Reduced Form Capital Optimization

We formulate banks’ capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This reduced form formulation admits an analytical solution, to the optimal leveraged balance sheet (LBS) and risk weighted assets (RWA) target of banks’ business units for achieving the best return on capital.