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Title: Grouped portfolio optimization with pessimistic risk measure Authors:  Sung Chul Hong - University of Seoul (Korea, South) [presenting]
Eun Young Ko - University of Seoul (Korea, South)
Hosik Choi - Kyonggi University (Korea, South)
Jong-june Jeon - University of Seoul (Korea, South)
Abstract: In portfolio optimization theory recent studies of risk measures lead to a new strategy of the optimal asset allocation beyond the Markowitz mean-variance model. In particular, the $\alpha$-risk receives much attention as one of the pessimistic risk measures. It is known that minimizing $\alpha$-risk on portfolio management is closely related to the quantile regression model and thus various strategies of asset allocation can be derived from variants of quantile regression model. On this approach we propose an optimization method of portfolio that provides sparse and group-wise selection of assets based on $\alpha$-risk. We formulate the problem as the regularized quantile regression model and solve our problem by ADMM algorithm. We show the sparsity of asset allocation by numerical simulations and we also investigate out-of-sample performance in terms of various risk measures in real data analysis.