We argue that active management's popularity is not puzzling despite the industry's poor track record. Our explanation features decreasing returns to scale: As the industry's size increases, every manager's ability to outperform passive benchmarks declines. The poor track record occurred before...

"We analyze the equilibrium size of the active management industry and the role of historical data--how investors use it to decide how much to invest in the industry, and how researchers use it to judge whether the industry's size is reasonable. As the industry's size increases, every manager's...

Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many proposals to address the first question exist already. This paper addresses the second question. We promote a new nonlinear shrinkage estimator of the...

Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how...