Optimal stress tests and cash-in-the-market pricing

Abstract

After the global financial crisis, stress tests have become a common tool for regulators to maintain financial stability. However, the welfare implications of stress tests remain unclear. This paper examines the optimal design of stress tests using Bayesian Persuasion within a fundamental bank run framework to address how informative bank stress tests should be. Our model indicates that the optimal disclosure policy depends on the amount of cash in the market during a liquidity shortage. When there is a bank run and insufficient cash in the market to pay the fair value of a risky asset, there is cash-in-the-market pricing. If both market liquidity and market prior belief are low, then there is cash-in-the-market pricing in the entire bank run region. The regulator can improve social welfare in this region by conducting stress tests to avoid costly bank runs. Partially informative stress test design is optimal: it assigns passing grades to all the good banks but assigns failing grades to only some bad banks to ensure the credibility of the test. As prior beliefs about the market increase, the optimal stress test fails fewer bad banks. Put differently, the optimal partial information test becomes less informative as market prior beliefs strengthen. When market liquidity is high but market confidence is low, then there is cash-in-the-market pricing in the upper part of the bank run region. The regulator can also improve social welfare in this region with weakly optimal, fully informative tests. Full information stress tests are optimal in this region because not all runs are costly when market liquidity is high. Non-informative stress tests are optimal in the lower part of the bank-run region where the risky asset's price is determined at fair value. Moreover, it is demonstrated that non-informative stress tests are optimal in the no bank run region for both high and low liquidity levels.