Fixed Income

Fixed-income securities have standardized features that define their cash flows and risks. This section examines key bond characteristics including maturity, par value, coupon structure, and embedded options. The bond indenture is the legal contract specifying all terms and conditions. Covenants protect bondholders through restrictions on issuer actions - affirmative covenants require certain actions while negative covenants prohibit potentially harmful activities.

Key Concepts Covered:

• Core features: maturity, par value, coupon rate, and payment frequency
• Embedded options: call provisions, put provisions, conversion features
• Bond indenture contents and legal obligations
• Affirmative covenants: required actions protecting bondholders
• Negative covenants: prohibited actions limiting issuer flexibility

Fixed-income instruments have diverse cash flow structures beyond simple fixed coupons. This section explores amortizing bonds, floating-rate notes, zero-coupon bonds, and bonds with contingent cash flows. Embedded options create contingent cash flows benefiting either issuers (call options) or investors (put options). Legal, regulatory, and tax environments significantly affect bond issuance and trading, creating differences across jurisdictions and influencing yields.

Key Concepts Covered:

• Cash flow structures: fixed, floating, amortizing, zero-coupon
• Contingent cash flows from embedded options
• Options benefiting issuers: call provisions, prepayment rights
• Options benefiting investors: put provisions, conversion rights
• Legal, regulatory, and tax impacts on issuance and trading

Fixed-income markets are large and diverse with many distinct segments. This section describes market participants including issuers (governments, corporations, securitization vehicles) and investors (institutions, individuals, central banks). Fixed-income indexes serve benchmarking and passive investment purposes. Primary markets for debt issuance differ from equity IPO processes. Secondary market trading in bonds is predominantly over-the-counter rather than exchange-traded, affecting liquidity and transparency.

Key Concepts Covered:

• Fixed-income market segments and participant types
• Issuers: governments, corporations, supranationals, securitizations
• Investor base: institutional vs. retail
• Fixed-income index types and their uses
• Primary vs. secondary markets: issuance and trading differences from equities

Corporations access fixed-income markets for both short-term and long-term financing. This section compares short-term funding sources including commercial paper, bank loans, and repos. Repurchase agreements (repos) are secured short-term lending transactions widely used in money markets. Long-term corporate debt markets segregate by credit quality, with investment-grade and high-yield issuers having very different investor bases, covenants, and pricing. Understanding these market segments helps assess funding risks.

Key Concepts Covered:

• Short-term corporate funding: commercial paper, bank credit, repos
• Repurchase agreements: mechanics, uses, benefits, and risks
• Investment-grade vs. high-yield corporate bonds
• Covenant differences across credit quality spectrum
• Funding flexibility and refinancing risk considerations

Government debt markets are the largest and most liquid fixed-income segments. This section examines funding choices for sovereign governments, non-sovereign (local/regional) governments, quasi-government entities, and supranational agencies like the World Bank. Each issuer type has different credit risk profiles and market access. Government bond markets differ from corporate markets in size, liquidity, regulation, and investor base, with implications for pricing and trading.

Key Concepts Covered:

• Sovereign government debt and its unique credit considerations
• Non-sovereign and quasi-government entity debt
• Supranational agency bonds: World Bank, regional development banks
• Government vs. corporate bond market differences
• Liquidity, transparency, and regulatory distinctions

Bond pricing is the foundation of fixed-income analysis. This section teaches how to calculate bond prices using yield-to-maturity, including handling accrued interest for trades between coupon dates. Understanding the inverse relationship between bond prices and yields is fundamental. The relationships among price, coupon, maturity, and YTM reveal whether bonds trade at premium, par, or discount. Matrix pricing estimates values for bonds without active trading using prices of similar securities.

Key Concepts Covered:

• Bond pricing calculations on and between coupon dates
• Inverse relationship between bond prices and yields
• Premium, par, and discount pricing relative to coupon and YTM
• Price sensitivity to changes in maturity and coupon rate
• Matrix pricing for illiquid or new securities

Multiple yield measures exist for fixed-rate bonds, each serving different purposes. This section covers yield calculations with different compounding conventions and time periods. Yield spreads measure the additional compensation for credit risk and other factors relative to benchmark rates. Understanding various spread measures (nominal spread, Z-spread, OAS) and their interpretations is essential for relative value analysis and credit assessment.

