Long forward probabilities, recovery, and the term structure of bond risk premiums

This paper examines the assumption of transition independence of the stochastic discount factor (SDF) in the bond market. This assumption underlies the recovery result of Ross 2015. Following the methodology of Alvarez and Jermann 2005 and Hansen and Scheinkman 2009, we estimate the martingale component in the long-term factorization of the SDF using U.S. Treasury data. The empirically estimated martingale component is highly volatile and produces a downward-sloping term structure of bond Sharpe ratios. In contrast, the transition independence assumption implies a degenerate martingale component and an upward-sloping term structure of bond Sharpe ratios. Thus, transition independence is inconsistent with our empirical results.