基于UPM-LPM的增强指数投资策略

增强指数投资策略的理念是基于部分成份股构建指数跟踪组合，以期在跟踪指数趋势的同时，获取超出指数平均收益的超额收益。本文将指数收益率作为目标收益，拓展经典下偏矩（Lower Partial Moment，LPM）的概念，使其适应于增强指数投资策略建模，同时给出上偏矩（Upper Partial Moment，UPM）的定义，进而构建基于UPM-LPM之比的增强指数模型。为解决模型的求解复杂性和高维投资组合的"维数灾难"问题，本文运用非参数核估计方法直接得到跟踪组合的密度函数，进而得到跟踪组合的LPM和UPM的解析表达式，避免对组合中各资产之间的高维联合分布进行估计，大幅度降低了估计的维度，克服"维数灾难"问题。而且LPM和UPM的核估计量是组合头寸的光滑函数，具有任意阶导数，便于优化问题求解。最后，本文运用沪深股票市场上五个常用指数及其成份股数据，检验模型在实际金融市场中的表现，结果表明：本文提出的增强指数模型能够战胜指数，同时实现跟踪指数趋势并获取稳健超额收益的目标。

Enhanced Indexation Investment Strategies Based on UPM-LPM Ratio

The index-linked trades have become especially prevalent in the asset management industry in the last decades, as investors tend to require benchmarking as a mechanism to evaluate portfolio performance.Index tracking models and Enhanced indexation models are two particularly popular index trading models. Index tracking models aim to reproduce the performance of a stock market index, but without purchasing all of the stocks that make up the index.Enhanced indexation models (EIM) are related to index tracking, in the sense that they also consider a specific indexas a reference. They however aim to outperform the index by generating excess return.The prior EIM are mostly concentrated on overcoming the computational difficulty raised by restricting the cardinality of the portfolios-not on answering the question if they do attain their stated purpose, i.e. obtain returnin excess of the index. In this paper, the enhanced indexation investment strategies that adopt subset of the constituent stocks to construct portfolios to track the benchmark index trend are studied and excess returns relative to index is obtained. As a risk measure, an attractive propertiesof Lower Partial Moment (LPM) is that most other downside risk measures can be specified as special cases of LPM. However, the LPMs has not been used to study the index-linked trade models.Therefore the concept of LPM is extended to suit to the enhanced indexation model by using the index return as target return. In addition, the definition of the Upper Partial Moment (UPM) is given, and then enhanced indexation models are constructed based on the UPM-LPM ratio.In order to solve the complex nonlinear problem and tackle ‘dimensional curse’ induced by large scale portfolio selection, kernel estimation method is used to obtain tracking portfolios' density function directly without considering the high dimensional joint distribution of assets' returns, which can overcome the ‘dimensional curse’ problem. Furthermore, the LPM and UPM kernel estimators, which are smooth functions of the positions and have arbitrary order derivatives, can significantly reduce the complexity of solving these models. Finally, we adopt five common indicesand their constituent stocks from Shanghai and Shenzhen securities markets to test our models' performance. The period from 4 January 2005 to 31 December 2016 is concentrated on, spanning the global and post-global financial crisis. The empirical results show that our models outperform the indices and the tracking portfolios selected by the model with considering target index return is very robust. Our approach has potential applications to better manage pension funds, public funds, private equity funds and fund of funds.