Treasury Bill

Every financial calculation involving a risk-free rate — from the Capital Asset Pricing Model to bond yield spreads to option pricing — uses the T-bill yield as its empirical proxy for the risk-free return available in the market. The Treasury bill's mechanics, its auction process, its discount pricing, its tax treatment, and its distinction from Treasury notes and Treasury bonds are directly tested on the Series 7 and Series 65 examinations.

The Discount Pricing Mechanism — How T-Bills Work

The Treasury bill is unique among United States government securities in that it is issued and traded not at face value with a coupon rate but at a discount — a price below its face value — with no periodic interest payments during its life. The investor's return is realised entirely at maturity when the Treasury redeems the bill at its full face value.

The minimum purchase denomination for Treasury bills is one hundred dollars, with purchases made in increments of one hundred dollars and a maximum non-competitive purchase of ten million dollars at a single auction. A Treasury bill with a face value of ten thousand dollars purchased at a discount of two percent would be acquired at nine thousand eight hundred dollars. At maturity the investor receives the full ten thousand dollar face value — the two hundred dollar difference between the purchase price and the redemption value is the investor's return.

This discount structure means the Treasury bill's return is expressed in two distinct but related ways — the discount rate and the investment rate. The discount rate — the rate quoted in Treasury auctions — expresses the return as a percentage of the face value over a three hundred and sixty day year. The investment rate — also called the bond equivalent yield or coupon equivalent yield — expresses the same return as a percentage of the actual purchase price over a three hundred and sixty-five day year, making it directly comparable to the yields quoted on coupon-bearing notes and bonds. Because the purchase price is less than face value and the year is expressed as three hundred and sixty-five rather than three hundred and sixty days, the investment rate is always slightly higher than the discount rate for the same T-bill.

A worked example clarifies both measures. A thirteen-week T-bill with a face value of ten thousand dollars is purchased at a discount of five percent on an annualised discount basis. The discount amount equals ten thousand multiplied by five percent multiplied by ninety-one divided by three hundred and sixty — equalling approximately one hundred and twenty-six dollars and thirty-nine cents. The purchase price is ten thousand minus one hundred and twenty-six dollars and thirty-nine cents — equalling nine thousand eight hundred and seventy-three dollars and sixty-one cents. The investment rate equals the one hundred and twenty-six dollar and thirty-nine cent return divided by the nine thousand eight hundred and seventy-three dollar and sixty-one cent investment, multiplied by three hundred and sixty-five divided by ninety-one — producing an investment rate slightly above five percent that is the directly comparable yield for that T-bill.

Available Maturities — The Complete T-Bill Term Structure

Treasury bills are currently issued in the following maturities as specified on the TreasuryDirect website — four weeks, six weeks, eight weeks, thirteen weeks, seventeen weeks, twenty-six weeks, and fifty-two weeks — as well as Cash Management Bills with variable maturities issued at irregular intervals when the Treasury needs to address temporary cash flow gaps in the government's financing.

The four-week, six-week, eight-week, thirteen-week, seventeen-week, and twenty-six week Treasury bills are auctioned weekly. The fifty-two week Treasury bill is auctioned every four weeks — monthly. Cash Management Bills are not sold through TreasuryDirect and are available only through banks, brokers, and dealers.

The historical development of the T-bill maturity spectrum reflects the Treasury's evolving short-term borrowing needs. The thirteen-week and twenty-six week bills have been the core T-bill maturities since 1972. The four-week bill was introduced in 2001. The eight-week bill was introduced in 2018. The seventeen-week bill was introduced in October 2022. The six-week bill was the most recent addition, introduced in 2025 — reflecting the Treasury's ongoing refinement of its short-term financing toolkit to manage cash flows efficiently.

The Auction Process — Competitive and Non-Competitive Bidding

The Treasury sells T-bills through a uniform-price Dutch auction conducted by the Bureau of the Fiscal Service — a process in which all successful bidders pay the same price regardless of the price they individually bid, with that price determined by the competitive bidding process.

