静态证券组合理论与CAPM—金融理论及其应用（Ⅱ）

1 前言在静态证券组合理论中,我们假定投资者是依据收益率的均值和方差来决定证券组合的.亦即使均值增大、方差减小的投资.这个资产选择的均值方差模型,从大约40年前的Markowitz(1952)以来,大量地被运用于金融中,其理由,并不在于其假定的一般性,而是在于其优良的解析性.而且,如果在均值方差模型上附加上供需均衡条件,就可以导出被称为资产期望收益率的资本性资产评价模型(Capital Asset Pricing Model(CAPM)),这在现今都是一个最重要的资产评价模型. 本文将简洁地说明静态证券组合理论,导出关于均衡中的资产期望收益率的结果.另外,作为CAPM的应用.介绍资本预算法及其对证券投资的应用.本文的构成:第2节是静态证券组合理论;第3节是为引入CAPM的前沿证券组合的数理;第4节是CAPM;第5节是CAPM的应用;最后是结论.     

几种基于CAPM的最优投资组合构造方案及其比较

本文在William Sharpe的资本资产定价模型（简称CAPM）的基础上,考虑了条件CAPM,就条件CAPM中的β系数为常数和时变系数两种情况,在不同的假设下分别给出了描述真实市场的模型,利用此模型给出了条件CAPM中模型参数的估计方法。对每种不同的描述真实市场的模型,我们选用了上海股市的若干股票构造了最优投资组合,并进行投资组合评估分析,最后对这几种情况下的最优投资组合的表现进行了比较。     

基于贝叶斯伪设计与组合样本的候选者数据库网络调查的推断研究

候选者数据库网络调查的推断问题是网络调查发展中迫切需要解决的问题.基于此,提出基于贝叶斯伪设计与组合样本的非概率抽样推断方法:将网络候选者数据库的调查样本与概率样本结合,根据贝叶斯定理推导出网络候选者数据库的调查样本单元的伪权数构造式,再利用两个样本数据共同估计总体均值,最后利用Bootstrap和Jackknife方法来计算总体均值估计的方差估计.研究结果表明:基于贝叶斯伪设计与组合样本的总体均值估计比使用Elliot方法估计的总体均值偏差更小,估计效果较好;方差估计方面,Bootstrap方差估计比Jackknife方差估计的效果好.     

基于超总体伪设计与组合样本的候选者数据库网络调查的推断研究

候选者数据库网络调查的推断问题是网络调查发展中迫切需要解决的问题.基于此,提出基于超总体伪设计与组合样本的非概率抽样推断方法:对网络候选者数据库的调查样本建立超总体模型来构造伪权数,并根据网络候选者数据库的调查样本和概率样本的组合样本计算总体均值的估计,最后根据超总体模型的方差估计理论推导出目标总体均值估计的方差估计式,同时采用Bootstrap与Jackknife方法来估计总体均值估计的方差,并比较不同方差估计方法的效果.研究结果表明:基于超总体伪设计与组合样本的总体均值估计效率高于仅使用概率样本的估计和仅使用网络候选者数据库的调查样本加权的估计,估计效果较好;方差估计方面,采用VM1、VM2与VM3方法计算的方差估计相比而言更好.     

CVaR鲁棒均值-CVaR投资组合模型与求解

传统的均值-风险(包括方差、VaR、CVaR等)组合选择模型在计算最优投资组合时,常假定均值是已知的常值,但在实际资产配置中,收益的均值估计会有偏差,即存在着估计风险.在利用CVaR测度估计风险的基础上,研究了CVaR鲁棒均值-CVaR投资组合选择模型,给出了另外两种不同的求解方法,即对偶法和光滑优化方法,并探讨了它们的相关性质及特征,数值实验表明在求解大样本或者大规模投资组合选择问题上,对偶法和光滑优化方法在计算上是可行且有效的.     

