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Posts Tagged ‘Joel Greenblatt’

In the How to beat The Little Book That Beats The Market (Part 1 2, and 3) series of posts I showed how in Quantitative Value we tested Joel Greenblatt’s Magic Formula (outlined in The Little Book That (Still) Beats the Market) and found that it had consistently outperformed the market, and with lower relative risk than the market.

We sought to improve on it by creating a generic, academic alternative that we called “Quality and Price.” Quality and Price is the academic alternative to the Magic Formula because it draws its inspiration from academic research papers. We found the idea for the quality metric in an academic paper by Robert Novy-Marx called The Other Side of Value: Good Growth and the Gross Profitability Premium. Quality and Price substitutes for the Magic Formula’s ROIC a quality measure called gross profitability to total assets (GPA), defined as follows:

GPA = (Revenue − Cost of Goods Sold) / Total Assets

In Quality and Price, the higher a stock’s GPA, the higher the quality of the stock.

The price ratio, drawn from the early research into value investment by Eugene Fama and Ken French, is book value-to-market capitalization (BM), defined as follows:

BM = Book Value / Market Price

The Quality and Price strategy, like the Magic Formula, seeks to differentiate between stocks by equally weighting the quality and price metrics. Can we improve performance by seeking higher quality stocks in the value decile, rather than equal weighting the two factors?

In his paper The Quality Dimension of Value Investing, Novy-Marx considered this question. Novy-Marx’s rationale:

Value investors can also improve their performance by controlling for quality when investing in value stocks. Traditional value strategies formed on price signals alone tend to be short quality, because cheap firms are on average of lower quality than similar firms trading at higher prices. Because high quality firms on average outperform low quality firms, this quality deficit drags down the returns to traditional value strategies. The performance of value strategies can thus be significantly improved by explicitly controlling for quality when selecting stocks on the basis of price. Value strategies that buy (sell) cheap (expensive) firms from groups matched on the quality dimension significantly outperform value strategies formed solely on the basis of valuations.

His backtest method:

The value strategy that controls for quality is formed by first sorting the 500 largest financial firms each June into 10 groups of 50 on the basis of the quality signal. Within each of these deciles, which contain stocks of similar quality, the 15 with the highest value signals are assigned to the high portfolio, while the 15 with the lowest value signals are assigned to the low portfolio. This procedure ensures that the value and growth portfolios, which each hold 150 stocks, contain stocks of similar average quality.

Novy-Marx finds that the strategy “dramatically outperform[s]” portfolios formed on the basis of quality or value alone, but underperforms the Greenblatt-style joint strategy. From the paper:

The long/short strategy generated excess returns of 45 basis points per month, 50% higher than the 31 basis points per month generated by the unconditional quality strategy, despite running at lower volatility (10.4% as opposed to 12.2%). The long side outperformed the market by 32 basis points per month, 9 basis points per month more than the long-only strategy formed without regard for price. It managed this active return with a market tracking error volatility of only 5.9%, realizing an information ratio of 0.63, much higher than the information ratio of 0.42 realized on the tracking error of the unconditional long-only value strategy.

For comparison, Novy-Marx finds the Greenblatt-style joint 50/50 weighting generates higher returns:

The long/short strategy based on the joint quality and value signal generated excess returns of 61 basis points per month, twice that generated by the quality or value signals alone and a third higher than the market, despite running at a volatility of only 9.7%. The strategy realized a Sharpe ratio 0.75 over the sample, almost two and a half times that on the market over the same period, despite trading exclusively in the largest, most liquid stocks.

The long side outperformed the market by 35 basis points per month, with a tracking error volatility of only 5.7 percent, for a realized information ratio of 0.75. This information ratio is 15% higher than the 0.65 achieved running quality and value side by side. Just as importantly, it allows long-only investors to achieve a greater exposure to the high information ratio opportunities provided by quality and value. While the strategy’s 5.7% tracking error still provides a suboptimally small exposure to value and quality, this exposure is significantly larger than the long-only investor can obtain running quality alongside value.

And a pretty chart from the paper:

Novy-Marx 2.1

We tested the decile approach and the joint approach in Quantitative Value, substituting better performing value metrics and found different results. I’ll cover those next.

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In How to Beat The Little Book That Beats The Market: Redux (and Part 2) I showed how in Quantitative Value we tested Joel Greenblatt’s Magic Formula outlined in The Little Book That (Still) Beats the Market).

