Spotlight: Basil Williams

Optimal Stress Tests and Bank Portfolio Choice

Assistant professor Basil Williams

Basil Williams

How can we properly monitor and regulate banks in order to lower the likelihood of bank failure during a crisis? One way of monitoring banks is by performing a stress test, which is a simulation that predicts whether a bank will be able to meet its obligations to creditors in the event of various stressors, such as a changing interest rate or a rise in unemployment. The Dodd-Frank Act requires large financial institutions to conduct stress tests twice per year, once by regulators, and once internally. If banks are found to perform poorly in a stress test, then regulators require them to adjust their capital and liquidity buffers so that they can respond better to stressful scenarios. Because regulators have great flexibility in designing the test, it is crucial to examine how a test might be optimally designed. It might seem that an ideal stress test would give the greatest amount of information about a bank’s ability to pay its investors, so that regulators can respond in an optimal fashion to the bank’s condition.   However, if a solvent bank is temporarily illiquid, revealing too much information may spook investors, causing them to simultaneously demand their deposits, overwhelming the bank’s ability to pay immediately, and thereby making an otherwise viable bank go bankrupt. So it is not clear that a perfectly precise test is optimal. My paper examines the structure of optimal stress tests using a model of bank runs, and shows that (1) in times of low confidence in the banking sector, stress tests which are only partially informative are optimal because they reduce the likelihood of runs, and (2) well designed stress tests may reduce the optimal liquidity buffer of banks and allow banks to offer higher interest rates to depositors. My model assumes that banks hold long term assets which may be liquidated early only at a deep cost. If investors lose confidence in the bank, they may run---i.e., demand immediate withdrawal of their deposits. If the mass of withdrawals overwhelms the bank’s ability to repay, the bank may be forced to liquidate long term assets by selling them at a deep discount. Regulators, however, may partially avoid these liquidation costs by designing a stress test that reveals information in such a way as to reduce the likelihood of runs. So although in practice it may be efficient to let some poorly managed banks fail, the liquidation costs assumed in my model imply that all runs are inefficient, and the regulator’s goal is therefore to minimize the likelihood of runs. In my model, which builds on the setup of Allen and Gale (1998), a set of consumers have money that they would like to invest in a high return long term asset, but they know there is the possibility that they will need the money before the asset matures. They deposit their money with a bank in exchange for (1) a promised interest rate higher than what they could achieve on their own and (2) the right to withdraw their money early if needed. Banks choose the promised interest rate for early and late withdrawers, and fund the interest by investing the deposits into two assets: a safe, liquid, low-return assets, and a risky, illiquid, high-return assets. Banks also choose how much of the safe asset to set aside as a liquidity buffer in case the risky asset is shown to have low value. After depositing their money and observing the banks’ chosen portfolio of assets, depositors learn whether they need their money sooner or later, and they also receive a public signal about the future return of the risky asset. If this signal indicates a low enough future return, then otherwise patient investors run on the bank, which is then forced to perform costly liquidation of all assets. Unlike the model of Allen and Gale (1998), in my model depositors receive only a noisy public signal about the bank’s assets, so that although the signal affects their beliefs about the risky asset’s future return, they are still uncertain about its ultimate value. The remaining uncertainty creates scope for additional disclosure via a stress test, which I formalize using the Bayesian persuasion framework of Kamenica and Gentzkow (2011). Under this framework, stress tests are conceptualized as a distribution of signals, conditional on the true future return of the risky asset. Both the structure and result of the stress tests are public information, and the test is costless to perform, so neither information asymmetries nor auditing costs exist as frictions in the model. Despite the frictionless nature of the tests, my model shows that it may be optimal for the stress test to only partially reveal the quality of the bank’s assets. That is, if the original public signal damages depositor confidence enough to induce them to run, regulators may reduce the likelihood of a run by performing a stress test which only partially resolves depositors’ uncertainty about the quality of the banks’ assets. In particular, it is optimal to design a test that passes all banks holding assets that will give a high payoff in the future, and has some probability of passing banks with assets that give a lower return in the future. To understand the intuition behind this surprising result, recall that the regulator’s goal is to minimize the likelihood of runs in order to avoid the costly early liquidation of long-term assets. To accomplish this, it is necessary to fail only just enough banks to maintain the credibility of the passing grade, so that a passing grade improves confidence sufficiently to prevent a run. I also find that the lower the initial public confidence in the risky assets, the more stringent the optimal stress tests must be. In particular, in times of very low depositor confidence in the bank, bad banks should receive passing grades with less and less likelihood. Intuitively, low public confidence in the banking sector requires a very strong signal of quality in order to prevent runs. The harder a test is to pass, the stronger the signal of quality given by a passing grade, and the resulting improved confidence is then sufficient to prevent runs. My research also examines the relationship between well-designed stress tests and the bank's optimal portfolio and contract, showing that stress tests and liquidity buffers may be seen as policy substitutes for preventing runs. Specifically, because optimal stress tests reduce the likelihood of runs, the need for a liquidity cushion for run prevention is not as high as it would be otherwise. In addition, well-designed stress tests enable banks to offer a higher interest rate to early withdrawers. The reason is that without stress tests, raising the promised deposit return to early withdrawers may raise the probability of runs by making early withdrawal more attractive, whereas optimal stress tests reduce that risk by lowering the likelihood of runs, so the optimal deposit return rises. In summary, the model formally illustrates a less-discussed channel through which stress tests relate to banks: they not only reveal the quality of a bank’s assets, but also affect its viability by influencing the behavior of the bank’s depositors. If stress tests are designed to partially reveal information in an optimal way, runs are less likely to occur. In addition, the model informs policy debates about the optimal liquidity requirements for banks, pointing out that by filling the role of run reduction which liquidity requirements were intended for, well-designed stress tests may allow banks to hold lower liquidity buffers than otherwise.