Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high sensitivity to change in input parameters. The heavy-tail characteristics of financial time series are in fact the cause for these erratic fluctuations of weights that consequently create substantial transaction costs. In robustifying the weights we present a toolbox for stabilizing costs and weights for global minimum Markowitz portfolios. Utilizing a projected gradient descent (PGD) technique, we avoid the estimation and inversion of the covariance operator as a whole and concentrate on robust estimation of the gradient descent increment. Using modern tools of robust statistics we construct a computationally efficient estimator with almost Gaussian properties based on median-of-means uniformly over weights. This robustified Markowitz approach is confirmed by empirical studies on equity markets. We demonstrate that robustified portfolios reach the lowest turnover compared to shrinkage-based and constrained portfolios while preserving or slightly improving out-of-sample performance.
翻译:Markowitz 平均差值组合,以中值和共差为样本,作为输入参数,在实践中有许多问题。由于估算错误,这些组合在抽样中表现不佳,它们经历极端重力,同时对输入参数的变化具有高度敏感性。金融时间序列的重尾特征实际上是造成加权变化不定的原因,从而产生巨大的交易成本。在强化我们提出的全球最低马尔科威茨组合稳定成本和重量的工具箱的权重时,利用预测的梯度下降(PGD)技术,我们避免估计和颠倒整个变量运行者,并集中精力对梯度下降增量进行稳健的估计。我们使用现代的稳健统计工具,根据平均重量的中值构建一个计算高效的估算器,几乎高斯的特性。这种稳健的马尔科维茨方法得到了股票市场经验研究的证实。我们证明,强的组合在保持或略微改进外延值组合的同时,达到与缩小和受制约的组合相比的最低营业率。