Some properties of the maximum loss on loan portfolios

Estimating losses on portfolios both theoretically and technically is an interesting and hard issue because the comprehensive formulation of the problem results in a complicated task to solve. Simulation algorithms are among the most popular, currently available procedures used by financial institutions and striving to obtain closed form formulas to see the structure of the maximum loss requires the exploration of additional properties of the maximum loss problem. We prove that within a given Mahalanobis distance, under assumptions, the maximum loss on a loan portfolio is located at the frontier of this distance, and this property allow us to set up closed forms to define efficient initial solutions. The performance of these initial solutions is compared to the optimum solution when we have two variables indicating the state of the macro economy. The supposed advantage of this approach would appear in case of large number of macro variables, but this requires further research and investigation. We found that the initial solutions generated by the compact forms underestimates losses only with insignificant manner compared to the optimum solution for a particular set of maximum loss problems.