Portfolio Optimization with Sparse Multivariate Modelling

TL;DR

This paper introduces a sparse elliptical modeling approach for portfolio optimization, addressing modeling errors, non-stationarity, and parameter uncertainty, leading to more stable and higher likelihood portfolios.

Contribution

It proposes a novel L0-norm sparse elliptical model and demonstrates its effectiveness in improving portfolio stability and out-of-sample performance compared to full models.

Findings

Sparse models outperform full models in out-of-sample likelihood.

Larger training sets improve long-term likelihood stability.

Portfolio performance deteriorates with very large training sets due to non-stationarity.

Abstract

Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2. uncertainties resulting from parameters' sampling error; 3. intrinsic non-stationarity of these systems. For what concerns point 1. we propose a L0-norm sparse elliptical modeling and show that sparsification is effective. The effects of points 2. and 3. are quantifified by studying the models' likelihood in- and out-of-sample for parameters estimated over train sets of different lengths. We show that models with larger off-sample likelihoods lead to better performing portfolios up to when two to three years of daily observations are included in the train set. For larger train sets, we found that portfolio performances deteriorate and detach from the models' likelihood, highlighting the role of non-stationarity. We further investigate this phenomenon by studying the out-of-sample likelihood of individual observations showing that the system changes significantly through time. Larger estimation windows lead to stable likelihood in the long run, but at the cost of lower likelihood in the short-term: the `optimal' fit in finance needs to be defined in terms of the holding period. Lastly, we show that sparse models outperform full-models in that they deliver higher out of sample likelihood, lower realized portfolio volatility and improved portfolios' stability, avoiding typical pitfalls of the Mean-Variance optimization.