Bond Equivalent Yield Calculator

Understanding Bond Equivalent Yield (BEY)

The Bond Equivalent Yield (BEY) is a financial metric used to calculate the annualized yield on short-term, discount money market instruments (such as U.S. Treasury bills and commercial paper) so their return can be directly compared to standard coupon-bearing bonds.

Why BEY is Necessary

Money market discount instruments are quoted using a 360-day bank discount convention without compounding. In contrast, corporate and government bonds pay semi-annual coupons on a 365-day year basis. The BEY converts the short-term discount yield into an annualized 365-day yield, enabling fair apples-to-apples comparison across fixed-income investments.

Bond Equivalent Yield Formula

Given a face value ($F$), purchase price ($P$), and days to maturity ($d$):

$$BEY = \frac{F - P}{P} \times \frac{365}{d} \times 100\%$$

To convert directly from a quoted Bank Discount Yield ($y_d$):

$$BEY = \frac{365 \cdot y_d}{360 - (y_d \cdot d)}$$

BEY vs Bank Discount Yield vs Effective Annual Yield

• Bank Discount Yield (BDY): Uses face value as the denominator and assumes a 360-day year ($y_d = \frac{F-P}{F} \times \frac{360}{d}$).
• Bond Equivalent Yield (BEY): Uses purchase price as the denominator and assumes a 365-day year. BEY is always higher than BDY.
• Effective Annual Yield (EAY): Accounts for compound interest over multiple holding periods within a year ($EAY = (1 + \frac{F-P}{P})^{365/d} - 1$). EAY is higher than BEY.