Sparse Unit-Sum Regression
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This paper considers sparsity in linear regression under the restriction that the regression weights sum to one. We propose an approach that combines ℓ_0- and ℓ_1-regularization. We compute its solution by adapting a recent methodological innovation made by Bertsimas et al. (2016) for ℓ_0-regularization in standard linear regression. In a simulation experiment we compare our approach to ℓ_0-regularization and ℓ_1-regularization and find that it performs favorably in terms of predictive performance and sparsity. In an application to index tracking we show that our approach can obtain substantially sparser portfolios compared to ℓ_1-regularization while maintaining a similar tracking performance.
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