Course Content
FIXED-INCOME SECURITIES: DEFINING ELEMENTS
This chapter is covered under study session 14, reading 42 of the study materials provided by the Institute. After reading this chapter, a student should be able to: a. describe basic features of a fixed-income security; b. describe the content of a bond indenture; c. compare affirmative and negative covenants and identify examples of each; d. describe how legal, regulatory, and tax considerations affect the issuance and trading of fixed-income securities; e. describe how cash flows of fixed-income securities are structured; f. describe contingency provisions affecting the timing and/or nature of cash flows of fixed-income securities and identify whether such provisions benefit the borrower or the lender.
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LOS A: Basic Features of a Fixed-Income Security
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LOS D: Legal, Regulatory & Tax Considerations
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LOS E: Structure of a Bond’s Cash Flow
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LOS F: Contingency Provisions
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FIXED-INCOME MARKETS: ISSUANCE, TRADING, AND FUNDING
This chapter is covered under study session 14, reading 43 of the study material provided by the Institute. After reading this chapter, a student should be able to: describe classifications of global fixed-income markets; b describe the use of interbank offered rates as reference rates in floating-rate debt; c describe mechanisms available for issuing bonds in primary markets; d describe secondary markets for bonds; e describe securities issued by sovereign governments; f describe securities issued by non-sovereign governments, quasi-government entities, and supranational agencies; g describe types of debt issued by corporations; h describe structured financial instruments; i describe short-term funding alternatives available to banks; j describe repurchase agreements (repos) and the risks associated with them.
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LOS A and B: Bond Market Classification
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LOS C: Primary Markets
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LOD D: Secondary Market
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LOS E: Sovereign Bonds
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LOS F: Non-Sovereign Bonds, Supernational, & Quasi-Government Bonds
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LOS G: Corporate Bonds
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LOS H: Structured Financial Instruments
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LOS I: Short-term Funding
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LOS J: Repurchase Agreements
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INTRODUCTION TO FIXED-INCOME VALUATION
This chapter is covered under study session 14, reading 44 of the study material provided by the Institute. After reading this chapter, a student should be able to: a calculate a bond’s price given a market discount rate; b identify the relationships among a bond’s price, coupon rate, maturity, and market discount rate (yield-to-maturity); c define spot rates and calculate the price of a bond using spot rates; d describe and calculate the flat price, accrued interest, and the full price of a bond; e describe matrix pricing; f calculate annual yield on a bond for varying compounding periods in a year; g calculate and interpret yield measures for fixed-rate bonds and floating-rate notes; h calculate and interpret yield measures for money market instruments; i define and compare the spot curve, yield curve on coupon bonds, par curve, and forward curve; j define forward rates and calculate spot rates from forward rates, forward rates from spot rates, and the price of a bond using forward rates; k compare, calculate, and interpret yield spread measures.
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LOS A: Bond Price and Time Value of Money
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LOS B: Relationships Among a Bond’s Price, Coupon Rate, Maturity, and Market Discount Rate
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LOS C: Spot Rates
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LOS D: Flat Price, Accrued Interest & Full Price
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LOS E: Matrix Pricing
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LOS F, G, and H: Yield Measures
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LOS I: Term Structure of Yield
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LOS K: Yield Spread
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INTRODUCTION TO ASSET-BACKED SECURITIES
This chapter is covered under study session 14, reading 45 of the study material provided by the Institute. After reading this chapter, a student should be able to: a. explain benefits of securitization for economies and financial markets; b. describe securitization, including the parties involved in the process and the roles they play; c. describe typical structures of securitizations, including credit tranching and time tranching; d. describe types and characteristics of residential mortgage loans that are typically securitized; e. describe types and characteristics of residential mortgage-backed securities, including mortgage pass-through securities and collateralized mortgage obligations, and explain the cash flows and risks for each type; f. define prepayment risk and describe the prepayment risk of mortgage-backed securities; g. describe characteristics and risks of commercial mortgage-backed securities; h. describe types and characteristics of non-mortgage asset-backed securities, including the cash flows and risks of each type; i. describe collateralized debt obligations, including their cash flows and risks.
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Introduction
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LOS A: Benefits of Securitization
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LOS B and C: Securitization
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LOS D: Residential Mortgage Loans
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LOS E: Mortgage Pass-Through Securities
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LOS E: Collateralized Mortgage Obligations (CMOs)
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Non-Agency Residential Mortgage Backed Security
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LOS G: Commercial Mortgage-Backed Securities (CMBS)
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Auto Loan-Backed Securities (ALBs)
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Credit Card Receivable- Backed Securities
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Collateralized Debt Obligations (CDOs)
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UNDERSTANDING FIXED-INCOME RISK AND RETURN
This chapter is covered under study session 15, reading 46 of the study materials provided by the Institute. After reading this chapter, a student should be able to: a. calculate and interpret the sources of return from investing in a fixed-rate bond; b. define, calculate, and interpret Macaulay, modified, and effective durations; c. explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options; d. define key rate duration and describe the use of key rate durations in measuring the sensitivity of bonds to changes in the shape of the benchmark yield curve; e. explain how a bond’s maturity, coupon, and yield level affect its interest rate risk; f. calculate the duration of a portfolio and explain the limitations of portfolio duration; g. calculate and interpret the money duration of a bond and price value of a basis point (PVBP); h. calculate and interpret approximate convexity and distinguish between approximate and effective convexity; i. estimate the percentage price change of a bond for a specified change in yield, given the bond’s approximate duration and convexity; j. describe how the term structure of yield volatility affects the interest rate risk of a bond; k. describe the relationships among a bond’s holding period return, its duration, and the investment horizon; l. explain how changes in credit spread and liquidity affect the yield-to-maturity of a bond and how duration and convexity can be used to estimate the price effect of the changes.
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LOS A: Sources of Return
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LOS B, C, and D: Interest Rate Risk
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LOS F: Duration of a Bond Portfolio
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LOS G: Money Duration
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LOS G: Price Value of a Basis Point
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LOS H: Convexity of a Bond
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Investment Horizon
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LOS L: Credit and Liquidity Risk
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FUNDAMENTALS OF CREDIT ANALYSIS
This chapter is covered under study session 15, reading 47 of the study material provided by the Institute. After reading this chapter, a student should be able to: a. a describe credit risk and credit-related risks affecting corporate bonds; b. describe default probability and loss severity as components of credit risk; c. describe seniority rankings of corporate debt and explain the potential violation of the priority of claims in a bankruptcy proceeding; d. distinguish between corporate issuer credit ratings and issue credit ratings and describe the rating agency practice of “notching”; e. explain risks in relying on ratings from credit rating agencies; f. explain the four Cs (Capacity, Collateral, Covenants, and Character) of traditional credit analysis; g. calculate and interpret financial ratios used in credit analysis; h. evaluate the credit quality of a corporate bond issuer and a bond of that issuer, given key financial ratios of the issuer and the industry; i. describe factors that influence the level and volatility of yield spreads; j. explain special considerations when evaluating the credit of high yield, sovereign, and non-sovereign government debt issuers and issues.
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LOS A and B: Credit Risk
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LOS C, D, and: E Capital Structure and Seniority
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LOS F, G, H, I: Credit Analysis
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LOS J: Special Consideration
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Fixed Income
About Lesson