金融理论概要——金融理论及其应用（I）

1 前言金融理论是从何开始的呢?我们认为其开端恐怕是Modigliani和Miller(1958)的看上去甚为简单的命题,即“在一切状态下,具有同一利益的证券组合拥有同一价格”. 在这个连载的第一篇里,概括地考察一下关于金融经济的资本市场方面的3个重要课题.第1是Markowitz(1952)和Tobin(1958)的均值方差证券组合理论.和Black(1972),Lintner(1965),Mossin(1965),Sharpe(1964)等人求得的关于收益率在市场均衡下的关系,即资本资产评价模型CAPM(Capital Asset Pricing Model).第2个主题是通过把个人一生效用最大化     

长度偏差右删失数据下[1mm]比例均值剩余寿命模型的估计方法

本文考虑了长度偏差右删失数据下均值剩余寿命模型的统计推断.当截断变量满足平稳性假设时,长度偏差右删失数据比左截断右删失数据具有更多的信息.为了提高参数估计的效率,我们在估计方程构造中添加了额外信息,通过组合方法获得了新的估计.模拟研究的结果也表明,组合估计方程的方法比仅考虑左截断右删失数据的方法更有效,结果表现更好.     

长度偏差右删失数据下比例均值剩余寿命模型的估计方法

本文考虑了长度偏差右删失数据下均值剩余寿命模型的统计推断.当截断变量满足平稳性假设时,长度偏差右删失数据比左截断右删失数据具有更多的信息.为了提高参数估计的效率,我们在估计方程构造中添加了额外信息,通过组合方法获得了新的估计.模拟研究的结果也表明,组合估计方程的方法比仅考虑左截断右删失数据的方法更有效,结果表现更好.     

一般线性混合模型中的最佳线性无偏估计和谱分解估计

该文在一般线性混合模型中, 研究了固定和随机效应线性组合的估计问题.对观测向量的协方差阵可以为奇异矩阵情形下,导出了该组合的最佳线性无偏估计,并证明了它的唯一性.在一般线性混合模型的特例, 三个小域模型下, 得到了小域均值u_i 和方差分量的谱分解估计. 进而, 获得了基于谱分解估计的两步估计均方误差的二阶逼近.     

基于风险测度CaR_k的最优投资组合(英文)

本文定义一种k阶在险资本值(CaRk)来度量风险,并研究在经典Black-Scholes市场中的均值-CaRk最优投资组合问题,给出了CaRk的显示表达式,并得到了均值-CaRk最优投资组合问题的最优策略及相应的最优财富值.     

Projection Pricing

A significant problem in modern finance theory is how to price assets whose payoffs are outside the span of marketed assets. In practice, prices of assets are often assigned by using the capital asset pricing model (CAPM). If the market portfolio is efficient, the price obtained this way is equal to the price of an asset whose payoff, viewed as a vector in a Hilbert space of random variables, is projected orthogonally onto the space of marketed assets. This paper looks at the pricing problem from this projection viewpoint. It is shown that the results of the CAPM formula are duplicated by a formula based on the minimum-norm portfolio, and this pricing formula is valid even in cases when there is no efficient portfolio of risky assets. The relation of the pricing to other aspects of projection are also developed. In particular, a new pricing formula, called the correlation pricing formula, is developed that yields the same price as the CAPM, but is likely to be more accurate and more convenient than the CAPM in some cases.     

Capital Asset Pricing Model (CAPM) with drawdown measure

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM) stated in both single and multiple sample-path settings. The drawdown beta in the CAPM has a simple interpretation and is evaluated for hedge fund indices from the HFRX database in the single sample-path setting. Drawdown alpha is introduced similarly to the alpha in the classical CAPM and is evaluated for the same hedge fund indices. Both drawdown beta and drawdown alpha are used to prioritize hedge fund strategies and to identify instruments for hedging against market drawdowns.     

Empirical analysis on risk of security investment

The paper analyzes the theory and application of Markowitz Mean-Variance Model and CAPM model. Firstly, it explains the development process and standpoints of two models and deduces the whole process in detail. Then 30 stocks are choosen from Shangzheng 50 stocks and are testified whether the prices of Shanghai stocks conform to the two models. With the technique of time series and panel data analysis, the research on the stock risk and effective portfolio by ORIGIN and MATLAB software is conducted. The result shows that Shanghai stock market conforms to Markowitz Mean-Variance Model to a certain extent and can give investors reliable suggestion to gain higher return, but there is no positive relation between system risk and profit ratio and CAPM doesn＇t function well in China＇s security market.     

