Holding period yield (HPY) is the unannualized percentage return on an asset or portfolio of assets from purchase date to its maturity or sale equaling the sum of increase (decrease) in its value above (below) its purchase price plus any investment income to be received during the holding period. Where BDY is based on a 360‐day year, HPY is the return only over the holding period, which could be of any length. Because HPY is based on the purchase price of the investment, it is a true yield. HPY is used to compare the expected return on any kind of instrument to its actual return, where F is face value, P is purchase price and D1 is distribution of income during the holding period or at maturity:
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
Money market yield (MMY) is the total return on money market instruments equal to the increase (decrease) in value of an instrument above (below) its purchase price plus any investment income based on a 360-day year, without compounding – essentially the holding period yield (HPY) adjusted to a 360-day basis. The quoted yield on pure discount money market instruments, such as T-bills, is made comparable to the add-on yield (AOY) quoted on interest-bearing money market instruments paying interest on a 360-day basis, where HPY is holding period yield ((P – F)/P) and t is the number of days remaining to maturity:
MMY = [(P – F)/P] x (360/t) = HPY x (360/t)
If the price is not known but the bank discount yield (BDY) is quoted, the money market yield (MMY) of a T-bill can be determined as follows:
MMY = (360 x BDY)/[(360 – t) x BDY)]
Because MMY does not account for the effect of compounding and discounts the total return on a linear basis, money market yield is not directly comparable to bond yields compounded semiannually or annually.
MMY is a true yield based on the investment’s lower price, which makes it greater than an investment’s BDY. MMY is also greater than the HPY since HPY is not annualized and is based on a holding period of less than a year.