Illiquide Assets in der Portfoliooptimierung

When optimizing a portfolio, which comprises liquid as well as illiquid assets, under the constraint of a liquidity requirement, one has to take into account the particular characteristics of illiquid assets. Illiquid assets in this context have the constituting property that they can only be sold as a whole and – if sold on a short term basis – selling leads to losses. Performing the analysis of a single period model in a mean downside risk framework with one liquid and one illiquid asset, significant differences are proven in comparison to the results of an optimization concerning solely liquid assets. For example, although the return on assets is safe in the first scenario, the portfolio value is already risky due to the uncertain liquidity requirement and situations arise where the allocation to both the liquid and the illiquid asset is optimal. Furthermore, when asset returns are uncertain, the expected portfolio value depends on the assets’ variances and can even be increased by positive correlations.     

Overviewing the transition of Markowitz bi-criterion portfolio selection to tri-criterion portfolio selection

Over 60 years ago, Markowitz introduced the mean-variance efficient frontier to finance. While mean-variance is still the predominant model in portfolio selection, it has endured many criticisms. One serious one is that it does not allow for additional criteria. The difficulty is that the efficient frontier becomes a surface. With it now possible to compute such a surface, we provide an overview on how Markowitz’s risk-return (bi-criterion) portfolio selection can be extended to tri-criterion portfolio selection. With a focus on the geometry of the extension, many graphs are used to illustrate.     

A Model of the Consumption Response to Fiscal Stimulus Payments

A wide body of empirical evidence finds that approximately 25 percent of fiscal stimulus payments (e.g., tax rebates) are spent on nondurable household consumption in the quarter that they are received. To interpret this fact, we develop a structural economic model where households can hold two assets: a low‐return liquid asset (e.g., cash, checking account) and a high‐return illiquid asset that carries a transaction cost (e.g., housing, retirement account). The optimal life‐cycle pattern of portfolio choice implies that many households in the model are “wealthy hand‐to‐mouth”: they hold little or no liquid wealth despite owning sizable quantities of illiquid assets. Therefore, they display large propensities to consume out of additional transitory income, and small propensities to consume out of news about future income. We document the existence of such households in data from the Survey of Consumer Finances. A version of the model parameterized to the 2001 tax rebate episode yields consumption responses to fiscal stimulus payments that are in line with the evidence, and an order of magnitude larger than in the standard “one‐asset” framework. The model's nonlinearities with respect to the rebate size and the prevailing aggregate economic conditions have implications for policy design.     

基于随机久期缺口控制的全资产负债优化模型

资产负债管理是银行等金融机构在负债结构和总量一定的前提下,通过对资产进行优化配置,达到资产流动性、盈利性和安全性“三性”之间的平衡。本文基于CIR动态利率期限结构求解随机久期,对包括增量和存量在内的全部资产负债组合的久期缺口进行预留和约束,构建资产负债优化模型控制利率风险。本文的创新与特色有三:一是以控制CIR利率期限结构的随机久期缺口为约束条件建立非线性规划模型、对资产配置进行利率风险免疫,反映了利率随时间的动态变化,突破了Macaulay久期、FW久期等现有研究的利率随时间的变化是固定不变或平行移动的限定条件,使资产配置的利率风险免疫更加符合现实情况。二是建立了包括增量资产负债与存量资产负债的全资产负债优化配置模型,改变了现有资产负债模型大多只考虑增量资产负债、而忽略存量资产负债的弊端。三是以市场利率朝着最不利方向变动时、预留缺口损失后的资本充足率仍满足监管要求为约束条件,保证了在利率不利变动情况下损失仍在可控范围内,在利率有利变动时银行净值增加。     

基于通货膨胀和风险偏好视角的资产配置研究

不确定条件下的资产配置问题无论对于学术研究还是投资行为都具有重大的理论和实际意义。本文选取广义范围上的现金、股票、债券作为投资者进行资产配置的产品,在CRRA(Constant Relative Risk Aversion)和HARA(Hyperbolic Absolute Risk Aversion)两种偏好假设下,分别求出了投资者效用最大化时的最优财富以及最优资产组合中各资产的权重,并比较分析了两种偏好假设下通货膨胀、风险偏好、投资期限三种因素对资产配置的影响。研究结论表明:通货膨胀会影响股票和债券的风险溢价,进而影响最优资产组合中各资产的权重;股票的权重不会受投资期限的影响,在通货膨胀率和风险偏好不变时,其值始终为一常数,但债券和现金的权重则由投资期限、通货膨胀和风险偏好共同决定;此外,在CRRA和HARA偏好假设下,以上三种因素对资产配置的影响存在较大差异,特别是在HARA框架下存在买空行为。     

