Bond Equivalent Yield (BEY) Calculator

Bond Equivalent Yield (BEY)

The Bond Equivalent Yield standardizes yields so that investors can compare discount securities (like Treasury bills) with coupon-bearing bonds on a fair, apples-to-apples basis. Without this conversion, comparing a T-bill’s discount yield to a bond’s coupon yield is misleading.

Two common BEY calculations:

1. From a discount security (T-bill, commercial paper):

BEY = [(Face - Price) / Price] × (365 / Days to Maturity)

This converts the purchase discount into an annualized rate using a 365-day year.

2. From a semi-annual yield (bond convention):

BEY = 2 × Semi-annual Yield

Most US bonds pay coupons semi-annually. BEY simply doubles the semi-annual rate to express it as an annual figure. That is the standard bond market convention.

Why the conversion matters:

T-bills are quoted on a bank discount basis:

Discount Yield = [(Face - Price) / Face] × (360 / Days)

This is misleading because:

• It uses face value (not price paid) in the denominator
• It uses a 360-day year instead of 365

BEY corrects both distortions, making T-bill yields comparable to coupon bond yields.

Example:

• 90-day T-bill, face value $10,000, price $9,850
• Discount yield = ($150 / $10,000) × (360/90) = 6.00%
• BEY = ($150 / $9,850) × (365/90) = 6.18%

The T-bill actually yields 6.18% on a bond-equivalent basis, not the 6.00% it is quoted at. Both corrections push the same way, so the quoted discount yield always understates what you are really earning.

Bills longer than six months use a different formula

The simple version above is only correct for bills of 182 days or less. That is not a technicality, it is about what you are comparing against. A coupon bond that runs longer than six months pays you a coupon at the six-month mark, which you can reinvest. To put a 52-week bill on the same footing, the annualized rate has to allow for that compounding, and the simple formula has nowhere to put it.

Treasury publishes a separate coupon-equivalent formula for bills over 182 days, and it is a quadratic rather than a division:

i = [ −(2n/365) + 2 × √( (n/365)² − (2n/365 − 1) × (1 − F/P) ) ] ÷ (2n/365 − 1)

The difference is not enormous but it is not noise either. A 364-day bill priced at $9,494.44 per $10,000 comes out at 5.34% on the simple formula and 5.27% on the proper one, a gap of about 7 basis points. On a $10 million position that is $7,000 a year of yield that was never there. This calculator picks the right formula for you based on the days you enter, and tells you which one it used.

When to use BEY:

• Comparing T-bill returns to short-term bonds or CDs
• Evaluating money market instruments
• Translating any semi-annual bond yield into an annual rate