Weighting Bonds By Probability Of Default

Last Updated: 30 November 2022

In previous reports (Benzschawel, Lee and Hawker [2011]; and Benzschawel, Lee, Hawker and Craft [2012]), we introduced the concept of adjusting the weights of bond indexes of default-risky assets by their relative default probabilities (PDs). That is, we presented several methods for underweighting the riskiest sovereigns in Citigroup’s World Government Bond Index (WGBI) in favour of those with lower risk. It was suspected that such adjustments would reduce monthly index turnover by reducing the amounts of bonds entering and exiting owing to movements in their credit quality between investment-grade and high yield. In those reports, we used our recently developed market-implied method for estimating sovereigns’ physical PDs (Benzschawel and Lee [2011]; Benzschawel and Assing [2012]; and Benzschawel [2012]) as the basis for comparing several methods of adjusting weights in the index.

Our initial studies demonstrated that adjusting WGBI sovereigns’ capitalisation-based weightings based on averaging the logarithms of countries’ PDs had advantages over simple PD averages. That is, adjusting WGBI weightings based on logarithms of sovereigns’ PDs better preserves the average letter rating of the original WGBI and generates less extreme distributions of sovereign weights than do similar adjustments based on linear PDs. In this report, we evaluate the relative risk/reward characteristics of the standard capitalisation-weighted WGBI versus those resulting from adjusting country weights by their relative risk of default over the period from 1999 through 2012. As described below, we find that adjusting sovereign contributions to the WGBI by their estimated PDs:

  • Reduces overall default risk of WGBI portfolios
  • Provides greater risk-adjusted returns
  • Finally, although we describe our PD-weighting method in the context of the WGBI, the method is general enough to be applied to any index with a credit-based criterion for inclusion.

The World Government Bond Index
Citigroup’s World Government Bond Index comprises investment-grade sovereign debt from 23 countries, denominated in 14 currencies.1  Inclusion in the WGBI is dependent upon market size, credit quality and government policy. As is typical of many credit indexes, the obligor and asset composition is adjusted each month to include new issues and eligible markets, and to exclude markets and issues no longer meeting index criteria. One problem for index managers and investors is that monthly index adjustments can introduce large discrete changes, requiring costly buying and selling of securities in order to rebalance. In the WGBI, this can be particularly severe if a large sovereign issuer deteriorates and gets excluded from the index (Greece, July 2010) or an improving, but still risky, major sovereign issuer is added (Mexico, October 2010). We have been exploring methods to minimise these discrete changes in index portfolio composition while at the same time enhancing risk-adjusted returns. Our approach is to adjust countries’ contributions in the WGBI by their relative default probabilities as estimated from Citi’s market-implied default model.


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