Fixed Income Valuation and Analysis

After listening to this lecture, you should be able to:

• describe relationships among spot rates, forward rates, yield to maturity, expected and realized returns on bonds, and the shape of the yield curve;
• describe the forward pricing and forward rate models and calculate forward and spot prices and rates using those models;
• describe how zero-coupon rates (spot rates) may be obtained from the par curve by bootstrapping;
• describe the assumptions concerning the evolution of spot rates in relation to forward rates implicit in active bond portfolio management;

After listening to this lecture, you should be able to:

• describe the strategy of riding the yield curve;
• explain the swap rate curve and why and how market participants use it in valuation;
• calculate and interpret the swap spread for a given maturity;
• describe the Z-spread; i describe the TED and Libor–OIS spreads;

After listening to this lecture, you should be able to:

• explain traditional theories of the term structure of interest rates and describe the implications of each theory for forward rates and the shape of the yield curve;
• describe modern term structure models and how they are used;
• explain how a bond’s exposure to each of the factors driving the yield curve can be measured and how these exposures can be used to manage yield curve risks;
• explain the maturity structure of yield volatilities and their effect on price volatility.

At the end of this lecture, you should be able to:

• explain what is meant by arbitrage-free valuation of a fixed-income instrument;
• calculate the arbitrage-free value of an option-free, fixed-rate coupon bond;
• describe a binomial interest rate tree framework;
• describe the backward induction valuation methodology and calculate the value of a fixed-income instrument given its cash flow at each node;

After listening to this lecture, the student should be able to:

• describe the process of calibrating a binomial interest rate tree to match a specific term structure;
• compare pricing using the zero-coupon yield curve with pricing using an arbitrage-free binomial lattice;
• describe path-wise valuation in a binomial interest rate framework and calculate the value of a fixed-income instrument given its cash flows along each path;
• describe a Monte Carlo forward-rate simulation and its application.

After completing this lecture, the student should be able to:

• describe fixed-income securities with embedded options;
• explain the relationships between the values of a callable or putable bond, the underlying option-free (straight) bond, and the embedded option;
• describe how the arbitrage-free framework can be used to value a bond with embedded options;
• explain how interest rate volatility affects the value of a callable or putable bond;
• explain how changes in the level and shape of the yield curve affect the value of a callable or putable bond;
• calculate the value of a callable or putable bond from an interest rate tree;

After completing this lecture, the student should be able to:

• explain the calculation and use of option-adjusted spreads;
• explain how interest rate volatility affects option-adjusted spreads;
• calculate and interpret effective duration of a callable or putable bond;
• compare effective durations of callable, putable, and straight bonds;
• describe the use of one-sided durations and key rate durations to evaluate the interest rate sensitivity of bonds with embedded options;
• compare effective convexities of callable, putable, and straight bonds;

After completing this lecture, the student should be able to:

• describe defining features of a convertible bond;
• calculate and interpret the components of a convertible bond’s value;
• describe how a convertible bond is valued in an arbitrage-free framework;
• compare the risk–return characteristics of a convertible bond with the risk-return characteristics of a straight bond and of the underlying common stock.

After listening to this lecture, the student should be able to:

• explain probability of default, loss given default, expected loss, and present value of the expected loss and describe the relative importance of each across the credit spectrum;
• explain credit scoring and credit ratings, including why they are called ordinal rankings;
• explain strengths and weaknesses of credit ratings; d explain structural models of corporate credit risk, including why equity can be viewed as a call option on the company’s assets;
• explain reduced form models of corporate credit risk, including why debt can be valued as the sum of expected discounted cash flows after adjusting for risk;
• explain assumptions, strengths, and weaknesses of both structural and reduced form models of corporate credit risk;

After completing this lecture, the student should be able to:

• explain the determinants of the term structure of credit spreads;
• calculate and interpret the present value of the expected loss on a bond over a given time horizon;
• compare the credit analysis required for asset-backed securities to analysis of corporate debt.