We created a generic, academic alternative to the Magic Formula that we call “Quality and Price,” that substituted for EBIT/TEV as its price measure the classic measure in finance literature – book value-to-market capitalization (BM):

BM = Book Value / Market Price

Quality and Price substitutes for ROIC a quality measure called gross profitability to total assets (GPA). GPA is defined as follows:

GPA = (Revenue − Cost of Goods Sold) / Total Assets

Like the Magic Formula, it seeks to identify the best combination of high quality and low price. The difference is that Quality and Price substitutes different measures for the quality and price factors. There are reasonable arguments for adopting the measures used in Quality and Price over those used in the Magic Formula, but it’s not an unambiguously more logical approach than the Magic Formula. Whether one combination of measures is better than any other ultimately depends here on their relative performance. So how does Quality and Price stack up against the Magic Formula?

Here are the results of our study comparing the Magic Formula and Quality and Price strategies for the period from 1964 to 2011. Figure 2.5 from the book shows the cumulative performance of the Magic Formula and the Quality and Price strategies for the period 1964 to 2011.

Magic Formula vs Quality and Price

Quality and Price handily outpaces the Magic Formula, turning $100 invested on January 1, 1964, into $93,135 by December 31, 2011, which represents an average yearly compound rate of return of 15.31 percent. The Magic Formula turned $100 invested on January 1, 1964, into $32,313 by December 31, 2011, which represents a CAGR of 12.79 percent. As we discuss in detail in the book, while much improved, Quality and Price is not a perfect strategy: the better returns are attended by higher volatility and worse drawdowns. Even so, on risk-adjusted basis, Quality and Price is the winner.

Figure 2.7 shows the performance of each decile ranked according to the Magic Formula and Quality and Price for the period 1964 to 2011. Both strategies do a respectable job separating the better performed stocks from the poor performers.

Qp MF Decile

This brief examination of the Magic Formula and its generic academic brother Quality and Price, shows that analyzing stocks along price and quality contours can produce market-beating results. This is not to say that our Quality and Price strategy is the best strategy. Far from it. Even in Quality and Price, the techniques used to identify price and quality are crude. More sophisticated measures exist.

At heart, we are value investors, and there are a multitude of metrics used by value investors to find low prices and high quality. We want to know whether there are other, more predictive price and quality metrics than those used by Magic Formula and Quality and Price.

In Quantitative Value, we conduct an examination into existing industry and academic research into a variety of fundamental value investing methods, and simple quantitative value investment strategies. We then independently backtest each method, and strategy, and combine the best into a new quantitative value investment model.

Order from Quantitative Value from Wiley FinanceAmazon, or Barnes and Noble.

Click here if you’d like to read more on Quantitative Value, or connect with me on LinkedIn.

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In How to Beat The Little Book That Beats The Market: Redux I showed how in Quantitative Value we tested Joel Greenblatt’s Magic Formula outlined in The Little Book That (Still) Beats the Market). We found that Greenblatt’s Magic Formula has consistently outperformed the market, and with lower relative risk than the market, but wondered if we could improve on it.

We created a generic, academic alternative to the Magic Formula that we call “Quality and Price.” Quality and Price is the academic alternative to the Magic Formula because it draws its inspiration from academic research papers. We found the idea for the quality metric in an academic paper by Robert Novy-Marx called The Other Side of Value: Good Growth and the Gross Profitability Premium. The price ratio is drawn from the early research into value investment by Eugene Fama and Ken French. The Quality and Price strategy, like the Magic Formula, seeks to differentiate between stocks on the basis of … wait for it … quality and price. The difference, however, is that Quality and Price uses academically based measures for price and quality that seek to improve on the Magic Formula’s factors, which might provide better performance.

