This week we look at index funds, and specifically at problems that certain types of capitalization weighted index funds have. It is intuitively obvious that capitalization-weighted indexes have a larger proportion of their assets in the larger stocks. (Capitalization-weighted means that larger stocks are given more "weight" or proportion of the index or fund.) But is this what a rational investor should actually want? I think the information we look at today will surprise many.

On my way in to Las Vegas last Wednesday, I read a very interesting op-ed piece by Professor Jeremy Siegel of Wharton Business School. Basically, he says that "Fundamentally weighted indexes are the next wave of investing." On May 13, 2005, I highlighted new research by good friend Rob Arnott, where he laid out the intellectual and practical arguments for a new type of fundamentally weighted index. By that, I mean that he says stock indexes and the funds associated with them should be based upon the underltying fundamentals of the companies and not just the size of the company. At that time I said his work would be the basis for a revolution in investing and would become hugely successful. The last year has proven me right. And now, these ideas are becoming mainstream enough to make the Wall Street Journal.

Why should the average investor care? Because fundamental indexing (and we will go into what that means below) is going to come to a 401k or pension plan near you. As we will see, this type of index is clearly superior to your average offering in such plans, and offers 2% or more of alpha per year over regular index funds. And 2% is huge over the lifetime of a pension fund. Let's look at what Siegel said:

"This new paradigm claims that the prices of securities are not always the best estimate of the true underlying value of the firm. It argues that prices can be influenced by speculators and momentum traders, as well as by insiders and institutions that often buy and sell stocks for reasons unrelated to fundamental value, such as for diversification, liquidity and taxes. In other words, prices of securities are subject to temporary shocks that I call 'noise' that obscures their true value. These temporary shocks may last for days or for years, and their unpredictability makes it difficult to design a trading strategy that consistently produces superior returns. To distinguish this paradigm from the reigning efficient market hypothesis, I call it the 'noisy market hypothesis.'

"The noisy market hypothesis easily explains the size and value anomalies. If a stock price falls for reasons unrelated to the changes in the fundamental value, then it is likely - but not certain - that overweighting such a stock will yield better than normal returns. On the other hand, stocks that rise in price more than their fundamentals become 'large stocks' with high P/E ratios that are likely to underperform.

"These discrepancies are not easy to arbitrage away on a stock-by-stock basis. The noisy market hypothesis does not say that every stock that changes price does so by more than what is justified by fundamentals. Any particular stock may still be undervalued when it moves up in price or overvalued when it moves down. New research indicates that there is a simple way that investors can capture these mis-pricings and achieve returns superior to capitalization-weighted indexes. This is through a strategy called 'fundamental indexation.' Fundamental indexation means that each stock in a portfolio is weighted not by its market capitalization, but by some fundamental metric, such as aggregate sales or aggregate dividends. Like capitalization-weighted indexes, fundamental indexes involve no security analysis but must be rebalanced periodically by purchasing more shares of firms whose price has gone down more than a fundamental metric, such as sales, and selling shares in those firms whose price has risen more than the fundamental metric....

"With the advent of fundamental indexes, we're at the brink of a huge paradigm shift. The chinks in the armor of the efficient market hypothesis have grown too large to be ignored. No longer can advisers claim that capitalization-weighted indexes afford investors the best risk and return tradeoff. The noisy market hypothesis, which makes the simple yet convincing claim that the prices of securities often change in ways that are unrelated to fundamentals, is a much better description of reality and offers a simple explanation for why value-based investing beats the market."

Siegel gave credit to my good friend Rob Arnott for the basic research. Rob challenged the conventional thinking with an explosive new study published last year (and highlighted here) in the Financial Analyst Journal. He also summarized it in a speech at my Accredited Investor Strategic Investment Conference last year. We're going to look again at a part of that speech today.

As usual, whenever Arnott's involved you have to have your thinking cap on. You will want to pay attention to this article, as Rob is going to show us how to get an extra 2% of alpha on our stock portfolios. So put up your tray tables and put on your seatbelts.

Today's letter will be a little bit different than my usual format in that almost the entire content will be directly quoting Arnott's speech. When the word "I" is used, it is Rob. So in place of the usual quotes, readers should assume that the content and intellectual property is essentially Rob's. If I want to get in a clarifying or personal side note, I will simply put it in brackets [like this].

