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Open AccessArticle

Relative Entropy and Minimum-Variance Pricing Kernel in Asset Pricing Model Evaluation

Department of Business Administration, Rey Juan Carlos University, 28032 Madrid, Spain
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Entropy 2020, 22(7), 721; https://doi.org/10.3390/e22070721
Received: 31 May 2020 / Revised: 19 June 2020 / Accepted: 22 June 2020 / Published: 30 June 2020
(This article belongs to the Section Multidisciplinary Applications)
Recent literature shows that many testing procedures used to evaluate asset pricing models result in spurious rejection probabilities. Model misspecification, the strong factor structure of test assets, or skewed test statistics largely explain this. In this paper we use the relative entropy of pricing kernels to provide an alternative framework for testing asset pricing models. Building on the fact that the law of one price guarantees the existence of a valid pricing kernel, we study the relationship between the mean-variance efficiency of a model’s factor-mimicking portfolio, as measured by the cross-sectional generalized least squares (GLS) R2 statistic, and the relative entropy of the pricing kernel, as determined by the Kullback–Leibler divergence. In this regard, we suggest an entropy-based decomposition that accurately captures the divergence between the factor-mimicking portfolio and the minimum-variance pricing kernel resulting from the Hansen-Jagannathan bound. Our results show that, although GLS R2 statistics and relative entropy are strongly correlated, the relative entropy approach allows us to explicitly decompose the explanatory power of the model into two components, namely, the relative entropy of the pricing kernel and that corresponding to its correlation with asset returns. This makes the relative entropy a versatile tool for designing robust tests in asset pricing.
Keywords: pricing kernel; factor-mimicking portfolio; relative entropy; Kullback-Leibler divergence; Hansen-Jagannathan bound; CAPM; Fama-French model; consumption-CAPM pricing kernel; factor-mimicking portfolio; relative entropy; Kullback-Leibler divergence; Hansen-Jagannathan bound; CAPM; Fama-French model; consumption-CAPM
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MDPI and ACS Style

Rojo-Suárez, J.; Alonso-Conde, A.B. Relative Entropy and Minimum-Variance Pricing Kernel in Asset Pricing Model Evaluation. Entropy 2020, 22, 721.

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