On the number of securities which constitute an efficient portfolio

The purpose of this paper is to discuss the relationship between the number of securities which constitute an efficient portfolio as defined by the standard mean-variance portfolio selection model and the number of periods used to compute the efficient portfolio. It is shown that the number of data gives the upper bound of the number of securities which constitute an efficient portfolio, when each efficient portfolio is unique for a given expected return. Empirical tests based on actual return data show that this upper bound is very tight when the number of data is small. However, when more data are used, the upper bound becomes looser. This result is incompatible with the market efficiency. These empirical tests also indicate that a very tight upper bound often causes a degenerate case ensuring zero-variance portfolios.     

An analytic derivation of admissible efficient frontier with borrowing

The admissible efficient portfolio selection problem for risky assets has been discussed by Zhang and Nie. In this paper, the admissible efficient portfolio model is proposed under the assumption that there exists the borrowing (money or a risk free asset) case. The admissible efficient frontiers are developed by the spreads of expected return and risk from admissible errors. The analytic forms of the admissible efficient frontiers when short sales are not allowed on all risky assets are derived from two cases: the borrowing with an upper bound constraint, or without an upper bound constraint. The influence on the admissible efficient frontier is explained under the different interest rates of the borrowing. The differences between the results with the borrowing and the results without the borrowing is revealed by a real numerical example.     

The efficient frontier for bounded assets

This paper develops a closed form solution of the mean-variance portfolio selection problem for uncorrelated and bounded assets when an additional technical assumption is satisfied. Although the assumption of uncorrelated assets is unduly restrictive, the explicit determination of the efficient asset holdings in the presence of bound constraints gives insight into the nature of the efficient frontier. The mean-variance portfolio selection problem considered here deals with the budget constraint and lower bounds or the budget constraint and upper bounds. For the mean-variance portfolio selection problem dealing with lower bounds the closed form solution is derived for two cases: a universe of only risky assets and a universe of risky assets plus an additional asset which is risk free. For the mean-variance portfolio selection problem dealing with upper bounds, the results presented are for a universe consisting only of risky assets. In each case, the order in which the assets are driven to their bounds depends on the ordering of their expected returns.     

证券组合选择的有效子集

本文引进证券组合选择的有效子集概念。有效子集可取代原有的基本证券集来生成Markowitz有效组合前沿。本文给出一个证券集的子集是全集的有效子集的充要条件。在理论上，这是一条新的k-基金分离定理；在实际应用上，这有可能用来减少计算有效组合前沿的计算量。     

极大极小投资组合选择模型和均衡价格系统

讨论了市场上不存在无风险资产条件下投资组合选择的极大极小模型,推导出市场上不存在无风险资产时极大极小模型的最优投资策略和有效前沿,得到了资本市场均衡时存在唯一的非负均衡价格系统的充分必要条件和各资产均衡价格的解析表达式.     

证券集的组合前沿分类与有效子集

本文通过引入证券价格 ,讨论一般证券集组合前沿的分类 ,并据此直接证明判定某个证券子集是全集的有效子集的一个充要条件     

不允许卖空证券组合选择的有效子集

证券组合选择的有效子集是指它可取代原有的基本证券集来生成Markowits有效组合前沿.本文给出一个证券集的子集在不允许卖空的条件下是全集的有效子集的充要条件。     

基于基准过程的动态均值-方差最优投资组合选择

利用动态规划方法研究了基于基准过程的动态均值-方差最优投资组合问题,证明了识别定理,得到了剩余过程的均方最优投资策略和有效前沿.     

Markov-modulated mean-variance problem for an insurer

In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.     

Linear-quadratic efficient frontiers for portfolio optimization

Finding portfolios with given mean return and minimal lower partial mean or variance, two risk criteria of interest in the theory of optimal portfolio selection, is a stochastic linear-quadratic program that can be converted to a large-scale linear or quadratic program when the asset returns are finitely distributed. These efficient frontiers can be computed on presently available platforms for problems of reasonable size; we discuss our experience with a problem involving one thousand assets. Asymptotic statistics for stochastic programs can be applied to justify sampling as a means to approximate continuous distributions by finite distributions.     

Single-Period Markowitz Portfolio Selection,Performance Gauging,and Duality: A Variation on the Luenberger Shortage Function

The Markowitz portfolio theory (Ref. 1) has stimulated research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single-period portfolio selection from a theoretical perspective and generalizes currently used efficiency measures into the full mean-variance space. We introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of the Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency; furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimization.     