效用函数意义下投资组合有效选择问题的研究

我们知道,每个投资者在进行投资过程中,都有自己对收益与风险的偏好程度,即投资活动要遵循一个关于收益与风险的效用函数。按照古典经济学的分析,这个效用函数称为无差异曲线 (IDC),它是用均值 -方差来表现风险 -回报率相互替换的大小和形式的。每个投资者都拥有一条无差异曲线来表示他对于预期回报率和标准差的偏好。那么投资者如何确定他的一条无差异曲线,使他的最佳资产组合位于这条无差异曲线上 ?本文运用自己独创的一种几何方法解决了这个难题。本文首先把Markowitz模型的有效前沿用投资组合的权重向量表示出来,然后将无差异曲线也用抽资组合的权重向量表示出来,再由资产组合的有效选择原则就求出这个无差异曲线了。     

不允许卖空下证券投资组合的区间二次规划问题

本文基于经典的Markowitz均值-方差模型,针对市场上不允许卖空的情况,提出了证券投资组合的区间二次规划模型,通过应用区间数排序方法(区间序关系、区间可能度和区间可接受度),给出了两种证券投资组合的区间非线性优化的数学转化模型,从而将不确定性证券投资组合模型转化为确定性的证券投资组合二次规划模型进行求解,并对由本文给出的三种求解方法与传统方法进行了比较。     

随机跳跃幅度的最优消费与证券选择策略问题

在最优消费与证券选择问题中,假定投资市场有两种资产可供选择:一种为无风险资产(银行债券),另一种为风险资产(股票).由于受重大信息的影响,风险资产的价格往往会产生跳跃.文章研究了这种带跳跃的投资问题,用泊松过程与布朗运动模拟了投资者的财富过程.为使投资者在整个生命周期的消费效用期望值最大,在跳跃幅度为一随机变量的条件下,利用贝尔曼动态规划原理,导出了最优消费及投资策略所满足的方程组,并且在跳跃幅度的概率分布已知的情况下,针对具体的参数值,给出了最优初始策略的数值解与最大消费效用期望值.     

考虑损失规避的期望效用投资组合模型

投资者行为的本质特征会影响投资者对不同风险资产的投资决策。本文从期望效用最大化的角度研究不同风险资产的配置问题,并将人的心理活动引入了投资组合模型之中。论文借鉴了损失规避这个重要的概念,将投资者的效用函数表示为期末财富和财富变化的函数;建立了基于损失规避的最优投资组合模型;并对我国上海股票市场进行了实证分析,得到了在财富变化的不同关心程度下的组合前沿。     

Applying the Partitioned Multiobjective Risk Method (PMRM) to Portfolio Selection

The analysis of risk-return tradeoffs and their practical applications to portfolio analysis paved the way for Modern Portfolio Theory (MPT), which won Harry Markowitz a 1992 Nobel Prize in Economics. A typical approach in measuring a portfolio's expected return is based on the historical returns of the assets included in a portfolio. On the other hand, portfolio risk is usually measured using volatility, which is derived from the historical variance-covariance relationships among the portfolio assets. This article focuses on assessing portfolio risk, with emphasis on extreme risks. To date, volatility is a major measure of risk owing to its simplicity and validity for relatively small asset price fluctuations. Volatility is a justified measure for stable market performance, but it is weak in addressing portfolio risk under aberrant market fluctuations. Extreme market crashes such as that on October 19, 1987 ("Black Monday") and catastrophic events such as the terrorist attack of September 11, 2001 that led to a four-day suspension of trading on the New York Stock Exchange (NYSE) are a few examples where measuring risk via volatility can lead to inaccurate predictions. Thus, there is a need for a more robust metric of risk. By invoking the principles of the extreme-risk-analysis method through the partitioned multiobjective risk method (PMRM), this article contributes to the modeling of extreme risks in portfolio performance. A measure of an extreme portfolio risk, denoted by f(4), is defined as the conditional expectation for a lower-tail region of the distribution of the possible portfolio returns. This article presents a multiobjective problem formulation consisting of optimizing expected return and f(4), whose solution is determined using Evolver-a software that implements a genetic algorithm. Under business-as-usual market scenarios, the results of the proposed PMRM portfolio selection model are found to be compatible with those of the volatility-based model. However, under extremely unfavorable market conditions, results indicate that f(4) can be a more valid measure of risk than volatility.     

