Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models

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See all articles by Svetlana Bryzgalova

Svetlana Bryzgalova

London Business School - Department of Finance

Jiantao Huang

London School of Economics & Political Science (LSE) - Department of Finance

Christian Julliard

London School of Economics & Political Science (LSE) - Department of Finance; Centre for Economic Policy Research (CEPR)

Date Written: September 1, 2019

Abstract

We propose a novel, and simple, Bayesian estimation and model selection procedure for cross-sectional asset pricing. Our approach, that allows for both tradable and non-tradable factors, and is applicable to high dimensional cases, has several desirable properties. First, weak and spurious factors lead to diffuse, and centered at zero, posteriors for their market price of risk, making such factors easily detectable. Second, posterior inference is robust to the presence of such factors. Third, we show that flat priors for risk premia lead to improper marginal likelihoods, rendering model selection invalid. Therefore, we provide a novel prior, that is diffuse for strong factors but shrinks away useless ones, under which posterior probabilities are well behaved, and can be used for factor and (non necessarily nested) model selection, as well as model averaging, in large scale problems. We apply our method to a very large set of factors proposed in the literature, and analyse 2.25 quadrillion possible models, gaining novel insights on the empirical drivers of asset returns.

Keywords: Cross-sectional asset pricing, factor models, model evaluation, multiple testing, data mining, p-hacking, Bayesian methods

JEL Classification: G12, C11, C12, C52, C58

Suggested Citation

Bryzgalova, Svetlana and Huang, Jiantao and Julliard, Christian, Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models (September 1, 2019). Available at SSRN: https://ssrn.com/abstract=

Svetlana Bryzgalova

London Business School - Department of Finance ( email )

Sussex Place
Regent's Park
London NW1 4SA
United Kingdom

Jiantao Huang

London School of Economics & Political Science (LSE) - Department of Finance ( email )

Houghton St, Holborn
London, WC2A 2AE
Great Britain

Christian Julliard (Contact Author)

London School of Economics & Political Science (LSE) - Department of Finance ( email )

United Kingdom

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

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