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Lesson 2 of 3 11–14% of the exam

Government bond auctions and trading vs corporate bonds

Governments sell bonds by public auction on a regular calendar, not through opportunistic underwritten deals. Bids are filled from the lowest yield up to a cut-off; in a single-price auction every winner pays the same price. Afterwards government bonds trade over the counter, are the most liquid bonds, and attract many holders with non-economic motives.

6 min cram, 26 min full read. Based on the 2027 CFA® Program Level I curriculum, Fixed Income, Learning Module 5. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Sovereign debt: who borrows, in what currency, for how long, Primary and secondary bond markets vs equity markets

On the exam

  • Contrast the issuance and trading of government and corporate fixed-income instruments

Contrast the issuance and trading of government and corporate fixed-income instruments. Expect: competitive vs non-competitive bids; single-price vs multiple-price auctions; primary dealers; on-the-run vs off-the-run; the effect of reserve currencies. A cut-off yield from a bid table is the one calculation.

How deeply to learn each part
Know the idea
Understand it in general. It frames other topics, but you will not calculate with it.
Use it
Understand it well enough to solve a question with it. Recognize when it applies.
Memorize
Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

Cram mode: the one-screen version of this lesson. Switch to Full for the explanations, worked examples and interactives.

How is a government bond auction run?

Governments sell debt by public auction, led by the treasury or finance ministry on standard procedures and a regular calendar. Corporate issuers instead use investment bank underwriters and time a deal when the market suits them.

An auction has four steps.

  1. The debt office announces the amount and type of bonds, the auction and issue dates, the maturity and the bidding times.
  2. Dealers, institutional investors and individuals bid. A competitive bid gives a price (or yield) and an amount; if the auction price ends up worse than the bid, it gets nothing. A non-competitive bid gives an amount only, accepts the auction price and is always filled.
  3. All non-competitive bids are accepted first. Competitive bids are ranked from the lowest yield (highest price) upward until the offering is filled. The last yield needed is the cut-off yield , also called the stop yield. Bids above it receive nothing.
  4. Securities are delivered and the proceeds paid.
How a government auction allocates bonds
Government auctionannounced, bid, allocated, settled
  • Non-competitive bids Memorize amount only; always filled at the auction price; filled first
  • Competitive bids Memorize yield and amount; ranked from the lowest yield up until the offering is filled
    • Single-price (uniform) Memorize every winner pays the cut-off price; broader distribution, steadier yields
    • Multiple-price (discriminatory) Memorize each winner pays its own bid; can concentrate large bids
Amount left for competitive bids Use it
C=Offering−Non-competitive bidsC = \text{Offering} - \text{Non-competitive bids}
Fill at the cut-off yield Use it
F=C−BAF = \frac{C - B}{A}

Here CC is the amount for competitive bids, BB the cumulative bids below the cut-off yield and AA the bids at the cut-off yield.

Rearrange itAmount left for competitive bids: solve for any input
The question asks for
A government offers 5 billion of bonds and receives 0.6 billion of non-competitive bids. The amount that must be filled from competitive bids is closest to:

5 − 0.6 = 4.4 billion

Amount for competitive bids (billions)4.4

On your calculator
  1. 5−0.6=billions left for competitive bids
  1. 5ENTER0.6−billions left for competitive bids

ENTER enter (on the HP, puts the number on the stack)

Rearrange itFill at the cut-off yield: solve for any input
The question asks for
4.4 billion must be filled from competitive bids. Bids at lower yields total 3.7 billion, and 1 billion is bid at the cut-off yield. A bidder at the cut-off receives closest to:

(4.4 − 3.7) ÷ 1 = 70.00%

Share of cut-off bids filled70.00%

On your calculator
  1. 4.4−3.7=÷1=fill as a decimal
  1. 4.4ENTER3.7−1÷fill as a decimal

ENTER enter (on the HP, puts the number on the stack)

InteractiveRun a government bond auction

Try this 0 of 3

  • Switch to multiple-price and see who pays the most
  • Lower the cut-off to 3.97% by changing only the non-competitive amount
  • Make the offering so big that every competitive bid is filled
Edit the competitive bids
Left for competitive bidsEUR 4.4 bn
Cut-off yield4.00%
Fill at 4.00%70%
Issuer raisesEUR 5 bn
  • Non-competitive
  • Filled
  • Not filled
0Offering 5 bnNon-compalways3.92%bid Cfull3.95%bid Efull3.97%bid Afull4.00%bid D70%4.03%bid Bnone
Bids ranked from the lowest yield (highest price)
Yield bidBid (bn)Cum. (bn)Gets (bn)Pays
Non-comp.amount only0.6–0.6100.00
3.92%bid C111100.00
3.95%bid E1.52.51.5100.00
3.97%bid A1.23.71.2100.00
4.00%bid D14.70.7100.00
4.03%bid B0.85.50–

Cut-off yield 4.00%. Bids at 4.00% get 70% of what they asked for; the bid above it gets nothing. Single-price: every winner, and every non-competitive bidder, pays 100.00.

