Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Wednesday, April 13, 2016
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Long Forward Measure, Recovery, and the Term Structure of Bond Risk Premiums

Abstract:   In the first part of the talk, we extend the long-term factorization of the pricing kernel introduced by Alvarez and Jermann (2005) in discrete-time ergodic environments and by Hansen and Scheinkman (2009) in Markovian environments to general semimartingale environments. The long-term factorization is an alternative to the familiar risk-neutral factorization, where the pricing kernel is factorized into discounting at the rate of return on the long bond and a martingale that accomplishes a change of probabilities to the long forward measure. A sufficient condition is given that guarantees convergence in semimartingale topology of trading strategies that invest in T-maturity pure discount bonds to the long bond and convergence in total variation of T-forward measures to the long forward measure. Under the long forward probabilities, the long bond is growth optimal, so that only the (negative of the) covariance with the (reciprocal of the) long bond earns excess return. The volatility of the martingale component drives the wedge between data-generating and long forward probabilities. When the Markov property is imposed, the operator theory-based results of Hansen and Scheinkman (2009) linking the long-term factorization with the principal eigenfunction of the pricing operator are naturally recovered from our martingale formulation.

In the second part of the talk, we empirically estimate the long-term factorization in the US Treasury bond market, and show that the martingale component 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. These results imply that the transition independence and degeneracy of the martingale component that underpin the Recovery Theorem of Ross are implausible assumptions in the bond market.


Speaker:  Vadim Linetsky
Institution:  Northwestern

Event Organizer:   Erhan Bayraktar


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