Fixed Income Investments Analysis KASNEB Notes

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This paper is intended to equip the candidate with knowledge, skills and attitudes that will enable him/her to value, analyse and determine risk associated with fixed income securities.


A candidate who passes this paper should be able to:

  • Identify various types of fixed income instruments
  • Assess various types of risks associated with fixed income instruments
  • Analyse interest rate volatility using the term structure of interest rate approach
  • Value and analyse fixed income instruments
  • Value bonds using interest rate models
  • Determine the value of bonds using yield and spread analysis
  • Apply pricing strategies and evaluate the risk of fixed income securities
  • Apply the models to determine credit default rates.


Overview of fixed income securities

  • Basic features of fixed income securities
  • Types of fixed income securities
  • Bond indenture; affirmative and negative covenants; effect of legal, regulatory and tax considerations on the issuance and trading of fixed income securities
  • Structure of cash flows of fixed income securities; contingency provisions affecting the timing and/or nature of cash flows of fixed income securities
  • Risks associated with fixed income securities

Markets of fixed income securities: Issuance, trading and funding

  • Classifications of global fixed income markets
  • Interbank offered rates as reference rates in floating-rate debt; mechanisms available for issuing bonds in primary markets; secondary markets for bonds; securities issued by sovereign governments, non-sovereign governments, government agencies and supranational entities; debt securities issued by corporations; short-term funding alternatives available to banks; repurchase agreements (repos)

Fundamentals of fixed income valuation

  • Determination of price of the bond given a market discount rate
  • Relationships among a bond’s price, coupon rate, maturity and market discount rate (yield-to-maturity)
  • Bonds price quotation: spot rates; flat price(clean price), accrued interest and the full price of a bond(dirty price)
  • Matrix pricing of a bond
  • Yield measures for fixed-rate bonds, floating-rate notes and money market instruments
  • Term structure of interest rate: pure expectation theory, liquidity preference theory, market segmentation theory; implications of the yield curve for the yield-curve theories
  • Spot curves, yield curve on coupon bonds, par curve and forward curve
  • Forward  rates; determination of   spot rates from forward rates, forward rates from spot rates and the price of a bond using forward rates; yield spread measures
  • Bond refinancing/refunding

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Fixed income risk and return

  • Return from investing in a fixed-rate bond
  • Bond duration measures: Macaulay duration, modified duration and effective durations, portfolio duration; money duration of a bond and price value of a basis point (PVBP)
  • Effective duration as a measure of interest rate risk for bonds with embedded options
  • Key rate duration as a measure of sensitivity of bonds to changes in the shape of the benchmark yield curve
  • Effect of a bond’s maturity, coupon, embedded options and yield level to its interest rate risk
  • Bond convexity: approximate convexity; effective convexity; determination of percentage price change of a bond for a specified change in yield, given the bond’s approximate duration and convexity
  • Effect of term structure of yield volatility on the interest rate risk of a bond; relationships among a bond’s holding period return, its duration and the investment horizon
  • Effect of changes in credit spread and liquidity on yield-to-maturity of a bond and how duration and convexity can be used to estimate the price effect of the changes

Credit risk management

  • Credit risk and credit-related risks affecting corporate bonds; seniority rankings of corporate bonds; potential violation of the priority of claims in a bankruptcy proceeding; corporate issuer credit ratings; issue credit ratings; rating agency practice of “notching”; risks in relying on ratings from credit rating agencies; components of traditional credit analysis
  • Financial ratios used in credit analysis; credit quality of a corporate bond issuer given key financial ratios of the issuer and the industry
  • Factors influencing the level and volatility of yield spreads; determination of return impact of spread changes; special considerations when evaluating the credit of high yield, sovereign and municipal debt issuers and issues

The term structure and interest rate dynamics

  • Relationships among spot rates, forward rates, yield to maturity, expected and realised returns on bonds and the shape of the yield curve
  • Forward pricing and forward rate models: determination of forward and spot prices and rates using those models
  • Assumptions concerning the evolution of spot rates in relation to forward rates implicit in active bond portfolio management; the strategy of riding the yield curve
  • Swap rate curve: its use in valuation by market participants; determination and interpretation of the swap spread for a default-free bond; the Z-spread; treasury and Euro dollar(TED) spread and London interbank offer rate(LIBOR) – OIS spreads
  • Review of traditional theories of the term structure of interest rates; the implications of each theory to forward rates and the shape of the yield curve
  • Modern term structure models and their use; measuring the bond’s exposure to each of the factors driving the yield curve and how these exposures can be used to manage yield curve risks; maturity structure of yield volatilities and their effect on price volatility

The arbitrage-free valuation framework

  • Overview of arbitrage-free valuation of a fixed-income instrument
  • Computation of the arbitrage-free value of an option-free, fixed-rate coupon bond
  • Binomial interest rate tree framework: the backward induction valuation methodology and computation of the value of a fixed-income instrument given its cash flow at  each node; process of calibrating a binomial interest rate tree to match a specific term structure
  • Pricing using the zero-coupon yield curve and pricing using an arbitrage-free binomial lattice; path wise valuation in a binomial interest rate framework and computation of the value of a fixed-income instrument given its cash flows along each path
  • Monte Carlo forward-rate simulation and its application

Valuation and analysis of bonds with embedded options

  • Overview of fixed-income securities with embedded options
  • Relationships between the values of a callable or putable bond, the underlying option-free (straight) bond and the embedded option; Use of the arbitrage-free framework to value a bond with embedded options
  • Effect of interest rate volatility on the value of a callable or putable bond
  • Effect of changes in the level and shape of the yield curve on the value of a callable bond
  • Determination of the value of a callable or putable bond from an interest rate tree; option-adjusted spreads (OAS); effect of interest rate volatility on option-adjusted spreads
  • Effective duration of callable, putable and straight bonds; use of one-sided durations and key rate durations to evaluate the interest rate sensitivity of bonds with embedded options
  • Effective convexities of callable, putable and straight bonds
  • Determination of the value of a capped or floored floating-rate bond
  • Defining features of a convertible bond; components of a convertible bond’s value; valuation of convertible bond in an arbitrage-free framework; risk–return characteristics of a convertible bond, straight bond and underlying common stock.

Credit analysis models

  • Overview of credit analysis models; probability of default, loss given default, expected loss and present value of the expected loss and relative importance of each across the credit spectrum
  • Credit scoring and credit ratings; ordinal rankings
  • Strengths and weaknesses of credit ratings
  • Structural models of corporate credit risk: reasons for equity being viewed as a call option on the company’s assets; reduced form models of corporate credit risk
  • Reasons for debt being valued as the sum of expected discounted cash flows after adjusting for risk
  • Assumptions, strengths and weaknesses of both structural and reduced form models of corporate credit risk
  • Determinants of the term structure of credit spreads; present value of the expected loss on a bond over a given time horizon
  • Credit analysis required for asset-backed securities
  • Credit analysis of corporate debt

Emerging issues and trends

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