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Identification-robust estimation and testing of the zero-beta CAPM

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  • Marie-Claude Beaulieu

    ()

  • Jean-Marie Dufour

    ()

  • Lynda Khalaf

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.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2011s-21.

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Date of creation: 01 Feb 2011
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Handle: RePEc:cir:cirwor:2011s-21

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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.;

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Cited by:
  1. Sriananthakumar, Sivagowry, 2013. "Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach," Economic Modelling, Elsevier, vol. 33(C), pages 126-136.
  2. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.

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