Volume 2, No. 2, Second Quarter 2004

Practitioner’s Digest • Vol. 2, No. 2

The “Practitioners Digest” emphasizes the practical significance of manuscripts featured in the “Insights” and “Articles” sections of the journal. Readers who are interested in extracting the practical value of an article, or who are simply looking for a summary, may look to this section.

Predictions of Default Probabilities in Structural Models of Debt

by: Hayne E. Leland

This paper examines default probabilities predicted by alternative "structural" models of risky corporate debt. We focus on default probabilities rather than credit spreads because (i) they are not affected by additional market factors such as liquidity and tax differences; and (ii) prediction of the relative likelihood of default is often stated as the objective of bond ratings. We have three objectives:
(1) To distinguish "exogenous default" from "endogenous default" models
(2) To compare these models' predictions of default probabilities, given common inputs
(3) To examine how well these models capture actual average default frequencies, as reflected in Moody's (2001) corporate bond default data 1970-2000.
We find that endogenous and exogenous default boundary models fit observed default frequencies very well for horizons 5 years and longer, for both investment grade and non-investment grade ratings. Shorter-term default frequencies tend to be underestimated. This suggests that a jump component should be included in asset value dynamics.
Both types of structural models fit available default data equally well. But the models make different predictions about how default probabilities and recovery rates change with changes in debt maturity or asset volatility. Further data and testing will be needed to test these differences. Finally, we compare and contrast these structural models' default predictions with a simplified version of the widely-used Moody's-KMV "distance to default" model described in Crosbie and Bohn (2002).

Structural Versus Reduced Form Models: A New Information Based Perspective

by: Robert A. Jarrow and Philip Protter

This paper compares structural versus reduced form credit risk models from an information based perspective. We show that the difference between these two models types can be characterized in terms of the information assumed known by the modeler. Structural models assure that the modeler has the same information set as the firm's manager - complete knowledge of all the firm's assets and liabilities. In most situations, this knowledge leads to predictable default time. In contracts, reduced form models assume that the modeler has the same information set as the market - incomplete knowledge of the firm's condition. In most cases, the imperfect knowledge leads to an inaccessible default time. As such, we argue that the key distinction between structural and reduced form models is not whether the default is predictable or inaccessible, but whether the information set is observed by the market or not. Consequently, for pricing and hedging, reduced form models are the preferred methodology.

Non-Parametric Analysis of Rating Transition and Default Data

by: Peter Fledelius, David Lando and Jens Perch Nielsen

Non-parametric analysis of rating transition intensities is a powerful way of visualizing such effects and is therefore useful both for quickly understanding the behavior of a rating system and for exploring data before setting up a full statistical model. In this paper we illustrate the use of non-parametric and smoothing methods for analyzing rating transitions by showing how the time spent in a particular rating class and the direction of the move into this class influence transition intensities away from the class.

Correlated Default Processes: A Criterion-Based Copula Approach

by: Robert A. Jarrow and Philip Protter

Modeling correlated default risk is a new phenomenon currently sweeping through the credit markets. In this paper, we develop a methodology to model, simulate and assess the joint default process of hundreds of issuers. Our study is based on a data set of default probabilities supplied by Moody's Risk Management Services. We undertake an empirical examination of the joint stochastic process of default risk over the period of 1987-2000 using copula functions. To determine the appropriate choice of the joint default process, we propose a new metric. This metric accounts for different aspects of default correction, namely (i) level, (ii) asymmetry and (iii) tail-dependence and extreme behavior. Our model, based on estimating a joint system of over 600 issuers, is designed to replicate the empirical joint distribution of defaults. A comparison of a jump model and a regime-switching model shows that the latter provides a better representation of the properties of correlated default. We also find that the skewed double-exponential distribution is the best choice for the marginal distribution of each issuer's hazard rate process, and combines well with the normal, Gumbel, Clayton and students copulas in the joint dependence relationship amongst issuers. As a complement to the methodological innovation, we show that (a) appropriate choices of marginal distributions and copulas are essential in modeling correlated default, (b) accounting for regimes is an important aspect of joint specifications of default risk, and (c) misspecification of credit portfolio risk can occur easily if joint distributions are inappropriately chosen. The empirical evidence suggests that improvements are indeed possible over the standard Gaussian copula used in practice.

Fiduciary Funds

by: Jack L. Treynor

“Case Studies” presents a case pertinent to contemporary issues and events in investment management. Insightful and provocative questions are posed at the end of each case to challenge the reader. Each case is an invitation to the critical thinking and pragmatic problem solving that are so fundamental to the practice of investment management.

Private Equity Returns

by: Robert J. Hendershott

“Surveys& Crossovers” This section provides surveys of the literature in investment management or short papers exemplifying advances in finance that arise from the confluence with other fields. This section acknowledges current trends in technology, and the cross-disciplinary nature of the investment management business, while directing the reader to interesting and important recent work.

The Bond King: Investment Secrets From Pimco's Bill Gross

by: Timothy Middleton • reviewed by: Bruce Grantier

Portfolio Theory and Performance Analysis

by: Noel Amenc and Veronique Le Sourd • reviewed by: Craig W. French

“Book Reviews” identifies important, and often popular, new books from a wide range of investment topics. Beyond providing a summary and review of the content and style of the books, “Book Reviews” seeks to contribute to a conscious, critical, and informed approach to investment literature.

Valuing High Yield Bonds: A Business Modeling Approach

by: Thomas S. Y. Ho and Sang Bin Lee

This paper proposes a valuation model of a bond with default risk. Extending from the Brennan and Schwartz real option model of a firm, the paper treats the firmas a contingent claim on the business risk. This paper introduces the “primitive firm,” which enables us to value firms with operating leverage relative to a firm without operating leverage. This paper emphasizes the business model of the firm, relating the business risk to the firm’s uncertain cash flow and its assets and liabilities. In so doing, the model can relate the financial statements to the risk and the value of the firm. The paper then uses Merton’s structural model approach to determine the bond value. This model considers the fixed operating costs as payments of a “perpetual debt,” and the financial debt obligations are junior to the operating costs. Using the structural model framework, we relative value the bond to the observed firm’s market capitalization, and provide a model that is empirically testable. We also show that this approach can better explain some of the high yield bond behavior. In sum, this model extends the valuation of high yield bonds to incorporate the business models of the firms and endogenizes the firm value stochastic process, which is a key element in high yield valuation, in practice.We have shown that in relating the firm’s business model to the firm value, the resulting firm value stochastic process affects the bond value significantly.