Research On Nonparametric Frontier-Based Estimation Methods And Applications Of Portfolio Efficiency

With the booming development of financial globalization,the supply of products and services in the financial market has become increasingly diversified and complex.With a wide range and enormous scale of financial products,how to build an effective approach for assessing the performance of portfolio is an important issue for all participants in the financial market.As a data-driven multidimensional evaluation methodology,the nonparametric frontier-based methods have been gradually and partially transposed to the analysis of portfolio efficiency.However,there are still several shortcomings in the theory and practice of nonparametric frontier-based portfolio assessment methods in existing studies.How to effectively capture the complex characteristics of asset returns and the mixed risk preferences of investors,and further integrate these factors into nonparametric frontier-based portfolio efficiency evaluation models,so as to construct the corresponding portfolio screening and optimization strategies.All of these are key issues that need to be addressed in both academic and practical fields.In view of this,this paper focuses on developing the nonparametric frontier-based methods for handling the assessment of portfolio performance from both static and dynamic perspectives.Targeting to improve the performance of nonparametric frontier-based methods for efficiency estimation and strategy optimization,a series of nonparametric frontier(metafrontier)-based methods are constructed for estimating portfolio efficiency and Luenberger portfolio index under different scenarios,and further applies the proposed methods to the portfolio selection and optimization.The main research contents are as follows.Firstly,for the portfolio evaluation with complex return characteristics,the theoretical nature and appropriateness of the nonparametric frontier estimator are yet to be demonstrated.In view of this,the necessity of multiple time periods and multiple moments for portfolio efficiency evaluation is clarified.In the return-risk framework,the portfolio possible sets of single/multiple periods and multiple moments satisfying different return-to-scale assumptions are constructed,and the corresponding portfolio evaluation models are proposed with the shortage function measures.Combining the convexity and return-to-scale assumptions from production theory,a series of nonparametric frontier evaluation methods are proposed for estimating the above portfolio possibility sets and portfolio efficiency measures,and the convergence of the single/multi-time nonparametric frontier estimators is systematically demonstrated when the return and risk measures satisfy different properties,respectively.These proposed methods are empirically applied to hedge fund data,since this category of funds is known to be subject to non-normal return distributions.In the empirical part,both the applicability of the proposed nonparametric efficiency estimates and the variability among these estimators are tested,and further the impact of multiple periods and higher-order moments on portfolio efficiency distributions are examined.This provides a theoretical support for investors on the choice of evaluation methods,and also enriches the traditional portfolio evaluation theory.Secondly,most existing studies on portfolio evaluation are limited to static analysis,hardly applied to examine the dynamic efficiency evolution of portfolios and the attribution of efficiency changes.To tackle this issue,the efficiency evolution and the attribution of efficiency change are investigated from a dynamic perspective.Combining the single/multi-period nonparametric frontier estimates with Luenberger productivity index,the single/multi-period,multi-moment Luenberger portfolio indices are proposed,which provide consistent estimates for the Luenberger portfolio indices driven by the diversified portfolio models.By the convexity and returns-to-scale assumptions,both contemporaneous and intertemporal shortage functions are proposed in the single/multiple-period and multi-moment framework,to construct the corresponding Luenberger portfolio index.Furthermore,the underlying mechanism of portfolio efficiency changes is investigated through the decomposition of this Luenberger portfolio index.The validity and applicability of the proposed Luenberger portfolio index is demonstrated using hedge fund data,and the effect of multiple periods and multiple moments on the Luenberger portfolio index are tested.This work serves to offer a theoretical guidance to both individual investors for investment decisions,as well as a useful reference to portfolio managers for asset allocations.Thirdly,the existing studies always assume that the portfolios to be evaluated are homogeneous,however,there exists heterogeneity in the investment techniques of different categories of portfolios,so it seems to be unfair to compare their relative efficiency directly.Accounting for the heterogeneity among portfolio groups,the metafrontier and within-group portfolio possibility sets are constructed and then the corresponding portfolio efficiency measures are proposed in the single/multi-period framework,respectively.Combining the assumptions of convexity of within-group investment technology and returns to scale,a series of portfolio performance measures based on the extension of shortage function measures and the nonparametric metafrontier and within-group frontiers are proposed.Furthermore,the metafrontier portfolio efficiency measure is decomposed into within-group efficiency and technology different gap,where the former measures relative performance among peers and measure the potential gains if portfolio managers are willing to change their initial investment technology or styles.Using actual data from categories of funds,we investigate the heterogeneity across categories of funds,and further analyze the impact of the specification factors of the nonparametric metafrontier portfolio evaluation model on the metafrontier efficiency and its components.It opens up a novel perspective on the performance assessment of portfolio across categories,and can ensure the fairness of portfolio evaluation to certain extent.Fourthly,there also exists a clear heterogeneity in the efficiency change characteristics and patterns among different categories of portfolios,but the dynamic evaluation of portfolios accounting for heterogeneity has not been yet explored.To investigate this difficulty,based on the metafrontier efficiency measures,the metafrontier Luenberger portfolio indices are developed to analyze the dynamic efficiency and attribution problems of the efficiency changes for heterogeneous portfolios.Combining the assumptions of convexity of within-group investment technology and returns to scale,the contemporaneous and intertemporal metafrontier shortage function measures and the corresponding metafrontier Luenberger portfolio indices are constructed in the single/multi-period frameworks,respectively.Furthermore,the full decomposition of the single/multi-period metafrontier Luenberger portfolio indices are proposed to investigate the causes of efficiency changes for different categories of portfolios.Different groups of fund data are employed to test the feasibility and usefulness of the proposed metafrontier Luenberger indices,and to further explore the impact of the multiple periods,multiple moments and within-group convexity assumptions on the metafrontier Luenberger index and its full decomposition.This work helps to understand the performance heterogeneity of different categories of portfolios in a comprehensive way,and to give useful information for the adjustment and optimization of dynamic investment decisions of actual investors and portfolio managers.Finally,the available studies are all ex-post evaluations based on historical data,while their out-of-sample performance remains to be tested.Responding to a practical problem,this paper designs the buy-and-hold backtesting schemes to evaluate and compare the outof-sample performance of different nonparametric frontier(metafrontier)-based and frontier(metafrontier)Luenberger-based portfolio evaluation methods,exploring the practical effectiveness of each nonparametric portfolio evaluation methods in the selection and optimization of portfolios.The backtesting results show that the nonparametric frontier(metafrontier)-based and frontier(metafrontier)Luenberger-based evaluation methods in the multi-period and multi-moment frameworks establish an overall dominance than those in the traditional mean-variance frameworks,demonstrating the usefulness and feasibility of the proposed multi-time and multi-moment nonparametric frontier-based efficiency estimation methods in actual investment.This work contributes to the application research of portfolio evaluation methods,which is an important guidance for individual and institutional investors to develop investment strategies in the actual financial market.