图结构是广泛用于描述生物学信息的一个重要方法。考虑到不同资产之间的相互影响作用,引入图结构来描述高维资产之间包含的信息,建立了一种基于图结构约束的最小方差资产组合模型,并且提供了一种有效的坐标下降优化算法。研究结果表明,基于图结构约束的资产组合模型在收益率、波动率和变量选取方面优于传统的资产组合模型,该模型对金融机构的投资决策有重要的实际意义。
Minimum variance portfolio models mentioned by traditional literature were all brought out by exerting different penalties, and these models always ignored interactions between high-dimensional assets. When variables highly correlated, Lasso could not get suitable variables. So we referred to Li Caiyan and Li Hongzhe's way that combined graph structure penalty with MVP model with L1 penalty. And the correlations between assets by graph structure are described in order to get assets more accurately. The purpose of the paper is to provide theoretical and decisive inferences. The MVP model with graph structure is showed below: Minimize ωT∑ω+λ1‖ω‖1+λ2ωTLω Subject to ωT1p=1 For concise computation, we made λ=λ1+λ2 and θ=λ1/λ1+λ2, so the problem could be transmitted to this one: Minimize ωT∑ω+λθ‖ω‖1+λ(1-θ)ωTLω Subject to ωT1p=1 When ∑、L、λ and θ are given, it is the model that we fully focused on. Some properties of solves are given under the structure of regulated methods. With combinations between an coordinate algorithm and improvement of Yen, an efficient algorithm is also brought about.A-shares data of Shanghai Stock Market is used to conduct empirical analysis. Time varied from Jan.4th to Mar.29th in 2013. The data contained 56 observations and 818 stocks. The empirical analysis showed that: (1) The model with graph structure is better than other models in returns. (2) The model with graph structure is feasible in returns. (3) The sharp ratio of Graph1-MVP is positive, and the sharp ratio of Graph3-MVP is the highest among all models with negative ratio. (4) The probability of short is comparable small and this result could be due to the equation constriction that sum of weights is 1. (5)L1-MVP and Graph1-MVP could get the least number of assets. In summary, It is concluded that MVP model with graph structure can be advantageous in choose of asset. In the future, we could do further on the penalty of MVP model, or different penalties in other models could be considered to get better portfolios.
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