Key Concepts Covered:

• Yield calculations for different compounding periods
• Yield-to-maturity, current yield, and yield-to-call comparisons
• Nominal spread: spread over benchmark government bond
• Z-spread: constant spread over spot curve
• Option-adjusted spread (OAS) for bonds with embedded options

Floating-rate instruments have coupons that reset periodically based on reference rates. This section teaches yield spread calculations for floaters including quoted margin and discount margin measures. Money market instruments like Treasury bills and commercial paper use different yield conventions (discount basis, add-on basis) requiring conversion for comparison. Understanding these specialized yield measures is necessary for analyzing short-term fixed-income securities.

Key Concepts Covered:

• Floating-rate note mechanics and coupon reset formulas
• Quoted margin vs. discount margin for floaters
• Money market yield conventions: discount basis vs. add-on basis
• Treasury bill yields and bond equivalent yields
• Comparing yields across different instrument types and conventions

The term structure of interest rates describes how yields vary with maturity. This section defines spot rates (zero-coupon rates) and shows how to build the spot curve for bond pricing. Par rates represent yields on hypothetical par bonds. Forward rates are future interest rates implied by current spot rates, reflecting market expectations. Understanding relationships among spot, par, and forward curves is essential for fixed-income analysis and trading strategies.

Key Concepts Covered:

• Spot rates and the spot curve for bond valuation
• Par rates and constructing the par curve
• Forward rates: calculating from spot rates and vice versa
• Pricing bonds using spot rates vs. forward rates
• Interpreting curve shapes and implied forward rate expectations

Fixed-income returns come from multiple sources including coupon income, reinvestment of coupons, and capital gains or losses. This section decomposes bond returns into these components. Macaulay duration measures the weighted average time to receive cash flows and indicates interest rate sensitivity. The relationship between holding period return, duration, and investment horizon reveals important immunization concepts for matching assets and liabilities.

Key Concepts Covered:

• Sources of bond return: coupon income, reinvestment, price change
• Macaulay duration: definition, calculation, and interpretation
• Duration as weighted average time to cash flows
• Relationship between holding period return and duration
• Investment horizon matching and immunization concepts

Duration measures quantify interest rate risk in various useful forms. This section covers modified duration (percentage price change per yield change), money duration (dollar price change), and price value of a basis point (PVBP). Understanding how maturity, coupon, and yield levels affect duration helps assess relative interest rate risk. Duration properties guide portfolio construction and interest rate hedging strategies.

Key Concepts Covered:

• Modified duration: percentage price sensitivity to yield changes
• Money duration: dollar price change for yield movements
• Price value of a basis point (PVBP or DV01)
• Effects of maturity, coupon, and yield level on duration
• Using duration for hedging and portfolio management

Duration is a linear approximation of bond price changes, but bond price-yield relationships are curved (convex). This section introduces convexity as the second-order effect improving price change estimates. Convexity is beneficial for bondholders as it means prices rise more when yields fall than they decline when yields rise. Portfolio duration and convexity can be calculated as weighted averages, though these measures have limitations for complex portfolios.

Key Concepts Covered:

• Convexity: measuring curvature in price-yield relationship
• Convexity adjustment improving duration-based price estimates
• Positive convexity benefits for bondholders
• Estimating price changes using duration and convexity together
• Portfolio duration and convexity: calculations and limitations

Bonds with embedded options require more sophisticated risk measures than simple duration and convexity. This section introduces effective duration and effective convexity which properly account for how cash flows change when interest rates change (e.g., callable bonds). Key rate duration measures sensitivity to specific points on the yield curve, enabling more precise hedging. Empirical duration uses statistical relationships while analytical duration uses pricing models.

Key Concepts Covered:

• Effective duration and convexity for bonds with embedded options
• Why standard duration fails for callable and putable bonds
• Key rate duration: sensitivity to specific curve points
• Applications in yield curve risk management
• Empirical vs. analytical duration approaches

Credit risk represents the possibility of loss from a borrower failing to make promised payments. This section breaks credit risk into its components: probability of default (likelihood of non-payment) and loss given default (severity of loss). Credit ratings from agencies provide standardized assessments but have important limitations. Yield spreads compensate for credit risk and fluctuate based on macroeconomic conditions, market sentiment, and issuer-specific factors.

