  Over the past half-century, the empirical finance community has produced vast
literature on the advantages of the equally weighted S\&P 500 portfolio as well
as the often overlooked disadvantages of the market capitalization weighted
Standard and Poor's (S\&P 500) portfolio (see \cite{Bloom}, \cite{Uppal},
\cite{Jacobs}, \cite{Treynor}). However, portfolio allocation based on Tukey's
transformational ladde have, rather surprisingly, remained absent from the
literature. In this work, we consider the S\&P 500 portfolio over the 1958-2015
time horizon weighted by Tukey's transformational ladder (\cite{Tukey2}):
$1/x^2,\,\, 1/x,\,\, 1/\sqrt{x},\,\, \text{log}(x),\,\, \sqrt{x},\,\, x,\,\,
\text{and} \,\, x^2$, where $x$ is defined as the market capitalization
weighted S\&P 500 portfolio. Accounting for dividends and transaction fees, we
find that the 1/$x^2$ weighting strategy produces cumulative returns that
significantly dominates all other portfolios, achieving a compound annual
growth rate of 18\% over the 1958-2015 horizon. Our story is furthered by a
startling phenomenon: both the cumulative and annual returns of the $1/x^2$
weighting strategy are superior to those of the $1/x$ weighting strategy, which
are in turn superior to those of the 1/$\sqrt{x}$ weighted portfolio, and so
forth, ending with the $x^2$ transformation, whose cumulative returns are the
lowest of the seven transformations of Tukey's transformational ladder. The
order of cumulative returns precisely follows that of Tukey's transformational
ladder. To the best of our knowledge, we are the first to discover this
phenomenon.

Portfolio Management