Volume 3, No. 4, Fourth Quarter 2005

Revisiting the Slope of the Credit Curve

by: David Lando and Allan Mortensen

The term structure of interest rates contains information about the market's expectations of the direction of future interest rates. Similarly, the term structure of credit spreads contains information about the market's perception of future credit spreads. The term structure of credit spreads is closely linked with conditional default probabilities and this link suggests a downward sloping term structure of credit spreads for high risk issuers, whose default probability conditional on survival is likely to decrease. This paper shows that for sufficiently low credit quality, as defined by the level of credit spreads, this holds true most of the time when spreads are taken from credit default swap (CDS) markets. We also discuss why CDS markets give a better way of analyzing this problem than bond price data.

Default Correlation in Reduced-Form Models

by: Fan Yu

Reduced-form models have proven to be a useful tool for analyzing the dynamics of credit spreads. However, some have recently questioned their ability to match the level of empirical default correlation. The key concern appears to be the assumption that defaults are independent conditional on the state variables driving the default intensity. In this paper, I use a "thought experiment" as well as numerical examples calibrated to recent studies to show that the model-implied default correlation can be quite sensitive to the common factor structure imposed on the default intensity. Therefore, the "inability" of reduced-form models to generate sufficient default correlation has more to do with a restrictive common factor structure than the assumption of conditional independence.

Reduced Form vs. Structural Models of Credit Risk: A Case Study of Three Models

by: Navneet Arora, Jeffrey R. Bohn and Fanlin Zhu

In this paper, we empirically compare two structural models (basic Merton and Vasicek- Kealhofer (VK)) and one reduced-form model (Hull-White (HW)) of credit risk. We propose here that two useful purposes for credit models are default discrimination and relative value analysis. We test the ability of the Merton and VK models to discriminate defaulters from non-defaulters based on default probabilities generated from information in the equity market. We test the ability of the HW model to discriminate defaulters from non-defaulters based on default probabilities generated from information in the bond market. We find the VK and the HW models exhibit comparable accuracy ratios as well as substantially outperform the simple Merton model. We also test the ability of each model to predict spreads in the credit default swap (CDS) market as an indication of each model's strength as a relative value analysis tool. We find the VK model tends to do the best across the full sample and relative sub-samples except for cases where an issuer has many bonds in the market. In this case, the HW model tends to do the best. The empirical evidence will assist market participants in determining which model is most useful based on their purpose in hand. On the structural side, a basic Merton model is not good enough; appropriate modifications to the framework make a difference. On the reduced-form side, the quality and quantity of data make a difference; many traded issuers will not be well modeled in this way unless they issue more traded debt. In addition, bond spreads at shorter tenors (less than two years) tend to be less correlated with CDS spreads. This makes accurate calibration of the term-structure of credit risk difficult from bond data.

Decomposing and Managing Multivariate Risks: The Case of Variable Annuities

by: Thomas S. Y. Ho and Blessing Mudavanhu

The market of variable annuities has grown tremendously in recent years and has become a significant part of our capital markets. These equity and interest rate structured products offer a broad range of guarantees, whose risks are typically borne by the insurers' balance sheets. The limited risk capital of the life insurance industry may constrain the future growth of the market, and therefore the management of the risk of these guarantees is an urgent problem to address. In this paper, we apply a decomposition methodology to identify the risks of these guarantees. We then discuss the hedging strategies in managing them within the context of an investment process. Finally, we discuss the broad applications of the methodology.

Great Moments in Financial Economics: IV. The Fundamental Theorem (Part I)

by: Mark Rubinstein

This is the fourth in a series of articles in this Journal examining the historical origins of key ideas in the history of financial economics. The fundamental theorem asserts: there are no arbitrage opportunities if and only if state-prices exist. Like Newton's laws of motion, though highly abstract, it underlies the most important results in financial economics. The paper starts with some necessary background, explaining the related trio of ideas, subjective probabilities, risk-neutral probabilities and state-prices. Our search for the origins of the concept of state-prices will take us back several centuries to some work of Edmund Halley and Christiaan Huygens, who were financial economists on the side. In a Great Moment in the history of financial economics in 1953, the first clear and general application of state-prices to economics appears in the work of Kenneth Arrow. Less well known is some early important commentary by the economist Jacques Dreze. In the middle 1970's Mark Rubinstein and Stephen Ross may have been the first financial economists to appreciate the link between arbitrage and state-prices in incomplete markets, with the first completely clear statement and proof of the theorem provided by Ross. I then show how starting with the theorem, the important results of asset price theory (in particular, the CAPM) can be derived.

An extension of the fundamental theorem which anticipates modern option pricing will be discussed in Part II of this article which will appear in the next issue of the Journal.

Quiz for Fed Candidates

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.

Freakonomics

by: Steven D. Levitt and Stephen J. Dubner • reviewed by: Tim Adler

The Future for Investors: Why the Tried and True Triumph over the Bold and the New

by: Jeremy J. Siegel • reviewed by: Bruce Grantier

“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.

Answers to Quiz for Fed Candidates

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.

Practitioner’s Digest • Vol. 3, No. 4

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.