Capital asset pricing models revisited: Evidence from errors in variables

Optimally weighting higher-moment instruments to deal with measurement errors in financial return models

“…More precisely, we propose a new weighting of two well-known cumulant instruments originally designed to tackle errors-in-variables, which are the Durbin (1954) and Pal (1980) estimators, and use it as an input to the two-stage least squares (TSLS) and the generalized method of moments (GMM) estimations. Our new optimal instruments are in line with the works of Fuller (1987), Dagenais and Dagenais (1997), Cragg (1997), Lewbel (1997), Coën and Racicot (2007) and Meng et al (2011). It is well-known that the Durbin and Pal's instruments lack robustness (Cheng and Van Ness, 1999) and they thus tend to be neglected by the academics.…”

“…To build this test, we rely on the Hausman (Hausman, 1978;McKinnon, 1992;Coën and Racicot, 2007) artificial regression, as given by (13), which we write as:…”

Dynamic Hedge Fund Style Analysis With Errors‐in‐variables

“…We use the method developed by Dagenais and Dagenais (1997) and applied by Coën and Racicot (2007) and Carmichael and Coën (2008), thereby creating new regressors that account for the estimated measurement errors using the higher moments, that is, the (cross) skewness and the (cross) kurtosis. To compute the EIV series corresponding to each selected benchmark, we use the following and we estimate k (artificial) OLS regressions : 8 with where n is the number of observations; i is a ( n × 1) vector where the elements are all one; I n and I k are identity matrices of order n and k , respectively; F denotes a ( n × k ) matrix containing the k selected benchmarks; * is the Hadamard element‐by‐element matrix multiplication operator; the matrix f stands for the matrix F calculated in mean deviation; is a ( n × k ) matrix containing estimators of the true benchmarks; and is a ( n × k ) matrix standing for the estimated matrix of error terms (estimates of EIV).…”

On Optimal Instrumental Variables Generators, with an Application to Hedge Fund Returns

“…The originality of this test lays in the choice of new instruments based on cumulants, which were introduced only recently in the literature of risk. We relate this financial literature to the econometric works of Dagenais and Dagenais (1997) and later generalized to financial applications by Racicot (2003) and Coën and Racicot (2007). These researchers propose cumulants of endogenous variables of a model as optimal instruments to discard specification errors.…”