Before revision:  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 .
After revision:  We address these shortcomings and develop an approach to construct sparse portfolios in high dimensions. Our contribution is twofold: from the theoretical perspective, we establish the oracle bounds of sparse weight estimators and provide guidance regarding their distribution. From the empirical perspective, we examine the merit of sparse portfolios during different market scenarios. We find that in contrast to non-sparse counterparts, our strategy is robust to recessions and can be used as a hedging vehicle during such times .