基于最速曲线的投资组合调整方法

Portfolio Rebalancing Method Based on Brachistochrone Curve

均值方差模型自1952年被提出以来在单期投资组合优化理论与实践中一直扮演着十分重要的角色。然而因为资金具有时间价值,所以投资者总是希望能够尽快实现他们的投资目标。鉴于此,本文利用数学中著名的最速曲线提出了一种新的投资组合调整方法并探讨其求解步骤。该方法在建模过程中考虑了投资活动中普遍存在的时间效应和处置效应两种现象。德国股票市场和中国股票市场中的实证结果不仅证实了投资组合调整的必要性,而且说明了新方法的实用性和有效性。

The mean-variance model has played a crucial role in single-period portfolio optimization theory and practice since it is proposed by Markowitz in 1952.Nevertheless,due to the time value of capital,investors would like to achieve their scheduled targets as soon as possible.To this end,we propose a new method for portfolio rebalancing based on the famous brachistochrone curve in mathematics and further discuss the solution steps of it.This approach allows us to model the well-known horizon effect and disposition effect phenomena in finance.The empirical results in the German Stock Exchange Market and Chinese Stock Market not only confirm the necessity of portfolio rebalancing,but also show the effectiveness of the new method.