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I thought S&P 500 would contain the top 500 U.S. companies by market cap, but apparently that is not the case?

e.g., Facebook (FB) was only recently added and has market cap of $100B whereas LabCorp (LH) is currently a S&P 500 member (according to Wikipedia) and has market capitalization of less than $10B.

Is there a simple rule or formula determining what companies make up the S&P 500?

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The S&P 500 index is maintained by S&P Dow Jones Indices, a division of McGraw Hill Financial. Changes to the index are made periodically, as needed. For Facebook, you'll find it mentioned in this December 11, 2013 press release (PDF). Quote:

New York, NY, December 11 , 2013 – S&P Dow Jones Indices will make the following changes to the S&P 100, S&P 500, MidCap 400 and S&P SmallCap 600 indices after the close of trading on Friday, December 20:

  • Facebook Inc. (NASD:FB) will replace The Williams Companies Inc. (NYSE:WMB) in the S&P 100, and Facebook will replace Teradyne Inc. (NYSE:TER) in the S&P 500 [...]

You can find out more about the S&P 500 index eligibility criteria from the S&P U.S. Indices methodology document (PDF). See pages 5 and 6:

Eligibility Criteria

Additions - S&P 500, S&P MidCap 400 and S&P SmallCap 600 Market Capitalization.

Market Capitalization - [...]

Liquidity - [...]

Domicile - [...]

Public Float - [...]

Sector Classification - [...]

Financial Viability - Usually measured as four consecutive quarters of positive as reported earnings. [...]

Treatment of IPOs - Initial public offerings should be seasoned for 6 to 12 months before being considered for addition to an index.

Eligible Securities - [...]
[...]

Timing of Changes

Changes to the U.S. indices other than the TMIX are made as needed, with no annual or semi-annual reconstitution. [...]

LabCorp may have a smaller market cap than Facebook, but Facebook didn't meet all of the eligibility criteria – for instance, see the above note about "Treatment of IPOs" – until recently.

Note also that "Initial public offerings should be seasoned for 6 to 12 months" implies somebody at S&P makes a decision as to the exact when.

As such, I would say, no, there is no "simple rule or formula", just the methodology above as applied by the decision-makers at S&P.

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S & P's site has a methodology link that contains the following which may be of use:

Market Capitalization. Unadjusted market capitalization of US$ 4.6 billion or more for the S&P 500, US$ 1.2 billion to US$ 5.1 billion for the S&P MidCap 400, and US$ 350 million to US$ 1.6 billion for the S&P SmallCap 600. The market cap of a potential addition to an index is looked at in the context of its short- and medium-term historical trends, as well as those of its industry. These ranges are reviewed from time to time to assure consistency with market conditions.

Liquidity. Adequate liquidity and reasonable price – the ratio of annual dollar value traded to float adjusted market capitalization should be 1.00 or greater, and the company should trade a minimum of 250,000 shares in each of the six months leading up to the evaluation date.

Domicile. U.S. companies. For index purposes, a U.S. company has the following characteristics:

  1. File 10-K annual reports and should not be considered a foreign entity by the SEC.
  2. The U.S. portion of fixed assets and revenues constitutes a plurality of the total, but need not exceed 50%. When these factors are in conflict, assets determine plurality. Revenue determines plurality when there is incomplete asset information.
  3. The primary listing of the common stock is the NYSE (including NYSE Arca and NYSE MKT), the NASDAQ Global Select Market, the NASDAQ Select Market or the NASDAQ Capital Market. ADRs are not eligible for inclusion.
  4. A corporate governance structure consistent with U.S. practice. If criteria #2 is not met or is ambiguous, S&P Dow Jones Indices may still deem it a U.S. company for index purposes if its primary listing, headquarters and incorporation are all in the U.S. and/or a “domicile of convenience” (see Appendix A). In situations where the only factor suggesting that a company is not a U.S. company is its tax registration in a “domicile of convenience” or another location chosen for tax-related reasons, S&P Dow Jones Indices normally determines that the company is still a U.S. company.

The final determination of domicile eligibility is made by the U.S. Index Committee.

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