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．     

组合投资与资本资产定价模型

根据效用理论 ,投资者在期望效用最大化准则下选择组合投资方案 ,通过改进均值 -方差模型假定 ,在完全市场 ( perfect markets)条件下由组合投资模型推导出广义的资本资产定价模型 .并证明了在投资者具有二次效用 ,或者收益率服从联合正态分布的情形下 ,它与夏普 -林特纳的资本资产定价模型 ( CA PM)一致     

Equilibrium in an ambiguity-averse mean–variance investors market

In a financial market composed of n risky assets and a riskless asset, where short sales are allowed and mean–variance investors can be ambiguity averse, i.e., diffident about mean return estimates where confidence is represented using ellipsoidal uncertainty sets, we derive a closed form portfolio rule based on a worst case max–min criterion. Then, in a market where all investors are ambiguity-averse mean–variance investors with access to given mean return and variance–covariance estimates, we investigate conditions regarding the existence of an equilibrium price system and give an explicit formula for the equilibrium prices. In addition to the usual equilibrium properties that continue to hold in our case, we show that the diffidence of investors in a homogeneously diffident (with bounded diffidence) mean–variance investors’ market has a deflationary effect on equilibrium prices with respect to a pure mean–variance investors’ market in equilibrium. Deflationary pressure on prices may also occur if one of the investors (in an ambiguity-neutral market) with no initial short position decides to adopt an ambiguity-averse attitude. We also establish a CAPM-like property that reduces to the classical CAPM in case all investors are ambiguity-neutral.     

Robust portfolio choice with CVaR and VaR under distribution and mean return ambiguity

We consider the problem of optimal portfolio choice using the Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR) measures for a market consisting of n risky assets and a riskless asset and where short positions are allowed. When the distribution of returns of risky assets is unknown but the mean return vector and variance/covariance matrix of the risky assets are fixed, we derive the distributionally robust portfolio rules. Then, we address uncertainty (ambiguity) in the mean return vector in addition to distribution ambiguity, and derive the optimal portfolio rules when the uncertainty in the return vector is modeled via an ellipsoidal uncertainty set. In the presence of a riskless asset, the robust CVaR and VaR measures, coupled with a minimum mean return constraint, yield simple, mean-variance efficient optimal portfolio rules. In a market without the riskless asset, we obtain a closed-form portfolio rule that generalizes earlier results, without a minimum mean return restriction.     

Theoretical and empirical estimates of mean–variance portfolio sensitivity

This paper studies properties of an estimator of mean–variance portfolio weights in a market model with multiple risky assets and a riskless asset. Theoretical formulas for the mean square error are derived in the case when asset excess returns are multivariate normally distributed and serially independent. The sensitivity of the portfolio estimator to errors arising from the estimation of the covariance matrix and the mean vector is quantified. It turns out that the relative contribution of the covariance matrix error depends mainly on the Sharpe ratio of the market portfolio and the sampling frequency of historical data. Theoretical studies are complemented by an investigation of the distribution of portfolio estimator for empirical datasets. An appropriately crafted bootstrapping method is employed to compute the empirical mean square error. Empirical and theoretical estimates are in good agreement, with the empirical values being, in general, higher.     

Mean-variance versus expected utility in dynamic investment analysis

Given the existence of a Markovian state price density process, this paper extends Merton??s continuous time (instantaneous) mean-variance analysis and the mutual fund separation theory in which the risky fund can be chosen to be the growth optimal portfolio. The CAPM obtains without the assumption of log-normality for prices. The optimal investment policies for the case of a hyperbolic absolute risk aversion (HARA) utility function are derived analytically. It is proved that only the quadratic utility exhibits the global mean-variance efficiency among the family of HARA utility functions. A numerical comparison is made between the growth optimal portfolio and the mean-variance analysis for the case of log-normal prices. The optimal choice of target return which maximizes the probability that the mean-variance analysis outperforms the expected utility portfolio is discussed. Mean variance analysis is better near the mean and the expected utility maximization is better in the tails.     

资本资产定价模型的改进及在中国股市的实证分析

对于投资者来说,具备有效的评估价值和风险关系的理论工具十分重要.以中国股票市场的数据对资本资产定价模型进行了实证检验,面对并不理想的检验结果,借用因素模型的研究方法,在传统模型中引入其他可能影响资产回报的因素,利用中国股市的数据对改进的模型进行了实证检验,并与传统模型的检验结果相比较,发现改进模型的解释力相对于传统模型有了显著的提高.