Simple and Efficient Portfolio Construction with Implicit Covariance Estimation: The Ant Strategy

Abstract

It is well known that Modern Portfolio Theory does only work in theory. It requires a reliable estimation of expected returns and the expected covariance matrix. The universe of assets must form a multivariate normal distribution. One needs a long time series of historic data to estimate the covariances. But the covariances are not stationary. They change over time. The Ant Strategy avoids the explicit covariance estimation at all. One starts with an initial population of random portfolios and improves them with Differential Evolution. The optimization criterion is the risk adjusted return of the portfolio itself. The covariance matrix is only implicitly taken into account by the performance of the portfolio. The behavior of this method is demonstrated for a diversified asset-universe defined and for the Nasdaq-100. The results are compared to a Momentum approach called the Donkey developed in previous working papers. The Ants have an edge over the Donkey.