中国股市的投资组合分析

本文从马柯维茨投资组合理论出发 ,对沪、深股市进行实证分析 ,并对投资组合的时变特征、组合规模进行了讨论     

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.     

Optimal dividends in the dual model

The optimal dividend problem proposed by de Finetti [de Finetti, B., 1957. Su un’impostazione alternativa della teoria collettiva del rischio. In: Transactions of the XVth International Congress of Actuaries, vol. 2. pp. 433-443] is to find the dividend-payment strategy that maximizes the expected discounted value of dividends which are paid to the shareholders until the company is ruined or bankrupt. In this paper, it is assumed that the surplus or shareholders’ equity is a Lévy process which is skip-free downwards; such a model might be appropriate for a company that specializes in inventions and discoveries. In this model, the optimal strategy is a barrier strategy. Hence the problem is to determine b^∗, the optimal level of the dividend barrier. A key tool is the method of Laplace transforms. A variety of numerical examples are provided. It is also shown that if the initial surplus is b^∗, the expectation of the discounted dividends until ruin is the present value of a perpetuity with the payment rate being the drift of the surplus process.     

不确定条件下具有容差项的Markowitz证券组合投资模型的最优化解法

在分析证券市场中证券组合投资不确定性质的基础上,通过对Markowitz模型中证券期望收益与方差引入容差项来度量证券市场的不确定性,建立了不确定条件下具有容差项的Markowitz证券组合投资模型;分类讨论了容差的上界与下界所对应的两类有效组合前沿,得到了不确定条件下的证券组合投资模型的最优化解法及相关定理;最后给出了一个具体的数值实例．     

A tail-revisited Markowitz mean-variance approach and a portfolio network centrality

A measure for portfolio risk management is proposed by extending the Markowitz mean-variance approach to include the left-hand tail effects of asset returns. Two risk dimensions are captured: asset covariance risk along risk in left-hand tail similarity and volatility. The key ingredient is an informative set on the left-hand tail distributions of asset returns obtained by an adaptive clustering procedure. This set allows a left tail similarity and left tail volatility to be defined, thereby providing a definition for the left-tail-covariance-like matrix. The convex combination of the two covariance matrices generates a “two-dimensional” risk that, when applied to portfolio selection, provides a measure of its systemic vulnerability due to the asset centrality. This is done by simply associating a suitable node-weighted network with the portfolio. Higher values of this risk indicate an asset allocation suffering from too much exposure to volatile assets whose return dynamics behave too similarly in left-hand tail distributions and/or co-movements, as well as being too connected to each other. Minimizing these combined risks reduces losses and increases profits, with a low variability in the profit and loss distribution. The portfolio selection compares favorably with some competing approaches. An empirical analysis is made using exchange traded fund prices over the period January 2006–February 2018.

     

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。     

有交易成本的投资组合策略

金融市场都存在交易成本,为此,本文建立了有交易成本的投资组合模型,讨论了模型解的条件,并提出模型的通用数值解法,最后给出了应用举例．     

On the dual test for SSD efficiency : With an application to momentum investment strategies

This paper analyzes the dual formulation of Post’s [Post, T., 2003. Empirical tests for stochastic dominance efficiency. Journal of Finance 58, 1905–1932] test for second-order stochastic dominance (SSD) efficiency of a given investment portfolio relative to all possible portfolios formed from set of assets. In contrast to the earlier work, we (1) provide a direct proof for the dual that does not rely on expected utility theory, (2) adhere to the original definition of SSD, (3) phrase in terms of a general polyhedral portfolio possibilities set and (4) construct a SSD dominating benchmark portfolio from the optimal solution. To illustrate the dual SSD test, we apply the test to analyze the effect of short-selling restrictions on the profitability of momentum investment strategies.     

On the equivalence of quadratic optimization problems commonly used in portfolio theory

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e., the Markowitz mean–variance problem as well as the problems based on the mean–variance utility function and the quadratic utility. Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean–variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean–variance efficient.     

Robustness of optimal portfolios under risk and stochastic dominance constraints

Solutions of portfolio optimization problems are often influenced by a model misspecification or by errors due to approximation, estimation and incomplete information. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. We shall deal with output analysis and stress testing with respect to uncertainty or perturbations of input data for static risk constrained portfolio optimization problems by means of the contamination technique. Dependence of the set of feasible solutions on the probability distribution rules out the straightforward construction of convexity-based global contamination bounds. Results obtained in our paper [Dupa?ová, J., & Kopa, M. (2012). Robustness in stochastic programs with risk constraints. Annals of Operations Research, 200, 55–74.] were derived for the risk and second order stochastic dominance constraints under suitable smoothness and/or convexity assumptions that are fulfilled, e.g. for the Markowitz mean–variance model. In this paper we relax these assumptions having in mind the first order stochastic dominance and probabilistic risk constraints. Local bounds for problems of a special structure are obtained. Under suitable conditions on the structure of the problem and for discrete distributions we shall exploit the contamination technique to derive a new robust first order stochastic dominance portfolio efficiency test.     

