新的指数跟踪方法及其应用

文章提出了一种新的非完全复制指数跟踪方法。该方法基于选择具有一定优良性质的股票组合的基础,构建跟踪组合来跟踪指数。新方法突破了文献已有方法事先指定股票来构造指数跟踪的传统框架,更有实际价值。实证分析表明,采用该方法构建的跟踪策略通过选择较少的股票同时得到的跟踪误差也较小,且优于目前比较流行的分层抽样策略。最后应用所给的方法对沪深300指数进行了股指期货的期现套利研究,结果表明该策略比文献已有的方法存在更大的套利空间。     

基于Sparse-Group Lasso的指数跟踪

在指数跟踪问题中,股票指数与行业板块的相关性往往是集中在某些特定的行业,且行业走向通常由几个有影响力的公司决定,因此如何选取具有代表性的行业和公司是提高跟踪精度的一个很好的切入点.在以往的研究方法中,Lasso等变量选择方法忽略了行业因素的影响,而分层抽样则忽略了不同行业和股票指数关联性大小的不同.文章引入Sparse-Group Lasso方法,实现了对行业及行业内部单一股票的筛选,同时对跟踪误差的定义进行扩展,综合考虑线性和非线性两种跟踪误差的优点对股票组合的权重进行优化.实证表明,基于Sparse-Group Lasso方法筛选的股票组合的稳健性一致优于依据市值筛选的股票组合,当股票组合规模较小时,基于Sparse-Group Lasso方法筛选的股票组合的跟踪误差也要优于依据市值进行筛选股票的方法.     

股指期货套利中的最优现货组合构建策略研究

针对如何构建与股指期货联动性较好的现货组合问题,本文提出采用两阶段优化策略以提高组合的跟踪准确度。第一阶段,利用基于独立成分分析与模糊C均值算法相结合的时间序列聚类方法将沪深300股指期货对应的成分股进行聚类;第二阶段,对聚类之后的结果进行指数优化复制,以跟踪误差最小为目标,确定跟踪组合的成分股权重。实证研究表明,本文所提出的两阶段优化策略可以较好地改进指数跟踪效果。     

基于Spatial AIC准则的空间自回归模型变量选择研究

变量选择直接决定着空间计量经济模型的有效程度与实证研究结果。为有效解决空间自回归模型(即SAR模型)的变量选择问题,本文利用Kullback-Laible信息量最大化,把AIC准则运用到SAR模型构建,推导出Spatial AIC统计量,提出Spatial AIC准则。然后利用统计理论证明Spatial AIC准则选择SAR模型变量的渐近最优性;利用蒙特卡洛模拟方法,比较Spatial AIC准则、经典AIC准则和Lasso方法用于SAR模型变量选择的有限大样本性质;利用空间相关的沪深300成分股股票收益率数据,采用Spatial AIC准则和Lasso方法,分别构建股票收益率财务因素的空间自相关模型,实证比较其相对有效性。三种结果均表明Spatial AIC准则能够更好地解决SAR模型变量选择问题。     

一般M-V模型中的有效证券组合及无套利分析

本文研究了协方差阵奇异时一般M-V模型中的有效证券组合, 得到了证券市场存在有效证券组合的充要条件, 并给出了有效证券组合的通解和有效前沿的性质. 最后, 本文还在奇异协方差阵下进行了无套利分析, 得到了证券市场无套利的充要条件, 从而证明了Szeg\"{o}的猜想.     

改进的自适应Lasso方法在股票市场中的应用

在金融领域,自适应Lasso被广泛的用于股票价格预测模型中的变量选择和参数估计。然而,自适应Lasso是针对非时间序列模型提出的,忽略了时间序列模型特定的结构,比如时间序列模型中通常会出现滞后阶数越靠后,对未来的预测能力越弱的特性,从而,容易造成估计及预测不精确。因此,时间序列模型的变量选择惩罚参数的设计应与滞后阶数相关,即对越靠后的滞后阶数应加上越大的惩罚。为了充分考虑时间序列模型的特性且保留自适应Lasso的优点,本文针对时间序列AR(p)模型提出一种改进的自适应Lasso(MA Lasso)方法,通过在自适应Lasso惩罚基础上乘以一个关于滞后阶数单调不减的函数来达到目标。这样设计的惩罚参数的另一个优点是通过选取特定的惩罚参数,Lasso,自适应Lasso方法都是MA Lasso方法的特例。进一步,对于AR(p)模型中另一个重要参数p的选择问题,本文提出一种改进的BIC模型准则来选择p。最后,将MA Lasso方法应用到中证100指数中,实证分析表明,与Lasso和自适应Lasso相比,MA Lasso选择最简模型且预测效果最佳,即选择最少的预测变量的同时且具有最小的模型预测误差。     