Competitive bidders — primarily primary dealers, institutional investors, foreign central banks, and other sophisticated market participants — submit bids specifying the exact discount rate they are willing to accept. Bids are ranked from lowest discount rate — highest price, most favourable to the Treasury — to highest discount rate — lowest price, least favourable to the Treasury. The Treasury accepts bids starting from the lowest discount rate and working upward until the full amount being offered is awarded. The stop-out rate — the highest discount rate accepted — becomes the single uniform auction clearing rate that all successful bidders pay, regardless of the lower rates they individually bid. A competitive bidder may purchase no more than thirty-five percent of the total offering amount at any single auction.

Non-competitive bidders — primarily individual investors purchasing through TreasuryDirect and smaller institutions — do not specify a rate. They agree in advance to accept whatever rate is determined by the competitive auction process. In exchange for accepting the market-clearing rate, non-competitive bidders are guaranteed to receive their full requested amount of T-bills, subject to the maximum purchase limit of ten million dollars per auction. All non-competitive bids are filled first, and their requested amounts are subtracted from the total offering before the competitive awards are determined.

Individual investors can purchase T-bills directly from the Treasury at no cost through TreasuryDirect — the government's online platform at TreasuryDirect.gov — submitting non-competitive bids and having the T-bills credited directly to their TreasuryDirect account at the auction clearing rate. Alternatively, investors can purchase T-bills through banks, broker-dealers, and financial intermediaries who may charge transaction fees but provide the convenience of integration with the investor's existing brokerage accounts.

The Risk-Free Rate Benchmark — T-Bills in Financial Theory

The Treasury bill yield serves as the empirical proxy for the theoretical risk-free rate of return in virtually all quantitative financial models — a role that makes the T-bill conceptually foundational to modern financial theory even for market participants who never directly purchase T-bills.

The risk-free rate is the return available to an investor with absolute certainty — no possibility of loss of principal — against which all other investments must be evaluated in terms of their risk premium. United States Treasury bills satisfy this theoretical requirement more completely than any other instrument because they combine the full faith and credit guarantee of the United States government — the world's reserve currency issuer and the most creditworthy sovereign in global financial markets — with the shortest maturity of any Treasury security, which essentially eliminates interest rate risk for investors holding to the very near-term maturity. A thirteen-week T-bill held to maturity returns a known, certain dollar amount regardless of what happens to interest rates, equity markets, or the broader economy — making it as close to the theoretical risk-free investment as any real-world instrument can achieve.

The Capital Asset Pricing Model — covered in the Security Market Line entry of this dictionary — uses the T-bill rate as the risk-free rate in the formula that the expected return on any security equals the risk-free rate plus beta multiplied by the equity risk premium. The Sharpe ratio — covered in the Sharpe Ratio entry — uses the risk-free rate as the benchmark from which excess return is measured. Option pricing models including Black-Scholes use the risk-free rate as one of the five inputs determining option premiums. Yield spreads on corporate bonds, agency bonds, and municipal bonds are conventionally expressed as the spread above the comparable Treasury yield — a comparison that uses T-bill yields for short-maturity credit instruments.

Tax Treatment — The Federal-Only Exemption

Treasury bill interest income is subject to federal income tax in the year the bill matures — even though the interest is economically accruing during the entire holding period, for tax purposes it is recognised as income in the year of maturity when the face value is received. For a fifty-two week T-bill purchased in December and maturing the following December, the entire return is taxable in the year of maturity rather than being split between the two calendar years of the holding period.

Treasury bill interest is specifically exempt from state and local income taxes under the constitutional doctrine of intergovernmental immunity — the principle that states may not tax the federal government's borrowing costs — codified in 31 U.S.C. 3124. This state and local tax exemption makes Treasury bills and all other Treasury securities more attractive than comparable taxable money market instruments for investors in high-income-tax states — particularly in states like California, New York, and New Jersey where the combined state and local income tax rate on investment income can approach or exceed ten percent. The after-tax yield comparison between a Treasury bill and a taxable money market fund must incorporate this state tax differential to be analytically valid.

