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Posts Tagged ‘Equal-Weight Index’

The rationale for a value-weighted index can be paraphrased as follows:

  • Most investors, pro’s included, can’t beat the index. Therefore, buying an index fund is better than messing it up yourself or getting an active manager to mess it up for you.
  • If you’re going to buy an index, you might as well buy the best one. An index based on the market capitalization-weighted S&P500 will be handily beaten by an equal-weighted index, which will be handily beaten by a fundamentally weighted index, which is in turn handily beaten by a “value-weighted index,” which is what Greenblatt calls his “Magic Formula-weighted index.”

According to Greenblatt, the second point looks like this:

Market Capitalization-Weight < Equal Weight < Fundamental Weight < “Value Weight” (Greenblatt’s Magic Formula Weight)

In chart form (from Joel Greenblatt’s Value Weighted Index):

There is an argument to be made that the second point could be as follows:

Market Capitalization-Weight < Equal Weight < “Value Weight” (Greenblatt’s Magic Formula Weight) <= Fundamental Weight

Fundamental Weight could potentially deliver better returns than “Value” Weight, if we select the correct fundamentals.

The classic paper on fundamental indexation is the 2004 paper “Fundamental Indexation” by Robert Arnott (Chairman of Research Affiliates), Jason Hsu and Philip Moore. The paper is very readable. Arnott et al argue that it should be possible to construct stock market indexes that are more efficient than those based on market capitalization. From the abstract:

In this paper, we examine a series of equity market indexes weighted by fundamental metrics of size, rather than market capitalization. We find that these indexes deliver consistent and significant benefits relative to standard capitalization-weighted market indexes. These indexes exhibit similar beta, liquidity and capacity compared to capitalization-weighted equity market indexes and have very low turnover. They show annual returns that are on average 213 basis points higher than equivalent capitalization-weighted indexes over the 42 years of the study. They contain most of the same stocks found in the traditional equity market indexes, but the weights of the stocks in these new indexes differ materially from their weights in capitalization-weighted indexes. Selection of companies and their weights in the indexes are based on simple measures of firm size such as book value, income, gross dividends, revenues, sales, and total company employment.

Arnott et al seek to create alternative indices that as efficient “as the usual capitalization-weighted market indexes, while retaining the many benefits of capitalization- weighting for the passive investor,” which include, for example, lower trading costs and fees than active management.

Interestingly, they find a high degree of correlation between market capitalization-weighted indices and fundamental indexation:

We find most alternative measures of firm size such as book value, income, sales, revenues, gross dividends or total employment are highly correlated with capitalization and liquidity, which means these Fundamental Indexes are also primarily concentrated in the large capitalization stocks, preserving the liquidity and capacity benefits of traditional capitalization- weighted indexes. In addition, as compared with conventional capitalization-weighted indexes, these Fundamental Indexes typically have substantially identical volatilities, and CAPM betas and correlations exceeding 0.95. The market characteristics that investors have traditionally gained exposure to, through holding capitalization-weighted market indexes, are equally accessible through these Fundamental Indexes.

The main problem with the equal-weight indexes we looked at last week is the high turnover to maintain the equal weighting. Fundamental indexation could potentially suffer from the same problem:

Maintaining low turnover is the most challenging aspect in the construction of Fundamental Indexes. In addition to the usual reconstitution, a certain amount of rebalancing is also needed for the Fundamental Indexes. If a stock price goes up 10%, its capitalization also goes up 10%. The weight of that stock in the Fundamental Index will at some interval need to be rebalanced to its its Fundamental weight in that index. If the rebalancing periods are too long, the difference between the policy weights and actual portfolio weights become so large that some of the suspected negative attributes associated with capitalization weighting may be reintroduced.

