On the non-stationarity of financial time series: impact on optimal portfolio selection

TL;DR

This paper examines how non-stationarity in financial time series affects correlation estimates and portfolio optimization, revealing that longer data series do not necessarily improve accuracy and highlighting spectral instabilities in correlation matrices.

Contribution

It provides empirical evidence on the drawbacks of using standard correlation estimators in non-stationary markets and analyzes spectral properties affecting portfolio stability.

Findings

Longer time series do not always yield better correlation estimates.

Non-stationarity causes spectral instabilities in correlation matrices.

Portfolio risk underestimations are linked to spectral instabilities.

Abstract

We investigate the possible drawbacks of employing the standard Pearson estimator to measure correlation coefficients between financial stocks in the presence of non-stationary behavior, and we provide empirical evidence against the well-established common knowledge that using longer price time series provides better, more accurate, correlation estimates. Then, we investigate the possible consequences of instabilities in empirical correlation coefficient measurements on optimal portfolio selection. We rely on previously published works which provide a framework allowing to take into account possible risk underestimations due to the non-optimality of the portfolio weights being used in order to distinguish such non-optimality effects from risk underestimations genuinely due to non-stationarities. We interpret such results in terms of instabilities in some spectral properties of portfolio correlation matrices.