Treasury Bills Versus Treasury Notes and Treasury Bonds

The Series 7 and Series 65 examinations directly test the distinctions among the three primary categories of marketable Treasury securities — Treasury bills, Treasury notes, and Treasury bonds — which differ in maturity, interest payment structure, and the mechanism through which they compensate investors.

Treasury bills have original maturities of one year or less — four weeks through fifty-two weeks — are issued at a discount with no periodic interest payments, and the entire return is the difference between the purchase price and the face value at maturity. Treasury bills are zero-coupon instruments.

Treasury notes have original maturities of two, three, five, seven, and ten years — are issued at or near face value — and pay semi-annual coupon interest at a fixed rate throughout their lives until maturity when the face value is also returned. Treasury notes are coupon-bearing instruments with interest payments every six months.

Treasury bonds have original maturities of twenty and thirty years — are structured identically to Treasury notes with semi-annual coupon interest and face value at maturity — but carry the longest maturities of any standard Treasury marketable security, making them the most interest-rate-sensitive segment of the Treasury market. Treasury bonds are also coupon-bearing instruments.

The critical structural distinction is that only Treasury bills are discount instruments — all other Treasury marketable securities including notes and bonds are coupon instruments. This structural difference means that T-bill buyers collect no income during the holding period and receive the entire return at maturity, while note and bond buyers receive regular semi-annual income throughout the holding period and face value at maturity.

T-Bills in the Federal Reserve's Monetary Policy Operations

Treasury bills are the primary instrument through which the Federal Reserve conducts open market operations — the mechanism by which the Fed manages the supply of reserves in the banking system to influence short-term interest rates in pursuit of its dual mandate under 12 U.S.C. 225a.

When the Federal Reserve purchases Treasury bills from primary dealers in the open market — an expansionary open market purchase — it credits the selling dealer's reserve account at the Fed, injecting reserves into the banking system and increasing the supply of federal funds available for overnight lending among banks. This increased reserve supply drives the federal funds rate — the overnight interbank lending rate — downward toward the Fed's target. When the Fed sells Treasury bills to primary dealers — a contractionary open market sale — it debits the purchasing dealer's reserve account, withdrawing reserves from the banking system and putting upward pressure on the federal funds rate.

The Fed's Open Market Desk at the Federal Reserve Bank of New York conducts these operations daily in the Treasury market — and T-bills are the preferred instrument for short-term liquidity management because their short maturities minimise the interest rate risk of the Fed's own portfolio while providing maximum operational flexibility to add or withdraw reserves as needed to maintain the federal funds rate within the Federal Open Market Committee's target range.

How a Bid for a Treasury Bill Must Be Written

Every bid entered into a Treasury bill auction, competitive or non-competitive, must state the par amount of securities bid for, and that amount must equal or exceed the minimum to bid amount stated in the auction announcement for that particular offering — where a bidder wants more than the minimum, the amount bid for must be in the multiple that the same announcement states. The announcement, rather than the bidder, therefore fixes both the floor beneath a valid bid and the step by which it may rise, and a bid for an amount falling between two of those steps does not meet the requirement.

A competitive bid for a Treasury bill names a discount rate rather than a dollar price, and the form of that rate is prescribed rather than left to the bidder — the rate is expressed with three decimals in increments of five thousandths of one percent, so that the third decimal must be either a zero or a five, as in five point three two zero or five point three two five. A rate such as five point three two three cannot be bid, because it does not fall on one of the permitted increments.

Because the third decimal is part of the required form rather than an optional refinement, a competitive bid written with fewer than three decimals is completed by the Treasury rather than rejected — the missing decimals are treated as zeros, so that a bid written five point three two is treated as a bid of five point three two zero, and a bid written five is treated as a bid of five point zero zero zero.

What a Competitive Bid May Say, and for Whose Account It May Be Entered

The discount rate a competitive bidder names may be zero as well as a positive number, so a bid that offers to buy the bill at its full face value and take no discount at all is a validly formatted competitive bid rather than a defective one.

