Time to Build and Bond Risk Premia

Abstract

This paper studies the impact of time to build on the term structure of interest rates in an otherwise standard Cox, Ingersoll and Ross (1985a, 1985b, CIR) production economy. Due to time to build, production depends not only on the current business condition as in the original CIR, but also on past conditions over the production period. This causes equilibrium quantities, including the short rate, forward rates, and bond returns, to depend on the historical path of the production opportunities. Production delay that accumulates uncertainty over the time to build generates significant time variations in bond risk premia. Bond returns can be predicted by current forward rates, as well as their lagged values, since current market states not only affect the current short rate but also the short rate in a distant future. Due to the path dependence, risk premia cannot be fully spanned by current yields. We show that time to build improves the ability of the CIR in generating empirical facts.

Keywords: Time to build, CIR model, bond risk premia, path dependence, Non- Markovian asset pricing, stochastic delay differential equations.

JEL Classification: D51, E43, G12