Before revision:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2,  1/x,  1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} ,  x , x^2 (in our setting, x is the market capitalization weighted portfolio ) .
After revision:  The portfolio weighting strategies we consider are the seven transformations of Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, 1/x, 1/\sqrt{x}, \log (x), \sqrt{x,\,\, x,\,\, x^2} , x is the market capitalization weighted portfolio ) .