In a recent article Fabozzi and Francis [3] presented the results of empirical tests designed to determine if the regression coefficients of the single-index market model were significantly different in bull and bear markets. Using three alternative definitions of bull and bear markets, Fabozzi and Francis (FF) concluded the coefficients of the single-index market model were not significantly different in the two types of markets.

The mathematical difficulties encountered when attempting to express the internal rate of return (IRR) of a combination of two or more investments as a weighted algebraic sum of the individual investments' IRRs has been recognized in the financial literature for some time. However, in a recent issue of this journal, Professors Reilly and Wecker (hereafter R-W) [3] apply the well-known mathematical impossibility of expressing the root(s) of a polynomial as an algebraic combination of the roots of related polynomials to question the validity of the weighted cost of capital (kw) concept.