Bond Equivalent Yield Calculator

Background.

Treasury bills pay no coupon. You buy one below face value, and the gap between what you pay and what you get back at maturity is the entire return. The traditional way of quoting bills makes that return look smaller than it is: the bank discount rate measures the gap against face value rather than against the money you actually put in, and spreads it over a 360-day year.

The bond-equivalent yield corrects both. It divides the dollar gain by the purchase price, then scales that holding-period return up to a 365-day year, so a 13-week bill, a 26-week bill and a coupon-paying note can be set side by side on something close to the same footing. It also goes by the name coupon-equivalent yield, and Treasury auction results list an investment rate of this kind beside each bill's discount rate.

The difference is not cosmetic. A bill bought at $980 that repays $1,000 in 90 days carries a discount rate of exactly 8.00% but a bond-equivalent yield of about 8.28%. Anyone weighing a bill against a savings account, or a treasurer comparing it with a short-dated note, needs the second number.

The annualisation is simple rather than compounded: the period's return is multiplied by 365 over the number of days, with no allowance for reinvesting the proceeds. It always uses a 365-day year, ignores fees, taxes and settlement lags, and applies the same simple formula at every maturity, whereas the standard coupon-equivalent figure for bills running longer than six months adds an adjustment for the notional half-yearly coupon. A price at or above the redemption value is refused, because there is no discount left to annualise.

What is bond equivalent yield calculator?

Bond-equivalent yield (BEY) is the annualised simple return on an instrument bought at a discount and redeemed at a fixed amount, with nothing paid in between. It is the dollar gain as a fraction of the purchase price, multiplied by 365 divided by the days remaining to maturity, and expressed as a percentage. Using the price paid as the base and a 365-day year puts a bill's return much closer to the yields quoted on coupon-paying notes and bonds than its discount rate is.

How to use this calculator.

1. 01Enter the purchase price: what you paid or will pay. Keep it on the same scale as the redemption value, either both per $100 of face value or both in dollars for the whole holding.
2. 02Enter the redemption value, normally the face value paid at maturity. It has to be higher than the purchase price.
3. 03Enter the days to maturity, counted from the date the purchase settles (or the issue date, for a bill bought at auction) to the maturity date.
4. 04Read the yield as an annual percentage and compare it with other instruments' bond-equivalent figures, not with a quoted discount rate.

The formula.

BEY = (F − P) / P × 365 / t × 100%, where P is the purchase price, F the redemption value and t the days to maturity. The first part, (F − P) / P, is the holding-period return: the profit as a share of the money invested. Multiplying by 365 / t scales it to a year as though the same trade could be repeated back to back without compounding, and the 100 turns a fraction into a percentage. A lower price raises the yield twice over, because the gain grows while the base shrinks. Days to maturity has the strongest pull on short instruments: the same $20 gain earned in 30 days instead of 90 triples the annual figure. The bank discount rate, (F − P) / F × 360 / t, divides by face value and uses 360 days, so for any discount bill it comes out lower than the BEY.

A worked example.

Frequently asked questions.

References& sources.

1. [1]FINRA, Bonds and bond yield investor education.
2. [2]U.S. Treasury, Treasury Bills: Rates and Terms.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.