A Binomial Zero Coupon Model of Expected Bond Returns Term Structure

Abstract

We propose, analyze, and implement a model for the estimation of zero-coupon expected bond returns (EBR), expanding the model developed by Afik and Benninga (AB, 2010). The central idea of AB is to use the matrix of rating transitions to estimate a Markov model of the EBR. Unlike AB, this paper presents a tree like model that can be used to aggregate market data for each rating category and extract its zero-coupon term structure of EBR and its yield risk premium components, including a certainty equivalence premium which is related to the systematic risk of the CAPM. We use corporate bond transaction data from the United States and a rating agency transition matrix to extract the term structure of EBR and its components and the term structure of risk-neutral default probabilities. We then apply our model and its results to the estimation of CDS premium term structure and implement it on our US bond market data set. We believe this model can be extended and applied to a variety of research and practical purposes. A few early examples are included in our forthcoming papers on implied recovery rates, abnormal returns and premia, and market implied bond rating.