Key Concepts Covered:

• Credit risk components: probability of default and loss given default
• Credit ratings: uses, methodologies, and limitations
• Expected loss calculations from PD and LGD
• Factors driving yield spread levels and volatility
• Macroeconomic, market, and issuer-specific spread determinants

Evaluating government credit requires different analytical approaches than corporate analysis. This section explores unique considerations for sovereign debt including monetary policy independence, ability to tax, and political stability. Non-sovereign governments (states, municipalities) have different revenue sources and constraints. Quasi-government entities blend public purpose with varying degrees of government support. Each issuer type presents distinct credit risk profiles requiring specialized analysis.

Key Concepts Covered:

• Sovereign credit analysis: fiscal position, monetary policy, political factors
• Debt sustainability analysis for government issuers
• Non-sovereign government credit: revenue sources and constraints
• Quasi-government entities and implicit government support
• Special considerations: currency risk, political risk, legal systems

Corporate credit analysis combines qualitative assessment of business fundamentals with quantitative financial ratio analysis. This section covers both dimensions including competitive position, management quality, industry dynamics, and financial leverage. Key credit ratios measure ability to service debt including coverage ratios and leverage ratios. Understanding debt seniority, security (collateral), and bankruptcy priority is crucial as these factors determine recovery rates and affect credit ratings.

Key Concepts Covered:

• Qualitative factors: industry, competitive position, management, strategy
• Quantitative factors: leverage, coverage, cash flow, profitability ratios
• Debt seniority rankings: senior, subordinated, junior
• Secured vs. unsecured debt and collateral protection
• Bankruptcy priority of claims and recovery rate implications

Securitization transforms pools of financial assets into tradable securities. This section explains the securitization process and its economic benefits. Issuers can remove assets from balance sheets and access capital markets. Investors gain access to diversified asset pools with different risk-return profiles. Economies benefit from improved capital allocation. Key parties include originators, servicers, special purpose vehicles, and credit enhancers, each playing distinct roles in the structure.

Key Concepts Covered:

• Securitization process and structure fundamentals
• Benefits for issuers: balance sheet management, funding access
• Benefits for investors: diversification, customized risk exposures
• Economic benefits: capital allocation efficiency, risk transfer
• Key parties: originators, SPVs, servicers, trustees, credit enhancers

Asset-backed securities represent claims on pools of assets beyond mortgages. This section covers covered bonds which remain on issuer balance sheets unlike traditional ABS. Credit enhancement structures (subordination, overcollateralization, reserve accounts) protect senior tranches from losses. Non-mortgage ABS types include auto loans, credit cards, student loans, and equipment leases, each with distinct cash flow patterns and risks. Collateralized debt obligations (CDOs) add another layer of complexity.

Key Concepts Covered:

• Covered bonds vs. traditional ABS: structural differences
• Credit enhancement: subordination, overcollateralization, reserve accounts
• Auto loan ABS: characteristics and prepayment patterns
• Credit card ABS: revolving structures and early amortization
• Student loan and equipment lease ABS features
• Collateralized debt obligations (CDOs): structure and risks

Mortgage-backed securities are major fixed-income instruments with unique characteristics. Prepayment risk - borrowers paying off mortgages early - creates cash flow uncertainty. Time tranching structures (sequential-pay CMOs) allocate prepayment risk across tranches. This section covers residential mortgage fundamentals affecting prepayment (rates, refinancing incentives, housing turnover). MBS types from pass-throughs to complex CMOs have different risk profiles. Commercial MBS backed by income properties have distinct characteristics from residential MBS.

Key Concepts Covered:

• Prepayment risk: causes, measurement, and investor implications
• Time tranching structures and sequential-pay CMOs
• Residential mortgage loan features: fixed vs. adjustable rate, conforming vs. non-conforming
• Mortgage pass-through securities and their cash flow characteristics
• Collateralized mortgage obligations (CMOs): PAC bonds, support tranches
• Commercial MBS: loan structures, property types, and risks