Problems with extending conclusions between Bowman's paradox and Beta's death

This issue of Omega contains a commentary by P.L. Brockett, W.W. Cooper, K.H. Kwon, and T.W. Ruefli on the review of Bowman's paradox by Nickel and Rodríguez, published in the February 2002 issue of Omega. In their commentary, the authors describe an article, published in the 1992 issue of Decision Sciences but not covered by the review, and claim that they had previously overcome three of the outstanding problems noted in Nickel and Rodríguez's review. This reply to the commentary proves that the conclusions drawn in the review by Nickel and Rodríguez are relevant in spite of the Brockett et al. arguments against them. In this reply, we show that the paper by Brockett et al. neither explains Bowman's paradox nor resolves its underlying problems. First, the definitions of risk and return measures are mathematically linked, and second, a cross-sectional methodology is used. We also provide our opinion on what would be necessary to bear in mind in order to extend any conclusion from Bowman's paradox to beta's death and vice versa.