I use the second Hansen and Jagannathan (1997) distance measure (HJD) to examine whether index-based models similar to Cremers, Petajisto, and Zitzewitz (forthcoming) are more reliable benchmark models of expected returns than the Fama and French (1993) and Carhart (1997) models in U.K. stock returns. I use the second HJD as it is important to take account of pricing errors over possible contingent claims when considering benchmark models that are used in fund performance applications (Wang & Zhang, 2012). I find that all of the candidate benchmark models are misspecified. I find that conditional multifactor models provide significant lower second HJD compared to the unconditional factor models. I find that there is nothing to be gained in terms of significant lower second HJD in using the index-based models compared to the conditional Carhart model. My results suggest that among the models I consider, the most reliable models are the conditional Carhart model and the conditional seven-index model of Cremers et al.
- no arbitrage
- index-based models
- benchmark models of expected returns