John Mauldin writes one of the most thought-provoking weekly newsletters related to investing. This past week's newsletter is no exception, as he focuses on the work of Research Affiliates chairman and editor of the Financial Analysts Journal Rob Arnott, who has recently authored a study with Jason Hsu and Phil Moore evaluating the performance of the economic theories that underlie the construction of today's major stock market indices, such as the S&P 500. The study is available at the Research Affiliates' web site as a 1.3MB PDF document. What follows below are excerpts taken from a speech given by Rob Arnott at Mauldin's Accredited Investor Strategic Investment Conference in April 2005, as reported by Mauldin in his newsletter. Emphasis and links added are mine.

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.

So this is the first time we've circled back to some concrete implications for the market. It means that 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.

Now while it's a bad index, equal weighting will outperform a cap-weighted index. 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.

Mauldin describes the math behind Arnott's 33% return: "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."

Returning to Arnott's comments:

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'd 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 under-perform 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?

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.

Here is a small version of the graph Arnott describes above. Click the image for a slightly larger and clearer version:

Returning again to Arnott's comments:

So fundamental indexing does appear to offer structural advantages over conventional capitalization weighting. How does it work over time?.... 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.

Mauldin notes that "reference cap is what Rob uses to mean his universe of the largest 1000 stocks." His newsletter also contains the tables illustrating the data cited by Arnott above, including the statistical correlation data (t-statistics) that preface Arnott's following comments:

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.

There's some more, but the excerpts provided above cover the main points of Arnott's paper and speech. The full text of Mauldin's newsletter with all tables and graphs illustrating Arnott's points is available at Investors Insight.

It's certainly food for thought when considering what to do with your investment portfolio!

Labels: fundamental indexing, investing

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