for the construction of ideal indexes. With better tools, investors will be able to make better decisions about how their money is managed. Some indexes already incorporate some of these proposals, but no index incorporates all the guidelines.

These guidelines are not intended to make the lives of index fund managers easier. An index fund is a rational investment only if it provides an alternative to active management in a low-cost, relatively tax-efficient way, or if it offers exposure to a segment of the market in which active management is difficult, if not impossible. For instance, micro-cap stocks are too illiquid to be managed actively in a portfolio with high turnover. Indexes designed only to simplify the lives of indexers probably wouldn't meet these criteria. However, if the rules for creating indexes based on the behavior of active managers also simplify the indexers' job, so much the better!

I. Rely on Objective, Not Subjective, Rules

An index can be rules-based and objectively maintained, with no ambiguity about when a stock should be included or excluded. Alternatively, an index can be more subjectively reconstituted by an individual or committee according to broad guidelines. Each approach has pros and cons.

A purely objective approach ensures absolute style integrity and total transparency, precluding debate about the merits of including one stock or another. However, it also can, but does not have to, result in short bursts of high turnover, raising costs and tax inefficiency. Active managers, even those with high portfolio turnover, don't implement six months' or a year's volume of portfolio adjustments on a single day.

On the other hand, a subjective approach to index maintenance may allow for more orderly management of changes. This approach, however, is subject to committee decisions that do not represent the decision process of active management.

The most important characteristic of indexes tracking the market's subsectorsin essence, sectors created and defined by managersshould be that they accurately reflect the thought processes of active management. For that reason, style integrity is extremely important, and an objective set of rules for creating an index is preferable to the vagaries introduced by a subjective process.

II. Adjust Weightings for Cross-Holdings/Float

For the purposes of determining a company's size and capitalization category, it is necessary to take into account all of a company's outstanding shares, because the stock's performance is influenced by the economic size of the company. However, in determining the stock's weight in an index a different standard should be used.

The investment universe available to active investors should be the starting point for all indexes. Many companies have shares that are closely held by individual investors, or cross-held by other corporations or governments. To the extent that these positions represent strategic long-term holdings that do not 'float' on the market, they should not be used to calculate the stock's weight in the index, and thus its contribution to the index's return. They are not a part of active investors' opportunity set.Including these shares in a benchmark distorts its return relative to the universe of active investors because, in aggregate, the managers cannot own all of the shares outstanding. In truth, there is probably no index-related issue less debatable than this. In fact, two major global indexes, the MSCI and FTSE indexes, have recently been reconstituted to adjust for shares that don't float. Although these changes resulted in hundreds of billions of dollars' worth of transactions for index and active funds, causing large transaction costs, those short-term costs will improve the long-term integrity of the indexes.

III. Define Market Capitalization as a Band, Not a Line in the Sand

Indexes based on market capitalization must be periodically reconstituted to ensure that they reflect the performance of the market segment they purport to measure. Both objectively and subjectively determined indexes currently capture this concept, to varying degrees. In each case, the rebalancing usually results in significant market impact on the stocks affected and unnecessary turnover and transaction costs. This marketplace turmoil is not prima facie evidence of poor index construction. However, rebalancing as it is now practiced doesn't reflect how active managers adjust their portfolios, and, therefore, leads to the creation of an inappropriate benchmark.

Active managers do not unanimously agree on the boundaries between two capitalization ranges. One manager might classify a $4 billion company as large-cap, while another might consider it mid-cap. To capture this ambiguity, an index's demarcation between capitalization ranges should be a band, not a line in the sand. If a stock's relative market capitalization changes so that it enters the band, the stock remains a constituent in the index to which it was previously assigned. It migrates to the other index only if it exits the opposite side of the band. A small-capitalization stock will remain in the small-cap index even if its market cap grows into the range that may have demarcated 'large-cap' when the index was first established. It will become a large-cap stock only if its market capitalization moves past the upper edge of the band.

The advantages of these bands would be twofold: First, they would reduce turnover during periodic index rebalancings, as stocks would not vacillate between one index and another based on minor changes in their market capitalizations. Second, and more important, these bands would more accurately reflect the way active managers think of their investment universe. Managers do not summarily throw a stock overboard because it crosses an imaginary line. They frequently continue to hold it even though a manager with a different investment style might consider it to be in a different index classification.

