Extended market index fund
An extended market index, or completion index, fund is combined with an S&P 500 fund such that the total "completes" the composition of the US total stock market.
Extended market index funds contain small-cap and mid-cap companies, but not large-cap companies listed in the S&P 500 Index. These funds are designed for investors already using S&P index funds. 
Vanguard offers an Vanguard Extended Market Index Fund (VEXMX for investor shares, VEXAX for Admiral shares, VXF for the ETF). Other companies offer similar "extended market index" or "completion index" funds. These funds hold all, or most, of the stocks not included in the S&P 500 index. [note 1]
How to use an extended market fund
Primarily, these funds should be used by investors who want to invest in the total market, and would like to use a total stock market fund, but who, for whatever reason, find it necessary to hold a separate S&P 500 index fund. There is no well-known investment theory that ascribes any particular virtue to "the total market except for the S&P 500" as an entity in itself. Investors who want to depart from total market weighting and choose their own proportion of large-cap stocks, probably want to adjust mid-cap and small-cap exposure independently too.
The obvious reason why an investor would want the "Total Market with the S&P 500 stocks removed" is that the investor already holds an S&P 500 index fund. An investor might be constrained by limited choices in a 401(k) plan, or by existing holdings of an S&P 500 fund in a taxable account that can't be exchanged without adverse tax consequences. Obviously, any investor who is not constrained to hold an S&P 500 index fund can simply invest in a Total Stock Market index fund.
Investors desiring to duplicate the total market portfolio using an extended market fund should manage their portfolio so as to include the S&P 500 fund and an Extended Market Index fund in about an 80%/20% proportion, and they will then be essentially holding the market.
The 80%/20% ratio may require rebalancing from time to time, and the ratio may change with the composition of the total market. This does not need to be done frequently or with scrupulous accuracy. One convenient source for the proper current percentage composition is Vanguard's benchmark comparison.
Overlap and other niceties
- Vanguard's Extended Market Index Fund tracks the Standard & Poor's Completion Index, which is the S&P Total Stock Market Index with the S&P 500 stocks removed. So, if you add them back in the proper proportion (and rebalance as needed), the mix tracks S&P Total Stock Market Index. Vanguard Total Stock Market Index Fund tracks a different index provider's Total Market index, the CRSP US Total Market Index, so in theory the results are not identical.
- Most or all "completion indexes" complete the S&P 500. So, there is no overlap, no duplicated stocks in any mix of an S&P 500 fund and a completion index fund.
- The S&P 500 is mostly large-cap and often thought of as large-cap, but it is not a pure large-cap index. Therefore, a completion index is not a pure combination of mid- and small-caps. Furthermore, different index providers divide the market between between large, mid, and small in different ways. Thus, for example, if an investor mixes funds based on different index provider's indexes, there can be significant overlap between these providers' large cap index funds and an S&P completion fund. [note 2]
- These are theoretical issues. The differences involved are small, and probably of concern only to purists.
- The extended market index is overweight in mid-cap growth. This probably isn't important, but it does underline the fact that the extended market index is not the most suitable choice for fine control of "style box" weights in an overall portfolio.
Mid-cap growth overweight
The S&P 500 is S&P's choice of "leading companies in leading industries." In 1957 when the index was developed, it was intended to represent, one could say, the whole market as seen by "normal" investors. Conventional wisdom at the time was that, in the language used by Benjamin Graham, "defensive investors" should limit themselves to "primary companies" in an industry. It wasn't until the eighties that the conventional wisdom began to advocate small-caps, and not until the nineties that people began to think of value and growth as numerically defined categories whose weight should be consciously chosen. The S&P 500's mid-cap holdings include an underweight to mid-cap growth that easily escapes notice because it's a small imbalance within the mid-caps which comprise only 13% of the S&P 500.
Morningstar's "holding style" chart for VEXMX follows. Notice 11/13/21 imbalance.
The corresponding chart for the Vanguard 500 Index fund, which tracks the S&P 500, shows the deficit in mid-cap growth, 5/5/3.
Dissenting views, and constrained choices in employer provided plans
Is an extended market index fund an appropriate tool for implementing a "small-cap tilt?"
