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Archive for the ‘Stocks’ Category

What do requests for confidentiality reveal about hedge fund portfolio holdings? In Uncovering Hedge Fund Skill from the Portfolio Holdings They Hide, a paper to be published in the upcoming Journal of Finance (or see a February 2012 version on the SSRN), authors Vikas Agarwal, Wei Jiang, Yuehua Tang, and Baozhong Yang ask whether confidential holdings exhibit superior performance to holdings disclosed on a 13F in the ordinary course.

Institutional investment managers must disclose their quarterly portfolio holdings in a Form 13F. The 13(f) rule allows the SEC to delay disclosure that is “necessary or appropriate in the public interest or for the protection of investors.” When filers request confidential treatment for certain holdings, they may omit those holdings off their Form 13F. After the confidentiality period expires, the filer must reveal the holdings by filing an amendment to the original Form 13F.

Confidential treatment allows hedge funds to accumulate larger positions in stocks, and to spread the trades over a longer period of time. Funds request confidentiality where timely disclosure of portfolio holdings may reveal information about proprietary investment strategies that other investors can free-ride on without incurring the costs of research. The Form 13F filings of investors with the best track records are followed by many investors. Warren Buffett’s new holdings are so closely followed that he regularly requests confidential treatment on his larger investments.

Hedge funds seek confidentiality more frequently than other institutional investors. They constitute about 30 percent of all institutions, but account for 56 percent of all the confidential filings. Hedge funds on average relegate about one-third of their total portfolio values into confidentiality, while the same figure is one-fifth for investment companies/advisors and one-tenth for banks and insurance companies.

The authors make three important findings:

  1. Hedge funds with characteristics associated with more active portfolio management, such as those managing large and concentrated portfolios, and adopting non-standard investment strategies (i.e., higher idiosyncratic risk), are more likely to request confidentiality.
  2. The confidential holdings are more likely to consist of stocks associated with information-sensitive events such as mergers and acquisitions, and stocks subject to greater information asymmetry, i.e., those with smaller market capitalization and fewer analysts following.
  3. Confidential holdings of hedge funds exhibit significantly higher abnormal performance compared to their original holdings for different horizons ranging from 2 months to 12 months. For example, the difference over the 12-month horizon ranges from 5.2% to 7.5% on an annualized basis.

Read a February 2012 version on the SSRN.

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The Superinvestors of Graham-and-Doddsville is a well-known article (see the original Hermes article here.pdf) by Warren Buffett defending value investing against the efficient market hypothesis. The article is an edited transcript of a talk Buffett gave at Columbia University in 1984 commemorating the fiftieth anniversary of Security Analysis, written by Benjamin Graham and David L. Dodd.

In a 2006 talk, “Journey Into the Whirlwind: Graham-and-Doddsville Revisited,” Louis Lowenstein*, then a professor at the Columbia Law School, compared the performance of a group of “true-blue, walk-the-walk value investors” (the “Goldfarb Ten”) and “a group of large cap growth funds” (the “Group of Fifteen”).

Here are Lowenstein’s findings:

For the five years ended this past August 31, the Group of Fifteen experienced on average negative returns of 8.89% per year, vs. a negative 2.71% for the S&P 500.4 The group of ten value funds I had studied in the “Searching for Rational Investors” article had been suggested by Bob Goldfarb of the Sequoia Fund.5 Over those same five years, the Goldfarb Ten enjoyed positive average annual returns of 9.83%. This audience is no doubt quick with numbers, but let me help. Those fifteen large growth funds underperformed the Goldfarb Ten during those five years by an average of over 18 percentage points per year. Hey, pretty soon you have real money. Only one of the fifteen had even modestly positive returns. Now if you go back ten years, a period that includes the bubble, the Group of Fifteen did better, averaging a positive 8.13% per year.Even for that ten year period, however, they underperformed the value group, on average, by more than 5% per year.6 With a good tailwind, those large cap funds were not great – underperforming the index by almost 2% per year – and in stormy weather their boats leaked badly.

Lowenstein takes a close look at one of the Group of Fifteen (a growth fund):

The first was the Massachusetts Investors Growth Stock Fund, chosen because of its long history. Founded in 1932, as the Massachusetts Investors Second Fund, it was, like its older sibling, Massachusetts Investors Trust, truly a mutual fund, in the sense that it was managed internally, supplemented by an advisory board of six prominent Boston businessmen.7 In 1969, when management was shifted to an external company, now known as MFS Investment Management, the total expense ratio was a modest 0.32%.

