Forces that Shape the Yield Curve: Parts 1 and 2

The yield curve is shaped by (1) expectations of the future path of short-term interest rates and (2) uncertainty about the path. Uncertainty affects the yield curve through two channels: (1) investors' attitudes toward risk as reflected in risk premia, and (2) the nonlinear relation between yields and bond prices (known as convexity). The way in which these forces simultaneously work to shape the yield curve can be understood in terms of the conditions that guarantee the absence of arbitrage opportunities. The purpose of this paper is to provide an introduction to the modern theory of the term structure of interest rates using high-school algebra. In order to present the theory correctly, one must take uncertainty seriously. Nevertheless, the source of uncertainty can be modeled quite simply: All uncertainty is resolved by a single flip of a coin. In this setting, the author can rigorously present all three forces that shape the yield curve: expectations, risk aversion, and convexity. The analysis is organized around the conditions that guarantee the absence of arbitrage opportunities.