Long Forward Probabilities, Recovery and the Term Structure of Bond Risk Premiums

TL;DR

This paper examines the properties of long forward probabilities and the martingale component in bond risk premiums, revealing their volatility and implications for the term structure of bond Sharpe ratios and growth optimality.

Contribution

It demonstrates that the martingale component is highly volatile and inconsistent with growth optimality, while long forward probabilities better explain the observed term structure.

Findings

Martingale component is highly volatile and produces a downward-sloping Sharpe ratio term structure.

Long forward probabilities forecast an upward-sloping Sharpe ratio term structure.

Long bonds are consistent with growth optimality under long forward probabilities.

Abstract

We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond Sharpe ratios, and implies that the long bond is far from growth optimality. In contrast, the long forward probabilities forecast an upward sloping term structure of bond Sharpe ratios that starts from zero for short-term bonds and implies that the long bond is growth optimal. Thus, transition independence and degeneracy of the martingale component are implausible assumptions in the bond market.