A bidder must choose between the two routes into a single auction and may not take both — a bidder who is bidding competitively in an auction may not also bid non-competitively in that auction, and a bidder who is bidding non-competitively may not also bid competitively in it. The exclusion is written into both halves of the circular, once as a restriction on non-competitive bidding and once as a restriction on competitive bidding, so that neither route can be used to supplement the other within the same offering.

The destination of the securities also limits which route is open. A bidder may not bid competitively for securities that are to be held directly with the Treasury, so an investor whose bills are to be credited to an account held with the Treasury itself is confined to the non-competitive route and to the rate that the competitive process determines.

The Positions That Close the Non-Competitive Route

A bidder who already holds a position in the very bill being auctioned may not bid non-competitively for it. The bar reaches a position in when-issued trading in the security being auctioned, and a position in futures or forward contracts on it, and it is drawn as a window rather than as a moment — a position held at any time between the date of the auction announcement and the time the auction results are announced closes the non-competitive route for that bidder in that auction.

Within that same window a non-competitive bidder is also barred from committing the securities it is acquiring before it has them, and may not enter into any agreement to purchase, to sell or otherwise to dispose of the securities it is acquiring in the auction. The restriction is on the agreement rather than on the eventual sale, so a bidder that has arranged the onward disposal of its bills while the window is open has disqualified its non-competitive bid even though settlement of that arrangement would fall later.

The futures contracts that close the non-competitive route are defined by what they can be settled against rather than by the bidder's intention, and they are of three kinds — a contract that requires delivery of the specific security being auctioned, a contract for which the security being auctioned is one of several securities that may be delivered, and a contract that is cash-settled and so calls for no delivery of the bill at all.

The Reinvestment Request, and the Reduction of an Oversized Competitive Bid

The ten million dollar ceiling on a non-competitive bid has an exception that follows the money rather than the bidder. Where a bidder is bidding solely through a request to reinvest the proceeds of a maturing security held directly with the Treasury, the maximum bid limitation does not apply, so the whole of those maturing proceeds may be rolled into the new bill however large they are.

A reinvestment request of that kind is itself a non-competitive bid rather than a separate category of instruction, which settles the rate at which the rolled proceeds go in: the holder names no rate and takes whatever rate the competitive process determines, exactly as any other non-competitive bidder does, while keeping the guarantee that the amount requested is filled.

On the competitive side the circular sets no limit at all on the total amount a bidder may bid for, whether that total is bid at one discount rate or spread across several different discount rates. What it limits is the amount recognised at any single discount rate: a competitive bid at one discount rate that exceeds thirty-five percent of the offering amount is reduced to thirty-five percent of the offering amount, so that on an offering of ten billion dollars the largest bid recognised at any one discount rate from any one bidder is three and a half billion dollars. The circular deals with limits on what a bidder may be awarded separately from this reduction of what it may bid.

The Order in Which the Treasury Fills the Book

An auction has two separate cut-offs rather than one. The non-competitive bids that are accepted in full are those submitted by the non-competitive bidding deadline, while the competitive book is worked through only after the closing time for the receipt of competitive bids — so a bid's route determines which cut-off it must meet.

Filling the non-competitive bids first has a limit, because the competitive bids are what produce the rate in the first place. Where the non-competitive bids would absorb all or most of the offering amount, the Treasury accepts competitive bids in an amount sufficient to provide a fair determination of the discount rate for the bills being auctioned — so an auction swamped by non-competitive demand still takes in enough competitive bids to set a rate, rather than being awarded at no rate at all.

Once the book is worked through from the lowest discount rate upward, the bids divide into two classes with quite different outcomes. Every accepted bid at a rate below the highest accepted rate is awarded in full, and it is only the bids standing at the highest accepted rate that are cut down, because that is where the offering amount runs out part-way through a tier of bids.

Proration at the Highest Accepted Rate, Worked Through

The cut applied at the highest accepted rate is a percentage, and the percentage is derived rather than chosen. The Treasury divides the par amount still needed to fill the offering by the par amount of the bids standing at the highest accepted rate, and rounds the result up to the next hundredth of a whole percentage point — every bid at that rate is then awarded that percentage of the amount it bid for.