Building the Bands and Defining Capitalization Ranges

The capitalization bands should be based on the relative sizes of stocks, rather than on static dollar figures that may or may not be appropriate as the market rises and falls. For instance, the initial cutoff for a large-cap index could be the 700th-largest stock, as measured by total, as opposed to float-adjusted, market capitalization. Or it might be the stock representing the 85th percentile of the stock market's capitalization. (These boundaries are just suggestions, but they are roughly appropriate.)

The band around the large-capitalization cutoff could be plus or minus 150 stocks, or plus or minus five percentage points of market capitalization. A stock previously classified as small- or mid-cap would be added to the large-cap index once it became the 549th-largest stock, or the stock representing the 79th percentile of market capitalization. Similarly, a stock would be removed from the large-cap index when it became the market's 851st largest stock, or the stock representing the 91st percentile of market capitalization.

The small-cap index should be a complement of the large-cap index, with an initial cutoff of perhaps 700 for the largest stock and, as suggested above, 2,500 for the smallest stock. (The absence of a mid-cap index separating large- and small caps may seem odd, but this construction better reflects active managers' capitalization exposure.) The cutoffs should be bounded by the 300-stock bands used in the large-cap index. While the top cutoff may seem high, it reflects the holdings of small-cap managers. In fact, the performances of the Russell 2500 and Wilshire 4500 Indexes-both of which include mid-caps and small-caps-more closely correlate to the performance of small-cap managers than does that of the strictly small-cap Russell 2000 Index. Stocks smaller than the 2,500th stock could comprise a microcap index (a segment for which no index yet exists).

Range Of Stocks Included In Capitalization Indexes

The mid-cap index would overlap the large-cap and small-cap indexes, with initial break points at perhaps the 400th-largest stock at the top and the 1200th-largest stock at the bottom, with both cutoffs surrounded by 300-stock bands. Figure 1 illustrates this concept. The first column shows the total stock market. The second column shows the universe of large-cap stocks; the third, that of small-cap stocks; and the fourth, that of mid-cap stocks. The dot-dash-dot lines show the initial cutoffs for the different capitalization ranges. The dash-dash-dash lines show the bands, or hurdles, that a stock must cross in order to move from one capitalization range to another.

Some investors may be concerned that, because the mid-cap index overlaps the large- and small-cap indexes, the three together would not replicate the total stock market. But overlap is a problem that investors already face when combining two or more actively managed funds, or even when complementing an active fund with an index fund. Active managers follow no hard-coded rules about market capitalization. Two managers with different mandates will frequently consider the same stock to be in their target ranges. An investor who wants a total-market index is better off investing in one directly than trying to build one with sub-indexes.

IV. Determine Style in Two Dimensions

Most widely accepted indexes consider value and growth stocks to be complements of each other. By this definition, a growth stock is anything that is not a value stock, and a value stock is anything that is not a growth stock. The delineation typically depends upon a single factor, such as price/book ratio, or perhaps a combination of several factors blended into a single style rank for every stock, as depicted in the spectrum below:

Active managers do not believe their world is flat. A value manager may hold a stock owned by a growth manager. The stock may fully satisfy the requirements of both. A value manager might require that a stock have a low price/earnings ratio, for example, but would certainly not be dismayed to see that it also enjoyed strong growth prospects. Nor would a growth manager exclude a stock that met his or her requirements for growth just because it sported a low valuation.

Using their own independent criteria, value and growth managers occasionally fish from the same pond. Conversely, some stocks are attractive to neither. For active managers, stocks don't fall into rank on a simple line like that shown above; instead, the delineation between value and growth is two-dimensional.

Value managers emphasize a company's fundamentals relative to its current price, including price/earnings, price/book, price/sales and dividend/price (yield) ratios. They analyze companies based on these criteria and subject those that pass a certain hurdle to further analysis. Growth managers, by contrast, place the primary emphasis on characteristics such as earnings growth, sales growth, and margin growth. Working independently, value and growth managers analyze companies along their own growth or value spectra. Their combined view, with the dotted lines demarcating each category's hurdle rates, is shown in the graphic below.

In two dimensions, some stocks are pure value or growth, others are both value and growth, while still others appeal to neither growth nor value managers. Based on a stock's price ratios, for example, a value manager might conclude that it is a value stock. Evaluating its sales and earnings growth, a growth manager might conclude that the same security is a growth stock. Using two distinct methodologies, both managers determine that the stock is a component of their universe. Style-based indexes should reflect this reality, rather than forcing a stock into one category or the other. Consequently, growth and value indexes, as subsets of broader indexes, should not be perfect complements.

