A Primer on Risk-Free Bonds

Abstract

This note explores the first principles of pricing financial contracts. Debt contracts go by many names, but the term bond is used in this note to denote any market-traded debt contract. The note is divided into three sections. The first section examines the simplest of financial contracts—the zero-coupon risk-free bond contract. The second section examines bonds with the additional complexity of coupon payments. The third section examines the expectations theory, the fundamental theory for why yields vary over different maturities, and introduces the construct of a yield curve. The basic concepts and principles associated with the risk-free bonds discussed in this note provide an important foundation for understanding more complex securities.

Excerpt

UVA-F-1861

Feb. 1, 2019

A Primer on 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 payments 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 replicate the truck's signature dish—the Big Kahuna chicken teriyaki sandwich. What is the value of Rupert's home-cooked replication of the Big Kahuna sandwich? Since the two sandwiches are identical, both 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 contract that we “cook up” by combining other contracts that are traded in security markets.

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Keywords: law of one price, zero-coupon bonds, yield curve, effective annual rate, financial contracts