基于投资者情绪的投资组合模型研究

本文在假设投资者风险厌恶、且其风险厌恶程度受其情绪影响的条件下,以投资者效用最大化为决策目标,建立基于投资者情绪的投资组合模型从理论上研究投资者情绪对投资组合结构及其收益-风险关系的影响。研究结果表明,当投资者过度乐观时,其将通过银行借贷融资等方式购买超额风险资产;当投资者情绪处于相对理性状态时,其将合理分配无风险资产和风险资产的投资比例;当投资者情绪处于悲观状态时,其将卖空风险资产。当投资者情绪处于过度乐观和相对理性状态时,投资组合预期超额收益与风险正相关;当投资者情绪处于悲观状态时,投资组合预期超额收益与风险负相关。论文研究结果修正了前人的相关研究结论,是对传统投资组合理论的深化和发展。     

基于半离差风险收益的投资组合管理优化模型研究

本文在对投资组合管理理论分析的基础上,利用半离差法计算组合投资的风险与收益,克服了H. Markowitz提出的均值一方差模型研究的不足以及半方差模型的烦琐,提出了基于半离差风险收益的多目标优化模型;假设投资组合一般包括三种资产形式:股票、债券、现金。引进了机会成本概念在投资选择中的重要性,更加符合我国投资者的实际,便于操作,这为证券投资组合优化提供了一种新的方法,并有一定的参考借鉴价值。     

基于股价预测的泛证券投资组合策略

本文基于期望效用最大化和L₁-中位数估计研究了在线投资组合选择问题。与EG（Exponential Gradient）策略仅利用单期价格信息估计价格趋势不同,本文将利用多期价格信息估计价格趋势,以提高在线策略的性能。首先,基于多期价格数据,利用L₁-中位数估计得到预期价格趋势。然后,通过期望效用最大化,提出一个新的具有线型时间复杂度的在线策略,EGLM（Exponential Gradient via L₁-Median）。并通过相对熵函数定义资产权重向量的距离,进而证明了EGLM策略具有泛证券投资组合性质。最后,利用国内外6个证券市场的历史数据进行实证分析,结果表明相较于UP（Universal Portfolio）策略和EG策略,EGLM策略有更好的竞争性能。     

有效市场投资组合的识别与确定

Sharp、Lintner和Mossin发现的资本资产定价模型(CAPM)是一个一般均衡模型,不仅使人们提高了对市场行为的了解,而且还提供了实践上的便利,同时也为评估风险调整中的业绩提供了一种实用的方法。因此CAPM为投资组合分析的多方面的应用提供了一种原始的基础。然而,在1977年RichardRoll对CAPM的检验提出了尖锐的批评,批评的关键之一就是有效市场投资组合是否能得到识别。本文运用自己独创的一种几何方法解决了这个长达二十余年的国际性难题。本文首先把Markowitz模型的有效前沿用投资组合的权重向量表示出来,然后将资本市场线(CML)也用投资组合的权重向量表示出来,再由CML的定义就求出这个有效市场投资组合了。     

动态均值-方差资产组合的有效性:时变风险容忍度视角

尽管均值-方差模型在静态资产组合优化过程中得到广泛运用并证明是有效的,但在动态情景下,均值-方差模型运用于动态资产组合优化过程中的有效性问题引起人们的质疑：一是常风险规避系数的设定不符合事实;二是投资者偏好设定不符合动态情景下的主流效用函数族。鉴于此,本文假设投资者风险容忍度是资产组合投资期与投资者期望收益率的函数,研究动态均值-方差资产组合的有效性问题。基于均值-方差分析框架构建时变风险容忍度下的动态资产组合模型;运用伊藤定理和拉格朗日乘子法获得最优资产组合封闭解;基于二次效用偏好下的动态资产组合,从资产组合策略、夏普率、确定性等价收益率和有效前沿等视角验证动态均值-方差资产组合策略和业绩,并予以实证。结果表明：动态均值-方差资产组合不但具有同等业绩而且体现了其灵活性和风险对冲价值;尽管动态均值-方差资产组合表现出高杠杆性,但其确定性等价收益率较高,且随投资期的增加呈现倒U型趋势;动态均值-方差资产组合的投资期效应显著,强于投资者期望收益率。研究指出,时变风险容忍度下的动态均值-方差资产组合管理和优化策略有效,但在短投资期（低于12个月）和（或）低期望收益率下并不适用。研究不但拓展了均值-方差模型在动态情境下的应用,而且体现了投资者源于心理和（或）其财富变化的投资行为调整。     

