How this instrument works
Treasury bills, commercial paper, and bankers' acceptances trade at a discount rather than paying a stated coupon: you buy below face value and collect the full face amount at maturity. Dealers quote these instruments on a bank discount basis — the dollar discount divided by face value, annualized over a 360-day year — which is not the same number as the return an investor actually earns on the money put up.
Bond-equivalent yield restates that quote so it lines up with how coupon bonds and notes are priced. The numerator is still the discount earned, but the denominator switches to the price actually paid rather than face value, and the year switches to 365 days instead of 360. Both changes push the number up: BEY is always a little higher than the bank discount rate on the same bill, because the true cost base is smaller than face value and the true year is longer than the money-market convention assumes.
The formula is a simple annualization, not a compounding one — it scales a known holding-period return straight to a calendar year and stops there. It assumes the bill is held to maturity at the quoted price and ignores taxes entirely. For bills held longer than roughly six months, some trading desks switch to a semiannual-compounding variant instead, since stretching a holding-period return in a straight line starts to overstate the annual figure once that period passes half a year.
- Enter the Face value, $ — the amount the bill pays out at maturity.
- Enter the Purchase price, $ — what you actually paid today, below face value.
- Enter Days to maturity — the number of days between settlement and maturity.
- Read Bond-equivalent yield, % — the annualized return on the price you paid, quoted on the same 365-day basis as coupon bonds.
Worked example — a 182-day Treasury bill
A $1,000 Treasury bill purchased for $980 matures in 182 days, just under six months. The discount is $20, and that $20 was earned on a $980 outlay rather than the $1,000 face value, so the return per dollar invested is $20 divided by $980, or 0.020408.
Annualizing over a 365-day year with 182 days held multiplies that figure by 365 divided by 182, or 2.005495, and multiplying by 100 converts it to a percentage: a bond-equivalent yield of 4.0928%. That is the number to set beside a six-month coupon note's yield, not the lower discount rate a dealer might quote on the same bill.
Questions
What does bond-equivalent yield actually measure?
It is the annualized return on the price you paid for a discount instrument, such as a Treasury bill, expressed on the same 365-day basis used for coupon-bearing bonds and notes. It lets you set a T-bill's return directly beside a bond's stated yield without converting units by hand.
Why is BEY higher than the T-bill's quoted discount rate?
The quoted bank discount rate divides the dollar discount by face value and annualizes over 360 days; BEY divides the same discount by the smaller price actually paid and annualizes over 365 days. Both changes push the figure up — on the golden example here, a discount rate near 3.96% becomes a BEY of 4.09%.
Does bond-equivalent yield compound interest?
No — it is a simple, straight-line annualization of a single known return, not a compounded rate. For bills maturing in six months or less this tracks the real annualized return closely; for longer maturities some desks add a semiannual-compounding adjustment instead, since plain annualizing starts to overstate returns past a half-year holding period.
Can I use this formula for a coupon-paying bond?
No. This formula prices a single discount-to-face payoff — the shape of a Treasury bill, commercial paper note, or zero-coupon instrument. A coupon-paying bond returns cash periodically before maturity, so its yield needs a present-value calculation that discounts each coupon separately; that is what a yield-to-maturity figure solves for, not this one.
What happens if I buy the bill at exactly face value?
The yield is zero. With no gap between price and face value there is no discount to annualize, regardless of how many days remain to maturity — the formula's numerator, face value minus price, is zero, and zero times any annualizing factor still leaves zero.
Why does the days figure matter so much to the result?
It sets the annualizing factor, 365 divided by days. A 91-day bill has that factor near 4, stretching a small discount into a much larger annual figure; a bill held the full 365 days has a factor of exactly 1, so its BEY equals the simple discount return with no stretching at all. Short-dated bills show punchier annualized yields for the same dollar discount.
References
- TreasuryDirect — U.S. Department of the Treasury, marketable securities
- Investor.gov — U.S. SEC guide to bonds and fixed-income products
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.