Defining, Estimating and Using Credit Term Structures. Part 2: Consistent Risk Measures

November 2004 1 Defining, Estimating and Using Credit Term Structures
Part 2: Consistent Risk Measures In the second part of our series we suggest new definitions of credit bond duration and convexity that remain consistent across all levels of credit quality including deeply distressed bonds and introduce additional risk measures that are consistent with the survival-based valuation framework. We then show how to use these risk measures for the construction of market neutral portfolios. INTRODUCTION This paper continues our investigation of the consistent valuation methodology for credit- risky bonds (see Berd, Mashal, and Wang [2004a], cited hereafter as Part 1). In the previous article we have developed a set of term structures that are estimated using all the bonds of a given issuer (or sector) as a whole, rather than a specific bond of that issuer. In particular, our primary measure, the term structure of survival probabilities, clearly refers to the issuer and not to any particular bond issued by this issuer. However, when considering a particular bond, investors typically ask three questions: • Is this bond rich or cheap compared with other bonds of the same issuer or sector? • How much excess return does this bond provide for taking on the credit risk? • How can we monetize these relative values, once we measure them? The answer to the first question lies in the comparison of the observed bond price with the fair value price given by the fitted issuer credit term structures. The OAS-to-Fit measure, introduced in Part 1, gives an unambiguous and consistent answer to this question, free of biases associated with the term to maturity or level of coupon, which plague the conventional spread measures. The answer to the second question then becomes straightforward, since we have already determined in the previous step the term structure of “fair value” par spreads of the issuer with respect to the underlying credit risk-free market. By adding the consistent issuer- specific and bond-specific spread measures we are able to give a robust definition of a bond spread and sidestep the ambiguities associated with non-par bond excess return estimation.
In order to answer the last question one must devise a recipe for hedging and risk managing credit bonds, which of course requires calculation of various sensitivity measures. Derivation of such measures and in particular the consistent definition of a bond’s duration and convexity, as well as the bond’s sensitivity to hazard rates and recovery values within the survival-based valuation framework are the objectives of the present paper. We will show that the correctly defined duration of credit bonds is often significantly shorter than the widely used modified adjusted duration. This disparity helps explain the fact that high yield bonds do not have quite the same degree of interest rate sensitivity as high grade ones and is especially evident for distressed bonds, for which a 10-year maturity bond may Arthur M. Berd Lehman Brothers Inc.

Roy Mashal Lehman Brothers Inc.

Peili Wang Lehman Brothers Inc. Berd, Mashal, Wang | Defining, Estimating and Using Credit Term Structures
Part 2

November 2004 2 have a duration as low as 1 year. This fact is well known to portfolio managers qualitatively – our paper provides its quantitative formulation.
The flip side of the same coin is the apparent negative correlation between interest rates and the conventionally defined credit spreads (OAS). It results in a similar effect of a dampened effective duration of credit bonds, as explained in Berd and Ranguelova (2003) and Berd and Silva (2004). We argue that a large portion of this negative correlation is “optical” in nature and is due to a misspecification of credit risk by the conventional OAS spread measures. We also show that what is commonly regarded as a convexity measure for (both credit and Treasury) bonds is also a “duration” measure with respect to interest rate curve steepening/flattening moves. This is an important observation because the so-called “convexity trades” often under- or outperform not due to directional changes in interest rates, but because of the changes in the shape of the curve – as was the case, for example, during the past year and a half. Finally, we present a concise and simple recipe for setting up well-hedged portfolios of bonds that generalizes the well-known duration-neutral and barbell trading strategies. We discuss how to choose the risk dimensions with respect to which one might wish to be hedged and how to find optimal security weights in the corresponding portfolios. SURVIVAL-BASED MODELING OF CREDIT-RISKY BONDS Let us start with a brief reminder of the survival-based valuation methodology, following Part 1 of this series. Consider a credit-risky bond that pays fixed cash

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