Whence LASSO? A Rational Interpretation

Abstract

This paper rationalizes the use of LASSO for return predictions based on uncertain fat-tail priors and max-min robust optimization. Our theory excludes heuristic learning or restrictive prior assumptions in the statistical interpretation of LASSO by its inventor Tibshirani (1996). In our setting, agents (arbitrageurs) are uncertain about the scale of fat-tail shocks. In equilibrium, they ignore a range of ambiguous signals and respond linearly to almost unambiguous signals. Using this LASSO equivalent strategy, arbitrageurs amass extra market power which induces a "cartel'" to protect their total profit from being competed away. This result shows a new mechanism for limited arbitrage.

Keywords: LASSO, Fat Tails, Model Risk, Robust Optimization, Limits to Arbitrage

JEL Classification: C44, D81, G12, G14