Identification-Robust Estimation and Testing of the Zero-Beta CAPM

Posted: 14 Feb 2011

See all articles by Marie-Claude Beaulieu

Marie-Claude Beaulieu

Laval University - Centre de recherche en économie et finance appliquée (CRÉFA)

Jean-Marie Dufour

McGill University

Lynda Khalaf

Université Laval - Département d'Économique

Date Written: February 11, 2011

Abstract

We propose exact simulation-based procedures for: (i) testing mean-variance efficiency when the zero-beta rate is unknown, and (ii) building confidence intervals for the zero-beta rate. On observing that this parameter may be weakly identified, we propose LR-type statistics as well as heteroskedascity and autocorrelation corrected (HAC) Wald-type procedures, which are robust to weak identification and allow for non-Gaussian distributions including parametric GARCH structures. In particular, we propose confidence sets for the zero-beta rate based on “inverting” exact tests for this parameter; these sets provide a multivariate extension of Fieller’s technique for inference on ratios. The exact distribution of LR-type statistics for testing efficiency is studied under both the null and the alternative hypotheses. The relevant nuisance parameter structure is established and finite-sample bound procedures are proposed, which extend and improve available Gaussianspecific bounds. Furthermore, we study the invariance to portfolio repacking property for tests and confidence sets proposed. The statistical properties of available and proposed methods are analyzed via aMonte Carlo study. Empirical results on NYSE returns show that exact confidence sets are very different from the asymptotic ones, and allowing for non-Gaussian distributions affects inference results. Simulation and empirical results suggest that LR-type statistics - with p-values corrected using the Maximized Monte Carlo test method - are generally preferable to their Wald-HAC counterparts from the viewpoints of size control and power.

Keywords: capital asset pricing model, CAPM, Black, mean-variance efficiency, non-normality, weak identification, Fieller, multivariate linear regression, uniform linear hypothesis, exact test, Monte Carlo test, bootstrap, nuisance parameters, GARCH, portfolio repacking

JEL Classification: C3, C12, C33, C15, G1, G12, G14

Suggested Citation

Beaulieu, Marie-Claude and Dufour, Jean-Marie and Khalaf, Lynda, Identification-Robust Estimation and Testing of the Zero-Beta CAPM (February 11, 2011). CIRANO - Scientific Publications 2011s-21, Available at SSRN: https://ssrn.com/abstract=1759960 or http://dx.doi.org/10.2139/ssrn.1759960

Marie-Claude Beaulieu

Laval University - Centre de recherche en économie et finance appliquée (CRÉFA) ( email )

Pavillon Palasis-Prince
Quebec G1K 7P4
Canada

Jean-Marie Dufour (Contact Author)

McGill University ( email )

Department of Economics, McGill University
Leacock Building Room 443, 855 Sherbrooke West
Montreal, Quebec H3A 2T7
Canada
(1) 514 398 6071 (Phone)
(1) 514 398 4800 (Fax)

HOME PAGE: http://www.jeanmariedufour.com

Lynda Khalaf

Université Laval - Département d'Économique ( email )

2325 Rue de l'Université
Ste-Foy, Quebec G1K 7P4 G1K 7P4
Canada
418-656-2131-2409 (Phone)
418-656-7412 (Fax)

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