Misunderstanding risk and return?

In a seminal contribution, Campbell (1996) [Campbell, J., 1996, Understanding Risk and Return, Journal of Political Economy 104(2), 298-345] proposed a methodology based on a VAR(1) process to test Merton’s Intertemporal CAPM. Innovations in predictors of portfolio returns are estimated and used as risk factors in an asset pricing model. One key element is the triangularization of the VAR system used to obtain orthogonal innovations. We show that this procedure makes the cross-sectional prices of risk associated with the predictors non identifiable. This is because they depend on the arbitrary ordering of the variables in the VAR. Moreover, since the factors are orthogonal to the market and to one another, the comparison with alternative multi-factor models is problematic. To illustrate, we revisit recent results that allegedly showed that innovations in the predictors drive the two Fama-French factors out in the cross section of portfolio excess returns and concluded that HML and SMB proxy for time-varying investment opportunities. We show that these results are mainly a statistical artifact of the methodology used to obtain orthogonal innovations.