What is the overall market worth? That question, although simplistic, has been the source of endless debates among financial academics and professionals. One example of this controversy concerns strategies for so-called capitalization versus fundamental-weighted market indexes. Both sides of the debate have well-known proponents and a good case to make. In this article, we'll look at the ideas and evidence underlying this issue and consider it in the larger context of passive and active investment strategies.

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A Brief History of Indexing
In 1952, Harry Markowitz published his breakthrough work on the modern portfolio theory (MPT) in the Journal of Finance. In 1964, William Sharpe built on Markowitz's work in presenting the underlying rationale for the capital asset pricing model (CAPM). In between these two groundbreaking events, in 1957, Standard & Poor's Company launched the S&P 500 Stock Index, which is widely regarded as the first real-time proxy for the broad-based stock market.

Why is this sequence of events important? One of the basic concepts deriving from Markowitz, Sharpe and their contemporaries was the mean-variance efficiency theory. The market, according to CAPM, is mean-variance efficient. With the introduction of the S&P 500, the "market" now had a real-world meaning and thus MPT could emerge from the abstract realm of academics to be used by actual investors, traders and strategists.

The S&P 500, like most security indexes that followed, is a capitalization-weighted index. The larger a constituent member's market cap is, the larger its weight in the index. This makes intuitive sense as a proxy for the value of the market, just as one could say that the value of a supermarket is the number of product units in stock times the unit prices, where the "weighting" goes up or down along with supply and demand. (To learn more about supply and demand, read Macroeconomic Analysis and Economics Basics.)

Investors find this weighting system useful in serving two principal objectives: First, as a means to obtain passive investment exposure to the overall market. Secondly, the S&P 500 index serves as a benchmark for comparing the performance of active investment strategies aiming to "beat the market". Moreover, the S&P is the gold standard for measuring the success of active equity managers and how consistently they can beat the S&P 500 over time. (Keep reading about benchmarks in Benchmark Your Returns With Indexes.)

Here Come the Fundamentalists
Ever since its inception, cap weighting has faced criticism from various observers. Most of this criticism has been limited to the daunting pages of financial theory journals - until the infamous dotcom stock bubble burst in 2000. The bubble was a catalyst because it focused on the culpability of cap-weighted indexes in the context of yet another long-running debate in finance: The relationship between value and price.

A group of investment experts coalesced around an alternative approach to cap-weighted indexing that involved the creation of fundamentally weighted indexes. In a standard-bearing paper called "Fundamental Indexation" published in the Financial Analysts Journal in 2005, Robert Arnott, Jason Hsu and Philip Moore introduced what they called a "Main Street" definition of the market as opposed to the "Wall Street" measure of market cap.

Value and Price
In a cap-weighted index, the weight of any constituent increases as its stock price increases. The question then turns to how useful the price is as a reflection of the security's intrinsic value. For easily understandable reasons, the bubble and its aftermath invited the close scrutiny of this question.

Let us return briefly to the world of financial theory. A widely-known theory called the efficient market hypothesis (EMH) argues that the price of any given traded security reflects all relevant known and available information, and that any changes in the information are reflected instantaneously in the security's price - in other words, price always equals true or intrinsic value and market-beating techniques such as charting or fundamental analysis are essentially a waste of time. However, most market practitioners believe that a price at any given time equals true value, plus or minus a random error or "noise." In a competitive marketplace, price will tend to converge toward value over time, but that could be a short, medium or long time frame, depending on the noise factor. (To learn more about market efficiency, check out Working Through The Efficient Market Hypothesis, What Is Market Efficiency? and Mad Money ... Mad Market?)

The point is that if one assumes some stocks are trading above or below their true values, by extension, they will also be trading above their true market-efficient weightings. For example, if a stock is trading at x + ε (where its true intrinsic value is x) then ε, the price error, is also a weighting error in the index. Moreover, we expect that through market forces, the price will tend to converge toward x over time (in this case, it will decrease from x + ε back to x). The opposite is true if the stock is trading at x – ε. Thus, in a cap-weighted index, these overvalued stocks will have a higher weighting than they deserve and the undervalued stocks will have a lower weight. According to the supporters of fundamental indexing, this will detract from performance over time.

Back to the Fundamentalists
So if not market cap, what is the right weighting measure for an index? Arnott, Hsu and Moore used six alternative measures of size:

Main Street
hashed it out.

An Index by Another Name
The other side of the argument, though, led by the likes of Vanguard founder John Bogle and financial author Burton Malkiel, maintains that fundamental indexing ignores the important consideration of fees and transaction expenses. After all, it is not possible to invest directly in an index in a costless transaction.

Bogle, Malkiel and others who agreed with their position argued that, once these costs were factored into the equation, the seeming advantages of fundamental indexing dissipate. Fundamental indexing requires occasional rebalancing. In order to maintain fidelity to the weighting measure - for example, sales or cash flow - one has to periodically rebalance the index through purchases and sales - selling in cases where price appreciated more than the weighting measure and buying where the reverse is true. In a market cap weighted index, this is not necessary because weights automatically rebalance when prices are marked to market. This implies a higher cost structure for fundamental index vehicles than for the traditional passive index funds offered by the likes of Bogle's own Vanguard.

The implications of this argument are that fundamental indexing really is not indexing in the sense of a purely passive strategy where you buy exposure to the market and then effectively do nothing. It is possible to argue that rebalancing itself is an "action," however simple, and therefore, like any active management strategy, it should be benchmarked to a purely passive strategy, net of fees, to prove its value.

The Bottom Line
In the end, both sides of the debate are right. The cap-weighted proponents are correct in arguing that the true test for any new paradigm is whether it can deliver the most value over the long term after taking into consideration the total cost to the investor. They also are sensible in saying that the acceptable economic definition of a "market" is simply the aggregate units of each product available times each product's unit price.

On the other hand, the fundamental index supporters make a good case, saying that separating a security's portfolio weight from its pricing error is desirable and can mitigate the severity of an event like the aftermath of a bubble, when price-value disparities become large. Thanks to competition and Adam Smith's invisible hand, we can expect to have an ever-increasing range of choices to act as we deem fit, whether it's with both strategies, one strategy or none at all.

To learn more about index investing, read our Index Investing tutorial.

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