一类稀疏投资组合双层参数估计模型及其应用

带基约束的投资组合问题是近年来投资组合领域的热点问题,但是参数不确定性直接影响了模型的效果。带基约束的投资组合问题所涉及的参数不仅包括以往研究认为非常重要的预期收益率,还包括控制投资组合规模的稀疏度,尤其是最优稀疏度估计方面的专门研究还十分匮乏。为了使带基约束的投资组合模型更好地为投资决策服务,本文从投资者效用出发,用双层规划的思想构建了带基约束的投资组合双层参数估计模型。然后根据模型的特点,设计了无导数优化算法框架,并基于ADMM对算法子问题进行求解。本文实验针对真实的市场数据给出了预期收益率和最优稀疏度的估计,接着通过与等权重策略和含上下界约束的均值-方差模型进行比较,说明了模型及算法的有效性和实用性。最后,将本文提出的双层参数估计模型推广到了更一般的形式。     

Risk‐Based Sampling: I Don't Want to Weight in Vain

Recently, there has been considerable interest in developing risk‐based sampling for food safety and animal and plant health for efficient allocation of inspection and surveillance resources. The problem of risk‐based sampling allocation presents a challenge similar to financial portfolio analysis. Markowitz (1952) laid the foundation for modern portfolio theory based on mean‐variance optimization. However, a persistent challenge in implementing portfolio optimization is the problem of estimation error, leading to false “optimal” portfolios and unstable asset weights. In some cases, portfolio diversification based on simple heuristics (e.g., equal allocation) has better out‐of‐sample performance than complex portfolio optimization methods due to estimation uncertainty. Even for portfolios with a modest number of assets, the estimation window required for true optimization may imply an implausibly long stationary period. The implications for risk‐based sampling are illustrated by a simple simulation model of lot inspection for a small, heterogeneous group of producers.     

基于M-SemiA.D组合投资模型及对上海股市实证研究

马柯威茨的均值-方差(M-V)模型中以方差度量风险存在两个致命的缺陷,为了更精确度量风险,作者提出了半绝对离差(SemiA.D)概念,并以此对M-V模型进行改进。通过对上海有代表性的50支股票复权价进行分析,我们得到:在每个期望收益率水平上,基于M-SemiA.D模型的投资组合都优于M-V模型中的投资组合,并且有效投资组合满足两基金分离定理。     

均值-方差模型具有一般不确定性下的最优资产组合选择

引入以记忆系数和无差异系数表征的随机变量测度均值-方差模型的一般不确定性特征,反映投资者的模型信任程度,研究均值-方差模型具有一般不确定性下的最优资产组合选择问题。基于资本市场线理论,构建最优资产组合选择是模型信任程度和基于均值-方差模型的传统资产组合选择的线性函数;基于记忆系数和无差异系数的不同组合,运用基于事例推理的方法求解二次效用投资者的最优模型信任程度,获得均值-方差模型具有一般不确定性下的最优资产组合,并以上证综指1997年1月-2014年8月的月度收益数据形成两个研究样本予以实证比较研究。结果表明,较大风险规避投资者,在较大记忆系数和较小无差异系数下,其模型信任程度调整较快、资产组合调整幅度大,表现出可获得性和代表性行为偏差,通常采取积极资产组合策略;反之,其模型信任程度调整渐进、资产组合调整幅度小,表现出锚定性和保守性行为偏差,通常采取消极资产组合策略;模型一般不确定性对最优资产组合选择的影响强于股票市场记忆性的影响。研究体现了投资者的有限理性,将传统的资产组合选择问题延伸至行为金融学领域。     

基于EVT-POT-SV-MT模型的极值风险度量

针对金融资产收益的异常变化,采用SV-MT模型对风险资产的预期收益做风险补偿并捕捉收益序列的厚尾性、波动的异方差性等特征,将收益序列转化为标准残差序列,通过SV-MT模型与极值理论相结合拟合标准残差的尾部分布,建立了一种新的金融风险度量模型——基于EVT-POT-SV-MT的动态VaR模型.通过该模型对上证综指做实证分析,结果表明该模型能够合理有效地度量上证综指收益的风险.