基于股价预测的泛证券投资组合策略

本文基于期望效用最大化和L₁-中位数估计研究了在线投资组合选择问题。与EG（Exponential Gradient）策略仅利用单期价格信息估计价格趋势不同，本文将利用多期价格信息估计价格趋势，以提高在线策略的性能。首先，基于多期价格数据，利用L₁-中位数估计得到预期价格趋势。然后，通过期望效用最大化，提出一个新的具有线型时间复杂度的在线策略，EGLM（Exponential Gradient via L₁-Median）。并通过相对熵函数定义资产权重向量的距离，进而证明了EGLM策略具有泛证券投资组合性质。最后，利用国内外6个证券市场的历史数据进行实证分析，结果表明相较于UP（Universal Portfolio）策略和EG策略，EGLM策略有更好的竞争性能。

Universal Portfolio Strategy Based on Forecasting Price

Portfolio selection is a practical financial problem. It is mainly concerned with determining a strategy for allocating the wealth among a set of financial assets under an uncertain environment. Markowitz (1952) proposed the Mean-Variance Theory and pioneered the quantitative research methodology in portfolio selection. This approach assumes that investors have the ability to achieve full statistic information of prices, which, however, violates the real world. The strong statistic assumption determines this approach's poor performance in practical application. Following the Kelly investment model (1956), Cover (1991) proposed the on-line portfolio selection model, which has none statistic assumption of price. In this paper, the on-line portfolio selection is followed and the improved on-line strategies are studied.
An on-line portfolio selection problem based on the expected utility maximization and L₁-median estimator is investigated in this paper. Considering the EG strategy estimate next price trend with only one-period price information which is not sufficient, the next price trend with multi-period price information is estimated and the performance of on-line strategy is improved.
Firstly, the Modified Weiszfed algorithm is applied to calculate the L₁-median estimator of multi-period price. Based on the L₁-median estimator, the estimation of future price trend is given by the ratio of L₁-median estimator to close price. Then, via maximizing utility, a novel on-line strategy named EGLM (Exponential Gradient via L₁-Median) is proposed. With portfolio vectors' distance defined by the relative entropy function, it is proved that EGLM is a universal portfolio. Therefore, as a universal portfolio, EGLM could achieve as much approximate return as BCRP. Meanwhile, by algorithm analyzing, it is found that EGLM's time complexity is O(mn)+O(Mn), which is linear with respect to m, number of securities, and is significant less that UP's O(n^m). Thus, the proposed EGLM is suitable for real-world large-scale applications.Finally, based on 6 datasets from domestic and foreign real markets, an experiment is given to illustrate the usefulness and effectiveness of EGLM. The results show that EGLM has not only better performance of return but also better trade-off between return and risk than UP and EG.
With the proposed EGLM strategy and its linear time complexity, investors can gather more precise information about securities' prices and save more calculating time. EGLM has not only the universal character but also good performance in practical performance.