Recently, the authors of (\mbox{%DIFAUXCMD Ernst0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization }  weighted S\&P 500 portfolio as well as those of the equally weighted S\&P 500 portfolio .0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ). However, rather surprisingly, portfolio allocation based on the seven simple transformations of John Tukey's ladder are nowhere to be found in the literature. } In this work, we find superior S\&P 500 portfolio weighting strategies to that of the MaxMedian rule, calculated over an updated 1958-2015 time horizon . 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 ) . We find that the 1/x^2 weighting strategy produces cumulative returns which significantly dominate all other portfolios, posting an annual geometric mean return of 20.889 \\%DIF < . In addition, we show that the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of Tukey's transformational ladder. It is astonishing that the ranking of portfolio performance (from best to worst) precisely follows that of the late John Tukey's transformational ladder.\end{abstract} %DIF > . Further, the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of John Tukey's transformational ladder. Rather shockingly, the order of cumulative returns precisely follows that of John Tukey's transformational ladder. To the best of our knowledge, we are the first to discover this phenomenon.
0pt%DIFAUXCMD ) empirically showed that over the 1958-2014 horizon, the returns of the MaxMedian S\&P 500 portfolio (see \mbox{%DIFAUXCMD thomp2}0pt%DIFAUXCMD ) substantially exceed both those of the market capitalization } Over the past half century, portfolio managers have carefully documented the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted S\&P 500 portfolio (see \mbox{%DIFAUXCMD Bloom0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Uppal}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Jacobs}0pt%DIFAUXCMD , \mbox{%DIFAUXCMD Treynor}0pt%DIFAUXCMD ). However, rather surprisingly, portfolio allocation based on the seven simple transformations of John Tukey's ladder are nowhere to be found in the literature. } In this work, we consider the S\&P 500 portfolio over the 1958-2015 time horizon weighted using John Tukey's transformational ladder (\cite{Tukey2}): 1/x^2, \,\, 1/x, \,\, 1/\sqrt{x}, \,\, \text{log (x), \,\, \sqrt{x,\,\, x,\,\, x^2} , where x is the market capitalization weighted portfolio . We find that the 1/x^2 weighting strategy produces cumulative returns which significantly dominates all other portfolios, achieving an annual geometric mean return of 20.889 \\%DIF < . In addition, we show that the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of Tukey's transformational ladder. It is astonishing that the ranking of portfolio performance (from best to worst) precisely follows that of the late John Tukey's transformational ladder.\end{abstract} %DIF > . Further, the 1/x^2 weighting strategy is superior to a 1/x weighting strategy, which is in turn superior to a 1/\sqrt{x} weighted portfolio, and so forth, culminating with the x^2 transformation, whose cumulative returns are the lowest of the seven transformations of John Tukey's transformational ladder. Rather shockingly, the order of cumulative returns precisely follows that of John Tukey's transformational ladder. To the best of our knowledge, we are the first to discover this phenomenon.
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