The Magic Formula uses Greenblatt’s version of return on invested capital (ROIC) as a proxy for a stock’s quality. The higher the ROIC, the higher the stock’s quality and the higher the ranking received by the stock. Quality and Price substitutes for ROIC a quality measure we’ll call gross profitability to total assets (GPA). GPA is defined as follows:

GPA = (Revenue − Cost of Goods Sold) / Total Assets

In Quality and Price, the higher a stock’s GPA, the higher the quality of the stock. The rationale for using gross profitability, rather than any other measure of profitability like earnings or EBIT, is simple. Gross profitability is the “cleanest” measure of true economic profitability. According to Novy-Marx:

The farther down the income statement one goes, the more polluted profi tability measures become, and the less related they are to true economic profi tability. For example, a firm that has both lower production costs and higher sales than its competitors is unambiguously more profitable. Even so, it can easily have lower earnings than its competitors. If the firm is quickly increasing its sales though aggressive advertising, or commissions to its sales force, these actions can, even if optimal, reduce its bottom line income below that of its less profitable competitors. Similarly, if the firm spends on research and development to further increase its production advantage, or invests in organizational capital that will help it maintain its competitive advantage, these actions result in lower current earnings. Moreover, capital expenditures that directly increase the scale of the firm’s operations further reduce its free cash flows relative to its competitors. These facts suggest constructing the empirical proxy for productivity using gross profits.

The Magic Formula uses EBIT/TEV as its price measure to rank stocks. For Quality and Price, we substitute the classic measure in finance literature – book value-to-market capitalization (BM):

BM = Book Value / Market Price

 We use BM rather than the more familiar price-to-book value or (P/B) notation because the academic convention is to describe it as BM, and it makes it more directly comparable with the Magic Formula’s EBIT/TEV. The rationale for BM capitalization is straightforward. Eugene Fama and Ken French consider BM capitalization a superior metric because it varies less from period to period than other measures based on income:

We always emphasize that different price ratios are just different ways to scale a stock’s price with a fundamental, to extract the information in the cross-section of stock prices about expected returns. One fundamental (book value, earnings, or cashflow) is pretty much as good as another for this job, and the average return spreads produced by different ratios are similar to and, in statistical terms, indistinguishable from one another. We like [book-to-market capitalization] because the book value in the numerator is more stable over time than earnings or cashflow, which is important for keeping turnover down in a value portfolio.

Next I’ll compare show the results of our examination of Quality and Price strategy to the Magic Formula. If you can’t wait, you can always pick up a copy of Quantitative Value.

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Last May in How to beat The Little Book That Beats The Market: An analysis of the Magic Formula I took a look at Joel Greenblatt’s Magic Formula, which he introduced in the 2006 book The Little Book That Beats The Market (now updated to The Little Book That (Still) Beats the Market).

Wes and I put the Magic Formula under the microscope in our book Quantitative Value. We are huge fans of Greenblatt and the Magic Formula, writing in the book that Greenblatt is Benjamin Graham’s “heir in the application of systematic methods to value investment”.

The Magic Formula follows the same broad principles as the simple Graham model that I discussed a few weeks back in Examining Benjamin Graham’s Record: Skill Or Luck?. The Magic Formula diverges from Graham’s strategy by exchanging for Graham’s absolute price and quality measures (i.e. price-to-earnings ratio below 10, and debt-to-equity ratio below 50 percent) a ranking system that seeks those stocks with the best combination of price and quality more akin to Buffett’s value investing philosophy.

The Magic Formula was born of an experiment Greenblatt conducted in 2002. He wanted to know if Warren Buffett’s investment strategy could be quantified. Greenblatt read Buffett’s public pronouncements, most of which are contained in his investment vehicle Berkshire Hathaway, Inc.’s Chairman’s Letters. Buffett has written to the shareholders of Berkshire Hathaway every year since 1978, after he first took control of the company, laying out his investment strategy in some detail. Those letters describe the rationale for Buffett’s dictum, “It’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price.” Greenblatt understood that Buffett’s “wonderful-company-at-a-fair-price” strategy required Buffett’s delicate qualitative judgment. Still, he wondered what would happen if he mechanically bought shares in good businesses available at bargain prices. Greenblatt discovered the answer after he tested the strategy: mechanical Buffett made a lot of money.

Wes and I tested the strategy and outlined the results in Quantitative Value. We found that Greenblatt’s Magic Formula has consistently outperformed the market, and with lower relative risk than the market. Naturally, having found something not broke, we set out to fix it, and wondered if we could improve on the Magic Formula’s outstanding performance. Are there other simple, logical strategies that can do better? Tune in soon for Part 2.

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The only fair fight in finance: Joel Greenblatt versus himself. In this instance, it’s the 250 best special situations investors in the US on Joel’s special situations site valueinvestorsclub.com versus his Magic Formula.

