We relax a number of assumptions in Alexeev and Tapon (2012) in order to account for non-normally distributed, skewed, multi-regime, and leptokurtic asset return distributions. We calibrate a Markov-modulated Levy process model to equity market data to demonstrate the merits of our approach, and show that the calibrated models do a good job of matching the empirical moments. Finally, we argue that much of the related literature on portfolio diversification relies on assumptions that are in tension with certain observable regularities and which, if ignored, may lead to underestimation of risk.