“How Many Bonds? Estimating the number of individual bonds required to minimize the impact of default risk.” That is the title of a paper by Sobczyk, Shayne, and Mashayekhi (available from the BondDeskGroup and published Dec, 2010) that you might enjoy digging into. For sure, the topic is an important one, and the paper can be easily understood, even by the mathematically challenged. Their conclusion is as follows: The results of our analysis indicate that for preventing extreme default losses in a portfolio of investment grade corporate bonds, as few as ten bonds are sufficient to gain a substantial portion of the maximum diversification benefits that can be achieved. In other words, while adding bonds (from distinct issuers) to a bond portfolio always results in a lower likelihood of extreme losses (due to defaults), we find that the marginal diversification benefits diminishes substantially after adding ten bonds. [To establish that result, they use] “… the so called Gaussian copula approach. In other words, each portfolio loss distribution can be described through combination of joint cumulative density functions of multivariate Gaussian distributions of marginal default probabilities and correlations. And that is exactly where I’m betting they’ve made their mistake, because the equations that underlie the Gaussian copula are known to depend on bogus assumptions, well-disclosed in a Wired article that appeared almost two years (Feb, 2009) before the publication of their paper. In other words, their suggestion that ten bonds might be enough to mitigate risk needs to be re-examined. Fortunately, their paper clearly describes their methodology and cites their data sources. So replicating their experiment should be straight-forward research work of the sort you had to do as an undergrad, no matter your major. (“So and so is claiming such and such is the case. Has he/she really established that is so? Support or refute in 5-10 pages, due next Monday.”) If you do choose to tear into their paper, you might also want to look at Fridson and Goa’s 1998 paper, “How Many High Yield Bonds Make a Diversified Portfolio? (reprinted in Barnhill et al, High-Yield Bonds: Market Structure, Portfolio Management, and Credit Modeling ) in which they argue that far many more bonds are needed than a mere ten. "One counterintuitive implication of the methodology we have outlined is that the number of issues required to obtain satisfactory diversification *increases* as the credit quality improves." (p.378)Charlie
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