The Journal of PorTfolio ManageMenT 119SPecial 40Th anniverSary iSSue

Anchored in Reality or Blinded by a Paradigm: The Role of Cap-Weighted Indices in the FutureMarc r. reinganuM

Marc r. reinganuM

is senior managing director and chief quantitative strategist at State Street Global Advisors in Boston, MA.marc_reinganum@ssga.com

Long before investors could inex-pensively purchase exposure to cap-weighted market indices, there existed a cap-weighted market port-

folio. This is not a profound insight but a tautology, a matter of simple arithmetic. For equities, the weight of an individual stock is its total market value (price times the number of shares outstanding) divided by the aggregate market value of all stocks. Price is assumed to be observed in the market, and the number of shares outstanding for a given stock is just the sum of every investor’s indi-vidual holdings of that stock, a quantity that is often approximated from information con-tained in periodic company filings.

In its raw form, the market portfolio is just a calculation, a descriptive statistic with no meaning other than the underlying arithmetic. This arithmetic does not tell us whether the market portfolio is an equi-librium or disequilibrium portfolio. The arithmetic does not inform us whether this portfolio is optimal for any one investor, much less optimal for all investors. This arithmetic does not reveal whether the prices of individual stocks are correct or whether they accurately ref lect information or not. The arithmetic cannot distinguish between the wisdom of crowds versus the folly of fools. The arithmetic of the calculation does not in itself guarantee liquidity for the underlying stocks. Even large-scale transparency may not be so

easily achieved without efficient computing and data collection. By itself, the arithmetic of these calculations does not imply that any investor will or should hold the market-cap-weighted portfolio.

So how did these cap-weighted market portfolios, these simple arithmetic calcula-tions, become so central in the practice of investments? The ascent of market-cap-weighted indices did not happen over-night on one day. The theoretical precursor probably can be traced back to Markowitz [1952], whose work established the principle of a mean-variance-eff icient portfolio—a portfolio that simultaneously minimizes return variance for a given level of expected return and maximizes expected return for a given level of return variance. Markowitz’s work strongly suggested that each investor should select some portfolio on the efficient boundary; the precise portfolio selected by an individual would depend on that individ-ual’s preferences regarding risk and return. Still Markowitz’s insights on portfolio selec-tion yield no particular revelation about the potential signif icance of the cap-weighted market portfolio or even whether the cap-weighted market portfolio is an eff icient portfolio itself.

From a theoretical perspective, the cap-weighted market portfolio burst onto the investment scene with pioneering work by Sharpe [1964] and Lintner [1965], collectively

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120 The role of caP-WeighTed indiceS in The fuTure SPecial 40Th anniverSary iSSue

known as the capital asset pricing model (CAPM). Within the CAPM framework, the cap-weighted market portfolio took on a central role. Not only was this port-folio an economic equilibrium portfolio; it was the only portfolio of risky assets that any investor needs to hold. That is, an individual creates their optimal portfolio by simply investing in two assets: the risk-free asset and the cap-weighted market portfolio. The cap-weighted market portfolio affords the most favorable risk/return tradeoff (Sharpe ratio) for all investors. No portfolio has a higher Sharpe ratio than the market portfolio. It’s just that simple. To obtain expected returns greater than the market, an investor would borrow at the risk-free rate and invest the proceeds in the market portfolio (leverage).

In the CAPM world, the market portfolio is clearly a boon for investors. Individuals merely need to decide what proportion of their wealth shall be invested in the market and what proportion shall be invested in the risk-free asset. Investing can’t get much easier than that! And firms eventually tried to make it even easier by manufac-turing cap-weighted market indices for investor use.

There is no free lunch in economic theory, and the simplicity and elegance of the CAPM comes at the cost of some heroic underlying assumptions. The assump-tions inculde: 1) investors can borrow or lend at the risk-free rate of interest; 2) the time horizon is one period; 3) security returns are characterized by the normal dis-tribution; 4) all investors have equal and costless access to information; 5) investors have homogeneous expec-tations, that is, all investors completely agree about the values of security means, variances, and correlations; and 6) there are no transaction costs or taxes. Of course, Sharpe and Lintner recognized that their assumptions were unrealistic and restrictive. But the value of the theory would be determined by how well it empirically approximated observable data.