Prices are per 100 of par for a 10-year bond paying a 4% annual coupon. A yield bid below 4% means a price above 100.

Show working

Left for competitive bids = offering − non-competitive = 5 − 0.6 = 4.4 bn

Cumulative, lowest yield first: 3.92% → 1 · 3.95% → 2.5 · 3.97% → 3.7 · 4.00% → 4.7 · 4.03% → 5.5

The 4.00% level takes the total past 4.4, so it is the cut-off. Fill there = (4.4 − 3.7) ÷ 1 = 70.0%

Single-price: everyone pays the price at 4.00%, 100.0000. Issuer raises 5 × 100.0000 ÷ 100 = EUR 5 bn.

Pro rata fill at the cut-off
  1. 4.4−3.7=÷1=0.7, the share each cut-off bid receives
  1. 4.4ENTER3.7−1÷0.7, the share each cut-off bid receives

ENTER enter (on the HP, puts the number on the stack)

Price at 4.00% on your calculator
  1. 2NDCLR TVM
  2. 10N4I/Y4PMT100FV
  3. CPTPV−100.00

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · FV future value · CPT compute · PV present value

  1. fCLEAR FIN
  2. 10n4i4PMT100FV
  3. PV−100.00

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Fill from the lowest yield up; where the money runs out is the cut-off.

What changes between a single-price and a multiple-price auction?

Both rank bids the same way. They differ in what winners pay.

A single-price auction (uniform price) charges every winner the price at the cut-off yield, and the bonds carry one coupon. Bidders need not fear overpaying, so they bid more aggressively. The auction tends to lower the issuer’s cost, spread bonds more widely and reduce yield volatility. A government that suffers partly failed auctions may switch to it for that reason.

A multiple-price auction (discriminatory) charges each winner the price it bid. The same bond sells at different prices, and large bids can end up concentrated among a few bidders, because investors must accept their own price.

In the example, under single-price everyone, including the non-competitive bidders, pays the price at 4.00%. Under multiple-price, the 3.92% bidders pay the higher price that matches their lower yield. For a 10-year, 4% annual-pay bond, the price at 3.92% is 100.65, against 100.00 at 4.00%.

Price at 3.92% on your calculator
  1. 2NDCLR TVM
  2. 10N
  3. 3.92I/Y
  4. 4PMT
  5. 100FV
  6. CPTPV −100.65 (the sign shows a payment out)

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · FV future value · CPT compute · PV present value

  1. fCLEAR FIN
  2. 10n
  3. 3.92i
  4. 4PMT
  5. 100FV
  6. PV −100.65 (the sign shows a payment out)

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

A primary dealer is a financial intermediary the government designates to take part in every auction with competitive bids. Primary dealers often act as the central bank’s counterparty when it trades securities for monetary policy, and pass on bids from foreign central banks and other indirect bidders. Investors may also bid directly through the debt office.

How do government bonds trade afterwards?

Once issued, government bonds trade much like private bonds: mostly over the counter through broker-dealers. A few markets use an exchange. The government is usually the largest borrower in its market and its bonds are the most liquid.

The most recently issued bond of each maturity belongs to the on-the-run securities . It is the most liquid and sets benchmark yields, and some of its trading is electronic. Older issues are off-the-run securities , which trade infrequently.

A difference that matters for the exam is who holds them. Many government bond investors have non-economic objectives.

Holders of government bonds with non-economic motives
Government bond holderstheir demand lowers sovereign borrowing costs
  • Central bank Use it monetary policy operations
  • Foreign central banks and governments Use it currency reserves
  • Banks and insurers Use it required or encouraged to hold them by regulation
  • State and local governments Use it restricted from holding other securities

These holders lower sovereign borrowing costs relative to private issuers. The effect is strongest for issuers of a reserve currency , one that central banks hold in large amounts and that is widely used in trade and finance. The US dollar, euro, Japanese yen, British pound, Swiss franc, Australian dollar and Chinese renminbi are reserve currencies. The dollar holds the largest share of reserves by far.

How do government and corporate bonds compare?