Wes Gray and crew at Empiritrage have pumped out some great papers over the last few years, and their Man vs. Machine: Quantitative Value or Fundamental Value? is no exception. Wes et al have set up an experiment comparing the performance of the stocks selected by the investors on the VIC – arguably the best 250 special situation investors in the US – and the top decile of stocks selected by the Magic Formula over the period March 1, 2000 through to the end of last year. The stocks had to have a minimum market capitalization of $500 million, were equally weighted and held for 12 months after selection.

The good news for the stocks pickers is that the VIC members handed the Magic Formula its head:

There’s slightly less advantage to the VIC members on a risk/reward basis, but man still comes out ahead:

Gray et al note that the Man-versus-Magic Formula question is a trade-off.

  • Man brings more return, but more risk; Machine has lower return, but less risk.
  • The risk/reward tradeoff is favorable for Man, in other words, the Sharpe ratio is higher for Man relative to Machine.
  • Value strategies dominate regardless of who implements the strategy.

Read the rest of the paper here.

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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.)

Buy my book The Acquirer’s Multiple: How the Billionaire Contrarians of Deep Value Beat the Market from on Kindlepaperback, and Audible.

Here’s your book for the fall if you’re on global Wall Street. Tobias Carlisle has hit a home run deep over left field. It’s an incredibly smart, dense, 213 pages on how to not lose money in the market. It’s your Autumn smart read. –Tom Keene, Bloomberg’s Editor-At-Large, Bloomberg Surveillance, September 9, 2014.

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Joel Greenblatt’s 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.”

Yesterday we examined the first point. Today let’s examine the second.

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

I think this chart is compelling:

It shows the CAGRs for a variety of indices over the 20 years to December 31, 2010. The first thing to note is that the equal weight index – represented by the &P500 Equal Weight TR – has a huge advantage over the market capitalization weighted S&P500 TR. Greenblatt says:

Over time, traditional market-cap weighted indexes such as the S&P 500 and the Russell 1000 have been shown to outperform most active managers. However, market cap weighted indexes suffer from a systematic flaw. The problem is that market-cap weighted indexes increase the amount they own of a particular company as that company’s stock price increases. As a company’s stock falls, its market capitalization falls and a market cap-weighted index will automatically own less of that company. However, over the short term, stock prices can often be affected by emotion. A market index that bases its investment weights solely on market capitalization (and therefore market price) will systematically invest too much in stocks when they are overpriced and too little in stocks when they are priced at bargain levels. (In the internet bubble, for example, as internet stocks went up in price, market cap-weighted indexes became too heavily concentrated in this overpriced sector and too underweighted in the stocks of established companies in less exciting industries.) This systematic flaw appears to cost market-cap weighted indexes approximately 2% per year in return over long periods.

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). Greenblatt describes it as randomizing the errors made by the market capitalization weighted index:

One way to avoid the problem of buying too much of overpriced stocks and too little of bargain stocks in a market-cap weighted index is to create an index that weights each stock in the index equally. 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. For this reason, equally weighted indexes should add back the approximately 2% per year lost to the inefficiencies of market-cap weighting.

While the errors are randomized in the equal weight index, they are still systematic – it still owns too much of the expensive stocks and too little of the cheap ones. Fundamental weighting corrects this error (again to a small degree). Fundamentally-weighted indexes weight companies based on their economic size using price ratios such as sales, book value, cash flow and dividends. The surprising thing is that this change is worth only 0.4 percent per year over equal weighting (still 3.1 percent per year over market capitalization weighting).

Similar to equally-weighted indexes, company weights are not affected by market price and therefore pricing errors are also random. By correcting for the systematic errors caused by weighting solely by market-cap, as tested over the last 40+ years, fundamentally-weighted indexes can also add back the approximately 2% lost each year due to the inefficiencies of market-cap weighting (with the last 20 years adding back even more!).

The Magic Formula / “value” weighted index has a huge advantage over fundamental weighting (+3.9 percent per year), and is a massive improvement over the market capitalization index (+7 percent per year). Greenblatt describes it as follows:

On the other hand, value-weighted indexes seek not only to avoid the losses due to the inefficiencies of market-cap weighting, but to add performance by buying more of stocks when they are available at bargain prices. Value-weighted indexes are continually rebalanced to weight most heavily those stocks that are priced at the largest discount to various measures of value. Over time, these indexes can significantly outperform active managers, market cap-weighted indexes, equally-weighted indexes, and fundamentally-weighted indexes.

