  This paper extends the long-term factorization of the stochastic discount
factor introduced and studied by Alvarez and Jermann (2005) in discretetime
ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in
Markovian environments to general semimartingale environments. The transitory
component discounts at the stochastic rate of return on the long bond and is
factorized into discounting at the long-term yield and a positive
semimartingale that extends the principal eigenfunction of Hansen and
Scheinkman (2009) to the semimartingale setting. The permanent component is a
martingale that accomplishes a change of probabilities to the long forward
measure, the limit of T-forward measures. The change of probabilities from the
data generating to the long forward measure absorbs the long-term risk-return
trade-off and interprets the latter as the long-term risk-neutral measure.
