Most financial advisors agree that it’s difficult to beat “the market”. It’s easy to define “beat the market” as generating an investment return (typically before tax, and typically ignoring transactions costs) that is greater than the market return.

But what, exactly, is “the market”?

Which Stocks in the Index?

In developing a stock market index, we have to define which stocks to include, and then what weight to give them.

But it’s far from simple.

We can say, for example, that we’re going to include all publicly traded stocks. But how do we determine what are all the publicly traded stocks?

There are, and have been, multiple stock exchanges in the US. Some of those exchanges, traditionally the NYSE but in recent decades the NASDAQ also, specialize in “big” companies while others (many exchanges have come and gone) may specialize in smaller or more niche companies, perhaps by geography, type, or industry.

In addition, new companies are continuously being added to stock exchanges (usually through Initial Public Offerings) and removed (either through delisting, acquisition, or bankruptcy).

The problem of identifying “the market” is not as simple as it first appeared.

These difficulties in identifying the market help explain how indexes like the Dow Jones Industrial Average came about. The DJIA focused on 30 of the “most important” companies. Most important typically means the biggest, but even when focusing only on the largest there is human judgment involved.

Once we’ve identified which stocks to include in the index, we then must decide how to weight them.

Weighting

There is no provably correct method of weighting stocks in an index.

As soon as we have more than one stock in an index, we have to make a decision regarding how to weight each stock. For example, suppose we had an index consisting of two stocks: Apple and Lincoln National Corp.

We could give each stock an equal weighting in the index. One argument against that is that Apple is much bigger than Lincoln. Apple is bigger by many measures – revenues, profits, and market capitalization for example. But perhaps surprisingly, Lincoln is larger by assets.

Why Most Indexes Are Weighted by Market Capitalization

Market capitalization weighting has tremendous practical advantages for actually running an index fund. That matters a lot if you’re running a fund. It may matter much less, or not at all, for a single investment portfolio.

The main advantage for funds is that market cap weighting makes a fund adjust automatically. For example, the S&P 500 is market cap weighted. That means that if a fund manager receives a new investment of, say, $1 million, he invests it into the stocks in the index in the same proportions as their weights in the index.

For example, Apple’s weight recently was about 7%, and Lincoln’s was about .01%.

Now suppose Lincoln has some fantastic results and increases in value by a factor of 10 (unlikely, but simply for illustration). What does the investment manager have to do to maintain the proper weighting? Nothing!

If the manager now gets another new investment of $1 million, he simply buys 10 times as much Lincoln (everything else equal) as he did for the prior $1 million that came into the fund.

And that, I believe, is the major reason for most indexes to be capitalization weighted.

Implications of Market Capitalization Weighting

You might wonder whether it is wise to buy 10 times as much of a stock after its price has increased by a factor of 10. Wouldn’t the stock be more likely to be “overvalued” if its price has increase by a factor of 10?

If the Efficient Market Hypothesis is true, the stock was fairly valued before and after the ten times price increase. To review, the Efficient Market Hypothesis states that the current market price of every stock is the “fair” or “correct” price, because that price, whatever it is, accurately reflects all available information.

Cap Weighting Systematically Penalizes Errors

We assume that investors want to maximize expected return for a given amount of risk. In a cap weighted portfolio, any divergence from “efficient” or “correct” pricing of any stock in the portfolio will, on average, reduce risk-adjusted performance.

That’s a bit of a mouthful. Let’s break it down with a simplified example. Suppose that we have only two stocks, ABC and XYZ. For simplicity, assume that both companies are identical in every way that matters, except they trade separately. Further suppose that we have been given by some omniscient source, the “correct” value of each. Again, by “correct” value we mean the actual present value of the future cash flows that the stock will produce.

Let’s further suppose that the “correct” value of each is $50. Each company is the same, so each has the same number of shares outstanding. Thus, the market capitalization of each is the same if the they both have the same stock price.

Again for simplicity, we’ll assume that $50 is the price which will give an expected one-year return of 10%. In other words, for this example, we’ll just assume that if you buy ABC, or XYZ, at $50, in one year you’ll earn a 10% return on that investment.

The Efficient Market Hypothesis states that both ABC and XYZ will be trading at $50 today. Thus, a market cap weighted portfolio will have a weight of 50% in ABC, and 50% in XYZ.

By our assumptions, the return on the index over a year will be 10%.

Effect of Estimation Error

But what if ABC is overvalued? Suppose that the “correct” value is $50, but for whatever reason, the market is pricing ABC at $60. Now, market cap weighting will require that the index consist of 54.54% ABC, and 45.45% XYZ.[1]

Now suppose a year passes, and ABC returns to its “correct” value. By our assumption, at the beginning of the year, the correct value of ABC was $50, and that fair value would increase by 10%. At the end of a year, the fair value would therefore be $55.

The same values apply to XYZ.

Here are the returns to each component of the market cap weighted index, and the return to the overall index.

The overvaluation of ABC has hurt in two ways. First, it caused the returns on ABC to be lower than they would otherwise have been, because ABC returned to its “correct” value. Second, it caused a heavier weighting to the overpriced security, and (necessarily) a lower weighting in the fairly priced security.

Undervaluation

By similar logic, market capitalization weighting will underweight “cheap” stocks. Thus, market capitalization weighting is “correct” only if all the stocks in the market are priced at exactly their “correct” prices.

That all stock prices should be “correct” at all times seems very unlikely.

In the next post, we’ll look at alternatives to market-cap weighting.

Next steps

Did you enjoy this blog post? If so, reply to this email and let us know.

If you are an established advisor who serves the high net worth market, and you’re seeking to grow AUM and value of your practice, you owe it to yourself to give us a call. Call us at 703 437 9720, or click below to schedule a conversation with Katherine.

Or, click here to request an advisor guide.

---

[1] Because ABC is now 60 and XYZ 50, the total market cap is 110, and 60/110 is 54.54%.