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## How to estimate the long-term return on stocks: What does the future hold?

Yesterday I looked at John Hussman’s method for estimating the long-term returns on stocks. The long-term return on a security consists of two parts: income (from dividends or interest payments), and capital gains (from price changes). For any future stream of income, the higher the price you pay , the lower the annual rate of return you will earn.

Hussman provides the following equation to mathematically estimate the total return on stocks over any future time horizon (annualized):

(1+g)(Original Yield/Terminal Yield)1/N - 1 + (Original + Terminal)/2

Where Original Yield is the original dividend yield (in decimal form), Terminal Yield is the dividend yield expected at the end of the holding period, N is the holding period in years, and g is the growth rate of dividends over the holding period.

Here’s my calculation. If I assume a dividend growth rate of 6 percent (about the long-run average*), the current S&P 500 dividend yield of 2.1 percent (from multpl.com), a terminal S&P 500 dividend yield of 4 percent (Hussman says that the dividend yield on stocks has historically averaged about 4 percent), the expected nominal return over ten years is 2.4 percent annually.

(1+0.06)(0.021/0.04)1/10 - 1 + (0.021 + 0.04)/2 = 0.02435

Ugly.

If I use multpl.com‘s mean and average long-term S&P 500 dividend yields of 4.46 and 4.39 percent respectively it gets uglier still, so I’m not going to bother.

Over 20 years the nominal return rises to 5.7 percent, and over 30 years 6.8 percent.

Still too ugly.

Hussman last calculated the 10-year S&P 500 total returns to be about 5.2 percent annually, and offers the following:

As a rule of thumb, a 1% market decline in a short period of time tends to increase the prospective 10-year return, not surprisingly, by about 0.1%. However, that approximation is less accurate over large movements or over extended periods of time, where growth in fundamentals and compounding effects become important.

The market is approximately flat since Hussman wrote his article on May 21, so the market decline should have had no impact. To get to Hussman’s 5.2 percent with my inputs, we have to assume a 9 percent growth rate (bullish!):

(1+0.09)(0.021/0.04)1/10 - 1 + (0.021 + 0.04)/2 = 0.05248

Or a terminal yield of 2.9 percent (still bullish):

(1+0.06)(0.021/0.0288)1/10 - 1 + (0.021 + 0.0288)/2 = 0.05194

I’ve got no idea why my calculation differs from Hussman’s. I’m all ears if anyone has any suggestions. Either way, even with outrageously bullish assumptions, 5.2 percent is not a great return. It’s about half the historical return of 10 percent. There are other methods of calculating expected returns that I’ll look at tomorrow.

* Hussman says:

Historically, earnings, dividends, revenues, book values and other stock market fundamentals have grown at a rate of 6% annually. Earnings are the most volatile of these, sometimes growing from trough-to-peak at rates approaching 20% annually, and sometimes plunging from peak-to- trough at rates approaching -20% annually. In fact, historically, earnings have been even more volatile than prices themselves. When measured from peak-to-peak or trough-to-trough however, earnings show exactly the same sturdy 6% annual growth rate that other stock market fundamentals exhibit. Over the past century, the highest growth rates over any 30-year period were 6.3% annually for dividends, and 7.8% for earnings (trough to peak).

## How to estimate the long-term return on stocks

There are a number of studies on the estimation of long-term returns to stocks. Ignoring the empirical research momentarily, the best explication of the estimation of long-term returns is by John Hussman in his article Valuations Matter. The logic is  straight forward.

According to Hussman, the long-term return on a security consists of two parts: income (from dividends or interest payments), and capital gains (from price changes). For any future stream of income, the higher the price you pay , the lower the annual rate of return you will earn:

Consider, for simplicity, a 30-year zero-coupon bond with a face value of \$100. If the bond is priced at a yield-to-maturity of 10%, it will cost you \$5.73 today. Over the coming 30 years, the price will advance to \$100, and your annualized return will be 10%. Just what you bargained for.

But what happens in the meantime? Suppose that over the first 10 years of your holding period, interest rates decline, and the yield-to-maturity on your bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be \$25.84. Now here’s the crucial point. Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to- maturity you bargained for when you bought the bond was only 10%, the return you have earned over the first 10 years is an impressive 16.26%!

By holding the security during a period when the yield-to-maturity is falling, you not only earn a return that is higher than the original yield to maturity, you earn a return that is dramatically higher than the future yield-to-maturity!

