HPY = [(F – P) + D1]/P
Given the bank discount yield (BDY), the equation for the calculation of the HPY of a t-bill or other pure discount instrument is:
HPY = BDY x (F – P)
HPY can also be determined when only the BDY and the number of days in the holding period are known as follows, where n is the number of days in the holding period:
HPY = [BDY x (n/360)]/[1 – BDY x (n/360)]
If only the money market yield (MMY) and the number of days remaining to the maturity (t) of an investment are known, HPY can be determined as follows:
HPY = MMY x t/360
If the effective annual yield (EAY) of an investment is known, the formula to solve for HPY in terms of EAY is:
HPY = (1 + EAY)(t/365) – 1