Given this design, a combination of value and growth index funds will result in some overlap in holdings. It will also exclude some stocks. But that is true of actively-managed portfolios as well. As in the case of market-cap-oriented funds, the combination of actively-managed growth and value funds does not yield a complete non-overlapping portfolio. If the style indexes are to be good benchmarks, they won't necessarily be perfect complements of each other. Index investors who want to combine value and growth should simply invest in a blended index.

This methodology would also allow us to create deep-value and aggressive-growth indexes by setting higher hurdles for those extreme styles. And as with the capitalization indexes, there should be bands around the growth and value demarcations.

V. Manage Stock Migration

Although market-cap and style-oriented bands would reduce turnover and better reflect the way active managers respond to changes in stock characteristics, there would still be those hard lines in the sand at the edges of a band. When a company crossed this edge, the stock would exit the index, and in the case of size indexes, migrate entirely from one classification to another. Once again, this is not an accurate representation of how active managers respond to secular shifts in the characteristics of a company. In reality, because managers act independently, there is no one point, or even brief period, in which they collectively decide to eliminate a stock that is leaving their investment style. One by one, they may act quickly, but as a group they remove such stocks from their portfolios gradually.

How can an index be made to reflect this reality? One way would be to divide the index into 12 equally sized subcomponents, with each subcomponent associated with a month of the year. If Stock A had a market capitalization of $12 billion, for example, each of the 12 subcomponents would contain $1 billion of Stock A. Every month, the subcomponent associated with that month would be opened up, analyzed, and reconstituted.

Figure 2 shows how this might look, using an imaginary set of indexes being reviewed in May 2002. The index sponsor has opened that month's subcomponent, which was established in May 2001, and analyzed the stocks to determine whether they still meet the index criteria. In May 2001, Stocks A, B, and C were large-cap, and Stock D small-cap. A year later, Stock C has migrated down to the small-cap category, and Stock D has migrated up to the large-cap category. The subcomponent's 1/12 position in Stock C is moved to the small-cap index, and its 1/12 position in D is moved to the large-cap index. Adjustments made in the May subcomponent have no effect on the other 11 subcomponents.

This process means that, during any one month, only 1/12 of a stock's float-adjusted market capitalization would be transferred from one index to another. At a minimum, it would take 12 months for a stock to entirely migrate from one index to another. During this transition period, the stock might be in two indexes, but the weights in the large- and small-cap indexes would be complementary. A particular stock might have 7/12ths of its weight in the large-cap index, for example, and 5/12ths in small cap.

This migration process more closely reflects how active managers invest. First, they do not, as a herd, pile into, or out of, a stock as it crosses a certain threshold. Instead, they collectively wade into and out of a position. An index that followed the same process would not only be a better benchmark, it would also benefit index fund investors by significantly reducing turnover and allowing the portfolio to be repositioned in a more orderly fashion, significantly reducing the fund's transaction costs by use of the monthly reconstitutions. The index itself would have lower embedded transaction costs, which would enhance long-term results.

It should be noted that most indexes currently lead to significant transaction costs when securities are added or subtracted. The cost of style integrity is disproportionately high for small-cap indexes, which have recently had annual turnover as high as 35% to 45%.


To create relevant benchmarks for actively-managed investments, our frame of reference should be the active managers themselves. It is these managers, not investment theory, that define growth and value, small-cap and large-cap. With indexes that mimic the thought processes of active managers, investors would have better tools for evaluating the performance of professional managers, helping them to make smarter decisions about their portfolio allocation. Consultants and researchers would also have better tools for attributing a portfolio performance to the returns of different investment styles.

A widespread misconception is that indexing works in large caps, but not in sectors such as small caps. At times, this conclusion appears to be supported by the data. But the data's real lesson is that we're measuring managers with the wrong yardsticks. With better benchmarks, outperforming-or underperforming-an index would no longer be a matter of holding stocks from a different universe. Performance would reflect the success of a manager's stock selections within the appropriate universe. Although it's unlikely that large numbers of active managers could boast of index-beating performance, even over short periods, these better indexes could in fact be a boon to talented active managers. Their relative success could be attributed to skill, not dismissed as an artifact of faulty benchmark construction.


This article originally appeared in the Q3 2003 edition of the Journal of Indexes.


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