Bond Equivalent Yield Calculator
This bond equivalent yield calculator restates the return on a short-term discount instrument, such as a Treasury bill, as an annual percentage you can compare against ordinary bonds. Discount instruments pay no coupon: instead you buy them below their face value and are repaid the full face value at maturity, and your return is that difference. The catch is that the return is earned over an odd number of days, often 90 or 180, so it needs annualising before you can line it up against a bond that quotes a yearly yield. Bond equivalent yield, or BEY, does exactly that using a 365-day year. Enter the face value the bill repays at maturity, the price you pay for it, and the number of days until it matures, and the calculator returns the discount in dollars, the holding period return over those days, and the annualised bond equivalent yield. The method takes the gain as a percentage of the price you actually paid, then scales it up by 365 divided by the days held. This is more useful than the bank discount rate quoted for bills, which measures the discount against face value on a 360-day year and understates the true return. Use bond equivalent yield to compare Treasury bills, commercial paper and other zero-coupon short-term paper against coupon-paying bonds and term deposits on a fair, annualised footing.
Buying a $100 bill for $98.50 with 182 days to maturity earns a $1.50 discount, a 1.52% holding period return. Annualised on a 365-day bond-equivalent basis, that is a yield of 3.05%.
Bond equivalent yield uses a 365-day year and the price paid, so it exceeds the bank discount rate. Not financial advice.
How it works
The calculator first finds the discount, which is the face value repaid at maturity minus the price you pay. Dividing that discount by the purchase price gives the holding period return, the plain percentage you earn over the days you hold the bill. To annualise, that return is multiplied by 365 divided by the number of days to maturity. Written out, bond equivalent yield equals ((face value minus price) divided by price) times (365 divided by days). Using the price paid as the base, rather than face value, and a 365-day year, rather than 360, makes the result directly comparable with the yields quoted on coupon bonds.
Worked example
Suppose a Treasury bill has a $100 face value, you buy it for $98.50, and it matures in 182 days. The discount is 100 minus 98.50, which is $1.50. The holding period return is 1.50 divided by 98.50, about 0.01523, or 1.52 percent over the 182 days. Annualising, you multiply by 365 divided by 182, which is about 2.005, giving a bond equivalent yield of 0.01523 times 2.005, about 0.03054, or 3.05 percent. That 3.05 percent is the figure you would compare against a one-year bond's yield.
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