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Welfare implications of bank valuation disagreement

by Dr Hormoz Ramian, Research Associate, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance

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Regulatory interventions have always been ensued by heated debates. In the years after the financial crisis reached its darkest moment, academic literature and high legislative chambers were inundated by discussions related to risk-based capital requirements. Opponents often have expressed dissatisfaction against the intervention arguing that capital holding above the laissez-faire outcome is expensive to the banking institutions leading to lower lending and ultimately suppressed economic growth. Proponents of the regulation have argued that fragility of the banking sector, that is associated with a significant economic cost to the society, rationalises the intervention.

Despite prolonged arguments presented by the opposing sides, these debates rarely reached an agreeable conclusion. An important but often ignored reason to the disagreement was that the arguments emanated from incomparable bases. More specifically, the opponents’ view presented by the banking institutions weighed heavily on the cost of equity as the central reason to rail against capital holdings above the laissez-faire outcome (Basel Committee on Banking Supervision Reports 2014, 2016, Acharya et al, 2017). Ignoring the underlying merits behind their argument for the moment, their perspective focused on the role of the asset prices as the main reason to advocate for capital deregulation. This stance, however, was not readily reconcilable with the proponents’ social perspective whose arguments mainly built on a welfare analysis that is concerned with the negative externalities associated with costly bank failure (Allen et al 2011, 2015, and Gersbach et al, 2017).

Much of the discussions among the academic and legislative literature on this context has understandably been devoted to the welfare implications of bank failure. For instance, James (1991) provides a comprehensive survey on loss given default across financial and non-financial sectors showing that the ex-post asset recovery rate may fall to 70 oer cent per dollar. Nonetheless, the opponents’ view on the cost of capital has remained a consistent defence that has languished further arguments to increase capital holding above Basel III. Recent empirical studies provide evidence that even in the presence of capital buffers in addition to the risk-based capital requirement, the banking institutions remain significantly undercapitalised (Piskorski et al, 2020).

Lack of a rigorous quantitative basis to evaluate the cost of capital for the banking institutions at an aggregate level is among the core reasons why the proponents have failed to discredit the merits behind capital deregulation. The methodological framework in my research first develops a foundation to establish a realistic valuation of the bank capital in a general equilibrium under aggregate uncertainty setting. This framework simultaneously integrates the asset pricing and banking regulation disciplines to provide a mapping between the cost of capital and welfare implications of bank failure. This salient connection serves as a solution to reconcile the two counterarguments in favour and against bank capital holding.

A comprehensive capital regulation that enhances the welfare considers three simple components: (i) how is the bank funded? (ii) what is the risk profile of the bank’s assets? (iii) what is the valuation of bank net worth? Existing studies focusing on bank funding show that government-guarantees provide welfare gains by preventing self-fulfilling runs on bank debt, even if not originally justified by fundamentals (Diamond–Dybvig, 1983). Nonetheless, government-guarantees break the link between the cost of debt and borrower’s default risk and lead to the under-capitalisation of the banking system. This gives rise to an alternative distortion generated by more frequent bank failure and motivates capital regulation which provides gains by lowering socially undesirable defaults. However, studies that concentrate on the liabilities provide limited predictions about the importance of bank assets composition. My research finds that the effectiveness of optimal capital regulation depends on the assets side of the bank balance sheet, particularly when the monetary policy targets reserves management. A large strand of literature focusing on the assets side of the bank balance sheet shows that conditioning the risk profile to capital provides welfare gains. However, this literature considers that households as the ultimate providers of financing, in the form of debt or equity, play a limited role or that the supply of financing is fixed. The finding in this context uncover that households’ optimal consumption-saving behaviour has important implications for the equilibrium cost of debt that is a determinant of the banking sector’s default risk. This equilibrium mechanism predicts that as the cost of debt falls, capital constraint becomes effectively overburdening and hence socially costly.

These shortcomings provide motivation to raise the following two questions: First, what is the optimal capital regulation of the banking system in an environment where the cost of financing (in the form of debt or equity) and risk profile of the asset side arise endogenously? Second, how does the effectiveness of this optimal capital regulation depend on the interest-on-excess-reserves (IOER) that is decided separately by the monetary authority? I address these questions by developing a general equilibrium model in which banks finance themselves by accepting deposits and raising equity from households, and invest their funds in excess reserves and loans subject to non-diversifiable risk.

The analysis in my research takes IOER as a given policy and shows that the optimal risk-weighted capital requirement offers welfare gains by lowering the likelihood of bank failure and its associated distortions that are ultimately borne by society (Admati and Hellwig, 2014). Nonetheless, the general equilibrium provides an additional important prediction. When the bank is required to raise more capital to satisfy the capital constraint, its demand for debt financing falls. This channel leads to a lower equilibrium deposit rate. Given any lending level, lower interest expenses expand the bank’s ability to meet its debt liabilities and enhance the bank’s solvency. The optimal risk-weighted capital regulation, even in general equilibrium, fails to consider this effect and hence becomes socially costly.

I show that when IOER is above the zero bound, a marginal decrease in this rate is accompanied by a proportional decrease in the equilibrium deposit rate. Because the proportion of deposits in liabilities always exceeds that of the reserves on the asset side of the balance sheet, lower IOER leads to a faster fall in interest expenses than interest incomes. As a result, the social cost of the optimal capital constraint, which is decided in isolation of the IOER policy, increases as IOER falls towards the zero bound. This finding is an important motivation for a jointly decided capital regulation and IOER. Particularly, a lower IOER that is accompanied by a looser capital constraint is able to expand the credit flow to the real economy, while the bank’s default likelihood remains constant.

This general equilibrium framework provides a secondary prediction: the relationship between the optimal capital regulation and IOER reverses when IOER becomes very low or falls below zero. This finding is important to effective policy analysis in the current era with low or negative interest rate environment. The finding of this research shows that any further reduction in this territory is accompanied by a nonresponsive equilibrium deposit rate because depositors always require strictly positive compensations for their time preference to forgo consumption. This nonproportional transmission mechanism from IOER to deposit rate indicates that the bank’s interest incomes from reserves fall faster than its interest expenses on deposits. Given any lending level, the bank’s solvency worsens, nonetheless, the capital regulation fails to consider this effect. An interactive policy initiative provides social value when a falling IOER, below zero bound, is accompanied by a stricter capital constraint.