Now, the rest of the story. Over the remaining 20 years of the bond, you will not earn 16.26% annually, but 7% annually. If you do the math, you will find that over the entire 30 year holding period, you will have made — surprise — 10% annually. Just what you bargained for originally.

Here Hussman applies the same logic to the stock market:

For stocks, the “yield-to-maturity” comes from two components: income plus capital gain. The income component is simply the dividend yield. Assume initially that the dividend yield is held constant over time (we’ll relax this assumption in a moment). If the dividend yield (Dividend/Price) is constant, then by definition, prices must grow at exactly the same rate as dividends grow. By definition, when the dividend yield is unchanged between the date you buy stocks and the date you sell them, your total return equals the dividend yield (income) plus the growth rate of dividends (capital gain).

As a rule, a good estimate of the “yield-to-maturity” on stocks is the 6% long term growth rate plus the dividend yield. But remember, your actual return will only be equal to this value if the dividend yield stays constant over the period that you hold stocks. As we saw in our example, if the yield falls during the period you are holding stocks, your actual return will be even higher than the yield-to-maturity that you bargained for. On the other hand, if the yield on stocks rises over your holding period, your actual return will be even less than the yield-to-maturity you bargained for.

Historically, the dividend yield on stocks has averaged about 4%, and has fluctuated both above and below this 4% figure. As a result, the historical average return on stocks has typically been 6% + 4% = 10%. That’s precisely where that 10% “historical return” on stocks comes from.

Hussman provides the following equation to mathematically estimate the total return on stocks over any future time horizon (annualized):

(1+g)(Original Yield/Terminal Yield)1/N - 1 + (Original + Terminal)/2

Where Original Yield is the original dividend yield (in decimal form), Terminal Yield is the dividend yield expected at the end of the holding period, N is the holding period in years, and g is the growth rate of dividends over the holding period.

I find the logic appealing, but we should also consider how well the equation predicts the subsequent performance of the market. Here’s a chart from a recent Weekly Market Comment showing the projections for 10-year annual total returns on the S&P 500 versus actual subsequent 10-year total returns:

Seems like a pretty good fit. The kicker: Hussman wrote his “Valuations Matter” article in June 1998, at which time he said of the market:

Currently, assuming dividend growth speeds up to a 6% rate and that the dividend yield is still just 1.4% in the future, the long term total return on stocks will be 7.4%. But here’s a more likely result: suppose the future dividend yield rises even a bit, even to just 2%. If that happens over the next 5 years, investors will earn a total return of zero over those 5 years. Over the next 10 years: just 4% annually. Over the next 20 years: 5.8% annually. Over the next 30 years: 6.4% annually. If the dividend yield rises to the historical average of 4% even 30 years from now, investors will have earned a total return of just 5% annually over that span. Consider that figure long and hard before trusting your retirement plans to a buy-and-hold approach in stocks.

It’s now 14 years since Hussman wrote the article. As difficult as it would been to believe it at the time, if anything, it seems at this point that Hussman was too optimistic.

Hussman’s rule of thumb seems like a sensible one:

You want to own stocks when the yield on stocks is high, or while favorable market action (interest rates, inflation, market breadth) are uniformly driving the yield downward. Beware when neither is true.

Tomorrow, I’ll show some estimates for the market as it stands now.

## Buffett buys newspaper division of Media General \$MEG

I’ve been closely following on Greenbackd the Kinnaras stoush with the board of Media General Inc (NYSE:MEG) over the last few months.

Kinnaras has been pushing the Board to “take advantage of the robust M&A market for both newspaper and broadcast television and to sell all operating units of MEG in order to retire existing corporate and pension debt and achieve a share price shareholders have rarely seen in recent years.”

It looks like Kinnaras has succeeded, with the board announcing recently that it had reached an agreement to sell its newspaper division, excluding the Tampa Tribune, to Warren Buffett’s BH Media Group for \$142 million. In addition, Buffett would also provide MEG with a new Term Loan and revolver in exchange for roughly 20 percent of additional equity.

MEG is a provider of local news in small and mid-size communities throughout the Southeastern United States. It owns three metropolitan and 20 community newspapers and 18 network-affiliated broadcast television stations Virginia/Tennessee, Florida, Mid-South, North Carolina, and Ohio/Rhode Island.

