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When I try to find, for example 3 months T-bill rate, how that rate is calculated?

getSymbols(Symbols = "DGS3MO", src = "FRED", auto.assign = FALSE) -> t3

tail(t3)

      DGS3MO

2017-06-28 1.02 2017-06-29 1.04 2017-06-30 1.03 2017-07-03 1.06 2017-07-04 NA 2017-07-05 1.05

How these yields are calculated? Is it bank discount yield, because that's how yield of T-bills is calculated by convention If I'm not wrong, or is it recalculated bond equivalent yield?

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  1. Annualized using a 360-day year or bank interest.
  2. On a discount basis

So it's on the bank discount yield. I have a problem understanding why the yield is changing daily? My answer is: since it is trading constantly on the secondary market, supply and demand determines price of the bill every day, so applying bank discount yield on that new prices we get new yields every day?

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The answer is buried in your question. If you look at the underlying data from FRED you'll see their method.

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