Default clustering in large portfolios: Typical events

We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to all firms, and past defaults. We prove a law of large numbers for the default rate in the pool, which describes the "typical" behavior of defaults.Comment: Published in at http://dx.doi.org/10.1214/12-AAP845 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Macroeconomic Effects of Corporate Default Crises: A Long-Term Perspective

Using an extensive new data set on corporate bond defaults in the U.S. from 1866 to 2010, we study the macroeconomic effects of bond market crises and contrast them with those resulting from banking crises. During the past 150 years, the U.S. has experienced many severe corporate default crises in which 20 to 50 percent of all corporate bonds defaulted. Although the total par amount of corporate bonds has often rivaled the amount of bank loans outstanding, we find that corporate default crises have far fewer real effects than do banking crises. These results provide empirical support for current theories that emphasize the unique role that banks and the credit and collateral channels play in amplifying macroeconomic shocks.

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 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

Optimal Credit Swap Portfolios

This paper formulates and solves the selection problem for a portfolio of credit swaps. The problem is cast as a goal program that entails a constrained optimization of preference-weighted moments of the portfolio value at the investment horizon. The portfolio value takes account of the exact timing of protection premium and default loss payments, as well as any mark-to-market profits and losses realized at the horizon. The constraints address collateral and solvency requirements, initial capital, position limits, and other trading constraints that credit swap investors often face in practice. The multimoment formulation accommodates the complex distribution of the portfolio value, which is a nested expectation under risk-neutral and actual probabilities. It also generates computational tractability. Numerical results illustrate the features of optimal portfolios. In particular, we find that credit swap investment constraints can have a significant impact on optimal portfolios, even for simple investment objectives. Our problem formulation and solution approach extend to corporate bond portfolios and mixed portfolios of corporate bonds and credit derivatives