Un-Diversifying During Crises: Is It a Good Idea?

Abstract

High levels of correlation among fi nancial assets, as well as extreme losses, are typical during crisis periods. In such situations, quantitative asset allocation models are often not robust enough to deal with estimation errors and lead to identifying underperforming investment strategies. It is an open question if in such periods, it would be better to hold diversifi ed portfolios, such as the equally weighted, rather than investing in few selected assets. In this paper, we show that alternative strategies developed by constraining the level of diversifi cation of the portfolio, by means of a regularization constraint on the sparse l q-norm of portfolio weights, can better deal with the trade-off between risk diversifi cation and estimation error. In fact, the proposed approach automatically selects portfolios with a small number of active weights and low risk exposure. Insights on the diversifi cation relationships between the classical minimum variance portfolio, risk budgeting strategies, and diversifi cation-constrained portfolios are also provided. Finally, we show empirically that the diversifi cation-constrainedbased l q-strategy outperforms state-of-art methods during crises, with remarkable out-of-sample performance in risk minimization.

Sparse portfolio selection via the sorted ℓ1-Norm

“…This section studies the out-of-sample performance of the SLOPE procedure, considering a minimum variance framework, as typical of most studies (see i.e. Jagannathan and Ma (2003), Brodie et al (2009), DeMiguel et al (2009a, Giuzio and Paterlini (2016)).…”

“…After falling slightly, the correlation increases again in 2012, during the European sovereign debt crisis. The correlation coefficient plays an important role for our following analysis, as increased positive correlation among the constituents is reported to reduce the effects of diversification (Choueifaty and Coignard 2008, You and Daigler 2010, Giuzio and Paterlini 2016. For all portfolios, the optimal weights vector, ŵt , depends on the choice of the optimal λ parameter value.…”

“…Although, the RIDGE penalty stabilizes the mean-variance optimization, as it controls for multicollinearity, the shape of the penalty does not promote sparsity, leading to portfolios with an undesirably large number of active positions (Carrasco and Noumon 2012). Despite its appealing properties, the LASSO has reported shortcomings of (a) large biased coefficient values (Gasso et al 2010, Fastrich et al 2015, of (b) reduced recovery of sparse signals when applied to highly dependent data, like crisis periods (Giuzio and Paterlini 2016), and of (c) randomly selecting among equally correlated coefficients (Bondell and Reich 2008). Moreover, it is ineffective in presence of short selling (i.e.…”

“…To overcome these limitations, non-convex penalties, like the q -Norm, the log and the SCAD penalty have recently gained increased attention in the portfolio literature (Gasso et al 2010, Fastrich et al 2014, Xing et al 2014, Chen et al 2017). Among these penalties, the q -Norm with 0 < q < 1 has shown remarkable theoretical and empirical properties compared to the classic LASSO (Saab et al 2008, Fastrich et al 2014, Chen et al 2017, Giuzio and Paterlini 2016. In particular, Fernholtz et al (1998) show that the q -Norm can be interpreted as a measure of diversification of a portfolio.…”

Critical Decisions for Asset Allocation via Penalized Quantile Regression

“…For instance, Fastrich et al (2015) showed that sparse portfolios derived from penalized regression models provide improvements in terms of a lower concentration and turnover. Giuzio and Paterlini (2018) highlighted the positive impact of regularized models on the portfolio performance during stressed market conditions. Kremer et al (2018) used regularization techniques to minimize the risk in multi-factor portfolios.…”