I like Greenblatt’s approach. I’ve got two small criticisms:

1. I’m not sure that his Magic Formula weighting is genuine “value” weighting. Contrast Greenblatt’s approach with Dylan Grice’s “Intrinsic Value to Price” or “IVP” approach, which is a modified residual income approach, the details of which I’ll discuss in a later post. Grice’s IVP is a true intrinsic value calculation. He explains his approach in a way reminiscent of Buffett’s approach:

[How] is intrinsic value estimated? To answer, think first about how much you should pay for a going concern. The simplest such example would be that of a bank account containing $100, earning 5% per year interest. This asset is highly liquid. It also provides a stable income. And if I reinvest that income forever, it provides stable growth too. What’s it worth?

Let’s assume my desired return is 5%. The bank account is worth only its book value of $100 (the annual interest payment of $5 divided by my desired return of 5%). It may be liquid, stable and even growing, but since it’s not generating any value over and above my required return, it deserves no premium to book value.

This focus on an asset’s earnings power and, in particular, the ability of assets to earn returns in excess of desired returns is the essence of my intrinsic valuation, which is based on Steven Penman’s residual income model.1 The basic idea is that if a company is not earning a return in excess of our desired return, that company, like the bank account example above, deserves no premium to book value.

And it seems to work:

Grice actually calculates IVP while Greenblatt does not. Does that actually matter? Probably not. Even if it’s not what I think the average person understands real “value” weighting to be, Greenblatt’s approach seems to work. Why quibble over semantics?

2. As I’ve discussed before, Greenblatt’s Magic Formula return owes a great deal to his selection of EBIT/TEV as the price limb of his model. EBIT/TEV has been very well performed historically. If we were to substitute EBIT/TEV for the P/B, P/E, price-to-dividends, P/S, P/whatever, we’d have seen slightly better performance than the Magic Formula provided, but you might have been out of the game somewhere between 1997 to 2001.

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Joel Greenblatt’s 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.”

Let’s examine each of these points in some more depth.

Most investors, pro’s included, can’t beat the index.

The most famous argument against active management (at least by mutual funds) is by John Bogle, made before the Senate Subcommittee on Financial Management, the Budget, and International Security on November 3, 2003. Bogle’s testimony was on the then market-timing scandal, but he used the opportunity to speak more broadly on the investment industry.

Bogle argued that the average mutual fund should earn the market’s return less costs, but investors earn even less because they try to time the market:

What has been described as “a pathological mutation” in corporate America has transformed traditional owners capitalism into modern-day managers capitalism. In mutual fund America, the conflict of interest between fund managers and fund owners is an echo, if not an amplification, of that unfortunate, indeed “morally unacceptable”5 transformation. The blessing of our industry’s market-timing scandal—the good for our investors blown by that ill wind—is that it has focused the spotlight on that conflict, and on its even more scandalous manifestations: the level of fund costs, the building of assets of individual funds to levels at which they can no longer differentiate themselves, and the focus on selling funds that make money for managers while far too often losing money—and lots of it—for investors.

The net results of these conflicts of interest is readily measurable by comparing the long-term returns achieved by mutual funds, and by mutual fund shareholders, with the returns earned in the stock market itself. During the period 1984-2002, the U.S. stock market, as measured by the S&P 500 Index, provided an annual rate of return of 12.2%. The return on average mutual fund was 9.3%.6 The reason for that lag is not very complicated: As the trained, experienced investment professionals employed by the industry’s managers compete with one another to pick the best stocks, their results average out. Thus, the average mutual fund should earn the market’s return—before costs. Since all-in fund costs can be estimated at something like 3% per year, the annual lag of 2.9% in after-cost return seems simply to confirm that eminently reasonable hypothesis.

But during that same period, according to a study of mutual fund data provided by mutual fund data collector Dalbar, the average fund shareholder earned a return just 2.6% a year. How could that be? How solid is that number? Can that methodology be justified? I’d like to conclude by examining those issues, for the returns that fund managers actually deliver to fund shareholders serves as the definitive test of whether the fund investor is getting a fair shake.

This makes sense. Large mutual funds are the market, so on average earn returns that equate to the market average less costs. While it’s not directly on point, the huge penalty for timing and selection errors is worth exploring further.

