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Identify the influences on how likely a sovereign is to default, then explain how rating agencies gauge that risk and assess their approach.

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

The idea

How likely a sovereign is to default depends on its ability and willingness to pay. The influences are debt relative to GDP and to government revenue, the interest burden, the maturity and currency of the debt, the stability and breadth of the tax base, and growth. They also include the size of pension and social commitments, political and institutional quality, and any implicit backing from a stronger entity. Debt dynamics are simple. Let d₀ be this year's debt to GDP, i the interest rate, g nominal growth and p the primary deficit as a share of GDP. Next year's debt ratio, as a share of next year's GDP, is therefore d₁ = d₀ × (1 + i) ÷ (1 + g) + p. Rating agencies such as Moody's, S&P and Fitch combine quantitative and qualitative factors into an ordinal scale, where Baa3 or BBB− is the lowest investment grade. Critics say ratings lag markets, move in steps, and can be biased or herd together. Remember that a rating is an opinion on relative risk, not a probability.

Formulas

Next year's sovereign debt ratio

dₜ₊₁ = dₜ × (1 + r) ÷ (1 + g) + primary deficit

dₜ
debt to GDP this year
r
the average interest rate on the debt
g
nominal GDP growth
primary deficit
the deficit before interest, as a share of GDP

With r above g the ratio rises even with a balanced primary budget. Use nominal growth, and add a primary surplus as a negative deficit.

A practice question

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

Which factor is generally recognized as influencing the likelihood of a sovereign default?

  1. The market capitalization of the country's stock exchange relative to GDPWhy not: Equity market size does not measure a government's ability to service its debt.
  2. Debt relative to GDP and government revenue, including the interest bill - correct
  3. The nominal level of the exchange rate against the USD at year endWhy not: The level of a rate depends on units of account; what matters is the debt and currency mix and changes.
  4. The population density of the country and its largest citiesWhy not: Not a driver of fiscal capacity or debt service by itself.

Default likelihood depends on the debt load and the capacity to service it: debt to GDP, interest to revenue, the maturity and currency of the debt, and the tax base, growth and institutions behind it.

A harder one

Country X has debt of 900, an average interest rate of 5% and government revenue of 150. Country Y has debt of 400, an average interest rate of 8% and revenue of 80. Which country has the heavier interest burden relative to revenue, and what is the ratio?

  1. Country X, 30% of revenueWhy not: Calculates X's ratio but picks X because its debt and interest bill (45 versus 32) are larger in absolute terms; Y has the higher ratio.
  2. Country X, 6.0 times revenueWhy not: Uses debt to revenue instead of interest to revenue.
  3. Country Y, 40% of revenue - correct
  4. Country Y, 5.0 times revenueWhy not: Picks Y but reports debt to revenue, not the interest burden.

Interest to revenue: X = 900 x 5% / 150 = 45 / 150 = 30%; Y = 400 x 8% / 80 = 32 / 80 = 40%. Y's higher rate more than offsets its lower debt, so interest absorbs a larger share of revenue.

The hardest tier

A government's debt is 100% of GDP. Its average interest rate is 7%, nominal GDP growth is 1% and it runs a primary deficit of 2% of GDP. Using next-year debt/GDP = current debt/GDP x (1 + interest rate) / (1 + growth) + primary deficit, the debt ratio next year is closest to:

  1. 103.9%Why not: Subtracts the primary deficit as if it were a surplus.
  2. 105.9%Why not: Leaves out the primary deficit.
  3. 109.0%Why not: Ignores growth in the denominator.
  4. 107.9% - correct

100 x 1.07 / 1.01 = 105.94, plus the primary deficit of 2 gives 107.94%. Interest above growth plus a primary deficit makes the ratio rise, which is how debt becomes unsustainable.

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