The long-run excess optimal power utility of an informed investor and its approximation

We derive the mean, variances and variance bounds of optimal portfolios of informed and uninformed investors having power preference as presented in Buckley et al. (2012). In contrast, we give direct (non‐log‐linear) alternative representations of the optimal expected utilities and excess optimal utility of the informed investor in the long‐run. We also present a new approximation for the excess optimal utility of the informed investor when the relative risk aversion is close to 1. Our approximation of the excess utility is slightly larger but nests that which is presented in prior studies.