FRM Part I · FRM Exam Part I

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

Full chapter guide

Key formulas

Country risk premium (concept): Required return in a country = Mature market return + Country risk premium; Conceptual link only. The numerical estimation of the premium is covered in the equity risk premium topic.
Sources of country risk (checklist): Economic structure + Political institutions + Legal system + Life cycle + Default history; Use this list to classify any scenario in the question.
Default spread: Default spread = Yield on sovereign bond − Risk-free rate; Both bonds must be in the same currency and have the same maturity. For example, a USD-denominated sovereign bond versus a US Treasury.
Cost of sovereign debt: Yield = Risk-free rate + Default spread; The default spread is the sovereign's compensation for default risk in that currency.
Rating-based default spread: Default spread for country = Average spread of bonds in the same rating class; Used when a country has no traded bond or CDS. It treats all countries with the same rating as equally risky.
Approximate expected loss link: Default spread ≈ Probability of default × Loss given default; A rough approximation for small values. It ignores risk premium, liquidity and other components, so actual spreads are usually wider.
Investment-grade boundary: Investment grade: Baa3/BBB- or higher; below is speculative grade; Moody's uses Baa3 and S&P and Fitch use BBB- as the lowest investment-grade rating.
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.
Sovereign default spread: Default spread = Yield on country's government bond (in USD or EUR) − Yield on default-free bond of same currency and maturity; Use the same currency and similar maturity. Otherwise inflation or term differences contaminate the spread.
Country risk premium (CRP): CRP = Default spread × (σ equity ÷ σ government bond); The ratio is the relative volatility of the country's equity market to its bond market. It is usually above 1.
Total equity risk premium: ERP (country) = ERP (mature market) + CRP; Simple additive form. Mature market premium is typically from a market like the US.
Cost of equity with country risk: Cost of equity = Risk-free rate + β × ERP (mature) + CRP; This version adds the CRP in full, without scaling by beta. Read the question to see whether beta applies to CRP.
Country risk premium from default spread: CRP = Default spread × (σ equity ÷ σ government bond); Default spread is the sovereign yield over a default-free yield in the same currency. The ratio scales bond risk to equity risk.
Total equity risk premium: ERP(country) = ERP(mature) + CRP; Used when all firms are assumed to bear the full country risk.
Cost of equity, beta approach: Re = Rf + β × (ERP(mature) + CRP); CRP is scaled by beta. Assumes country risk exposure is proportional to beta.
Cost of equity, lambda approach: Re = Rf + β × ERP(mature) + λ × CRP; λ is the firm's exposure to country risk. Under the relative definition used here, an average firm has λ = 1 and a firm more exposed than average has λ above 1. Under the absolute definition (λ = % of revenues in the country), a firm with all its revenue in the country has λ = 1. Setting λ = 1 for every firm gives the flat view: Re = Rf + β × ERP + CRP.
Lambda from revenues: λ = (% revenues in country) ÷ (average % revenues in country for the typical firm); The relative measure, where an average firm has λ = 1. Other versions use the raw revenue share, production or regression. Check which definition the question gives.
Currency conversion of rates: (1 + r local) = (1 + r USD) × (1 + inflation local) ÷ (1 + inflation USD); Keeps the discount rate in the same currency as the cash flows.
Cost of capital: WACC = E/V × Re + D/V × Rd × (1 − t); The cost of debt should also include the country default spread.
Exposure-weighted country risk premium: CRP(firm) = Σ wᵢ × CRPᵢ; wᵢ is the share of revenue (or operations) in country i. Use where the firm operates, not where it is listed.
Country risk premium from spreads: CRP = Sovereign default spread × (σ equity ÷ σ government bond); A common approach: scale the sovereign spread by relative volatility of equities to bonds.
Cost of equity with country risk: Cost of equity = Rf + β × (mature market ERP) + λ × CRP; λ measures the firm's exposure to country risk. One variant sets λ = 1 for all; another uses β × (ERP + CRP). Follow the form stated in the question.
Expected cash flow adjustment: Expected CF = (1 − p) × CF if no event + p × CF if event; Use if you adjust cash flows for country risk. Then do not also add a premium for the same risk.

Quick revision

Country risk comes from economic, political, legal and sovereign debt factors.
A sovereign default can happen in local or foreign currency, and the risk differs between them.
Ratings rank default risk but often lag market changes.
Default spread is the yield gap between a country's bond and a default-free benchmark in the same currency.
Sovereign CDS spreads are market prices of default protection and can move faster than ratings.
CDS and bond spreads may differ because of liquidity, contract terms and market sentiment.
Country risk premium is a spread-based add-on to the mature market equity risk premium.
A common scaling multiplies the default spread by the ratio of equity volatility to bond volatility, as given in the question.
Cost of equity with country risk is the base cost of equity plus the country risk premium, with beta applied only if the method says so.
Do not count country risk in both the discount rate and the cash flows.
Companies are not equally exposed to country risk; it depends on where they earn revenue and produce.
Use the same currency for cash flows and discount rates.

Common mistakes

Treating country risk as only political risk Fix: Remember the full list: economic structure, politics, legal system, life cycle and default history all contribute.
Saying a country that defaulted once is permanently high risk Fix: Default history raises risk, but reforms and a long time since default can reduce it. Avoid absolute statements.
Treating a rating as a precise default probability. Fix: Remember that a rating is an ordinal rank within a broad bucket. Default probabilities come from historical default studies, and they vary over time.
Mixing currencies when computing the default spread. Fix: Always compare a USD sovereign bond with a US Treasury, and a EUR bond with a EUR risk-free benchmark.
Using recovery rate instead of 1 − R when computing default probability. Fix: Spread compensates for loss, which is 1 − R. Always divide by 1 − R.
Forgetting to convert bp to decimals. Fix: Divide bp by 10,000 before any calculation.
Using the default spread as the CRP without scaling. Fix: Always ask whether the question gives volatilities. If it does, multiply the spread by σ equity ÷ σ bond.
Inverting the volatility ratio (bond σ ÷ equity σ). Fix: Equity goes on top. Equities are normally more volatile, so the ratio should be above 1.
Multiplying the CRP by beta in the lambda approach Fix: In the lambda approach, beta multiplies only the mature ERP. Lambda multiplies the CRP.
Using the raw default spread as the CRP Fix: Scale it by σ equity ÷ σ bond. Equity is riskier than the sovereign bond, so the CRP is larger than the spread.

Exam tips

Questions often give one dominant fact. Label it before looking at the options.
Watch for absolute words such as 'always' and 'only'. They usually signal a wrong option.
Keep ability to pay (economic) separate from willingness to pay (political, legal).
Expect default history to be framed as a risk indicator, not a permanent verdict.
Link this topic to ratings and the country risk premium, since questions may combine them.
Expect conceptual questions on limitations. Learn the list: lagging, coarse, sticky, biased, inconsistent across agencies.
Know the investment-grade line: Baa3 or BBB- and above.
Always check the currency of the debt before comparing ratings or spreads.