Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance*

Abstract

We compare nonnested parametric specifications of the stochastic discount factor (SDF) using the conditional Hansen–Jagannathan (HJ-) distance. This distance measures the discrepancy between a parametric model-implied SDF and the admissible SDF’s satisfying all the conditional (dynamic) no-arbitrage restrictions, instead of just few unconditional no-arbitrage restrictions for managed portfolios chosen through the instrument selection. We estimate the conditional HJ-distance by a generalized method of moments estimator and establish its large sample properties for model selection purposes. We compare empirically several SDF models including multifactor beta pricing specifications and some recently proposed SDF models that are conditionally linear in consumption growth.

Regularized GMM for Time‐varying Models With Applications to Asset Pricing

“…where q = N K. The literature has documented substantial benefits of such transformations in different contexts, such as when estimating pricing functions and facilitating model misspecification tests (Hansen and Richard, 1987;Gagliardini and Ronchetti, 2020;Cui et al, 2021). We further denote q as the actual number of moment conditions used to conduct estimation.…”

“…Based on Lewbel's (2007) local smoothing GMM estimator, Gospodinov and Otsu (2012) propose estimating time-varying parameters via local kernel smoothing by using a nonparametric conditional moment. Gagliardini et al (2011) extend the nonparametric method-of-moments estimation to handle unconditional and conditional moment restrictions. Gagliardini and Ronchetti (2020) employ a local smoothing GMM to characterize a conditional Hansen-Jagannathan (HJ) distance for dynamic pricing errors.…”

“…Gagliardini et al (2011) extend the nonparametric method-of-moments estimation to handle unconditional and conditional moment restrictions. Gagliardini and Ronchetti (2020) employ a local smoothing GMM to characterize a conditional Hansen-Jagannathan (HJ) distance for dynamic pricing errors. Cui et al (2021) estimate time-varying price-dividend ratios using a global smoothing GMM approach based on Euler equations.…”

Three Essays in Econometrics

“…Recently, numerous approaches have been developed to compare asset pricing models; namely using Sharpe ratio-based statistics [Fama and French (2018), Kan et al (2019), Barillas et al (2020)], machine learning methods [Feng et al (2020), Gu et al (2020), Kozak et al (2020)], mispricing distance measures [Gospodinov et al (2013), Gagliardini and Ronchetti (2020), Zhang et al (2021)], and Bayesian methods [Barillas and Shanken (2018), Bryzgalova et al (2022)]. 2 While these newly introduced techniques may be sensitive to (i) distributional assumptions, (ii) hy- 1 The MCS can be interpreted as a test inversion of a sequential procedure, although Hansen et al (2011) do not present it in this way.…”

“… See Gospodinov et al (2013),Kan et al (2013), Shanken (2017), Feng et al (2020),Ahmed et al (2018),Barillas and Shanken (2018),Hou et al (2018),Huang et al (2018),Pukthuanthong et al (2018),Weigand (2019),Barillas et al (2020),Chib et al (2020),Gagliardini and Ronchetti (2020),Gu et al (2020),Kozak et al (2020),Gospodinov and Robotti (2021),Qu et al (2021),Bryzgalova et al (2022).…”