What is an Index?
You may have heard the following meaningless statistic thrown around by so-called “experts”:
“On average, the market rises by 10.4% per year.”
But just what does the term “market” refer to? Does it mean every stock that has ever existed? Does it take into account stocks that ceased to exist due to bankruptcy, merger, etc.? From what year to what year does the statistic hold? Finally, even if the statistic was true (it is not), then how would we go about replicating a “market portfolio” to achieve the same results? Do we solely include equities? What about including currencies, commodities, or the various derivatives markets? Do we look at national interests, or in the era of big multi-nationals, must we include the world markets?
As you can see, the above statement leaves us with more questions than answers. Therefore, when we refer to the market, we have to be more specific in our word choice.
What people typically refer to as “the market” is merely a subset of the market and it is usually composed of a collection of stocks that may give a typical investor a feel or expectation for something that is otherwise hard to quantify. Thus, any collection of stocks that is constructed for the purpose of giving a quantitative reflection of the market is what we call an index.
We use indexes for various purposes. The most notable of these purposes is to answer the question: “What did the markets do today?” Without indexes, we may not be able to come up with a simple answer to the question. However, when we hear statements such as “The Dow was up 250 points today,” or “the S&P 500 Index rose 35 points today,” we get a feel for the state of the markets. While the Dow Jones Industrial Average and the Standard and Poor 500 Indexes do not contain every stock in the market, we rely on them and a few others to summarize the financial world in one or two numbers due to their popularity.
Indexes may also represent a standard by which investment portfolios or investment managers are measured. While there are countless claims of investors “beating the market,” most investment portfolios tend to underperform the major indexes. Hence, those managers whose portfolios consistently outperform a major index are preferred over those that do not.
How is an index constructed?
To keep things simple, we will construct an index using only two stocks. Suppose we have two stocks trading for $100 per share: XYZ and ZYX. For simplicity’s sake, we will assume that both stocks have the same market capitalization. In other words, the number of outstanding shares multiplied by the stock price gives us the same number on both stocks. The reason for this assumption will become clearer later in the text.
The idea is that we want to keep track of XYZ and ZYX without having to look at both numbers. Therefore, we buy 100 shares of each stock. We have now spent 100×100 or $10,000 per stock for an index value of 20,000.
Then we may conclude that an index value of 20,000 is too cumbersome. Maybe an initial value of 100 would be preferable. That being the case, we divide the initial index value of 20,000 by an appropriate number to revalue the index at 100. We find that the number needed for this calculation is 200, since 20,000/200 = 100.
We then define the initial number 200 as the divisor.
We have now successfully created our index. As the component stocks move, so will the index.
Note, however, that in this particular index, the stock prices are equal – an equal amount of money is being committed to each component stock, and the market capitalization of both stocks is equal. What if the world is not perfect and prices are not equal? Then, which stock should have preference? If we put an equal amount of money into each stock, then lower priced stocks would have more shares in the index than higher priced stocks.
Maybe we should have an equal number of shares per stock in the index, but then a percentage move in a higher priced stock would be represented by a larger move in the index than an equal percentage move in a lower priced stock. Is that fair or representative of the market as a whole? And, how would we deal with stock splits?
Finally, remember that we are looking for a barometer of market value, and the companies with the highest market capitalization technically represent a larger piece of the pie that is our economy. Therefore, should we take market capitalization into account when considering how to structure our index?
All of these questions and more are at the core of basic index construction. Hence, the next chapter will cover basic index types, but also the pros and cons of each style.
Types of Indexes
Keeping in mind that an index is supposed to be a broad representation and measure of a market, there are several terms that must be defined to fully understand what any index is trying to quantify.
Weight: This number refers to the percentage of shares of each stock that goes into an index. There are three main ways in which stock weights are determined:
- Market Capitalization – Indexes that weight their stocks using this method follow the premise that if we are trying to obtain a fair representation of the market as a whole, then the companies that hold the largest market capitalization (total shares outstanding multiplied by the stock price) should have the larger say in the index. Therefore, the index should have a larger percentage of their shares in its distribution. As an example, the S&P 500 index is a market cap-weighted index.
- Price Weighted – Indexes that weight their stocks using this method put an equal number of shares of each component stock into the index. This method is easily replicable by unsophisticated investors who want to create a stock portfolio that mimics a particular index. A major drawback of price-weighted indexes is that a company with a high stock price receives a high weight in the index for no real reason. Therefore, events such as stock splits that do not change the value of a portfolio may significantly affect the behavior of the index. The Dow Jones Industrial Average is an example of a price-weighted index.
- Equal Dollar Weighted – Indexes that weight their stocks using this method put an equal dollar amount of each stock in the index. This reflects the tendency of some investors to create a portfolio in which a fixed amount of money goes into each stock selection. For example, a small investor with $32,000 to invest may decide to buy 400 shares of IBM trading for $80/share, or 100 shares of Google (GOOG) trading for $320 per share. The drawback of these indexes is that lower priced stocks randomly tend to move the index more than higher priced stocks. Several sector indexes such as the MSH or the XAL are examples of equal dollar-weighted indexes.
Divisor: Once we have decided on the proportionate number of shares per stock that an index will contain (based on the weighting method chosen), then each resulting value is multiplied by the price of its corresponding stock. These numbers are added together to give us the value of the index.
However, it is important to note that the actual numerical value has no significance. Therefore, indexes make use of a divisor – a number by which we divide the total original index value to create a new “easier” index value to track. The use of a divisor is also important to track changes to the index via certain corporate actions such as mergers, stock splits, special dividends, de-listings, additions, etc.
Impact: The impact number is much like the delta of each stock in the index. That is, it answers the question: For a $1 move in the stock, how much does the index change? Depending on how the index is weighted, the index will have a different impact number. However, no matter what kind of index we have, the impact number for a given stock is calculated as the weight of that stock in the index divided by the price of that stock.