Portfolio optimization with sparse multivariate modeling

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 $$L_0$$ L 0 -norm sparse elliptical modeling and show thatsparsification is effective. We quantify the effects of points 2. and 3. by studying the models’ likelihood in- and out-of-sample for parameters estimated over different train windows. We show that models with larger off-sample likelihoods lead to better performing portfolios only for shorter train sets. For larger train sets, we found that portfolio performances deteriorate and detaches from the models’ likelihood, highlighting the role of non-stationarity. Investigating the out-of-sample likelihood of individual observations we show 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 and conventional GARCH extensions by delivering higher out of sample likelihood, lower realized volatility and improved stability, avoiding typical pitfalls of conventional portfolio optimization approaches.