Bank capital allocation under multiple constraints

BIS Working Papers  |  No 666  | 
30 October 2017



We study how different constraints on banks' activities affect the allocation of capital across business units. In particular, we look at the interplay of risk-based and leverage-based constraints on banks' lending and market-making.


The paper underscores that internal capital reallocation should be taken into account when assessing the combined impact of regulation, internal risk management and risk perceptions on banks' behaviour. This is because capital reallocation creates links between seemingly separate business units of a bank holding company. For instance, a change in regulatory standards, a stress test or an actual tightening of financial conditions that directly affects only lending would spill over to market-making.


Our model establishes general patterns for banks' response to higher perceived risk, stricter regulation or more demanding risk management. When financial conditions tighten, capital becomes scarcer and the bank needs to shrink. In the process, capital flows internally to the unit that has become more profitable under the new conditions: the more efficient unit. We derive that larger and less risky units, or those with revenues more sensitive to downsizing, tend to be more efficient.

To show the knock-on effects of capital reallocation, we benchmark the model to data from large US banks. At the benchmark, the market-making unit is more efficient. Thus, market-making attracts capital and lending shrinks, irrespective of whether credit or market risk rises. For credit risk below its benchmark value, tighter leverage constraints may reduce market-making but support lending. These spillovers occur even when business units face independent risks and separate constraints. They result from centralised decision-making within a bank holding company.



Banks allocate capital across business units while facing multiple constraints that may bind contemporaneously or only in future states. When risks rise or risk management strengthens, a bank reallocates capital to the more efficient unit. This unit would have generated higher constraint- and risk-adjusted returns while satisfying a tightened constraint at the old capital allocation. Calibrated to US data, our model reveals that, when credit or market risk increases, market-making attracts capital and lending shrinks. Leverage constraints affect banks only when measured risks are low. At low credit risk, tighter leverage constraints may reduce market-making but support lending.

JEL classification: G21, G28, G3

Keywords: internal capital market, Value-at-Risk, leverage ratio, risk-adjusted return on capital