# Bond Equivalent Yield

Bond equivalent yield is the rate of return on a money market instrument that is calculated with reference to the purchase price of the instrument based on a 365-day year. It can be used to compare returns earned on the money market instrument with return earned by a bond.

Money market instruments such as T-bill, repos, commercial paper, etc. are issued on discount. They do not pay any periodic interest and their return results from the difference between their issue price and face value (also called par value or maturity value). Common measures of return on money market instruments such as bank discount yield and money market yield can’t be directly compared with capital market instruments such as bonds. This is because they are either calculated with reference to the face value i.e. the maturity value instead of the initial value and/or they are based on a 360-day year. The bond equivalent yield addresses both theses weaknesses and enables comparison.

Bond equivalent yield may also refer to yield to maturity annualized without compounding. For example, if a semi-annual bond’s internal rate of return is 4%, it is annualized on bond-equivalent basis by multiplying it with 2%.

## Formula

Bond equivalent yield can be calculated using the following formula:

$$BEY\ for\ money\ market=\frac{F-P}{P}\times\frac{365}{t}$$

Where F is the face value (i.e. par value) of the instrument, P is the issue price and t is the number of days between the issue date and maturity date.

Semiannual yield to maturity can be converted to bond-equivalent yield as follows:

$$BEY\ for\ bond=m\times periodic\ YTM$$

Where m is the number of coupon payments per year and periodic YTM is the periodic yield to maturity on a bond, i.e. the periodic interest rate that equates the bond’s future cash flows i.e. coupon payments and face value to its price.