Why a T-bill needs two different yields
A Treasury bill pays no coupon — you simply buy it below face value and receive the full face at maturity, and the difference is your return. The trouble is how that return gets quoted. Dealers traditionally use thebank discount yield, which divides the gain by the face value and annualizes over a 360-day year. That convention is convenient for money-market math, but it systematically understates the real economics: you never invested the face amount, and a year has 365 days. Thebond equivalent yield fixes both points so that a discount instrument can be set side by side with a coupon bond — see the relatedcurrent yield calculatorfor how coupon income is expressed on its own price basis.
The two conventions
Bank discount yield = (Face − Price) ÷ Face × 360 ÷ Days
Bond equivalent yield = (Face − Price) ÷ Price × 365 ÷ Days
where Face is the maturity value, Price is what you paid, and Days is the number of days remaining to maturity. The discount yield divides by Face over a 360-day year; the bond equivalent yield divides by the smaller Price over the actual 365-day year, which is why it is always the larger of the two.
What makes this calculator different
- Both conventions, side by side. It shows the bank discount yield and the bond equivalent yield together from the same inputs, so you can see exactly how the quoted number and the fair number diverge.
- It explains why BEY is larger. Dividing by the price rather than the face, and annualizing over 365 days instead of 360, both lift the figure — the calculator makes plain why the bond equivalent yield is the fairer measure of return.
- Works for any days-to-maturity. Whether the bill has a few weeks or many months left, the day-count is applied directly, so short and long maturities annualize correctly without guesswork.
Frequently asked questions
What is bond equivalent yield (BEY)?+
Bond equivalent yield restates the return on a discount instrument — such as a Treasury bill bought below face value — as an annualized yield that can be compared directly with coupon-bearing bonds. It measures the gain as a percentage of the price you actually paid, then annualizes that gain over a 365-day year. Because coupon bonds quote their yields on a price basis over a full calendar year, expressing a T-bill the same way lets you line the two up apples-to-apples.
How does BEY differ from the bank discount yield?+
The two conventions differ in both numerator and denominator. The bank discount yield measures the gain against the face value and annualizes over a 360-day year, while the bond equivalent yield measures the gain against the purchase price and annualizes over a 365-day year. Dividing by the smaller price instead of the larger face, and stretching across 365 days instead of 360, both push the bond equivalent yield higher than the discount yield for the same instrument.
Why is the discount yield misleading?+
The bank discount yield understates the true return for two reasons. It divides the dollar gain by face value rather than by the lower price you actually invested, which shrinks the apparent percentage return. It also uses a 360-day year, compressing the annualization. The result is a number that looks worse than the real economics, which is why it cannot be compared fairly against a coupon bond quoted on a 365-day, price basis.
When do you use BEY?+
Use bond equivalent yield whenever you need to compare a discount instrument against a coupon-bearing bond on equal terms. Treasury bills, commercial paper, and other zero-coupon, sold-at-a-discount securities are often quoted on a bank-discount basis, so converting them to BEY puts them in the same units as a note or bond yield. It is the standard way to decide, for example, whether a short T-bill or a comparable coupon security offers the better effective return.
What is the 360 vs 365 day-count difference?+
Day-count conventions decide how a partial-year holding period is scaled up to an annual figure. The bank-discount convention uses a 360-day year, a holdover from money-market practice, while the bond equivalent yield uses the actual 365-day calendar year. Annualizing the same holding-period gain over 365 days rather than 360 produces a slightly larger number, contributing to why BEY exceeds the discount yield.
Disclaimer: This calculator is foreducation and illustration only. Yield conventions are simplified models of return and ignore taxes, transaction costs, and reinvestment; its output is not a tradeable quote and actual returns will differ. Nothing here is investment, tax, or trading advice.