Suppose that after the non-competitive bids and the competitive bids at lower rates have been awarded, one billion three hundred and seventy million dollars of par remains to be filled, and the bids standing at the highest accepted rate total eight billion dollars. Dividing one billion three hundred and seventy million by eight billion gives seventeen point one two five percent, which rounded up to the next hundredth of a percentage point is a proration percentage of seventeen point one three percent.

Because one percentage is applied to every bid in that tier, the cut preserves the relative sizes of the bids standing there. A bidder that bid one hundred million dollars at the highest accepted rate receives seventeen million one hundred and thirty thousand dollars of bills, and a bidder that bid forty million dollars at the same rate receives six million eight hundred and fifty-two thousand dollars — each of them a little over one sixth of what it asked for, and the larger bid still two and a half times the smaller.

How the Award Arithmetic Is Rounded, and What a Basis Point Is Worth

The direction of that rounding has a consequence worth following through. The stated purpose of prorating is to keep the total amount of awards as close as possible to the announced offering amount, but the percentage is rounded up to the next hundredth of a point rather than to the nearest hundredth — so the total awarded comes out a little above the announced offering amount rather than a little below it. On the figures above, seventeen point one three percent of eight billion dollars is one billion three hundred and seventy million four hundred thousand dollars against one billion three hundred and seventy million needed, an overshoot of four hundred thousand dollars.

Award prices themselves carry a stated precision. Price calculations for awarded securities are made on the basis of price per hundred and are rounded to six decimal places, so that an award price takes a form such as ninety-nine point nine five four three two one rather than being carried to the nearest cent or to the nearest thirty-second.

The arithmetic of a discount quote also fixes what one basis point of rate is worth, and fixes it as a constant rather than as something that shifts with the level of rates. A bill's price is its face value less its face value multiplied by the quoted discount rate multiplied by the days to maturity over three hundred and sixty, so the price moves by face value multiplied by one basis point multiplied by days over three hundred and sixty for each basis point the quoted rate moves. On a one million dollar bill with ninety-one days to run, that is one million multiplied by zero point zero zero zero one multiplied by ninety-one divided by three hundred and sixty — twenty-five dollars and twenty-eight cents for every basis point, whether the quoted rate moves from two percent to two point zero one percent or from six percent to six point zero one percent.

The Same Book Awarded Two Ways

Where an auction is conducted as a multiple-price auction rather than a single-price auction, the non-competitive bidders are not awarded at the highest accepted rate. They are awarded at the price equivalent to the weighted average discount rate of the accepted competitive bids — so in a multiple-price auction the non-competitive bidder's price is set by the whole accepted competitive book rather than by its marginal tier.

The difference that makes to a non-competitive bidder can be computed from a book. Suppose the accepted competitive bids are four billion dollars at four point eight zero zero percent, four billion dollars at four point nine zero zero percent and two billion dollars at five point zero zero zero percent. The weighted average of the accepted rates is four point eight eight zero percent, and on a ninety-one day bill of one hundred thousand dollars face value the price equivalent to that average rate is ninety-eight thousand seven hundred and sixty-six dollars and forty-four cents, against ninety-eight thousand seven hundred and thirty-six dollars and eleven cents at the highest accepted rate of five percent. The non-competitive bidder therefore pays thirty dollars and thirty-three cents more per hundred thousand dollars of face value in the multiple-price auction than the single-price rule would have charged it.

For a competitive bidder the comparison runs the other way, and it can be put in dollars on the same book. A bidder that bid four point eight zero zero percent for one million dollars of a ninety-one day bill in an auction that stopped at five point zero zero zero percent pays nine hundred and eighty-seven thousand three hundred and sixty-one dollars and eleven cents under the single-price rule, which prices every award at the highest accepted rate, and nine hundred and eighty-seven thousand eight hundred and sixty-six dollars and sixty-seven cents under the multiple-price rule, which prices its award at the rate it bid itself — five hundred and five dollars and fifty-six cents more for the same bills, because the aggressive rate it named is the rate it is then charged.

