Variance Bounds on the Permanent and Transitory Components of Stochastic Discount Factors

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Nobel Lecture: Uncertainty Outside and Inside Economic Models (2014, background): “…on the frontier characterized in Hansen and Jagannathan’s study. and use of this specification of f gives rise to a bound that has been studied in several papers including Bansal and Lehmann ð1997Þ, Alvarez and Jermann ð2005Þ, Backus, Chernov, and Martin ð2011Þ, and Backus, Chernov, and Zin ð2014Þ.”
Long Term Risk: A Martingale Approach (2014, unknown): “…is generally opposite to the one described above, indicating that the martingale component in the long-term factorization is highly economically signiﬁcant, complementing empirical results in Alvarez and Jermann (2005), Bakshi and Chabi-Yo (2012), Boroviˇcka et al. (2016) and Christensen (2016a).”
Nonparametric stochastic discount factor decomposition (2014, background): “Bakshi and Chabi-Yo (2012, 2014) refine the bounds of Alvarez and Jermann (2005) and derive revealing bounds for the entropy of the square of the permanent component of the SDF.”