Timing and selection penalties

Timing and selection penalties eat a huge proportion of the return. These costs are the result of investors investing in funds after good performance, and withdrawing from funds after poor performance:

It is reasonable to expect the average mutual fund investor to earn a return that falls well short of the return of the average fund. After all, we know that investors have paid a large timing penalty in their decisions, investing little in equity funds early in the period and huge amounts as the market bubble reached its maximum. During 1984-1988, when the S&P Index was below 300, investors purchased an average of just $11 billion per year of equity funds. They added another $105 billion per year when the Index was still below 1100. But after it topped the 1100 mark in 1998, they added to their holdings at an $218 billion(!) annual rate. Then, during the three quarters before the recent rally, with the Index below 900, equity fund investors actually withdrew $80 billion. Clearly, this perverse market sensitivity ill-served fund investors.

The Dalbar study calculates the returns on these cash flows as if they had been invested in the Standard & Poor’s 500 Index, and it is that simple calculation that produces the 2.6% annual investor return. Of course, it is not entirely fair to compare the return on those periodic investments over the years with initial lump-sum investments in the S&P 500 Stock Index and in the average fund. The gap between those returns and the returns earned by investors, then, is somewhat overstated. More appropriate would be a comparison of regular periodic investments in the market with the irregular (and counterproductive) periodic investments made by fund investors, which would reduce both the market return and the fund return with which the 2.6% return has been compared.

But if the gap is overstated, so is the 2.6% return figure itself. For investors did notselect the S&P 500 Index, as the Dalbar study implies. What they selected was an average fund that lagged the S&P Index by 2.9% per year. So they paid not only a timing penalty, but a selection penalty. Looked at superficially, then, the 2.6% return earned by investors should have been minus 0.3%.

Worse, what fund investors selected was not the average fund. Rather they invested most of their money, not only at the wrong time, but in the wrong funds. The selection penalty is reflected by the eagerness of investors as a group to jump into the “new economy” funds, and in the three years of the boom phase, place some $460 billion in those speculative funds, and pull $100 billion out of old-economy value funds—choices which clearly slashed investor returns.

I can imagine how difficult the investment decision is for mutual fund investors. How else does an investor in a mutual fund differentiate between similar funds other than by using historical return? I wouldn’t select a fund with a poor return. I’d put my money into the better one. Which is what everyone does, and why the average return sucks so bad. How bad? Bogle has calculated it below.

Dollar-weighted returns

The calculation of dollar-weighted returns speaks to the cost of timing and selection penalties:

Now let me give you some dollars-and-cents examples of how pouring money into the hot performers and hot sector funds of the era created a truly astonishing gap between (time-weighted) per-share fund returns and (dollar-weighted) returns that reflect what the funds actually earned for their owners. So let’s examine the astonishing gap between those two figures during the recent stock market boom and subsequent bust.

Consider first the “hot” funds of the day—the twenty funds which turned in the largest gains during the market upsurge. These funds had a compound return of 51% per year(!) in 1996-1999, only to suffer a compound annual loss of –32% during the subsequent three years. For the full period, they earned a net annualized return of 1.5%, and a cumulative gain of 9.2%. Not all that bad! Yet the investors in those funds, pouring tens of billions of dollars of their money in after the performance gains began, earned an annual return of minus 12.2%, losing fully 54% of their money during the period.

Now consider sector funds, specific arenas in which investors can (foolishly, as it turns out) make their bets. The computer, telecommunications, and technology sectors were the favorites of the day, but only until they collapsed. The average annual returns of 53% earned in the bull market by a group of the largest sector funds were followed by returns of minus 31% a year in the bear market, a net annual return of 3% and a cumulative gain of 19.2%. Again, not too bad. Yet sector fund investors, similar to the hot fund investors I described earlier, poured billions of dollars in the funds as they soared, and their annual return averaged –12.1%, a cumulative loss of 54% of their capital, too.

While the six-year annual returns for these funds were hardly horrible, both groups did lag the 4.3% annual return of the stock market, as measured by the largest S&P 500 Index Fund, which provided a 29% cumulative gain. But the investors in that index fund, taking no selection risk, minimized the stock market’s influence on their timing and earned a positive 2.4% return, building their capital by 15% during the challenging period. Index investor +15%; sector fund and hot fund investor –54%. Gap: 69 percentage points. It’s a stunning contrast.

Bogle’s conclusion says it all: Index investor +15%; sector fund and hot fund investor –54%. Gap: 69 percentage points. It’s a stunning contrast.

Tomorrow, why fundamental indexing beats the market.

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