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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.