Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation, Second Edition

CHAPTER 2

Yield Curve Analysis

Spot Rates and Forward Rates

 

 

A bond’s yield is a measure of its potential return given certain assumptions about how the future will unfold. The yield curve is the graphical depiction of the relationship between the yield to maturity and term to maturity for bonds that are alike in every other respect except term to maturity. When market participants refer to the “yield curve,” they usually mean the U.S. Treasury yield curve. A key function of the Treasury yield curve is to serve as a benchmark for pricing bonds and to determine yields in all other sectors of the debt market (e.g., corporate debt, mortgages, bank loans, etc.) This is also true in bond markets around the world where government securities often serve as benchmark securities for pricing other instruments. The purpose of this chapter is to develop the fundamental tools of yield curve analysis. We discuss par rates, spot rates, and forward rates—how they are computed, how they are related to each other, and how they are utilized by market participants.

A BOND IS A PACKAGE OF ZERO-COUPON INSTRUMENTS

The traditional approach to valuation is to discount every cash flow of a fixed income security using the same interest or discount rate. The fundamental flaw of this approach is that it views each security as the same package of cash flows. For example, consider a 5-year U.S. Treasury note with a 6% coupon rate. The cash flows per $100 of par value would be nine payments of $3 every ...