In its day, the CAPM represented a radical, new approach to asset management—a one-size-f its-all model with no benefit associated with security selec-tion or active management of any type. As with any paradigm shift, adoption in practice is not instantaneous and the CAPM, with its profound implication about optimality of the cap-weighted market portfolio for all investors, was not an exception. Even in academic circles, the empirical plausibility of the CAPM was not widely acknowledged for nearly 10 years (for example, see Fama and MacBeth [1973] or Black et al. [1972]).

It took even longer for this paradigm to be widely embraced in the asset management industry. The prom-ulgation and acceptance of cap-weighted indices in prac-tice can perhaps be proxied by measuring the launch of mutual funds designed to passively track the S&P 500 Index. Exhibit 1 plots the number of S&P 500 Index mutual funds that were launched in each calendar year over the period from 1976 through 2010. The accep-tance and demand for this approach grew quite gradu-ally. The very first index mutual fund launch (VFINX) occurred in 1976. It took nearly six years before another firm offered such a product and three more years after that before this space had a third entrant. The explo-sive growth of cap-weighted S&P 500 Index products happened during the decade of the 1990s, more than a quarter century after Sharpe’s landmark paper but shortly following the recognition accorded this work by the Nobel Prize committee. The decade of the 1990s (1990–1999) witnessed the launch of 67% of all S&P 500 Index mutual funds over the 35 year period from 1976 through 2010. The peak year for S&P 500 index mutual fund launches was 1999. The first S&P 500 Index ETF (SPY) was launched in 1993.

A cynic (realist?) might argue that the skyrock-eting interest in and acceptance of cap-weighted market indices in the 1990s were not so much an intellectual embrace of Sharpe’s elegant economic theory by prac-tioners but a marketing/product analysis of stock market performance. In the 1980s, large-cap stocks experienced exceptionally good performance. On an annualized basis, the S&P 500 earned about +17.5%. For comparison, the Russell 2000 Index of small-cap stocks on an annualized basis returned about +11.5% over this ten-year period. In the second half of the 1980 decade, large-cap stocks did even better. On an annualized basis, the S&P 500 gained about +20% whereas the Russell 2000 returned about 10%. Exhibit 2 plots the annualized returns of the S&P 500 Index in the five decades since 1960 and illustrates that the 1980s and 1990s stand out like a sore thumb. For comparison, Exhibit 2 also includes the returns of the Russell 2000 in the most recent three decades.

Perhaps the avalanche of S&P 500 Index fund launches in the 1990s was just a manifestation of chasing past performance—hoping that past performance would persist going forward. From this perspective, one might not be surprised that 1999 was the year that experi-enced the greatest number of S&P 500 index mutual fund launches. In the prior year, 1998, the S&P 500

The Journal of PorTfolio ManageMenT 121SPecial 40Th anniverSary iSSue

Index gained +28.6% whereas the Russell 2000 experi-enced a change of -2.1%—a spread of more than 3,000 basis points! Even John Bogle’s 1976 index fund launch followed a calendar year in which the S&P 500 Index advanced by +31.6%.

In the 1990s, cap-weighted market indices became popular and widespread. Whether this growth was driven by marketing savvy or the eventual acceptance of an investment paradigm, the end result was the same: namely, by the end of the 1990s, cap-weighted market indices anchored many investment approaches. Entire investment architectures and systems of incentives for professionals managing assets developed around cap-weighted market indices. By the end of this decade, many institutions acted as if the CAPM were true or at least a good enough approximation. The theory of cap-weighted indices and the performance of cap-weighted indices came together in a powerful way, and this tec-tonic shift in the practice of finance swept away many previous approaches.

But what if this powerful melding of the theory and performance of cap-weighted indices in the 1990s was just an historical f luke, a mere coincidence? The theory and performance of cap-weighted indices cer-tainly coalesced in the 1990s, but would this ultimately turn out to be a bane rather than a boon for investors? That is, what if the theory is not such a good approxima-tion of reality and/or the performance from the 1980s and 1990s is not representative of realistic future expec-tations? Did this melding actually distract investors from seeking deeper insights about risk and return and better investment solutions? Stated differently, were investors understandably lulled into complacency and a false sense of security by the simplicity of cap-weighted indices?

Ironically, just as the industry was embracing cap-weighted indices in the 1990s, doubts about the empirical validity of the CAPM were beginning to coalesce in academia. Academic research often focused on another implication of the CAPM known as the security market line—the linear relationship between

e x h i b i t 1Number of S&P 500 Index Mutual Funds Launched by Calendar Year, 1976–2010

Source: Morningstar Direct.

