Treasury bonds are quoted as a percentage of face value, with the number after the hyphen representing 32nds of a point rather than cents. A quote of 102-16 means 102 and 16/32 percent of par, or $1,025 for every $1,000 of face value. Once you know the fractional shorthand, the labels for premium and discount, and how accrued interest changes what you actually pay at settlement, a Treasury quote reads cleanly.
The 32nds System
Under the federal rules for marketable Treasury securities in 31 CFR Part 356, bond and note prices are stated per 100 dollars of face value.1eCFR. 31 CFR Part 356 – Sale and Issue of Marketable Book-Entry Treasury Bills, Notes, and Bonds A quote of 100 means you pay exactly face value. Above 100, you pay more; below 100, less.
The digits after the hyphen are not decimals. They represent 32nds of a point. So 99-24 is not $99.24. It is 99 and 24/32, which equals 99.75 percent of face value, or $997.50 on a $1,000 bond. If the number after the hyphen were 16, you would divide 16 by 32 to get 0.50, for a total of 99.50 percent of par.
Some quotes include a plus sign. A quote of 99-24+ means 99 and 24.5/32, equivalent to 99 and 49/64. The plus adds half of one 32nd, which is 1/64 of a point. On a million-dollar position, 1/64 equals about $156, so these fine increments matter to professional desks. Electronic platforms may display even smaller sub-increments, but the plus sign is what you will see most often.
Par, Premium, and Discount
Because the quote is a percentage of face value, 100 is the dividing line. A quote of exactly 100 means the bond trades at par, and you pay dollar-for-dollar what the Treasury returns at maturity.1eCFR. 31 CFR Part 356 – Sale and Issue of Marketable Book-Entry Treasury Bills, Notes, and Bonds Anything above 100 is a premium. Anything below is a discount.
A bond trading at a premium usually carries a coupon rate higher than the current market yield, so buyers pay extra for the larger semiannual interest payments. A quote of 104-00 means you pay $1,040 for every $1,000 of face value and collect the higher coupon until the bond matures and returns $1,000. The premium is spent over the remaining life of the bond.
A discount runs the other way. A quote of 98-00 means you pay $980 per $1,000 bond, collect all the coupon payments, and receive the full $1,000 at maturity. Whether a bond trades at a premium or discount is driven mainly by how its coupon compares with the prevailing market yield.2TreasuryDirect. Understanding Pricing and Interest Rates
Bid and Ask
A live Treasury quote shows two numbers. The bid is the highest price a buyer will pay. The ask, sometimes called the offer, is the lowest price a seller will accept.3U.S. Securities and Exchange Commission. Bid Price You buy at the ask and sell at the bid. The gap is the spread.
Recently issued, actively traded bonds (the “on-the-run” issues) carry very tight spreads, often just 1/32 of a point or less. A bid of 101-28 against an ask of 101-29 is a 1/32 spread, worth about $0.31 per $1,000 of face value. Older issues that trade less frequently show wider spreads, so you give up more to get in and out.
What You Actually Pay at Settlement
The price on your screen is the clean price. It leaves out the interest that has accumulated since the bond’s last coupon payment. At settlement you pay the clean price plus that accrued interest, and the total is called the dirty price or invoice price. This surprises first-time Treasury buyers more than anything else in the quoting system.
The logic is straightforward. Treasury bonds pay interest every six months. If you buy halfway between coupon dates, the seller has held the bond for three months and earned three months of interest. That interest belongs to them, so you reimburse them at settlement. When the next full coupon arrives, you keep all of it, which offsets what you paid out up front.
Treasury bonds use an actual/actual day count for accrued interest, meaning the calculation uses the exact number of days since the last coupon and the exact number of days in the full coupon period.4U.S. Department of the Treasury. Interest Rates Frequently Asked Questions Nothing is rounded to 30-day months. On a bond with a 4% annual coupon ($20 per semiannual payment on $1,000 of face), if 91 days have passed out of a 182-day period, accrued interest is $20 × (91/182) = $10. You pay the clean price plus $10 per bond.5eCFR. 31 CFR 306.35 – Computation of Interest
Treasury trades settle the next business day on a T+1 cycle, and accrued interest runs through the settlement date, not the trade date, so an extra business day of interest gets added to your cost.6FINRA.org. Understanding Settlement Cycles: What Does T+1 Mean for You
Price, Coupon, and Yield
Most platforms show a yield to maturity next to the price, expressed as an annual percentage. It is the total return you would earn if you bought the bond at the current price, collected every coupon, and held to maturity. The number accounts for the coupons, the time value of money, and any premium or discount in the price.
Price and yield move in opposite directions.7Fidelity Investments. Price/Yield Calculator – Section: About Bond Prices and Yields When market rates rise, existing bonds with lower coupons become less attractive, prices fall, and the yield on those lower prices climbs. When rates fall, prices rise and yields drop.
Do not confuse the coupon rate with the yield. The coupon rate is set at auction and never changes. A bond issued with a 3.5% coupon pays $35 a year on every $1,000 of face value for its entire life. The yield to maturity moves constantly with the secondary-market price. When the yield to maturity sits above the coupon rate, the bond trades below par. When the yield is below the coupon, the bond trades above par.2TreasuryDirect. Understanding Pricing and Interest Rates
T-Bills and TIPS Are Quoted Differently
Not every Treasury security uses the 32nds system. Treasury bills, which mature in one year or less, pay no coupon. You buy at a discount and receive the full face value at maturity, with the difference acting as your interest.2TreasuryDirect. Understanding Pricing and Interest Rates
T-bill quotes are expressed as a discount rate rather than a price. Converting the rate to a dollar price uses this formula:
Price = Face Value × (1 − (discount rate × days to maturity) / 360)
A 26-week bill at a 4.5% discount rate prices out as $1,000 × (1 − (0.045 × 182) / 360) = $977.25. You pay $977.25 and receive $1,000 at maturity, pocketing $22.75.2TreasuryDirect. Understanding Pricing and Interest Rates The discount rate uses a 360-day year, a banking convention that slightly understates your actual return. Data providers often publish a bond equivalent yield alongside the discount rate; it uses a 365-day year and the actual price paid as the base, and runs a bit higher than the discount rate for an apples-to-apples comparison with coupon-bearing notes and bonds.
Treasury Inflation-Protected Securities add one more layer. A TIPS quote uses the same 32nds convention, but the quoted price is the real, inflation-adjusted clean price. To find what you actually pay, multiply the quoted price by an index ratio that reflects cumulative inflation since the bond was issued. The index ratio comes from changes in the Consumer Price Index. If the CPI has risen 5% since issuance, the ratio is roughly 1.05, and a TIPS quoted at 100-00 would have an inflation-adjusted principal of $1,050 per $1,000 of original face. Your settlement price is that adjusted principal plus accrued interest calculated on the adjusted amount. At maturity, you receive the inflation-adjusted principal or the original par value, whichever is greater.8TreasuryDirect. Treasury Inflation-Protected Securities (TIPS)