# The Problem With Indexes

This week we look at index funds, and specifically at the problems that the 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. But is this what a rational investor should actually want? I think the information we look at today will surprise many.

My good friend Rob Arnott has challenged the conventional thinking with an explosive new study just published in the Financial Analyst Journal. He also summarized it in a speech at my Accredited Investor Strategic Investment Conference last month. We're going to look 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.

But while we are taxiing down the runway, let me bring to your attention a great new book by yet another friend, Dr. Michael Roizen and Dr. Mehmet Oz. It is called "You: The Owner's Manual." It has been #1 on Amazon for more than a week, incredibly beating out Harry Potter. Of course, it helps that Oprah is raving about it, but well she should. (Note to my publisher: please book me on Oprah for the next book.)

Roizen is the anti-aging guru behind the RealAge series of books and Oz is a well know maverick that is changing the way heart surgery is practiced. They both have multiple New York Time's best sellers in their past and this time they have teamed up. They are both famous doctors with lots of degrees and honors. In short, they are the real deal in medical knowledge. Basically, they answer the question: "It's your body. Shouldn't you know how it works?"

The book is humorous, with lots of illustrations and drawings. It takes what can be a very complicated subject and makes it simple, but not simplistic. It doesn't dumb things down, it just makes them understandable. It will also help motivate you to change the little things in your life so you will live longer and better. You can order the book by going to Amazon.com. (By the way, it isn't just Oprah who has been raving about this book - Donnie Deutch, the Fox and Friends crew, Doctor Tim Johnson, and Diane Sawyer have all said on National TV that this is a great book, and more than one commentator has said their explanations on GMA last Monday were one of the reasons GMA trounced the Today show that day.) And now let's take off and think about indexes.

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 Analysts Journal. He has authored over sixty articles for journals such as the Financial Analysts 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 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 under perform 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.]

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?

**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 the 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, 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. I predict 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 will exploit this research, of that you can be sure. My prediction is that it will be hugely successful, as investors who must have exposure to the market seek ways to enhance their returns while reducing volatility.

**Napa Valley, Chicago and La Jolla**

As you read this, my daughter and I are in Napa Valley meeting with Rob Arnott, Peter Bernstein, Paul McCulley and others at a small gathering hosted by Rob and his firm Research Associates to discuss industry issues: specifically, does the rise of financial services to a 20% weighting of the S&P 500 index mean it is a bubble or a natural evolution in a service oriented economy? I will take notes and report back.

Rob will graciously be picking up the check at the French Laundry on Saturday night, which is one of the greatest French restaurants in the world. I think I gained about 2 pounds just reading the menu online. It looks like some extra workouts will be needed after this trip. I have been slowly losing weight, down about 20 pounds over the last 18 months, but there is still plenty more to go.

I will be in Chicago around June 7-8. The latter part of the next week I take my youngest son Trey (11) to La Jolla where Dad will work and he will take surfing lessons. There will be time to meet with clients in La Jolla. And then Father's Day and the next weekend my tribe invades Austin, going to spend the weekend with old friends Gary and Debi Halbert at their home on Lake Travis. This is going to be a fun family summer, with more events planned as we progress into July and August.

I will come back on Monday and then Wednesday morning I am going to have some steroid injections into my lower back. I am hopeful that it will help. We will see.

That's about it for today. I hope you have a great week.

Your hoping he can swing a golf club again analyst,

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