Abstract
Portfolio selection is a fundamental problem in finance with challenges of dimensionality and market complexities. This paper focuses on the prevalent strategy of passive portfolio management, called index tracking, considering the no-short sales, volatility, transaction costs, and the limited set of effective samples. An effective method is proposed for the high-dimensional sparse portfolio selection by using the nonconcave penalty SCAD and the nonnegative constraint. Oracle statistical properties are studied, and the Multiplicative Updates algorithm is applied for the method. The detailed comparisons of the proposed method with other existing nonnegative methods are shown in simulations and empirical analysis, which demonstrate that the proposed method has better performance.
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