a.  Duration is a good measure while estimating the percentage price change for a small change in interest rates, but the estimation becomes inferior with the larger change in interest rate. Therefore, the duration is only an approximation of a percentage price change for a small change in the yield.
The reason for this is, the duration is a first approximation for the small change in the yield.

b.  By using the second approximation, it can be improved. This approximation is known as convexity.

We can use the convexity measure of the security to approximate the change in price that is not explained by the duration.

c.  Consider the following diagram:

Convexity of a bond Fixed Income CFA Level 1 Study Notes

In the above diagram, we can see that due to an increase or decrease in the yield (by the amount Δbp+ and Δbp–). The duration of the bond reaches up to point C and B respectively. But these points lie on the line tangent to the price-yield curve. But to reach the point on the price-yield curve, up to point B’ and C’, there is a need for the convexity adjustment.

d.  The percentage change in the total price is a result of two effects, i.e. the first is a result of duration (called the first-order effect) and the second is a result of convexity (called the second-order effect).

percentage change in the total price Fixed Income CFA Level 1 Study Notes

The first part of the total percentage change is due to the duration, and the second part due to the convexity.

e.  The convexity of a bond can be calculated using either the closed-form formula or the approximate formula.

f.  The closed-form equation for calculating the convexity of a bond is:

Closed form equation for convexity Fixed Income CFA Level 1 Study Notes

g.  The approximate convexity can be calculated using the following equation:

h.  The one calculated above is the convexity of a bond in percentage terms. We can also calculate the money convexity of the bond or the convexity of a bond in dollar terms.
The equation for the money convexity of a bond is:

Money Convexity of a bond Fixed Income CFA Level 1 Study Notes

The first part of this equation refers to the first-order effect. Whereas, the second part refers to the second-order effect.

i.  When the bonds cash flows do not change as a result of the change in yield, we can use the approximate convexity measure, which is:

approximate convexity measure Fixed Income CFA Level 1 Study Notes

j.  However, when the cash flows changes, we need to calculate the effective convexity using the following equation:

Effective Convexity Fixed Income CFA Level 1 Study Notes

1.1.         Yield Volatility

a.  The yield volatility shows the number of basis points changes in the duration, due to certain basis point changes in the yield of a bond.

b.  There are mainly two sources of yield volatility:

     i.  Interest Rate Shifts. To manage the same, one needs to measure the interest rate risk first. Duration analysis is an important tool for the analysis of the sensitivity of portfolios to changes in interest rates.

    ii.  Changes in Volatility of Interest Rates. Although less common, this type of risk is a major component of the total risk of a fixed income portfolio. The greater the expected yield volatility, the greater is the interest rate risk for the given duration and current value of a position.

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