Complex Modern Portfolio Theory -- by Oliver Hellum, Theis I. Jensen, Bryan T. Kelly, Semyon Malamud

The literature has long wrestled with the practical usefulness of Modern Portfolio Theory (MPT), and extensive evidence shows its performance decreases rapidly with the number of assets (N ). We present several new and counterintuitive facts about MPT. Most importantly, the performance of MPT in fact increases with N once the number of assets exceeds the number of training observations (T ). This finding holds in a variety of settings: in conjunction with popular portfolio regularization methods, in a variety of asset universes, and when T is large or small.