Javed Farrukh, Mazur Stepan, Ngailo Edward
Örebro University School of Business, Örebro, Sweden.
Department of Mathematics, Linköping University, Linköping, Sweden.
J Appl Stat. 2020 Mar 5;48(3):517-535. doi: 10.1080/02664763.2020.1736523. eCollection 2021.
In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order non-central and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and -distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.
在本文中，我们考虑切点投资组合的估计权重。当假设回报服从独立且多元正态分布时，我们推导了这些权重的高阶非中心矩和中心矩的解析表达式。此外，还以封闭形式获得了估计权重的均值、方差、偏度和峰度的表达式。随后，我们通过模拟研究对结果进行补充，在该模拟研究中，模拟了来自多元正态分布的数据，并使用蒙特卡罗实验计算了估计权重的前四阶矩。值得一提的是，发现回报的分布假设很重要，尤其是对于前两阶矩。最后，通过利用纳斯达克证券交易所上市的四个金融指数的回报进行实证说明，我们观察到高阶矩中存在时间动态。
