椭球分布下带有潜在因子结构的高维投资组合构建方法

Large Portfolio Allocation under Elliptical Distribution with a Latent Factor Structure

考虑到金融收益数据的厚尾性,基于椭球分布的投资组合构建问题引起了学者的关注与讨论.本文考虑了高维资产收益具有潜在椭球因子模型结构的情形,并在二阶矩存在的条件下证明了椭球分布下均值-方差模型和无约束回归的等价性,该定理推广了椭球分布族均值-方差投资组合问题的等价无约束回归表示.最终,本文借助l1范数惩罚得到稀疏的最优投资组合.模拟结果表明,当收益存在厚尾性时,本文所提方法仍然能够在控制风险的基础上极大化预期收益,且表现优于现有的均值-方差类模型.最后,本文将所提方法应用到金融资产收益的数据集上进行实证,所提方法在控制风险的基础上能够获得较高的收益,进而验证了其优良表现.

In view of the heavy-tailedness of financial returns data,robust portfolio allocation problem under the general elliptical distribution framework arouse much attention.We consider a latent elliptical factor structure of the returns of large number of assets and then we prove the equivalence of mean-variance and unconstrained regression optimization problem under elliptical distribution with finite second moment,which generalizes the equivalent unconstrained regression representation of the meanvariance portfolio problem under the elliptical family.Finally,we resort 1-regression method to obtain the sparse optimal portfolio allocation.Simulation results show that the proposed method of constructing portfolios can still control for risk and attains the maximum expected return in heavy-tailed cases while the existing ones deteriorate.The superiority of our method is demonstrated through an real financial dataset and the yielded financial returns are encouraging.