基于随机微分博弈的最优投资

研究存在模型风险的最优投资决策问题,将该问题刻画为投资者与自然之间的二人-零和随机微分博弈,其中自然是博弈的"虚拟"参与者.利用随机微分博弈分析方法,通过求解最优控制问题对应的HJBI(Hamilton-Jacobi-Bellman-Isaacs)方程,在完备市场和存在随机收益流的非完备市场模型下,都得到了投资者最优投资策略以及最优值函数的解析表达式.结果表明,在完备市场条件下,投资者的最优风险投资额为零,在非完备市场条件下最优投资策略将卖空风险资产,且卖空额随着随机收益流波动率的增大而增加,随风险资产波动率增大而减少.     

PI(Portfolio Insurance)投资者特性研究

根据期权定价理论,分析了投资组合保险策略与期权的关系及投资组合保险策略与凸收益函数的关系,通过建立投资组合保险模型,得出不同条件下购买投资组合保险投资者的特点如下:1)随着财富的增加他们的风险承受能力比市场一般投资者增加的快;2)他们的市场预期比一般市场投资者更乐观,并且受益于投资组合保险.     

基于异质理念的动态组合选取模型

不同于传统的代表性经济人的动态投资组合选取模型,引入异质理念,考虑不同投资者的动态组合选取.由于投资者的乐观或悲观情绪直接影响了他对信息的评价,因此用随时间变化的参数体现投资者的情绪,随机组合收益分布是这个参数的函数,不同的投资者或者同一投资者在不同情绪下就有了自己独特的收益分布.通过对均值——方差目标函数的变形,给出了不同投资者对风险资产的最优投入、预期收益和方差的解析表达式,此三项不仅和投资者的风险厌恶度有关,而且和投资期长短有关、与投资者的情绪有关.在对香港恒生指数的实证分析显示,异质性严重影响投资者对风险资产的投入.     

基于长短记忆神经网络预测的大类资产因子配置研究

大类资产配置策略为资金相对庞大的机构投资者提供了一个有效获取稳健收益的手段,通过因子收益分布及相关性的预测能更好地进行大类资产配置.将大类资产因子配置的思想与机器学习算法预测有机结合,首先筛选宏观因子及风格因子,利用长短记忆神经网络(LSTM)方法预测组合收益,得到最优因子组合;然后结合最优因子组合中蕴含的信息,修正对资产预期收益率的估计并提出了大类资产的权重配置方案.通过在全球18种大类资产上进行的算例分析表明,采用本文模型得到的配置策略相较于其它模型有更高的收益风险比、较低的年化波动以及较小的最大回撤.研究结论可为机构投资者的大类资产配置提供理论借鉴.     

基于人工股票市场分析持有期对投资者收益的影响

基于对中国股票市场的连续竞价交易机制和投资者构成特征的分析,本文构建了一个向上增长的人工模拟订单驱动股票市场模型,其中投资者的持有期会受到股票价格波动的影响,并能够反映投资者的投资策略.模型能够得出一系列与实际股票市场一致的典型事实,如收益率分布的胖尾特征以及波动率的聚集等.本文通过模拟研究,分析了持有期对投资者收益的影响,结果表明,长期持有的投资者在向上增长的市场中可获得较高的平均收益.     

基于因子模型的指数跟踪及实证分析

指数跟踪是指数基金和机构投资者广泛使用的被动投资管理策略. 通过建立股票收益的多因子模型, 提出了将组合的贝塔值控制在合适范围内, 并在期望超额收益非负的条件下, 最小化组合风险的指数跟踪模型. 同时,考虑到实际需要, 在模型中限制了组合中股票的数量和持有量.实证分析结果表明, 通过选取不同的控制参数,
该模型产生的跟踪组合既能实现较小的跟踪误差,也能实现一定的超额收益.     

基于巨额损失波动性的最优投资决策研究

近年来伴随着金融市场广度与深度的不断拓展,频发的金融风险对世界经济及金融市场造成了巨大损失(如美国次贷危机),学者和投资者越来越关注规避小概率巨额风险的最优投资决策及有潜力风险资产遴选方法的研究.文章就此开展了如下研究:首先以损失超过VaR部分的条件期望CVaR作为投资者愿意承担风险的上限,改进投资预算约束为非紧约束,提出了基于巨额损失波动性的投资组合模型.数值试验验证了模型具有良好的收敛性,即使在生成较少数量的情景下也能快速收敛;当投资者对最低期望收益率要求不高时,不必全额投入预算资金就能满足投资者对预期收益的要求;随着投资者对最低期望收益率要求的提高,更多预算资金被投入可能带来更高收益的风险资产,资金预算约束逐渐趋于紧约束;模型给出的最优投资决策在样本外各滚动窗口测试中均实现了较高收益,但发生巨额损失的波动程度却显著降低,达到了控制小概率极端风险的目的.其次,结合常规基本面分析法和聚类分析技术,提出了风险资产的遴选方法.该方法适用于跨市场跨行业不同品种间风险资产的筛选,可兼顾同一类别内资产的同质性及不同类别资产间的异质性,以此达到分散化解风险的目的.实证研究表明,该方法遴选出的"少量"风险资产在各项评价指标上具有明显的优势,聚类技术的引入大大降低了投资者选择资产的难度.     