By way of introduction, Rob serves as Editor of the Financial Analyst Journal. He has authored over sixty articles for journals such as the Financial Analyst Journal, the Journal of Portfolio Management and the Harvard Business Review. He is Chairman of Research Associates and is sub-advisor for the Pimco All Asset Fund, which now has over $6 billion. Rob is one of those guys who by walking into any given room is one of the smartest guys in the room, if not the smartest.

Rob starts out with the point that most of the financial world revolves around the use of various economic theories [Now to Rob]:

Any given economic theory will perfectly describe the world as long as you agree with the underlying assumptions. More often than not, however, the underlying assumptions take us from the real world into a world of, well, theory.

One of the most famous theories is the capital-asset pricing model (or CAPM). It is the basis for a number of index models, especially capitalization-weighted indexes like the S&P 500.

Now, for most of us, our biggest bet is in equities. Is theory leading us astray here? Let's suppose we have a perfect crystal ball. It can't tell us the share prices of every asset a year from now, or two years from now, but it can tell us the cash flows into the future on every investment we could make. The crystal ball lets us calculate the true fair value of every asset in the market. If we know the true fair value, then the market value will match that, the capital-asset pricing model will be correct, and the index will be perfectly efficient, in the sense that there is no way to boost returns without boosting risk.

Now let's suppose our crystal ball is just a little bit cloudy and we can't see the future precisely. Then what winds up happening is that every asset is trading above or below true fair value. We can't know what true fair value is. But we can know that every stock, every asset, every bond is going to be trading above or below what its ultimate true fair value is. Even the most ardent fans of the efficient markets hypothesis would say, "That's reasonable. That's reality."

Now if every asset is trading above or below its true fair value, then any index that is capitalization-weighted (price-weighted or valuation-weighted) is automatically going to have us overexposed to every single asset that's trading above its true fair value and underexposed to every single asset that's trading below its true fair value.

[Read that again. This is one of the reasons why value investing beats indexing over the long term.]

So this is the first time we've circled back to some concrete implications for the market. It means that the capitalization-weighted indexes on which our entire industry relies are fundamentally, structurally flawed and will inherently overweight every stock that's above fair value and underweight every stock that's below fair value.

Now let's look at what that does to returns. If you put most of your money in assets that are above fair value, you have proportionately too little in assets that are below fair value, and you're getting a return drag. The cap-weighted indexes are producing returns that are below what they should be, below what would be available in a valuation-indifferent index.

If you construct an index that is valuation-indifferent, that doesn't care what the PE ratios are, that doesn't care what the market capitalization is, then return drag disappears - and you can quantify it. It's about two to four percent per year. And how many managers out there reliably add two to four percent per year in the very long run? Darn few of them.

[Other studies show that about 80% of mutual funds underperform the market.]

Now while it's a bad index, equal weighting will outperform a cap-weighted index. [Equal weighting means that you put the same amount of money in a stock, no matter what its capitalization or share price.] A lot of folks think that equal-weighted indexes outperform mainstream capitalization indexes because they have a small-stock bias. The theory being that small companies beat large because they have a value bias, and cheap stocks outperform expensive ones. That's not quite correct. What equal weighting does is underweight every stock that's large, regardless of whether it's cheap or dear, and overweight every stock that's small, regardless whether it's cheap or dear.

This means that from a valuation perspective every stock that's overvalued is overweight in the cap-weighted index, and in the equal-weighted index it's a crap shoot, 50/50. You have even odds, whether it's overvalued or undervalued, of being over- or underweight.

Let's look at this from the vantage point of a concrete example. Let's suppose we have a world with two stocks. Each has a true fair value of a hundred bucks, but the marketplace doesn't know what the true fair value is. One stock is estimated by the market to really be worth fifty bucks and the other is estimated to really be worth a hundred and fifty, but both valuations are wrong. Capitalization weighting puts 75 percent on that overvalued stock.

Now suppose over the next ten years, today's valuation errors are corrected. Both stocks move to a hundred dollars, but a new 50-percent error is reintroduced because news has come along and people have been drawn into the hype that one company looks really good and the other looks really bad. These errors are introduced into the pricing, and you have a steady state: the size of the errors stays steady, but the old errors have been corrected. In that world, the estimated cap-weighted return is zero, and the equal-weighted return is 33 percent.

[Both stocks start at $50 and $150 for a total portfolio of $200. In ten years, both stocks are worth $100. If you cap-weighted your portfolio, you would not have made anything. If you put an equal $100 into the companies, you would have made $100 on the lower priced stock and lost $33 on the higher priced stock, for a portfolio profit of $67 on your original $200. Thus Rob's 33% return.]

