Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance

Gagliardini, Patrick; Ronchetti, Diego

doi:10.2139/ssrn.2669464

Cited by 1 publication

(9 citation statements)

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“…Second, we propose several interpretations of this conditional HJ distance that complements the ones put forward by Gagliardini and Ronchetti (2016). A possible criticism against this conditional HJ distance is that it takes the unconditional expectation of the squared of the pricing errors on the most mispriced portfolios.…”

Section: Introductionmentioning

confidence: 86%

“…Following Gagliardini and Ronchetti's (2016) conditional extension of the HJ-distance, we define the conditional distance between our parametric model and the set of admissible SDFs as:…”

Section: Pseudo-true Sdfmentioning

confidence: 99%

“…However, we show that our characterization of the pseudo-true SDF as the only one able to price properly the scaled fundamental factors implies that its definition is immune to any shrinking of the information set, insofar as the relevant scaling weights are still included. Moreover, we are also able to characterize the pseudo-true SDF as minimizing the so-called conditional HJ distance that is defined, following Gagliardini and Ronchetti (2016), as the unconditional expectation of the conditional measure that one would have computed for a given information set.…”

Section: Introductionmentioning

confidence: 99%

“…However, as acknowledged by Nagel and Singleton (2011), their kernel-based nonparametric approach suffers from the curse of dimensionality that prevents them from including all the relevant state variables in the set of explanatory variables for nonparametric regression. Gagliardini and Ronchetti (2016) resort to the more promising approach of local GMM, extending to their context the asymptotic theory of Hall and Inoue (2003) for estimation with misspecified moment conditions. Although in this case it would be convenient to maintain a martingale difference sequence hypothesis that means that, in a way somewhat opposite to Nagel and Singleton (2011), one should include all the needed state variables in the nonparametric regression, irrespective of the curse of dimensionality.…”

Section: Introductionmentioning

confidence: 99%

“…It is then natural to define a pseudo-true value of the SDF parameters h by the accurate pricing on average of the local factors. In Section 3, we show that this pseudo-true SDF can also be characterized as minimizing the conditional HJ distance defined, following Gagliardini and Ronchetti (2016), as the unconditional expectation (over possible values of conditioning information sets) of the time-varying conditional measures. We argue that this conditional HJ distance provides the right mean-variance trade-off regarding the time series of conditional HJ distances for the realized sequence of information sets at each date.…”

Section: Introductionmentioning

confidence: 99%

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Pseudo-True SDFs in Conditional Asset Pricing Models*

Antoine

Proulx

Renault

2018

Journal of Financial Econometrics

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This article is motivated by the need to bridge some gap between modern asset pricing theory and recent developments in econometric methodology. While asset pricing theory enhances the use of conditional pricing models, econometric inference of conditional models can be challenging due to misspecification or weak identification. To tackle the case of misspecification, we utilize the conditional Hansen and Jagannathan (1997) (HJ) distance as studied by Gagliardini and Ronchetti (2016), but we set the focus on interpretation and estimation of the pseudo-true value defined as the argument of the minimum of this distance. While efficient Generalized Method of Moments (GMM) has no meaning for estimation of a pseudo-true value, the HJ-distance not only delivers a meaningful loss function, but also features an additional advantage for the interpretation and estimation of managed portfolios whose exact pricing characterizes the pseudo-true pricing kernel (stochastic discount factor (SDF)). For conditionally affine pricing kernels, we can display some managed portfolios which are well-defined independently of the pseudo-true value of the parameters, although their exact pricing is achieved by the pseudo-true SDF. For the general case of nonlinear SDFs, we propose a smooth minimum distance (SMD) estimator (Lavergne and Patilea, 2013) that avoids a focus on specific directions as in the case of managed portfolios. Albeit based on kernel smoothing, the SMD approach avoids instabilities and the resulting need of trimming strategies displayed by classical local GMM estimators when the density function of the conditioning variables may take arbitrarily small values. In addition, the fact that SMD may allow fixed bandwidth asymptotics is helpful regarding the curse of dimensionality. In contrast with the true unknown value for a well-specified model, the estimated pseudo-true value, albeit defined in a time-invariant (unconditional) way, may actually depend on the choice of the state variables that define fundamental factors and their scaling weights. Therefore, we may not want to be overly parsimonious about the set of explanatory variables. Finally, following Antoine and Lavergne (2014), we show how SMD can be further robustified to deal with weaker identification contexts. Since SMD can be seen as a local extension of the method of jackknife GMM (Newey and Windmeijer, 2009), we characterize the Gaussian * We gratefully acknowledge very helpful comments by Lars Peter Hansen and Sydney Ludvigson on an earlier draft of this article. We are also grateful to participants of the 2017 EC 2 conference in Amsterdam for insightful questions and remarks.

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Section: Introductionmentioning

confidence: 86%

“…Following Gagliardini and Ronchetti's (2016) conditional extension of the HJ-distance, we define the conditional distance between our parametric model and the set of admissible SDFs as:…”

Section: Pseudo-true Sdfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%