arXiv 2001.029662020-01q-fin.PM

全局最小方差投资组合的聚类方法

Clustering Approaches for Global Minimum Variance Portfolio

Jinwoo Park

摘要：

全局最小方差投资组合（GMVP）的投资组合权重的唯一输入是被考虑用于投资的资产的收益率的协方差矩阵。由于总体协方差矩阵是未知的，投资者通常使用历史数据来估计，虽然样本协方差矩阵是总体协方差矩阵的无偏估计，但它包含了大量的估计误差，尤其是当观测数据的数量不大于资产数量时。针对高维协方差矩阵难以一次性估计的问题，提出了一种基于聚类的股票协方差矩阵的估计方法，该方法分两步进行：首先在类内估计协方差矩阵，然后在类间估计协方差矩阵。它通过减少数据矩阵中的特征数量来减小估计误差。本文的动机是，估计误差仍然可以保持高，即使在聚类后，如果大量的股票聚集在一个单一的群体。本研究提出利用有界聚类方法，以限制最大聚类大小。实验结果表明，不仅样本内波动率与样本外波动率之间的差距缩小，而且样本外波动率也有所减小。这意味着我们需要一个有界的聚类算法，以便可以精确地控制最大聚类大小，以找到最佳的投资组合性能。

英文摘要：

The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical data to estimate it. Even though sample covariance matrix is an unbiased estimator of the population covariance matrix, it includes a great amount of estimation error especially when the number of observed data is not much bigger than number of assets. As it is difficult to estimate the covariance matrix with high dimensionality all at once, clustering stocks is proposed to come up with covariance matrix in two steps: firstly, within a cluster and secondly, between clusters. It decreases the estimation error by reducing the number of features in the data matrix. The motivation of this dissertation is that the estimation error can still remain high even after clustering, if a large amount of stocks is clustered together in a single group. This research proposes to utilize a bounded clustering method in order to limit the maximum cluster size. The result of experiments shows that not only the gap between in-sample volatility and out-of-sample volatility decreases, but also the out-of-sample volatility gets reduced. It implies that we need a bounded clustering algorithm so that maximum clustering size can be precisely controlled to find the best portfolio performance.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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