高维数据下的贝叶斯网络结构学习

贝叶斯网络模型作为一种传统有效的大数据图模型,因其具有因果和概率性语义等特点受到学者们的广泛研究。为了解决基于高维数据构建贝叶斯网络的难题,本文提出了一种适用于高维数据的贝叶斯网络结构学习算法—LTB算法,该算法由Lasso、Tabu Search算法和BIC结合。首先,运用Lasso降低协变量的维数,筛选出与目标变量关系密切的协变量将作为贝叶斯网络的顶点。然后,选择Tabu Search作为元启发式算法,选择BIC作为计算得分的方法,两者结合构建全局最优的贝叶斯网络结构。实证分析表明,LTB算法应用于上证综指影响因素的研究,既可以获得上证综指与其影响因素间的因果关系,也可以利用条件概率得到上证综指影响因素间的组合方式。     

带有组结构的稀疏模型的参数估计和变量选择方法

本文针对带有组结构的广义线性稀疏模型,引入布雷格曼散度作为一般性的损失函数,进行参数估计和变量选择,使得该方法不局限于特定模型或特定的损失函数.本文比较研究了Ridge,SACD,Lasso,自适应Lasso,组Lasso,分层Lasso,自适应分层Lasso和稀疏组Lasso共8种惩罚函数的特点和引入模型后参数估计和...     

包含股指期货的投资组合之风险研究——Copula方法在金融风险管理中的应用

本文运用Copula方法研究了含股指期货的投资组合的风险度量问题.由于股指期货和股票现货之间存在很大的相关性,因此在度量组合的风险时,各资产间的相关结构起到了关键作用,但这一相关结构很难用线性的相关系数去刻画,本文采用Copula模型来描述相关结构。而后,我们构建了基于Copula理论的风险度量指标PVaR,并验证了不同Copula模型的拟合效果.我们利用沪深300指数的数据来研究股指期货和现货的相关结构,并使用了多种Copula函数结合不同的边际分布假设进行了模拟,说明了Copula方法在风险度量尤其是包含了股指期货的投资组合的风险度量上具有较高的精确性.     

分组数据分位数回归模型的变量选择和估计北大核心CSCD

本文主要研究分组数据分位数回归模型的变量选择和估计问题.为了充分反映数据的分组信息,需要假定每组数据的回归系数可以分解成共性部分和分组后的个性部分.为了进行变量筛选,本文提出分解系数的Lasso估计,并进一步提出了自适应Lasso估计.在处理相应优化问题时,采用了变换观测矩阵的方法简化问题求解.本文给出了自适应Lasso估计的Oracle性质证明,并且通过数值模拟研究展示了所提方法的有限样本表现.最后,将此方法应用到乳腺浸润癌致病基因的变量筛选上来展示所提方法的实际应用表现.     

基于CVaR约束的指数组合优化模型及实证分析

随着指数衍生产品日益受到重视,指数化投资组合常被投资者或机构所采用,而用有限的资金按指数构成比例进行投资显然是不现实的,所以指数的最优误差追踪就显得更加重要。本文将追踪误差定义为证券投资组合收益率与所追踪的指数基准收益率之差,并在分析CvaR(ConditionalValue at Risk)的基础上,在无交易费用和有交易费用的情况下,建立了基于CVaR约束的追踪误差最小化的指数组合优化模型,对指数进行复制,并通过实证分析,得出了基于CVaR约束的追踪误差最小时的样本期内及样本期外的最优投资策略,验证了CVaR约束控制风险的有效性。     

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.     