基于背景风险和弹性增量的模糊投资组合研究

在金融市场中,投资者需要通过构建投资组合分散非系统风险,也需要考虑由收入、支出、健康状况等个人因素构成的背景风险.另外,在同一个投资组合中,不同的风险存量加上相同的弹性增量以后,投资者的满意度也不同.同时,证券市场中存在大量的模糊现象,模糊性比随机性更能刻画其不确定性特征.因此,提出了一个以投资者满意度为目标,包含背景风险、弹性增量等因素的模糊投资组合模型.最后,选取沪深证券市场数据分析了背景风险方差对投资组合的收益、方差和投资者满意度的影响.结果发现:背景风险的方差与投资组合的收益和投资者的满意度负相关,与投资组合的方差正相关,而且,在不同弹性存量的基础上,相同弹性增量的投资者满意度也是不同的.     

不完全市场中动态资产分配

在不完全市场条件下,通过确定方差-最优鞅测度,给出了动态均值-方差有效策略和有效前沿的解析表达式．动态均值-方差有效策略是二基金的买入-持有策略．基金一仅投资于无风险资产,基金二是动态调整的投资组合．应用资产的动态参数清楚地刻画了投资者持有二基金的数量和二基金的动态投资组合．并且证明了均值-方差有效前沿在期望收益-标准差空间是直线．     

基于不确定性期望效用模型的投资优化

针对资产的收益的分布不确切知道,并且所获得的矩信息也不是准确值的问题,提出了最大化最坏情形期望效用的鲁棒性方法.引入了凹凸类效用函数来度量模型不确定情形下投资者的效用,用一个不确定性结构来刻画资产收益的所有可能的分布和收益的矩信息,通过把具有不确定性结构的鲁棒性模型转化成参数二次规划问题,得到了最优投资策略、有效前沿和均衡价格的解析表示.方法为采用保守策略并且厌恶不确定性的投资者提供了一种有效的投资决策方案.     

Black-Litterman模型在大类资产配置中的应用:基于货币周期及风险平价策略的改进

Black-Litterman模型能够有效的解决均值-方差模型对输入(尤其是预期收益率)过于敏感的问题,从而使得其在实践中得到了广泛的应用。采用风险平价策略构造市场均衡组合,并采用基于货币周期的资产轮动收益构造主观观点组合,在将主观观点信心水平进行适当简化后,形成了改进后的Black-Litterman模型。利用我国资本市场上股票、商品和债券三种大类资产数据对改进后的Black-Litterman模型进行实证检验后发现:通过相对信心水平的调节,改进后的Black-Litterman模型能够对市场均衡组合和主观观点组合进行有效的平衡,且相对于其他资产配置组合及单种资产买入持有策略,Black-Litterman组合无论是在风险控制还是收益率上都表现的更为出色。实证结论充分说明了Black-Litterman模型的有效性,同时也从市场均衡组合、主观观点及信心水平三个方向指明了模型改进的方向。     

Portfolio-optimization models for small investors

Since 2010, the client base of online-trading service providers has grown significantly. Such companies enable small investors to access the stock market at advantageous rates. Because small investors buy and sell stocks in moderate amounts, they should consider fixed transaction costs, integral transaction units, and dividends when selecting their portfolio. In this paper, we consider the small investor’s problem of investing capital in stocks in a way that maximizes the expected portfolio return and guarantees that the portfolio risk does not exceed a prescribed risk level. Portfolio-optimization models known from the literature are in general designed for institutional investors and do not consider the specific constraints of small investors. We therefore extend four well-known portfolio-optimization models to make them applicable for small investors. We consider one nonlinear model that uses variance as a risk measure and three linear models that use the mean absolute deviation from the portfolio return, the maximum loss, and the conditional value-at-risk as risk measures. We extend all models to consider piecewise-constant transaction costs, integral transaction units, and dividends. In an out-of-sample experiment based on Swiss stock-market data and the cost structure of the online-trading service provider Swissquote, we apply both the basic models and the extended models; the former represent the perspective of an institutional investor, and the latter the perspective of a small investor. The basic models compute portfolios that yield on average a slightly higher return than the portfolios computed with the extended models. However, all generated portfolios yield on average a higher return than the Swiss performance index. There are considerable differences between the four risk measures with respect to the mean realized portfolio return and the standard deviation of the realized portfolio return.     

Portfolio Selection Problem with Minimax Type Risk Function

The investor's preference in risk estimation of portfolio selection problems is important as it influences investment strategies. In this paper a minimax risk criterion is considered. Specifically, the investor aims to restrict the standard deviation for each of the available stocks. The corresponding portfolio optimization problem is formulated as a linear program. Hence it can be implemented easily. A capital asset pricing model between the market portfolio and each individual return for this model is established using nonsmooth optimization methods. Some numerical examples are given to illustrate our approach for the risk estimation.     