Arnott et al construct their indices as follows:

[We] rank all companies by each metric, then select the 1000 largest. Each of these 1000 largest is included in the index, at its relative metric weight, to create the Fundamental Index for that metric. The measures of firm size we use in this study are:

• book value (designated by the shorthand “book” later in this paper),

• trailing five-year average operating income (“income”),

• trailing five-year average revenues (“revenue”),

• trailing five-year average sales (“sales”),

• trailing five-year average gross dividend (“dividend”),

• total employment (“employment”),

We also examine a composite, equally weighting four of the above fundamental metrics of size (“composite”). This composite excludes the total employment because that is not always available, and sales because sales and revenues are so very similar. The four metrics used in the composite are widely available in most countries, so that the Composite Fundamental Index could easily be applied internationally, globally and even in the emerging markets.

The index is rebalanced on the last trading day of each year, using the end of day prices. We hold this portfolio until the end of the next year, at which point we use the most recent company financial information to calculate the following year’s index weights.

We rebalance the index only once a year, on the last trading day of the year, for two reasons. First, the financial data available through Compustat are available only on an annual basis in the earliest years of our study. Second, when we try monthly, quarterly, and semi-annual rebalancing, we increase index turnover but find no appreciable return advantage over annual rebalancing.

Performance of the fundamental indices

The returns produced by the fundamental indices are, on average, 1.91 percent higher than the S&P500. The best of the fundamental indexes outpaces the Reference Capitalization index by 2.50% per annum:

Surprisingly, the composite rivals the performance of the average, even though it excludes two of the three best Fundamental Indexes! Most of these indexes outpace the equal-weighted index of the top 1000 by capitalization, with lower risk, lower beta.

Note that the “Reference Capitalization index” is a 1000-stock capitalization-weighted equity market index that bears close resemblance to the highly regarded Russell 1000, although it is not identical. The construction of the Reference Capitalization index allows Arnott et al to “make direct comparisons with the Fundamental Indexes uncomplicated by questions of float, market impact, subjective selections, and so forth.”

Value-Added

In the “value-added” chart Arnott et al examine the correlation of the value added for the various indexes, net of the return for the Reference Capitalization index, with an array of asset classes.

Here, we find differences that are more interesting, though often lacking in statistical significance. The S&P 500 would seem to outpace the Reference Capitalization index when the stock market is rising, the broad US bond market is rising (i.e., interest rates are falling), and high-yield bonds, emerging markets bonds and REITS are performing badly. The Fundamental Indexes have mostly the opposite characteristics, performing best when US and non-US stocks are falling and REITS are rising. Curiously, they mostly perform well when High Yield bonds are rising but Emerging Markets bonds are falling. Also, they tend to perform well when TIPS are rising (i.e., real interest rates are falling). Most of these results are unsurprising; but, apart from the S&P and REIT correlations, most are also not statistically significant.

Commentary

Arnott et al make some excellent points in the paper:

We believe the performance of these Fundamental Indexes are largely free of data mining. Our selection of size metrics were intuitive and were not selected ex post, based upon results. We use no subjective stock selection or weighting decisions in their construction, and the portfolios are not fine-tuned in any way. Even so, we acknowledge that our research may be subject to the following – largely unavoidable – criticisms:

we lived through the period covered by this research (1/1962-12/2003); we experienced bubble periods where cap-weighting caused severe destruction of investor wealth, contributing to our concern about the efficacy of capitalization-weighted indexation (the “nifty fifty” of 1971-72, the bubble of 1999-2000) and

• our Fundamental metrics of size, such as book value, revenues, smoothed earnings, total employment, and so forth, all implicitly introduce a value bias, amply documented as possible market inefficiencies or as priced risk factors. (Reciprocally, it can be argued that capitalization-weighted indexes have a growth bias, whereas the Fundamental Indexes do not.)

