Forces That Shape the Yield Curve
Economic Review, Vol. 86, No. 1, 2001
The yield curve shows how the yield on a government bond depends on the bond's maturity. Monetary policymakers and observers pay special attention to the shape of the yield curve as an indicator of the economic impact of current and future monetary policy. Without the proper analytical tools, however, drawing inferences from the yield curve can be difficult. This article uses high-school algebra to introduce those tools in a rigorous but accessible way.
The author develops the basic ideas about the yield curve using an analogy. Next, he discusses bond pricing in a world of perfect certainty, where no-arbitrage conditions are first worked out algebraically. The element of uncertainty is then added via a single flip of a coin, and the no-arbitrage conditions for bond prices are worked out for this scenario as well. These no-arbitrage conditions are shown to imply the existence of a risk premium that depends on the price of risk and the amount of risk. Finally, the article demonstrates how to translate the no-arbitrage condition for bond prices into a no-arbitrage condition for yields.
The author concludes that convexity "the nonlinear relation between bond yields and bond prices" leads to surprising and even counterintuitive results in yield-curve analysis. A firm grasp of the no-arbitrage conditions is therefore necessary in order to make sense of the shape of the yield curve.