How is bond equivalent yield measured?

The semiannual yield to maturity is the yield to maturity on a semiannual-pay bond equal to the discounted rate per semiannual period times two.  As such, these yields are not effective annualized yields, which include the effect of compounding per payment period.  Using the following equation, an annual YTM (EAY) on annual-pay bonds is converted to semiannual YTM (BEY):

BEY = [(1 + EAY)^1/2 – 1] x 2

Alternatively, the semiannual YTM (BEY) can be converted to annual YTM (EAY) – equivalent annual yield – using the following formula:

EAY = [1 + BEY/2)² − 1

Semiannual-pay bonds have a greater yield than annual-pay bonds when the yields are compared on an equivalent basis.  Furthermore, an instrument’s equivalent annual yield to maturity (EAY) is always greater than its bond equivalent yield because of the semiannual compounding of the interest to determine the effective annual yield.

Where bonds are quoted in terms of their annual yield to maturity (annual YTM), a conversion is required to calculate their bond equivalent yield (semiannual equivalent) on a semiannual bond basis.  The semiannual bond basis (SABB) is the stated annual rate on a bond that has a periodicity of two and calculated as the as the yield per semiannual period multiplied by two.

The stated annual yield (SAY) is annual return that does not account for intrayear compounding or consider the periodicity of the stated annual rate, where for an annual-pay bond the periodicity is one, for a semiannual-pay bond it is two, and for a quarterly-pay bond it is four.  To determine the stated annual yield based on monthly compounding, stated annual yield (SAY) must be converted to a periodicity of 12:

SAY = [(1 + SAY₁₂)/12)¹²

Rather than semiannual YTM, monthly cash flow yield (CFY) is used for quoting mortgage-backed securities and other amortizing asset-backed securities that have monthly cash flows, it incorporating a schedule of monthly cash flows based on prepayment assumptions.  It is a monthly internal rate of return based on the market price of the security.  The following formula is used to convert the monthly equivalent yield (MEY) of into a bond equivalent yield (BEY) in order to compare it to a yield on the semiannual bond basis:

BEY_MBS = [(1 + MEY)⁶ – 1] x 2