GovernmentCorporate
Primary salepublic auction on a regular calendarunderwritten deal, timed opportunistically
Intermediariesprimary dealersunderwriting banks, syndicate
Pricingset by bids (cut-off yield)negotiated with underwriters, spread over benchmark
Secondary marketOTC, deepest liquidity, on-the-run benchmarksOTC, liquidity varies widely
Holdersmany with policy or regulatory motivesmainly return-seeking investors
Go deeper Why a single-price auction can lower the issuer's cost

In a multiple-price auction a bidder who bids too aggressively pays too much (the winner’s curse). Bidders protect themselves by bidding higher yields, which raises the issuer’s cost. In a single-price auction the price depends on the cut-off, not on the bidder’s own number, so bids can be more honest and the cut-off yield is often lower.

Go deeper When-issued trading before an auction

Between the announcement and the auction, dealers often trade the new bond on a when-issued basis, promising to deliver it after it is issued. The when-issued yield gives bidders a market-based guide to the likely cut-off yield.

Go deeper Reserve currency status and its funding advantage

A reserve currency creates steady foreign demand for the issuer’s debt, because other countries must hold it for trade and as a store of value. That demand lets the issuer borrow more cheaply than its own economy alone would justify. The link to capital flows and exchange rates is covered in the economics topic.

Go deeper Why on-the-run bonds usually yield a little less

Investors pay for liquidity. The newest bond is easy to buy and sell, so its price tends to be a touch higher, and its yield a touch lower, than an otherwise similar older bond. That gap is a liquidity effect and not a difference in credit quality.

Exam tip Rank by yield from the lowest up, subtract the non-competitive bids first, and the cut-off is where the cumulative total passes the amount needed.

Memorize this

MemorizeAuction rules

Rule
Non-competitive bidamount only; always filled at the auction price
Competitive bidranked from the lowest yield (highest price) upward
Cut-off (stop) yieldthe highest yield needed to fill the offering; higher bids get nothing
Single-priceall winners pay the cut-off price
Multiple-priceeach winner pays its own bid

Memory hook Fill from the lowest yield up; where the money runs out is the cut-off.

Know it cold Amount for competitive bids = offering − non-competitive bids. Bidders at the cut-off may be filled pro rata.

MemorizeGovernment vs corporate bonds

GovernmentCorporate
Primary salepublic auction, regular calendarunderwritten, timed opportunistically
Intermediariesprimary dealersunderwriting banks
Pricingset by bids (cut-off yield)negotiated, spread over benchmark
Secondarymostly OTC, deepest liquidityOTC, liquidity varies
Holdersmany with policy or regulatory motivesmainly return-seeking

Memory hook Government = calendar and auction; corporate = underwriter and timing.

Know it cold On-the-run (newest) = most liquid, benchmark yield. Off-the-run (older) = trades less.

MemorizeReserve currencies

Memory hook USD, EUR, JPY, GBP, CHF, AUD, CNY. The USD is by far the largest.

Know it cold Non-economic demand lowers sovereign borrowing costs most for reserve-currency issuers.

How a government auction allocates bonds
Government auctionannounced, bid, allocated, settled
  • Non-competitive bids Memorize amount only; always filled at the auction price; filled first
  • Competitive bids Memorize yield and amount; ranked from the lowest yield up until the offering is filled
    • Single-price (uniform) Memorize every winner pays the cut-off price; broader distribution, steadier yields
    • Multiple-price (discriminatory) Memorize each winner pays its own bid; can concentrate large bids
Holders of government bonds with non-economic motives
Government bond holderstheir demand lowers sovereign borrowing costs
  • Central bank Use it monetary policy operations
  • Foreign central banks and governments Use it currency reserves
  • Banks and insurers Use it required or encouraged to hold them by regulation
  • State and local governments Use it restricted from holding other securities
Amount left for competitive bids Use it
C=Offering−Non-competitive bidsC = \text{Offering} - \text{Non-competitive bids}
Quick example

Offering 8.0 billion, non-competitive bids 1.4 billion. 8.0 − 1.4 = 6.6 billion must be filled by competitive bids.

On your calculator
  1. 8−1.4= 6.6
  1. 8ENTER1.4− 6.6

ENTER enter (on the HP, puts the number on the stack)

Fill at the cut-off yield Use it
F=C−BAF = \dfrac{C - B}{A}
Quick example

C = 6.6 billion; bids below the cut-off total B = 5.0; bids at the cut-off A = 3.2. (6.6 − 5.0) ÷ 3.2 = 50% of each cut-off bid is filled.