Portfolio Improvement by Using the Sharpe Rule and Value-at-Risk

This study discusses the applications of the Sharpe rule in portfolio measurement and management. It proposes that a portion of the portfolio value should be invested in some other assets for portfolio improvement. By applying the Sharpe rule, it can be determined that new stocks are worthy of adding to the old portfolio if they satisfy a condition, in which the average return rate of these stocks is greater than the return rate of the old portfolio multiplied by the sum of the elasticity of the VaR and 1. One attraction of our approach is diversification. A numerical example in the Hong Kong stock market is presented for illustration. Some experimental results show that a new portfolio with the 'highest' Sharpe ratio can be obtained by adding only a few new assets. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Studies on a general stock-bond integrated portfolio optimization model

The purpose of this paper is to extend a stock-bond integrated portfolio optimization model proposed by one of the authors in 1997 to the case where the universe covers risky (corporate) bonds in addition to stocks and risk-free (government) bonds. An integrated approach has been applied to Japanese market and was proved to generate a portfolio which usually outperforms standard asset allocation strategy. Inclusion of risky bonds is expected to lead to an even better portfolio. To properly handle risky bonds, we introduce a new scheme to quantify the risk associated risky bonds. We will demonstrate that the scheme proposed in this paper works very well, at least in the Japanese market.     

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.     

基于风险网络结构的资产分配策略研究

股票市场是一个高风险市场,如何在频繁发生的极端波动环境下进行有效的资产分配是当前热点问题。本文首次应用VaR模型构建股市风险网络,并基于风险网络模型进行最优投资组合成分选择,分析不同市场波动行情下最优资产分配权重和股票中心性的时变关系,融合风险网络时变中心性和个股表现提出新的动态资产分配策略(φ投资策略)。结果表明:在股市上涨和震荡期,股票中心性和最优投资组合权重呈正相关关系;股市下跌期,股票中心性和最优投资组合权重呈负相关关系;当φ>0.05时,投资者的合理投资区域向高中心性节点移动,反之。φ投资策略的绩效表现证明了风险网络结构能提高投资组合选择过程。此研究对于优化资产配置、提高投资收益、多元化分散投资风险具有重要意义。     

Developing a dynamic portfolio selection model with a self-adjusted rebalancing method

In this paper, we propose a comprehensive investment strategy for not only selecting but also maintaining an investment portfolio that takes into account changing market conditions. First, we implement a dynamic portfolio selection model (DPSM) that uses a time-varying investment target according to market forecasts. We then develop a self-adjusted rebalancing (SAR) method to assess the portfolio’s relevance to current market conditions, and further identify the appropriate timing for rebalancing the portfolio. We then integrate the DPSM and SAR into a comprehensive investment strategy, and develop an adaptive learning heuristic for determining the parameter of the proposed investment strategy. We further evaluate the performance of the proposed investment strategy by simulating investments with historical stock return data from different markets around the world, across a period of 10 years. The SAR Portfolio, maintained according to the proposed investment strategy, showed superior performance compared with benchmarks in each of the target markets.     

Integrated portfolio management with options

In this paper we examine the problem of managing portfolios consisting of both, stocks and options. For the simultaneous optimization of stock and option positions we base our analysis on the generally accepted mean–variance framework. First, we analyze the effects of options on the mean–variance efficient frontier if they are considered as separate investment alternatives. Due to the resulting asymmetric portfolio return distribution mean–variance analysis will be not sufficient to identify optimal optioned portfolios. Additional investor preferences which are expressed in terms of shortfall constraints allow a more detailed portfolio specification. Under a mean–variance and shortfall preference structure we then derive optioned portfolios with a maximum expected return. To circumvent the technical optimization problems arising from stochastic constraints we use an approximation of the return distribution and develop economically meaningful conditions under which the complex optimization problem can be transformed into a linear problem being comparably easy to solve. Empirical results based on both, empirical market data and Monte Carlo simulations, illustrate the portfolio optimization procedure with options.     

基于双重加权网络的股票强相关性分析

为分析股票间的强相关性,合理构建投资组合,选择中国股市煤炭电力板块93支股票,以股票上市时间至2011年2月11日每日收盘价和成交量,建立双重加权网络模型.在模型中,顶点是股票,双重边分别由股票间的成交量相关和回报相关建立,边上的权就是相关系数值.研究结果表明,网络顶点度服从幂律分布,负幂指数δ值约为0.02;单网络顶点度呈现"翘翘板"特点,即一个单网络中度大的顶点在另一个单网络中度很小;网络的模块具有同源性,即模块中顶点来自同一板块;网络的最大生成树明显以板块形成树分枝;网络树EGO结构体现企业间存在的生产材料和业务供求关系.