Median-adaptive portfolios: a minimum criteria approach to asset allocation

Abstract

We propose a new class of adaptive portfolios for asset allocation, based on a one-parameter variation of the equally weighted portfolio and the use of the median-ranked asset. Our methodological contribution offers a simple way of performing, static or optimized, allocation of assets in portfolios of any dimension, thus easily circumventing the “curse of dimensionality”. Our results show that, even for a static selection of the parameter that defines our allocation, we obtain improved performance compared to the equally weighted benchmark in all the standard metrics. For the case of an optimized selection of the parameter we offer results from minimum variance optimization, that do require the estimation of the covariance matrix, but our approach can easily be adapted to other kinds of portfolio objective functions. This new class of portfolios can easily be added to, as a complement or substitute, to any existing portfolio allocation method.