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We propose a joint distribution that decomposes asset returns into two independent components: an elliptical innovation (Gaussian) and a systematic non-elliptical latent process. The paper provides a tractable approach to estimate the underlying parameters and, hence, the assets' exposures to the latent non-elliptical factor. Additionally, the framework incorporates higher-order moments, such as skewness and kurtosis, for portfolio selection. Taking into account estimation risk, we investigate the economic contribution of the non-elliptical term. Overall, we find weak empirical evidence to support the inclusion of the non-elliptical term and, hence, the higher-order comoments. Nonetheless, our findings support the mean-variance (MV) decision rule that incorporates the elliptical term alone. Excluding the non-elliptical term results in more robust mean-variance estimates and, thus, enhanced out-of-sample performance. This evidence is significant among stocks that exhibit a strong deviation from the Gaussian property. Moreover, it is most pronounced during market turmoils, when exposures to the latent factor are highest. Overall, our paper advocates for shrinking away from the non-elliptical term, which is associated with higher estimation risk. |
