Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Abstract

Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

Common information in carry trade risk factors

“…∆N C t and ∆C t are nondurable and durable consumption growth. We use monthly growth rates in real per capita nondurables and durables consumption, which is adopted by Kan et al (2013). We employ personal durable and nondurable consumption expenditure data and adjust them using the consumer price index (durable and nondurable goods) and total population.…”

Linear Factor Models and the Estimation of Expected Returns

“…Formally, this is a test on (a component of) of λ being zero or not and, accordingly, the properties of risk price estimates for λ have been studied and compared. Examples include Shanken (1992), Jagannathan (1998),603-621 Kleibergen (2009, Lewellen, Nagel and Shanken (2010), Kan and Robotti (2011), Kan et al (2013).…”

Identification-Robust Factor Pricing: Canadian Evidence

“…In multivariate-regression financial models, finitesample testing is important because tests which are only approximate and/or do not account for non-normality can lead to unreliable empirical interpretations of standard financial models; see Shanken (1996), Campbell et al (1997), Beaulieu (2003, 2010), and Beaulieu, Dufour and Khalaf (2007, 2010a. In parallel, an emerging literature, which builds on Zhang (1999a, 1999b) recognizes the adverse effects of large numbers of factors; see Kleibergen (2009), Kan, Robotti and Shanken (2013), Kleibergen and Zhan (2013), Gospodinov, Kan and Robotti (2014), and Harvey, Liu and Zhu (2015). In this paper, we develop inference methods immune to both dimensionality and identification difficulties.…”

“…In contrast, Kan et al (2013), Kleibergen and Zhan (2013), and Gospodinov et al (2014) focus on model misspecification. assets adding momentum to the list of factors considered by L' Her et al (2004).…”