Reading a Discount Quote Backwards

The discount formula can be run in either direction, and running it backwards is how a price is turned into the rate that produced it. The dollar discount is the face value less the price; dividing that discount by the face value and multiplying by three hundred and sixty over the days to maturity gives the quoted discount rate. A one hundred thousand dollar bill with one hundred and eighty-two days to run, bought at ninety-seven thousand four hundred and seventy-two dollars and twenty-two cents, carries a discount of two thousand five hundred and twenty-seven dollars and seventy-eight cents — and two thousand five hundred and twenty-seven dollars and seventy-eight cents divided by one hundred thousand, multiplied by three hundred and sixty divided by one hundred and eighty-two, is five percent.

At a single quoted discount rate the dollar discount is proportional to the days to maturity, because the days enter the expression once and linearly. At five percent, a one hundred thousand dollar bill with ninety-one days to run is discounted by one thousand two hundred and sixty-three dollars and eighty-nine cents, and a one hundred thousand dollar bill with one hundred and eighty-two days to run is discounted by two thousand five hundred and twenty-seven dollars and seventy-eight cents — exactly twice as much, for exactly twice the term.

The gap between the two measures of a bill's return is not a fixed spread, and the algebra shows what moves it. Writing the discount rate as d and the days to maturity as t, the discount is the face value multiplied by d multiplied by t over three hundred and sixty, and the price is the face value less that amount — so the investment rate, which divides the discount by the price and annualises over three hundred and sixty-five days, reduces to three hundred and sixty-five over three hundred and sixty multiplied by d, all divided by one minus d multiplied by t over three hundred and sixty. The face value cancels out entirely, and the only place t survives is in the denominator, which shrinks as the term lengthens. At a quoted rate of five percent the investment rate is therefore about five point one three percent on a ninety-one day bill and about five point two zero percent on a one hundred and eighty-two day bill: the longer the bill at one quoted discount rate, the wider the gap between the two measures.

Examination Relevance and Key Takeaways

Treasury bills are tested on the Series 7 and Series 65 examinations in the context of government securities, discount pricing, the auction process, the risk-free rate, and the distinctions among Treasury bills, notes, and bonds.

The key points to retain are these.

A Treasury bill is a short-term United States government obligation with original maturity of one year or less — currently issued in maturities of four, six, eight, thirteen, seventeen, twenty-six, and fifty-two weeks plus irregular Cash Management Bills. T-bills are sold at a discount to face value and redeemed at full face value at maturity — the difference is the investor's entire return since T-bills pay no periodic coupon interest making them zero-coupon discount instruments. The minimum purchase is one hundred dollars in one hundred dollar increments with a ten million dollar maximum for non-competitive bids.

T-bills are sold through uniform-price Dutch auctions — competitive bidders specify a discount rate and all successful bidders pay the same stop-out rate determined by the auction — and non-competitive bidders who accept the auction rate are guaranteed their full requested amount. Individual investors purchase through TreasuryDirect at no fee. Treasury bill interest is subject to federal income tax in the year of maturity — exempt from state and local income taxes under 31 U.S.C. 3124 making them more attractive than taxable money market alternatives in high-tax states.

Treasury bills serve as the empirical proxy for the risk-free rate in the Capital Asset Pricing Model, the Sharpe ratio, option pricing models, and all yield spread calculations — because the full faith and credit United States government guarantee combined with the very short maturity essentially eliminates both credit risk and interest rate risk. The critical distinction from Treasury notes and bonds is the discount structure — T-bills are zero-coupon discount instruments with no periodic interest payments while notes and bonds are coupon instruments paying semi-annual interest with face value returned at maturity. Treasury notes carry maturities of two through ten years and Treasury bonds carry maturities of twenty and thirty years — both pay semi-annual coupons unlike the discount T-bill. The Federal Reserve conducts open market operations primarily through T-bill purchases and sales to manage banking system reserves and influence the federal funds rate toward the FOMC target.