Computation of mean-semivariance efficient sets by the Critical Line Algorithm

The general mean-semivariance portfolio optimization problem seeks to determine the efficient frontier by solving a parametric non-quadratic programming problem. In this paper it is shown how to transform this problem into a general mean-variance optimization problem, hence the Critical Line Algorithm is applicable. This paper also discusses how to implement the critical line algorithm to save storage and reduce execution time.     

在不允许卖空条件下的最优比例再保险投资

假设保险公司的盈余过程服从一个带扰动项的布朗运动,保险公司可以投资一个无风险资产和n个风险资产,还可以购买比例再保险,并且风险市场是不允许卖空的.本文在均值一方差优化准则下研究保险公司的最优投资一再保策略选择问题,利用LQ随机控制方法求解模型,得到了保险公司的最优组合投资策略的解析和保险公司投资的有效投资边界的解析表达...     

跳扩散市场投资组合研究

研究了连续时间动态均值-方差投资组合选择问题.假设风险资产价格服从跳跃-扩散过程且具有卖空约束.投资者的目标是在给定期望终止时刻财富条件下,最小化终止时刻财富的方差.通过求解模型相应的Hamilton-Jacobi-Bellmen方程,得到了最优投资策略及有效前沿的显示解.结果显示,风险资产的卖空约束及价格过程的跳跃因素对最优投资策略及有效前沿的是不可忽略的.     

证券数目变化时受到扰动的M-V有效前沿分析

基于M-V证券组合模型,在证券市场上不存在无风险资产且允许卖空条件下,探讨了证券数增加k种后原n种证券协方差矩阵发生改变情形下M-V证券组合有效前沿的漂移问题。通过引入扰动因子和扰动矩阵,给出了M-V证券组合有效前沿的漂移方向及其开口大小的变化情况．研究结果表明证券数增加了k种后有效前沿向左漂移以及它的开口变大,原证券组合的有效前沿完全落在新的证券组合可行集内．     

共同基金和无风险资产投资的最优策略

利用均值-方差模型,分析了非线性交易成本下的共同基金与无风险资产投资组合的有效边界和在一般的效用函数下讨论了投资者的最优投资策略.     

Heuristic algorithms for the cardinality constrained efficient frontier

This paper examines the application of genetic algorithm, tabu search and simulated annealing metaheuristic approaches to finding the cardinality constrained efficient frontier that arises in financial portfolio optimisation. We consider the mean-variance model of Markowitz as extended to include the discrete restrictions of buy-in thresholds and cardinality constraints. Computational results are reported for publicly available data sets drawn from seven major market indices involving up to 1318 assets. Our results are compared with previous results given in the literature illustrating the effectiveness of the proposed metaheuristics in terms of solution quality and computation time.     

全时段最优套期保值模型及实证研

针对传统套期保值模型只考虑套期保值资产在套期保值期末的风险及未能充分利用样本数据所提供的信息的问题,本文提出了一类同时考虑套期保值期内不同期限风险的全时段最优套期保值比率计算模型.全时段套期保值模型通过最小化套期保值资产在套期保值期内不同期限的风险将投资者面临的风险在整个套期保值期内稳定保持在一个较低的水平,并更充分的利用了资产历史价格样本数据所提供的信息.本文基于沪深300指数及其仿真股指期货的历史价格数据,对传统形式的三种套期保值模型与本文提出的三种全时段套期保值模型的套期保值效果进行了实证分析和比较,并使用GARCH模型比较分析了这些模型套期保值的动态效果,结果表明三种全时段模型的套期保值效果都要优于相应的传统模型,能有效地缓解提前终止套期保值时投资者所面临的风险.     

基于通货膨胀风险和Heston随机波动率下的最优资产配置

本文考虑了基于均值-方差准则下的连续时间投资组合选择问题。为了对冲市场中的利率风险和通货膨胀风险,假定市场上存在可供交易的零息名义债券和零息通货膨胀指数债券。另外,投资者还可以投资一个价格具有Heston随机波动率的风险资产。首先建立了基于均值-方差框架下的最优投资组合问题,然后将原问题进行转换,利用随机动态规划方法和对偶Lagrangian原理,获得了均值-方差准则下的有效投资策略以及有效前沿的解析表达形式,最后对相关参数的敏感性进行了分析。     

固定消费/收入模型下的M-V最优投资组合选择

本文研究了一个有固定消费/收入现金流的连续时间的最优投资组合选择问题.把投资者的财富用分离的思想来考虑.将投资者的财富分成两部分,消费/收入部分和投资部分,从而将原问题转化为不含消费/收入现金流的M-V投资组合选择的辅助问题.证明了辅助问题的最优投资策略就是原问题的最优策略,得到了原问题的最优策略及有效前沿并分析了消费/收入对投资的影响.