Efficiency-stability Trade-off in Financial Systems: a multi-objective optimization approach

In this paper, we address the efficiency-stability trade-off in the interbank (IB) market. The decision variable to be chosen by the financial regulator is the net worth-to-IB assets ratio assigned to each bank – the capital requirement (CR) – , aiming at minimizing both the fraction of IB assets lost as a consequence of an exogenous initial shock and the total net worth as a fraction of total IB assets. This framework is applied to a Brazilian data set considering two CR regimes: the homogeneous (same CR for all banks) and the heterogeneous regime (different CRs for each bank). The optimization in the heterogeneous regime is performed through a multi-objective optimization problem (MOP), solved through a multi-objective evolutionary algorithm based on decomposition (MOEA/D). We have found that the heterogeneous regime brings a Pareto gain over the homogeneous one: a smaller level of losses is achieved for the same aggregate CR. In the heterogeneous case, for each level of the initial shock, there is a critical value of aggregate CR below which financial crises become more frequent and more severe. Moreover, the decision variable assigned by different critical Pareto optimal points – i.e., those which generate values of CR close to its critical value – varies significantly. Finally, this variable is smaller and less dispersed for banks with a higher degree (i.e., those with more connections in the IB market, as well as a higher volume of IB assets and liabilities).