An Integrated Model for Liquidity Management and Short-Term Asset Allocation in Commercial Banks

Abstract

This work develops an integrated model for optimal asset allocation in commercial banks that incorporates uncertain liquidity constraints that are currently ignored by RAROC and EVA models. While the economic profit accounts for the opportunity cost of risky assets, what may even incorporate a market liquidity premium, it neglects the risk of failure due to the lack of sufficient funds to cope with unexpected cash demands arising from bank runs, drawdowns, or market, credit and operational losses, what may happen along with credit rationing episodes or systemic level dry ups. Given a liquidity constraint that can incorporate these factors, there is a failure probability that the constraint will not hold, resulting in a value loss for the bank, represented by a stochastic failure loss. By assuming that bankers are risk neutral in their decision about the size of the liquidity cushion, the economic profit less the possible losses due to the lack of liquidity is optimized, resulting in a short-term asset allocation model that integrates market, credit and operational risks in the liquidity management of banks. Even though a general approach is suggested through simulation, I provide a closed form solution for the failure probability, under some simplifying assumptions, that may be useful for research and supervision purposes as an indicator of the liquidity management adequacy in the banking system. I also suggest an extreme value theory approach for the estimation of the expected loss, departing from other liquidity management models that use a penalty rate over the demand of cash that exceeds the availability of liquid resources. The model was applied to Brazilian banks data resulting in gains over the optimization without liquidity considerations that are robust under several tests, giving empirical indications that the model may have a relevant impact on the value creation in banks.

Keywords: Liquidity risk, liquidity management, asset allocation, RAROC, EVA

JEL Classification: G21, G32