122 The role of caP-WeighTed indiceS in The fuTure SPecial 40Th anniverSary iSSue

an asset’s expected return and its beta, or relative risk in the market portfolio. This linear relationship between expected returns and betas is a mathematical manifes-tation of minimum-variance portfolios of which, in CAPM theory, the market portfolio is one. Violations of the security market line would imply that the cap-weighted market portfolio is neither an efficient nor a minimum-variance portfolio.

Academic tests of the CAPM aimed to discover potential anomalies in the security market line relation-ship. Not long after Fama and MacBeth [1973] had pre-liminarily vetted the CAPM, such anomalies began to surface. For example, Basu [1977] reported a value effect; that is, grouping securities on the basis of their price/earnings ratios investors could earn excess returns rela-tive to the security market line. The average returns of low P/E stocks exceeded the returns predicted by the CAPM. A few years after that, Banz [1981] and Rein-ganum [1981] reported another apparent misspecifica-

tion of the CAPM, the so-called size effect: on average, small-cap stocks earned meaningfully greater returns than would be implied by the CAPM. Rosenberg et al. [1985] researched another manifestation of the value effect by grouping securities on the basis of their book-to-market ratios.

Yet these anomalies did not seem to congeal into a force that would seriously challenge the CAPM in academic circles until Fama essentially repudiated major implications of his 1973 paper with co-author MacBeth and acted as a strong proponent of the anomalies. In 1992, Fama in collaboration with co-author French published “The Cross-Section of Expected Returns.” This syn-opsis of previous research proposed an empirical three-factor model of asset pricing: 1) a factor based on the size effect (small cap-large cap); 2) a factor based on the value effect measured using book-to-market ratios; and 3) a factor based on market returns, that is, a beta effect. The Fama-French [1992] work deviated substantially

e x h i b i t 2S&P 500 Index and Russell 2000 Index Annualized Returns by Decade

Source: Bloomberg.

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from the spirit and simplicity of the CAPM. Theoreti-cally, it seemed more closely aligned with the multifactor arbitrage pricing theory proposed by Ross [1976]. Unlike in Sharpe’s CAPM, the cap-weighted market portfolio is not the one and only portfolio investors need to own in the Fama-French structure. Rather, in the Fama-French paradigm, exposure to a cap-weighted market index rep-resents one risk factor among multiple risk factors that contribute to the return an asset is expected to earn over time. Holding the cap-weighted market portfolio for any investor portfolio is neither an implicit nor explicit ramification of Fama-French.

Following the publication of Fama-French, the investment lexicon has expanded to include other poten-tial factors such as momentum (for example, see Car-hart [1997]), quality (for example, see Sloan [1996]), and volatility (for example, see Ang et al. [2006]). Just as cap-weighted indices began to anchor investor port-folios in practice during the 1990s, these same cap-weighted indices were losing their centrality in advanced research.

Advanced research alone is not likely to debunk or dethrone a deep-rooted investment template, and by the end of the 1990s the CAPM and cap-weighted market indices anchored the analysis of many practitio-ners. Active management itself was de facto defined rela-tive to benchmark weights from cap-weighted indices The implied optimality of cap-weighted indices seemed to permeate the practice of finance; maybe around the edges, active management might serve up some alpha at the margin. But did cap-weighted indices really deliver on their promise both in theory and in performance?

In the decade following 1999, the total return of the S&P 500 was -1.0% on an annual basis— dramati-cally less than the 17.5% annualized return of this index in the 1980s and the 18.1% return in the 1990s—and trailed the +3.5% annualized return for the Russell 2000 during this decade. Since the peak of S&P 500 Index fund launches in 1999, this index has returned just 3.7% annualized through March 2014, lagging the Russell 2000 by about 380 basis points per year on average.

With the benefit of hindsight, one can perhaps more easily understand why the stellar performance of the S&P 500 in the 1980s and 1990s might be period specific. Perhaps the biggest economic force driving per-formance during the 1980s and 1990s was the steady decline in interest rates during those two decades. Over this period, the yields on U.S. ten-year Treasury bonds

declined from about 16% in the early 1980s to around 6%. The relationship between yields and the level of the S&P 500 is charted in Exhibit 3. Indeed, throughout most of the 1980s and 1990s, the returns of bonds and stocks were positively correlated as monetary authorities seemed more willing to accept economic slowdowns to combat inf lation. Larger corporations, which make up the great majority of the S&P 500, clearly gained from the decline in interest rates and, with easier access to credit markets, benefited differentially from increasing leverage. This is not to say interest rate declines alone accounted for stellar equity performance as, for example, technological change concurrently altered the composi-tion of sectors in the economy. Nonetheless, monetary policy, financial engineering, and technological change combined to create a golden era for equity performance based on cap-weighted indices—in particular, the most widely used index, the S&P 500.

