Fixed-Income Markets for Government Issuers: formula sheet

Key formulas

Issuer credit risk (loose rule of thumb)

Sovereign (own currency) is often the benchmark; other issuers usually trade at a spread above it

Not a strict ranking. Credit risk depends on each issuer's rating and any guarantee. Supranationals are generally rated very high, often AAA, and are not equivalent to unguaranteed agencies or local governments. Some are rated better than weak sovereigns.

Yield spread over sovereign

Spread = Yield on bond − Yield on sovereign bond of same currency and maturity

Used to compare agency, local government and corporate bonds with the government benchmark.

Discount (bill) price from face value

Price = Face value − Discount; Interest earned = Face value − Price

Bills are often zero-coupon, so the return comes only from buying below face value.

Rating relationship

Local currency rating ≥ Foreign currency rating (usually)

A usual pattern, not a law. Local currency debt is typically rated the same or higher.

Sovereign repayment test

Credit quality = ability to pay + willingness to pay

Both parts are needed. A government with ability but no willingness can still default.

Debt burden

Debt-to-GDP = Government debt ÷ GDP

Higher ratio means weaker fiscal position, all else equal. Look at trend and interest cost too.

Key factors to recall

Institutions, economy, fiscal, monetary, external position, event risk

Use this as a checklist for any sovereign credit question.

Single-price auction

All winners pay the price at the lowest accepted bid (highest accepted yield)

Also called Dutch auction or uniform-price auction.

Multiple-price auction

Each winner pays its own bid price

Also called American or discriminatory auction.

Bill pricing (discount instrument)

Price = Face value ÷ (1 + periodic yield)

Bills pay no coupon; the return is the gap between purchase price and face value.

Inflation-indexed principal (typical design)

Adjusted principal = Original principal × (1 + inflation over the period); Coupon = Fixed coupon rate × Adjusted principal

Coupon rate stays fixed but the cash coupon rises with inflation. Design details vary by country.

General obligation bond backing

GO bond repayment source = issuer's general taxing power

Credit analysis looks at the tax base, economy, debt burden and budget flexibility.

Revenue bond backing

Revenue bond repayment source = cash flows of the financed project

Look at the debt service coverage ratio, demand for the service and rate-setting power.

Debt service coverage ratio

DSCR = net revenue available for debt service ÷ debt service

A higher ratio means a larger cushion. A ratio below 1 means revenue does not cover payments.

Tax-equivalent yield

Taxable-equivalent yield = tax-exempt yield ÷ (1 − tax rate)

Use this to compare a tax-exempt municipal bond with a taxable bond. Use the investor's marginal tax rate as a decimal.

Support ranking

Explicit guarantee > implicit support > no support

Stronger support generally means credit risk closer to the sovereign and a tighter spread.

Quick revision

• A sovereign issuer is a national government borrowing in its own name.
• Sovereign debt often serves as the benchmark for pricing other bonds in the same currency.
• Debt issued in a government's own currency carries different risk from debt issued in a foreign currency.
• A government that can tax and, for local-currency debt, control its currency has more tools to meet obligations.
• Sovereign credit analysis looks at both ability and willingness to pay.
• Issuing in foreign currency exposes the government to exchange-rate risk it cannot fix by creating money.
• Auctions are a main way governments sell new bonds to investors.
• Know the difference between bills, notes and bonds by maturity and coupon features.
• Non-sovereign government issuers include local and regional governments and agencies.
• Quasi-government entities are often government-linked but are not the national government itself.
• Supranationals are issuers owned by several countries, such as multilateral development banks.
• When two options look alike, ask who ultimately backs the debt.

Common mistakes

• Treating all government-related bonds as sovereign bonds. Fix: Sovereign means the national government itself. Agencies, regional governments and supranationals are separate categories.
• Assuming sovereign bonds are risk-free. Fix: Sovereigns can default, especially on foreign-currency debt. They are a benchmark, not a guarantee.
• Saying local currency debt can never default. Fix: Remember it is usually lower risk, not risk-free. Printing money can cause inflation, and governments can choose not to pay.
• Considering only ability to pay. Fix: Always add willingness to pay: politics, institutions and repayment history.
• Saying winners in a single-price auction pay their own bids. Fix: Single means one price for everybody, set by the lowest accepted bid.
• Thinking non-competitive bidders state a price. Fix: Non-competitive bidders state only quantity and accept the auction result, filled before competitive bids.
• Treating all agency bonds as government-guaranteed. Fix: Check whether support is explicit or only implicit. Implicit support is not a legal promise.
• Thinking revenue bonds are backed by taxes. Fix: GO means taxing power. Revenue means only the project's cash flows.

Exam tips

• Questions often ask you to classify an issuer from a short description. Learn the four categories cold.
• Watch for foreign-currency wording. It signals higher sovereign default risk.
• Remember that quasi-government spreads depend on guarantees. Do not assume all are guaranteed.
• Expect conceptual questions, not heavy calculations. With no penalty for wrong answers, always pick an option after eliminating two.
• Expect conceptual three-option items. Look for the words 'local currency' and 'foreign currency' and apply the control-of-currency test.
• Eliminate options with absolute words such as 'always', 'never' or 'certain', since the ratings relationship is a general pattern.
• Link each clue to a factor: reserves and current account are external, deficits and debt are fiscal, inflation and central bank are monetary.
• Remember both ability and willingness to pay. Options that mention only one are often incomplete.