On your calculator
  1. 6.6−5=÷3.2= 0.5
  1. 6.6ENTER5−3.2÷ 0.5

ENTER enter (on the HP, puts the number on the stack)

How it is asked

  1. Cut-off yield from a bid table

    Offering 7.0 bn, non-competitive 0.3 bn, bids by yield. Cut-off?

    7.0 − 0.3 = 6.7 bn for competitive bids. Add bids from the lowest yield until 6.7 is passed. Traps: stopping short, or forgetting the non-competitive bids.

  2. Price paid in a single-price auction

    In a single-price auction a successful competitive bidder pays?

    The price at the cut-off yield. Trap: its own bid (that is multiple-price).

  3. Government vs corporate trading

    A key difference in trading government bonds versus corporate bonds?

    Many holders buy for policy or regulatory reasons. Traps: exchange trading; older issues more liquid.

  4. Non-competitive bidder

    What happens to a non-competitive bid?

    Always filled at the auction price. Trap: "might get nothing" (that is a competitive bid priced too high).

Exam traps

  • Ranking competitive bids from the highest yield down. Rank from the lowest yield (highest price) up.
  • Saying non-competitive bidders might get nothing. They are always filled.
  • Forgetting to subtract non-competitive bids before finding the cut-off.
  • Saying government bonds mostly trade on exchanges. Mostly over the counter; a few markets use an exchange.
  • Describing on-the-run bonds as the least liquid. They are the most recently issued, the most liquid and the benchmark.

Checkpoint

6 exam-style questions. About 90 seconds each.

  1. 1A sovereign offers USD 3.0 billion. Non-competitive bids total USD 0.4 billion. Competitive bids are 2.10% for 0.9 billion, 2.14% for 1.1 billion, 2.18% for 0.8 billion and 2.22% for 0.7 billion. The cut-off yield is closest to:

  2. 2In a single-price auction, a successful competitive bidder pays:

  3. 3Which feature best sets the market for a country's government bonds apart from the market for its corporate bonds?

  4. 4A government offers EUR 4.0 billion and receives EUR 0.5 billion of non-competitive bids. Competitive bids are 1.80% for 1.2 billion, 1.84% for 1.0 billion, 1.88% for 1.5 billion and 1.92% for 0.9 billion. A bidder at the cut-off yield will most likely receive about what share of its bid?

  5. 5A non-competitive bidder in a government bond auction:

  6. 6On-the-run government securities are best described as:

Key takeaways

  • Governments auction debt on a calendar; corporates use underwriters when markets suit them.
  • Non-competitive bids are always filled; competitive bids fill from the lowest yield up to the cut-off.
  • Single-price: one price for all winners. Multiple-price: each pays its bid.
  • On-the-run issues are the benchmarks; non-economic buyers lower sovereign yields.
Amount left for competitive bids Use it
C=Offering−Non-competitive bidsC = \text{Offering} - \text{Non-competitive bids}
Quick example

Offering 8.0 billion, non-competitive bids 1.4 billion. 8.0 − 1.4 = 6.6 billion must be filled by competitive bids.

On your calculator
  1. 8−1.4= 6.6
  1. 8ENTER1.4− 6.6

ENTER enter (on the HP, puts the number on the stack)

Fill at the cut-off yield Use it
F=C−BAF = \dfrac{C - B}{A}
Quick example

C = 6.6 billion; bids below the cut-off total B = 5.0; bids at the cut-off A = 3.2. (6.6 − 5.0) ÷ 3.2 = 50% of each cut-off bid is filled.

On your calculator
  1. 6.6−5=÷3.2= 0.5
  1. 6.6ENTER5−3.2÷ 0.5

ENTER enter (on the HP, puts the number on the stack)

All Fixed Income formulas, every lesson

Practice exam-style questions on Fixed-Income Markets for Government Issuers

Questions about this lesson?

Where this comes back

Questions candidates ask

What is the difference between a single-price and a multiple-price auction?

In a single-price auction all winning bidders pay the same cut-off price. In a multiple-price auction each pays the price it bid.

What is a non-competitive bid?

A bid for an amount only, which accepts whatever price the auction sets and is always filled.

What does on-the-run mean?

The most recently issued government bond of a given maturity. It is the most liquid and the usual benchmark.

What do primary dealers do?

They are designated intermediaries that must bid in the government's auctions, often trade with the central bank, and pass on bids from foreign central banks and other investors.

Spotted an error? Tell us and we will fix it.

  1. Sovereign debt: who borrows, in what currency, for how long
  2. Government bond auctions and trading vs corporate bonds
  3. Agency, municipal and supranational bonds

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