均值-方差-近似偏度投资组合模型和实证分析

均值-方差投资组合模型作为现代投资组合理论的基础, 采用方差作为风险度量,但忽略了投资组合收益的非对称性. 而考虑收益非对称性的基于偏度的投资组合模型由于非凸和非二次性 使模型难以求解. 本文提出用上下半方差的比值近似刻画偏度, 建立了均值-方差-近似偏度(MVAS）模型,并利用该模型对中国证券市场主要股票指数进行实证分析. 实证分析结果表明, 在收益率非正态分布的市场中,考虑了收益率非对称性的投资组合模型较传统的MV和MAD模型具有更优的表现.     

基于模糊收益率的最优投资组合模型

考虑了收益率为模糊数的投资组合问题.在一定置信水平上,用收益率波动差的平方和作为风险的度量,在预期收益率给定时,建立了风险最小化的投资组合模型.投资者可以参考其最优解来减小投资风险.最后给出了一个实例.     

证券投资组合理论的一种新模型及其应用

马科维茨(Markowitz)以证券收益率的方差作为投资风险的测度建立了组合证券投资模型，本基于熵的概念，在研究马科维茨(Markowitz)证券投资组合模型的基础上，分析了该模型用方差度量风险的不足，进而提出一种新的证券投资组合优化模型，并以实例作了说明。     

与TSD准则一致的组合证券投资分析

基于预先给定的目标收益率,利用投资者对低于目标收益率的风险损失和高于目标收益率的风险报酬之间的权衡,给出了一些非对称风险度量模型,特别其中一种风险度量是低于参考点的方差和高于参考点的方差的加权和,它利用二阶上偏矩来修正二阶下偏矩,进一步建立了在该非对称风险度量下的组合投资优化模型,并证明了该模型在三阶随机占优的意义下是有效的.此外,还给出了其它3个模型与三阶随机占优准则是否一致的结论,并对所给出的几个组合证券投资模型的求解方法及其应用进行了分析.以上研究和分析为投资者在选择投资模型时避免盲目性、任意性提供了有益的决策参考.     

基于模糊收益率的养老保险基金投资研究

结合中国养老保险基金投资现状,考虑预期收益率是模糊数的情形,利用可能性均值和可能性方差作为投资组合的预期收益率和风险,建立均值-方差组合投资模型.最后,利用lingo软件进行数值分析,表明此模型具有一定的实际应用价值.     

具有投资限制的风险资产模糊随机投资组合模型

研究了模糊随机环境下风险资产投资组合选择问题.利用模糊随机变量刻画风险资产的收益率,建立了具有投资限制的风险资产投资组合选择的一般模糊随机均值-方差模型,该模型包括了是否允许卖空及具有投资比例下界约束的情况.在此基础上,提出了具有梯形模糊随机收益率的具体投资组合优化模型,这些模型能够转化为二次规划问题求解.最后,利用上证50指数中的9种股票对模型进行了实证分析,结果表明模型能够有效分散非系统性风险.     

基于CVaR的债券投资组合模型

针对债券投资组合中的风险度量难题,用CVaR作为风险度量方法,构建了基于CVaR的债券投资组合优化模型.采用历史模拟算法处理模型中的随机收益率向量,将随机优化模型转化为确定性优化模型,并且证明了算法的收敛性.通过线性化技术处理CVaR中的非光滑函数,将该模型转化为一般的线性规划模型.结合10只债券的组合投资实例,验证了模型与算法的有效性.     

基于旋转算法的随机模糊均值-方差投资组合优化

Markowitz首先采用方差度量风险，并应用于投资组合优化中，大多数的均值方差模型仅对随机投资组合优化或模糊投资组合优化进行研究，然而，实际投资组合优化问题既包含随机信息也包含模糊信息。本文首先定义随机模糊变量的方差，并用其度量风险，提出了具有交易成本、借贷约束和阀值约束的均值-方差随机模糊投资组合优化模型。基于随机模糊理论，将上述模型转化为具有线性等式和线性不等式约束的凸二次规划问题，并得到其KKT条件。本文还提出改进的旋转算法求解上述模型，该算法消掉KKT条件中部分变量，减少计算量。最后，采用中国证券市场的实际数据进行样本内分析和样本外分析，验证了上述模型和算法的有效性。     

基于Clayton Copula-GARCH模型投资组合VaR的度量

运用Copula方法研究了含股指期货的投资组合的风险度量问题.首先采用不同的GARCH模型对单个资产收益率建模,然后选择Clayton Copula函数来描述投资组合各资产之间的相关结构,建立联合分布模型,进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的VaR.Kupiec检验表明,ClaytonCopula-GARCH模型在投资组合风险度量上具有较高的准确性.     

均值-叉熵证券投资组合优化模型

在研究马科维茨(Markowitz)证券投资组合模型的基础上,分析了该模型用方差度量风险的缺陷,进而提出用叉熵作为风险的度量方法,建立了均值-叉熵的投资组合优化模型.该模型计算简便,更易被一般投资人所使用.     

