The discount yield – the term used by the US Treasury (USDT) for bank discount yield (BDY) – is the yield quoted on US T-bills on a simple interest basis (i.e., without compounding) on an actual/360 basis, expressed as a percentage of the instrument’s face value. To calculate the discount yield for T-bills, the following equation is used, where F is face value, P is the purchase price and t the time to maturity in days:
Discount Yield = [(F – P)/F] x (360/t)
To compare the discount yield on T-bills to an investment yield on T-notes and T-bonds, the T-bill discount rate is converted to a seminannual-coupon paying equivalent. The formula used for the conversion of the discount yield of a T-bill to a bond equivalent yield (BEY) is, where DR is the discount rate (discount yield) expressed as a decimal, and t the number of days to maturity:
BEYT-Bill = (365 x DR)/[360 − (t x DR)]
The bond equivalent yield (BEY) is the total yield on investments that takes into account the interest applicable on bonds, which is the simple interest (uncompounded) semiannual bond yield on the actual/actual day-count basis. It is used to compare bonds with financial instruments having varying characteristics that mature on the same date. Quoting bond equivalent yields makes the semiannual-pay YTM of US Treasury notes and bonds directly comparable to the quoted yields of other financial instruments that are based on another payment frequency or yield basis.
If the bond equivalent yield is known, the following equation is used to determine the effective annual yield (EAY) of the instrument, where t is the remaining time to maturity:
EAY = {(1 + [BEY x (t/360)]}(365/t)
US Treasury curve rates are bond equivalent yields. A yield curve rate is an interest rate at a given point along a yield curve. The daily yield curve of the US Treasury plots the current and past secondary market yields on actively traded Treasury securities that pay interest on a semiannual basis. It is a par yield curve since it is derived from the yield to maturity on Treasury securities that trade at par.