  The Average Oracle, a simple and very fast covariance filtering method, is
shown to yield superior Sharpe ratios than the current state-of-the-art (and
complex) methods, Dynamic Conditional Covariance coupled to Non-Linear
Shrinkage (DCC+NLS). We pit all the known variants of DCC+NLS (quadratic
shrinkage, gross-leverage or turnover limitations, and factor-augmented NLS)
against the Average Oracle in large-scale randomized experiments. We find
generically that while some variants of DCC+NLS sometimes yield the lowest
average realized volatility, albeit with a small improvement, their excessive
gross leverage and investment concentration, and their 10-time larger turnover
contribute to smaller average portfolio returns, which mechanically result in
smaller realized Sharpe ratios than the Average Oracle. We also provide simple
analytical arguments about the origin of the advantage of the Average Oracle
over NLS in a changing world.
