The rate: an index that moves and a spread that does not. TreasuryDirect states that "the interest rate of an FRN is the sum of two components: an index rate and a spread." The regulation defines the index for floating rate notes as "the highest accepted discount rate on 13-week bills determined by Treasury auctions of those securities," and the index rate as the simple-interest money market yield, computed on an actual/360 basis and rounded to nine decimal places, derived from that discount rate. Treasury auctions the 13-week bill every week, so, in TreasuryDirect's words, "the index rate of an FRN is reset every week," taking effect the day after each bill auction. The spread is "the fixed amount over the life of a floating rate note that is added to the index rate," expressed in tenths of a basis point and set once, at the auction that first sells the note: it equals the high discount margin accepted in that auction. Section 356.20(c) puts the two together: the interest rate "will be the spread plus the index rate ... subject to a minimum daily interest accrual rate of zero percent." Interest accrues on the par value every day at that day's rate and is paid every three months.
Why the price sits near par and the income does not. A fixed-coupon note promises the same dollars every six months for years; when market rates rise above its coupon, the only way for a buyer to earn the market rate is to pay less for the note, so its price falls. A floating rate note's coupon rises with the market instead, so there is no stale promise for the price to adjust around, and the note trades close to par throughout its life. The interest rate risk has not disappeared; it has moved from the price to the income. A holder who needs a predictable payment has taken on uncertainty, and a holder who wants the principal to hold its value in a rising-rate market has found the security designed for that. The zero floor means the daily accrual rate cannot go negative even if the spread is negative and bill rates fall to zero; it does not mean the coupon is guaranteed to be positive in any meaningful amount.
How an FRN is bought at auction. Bidders in a floating rate note auction do not bid a yield; they bid a discount margin, "the margin over the index that equates the present values of the assumed cash flows on a floating rate note to the sum of the price of and accrued interest on the floating rate note." Competitive bids state the discount margin as a percentage with three decimals and may be positive, negative or zero. In a new-issue auction the high accepted discount margin becomes the note's spread for life and the price is at or near par; in a reopening the spread is already fixed, so a discount margin bid above or below it produces a price below or above par. Noncompetitive bidders, which is how individuals buy through TreasuryDirect, simply accept the result. The Treasury FRN is issued in $100 minimums and increments, with new issues in January, April, July and October and reopenings in every other month, and it is not eligible for STRIPS. Interest is subject to federal income tax in the year earned and exempt from state and local income tax, like other Treasury securities.
Floating rate notes outside the Treasury. Corporations, banks and government-sponsored enterprises issue floating rate notes on the same template: a reference rate that resets periodically plus a spread fixed at issue, with the payment frequency, reset dates and any caps or floors set out in the note's own terms. For decades the reference rate for US dollar floaters was LIBOR; it is now generally the Secured Overnight Financing Rate, which the New York Fed describes as "a broad measure of the cost of borrowing cash overnight collateralized by Treasury securities," and the statutory transition that replaced LIBOR in legacy contracts is covered on the SOFR page. Two things separate a corporate floater from the Treasury version. The spread is larger and reflects the issuer's credit, so a floater from a weak issuer can fall in price for reasons that have nothing to do with rates. And the reset is on the note's schedule rather than weekly, so between resets a corporate floater's price can drift from par as short-term rates move. Neither of those features has a Treasury analogue, and a reader comparing a Treasury FRN's spread with a bank floater's is comparing a term-premium with a credit spread.