Kinnaras’s Managing Member Amit Chokshi has a new post analyzing the sale and the valuation of the remaining rump of \$MEG. Chokshi sees the valuation as follows (against a prevailing share price of \$3.50):

A 6.8x multiple would imply a valuation of about \$8.50/share when using my estimates for how MEG’s capitalization will look post the BH Media transaction and accounting for BH Media’s warrants. By year-end, it is possible that another \$10-20MM in debt is reduced which would bring share value up close to \$1. The reason the jump is so significant is because each dollar of cash flow erases some very expensive debt. In addition, pure-play broadcasters are valued from 6-9x EV/EBITDA and one could argue that MEG deserves a valuation closer towards the mid point or higher for its peers when factoring the disposal of newspapers and accounting for the high quality locations of its key stations.

Lastly, as I’ve repeated in each prior post, another potential value creation event would be selling off the entire company. BH Media will now occupy a Board seat and I don’t expect the blind subservience other Board members have. Management has demonstrated a clear lack of competence in every facet of managing MEG. The only thing they have done thus far is get lucky in terms of finding a buyer for their assets and providing them financing. As an owner of MEG, BH Media will get an up close look at the type of management this team brings and I suspect will compare the value management adds or detracts. To any sane observer, management is just pitiful and MEG’s value suffers for it.

No position.

## Searching for Rational Investors In a Perfect Storm: Value Investing Through 1999-2003

Yesterday I covered a 2006 talk, “Journey Into the Whirlwind: Graham-and-Doddsville Revisited,” by Louis Lowenstein*, then a professor at the Columbia Law School, in which he compared the performance of a group of “true-blue, walk-the-walk value investors” and “a group of large cap growth funds”.

Lowenstein based the talk on an earlier paper he had written “Searching for Rational Investors In a Perfect Storm:”

In October, 1991, there occurred off the coast of Massachusetts a “perfect storm,” a tempest created by a rare coincidence of events. In the late ‘90s, there was another perfect storm, an also rare coincidence of forces which caused huge waves in our financial markets, as the NASDAQ index soared, collapsed, and bounced part way back.

What had happened to the so-called “rational” investors, the smart money, whom economists have for decades said would keep market prices in close touch with the underlying values? Despite the hundreds of papers on markets and their efficiency, it is a remarkable fact that no scholar, not one, has looked to see who are these rational, i.e., value, investors, how they operate, and with what results.

In the paper, Lowenstein decided to see how a group of ten value funds, selected by a knowledgeable manager, performed in the turbulent boom–crash–rebound years of 1999-2003. Did they suffer the permanent loss of capital of so many who invested in the telecom, media and tech stocks? How did their overall performance for the five years compare with the returns on the S&P 500?

To bring a group of rational/value investors out of the closet, I asked Bob Goldfarb, the highly regarded chief executive of the Sequoia Fund, to furnish the names of ten “true-blue” value funds, those which, as they say on the Street, don’t just talk the talk but walk the walk. (Had I prepared the list, I would have included Sequoia, but Goldfarb’s ten is Goldfarb’s ten.) They are all mutual funds, except for Source Capital, a closed-end fund which invests much like a mutual fund. The funds are as follows:

• Clipper Fund
• FPA Capital
• First Eagle Global
• Mutual Beacon
• Oak Value
• Oakmark Select
• Longleaf Partners
• Source Capital
• Legg Mason Value
• Tweedy Browne American Value

How did they perform?

For most managers, mimicking the index, it was difficult not to own Enron, Oracle and the like, but the ten value funds had stayed far away. Instead, they owned highly selective portfolios, mostly 34 stocks or less, vs. the 160 in the average equity fund. Reflecting their consistent and disciplined approach, they turned their portfolios at one-sixth the rate of the average fund. Bottom line: every one of the ten outperformed the index over the five year period, and as a group they did so by an average of 11% per year, the financial equivalent of back-to-back no-hitters.

The five-year 1999-2003 average annual returns were as follows:

Here’s a link to the article.

## The Superinvestors of Graham-and-Doddsville Revisited: Value Trounces Growth in Mutual Funds

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.

## Dividend Yield Doesn’t Work, What Does? Three Key Conclusions

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.

## Man versus Magic Formula: Joel Greenblatt’s Value Investors’ Club vs his Little Book

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.

## How To Beat Most Active Managers: A Performance Analysis of Fundamental Indexation With Different Price Ratios

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.”

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.

## Chart of Equal-Weight S&P500 Index vs Market Capitalization-Weight Index

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.

## Why Does an Equal-Weighted Portfolio Outperform Market Capitalization- and Price-Weighted Portfolios?

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.)