Developing and Maintaining an Equity Index Fund

An index fund is a portfolio of shares designed to replicate the investment performance of a market index. The index represents the behaviour of the market as a whole. This paper describes the selection of an index fund which minimizes expected tracking error. Using a multivariate model of returns on shares, a development of a univariate model by Taylor, the selection problem is formulated as a quadratic programme. The effects of various constraints on tracking error are demonstrated. Several policies for the readjustment of a fund are examined in the context of the differing objectives of fund managers. As a general rule, regular readjustment is shown to be a more expensive policy than irregular updating.     

Dynamic Index Tracking and Risk Exposure Control Using Derivatives

We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not directly tradable. Among our results, we establish a general tracking condition that relates the portfolio drift to the desired exposure coefficients under any given model. We also derive a slippage process that reveals how the portfolio return deviates from the targeted return. In our multi-factor setting, the portfolio’s realized slippage depends not only on the realized variance of the index but also the realized covariance among the index and factors. We implement our trading strategies under a number of models, and compare the tracking strategies and performances when using different derivatives, such as futures and options.     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.     

Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios

Index tracking is a passive investment strategy in which a fund (e.g., an ETF: exchange traded fund) manager purchases a set of assets to mimic a market index. The tracking error, i.e., the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable transaction cost and, accordingly, decreases the return of the constructed portfolio. On the other hand, a portfolio with a small cardinality may result in poor out-of-sample performance. Of interest is, thus, constructing a portfolio with good out-of-sample performance, while keeping the number of assets invested in small (i.e., sparse). In this paper, we develop a tracking portfolio model that addresses the above conflicting requirements by using a combination of L0- and L2-norms. The L2-norm regularizes the overdetermined system to impose smoothness (and hence has better out-of-sample performance), and it shrinks the solution to an equally-weighted dense portfolio. On the other hand, the L0-norm imposes a cardinality constraint that achieves sparsity (and hence a lower transaction cost). We propose a heuristic method for estimating portfolio weights, which combines a greedy search with an analytical formula embedded in it. We demonstrate that the resulting sparse portfolio has good tracking and generalization performance on historic data of weekly and monthly returns on the Nikkei 225 index and its constituent companies.     

Arbitrage and the tax code

We provide a detailed characterization of arbitrage-free asset prices in the presence of capital gains and income taxes. The distinguishing feature of our analysis is that we impose on the model two important features of the tax code: the limited use of capital losses and the inability to wash sell. We show that under remarkably mild conditions, the lack of pre-tax arbitrage implies the lack of post-tax arbitrage with the limited use of capital losses. The conditions are that the risk free interest rate be positive and that tax rates on interest income exceed capital gains tax rates. The result also holds when only a wash sale constraint is imposed and no investor holds a portfolio with a large capital loss. We allow investors to face different tax rates and have different bases for the calculation of capital gains taxes. The characterizations we provide have important implications for both asset pricing and portfolio choice. Our results imply that models that use arbitrage-free pre-tax models continue for derivative pricing and hedging are also arbitrage free in a world with taxes. Similarly, portfolio choice models with taxes typically specify pre-tax arbitrage free price processes and then analyze portfolio choice in the presence of taxes. In these models, it is unclear if portfolio recommendations are based on risk-return tradeoffs or on the arbitrage opportunities present in the model. Our results imply that if the above features of the tax code are modeled explicitly, then we can isolate the post-tax risk-return tradeoffs.     

股指期货考虑套期保值成本时的套期保值比率研究

所谓股指期货,就是以某种股票指数为标的物的金融期货合约.它同时具有股票与期货的特性,是组合投资者规避系统风险的重要金融衍生工具.针对股指期货,在考虑套期保值成本的前提下,利用套利和CAPM模型给出最优套期保值比率的计算公式.这将在一定的程度上,提高了计算的准确性,并且减少计算的工作量.     

Index tracking with fixed and variable transaction costs

Index tracking is a form of passive portfolio (fund) management that attempts to mirror the performance of a specific index and generate returns that are equal to those of the index, but without purchasing all of the stocks that make up the index. We present two mixed-integer linear programming formulations of this problem. In particular we explicitly consider both fixed and variable transaction costs. Computational results are presented for data sets drawn from major world markets.