An Introduction to Zero-Coupon Risk-Free Bonds

Abstract

This note introduces students to the basics of bonds and the time value of money through the simplest of financial contracts—the zero-coupon risk-free bond contract. The note covers the concepts of present value, yield to maturity, and bond pricing conventions. The note is appropriate as a companion for the Bond Trader simulation. A demo for this simulation is available at https://forio.com/simulate/darden/bond-trader-demo/. Excerpt UVA-F-1799 Rev. Sept. 7, 2018 An Introduction to Zero-Coupon Risk-Free Bonds One of the central principles of finance is that things that pay identical amounts have identical values. This principle is called the “Law of One Price.” The Law of One Price implies that one can value one financial contract by observing the value of another financial contract with similar expected return and risk. A related concept used in finance is that of “home cooking.” In financial markets one can “home cook” a version of a prevailing contract by combining existing financial products to create a “home-cooked” version. As such, the “home-cooked” version has the same value as, say, the “store-bought” version. As an example of this concept, suppose that you often buy chicken teriyaki sandwiches at a local food truck called the Big Kahuna. Your brother Rupert, an enterprising young man, has figured out how to exactly replicate the Big Kahuna chicken teriyaki sandwich. What is the value of Rupert's “home-cooked” exact replication of the Big Kahuna sandwich? Since the two sandwiches are identical, the sandwiches have the same value according to the Law of One Price. In finance, we will determine the value of a financial contract by observing the value of an identical replication of that contract that we can “cook up” by combining other contracts that are traded in security markets. In this note, we explore some first principles of pricing financial contracts using the Law of One Price. Although debt contracts go by many names, to simplify the discussion in this note we will use the term “bond” to denote any market-traded debt contract. Because the principles used to value simple contracts also apply to complicated contracts, we begin with the simplest of financial contracts—the zero-coupon risk-free bond contract. “Zero-coupon” bonds are simple promises to pay a certain amount at a specific point in time without any promise of making interest payments (or coupon payments) along the way. Zero-coupon bonds are simple IOUs. “Risk-free” bonds are promises that have certainty in the contracted payment. A risk-free promise of $ 1,000 is a sure promise that the payment will be made (there is no possibility of default or failure to make payment). . . .