FRM Part II · FRM Exam Part II

Country Risk: Determinants, Measures, and Implications: formula sheet

Full chapter guide

Key formulas

Debt-to-GDP ratio: Debt-to-GDP = Government debt ÷ GDP; Main solvency indicator. Higher is generally riskier, but there is no universal safe level.
Debt dynamics (approximate): Change in debt ratio ≈ (r − g) × previous debt ratio − primary balance ratio; r is the average interest rate on debt, g is nominal GDP growth, and primary balance is surplus before interest (positive reduces debt). If r > g, debt rises unless the primary surplus is large enough.
Debt-stabilising primary balance: Primary balance ratio = (r − g) × debt ratio; The primary surplus needed to hold the debt ratio constant. If g > r, the required balance is negative.
Sovereign default spread: Default spread = Sovereign bond yield − Risk-free yield (same currency); Compare bonds in the same currency, otherwise inflation differences distort the spread.
Spread and default probability (approximate): Spread ≈ PD × LGD; A rough risk-neutral link, ignoring risk premium and liquidity effects. LGD = 1 − recovery rate.
Investment-grade boundary: Investment grade: S&P/Fitch ≥ BBB-; Moody's ≥ Baa3; One notch lower is speculative grade. Crossing this line is a major event.
Local vs foreign currency ordering: Local currency rating ≥ Foreign currency rating (typically); A usual pattern, not a law. Reason: a government can create its own currency but not USD or EUR.
Market-implied rating spread idea: Spread gap = Market spread − Spread typical for the agency rating; A market spread far above the rating's typical level signals the market sees more risk than the agency does.
Default spread from bonds: Default spread = Yield on sovereign bond − Yield on risk-free bond (same currency, similar maturity); Use a hard-currency sovereign bond against a matching Treasury or Bund. Do not compare across currencies.
Approximate annual default loss from spread: Spread ≈ λ × (1 − R); λ is annual risk-neutral default probability, R is recovery rate. This is a rule of thumb, not exact.
Implied default probability: λ ≈ Spread ÷ (1 − R); Gives a risk-neutral probability, usually higher than the real-world probability.
Basis point conversion: 1 bp = 0.01% = 0.0001; Convert CDS quotes before using them in formulas.
CDS-bond basis: Basis = CDS spread − Bond default spread; A non-zero basis points to liquidity, funding, or contract differences.
Sovereign default spread: Default spread = Yield on sovereign bond (in USD or EUR) − Risk-free yield in the same currency; Both yields must be in the same currency and have similar maturity. A CDS spread or rating-based spread can stand in.
CRP from default spread: CRP = Default spread; The simplest approach. It treats sovereign default risk as the whole country premium.
CRP from relative volatility: CRP = Default spread × (σ country equity ÷ σ country government bond); The denominator is the volatility of the country's bond, not of the US equity market. The ratio is usually above 1.
Total equity risk premium: Total ERP = Mature market ERP + CRP; The mature premium comes from a market such as the US.
Cost of equity with a country premium: Cost of equity = Risk-free rate + Beta × (Mature ERP + CRP); This applies the CRP to every company equally. If the question scales the CRP by exposure, use Beta × Mature ERP + exposure × CRP.
Country equity risk premium: ERP(country) = ERP(mature market) + CRP; CRP is the added premium for the country, not a replacement for the mature market premium.
Country risk premium from sovereign spread: CRP = Default spread × (σ equity ÷ σ government bond); The volatility ratio scales a bond-based spread up to an equity-based premium. The ratio is usually above 1.
Lambda (revenue-based): λ(firm) = % of firm revenue in the country ÷ % of average firm revenue in that country; Measures exposure relative to a typical firm. Other lambda forms use production share or regression on country risk.
Cost of equity with lambda: Cost of equity = Rf + β × ERP(mature) + λ × CRP; Here beta applies to the mature premium only and lambda applies to the CRP.
Cost of equity with beta-scaled CRP: Cost of equity = Rf + β × (ERP(mature) + CRP); Assumes country risk exposure moves with beta.
Revenue-weighted CRP: CRP(firm) = Σ (revenue weight i × CRP i); Used for multinational firms with sales in several countries.
Weighted average cost of capital: WACC = E/(D+E) × Ke + D/(D+E) × Kd × (1 − t); Country risk enters Ke and also Kd through a higher default spread.

Quick revision

Sovereign default drivers: high debt, weak growth, external imbalances, political instability, weak institutions.
Sovereigns that borrow in foreign currency face more default risk than those that can print their own currency debt.
Investment grade is BBB- or above (S&P scale); below that is speculative grade.
Ratings are slow and ordinal; market measures react fast but include liquidity and risk appetite.
Sovereign CDS is the price of insurance against sovereign default; a wider spread means higher perceived risk.
Sovereign bond spread = sovereign yield minus a benchmark risk-free yield in the same currency and maturity.
Country default spread is a base for the country risk premium.
One common approach scales the default spread by the ratio of equity to bond volatility to get the equity country risk premium.
Cost of equity in a risky country = risk-free rate + beta × (mature market ERP + country risk premium) in one common approach.
Country risk affects firms through operations, sales location, currency and government links, not only where they are headquartered.
Sovereign risk often sets a practical ceiling on the ratings of firms in that country, though not always.
Match the currency of cash flows and discount rate; do not double count risk in both.

Common mistakes

Treating debt-to-GDP as the only determinant. Fix: Always weigh growth, interest cost, currency of debt, reserves and institutions. Some high-debt countries are low risk.
Saying a country with local-currency debt cannot lose investors money. Fix: Printing money avoids nominal default but can cause inflation and currency loss, so real returns suffer.
Saying the foreign currency rating is usually higher than the local currency rating. Fix: Remember the sovereign can print local currency but not USD or EUR. Local currency rating is usually equal or higher.
Treating a rating as a precise default probability. Fix: A rating is an ordinal opinion. Historical default rates by grade are averages and vary over time.
Subtracting a local-currency risk-free yield from a foreign-currency sovereign yield. Fix: Always match currency and maturity. A USD bond pairs with a US Treasury.
Treating the implied default probability as the real-world probability. Fix: Say it is risk-neutral. It includes a risk premium, so it usually overstates real-world default.
Treating the default spread as the equity risk premium. Fix: The default spread is a bond premium. To get an equity CRP, scale it by relative volatility if the question gives the data, then add it to the mature ERP.
Using the volatility ratio of the country's equity market to the US equity market in the CRP formula. Fix: In this method the ratio is the country's equity volatility divided by the same country's government bond volatility. Read the denominator carefully.
Using the country of incorporation to assign country risk Fix: Use revenue, production and funding locations. Incorporation is rarely the driver of exposure.
Multiplying beta by the CRP when the question uses lambda Fix: In the lambda method, beta multiplies only the mature ERP. Lambda multiplies the CRP.

Exam tips

Expect case-style questions with two countries that look similar on one metric. Find the differentiating factor.
Always state the currency of debt. It is a favourite test point.
Do the r − g arithmetic carefully and keep growth nominal if the rate is nominal.
Link default risk to the next step: ratings, spreads and country risk premium. Questions often move along that chain.
Watch for absolute words like always or only. They are usually wrong.
Expect case-style questions: match facts to factors (fiscal, external, institutional, political).
Learn the direction of the local vs foreign currency gap and its reason, and be ready for the exception of a country that has no own currency.
Watch for absolute words such as 'always' and 'never'. Rating rules are tendencies.