I am confident that the founders of the Massachusetts Investors Trust would no longer recognize their second fund, which has become a caricature of the “do something” culture. The expense ratio, though still below its peer group, has tripled. But it’s the turbulent pace of trading that would have puzzled and distressed them. At year-end 1999, having turned the portfolio over 174%, the manager said they had moved away from “stable growth companies” such as supermarket and financial companies, and into tech and leisure stocks, singling out in the year- end report Cisco and Sun Microsystems – each selling at the time at about 100 X earnings – for their “reasonable stock valuation.” The following year, while citing a bottom-up, “value sensitive approach,” the fund’s turnover soared to 261%. And in 2001, with the fund continuing to remark on its “fundamental . . .bottom-up investment process,” turnover reached the stratospheric level of 305%. It is difficult to conceive how, even in 2003, well after the market as a whole had stabilized, the managers of this $10 billion portfolio had sold $28 billion of stock and then reinvested that $28 billion in other stocks.

For the five years ended in 2003, turnover in the fund averaged 250%. All that senseless trading took a toll. For the five years ended this past August, average annual returns were a negative 9-1/2%. Over the past ten years, which included the glory days of the New Economy, the fund did better, almost matching the index, though still trailing our value funds by 4% a year. Net assets which had been a modest $1.9 billion at Don Phillips’ kickoff date in 1997, and had risen to $17 billion in 2000, are now about $8 billion.

If you’re feeling some sympathy for the passengers in this financial vehicle, hold on. Investors – and I’m using the term loosely – in the Mass. Inv. Growth Stock Fund were for several years running spinning their holdings in and out of the fund at rates approximating the total assets of the fund. In 2001, for example, investors cashed out of $17-1/2 billion in Class A shares, and bought $16 billion in new shares, leaving the fund at year end with net assets of about $14 billion. Having attracted, not investors, but speculators trying to catch the next new thing, management got the shareholders they deserved.

And the value investors?

Having updated my data through August of this year, I am happy to report that the Goldfarb Ten still look true blue – actually better than at year-end 2003. The portfolio turnover rates have dropped on average to 16% – translation, an average holding period of six years. Honey, what did you do today? Nothing, dear.The average cash holding is 14% of the portfolio, and five of the funds are closed to new investors.f Currently, however, two of the still open funds, Mutual Beacon and Clipper, are losing their managers. The company managing the Clipper Fund has been sold twice over and Jim Gipson and two colleagues recently announced they’re moving on. At Mutual Beacon, which is part of the Franklin Templeton family, David Winters has left to create a mutual fund, ah yes, the Wintergreen Fund. It will be interesting to see whether Mutual Beacon and Clipper will maintain their discipline.

Speaking of discipline, you may remember that after Buffett published “The Superinvestors,” someone calculated that while they were indeed superinvestors, on average they had trailed the market one year in three.20 Tom Russo, of the Semper Vic Partners fund, took a similar look at the Goldfarb Ten and found, for example, that four of them had each underperformed the S&P 500 for four consecutive years, 1996-1999, and in some cases by huge amounts. For the full ten years, of course, that underperformance was sharply reversed, and then some. Value investing thus requires not just patient managers but also patient investors, those with the temperament as well as intelligence to feel comfortable even when sorely out of step with the crowd. If you’re fretting that the CBOE Market Volatility Index may be signaling fear this week, value investing is not for you.

* Louis was father to Roger Lowenstein of Buffett: The Making of an American Capitalist.

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A recent study by Wes Gray and Jack Vogel, Dissecting Shareholder Yield, makes the stunning claim that dividend yield doesn’t predict future returns, but more complete measures of shareholder yield might hold some promise. Gray and Vogel say that, “regardless of the yield metric chosen, the predictive power of separating stocks into high and low yield portfolios has lost considerable power in the last twenty years.”

This seems to be part of a trend away from dividends and towards share repurchases, presumably for tax reasons:

Our work is related to previous research on payout yield as a predictor of future returns. Grullen and Michaely [2002] find that firms have substituted away from dividends towards share repurchases. Boudoukh et al (2007) construct two measures of payout yields (Dividends plus repurchases, as well as Dividends plus net repurchases). They find that these payout measures have more predictive ability than the dividend yield. We contribute to the literature by examining an additional variable to our payout yield, namely net debt pay down. Net debt pay down was first proposed by Priest and McClelland (2007), but is not rigorously analyzed. As a preview of our results, we find that the addition of net debt pay down helps performance, but is not a panacea. Similar to all yield metrics, results in the latter half of the sample (1992-2011) are not as strong as those in the first half of the sample (1972-1991).