Mean-variance models for portfolio selection with fuzzy random returns

This paper develops two novel types of mean-variance models for portfolio selection problems, in which the security returns are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. In the proposed models, we take the expected return of a portfolio as the investment return and the variance of the expected return of a portfolio as the investment risk. We assume that the security returns are triangular fuzzy random variables. To solve the proposed portfolio problems, this paper first presents the variance formulas for triangular fuzzy random variables. Then this paper applies the variance formulas to the proposed models so that the original portfolio problems can be reduced to nonlinear programming ones. Due to the reduced programming problems include standard normal distribution in the objective functions, we cannot employ the conventional solution methods to solve them. To overcome this difficulty, this paper employs genetic algorithm (GA) to solve them, and verify the obtained optimal solutions via Kuhn-Tucker (K-T) conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed models and methods.     

Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature

Since the pioneering work of Harry Markowitz, mean–variance portfolio selection model has been widely used in both theoretical and empirical studies, which maximizes the investment return under certain risk level or minimizes the investment risk under certain return level. In this paper, we review several variations or generalizations that substantially improve the performance of Markowitz’s mean–variance model, including dynamic portfolio optimization, portfolio optimization with practical factors, robust portfolio optimization and fuzzy portfolio optimization. The review provides a useful reference to handle portfolio selection problems for both researchers and practitioners. Some summaries about the current studies and future research directions are presented at the end of this paper.     

考虑投资者异质信念和目标优先级的投资组合问题研究

考虑证券市场的模糊不确定性及投资者的模糊决策特征,以资产收益、下方风险及流动性为模糊投资目标,构建考虑投资者异质信念和目标优先级的多目标投资组合模型。进一步,以我国主板、中小板和创业板市场为背景,采用CPT-TOPSIS交互式算法进行实证分析。研究发现:乐观、理性和悲观投资者权衡收益、风险和流动性目标时偏好的优先顺序不同,导致资产配置结构、最优决策和绩效表现存在差别。结果表明模糊多目标模型能够满足不同投资者权衡多目标的差异化投资需求,取得优于基准随机投资组合的投资效果,可作为投资者投资决策的参考依据。     

Optimal investment with a constraint on ruin for a fuzzy discrete-time insurance risk model

In this paper, we consider a mean–variance portfolio optimization problem for a fuzzy discrete-time insurance risk model. The model consists of independent, identically distributed net losses considered within successive time periods, and incorporates investment incomes from a two-asset portfolio. More precisely, in the beginning of each period, the surplus is invested in both a risk-free bond with fixed interest, and a risky stock with fuzzy return rate. Our purpose is to determine the proportion invested in the stock that maximizes the insurer’s expected wealth, while reducing his risks. Therefore, for this fuzzy model, we formulate mean–variance optimization problems that also include constraints on ruin, and we present a method for determining the resulting optimal proportion to be invested in the risky stock. This method is illustrated in a numerical study in which the fuzzy return rate is considered to be an adaptive fuzzy number that generalizes the well-known trapezoidal fuzzy number.     

A mean-absolute deviation-skewness portfolio optimization model

It is assumed in the standard portfolio analysis that an investor is risk averse and that his utility is a function of the mean and variance of the rate of the return of the portfolio or can be approximated as such. It turns out, however, that the third moment (skewness) plays an important role if the distribution of the rate of return of assets is asymmetric around the mean. In particular, an investor would prefer a portfolio with larger third moment if the mean and variance are the same. In this paper, we propose a practical scheme to obtain a portfolio with a large third moment under the constraints on the first and second moment. The problem we need to solve is a linear programming problem, so that a large scale model can be optimized without difficulty. It is demonstrated that this model generates a portfolio with a large third moment very quickly.Presently at Mitsubishi Trust Bank Co., Ltd.     

Portfolio selection based on fuzzy cross-entropy

In this paper, the Kapur cross-entropy minimization model for portfolio selection problem is discussed under fuzzy environment, which minimizes the divergence of the fuzzy investment return from a priori one. First, three mathematical models are proposed by defining divergence as cross-entropy, average return as expected value and risk as variance, semivariance and chance of bad outcome, respectively. In order to solve these models under fuzzy environment, a hybrid intelligent algorithm is designed by integrating numerical integration, fuzzy simulation and genetic algorithm. Finally, several numerical examples are given to illustrate the modeling idea and the effectiveness of the proposed algorithm.     

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.     

Mean-variance-skewness model for portfolio selection with fuzzy returns

Numerous empirical studies show that portfolio returns are generally asymmetric, and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same. In order to measure the asymmetry of fuzzy portfolio return, a concept of skewness is defined as the third central moment in this paper, and its mathematical properties are studied. As an extension of the fuzzy mean-variance model, a mean-variance-skewness model is presented and the corresponding variations are also considered. In order to solve the proposed models, a genetic algorithm integrating fuzzy simulation is designed. Finally, several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm.     

模糊线性规划在社保基金投资组合优化中的应用

如何选择一个满意的投资组合，在既定条件下实现一个最有效率的风险-收益搭配，是社保基金投资的关键问题，本通过建立和求解社保基金的投资风险最小化模糊线性规划模型和投资收益最大化模糊线性规划模型，试图优化社保基金的投资组合，章最后给出应用示例。