When Does Your Large Stock Outperform?

In the May, 2005 issue of the Financial Analyst Journal, I published a short study in which I looked back over the last 80 years and asked the question, "How often does the number-one-ranked company in market capitalization outperform the average stock over the next one year, three years, five years, and ten years?" And the simple answer seems to be that on average, over time, about 80 percent of the time, the largest-capitalization company underperforms over the next ten years.

Now the magnitude of that underperformance is in the 40 to 50 percentage-point range - it's huge. The largest-capitalization company, on average, underperforms the average stock by 40 to 50 percentage points over the next ten years. You would expect the same pattern but less reliably in the top ten companies. Some of the top ten will deserve to be there; their true fair value is higher. Some of them will not deserve to be there. This symmetric pattern of errors will push many that don't deserve to be there into that top ten, and some of the ones that do deserve to be there, out of the top ten.

What do we find? On average, over time, seven out of ten of the top-ten stocks underperform the average stock over the next ten years, and three out of ten outperform. Meaning three out of ten probably deserved to be in that top ten. The average underperformance: 26 percentage points over the next ten years. So this is huge.

Now, how do we reconcile the fact that capitalization-weighted portfolios are market clearing - that is they span the entire market, they cover everything in exactly the proportion that the market owns those assets - with a return drag that is so easy to eliminate?

Getting 2% of Alpha

This gets back to finance theory and the capital-asset pricing model. I had a discussion with the originators of the model. There were two notable originators: a fellow named Jack Treynor and a fellow named Bill Sharp. And Bill Sharp's take on this was very simple, and that's that this couldn't possibly be. Jack Treynor's take on it was just as simple: "Wow, this is neat, this is correct, let me write a paper on it documenting why it works." So a very different reaction from the two co-founders of the capital-asset pricing model.

But the simple fact is, the capital-asset pricing model works if your market portfolio spans everything: every stock, every bond, every house, every office building, everything you could invest in on the planet including human capital, including the net present value of all of your respective labors going into the future. There's no such thing as an index like that. It doesn't exist. So right off the bat you can say that the S&P 500 is not the market, and anyone who says that it's efficient because it is the market is missing the point: it's not the market.

Can we improve on cap weighting? Absolutely! Any index that is replicable, objective, and focused on large and liquid companies which are easily tradable is a potentially useful index. Any such index that is valuation-indifferent should beat the stock market. If it doesn't care what PE ratios are or what the price is when setting how large your investment in an asset should be, it should beat cap weighting.

What could you do that would do that? You could look at book values. Find the thousand largest companies by book value and create an index weighted by book value. Never mind what the price is, never mind what the market capitalization is, simply do it by book value. You could do it based on revenues: which companies have the highest revenue base or sales, and then weight them by revenues or sales. You could even do it based on head count. What are the thousand biggest employers in the United States? How many people do they employ, and weight the index by the number of employees.

You can do anything of this sort, anything that captures the scale of a company, so you have a bias towards large and liquid companies that is replicable and objective but that doesn't pay attention to valuation.

Does it work? You bet. The graph below shows that the thousand largest by capitalization over the past 43 years, the red line, would have taken every dollar you invested and turned it into 70 dollars. Well that's awesome, that's what a quarter-century bull market from '75 to '99 does -- the biggest bull market in US capital markets history.

Taking a dollar to seventy dollars is remarkable. But if you use any of these other measures, any of them, you do roughly twice as well. In fact a little better than twice as well for the average: 160 dollars for every dollar at starting value. It's a huge gap. Look also at what happened after '99. The S&P 500 is still down 10 percent in total return including income. Fundamentally weighted indexes: up 30 percent.

[Note: I am not sure if you will be able to see all the different hypothetical indexes, but that is not the point. The point is that they all beat the cap-weighted index and all do it in pretty much the same manner. In any given year, one might have been better than the other, but they ALL beat cap weighting. The pattern is what is important and not the details. Also note that the fundamental indexes are far less volatile and lose less in bear markets.]

Comparison of Indexes, 1962-2004

So fundamental indexing does appear to offer structural advantages over conventional capitalization weighting. How does it work over time? In the next chart geometric return is over on the left. The S&P 500 comes in at 10.53 percent a year over the last 43 years. The reference cap -- the thousand largest by cap without the ministrations of the committee that selects which companies make it into the S&P -- stands about 0.18 percent lower, at 10.35 percent per annum. The average of the fundamental indexes? The worst of the fundamental indexes produces a 12 percent annual return, much better than the conventional indexes. And the best produce almost 13 percent -- the average is 12.50 with excess returns of 2.15 percent.

