Skip to content

FRM Exam Part I · Country Risk: Determinants, Measures, and Implications

Sovereign CDS Spreads and Default Spreads Explained

Updated 11 October 2026 · Fact-checked

A sovereign CDS spread is the annual price, in basis points of notional, of insuring against a government's default. A sovereign bond default spread is its yield minus a risk-free yield. Both are market-based measures of country default risk. To solve questions, compare, convert and interpret them, noting their limits.

Understand Sovereign CDS and Default Spreads

A sovereign credit default swap (CDS) is insurance on a government's debt. The buyer pays a yearly premium, the CDS spread, quoted in basis points of notional. If the government defaults, the seller pays the loss, which is notional × (1 − recovery rate). A higher spread means the market sees more default risk.

A second market measure is the sovereign bond default spread. It is the yield on a government bond minus a risk-free yield of the same maturity and currency. Example: a USD-denominated bond from a country yields 6.5% and a US Treasury of the same maturity yields 4.0%. The default spread is 2.5%, or 250 bp.

Both measures are forward-looking and update daily, unlike ratings, which move slowly. In theory they should be close. A rough link is spread ≈ annual default probability × loss given default, so default probability ≈ spread ÷ (1 − recovery). This is an approximation that gives a risk-neutral probability, not a real-world one.

The two measures differ in practice. In theory, arbitrage links them: an investor who holds the bond and buys CDS protection has taken out most of the default risk, so the CDS spread should be close to the bond spread. In practice, funding cost, liquidity, counterparty risk and contract terms drive a gap between them. A bond purchase must be funded, while a CDS does not need that. The bond spread also reflects liquidity. A CDS has counterparty risk, contract-definition issues (what counts as a credit event, how restructuring is defined, which bond is cheapest to deliver) and thin trading for some countries. The comparison is only clean when the bond is in the same currency as the risk-free benchmark and the CDS. This gap is called the CDS-bond basis.

The key limitations to remember: the spread contains a risk premium as well as expected loss, so the implied default probability typically overstates the real-world default probability. Liquidity can be poor for smaller countries. The CDS market can be affected by speculation. A local-currency bond yield includes inflation and currency components, so it should not be compared directly with a USD risk-free rate. For country risk premiums, analysts often add a scaled default spread to the equity risk premium.

Key formulas to remember

Bond default spread
Default spread = Yield on sovereign bond − Yield on risk-free bond
Use the same maturity and the same currency. A USD bond is compared with a US Treasury.
CDS spread approximation
CDS spread ≈ PD × (1 − R)
PD is annual risk-neutral default probability, R is recovery rate. Approximate and ignores discounting and timing.
Implied default probability
PD ≈ CDS spread ÷ (1 − R)
Convert bp to decimals first: 150 bp = 0.0150.
CDS payout on default
Payout = Notional × (1 − R)
Recovery is expressed as a fraction of face value.
Annual CDS premium
Premium = Notional × spread
Paid by protection buyer, usually quarterly in practice.
CDS-bond basis
Basis = CDS spread − bond default spread (a common convention)
Under this convention, a positive basis means the CDS is more expensive than the bond spread suggests. Some texts define basis as bond spread minus CDS spread, which reverses the sign, so check the convention stated in the question.

How to solve Sovereign CDS and Default Spreads questions

Use this order for any question on sovereign CDS or default spreads.

  1. 1Identify which measure is given: CDS spread, bond yield, or bond spread, and the currency of the bond.
  2. 2Convert basis points to decimals (100 bp = 1% = 0.01).
  3. 3If a bond default spread is needed, subtract the risk-free yield of the same maturity and currency.
  4. 4If a probability is needed, apply PD ≈ spread ÷ (1 − R) using the stated recovery rate.
  5. 5If a dollar amount is needed, apply notional × spread for premium or notional × (1 − R) for payout.
  6. 6If the question is conceptual, state what the spread contains: expected loss plus risk premium, liquidity and other effects.
  7. 7Check the answer: the PD must be between 0 and 1, and the spread should not exceed the loss rate.

