Conference Agenda

We study three fundamental data challenges in empirical asset pricing: missing observations, infrequent measurements, and inherent noise in financial information. These challenges make firm characteristics uncertain inputs rather than fixed conditioning variables. We develop a Bayesian tensor model that treats characteristics as latent, exploits cross-sectional, characteristic-level, and time-series dependence, and generates posterior panels for missing and stale values. In global equities, accounting for characteristic uncertainty leaves systematic factor portfolios nearly unchanged, but substantially reduces the number of statistically significant residual alphas and attenuates arbitrage-portfolio Sharpe ratios. Averaging arbitrage portfolio weights across imputations yields more stable performance, especially internationally.

Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG), quantifying the unavoidable discrepancy between a model’s empirical fit and the population benchmark. Recovering the true population R2 , therefore, requires correcting observed predictive performance by this bound. Using a broad set of variables, including excess returns, yields, credit spreads, and valuation ratios, we find that the implied LLGs are large. This indicates that standard ML approaches can substantially understate true predictability in financial data. We also derive LLG-based refinements to the classic Hansen and Jagannathan (1991) bounds, analyze implications for parameter learning in general-equilibrium settings, and show that the LLG provides a natural mechanism for generating excess volatility.

Kelly, Malamud and Zhou (2024, KMZ) argue that simple models severely understate return predictability relative to complex ones in which the number of predictors vastly exceeds the number of training window observations. KMZ prove that under certain conditions expected out-of-sample forecast accuracy and portfolio performance are strictly increasing in model complexity. They call this the ‘Virtue of Complexity’ (VoC). I show that KMZ’s empirical VoC results are the consequence of two implementation choices: (1) a zero-intercept restriction imposed on the prediction models, and (2) an unconventional aggregation scheme used to construct performance measures for the machine learning models. Both of these choices artificially worsen the performance of KMZ’s ‘simple’ models and lead to absurd portfolio performance outcomes such as negative Sharpe ratios with corresponding positive expected returns. Using a simulation experiment, I show that equivalent VoC results can be obtained from artificially generated and thus unpredictable i.i.d. returns data. Overall, the performance of KMZ’s complex models is disappointing. Standard linear models estimated with an intercept term generate Sharpe ratios that are up to 40% larger than from KMZ’s complex models.