Fixed Income 4: Risk

C’s of credit analysis

Bottom-up (borrower-specific): Capacity, Capital, Collateral, Covenants, Character. Top-down (macro): Conditions, Country, Currency. In the event of default, HY issuers — typically limited to secured borrowing — tend to have lower losses than unsecured borrowers, since pledged collateral gives them a secondary source of repayment beyond the general asset pool.

Loss Given Default formula

LGD = EE × (1 − RR). LGD = Loss Given Default. EE = Expected Exposure (Exposure at Default) — total projected exposure if default occurs. RR = Recovery Rate — % of the claim recovered in default.

Expected Loss formula

EL = POD × LGD. EL = Expected Loss — the probability-weighted expected shortfall for a period. POD = Probability of Default. LGD = Loss Given Default.

Credit spread formula

Credit Spread ≈ POD × LGD (approximated via the G-spread: yield spread in bps over an actual/interpolated government bond). An investor is fairly compensated for credit risk when the credit spread equals the expected loss (EL) for the period.

Credit rating agency pitfalls

Ratings are issued on behalf of the bond issuer (issuer-paid model), and agencies may meet with issuers to obtain non-public information. Sole reliance on ratings has pitfalls: ratings are sticky and lag market pricing of credit risk (credit spreads move daily; ratings change less often, and similarly-rated bonds can trade at very different spreads, since ratings target expected loss while distressed-debt pricing focuses more on default timing/recovery). Some risks — litigation, environmental, natural disasters, leveraged transactions like debt-financed buybacks — are hard to capture and can cause split ratings (agencies disagreeing on the same issue). Ratings can also miss miscalculations or unforeseen changes (e.g. the 2008-09 subprime mortgage bond defaults, accounting fraud at Enron/WorldCom/Wirecard AG).

Price impact of a small/instantaneous spread change

%ΔPV(Full) = −AnnModDur × ΔSpread. AnnModDur = annualized modified duration. ΔSpread = the spread change, as a decimal. A spread decrease (increase) has a positive (negative) impact on price/return.

Price impact of a larger spread change (convexity-adjusted)

%ΔPV(Full) = −(AnnModDur × ΔSpread) + ½ × AnnConvexity × (ΔSpread)². AnnConvexity = annualized convexity, rescaled to the same order of magnitude as duration-squared when the spread change is expressed as a decimal (e.g. convexity 0.235 → rescale to 23.5).

Approximate annualized modified duration

AnnModDur ≈ (PV₋ − PV₊) / (2 × ΔYield × PV₀). PV₋ and PV₊ = the bond's prices if yield is decreased/increased by ΔYield from the initial price PV₀.

Approximate annualized convexity

ApproxCon = (PV₋ + PV₊ − 2 × PV₀) / (ΔYield² × PV₀). Uses the same PV₋, PV₊, PV₀, and ΔYield inputs as the modified duration approximation above.

Credit spread risk, the credit cycle, and reasons to hold HY bonds

Credit spread risk = risk of greater expected loss from changes in credit conditions due to macroeconomic, market, and/or issuer-specific factors. Spreads narrow as the credit cycle improves (narrowest near the top, when perceived credit risk is lowest) and widen as it deteriorates (widest near the bottom). Beyond the higher coupon, reasons to hold HY bonds: portfolio diversification (lower correlation with IG bonds and risk-free rates), capital appreciation (recovery or issuer-specific events like upgrades/M&A/management changes hit HY prices harder than IG), and equity-like returns with lower volatility (larger income component gives more stable returns than equities).

Sovereign creditworthiness — qualitative and quantitative factors

Ability to pay: qualitative factors are Government Institutions & Policy (rule of law, property rights, transparency, political stability), Fiscal Flexibility (fiscal discipline through economic cycles), Monetary Effectiveness (central bank independence/credibility), Economic Flexibility (economic size, diversification, growth potential), and External Status (trade/capital/FX policy, reserve-currency status); quantitative factors are Fiscal Strength (debt burden, debt affordability), Economic Growth and Stability (growth, cyclicality, size and income level), and External Stability (balance of payments, external debt burden, currency reserves). Willingness to pay also matters: sovereign immunity limits investors' legal recourse to force bankruptcy or liquidation, so recovery typically comes through negotiated debt restructuring (often IMF-supported) rather than legal enforcement.

Types of non-sovereign government issuers

Agencies: quasi-government entities fulfilling a government-sponsored public-service mission, often authorized by law/statute to issue debt; usually assumed to have high government support and typically share the sovereign's rating. Government sector banks/development financing institutions: specialized intermediaries sponsored by the sovereign for a specific market or policy objective, usually created/supported by the sovereign and rated similarly. Supranationals: entities backed jointly by a government and multilateral institutions (e.g. World Bank, regional development banks), which can also be rated equivalent to the sovereign based on strategic importance and implicit support. Regional governments: provincial/state/local governments (municipal bonds in the US, local authority bonds elsewhere) — benefit from the sovereign's governance and policy but creditworthiness can still vary significantly from the sovereign's.

General obligation vs. revenue bonds — who issues them

Both are issued by regional/municipal (non-sovereign) governments. GO bonds: unsecured, backed by the issuer's general revenues and taxing authority — not tied to a specific project. Revenue bonds: issued to finance a specific project (e.g. toll road, hospital, sports arena) and repaid from that project's revenue; also issued by supranational or other quasi-governmental entities (e.g. airport authorities, public utility companies) for infrastructure projects. Revenue bonds carry higher risk than GO bonds since cash flows depend on a single revenue source, so their analysis combines project analysis (need, utilization, economic base) with corporate-style analysis of cash flow and capital structure — versus GO bond analysis, which resembles sovereign analysis (ability to levy/collect taxes) but with more limited jurisdictional powers.

Corporate creditworthiness quantitative factors

Profitability: stable operating profit and recurring revenue. Leverage: total debt relative to assets/capital/cash flow — lower is preferred by debt investors. Liquidity: availability of short-term resources (cash, marketable securities, committed bank facilities) to meet near-term obligations. Coverage: periodic income or cash flow relative to debt service (interest and principal) or debt-like payments such as leases — greater coverage means more income/cash flow is available to pay fixed debt obligations, so higher coverage is stronger.