Working Papers

• Shrinkage Alignment in High-Dimensional Portfolios Last revised Nov 2025
  with Barry (Shikun) Ke
  SSRN
  Abstract

  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.

• A Financial Brain Scan of the LLM Last revised Aug 2025
  with Hui Chen, Antoine Didisheim, Luciano Somoza, and Hanqing Tian
  SSRN
  Abstract

  Emerging techniques in computer science make it possible to "brain scan" large language models (LLMs), identify the plain-English concepts that guide their reasoning, and steer them while holding other factors constant. We show that this approach can map LLM-generated economic forecasts to concepts such as sentiment, technical analysis, and timing, and compute their relative importance without reducing performance. We also show that models can be steered to be more or less risk-averse, optimistic, or pessimistic, which allows researchers to correct or simulate biases. The method is transparent, lightweight, and replicable for empirical research in the social sciences.

• Universal Portfolio Shrinkage Last revised Apr 2025
  with Bryan Kelly, Semyon Malamud, and Fabio Trojani
  R&R — Review of Financial Studies SSRN
  Abstract

  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.

Work in Progress

• Complex Rational Expectations Equilibria (CREE)
  with Bryan Kelly and Semyon Malamud
  Abstract

  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.