We study how shrinkage affects portfolio efficiency when the number of assets approaches or exceeds the sample size. Standard methods, such as ridge, impose uniform shrinkage, treating all assets as ex-ante identical and creating inefficiency when profitability is heterogeneous. Empirically, this “one-size-fits-all’’ design produces a hump-shaped relationship between model complexity and out-of-sample Sharpe ratios: adding assets can paradoxically reduce performance. We introduce shrinkage alignment, showing that efficiency requires matching shrinkage strength to each asset’s true profitability. Building on this insight, we propose Sharpe Ratio Shrinkage (SRS)—a data-driven approach that aligns shrinkage intensity with empirical Sharpe ratios. SRS outperforms conventional methods under profitability heterogeneity and restores the virtue of complexity in high-dimensional portfolio construction. 

We introduce a nonlinear covariance shrinkage method for building optimal portfolios. Our universal portfolio shrinkage approximator (UPSA) is given in closed form, is cheap to implement, and improves upon existing shrinkage methods. Rather than annihilating low-variance principal components of returns, UPSA instead reweights components to explicitly optimize expected out-of-sample portfolio performance. We demonstrate robust empirical improvements over alternative shrinkage methods in the literature.

 What happens in equilibrium when agents rely on Machine Learning? We introduce a novel analytical framework to solve equilibria in which rational agents employ overparameterized models. Our closed-form solution reveals that complexity resolves the Grossman-Stiglitz paradox, incentivizes information acquisition, and generates return predictability. This highlights an equilibrium “virtue of complexity”: larger models consistently outperform smaller ones out-of-sample. Strikingly, even with rational learning, price informativeness and return predictability may not improve over time.