Abstract
Factor portfolio is an important concept in the field of active portfolio management. However, the traditional factor portfolio lacks of theoretical results and is not investable since it is over-diversified. To extend its applicability and capacity, we propose a new approach to define and construct a regularized factor portfolio. The new factor portfolio is investable due to the sparsity of estimated weights, allows to control the risk of factor portfolio and the gross exposure on the weights of factor portfolio, and reduces the computational burden when the number of stocks is large. Under the new framework, we are able to develop risk theory for the optimal portfolios and provide an upper bound for the optimized risk, which is close to the theoretical optimal one. The performance of our new approach is illustrated by simulation and empirical studies on the stocks from Russell 1000.
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