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Outline the features of sovereign credit default swaps (CDS) and of sovereign credit spreads, and contrast sovereign spreads with credit ratings as risk indicators.

FRM® Part I · Valuation and Risk Models · Country Risk: Determinants, Measures, and Implications · FRM1.VR.5.f

The idea

A sovereign credit default swap is a contract in which the protection buyer pays a periodic premium, the CDS spread in basis points. The seller pays par minus the recovery value if a credit event such as failure to pay or restructuring occurs. A sovereign credit spread is the yield on its bond over the risk-free rate in the same currency, for example a USD sovereign bond over the US Treasury. A useful approximation for the annual default probability is PD = spread ÷ (1 − R). Here R is the recovery rate. Both spreads and CDS are market prices, so they are forward-looking, continuous and update daily, unlike ratings, which are ordinal, slow and agency opinions. But they also include risk premia and liquidity effects, and can be volatile. CDS also carries counterparty risk, especially if the seller is tied to the sovereign. Use both.

Formulas

Default probability implied by a sovereign spread

PD ≈ spread ÷ (1 − recovery rate)

PD
the approximate annual probability of default
spread
the bond yield over the risk-free rate in the same currency
recovery rate
the share of par recovered after default

A rough approximation, because spreads also carry liquidity and risk premia. The trap is dividing by the recovery rate instead of one minus it.

CDS protection payout on a credit event

payout = notional × (1 − recovery rate)

notional
the amount of protection bought
recovery rate
the share of the claim recovered on the reference obligation

Paid by the protection seller after a credit event. The CDS spread sets the premium the buyer pays, not the payout.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which description of a sovereign CDS is correct?

  1. The buyer makes one upfront payment and the seller then pays the bond's coupons until maturityWhy not: Misdescribes the contract: the buyer pays a running premium and the seller pays only on a credit event.
  2. The seller pays the periodic premium and the buyer receives par at maturityWhy not: Reverses the direction of the premium and misstates the payout.
  3. The buyer pays a periodic premium; on a credit event the seller pays par less recovery - correct
  4. The buyer pays the recovery value to the seller if the sovereign defaultsWhy not: Reverses the payoff: the seller compensates the buyer for the loss.

A CDS is insurance-like: the buyer pays a spread in basis points on the notional, and if a credit event such as failure to pay or restructuring occurs, the seller pays par less the recovery value.

A harder one

An investor buys protection on a sovereign with notional USD 25 million at a CDS spread of 250 basis points. A credit event occurs and the auction sets the recovery at 35% of par. The protection payout, excluding premiums, is closest to:

  1. USD 8.75 millionWhy not: Pays the notional times the recovery rate instead of the loss given default.
  2. USD 25.0 millionWhy not: Pays the full notional, ignoring the recovery value.
  3. USD 0.625 millionWhy not: Reports one year of premium (25 x 2.5%) instead of the payout.
  4. USD 16.25 million - correct

Payout = notional x (1 - recovery) = 25 x 0.65 = 16.25 million. The 250 basis point spread determines the premium, which is 25 x 2.5% = 0.625 million a year.

The hardest tier

A fund buys uncollateralized CDS protection on a sovereign from a large bank headquartered in that same country. What is the main weakness of the hedge?

  1. The CDS pays only on a downgrade, not on a default of the sovereign's bondsWhy not: CDS pays on defined credit events such as failure to pay or restructuring; a downgrade is not one.
  2. Wrong-way risk: sovereign default would likely impair the bank just when protection pays - correct
  3. Interest rate risk, since the CDS value moves one-for-one with the Treasury yield curveWhy not: CDS value is driven by credit spreads, not by the level of Treasury yields.
  4. Currency risk, since all sovereign CDS pay out in the sovereign's local currencyWhy not: Sovereign CDS are usually denominated in USD or EUR, not in the local currency.

The seller's ability to pay is correlated with the event insured: if the sovereign defaults, the domestic bank is likely to suffer too. This wrong-way risk is why collateral and counterparties outside the sovereign matter.

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