Tukey’s transformational ladder for portfolio management

Abstract

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 Bloomfield et al.

Portfolio Selection: The Power of Equal Weight

“…The index return is the change in value of a portfolio over a given holding period. We first calculate the index returns for both a equally weighted S&P 500 portfolio and a market capitalization weighted S&P 500 portfolio according to the index return formula as documented by CRSP 3 . CRSP computes the return on an index (R t ) as the weighted average of the returns for the individual securities in the index according to the following equation…”

Sampling James R. Thompson's inspired nonparametric portfolio approaches

“…It can be seen from Tables 7-9 that the cumulative values of the portfolios exactly follow the ordering inherent in the Tukey ladder. Ernst et al (2017a) are believed to be the first to have discovered this behavior. A graphical representation of the time series is presented in Figure 13 below.…”

“…The gamut runs from random, to sophisticated computationally derived, a la the Simugram™. Another approach advocated by Professor Thompson was weights derived through Tukey's “transformational ladder of powers,” investigated in Ernst, Thompson and Miao (Ernst, Thompson, & Miao, 2017a, 2017b). This general method of linearization first proposed by Tukey is seen as T ( x ) = x p , augmented by ln(x).…”

“…Dozens of graduate and undergraduate students in Rice University's Market Models class, and in independent research, have studied various permutations to the rule, such as different lookback and holding periods, other rebalancing rules, cash investment and constituent dropout programs, etc. Academic researchers have also validated and extended the concept, such as Affinito ( 2009), Ernst, Thompson and Miao (2017a, 2017b), and Tooth (2012. They have all studied the MaxMedian rule's efficacy over different study periods and have found the phenomenon persists.…”

Novel Classification of IoT Devices Based on Traffic Flow Features

“…Since the distribution of the obtained values (C u index) are asymmetric in nature (negative skewness) the data have been transformed. The data transformation method was selected using the Ladder of powers (Tukey method) to clearly show a suitable data transformation function to achieve normal distribution (Ernst et al, 2017). Table 3 shows the chi2 values of a particular transformation function.…”