An Inquiry into the Nature and Sources of Variation in the Expected Excess Return of a Long-Term Bond

Nonparametric Stochastic Discount Factor Decomposition

“…In contrast, the correlations for the parametric state process specifications are around the same level as the nonparametric estimates for low values of γ, but remain negative for larger values of γ. A recent literature has emphasized the role of positive dependence between the permanent and transitory components in explaining excess returns of long-term bonds (Bakshi and Chabi-Yo (2012), Gao Bakshi (2015a, 2015b)). Positive dependence also features in models in which the term structure of risk prices is downward sloping (see the example presented in Section 7.2 in ).…”

“…The methodology also allows researchers to estimate the yield and the change of measure which characterize pricing over long investment horizons. This approach is fundamentally different from existing empirical methods for studying the permanenttransitory decomposition, which produce bounds on various moments of the permanent and transitory components as functions of asset returns (Alvarez and Jermann (2005), Bakshi and Chabi-Yo (2012), Gao Bakshi (2015a, 2015b)). 1 Although presented in the context of SDF decomposition, the methodology can be applied to more general processes such as the valuation and stochastic growth processes in Hansen, Heaton, and Li (2008), Hansen and Scheinkman (2009), and Hansen (2012).…”

Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing

“…In related literature, an alternative approach to recovery has recently been put forward Martin (2014), who derived a lower bound for the expected excess return of an equity index in terms of equity index options, based on the negative covariance condition. Bakshi et al (2015) derived a similar lower bound for the expected excess return on the long bond. Schneider and Trojani (2015) extended the bounds to other moments and also considered upper bounds.…”

“…In particular, this long-term risk decomposition is of central importance in macro-finance, the discipline at the intersection of financial economics and macroeconomics. Hansen (2012), Hansen and Scheinkman (2012a), Hansen and Scheinkman (2012b), , , and Qin and Linetsky (2014) provide theoretical developments, and Bakshi and Chabi-Yo (2012) provide some further empirical evidence complementing the original empirical results of Alvarez and Jermann (2005). The mathematics underlying these developments is the Perron-Frobenius type theory governing positive eigenfunctions for certain classes of positive linear operators in function spaces.…”

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

“…This difference is so large and, hence, the martingale component is so volatile that we reject the null hypothesis that the martingale is equal to unity (and, hence, the data-generating probability measure is identical to the long-term risk neutral measure) at the 99.99% level. We note that our econometric approach in this paper is entirely different from the approaches of Alvarez and Jermann (2005), Bakshi and Chabi-Yo (2012) and Bakshi et al (2015) who rely on bounds on the transitory and martingale components, while we directly estimate a fully specified DTSM, explicitly accomplish the Perron-Frobenius extraction of Hansen and Scheinkman (2009) and obtain the permanent and mar-tingale components in the framework of our DTSM. We also note recent work by Christensen (2014) who develops a non-parametric approach to the Perron-Frobenius extraction and estimates permanent and transitory components under structural (Epstein-Zin and power utility) specifications of the SDF calibrated to real per-capita consumption and real corporate earnings growth.…”