[Reference cap is what Rob uses to mean his universe of the largest 1000 stocks.]

How Significant is the CAPM Alpha?

(For those who are familiar with statistics, when the T statistic (t-stat) is over three, it's very significant. If you risk adjust, what you find is that on a risk-adjust basis you are adding closer to 2.5 percent per annum, because not only are you adding return, you're reducing risk. You aren't committing so much to the popular high fliers, the Krispy Kremes of the world, and then watching them implode. And so the statistical significance on a risk-adjust basis is off the charts - nearly a four T statistic.)

How consistent is this approach? It's awfully consistent. During economic expansions, you add almost two percent a year. During recessions - when you most need those returns - you add three and a half percent. During bull markets you add 40 basis points. You don't really add anything in bull markets, because they are driven more by psychology than by the underlying fundamental realities of the companies.

And so during bull markets you keep pace. Which is good; it's important. During bear markets you find yourself adding 600 to 700 basis points per annum. Bear markets are when reality sets in and people say, "Show me the numbers." Bear markets are when this really comes on strong. Also, during periods of rising rates, two and a half percent added. During periods of falling rates, one and a half percent added.

Results in Expansion & Recession, Bull & Bear Markets, Rising and Falling Rates

So what we find is that in an environment of a recession or a bear market or rising rates, when people are forced to say, "Show me the numbers," it works particularly well; but it also works to a slightly lesser extent in the contrary environment. That's not the same as value investing. Value investing does not work, does not add value during expansions, bull markets, or periods of rising rates. So this winds up being a really dominant approach to equity investing, and it's brand new. The work on this was just published two weeks ago.

Is it an index? Of course it can be an index. Is it passive while it's replicable, formulaic, and objectively constructed? Yes. But is it a total market portfolio? Not in a theoretically robust capital-asset pricing model context, because it doesn't span things equivalent to their weight in the actual market.

Are the cap-weighted indexes efficient? That is to say, can you improve on them [by constructing better models and indexes] without taking on more risk? Yes, you can. The classic indexes are not the market, and no commercially viable market portfolio exists; and even if one did it wouldn't matter, because the capital-asset pricing model is predicated on so many structurally flawed assumptions that the notion that the cap-weighted indexes must be efficient is the same as the notion that the underlying assumptions must be true.

Back to John: There is a lot more, but we are running short on time. There are very real implications in this model for long-short investing. Last year I predicted large institutions and pension plans will eventually move large portions of their equity assets into models like this. What's a 2% difference worth? Let's assume that whatever portfolio you start with, in 36 years you end up with one billion dollars. If you can increase portfolio performance by just 2%, you will end up with $2 billion. A 2% alpha doubles your returns over the longer time horizons of pensions.

Rob's firm has begun to exploit this research, of that you can be sure. I have said I think this will be the fastest fund idea to grow to $100 billion in history, and in ten years I think it will capture the bulk of the long-only fund world, as investors who must have exposure to the market seek ways to enhance their returns while reducing volatility.

Rob wrote me yesterday. "The ETF is already out. PRF started trading in mid-December. It's had a 99% correlation with the S&P 500 and has added over 250 basis points already. PowerShares is rolling out a small stock ETF, and ten sector ETFs, probably in August, and International, Japan and Emerging Markets, probably in Q4."

There are groups forming funds all over the world based on Rob's work. Coincidentally, I talked with a director of PowerShares last night here in Vegas. He is more than very enthusiastic about the potential for new ETFs on a wide variety of investment themes.

Is this a magic fund idea? No, it will lose money in a bear market just like any long-only fund. So, in my opinion, the time is not quite right, as I think we still have some downside. But when it is, this will be an option you will want to heavily consider for the long-only portion of your investment portfolios.

John Mauldin is president of Millennium Wave Advisors, LLC, a registered investment advisor.  Contact John at John@FrontlineThoughts.com.

Disclaimer
John Mauldin is president of Millennium Wave Advisors, LLC, a registered investment advisor. All material presented herein is believed to be reliable but we cannot attest to its accuracy. Investment recommendations may change and readers are urged to check with their investment counselors before making any investment decisions.