The natural way to implement a "slice-and-dice" portfolio (dividing total stock market allocations into segments) is to use mutual funds that focus on and isolate the style factors; that is, funds that concentrate on one of the nine Morningstar style boxes. With regard to size alone, it seems illogical to use a fund that covers mid-cap and small-cap stocks.
While index funds targeted to particular style boxes might be better in theory, employer provided retirement plans frequently limit choices to actively managed funds with high expense ratios. An investor who desires to depart from market cap weighting with regard to size alone, and is limited by plan choices, may find that a low cost extended market index fund is the lowest cost way to implement the strategy.
Oftentimes, when the actual behavior of real-world small-cap and mid-cap funds are examined, surprises emerge. For example: Over a 10 year period (2002-2012), the growth charts for the Vanguard Small-Cap Index Fund (NAESX), Mid-Cap Index Fund (VIMVX), and Extended Market Fund are almost superimposed--it hardly seems to matter which is used. [note 3]
A number of forum members feel that, regardless of theory, and regardless of the rationale behind the construction of a completion index; as a practical matter an extended market index fund can be a perfectly good way to provide a degree of small-cap tilt. 
- Approximating total stock market
- US completion index returns
- Vanguard Extended Market Index Fund tax distributions
- The first sentence in Vanguard's description says, vaguely: "Seeks to track the performance of a benchmark index that measures the investment return of stocks from small and midsize companies," but the second sentence goes on to make things clearer: "Provides a convenient way to match the performance of virtually all regularly traded U.S. stocks except those in the S&P 500 Index."
The formal statement of strategy and policy goes on to say its goal is to "track the performance of the Standard & Poor’s Completion Index [which] contains all of the U.S. common stocks regularly traded on the New York and American Stock Exchanges, and the Nasdaq over-the-counter market, except those stocks included in the Standard & Poor’s 500 Index." The composition of the index (according to Morningstar as of 2/2012), consisted of 4% large-caps, 44% mid-caps, and 49% small-caps.
Similarly, the Fidelity Spartan Extended Market Index tracks the "Dow Jones U.S. Completion Total Stock Market Index," which contains the phrase "total market," and which Dow Jones calls "A subset of the Dow Jones U.S. Total Stock Market Index that excludes components of the S&P 500." See Dow Jones Total Market Indexes.
- For example, the most common MSCI index used for large cap stock index funds is the MSCI Prime market index, which is composed of the largest capitalization 750 stocks in the US market. The most commonly used Russell large cap index, the Russell 1000 index, is composed of the largest capitialization 1000 stocks in the US market. Note that the Vanguard Total Market Index fund, based on the CRSP US Total Market Index contains large cap, mid cap, small cap and micro cap stocks. The combination of Vanguard's Large Cap index fund and Vanguard's Small Cap fund (containing approximately 2400 market cap stocks) do not contain many micro cap stocks. The combination of an S&P 500 index fund and an extended market index fund will contain large cap, mid cap, small cap, and micro cap stocks. Micro cap stocks comprise approximately 1.5% of the total market.
- Some potential complicating factors, when examining historical Vanguard index fund returns revolve around the transition of the indexes from one index provider to another. Here are the transitions for Vanguard's index funds:
- Total Market Index: based on the Wilshire 5000 index (1992-2005); MSCI Broad Market Index (2005 - 2013); CRSP US Total Market Index (2013 - forward), for return dispersion see US total market index returns.
- Extended Market Index: based on the the Wilshire 4500 index (1987-2005); S&P Completion Index (2005 - forward), for return dispersion see Completion Index returns.
- Mid Cap Index: based on the S&P 400 index (1998- 2003); MSCI Mid Cap 450 (2005 - 2013); CRSP US Mid Cap Index (2013 - forward), for return dispersion see US mid cap index returns].
- Small Cap Index: based on the Russell 2000 index (1987-2003); MSCI US Small Cap 1750 Index (2003- 2013); CRSP US Small Cap Index (2013 - forward), for return dispersion see US small cap index returns.
- US Mid Cap:
- Mid Cap Index Fund (CRSP US Mid Cap) mutual fund and ETF;
- S&P Mid Cap 400 ETF.
- US Small Cap:
- Small Cap Index Fund (CRSP US Small Cap) mutual fund and ETF;
- S&P Small Cap 600 ETF and tax-managed mutual fund;
- Russell 2000 ETF.
- Now in wiki: Extended Market Index Funds, forum discussion