Large-Scale Loan Portfolio Selection

Operations Research, 64, 1239-1255, 2016

41 Pages Posted: 8 Aug 2015 Last revised: 3 Aug 2017

See all articles by Justin Sirignano

Justin Sirignano

Imperial College London - Department of Mathematics; University of Illinois at Urbana-Champaign

Gerry Tsoukalas

University of Pennsylvania - The Wharton School

Kay Giesecke

Stanford University - Management Science & Engineering

Date Written: May 28, 2016

Abstract

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 mortgage- and 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.

Keywords: loan portfolio optimization, loan, mortgage, loan portfolio, portfolio optimization, default, prepayment, machine learning, law of large numbers, central limit theorem

Suggested Citation

Sirignano, Justin and Tsoukalas, Gerry and Giesecke, Kay, Large-Scale Loan Portfolio Selection (May 28, 2016). Operations Research, 64, 1239-1255, 2016. Available at SSRN: https://ssrn.com/abstract=2641301 or http://dx.doi.org/10.2139/ssrn.2641301

Justin Sirignano (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

HOME PAGE: http://jasirign.github.io

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Gerry Tsoukalas

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

Kay Giesecke

Stanford University - Management Science & Engineering ( email )

475 Via Ortega
Stanford, CA 94305
United States
(650) 723 9265 (Phone)
(650) 723 1614 (Fax)

HOME PAGE: http://https://giesecke.people.stanford.edu

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