They also make some interesting commentary about global diversification using fundamental indexation:

For international and global portfolios, it’s noteworthy that Fundamental Indexing introduces a more stable country allocation than capitalization weighting. Just as the Fundamental Indexes smooth the movement of sector and industry allocations to mirror the evolution of each sector or industry’s scale in the overall economy, a global Fundamental Indexes index will smooth the movement of country allocations, mirroring the relative size of each country’s scale in the global economy. In other words, a global Fundamental Indexes index should offer the same advantages as GDP-weighted global indexing, with the same rebalancing “alpha” enjoyed by GDP-weighting. We would argue that the “alpha” from GDP-weighting in international portfolios is perhaps attributable to the elimination of the same capitalization-weighted return drag (from overweighting the overvalued countries and underweighting the undervalued countries) as we observe in the US indexes. This is the subject of some current research that we hope to publish in the coming year.

And finally:

This method outpaces most active managers, by a much greater margin and with more consistency, than conventional capitalization-weighted indexes. This need not argue against active management; it only suggests that active managers have perhaps been using the wrong “market portfolio” as a starting point, making active management “bets” relative to the wrong index. If an active management process can add value, then it should perform far better if it makes active bets against one of these Fundamental Indexes than against capitalization-weighted indexes.

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It’s a year old, but it’s still sweet. A chart from Tom Brakke’s Research Puzzle pix comparing the performance of the S&P500 and its equal weight counterpart from 2000 to March 2011:

Tom thinks the phenomenon might reverse:

At some point, however, this trade will flip back in a major way and the market-weighted indexes will be formidable competitors.  Will it only be when the market corrects?  We know from the 1990s that that doesn’t have to be the case — the biggest stocks can lead in an up market.  But whatever the cause of the change, should the behemoths that have been lagging get traction, it will cause significant disruption in a pattern that has gotten pretty comfortable.

For the reasons I’ve set out this week, I think that market cap-weighted indices suffer from the systematic flaw that they buy more of a particular stock as its market capitalization increases. A market capitalization-weight index will systematically invest too much in stocks when they are overpriced and too little in stocks when they are priced at bargain levels. An equally-weighted index will own more of bargain stocks and less of overpriced stocks. Since stocks in the index aren’t affected by price, errors will be random and average out over time.

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Yesterday I took a look at the different ways of structuring an index suggested by Joel Greenblatt.

Greenblatt finds that an equal-weight portfolio far outperforms a market capitalization weight portfolio.

And for good reason. Greenblatt says that market cap weighted indexes suffer from a systematic flaw – they increase the amount they own of a particular company as that company’s stock price increases.  So they systematically invest too much in stocks when they are overpriced and too little in stocks when they are priced at bargain levels. The equal weight index corrects this systematic flaw to a degree (the small correction is still worth 2.7 percent per year in additional performance). An equally-weighted index will still own too much of overpriced stocks and too little of bargain-priced stocks, but in other cases, it will own more of bargain stocks and less of overpriced stocks. Since stocks in the index aren’t affected by price, errors will be random and average out over time.

There is some good research on the structuring of indices. In a Janaury 2012 paper Why Does an Equal-Weighted Portfolio Outperform Value- and Price-Weighted Portfolios? Yuliya Plyakha, Raman Uppal and Grigory Vilkov examine the performance of equal-, value-, and price-weighted portfolios of stocks in the major U.S. equity indices over the last four decades (note that here “value” weight is used in the academic sense, meaning “market capitalization weight”).

The researchers find find that the equal-weighted portfolio with monthly rebalancing outperforms the value- and price-weighted portfolios in terms of total mean return, four factor alpha, Sharpe ratio, and certainty-equivalent return, even though the equal-weighted portfolio has greater portfolio risk. (It’s interesting that they find the equal-weighted index possesses alpha. I think that says more about the calculation of alpha than it does about the equal-weight index, but I digress.)

They find that total return of the equal-weighted portfolio exceeds that of the value- and price-weighted because the equal-weighted portfolio has both a higher return for bearing systematic risk and a higher alpha measured using the four-factor model. The higher systematic return of the equal-weighted portfolio arises from its higher exposure to the market, size, and value factors.

They seem to agree with Greenblatt when they find that the higher alpha of the equal-weighted portfolio arises from the monthly rebalancing required to maintain equal weights, which is a “contrarian strategy that exploits reversal and idiosyncratic volatility of the stock returns; thus, alpha depends only on the monthly rebalancing and not on the choice of initial weights.”

