Specification Tests of Asset Pricing Models Using Excess Returns

47 Pages Posted: 1 Aug 2006 Last revised: 6 Jul 2014

See all articles by Cesare Robotti

Cesare Robotti

Warwick Business School

Raymond Kan

University of Toronto - Rotman School of Management

Date Written: February 1, 2008

Abstract

In this paper, we discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. We point out that the popular way of specifying the stochastic discount factor (SDF) as a linear function of the factors is problematic because (1) the specification test statistic is not invariant to an affine transformation of the factors, and (2) the SDFs of competing models can have very different means. In contrast, an alternative specification that defines the SDF as a linear function of the de-meaned factors is free from these two problems and is more appropriate for model comparison. In addition, we suggest that a modification of the traditional Hansen-Jagannathan distance (HJ-distance) is needed when we use the de-meaned factors. The modified HJ-distance uses the inverse of the covariance matrix (instead of the second moment matrix) of excess returns as the weighting matrix to aggregate pricing errors. Asymptotic distributions of the modified HJ-distance and of the traditional HJ-distance based on the de-meaned SDF under the correctly specified model and the misspecified models are provided. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification. We show that failure to take model misspecification into account is likely to understate the standard errors of the estimates of the SDF parameters and lead us to erroneously conclude that certain factors are priced.

Keywords: Hansen-Jagannathan distance, excess returns, stochastic discount factors

JEL Classification: G12

Suggested Citation

Robotti, Cesare and Kan, Raymond, Specification Tests of Asset Pricing Models Using Excess Returns (February 1, 2008). FRB of Atlanta Working Paper No. 2006-10, EFA 2007 Ljubljana Meetings Paper, Journal of Empirical Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=921515 or http://dx.doi.org/10.2139/ssrn.921515

Cesare Robotti

Warwick Business School ( email )

West Midlands, CV4 7AL
United Kingdom

Raymond Kan (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S3E6
Canada
416-978-4291 (Phone)
416-971-3048 (Fax)

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