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Financial Instruments, Markets and Conventions / Fixed Income: Bonds, Yields, and Interest Rate Risk

Overview

Fixed-income instruments are the largest asset class in global capital markets and the primary source of the discount curve used to value every other instrument in the unit. The logic is direct: a bond is nothing but a scheduled sequence of cash flows (coupons and principal), and its price is the present value of those cash flows, discounted at rates that the market deems appropriate for the credit quality and maturity of the issuer. The discipline of discounting precisely is what makes fixed income the natural home for the time-value machinery introduced in Topic 1.

Three things are built here, one per lesson:

The pricing machinery. Every bond price is a sum of discounted cash flows. When the discount rate is a single yield (the YTM), prices and yields move inversely. When discount rates are maturity-specific zero rates, the coupon bond is valued as a portfolio of zero-coupon bonds — the discount-factor framework that underlies swap pricing, derivative valuation, and every application of the no-arbitrage toolkit.
The yield curve. Market rates are not a single number: they vary by maturity, forming the term structure of interest rates (the yield curve or zero curve). The zero curve is extracted from coupon bond prices by bootstrapping (following the same logic as Hull in Topic 1). This topic adds the economic theories — expectations, liquidity preference, market segmentation — that explain why the curve slopes as it does.
The risk measures. A bond's price changes when the yield moves. Duration captures the first-order (linear) sensitivity: a 1% rise in yield drops a bond's price by approximately its duration in percent. Convexity captures the curvature: because the price-yield relationship is convex, duration overestimates the price drop and underestimates the price rise. Together, DV01 (dollar duration), modified duration, and convexity constitute the standard toolkit for measuring and managing a bond portfolio's exposure to rate movements.

By the end of this topic you should be able to:

  • price a coupon bond using either a single YTM or a schedule of zero rates;
  • bootstrap a zero curve from observed coupon bond prices;
  • compute a bond's yield to maturity, par yield, and accrued interest;
  • interpret the term structure through the three standard theories (expectations, liquidity preference, market segmentation);
  • compute Macaulay duration, modified duration, DV01, and dollar convexity for a bond or portfolio;
  • use duration and convexity to approximate the price change from a yield shift;
  • describe the US Treasury market: auction mechanics, on-the-run vs off-the-run, STRIPS, and day-count conventions.

In this lesson

  1. Contents
  2. The big picture

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