The performance of cap-weighted indices has most likely disappointed investors since the 1990s. In the fol-lowing decade, monetary policy changed and markets coped with two devastating downturns—the def lation of the tech bubble and the global financial crisis. The prolonged unanticipated weak performance of cap-weighted indices undoubtedly stressed many actuarial assumptions about wealth accumulation. Just as the spectacular performance of cap-weighted indices in the 1980s and 1990s probably fueled the growth of these investment vehicles, so too the disappointing perfor-mance of these investment vehicles is probably causing investors to re-evaluate their investment philosophies and approaches.

New potential indices are challenging the supremacy of cap-weighted indices. The names of these new con-tenders are numerous, ranging from advanced beta to alternative beta to smart beta to sophisticated beta plus many others. The evidence from these new indices, rooted in the advanced academic research on anomalies and multifactor empirical models, actually suggests that producing alpha may be a no brainer—at least relative to a cap-weighted market index over time. This type of alpha can be manufactured inexpensively, likely placing downward pressure on fees, and might viewed as the reward for exposures to different categories of risk.

In the 1990s, cap-weighted indices seemed almost like a free lunch—an easily implemented portfolio with optimal risk and reward features. This portfolio was viewed not just as an exposure to market risk but as an

124 The role of caP-WeighTed indiceS in The fuTure SPecial 40Th anniverSary iSSue

optimal target to gauge portfolio performance. Although appealing, this view of the world probably turns out to be too simplistic. It may be prudent to recall the famous quote often attributed to Einstein: “Everything should be made as simple as possible but not simpler.”

As of the second decade of the twenty-first century, the preponderance of evidence suggests that cap-weighted market indices may not be optimal targets, the gold standard of performance applicable to all investors. Cap-weighted indices are still a valuable tool in the arsenal at the dis-posal of investors, but their role is evolving as investors recognize the need to manage a multiplicity of risks. Cap-weighted indices clearly offer investors exposure to some types of risk, but this exposure needs to be balanced, weighed, and combined with other equally compelling exposures such as size, value, volatility, and so on. The challenge for investors is to design a sensible, optimal combination of exposures in a way that meets their needs and attains portfolio efficiency in the Markowitz sense, that is, the highest level of expected portfolio total return for a given level of target total risk.

Sensible combinations of these expanded sets of potential new indices may differ in practical ways for different types of investors—one size is not likely to be optimal for all investors (a conclusion that is actually shared with a version of the CAPM developed by Black way back in 1972). As a result, investment commit-tees will need to revise and update their policy port-folios, performance measurement, and compensation schemes.

As investment solutions move away from cap-weighted centric defaults, active management will also need to evolve. Returns accruing from simple exposures to common risk factors will be available to investors through low-cost advanced beta type indices. Active management skill will need to be expressed either through the dynamic timing of risk exposures, the development of proprietary factors uncorrelated with widely known factors, idiosyncratic insights into indi-vidual f irms that are independent of their risk expo-sures, or portfolio construction techniques that help balance a client’s desired risk and return profile. Alpha

Source: Bloomberg.

e x h i b i t 3U.S. 10-Year Treasury Yields vs. S&P 500 Index Levels, January 1980–December 1999

The Journal of PorTfolio ManageMenT 125SPecial 40Th anniverSary iSSue

masquerading as advanced beta should not be highly compensated. The skill of active management will be defined relative to new investment committee policy portfolios, not cap-weighted benchmarks.

Cap-weighted market indices represented a crowning achievement in the development of invest-ment thinking and practice, clearly a boon for inves-tors. But for investors who stay solely anchored in this investment paradigm too long without broadening their investment horizons and strategies to take into account a changing investment landscape and a multiplicity of risks, the boon could easily morph into a bane.

ENDNOTE

The author would like to thank Jennifer Bender, Lynn Blake, Mark Cohen, Nat Evarts, Frank Fabozzi, George Hoguet, Bob Kearns, Claire Kurmel, Rick Lacaille, Aditya Manohar, Richard Parker, Toby Warburton, Winston Woo, and Volodymyr Zdorovtsov for their helpful comments and suggestions. Any errors or omissions are completely the responsibility of the author. This piece ref lects the views of the author and does not represent the official views of State Street Global Advisors or State Street Corporation.

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