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I am reading this article which discusses Tesla's stock (TSLA). The article states:

27.5 million shares of Tesla are held short, or about 41 percent of the float.

How can the number of shorted shares be known? Where are the numbers published?

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For a company listed on NASDAQ, the numbers are published on NASDAQ's site. The most recent settlement date was 4/30/2013, and you can see that it lists 27.5 million shares as held short.

Settlement Date    Short Interest   Avg Daily Share Volume      Days To Cover
  4/30/2013          27,501,901        3,453,140                7.964317

NASDAQ gets these numbers from FINRA member firms, which are required to submit them to the exchange twice a month:

Each FINRA member firm is required to report its “total” short interest positions in all customer and proprietary accounts in NASDAQ-listed securities twice a month. These reports are used to calculate short interest in NASDAQ stocks.

FINRA member firms are required to report their short positions as of settlement on (1) the 15th of each month, or the preceding business day if the 15th is not a business day, and (2) as of settlement on the last business day of the month.* The reports must be filed by the second business day after the reporting settlement date. FINRA compiles the short interest data and provides it for publication on the 8th business day after the reporting settlement date.

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