Pinches, George E. and Kent A. Mingo, "The Role of Subordination and Industrial Bond Ratings", Journal of Finance, Vol. 30, No. 1, (March 1975), pp. 201-206.

Introduction: In recent years a number of models for predicting corporate bond ratings have been developed [3, 4, 5, 8]. Horrigan [3] and the present authors [4] concluded that the subordinated status of a bond, as represented by a 0-1 dichotomous variable, was the most important variable in their respective models. The multiple discriminant model developed earlier [4] correctly predicted approximately 70 per cent of the bonds examined, but performed poorly for Baa-rated bonds. The inability of this model, and the previous model developed by Horrigan, to correctly predict Baa bonds is critical since this rating has become generally accepted in the investment community as the cutoff between investment and non-investment grade bonds. An examination of the bonds employed in our previous indicated that virtually all industrial bonds rated above Baa were non-subordinated, while all bonds rated Ba or B were subordinated. Only in the Baa category were there a large number of both non-subordinated and subordinated bonds. The use of a 0-1 dichotomous variable representing subordination may have caused predicted bond ratings to be either above or below the Baa group (where most bonds are either non-subordinated or subordinated) to the exclusion of the Baa group where a large number of both types of bonds existed. Thus, the relatively poor predictive ability for Baa bonds encountered by Horrigan and the present authors may be due to bias introduced through the use of the 0-1 variable representing subordination. the use of this variable also violates a basic assumption of multiple discriminant analysis--that of a multivariate normal distribution, in addition, in our previous study we assumed, but did not test for, equality of the group dispersion matrices. If the dispersion matrices are unequal, quadratic as opposed to linear classification rules are appropriate.

The purpose of this note was to further analyze the impact of subordination on ratings by examining two alternative models for predicting industrial bond ratings. In both these alternative models the equality of the group dispersion matrices were tested and, where appropriate, quadratic classification procedures employed.