[We demonstrate that the source of this extra alpha of the equal-weighted portfolio is the “contrarian” rebalancing each month that is required to maintain equal weights, which exploits the “reversal” in stock prices that has been identified in the literature (see, for instance, Jegadeesh (1990) and Jegadeesh and Titman (1993, 2002)).

To demonstrate our claim, we consider two experiments, which are in opposite directions. In the first experiment, we reduce the frequency for rebalancing the equal-weighted portfolio from 1 month, to 6 months and then to 12 months. If our claim is correct, then as we reduce the rebalancing frequency, we should see the alpha of the equal-weighted portfolio decrease toward the level of the alpha of the value- and price-weighted portfolios, which do not entail any rebalancing.

In the second experiment, we reverse the process and artificially fix the weights of the value- and price-weighted portfolios to give them the contrarian flavor of the equal-weighted portfolio. For instance, consider the case where the rebalancing frequency is t = 12 months. Then each month we change the weights of the value- and price-weighted portfolios so that they are the same as the initial weights at t = 0. Only after 12 months have elapsed, do we set the weights to be the true value and price weights. Then, again for the next 12 months, we keep the weights of the value- and price-weighted portfolios constant so that they are equal to the weights for these portfolios at the 12-month date. Only after another 12 months have elapsed do we set the weights to be the true value and price-weighted weights at t = 24 months. We undertake this experiment for rebalancing frequencies of 6 and 12 months. If our claim is correct, then as we keep fixed the weights of the value- and price-weighted portfolios for 6 months and 12 months, the alphas of these two portfolios should increase toward the alpha of the equal-weighted portfolio.

The results of both experiments confirm our hypothesis that it is the monthly rebalancing of the equal-weighted portfolio that generates the alpha for this strategy. Table 4 shows that as we reduce the rebalancing frequency of the equal-weighted portfolio from the base case of 1 month to 6 months and then to 12 months, the per annum alpha of the equal-weighted portfolio drops from 175 basis points to 117 basis points and then to 80 basis points.Once the rebalancing frequency of the equal-weighted portfolio is 12 months, the difference in the alpha of the equal-weighted portfolio and that of the value- and price-weighted portfolios is no longer statistically significant (the p-value for the difference in alpha of the equal- and value-weighted portfolios is 0.96 and for the difference of the equal- and price-weighted portfolios is 0.98).

Similarly, for the second experiment we see from Table 5 that once we hold constant the weights of the value- and price-weighted portfolios for 12 months and rebalance the weights only after 12 months, the differences in alphas for the equal-weighted portfolio relative to the value- and price-weighted portfolios is statistically insignificant (with the p-values being 0.65 and 0.30).

An important insight from these experiments is that the higher alpha of the equal-weighted portfolio arises, not from the choice of equal weights, but from the monthly rebalancing to maintain equal weights, which is implicitly a contrarian strategy that exploits reversal that is present at the monthly frequency. Thus, alpha depends on only the rebalancing strategy and not on the choice of initial weights.

Table 4 (Click to embiggen)

Table 5 (click to embiggen)


And two charts showing size and book-to-market measures:

Conclusion

Equal-weighting is a contrarian strategy that exploits the “reversal” in stock prices and eliminates some of the errors in market capitalization-weighted indices.

The monthly rebalancing of the equal-weighted portfolio generates the alpha for this strategy. As we reduce the rebalancing frequency of the equal-weighted portfolio from the base case of 1 month to 6 months and then to 12 months, the per annum alpha of the equal-weighted portfolio drops from 175 basis points to 117 basis points and then to 80 basis points.

For me, the most important part of the study is the finding that “The nonparametric monotonicity relation test indicates that the differences in the total return of the equal-weighted portfolio and the value- and price-weighted portfolios is monotonically related to size, price, liquidity and idiosyncratic volatility.” (Kidding, I’ve got no idea what that means.)

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