Quickest way: Spread ÷ loss rate shortcut

When to use it: Use when the question asks for an implied default probability or a CDS premium from given numbers.

  1. Write the loss rate as 1 − R.
  2. Divide the spread in decimals by the loss rate for PD.
  3. For cost, multiply notional by spread.
  4. Eliminate options that confuse bp with percent, or that use R instead of 1 − R.

Common mistakes in Sovereign CDS and Default Spreads

  • Using recovery rate instead of 1 − R when computing default probability.

    Both numbers are given and R looks like the relevant one.

    Fix: Spread compensates for loss, which is 1 − R. Always divide by 1 − R.

  • Forgetting to convert bp to decimals.

    Spreads are quoted as 200 bp and used raw.

    Fix: Divide bp by 10,000 before any calculation.

  • Treating implied PD as the real-world probability.

    The formula looks like a probability estimate.

    Fix: It is risk-neutral and includes a risk premium, so it usually overstates actual default likelihood.

  • Computing a bond spread against a risk-free bond in a different currency.

    Students use the home-country government rate by default.

    Fix: Match currency and maturity. A USD sovereign bond is compared with US Treasuries.

  • Assuming the CDS spread and bond spread must be equal.

    Arbitrage logic is overapplied.

    Fix: Remember the basis: liquidity, counterparty risk, contract terms and funding costs create differences.

Worked examples

Example 1

A country's 5-year sovereign CDS spread is 180 bp. The assumed recovery rate is 40%. Estimate the annual risk-neutral default probability.

Show the solution
  1. Convert the spread: 180 bp = 0.0180.
  2. Loss rate = 1 − 0.40 = 0.60.
  3. PD ≈ 0.0180 ÷ 0.60 = 0.03.

Answer: About 3.0% per year.

Example 2

A 10-year USD-denominated sovereign bond yields 6.2%. The 10-year US Treasury yields 4.1%. The country's 10-year CDS spread is 190 bp. Using the convention Basis = CDS spread − bond spread, find the bond default spread and the CDS-bond basis.

Show the solution
  1. Bond default spread = 6.2% − 4.1% = 2.1% = 210 bp.
  2. Basis = CDS spread − bond spread = 190 − 210 = −20 bp.

Answer: The bond default spread is 210 bp and the basis is −20 bp under this convention, so the CDS is cheaper than the bond spread implies. If a question defines basis as bond spread minus CDS spread, the sign is +20 bp for the same data.

Exam tips

  • Always check that the bond and the risk-free benchmark share currency and maturity.
  • Questions often test the interpretation: spreads include a risk premium, so implied PD is risk-neutral.
  • Do the bp-to-decimal conversion first to avoid an order-of-magnitude error.
  • For limitations, list liquidity, counterparty risk, contract definitions and speculation.
  • Remember CDS and bond spreads can diverge, so a basis is not an error.

Practice questions from Country Risk: Determinants, Measures, and Implications

Sovereign CDS and Default Spreads in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Sovereign CDS and Default Spreads: frequently asked questions

What is the difference between a sovereign CDS spread and a bond spread?

A CDS spread is the premium paid for insurance against default, quoted in bp of notional. A bond spread is the bond yield minus a risk-free yield. Both reflect default risk, but they differ because of liquidity, funding and contract features.

How do I estimate default probability from a CDS spread?

Divide the spread in decimals by one minus the recovery rate. For 150 bp and 40% recovery, PD ≈ 0.015 ÷ 0.60 = 2.5%. The result is a risk-neutral estimate.

Why is the implied default probability not the true probability?

The spread includes compensation for risk and illiquidity as well as expected loss. So the implied probability is usually higher than the real-world one.

What are the main limitations of sovereign CDS?

Thin trading for many countries, counterparty risk, disputes over what triggers payout, and speculative influence on prices. The spread may also not match the bond spread, so it must be read with care.