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Weigh CDS spreads, market-based credit default spreads and credit ratings against one another as default predictors, judging which is more reliable.

FRM® Part II · Credit Risk Measurement and Management · Country Risk: Determinants, Measures, and Implications · FRM2.CR.8.g

The idea

Three tools compete as predictors of sovereign default. Ratings are stable and based on analysis but slow. Bond yield spreads and CDS spreads are market-based, update continuously and usually move before downgrades, so they tend to predict better over short horizons. Their weakness is noise. A spread contains the expected loss plus a risk premium for bearing default risk, a liquidity premium, and counterparty and contagion effects, so the implied default probability usually exceeds the real-world one. Sovereign CDS markets can also be thin. Assume a constant hazard rate h, and let Pcum be the cumulative probability of default over T years. The hazard rate comes from the spread as follows. h = spread ÷ (1 − recovery rate). The cumulative probability then follows from it. Pcum = 1 − e^(−h × T). The sensible conclusion is that market spreads are the more timely signal, ratings the anchor, and neither should be read alone.

Formulas

Hazard rate implied by a credit spread

λ = spread ÷ (1 − R)

spread
the CDS spread or bond yield spread over the risk-free rate
R
the expected recovery rate

Gives a risk-neutral intensity, which exceeds the real-world one because spreads carry risk, liquidity and contagion premiums.

Cumulative default probability with a constant hazard rate

cumulative PD = 1 − e^(−λ × T)

λ
the constant hazard rate per year
T
the horizon, in years

Multiplying λ by T ignores survival and overstates the probability.

A practice question

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

Compared with sovereign ratings, market-based measures of default risk such as CDS spreads are generally:

  1. Slower to react, because agencies monitor sovereigns more closely than the market does.Why not: Reverses the relationship: markets react immediately while ratings are revised infrequently.
  2. More timely, because they update continuously as new information arrives. - correct
  3. Equally timely, because both are driven by the same underlying data.Why not: Prices change continuously while ratings change after committee decisions.
  4. Less informative about default, because they only reflect equity market movements.Why not: CDS and bond spreads are debt-market prices and contain default information.

Market prices incorporate information immediately and typically lead downgrades. Their cost is noise.

A harder one

Over a week with no country-specific news, the CDS spreads of ten emerging market sovereigns all widen by about 150 basis points while their ratings are unchanged. Which is the best interpretation?

  1. Each country's default probability has risen by exactly the same amount. Identical country-specific changes in ten countries at once would be an unlikely coincidence.Why not: The common move more plausibly reflects a common factor than identical country-specific changes.
  2. The ratings must be correct and the CDS market is irrelevant.Why not: Spreads carry information even when noisy; they should not be dismissed.
  3. The spreads reflect global risk aversion and liquidity or contagion effects, not only country-specific default risk. - correct
  4. CDS spreads can only move with ratings, so the widening is an error.Why not: Spreads update continuously and need not follow ratings.

Common movement points to a systematic component such as risk appetite, liquidity or contagion. This is a limitation of market-based measures.

The hardest tier

A sovereign's 5-year CDS spread is 420 basis points and the assumed recovery rate is 30 percent. Assuming a constant continuously compounded hazard rate, the implied cumulative probability of default over 5 years is closest to:

  1. 25.9 percent - correct
  2. 30.0 percentWhy not: Multiplies the annual hazard by 5 without allowing for survival, which overstates the cumulative probability.
  3. 21.0 percentWhy not: Uses the 4.2 percent spread as the hazard rate and multiplies by 5, ignoring loss given default.
  4. 18.9 percentWhy not: Uses the spread as the hazard rate (4.2 percent) in 1 - exp(-h x 5), ignoring loss given default.

h = 4.2% / (1 - 0.30) = 6.0% a year. Cumulative probability = 1 - exp(-0.06 x 5) = 1 - 0.7408 = 25.9%.

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