We examine theoretical and econometric issues in the estimation of risk premia in a linear factor model, when the model is possibly misspecified. Common empirical methodologies can produce very misleading results. With unspanned factors and possible model misspecification, there are problems not just in estimating the risk premia, but even in defining them unambiguously. We show that, for a given set of test assets, the risk premium of an unspanned factor is very sensitive to the choice of other factors in the model. However, the risk premium of the projection of the unspanned factor onto the asset space is robust to the choice of other factors. The problem is greatly exacerbated in the presence of model misspecification, and can occur even when the unspanned components of the factors are very small (relative to the spanned components). These results highlight the importance of using factor-mimicking portfolios, rather than unspanned factors, in estimation of linear factor models.