Abstract: Recent financial crises have focused attention on measuring bank health, interconnectedness, and systemic risk. In this paper, we propose a novel methodology to estimate the portfolio composition of banks as a function of daily stock returns. Building on a model where individual bank balance sheets connect through common holdings, we derive and solve a constrained semi-non-negative matrix factorization problem where the rows (corresponding to banks) of one latent matrix factor (representing asset holdings) are subject to probability constraints. While banks report their assets to regulators or the public at relatively low frequencies (e.g., quarterly or annually), estimating our factorization over a rolling window allows analysts to derive daily estimates of portfolio concentration in each bank, a measure of diversification, and common holdings across banks, a measure of market susceptibility to propagating shocks. We validate our estimates of asset holdings by showing they match real balance sheet data reported in regulatory filings. We also demonstrate the utility for prudential supervision and risk management from our approach: our two risk measures forecast other systemic risk and macroeconomic indicators and identify troubled banks well before the spate of bank failures in the first quarter of 2023. We also contribute methodologically by utilizing a Markov chain Monte Carlo estimator that resolves the well-known issues of scale and rotational invariance in non-negative matrix factorization models.

Short Bio: Shawn Mankad is an assistant professor of analytics at NCSU Poole College of Management. His research focuses on developing and applying statistical methods for addressing business, economic, and policy issues. He specializes in using text documents to explain and predict economic variables, and in the modeling of networks to characterize network structure evolution over time. Prior to NCSU, Prof. Mankad held a faculty position at Cornell University and was a visiting scholar at the Federal Reserve Bank of Philadelphia. His undergraduate degree is from Carnegie Mellon University in mathematics, and he received his PhD in statistics from the University of Michigan.