Large-Scale Loan Portfolio Selection

We consider the problem of optimally selecting a large portfolio of risky loans, such as mortgages, credit cards, auto loans, student loans, or business loans. Examples include loan portfolios held by financial institutions and fixed-income investors as well as pools of loans backing mortgageand asset-backed securities. The size of these portfolios can range from the thousands to even hundreds of thousands. Optimal portfolio selection requires the solution of a high-dimensional nonlinear integer program and is extremely computationally challenging. For larger portfolios, this optimization problem is intractable. We propose an approximate optimization approach that yields an asymptotically optimal portfolio for a broad class of data-driven models of loan delinquency and prepayment. We prove that the asymptotically optimal portfolio converges to the optimal portfolio as the portfolio size grows large. Numerical case studies using actual loan data demonstrate its computational efficiency. The asymptotically optimal portfolio’s computational cost does not increase with the size of the portfolio. It is typically many orders of magnitude faster than nonlinear integer program solvers while also being highly accurate even for moderate-sized portfolios. ∗Sirignano ([email protected]) and Giesecke ([email protected]) are from Stanford University, Management Science and Engineering. Tsoukalas ([email protected]) is from the Wharton School, University of Pennsylvania. The authors would like to thank Pierre Bonami (BONMIN), Nick Sahinidis (BARON) and Jonathan Currie (Opti Toolbox) for their help fine tuning the MINLP solvers used in the numerical studies section. We also thank participants at the IPAM Workshop on New Directions in Financial Mathematics for comments. Tsoukalas is thankful to the Wharton Dean’s Research Fund for a grant that supported this work.