Gray and Vogel examine four yield measures:

  • Dividends (DIV)
  • Dividends plus repurchases (PAY1)
  • Dividends plus net repurchases (repurchases minus equity issuance) (PAY2)
  • Dividends plus net repurchases plus net debt paydown (SH_YD)

Here’s their table of returns:

They find as follows:

We perform a similar study as Patel et al. on all our yield metrics, but focus on the dividend yield (DIV) and our complete shareholder yield metric (SH_YD) to assess the “high yield, low payout” outperformance hypothesis. We confirm the basic conclusion from Patel et al. that low payout firms outperform high payout firms across all yield quintiles. For example, in the top DIV quintile, high DIV firms earn 12.16% CAGR from 1972-2011, however, low payout firms earn 13.43%, and high payout firms earn 12.15%. After risk adjusting the results with the 3-factor model we find no evidence of outperformance for any DIV portfolio. In Table V we assess a variety of additional risk/reward characteristics. There is no clear evidence that splitting high DIV yield firms into low and high payout adds risk-adjusted value relative to the standard high DIV yield strategy. For example, max drawdowns suggest that high DIV, low payout strategies are actually riskier than high DIV, high payout strategies (64.35% drawdown compared to 58.27%). However, Sharpe and Sortino ratios are marginally higher for high DIV, low payout strategies relative to high DIV, high payout strategies.

When we examine high SH_YD stocks, we come to a similar conclusion: there is no conclusive evidence that separating stocks on payout percentage within a given yield category can systematically add value to an investment strategy.

In summary, we confirm that separating yield quintiles into low and high payout bins has worked historically on a raw returns basis for DIV. Nonetheless, an investigation of the strategy on a risk-adjusted basis and across different yield metrics and samples suggest there is no evidence that a high yield low payout strategy can help an investor predict stocks. If anything, the evidence suggests that investors should potentially investigate strategies that focus on low SH_YD low payout strategies. The alphas for these stocks are -6.30% for the Top 2000 sample and -5.33% for the S&P 500 sample; the additional risk/reward ratios in Table V also show terrible performance for the low SH_YD low payout strategies.

And the table showing the reduction in performance over time:

Gray and Vogel make three key points in their conclusion:

1. More complete yield measures improve performance.

2. All yield measures are becoming less effective over time.

3. Attempting to improve yield measures by separating on payout percentages is not a reliable tool to enhance investment returns.

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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.)

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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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Last week I looked at James Montier’s 2006 paper The Little Note That Beats The Market and his view that investors would struggle to implement the Magic Formula strategy for behavioral reasons, a view borne out by Greenblatt’s own research. This is not a criticism of the strategy, which is tractable and implementable, but an observation on how pernicious our cognitive biases are.

Greenblatt found that a compilation of all the “professionally managed” – read “systematic, automatic (hydromatic)” – accounts earned 84.1 percent over two years against the S&P 500 (up 62.7 percent). A compilation of “self-managed” accounts (the humans) over the same period showed a cumulative return of 59.4 percent, losing to the market by 20 percent, and to the machines by almost 25 percent. So the humans took this unmessupable system and messed it up. As predicted by Montier and Greenblatt.

Ugh.

Greenblatt, perhaps dismayed at the fact that he dragged the horses all the way to the water to find they still wouldn’t drink, has a new idea: value-weighted indexing (not to be confused with the academic term for market capitalization-weighting, which is, confusingly, also called value weighting).

I know from speaking to some of you that this is not a particularly popular idea, but I like it. Here’s Greenblatt’s rationale, paraphrased:

  • 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.”

I like the logic. I also think the data on the last point are persuasive. In chart form, the data on that last point look like this:

The value weighted index knocked out a CAGR of 16.1 percent per year over the last 20 years. Not bad.

Greenblatt explains his rationale in some depth in his latest book The Big Secret. The book has taken some heavy criticism on Amazon – average review is 3.2 out of 5 as of now – most of which I think is unwarranted (for example, “Like many others here, I do not exactly understand the reason for this book’s existence.”).

I’m going to take a close look at the value-weighted index this week.

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