We describe a method for estimating default probabilities (PDs) for risky obligors and apply that method to generate PDs for major sovereign issuers. We then show how these *market-implied* PDs can be used to weight obligor contributions to indexes of risky credits and highlight some features of PD-weighted indexes. Although several useful approaches for estimating PDs exist, including fundamental analysis, statistical models, structural models and the risk-neutral approach, none has proven entirely satisfactory. This is particularly true for sovereign credits (which often default strategically), heavily leveraged financial firms, private firms whose financials are not readily available and municipal bond issuers. Interest in a generally acceptable method for estimating PDs has increased recently due to the requirements of the impending Basel regulations, as well as firms’ needs to assess counterparty credit risk and make credit value adjustments to profit-and-loss on trading positions.

Another potential use for market-implied PDs is for differential weighting of obligor contributions to indexes of default-risky assets. Financial indexes offer investors a diversified exposure to given market segments as well as performance benchmarks for financial managers. However, monthly index adjustments can introduce large discrete changes in composition, requiring costly buying and selling of securities. This can be particularly severe if a large issuer’s credit deteriorates, resulting in exclusion. We introduce in this report a method for constructing indexes weighted by PDs from the market-implied PD model. Although we describe the method of constructing the index in terms of Citigroup’s World Government Bond Index,^{1} the method is general enough to be applied to any index with a credit-based criterion for inclusion.

**Market-Implied PDs**

We developed a procedure for measuring expectations of obligors’ PDs from the credit spreads and spread volatilities of their assets. The method first uses credit spreads, along with obligors’ model-based PDs, to estimate the current credit risk premium in order to determine the spread compensation per unit of default probability. Then, any firm’s bond spread and spread volatility are measured with respect to the current risk premium and, given an assumed value of recovery in default, can be used to infer a market-implied PD.

The market-implied PD framework views obligors’ spread as consisting of two parts: compensation for default; and compensation for credit spread volatility. The method is based on demonstrations that credit spreads, on average, are linear functions of spread volatility on logarithmic axes. That linear relationship holds, in general, for spreads overall and for spreads of bonds within individual ratings categories. Also, we assume that investors require the same level of spread compensation per unit of spread volatility regardless of its source. We go into more depth on the mechanics of this measure below.

Although there is demand for a market-based PD measure, accurate estimation of PDs has proven difficult for several reasons. First, changes in agency ratings tend to lag market spreads (Figure 1). That is, credit rating changes trail market perceptions of credit quality. Also, changes in default rates and credit spreads vary over the credit cycle and, while related, are not perfectly correlated (Figure 2). A major difficulty in inferring PDs from bond prices is that bond spreads contain a risk premium that is not related to default. If so, it should be possible to decompose a credit spread into components such that *s* = *s _{d}* +

*s*

_{?}, where

*s*is the compensation for default and

_{d}*s*

_{?}is the credit risk premium. For a bond of duration

*T*, the spread compensation for default,

*s*, can be approximated as:

_{d}(1) |

where LGD is *loss-given-default* or *1-R*, where *R* is the recovery value in default. The value of *s _{d}* can be thought of as the amount of spread necessary to equal the expected return of a U.S. Treasury issue of similar duration for a given expected default and recovery for the risky bond. Also, since

*s*=

*s*+

_{d}*s*

_{?}, if the credit spreads are used along with estimates of default probabilities, one can solve for the risk premium, defined as s

_{?}, using the following relation:

(2) |

Equations 1 and 2 can be derived directly from the bond price versus yield relationship.^{2}