SDF-Based Estimation of Linear Factor Models with Alternative Loss Functions

Abstract

Hansen and Jagannathan (1997) introduce a measure of model misspeci cation which is based on the L2-norm and which has been wildly used in recent years in order to estimate the parameters of linear factor models. Given the observed asymmetry and excess kurtosis of nancial returns, this paper introduces two alternative estimation methods which follow the same approach but replace its loss function. The rst one is based on the absolute value of the corresponding deviations while the second one uses a gain-loss ratio-based loss function. We show how these two estimation methods can be implemented by means of simple linear programming and Monte Carlo simulations are undertaken to assess the relative performance of all three methods under varying distributional assumptions. Our results show a promising behavior of the gainloss ratio-based estimates and they also emphasize the important gains that may be accomplished by using positivity constraints on the model’s associated stochastic discount factor. JEL classi cation: C13; C15; C63; G12 Keywords: Stochastic discount factor; Linear factor models; L1-norm based estimates; Hansen-Jagannathan measure; Gain-loss ratio Department of Economics and Management, NFH, University of Tromso, N-9037 Tromso, Norway. E-mail: Inaki.Rodriguez@nfh.uit.no. I would like to thank the Wallander Foundation for nancial support. I am also grateful to Enrique Sentana, Francisco Penaranda and seminar participants at the Universidad de Navarra and the Instituto de Empresa. Some of the issues brought up in this paper were partially dealt with in an unpublished manuscript by Clapham, Longarela and Nilsson (2005). The usual caveat applies.