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。     

Financial Giffen goods: Examples and counterexamples

In the basic Markowitz and Merton models, a stock’s weight in efficient portfolios goes up if its expected rate of return goes up. Put differently, there are no financial Giffen goods. By an example from mortgage choice we illustrate that for more complicated portfolio problems Giffen effects do occur.     

60 Years of portfolio optimization: Practical challenges and current trends

The concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making. In light of the 60 year anniversary of Harry Markowitz’s paper “Portfolio Selection,” we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice, including the inclusion of transaction costs, portfolio management constraints, and the sensitivity to the estimates of expected returns and covariances. In addition, we selectively highlight some of the new trends and developments in the area such as diversification methods, risk-parity portfolios, the mixing of different sources of alpha, and practical multi-period portfolio optimization.     

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.     

Robust asset allocation with conditional value at risk using the forward search

The well‐known Markowitz approach to portfolio allocation, based on expected returns and their covariance, seems to provide questionable results in financial management. One motivation for the pitfall is that financial returns have heavier than Gaussian tails, so the covariance of returns, used in the Markowitz model as a measure of portfolio risk, is likely to provide a loose quantification of the effective risk. Additionally, the Markowitz approach is very sensitive to small changes in either the expected returns or their correlation, often leading to irrelevant portfolio allocations. More recent allocation techniques are based on alternative risk measures, such as value at risk (VaR) and conditional VaR (CVaR), which are believed to be more accurate measures of risk for fat‐tailed distributions. Nevertheless, both VaR and CVaR estimates can be influenced by the presence of extreme returns. In this paper, we discuss sensitivity to the presence of extreme returns and outliers when optimizing the allocation, under the constraint of keeping CVaR to a minimum. A robust and efficient approach, based on the forward search, is suggested. A Monte Carlo simulation study shows the advantages of the proposed approach, which outperforms both robust and nonrobust alternatives under a variety of specifications. The performance of the method is also thoroughly evaluated with an application to a set of US stocks.     

Optimal coordinates for three-dimensional incompressible laminar boundary layers

This paper summarizes the basic theory of optimal coordinates for the three-dimensional incompressible boundary layers. Though in essence the results obtained in this paper form an extension of Kaplun's work in two dimensions, the additional considerations due to three-dimensionality have extended the scope and applicability of the theory of optimal coordinates to more complicated situations.

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Résumé Cet article résume la théorie fondamentale des coordinées optimales pour les couches limites incompressibles à trois dimensions. Les résultats donnés dans cet article ne sont essentiellement que la continuation des recherches de Kaplun faites sur les couches limites à deux dimensions; mais les considérations supplémentaires dues à la tri-dimensionalité ont permis d'augmenter la portée et les applications de la théorie des coordinées optimales à des situations plus compliquées.

     

工件具有任意尺寸的混合分批平行机排序问题的近似算法

本文考虑了工件具有任意尺寸且机器有容量限制的混合分批平行机排序问题。在该问题中, 一个待加工的工件集需在多台平行批处理机上进行加工。每个工件有它的加工时间和尺寸, 每台机器可以同时处理多个工件, 称为一个批, 只要这些工件尺寸之和不超过其容量; 一个批的加工时间等于该批中工件的最大加工时间和总加工时间的加权和; 目标函数是极小化最大完工时间。该问题包含一维装箱问题为其特殊情形, 为强NP-困难的。对此给出了一个$\left( {2 + 2\alpha+\alpha^{2}}\right)$-近似算法, 其中$\alpha$为给定的权重参数, 满足考虑了不同于Goldfarb和Iyengar （2003）的因子模型,通过横截面回归分析以及Fama-MacBeth估计构造了关于资产的平均收益向量和协方差矩阵的不确定性集合（置信区域）。基于这些不确定性集合以及Markowitz“均值-方差模型”的鲁棒投资组合问题,提出了多个鲁棒投资组合问题,并对应的推导出其等价的半正定规划形式,使得问题可以在多项式时间内求解。     

Inverse problem for a vibrating beam

Summary The problem of inferring the flexural rigidity and density of a beam from its eigenfrequencies is considered for the particular case in which one end is clamped. It is shown that three spectra associated with three sets of boundary conditions at the other end are required in order to insure a unique solution of the inverse problem. Furthermore, it is shown that this data set is equivalent to the information contained in the time history of the displacement and slope of the free end of the beam set in motion by a concentrated impulse.

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Résumé Cet article traite le problème relatif à la déduction des caractéristiques d'une barre à partir de ses fréquences propres. Bien que nos résultats soient généraux, nous considererons seulement le cas où la barre est encastrée à une extrémité. Nous montrerons que trois spèctres associés à trois types de conditions aux limites pour la seconde extrémité sont nécéssaires pour garantir l'unicité de la solution du problème inverse. De plus, nous montrerons que ces trois spèctres sont équivalents à l'information contenue dans les fonctions représentant le déplacement et la pente de l'extrémité libre de la barre mise en mouvement par un choc donné à cette extrémité.

     

目标规划法在证券组合投资中的应用

证券投资是目前我国经济中的一大热点。本以Markowitz证券组合投资理论为基础，运用目标规划的方法建立一种新的证券组合投资决策模型。在本模型中综合考虑了证券组合的收益，风险，交易费用等因素，对投资选择有效证券组合有一定的实用价值。