Un-diversifying during crises: Is it a good idea?

High levels of correlation among financial 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 diversified 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 diversification of the portfolio, by means of a regularization constraint on the sparse lq-norm of portfolio weights, can better deal with the trade-off between risk diversification 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 diversification relationships between the classical minimum variance portfolio, risk budgeting strategies, and diversification-constrained portfolios are also provided. Finally, we show empirically that the diversification-constrained-based lq-strategy outperforms state-of-art methods during crises, with remarkable out-of-sample performance in risk minimization.