Extended market index fund

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.

In other words, "Completion" = Total Market with the S&P 500 stocks removed.

How to use an extended market fund
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 maintain a holding of an S&P 500 index fund. There's really no other reason to use them, although a creative person might concoct one. 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 statistics.