A Basket Half Full: Sparse Portfolios
Ekaterina Seregina
The existing approaches to sparse wealth allocations (1) are suboptimal due
to the bias induced by $\ell_1$-penalty; (2) require the number of assets to be
less than the sample size; (3) do not model factor structure of stock returns
in high dimensions. We address these shortcomings and develop a novel strategy
which produces unbiased and consistent sparse allocations. We demonstrate that:
(1) failing to correct for the bias leads to low out-of-sample portfolio
return; (2) only sparse portfolios achieved positive cumulative return during
several economic downturns, including the dot-com bubble of 2000, the financial
crisis of 2007-09, and COVID-19 outbreak.