摩擦市场上允许买空卖空的投资组合问题

证券交易市场上存在着诸如交易费用、税收等摩擦.投资者在交易过程中,不可避免地要受到市场摩擦的影响.本文以投资者所获取的最大投资效用为目标函数,建立了摩擦市场上最优投资组合问题的数学模型;同时对于之前解决此类问题的很多文章中“证券市场不允许买空卖空风险资产和借贷无风险资产”的假设条件做了扩展,得到一个摩擦市场上适用于“允许买空卖空或借贷”的证券投资组合的二次规划模型.     

具有最小交易量限制的多阶段均值-半方差投资组合优化

考虑交易成本,借款约束和阈值约束,文章提出了具有最小交易量限制的多阶段均值-半方差投资组合模型。该模型是具有路径依赖性的混合整数动态优化问题,还是NP完全问题。文章提出了前向动态规划方法求解。最后,通过一个算例比较不同风险约束下的最优投资策略,从而验证模型和算法的有效性。     

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。     

具有资本结构因子和交易成本的证券组合投资模型

在介绍经典的Harry Markowitz均值-方差投资组合模型的基础上,建立了含有资本结构因子和交易成本的证券组合最优化模型,在组合中不含有无风险证券和含有无风险证券的条件下,分别给出最优投资比例及有效边界,并讨论了资本结构因子与交易成本对有效边界的影响.     

The tradeoff between mutual fund and direct stock investments: a theoretical analysis involving different types of investors

We study the tradeoff between direct and indirect stock investments through equity mutual funds for a utility-maximizing investor. Whereas direct investments impose higher transaction costs on the formation of a well-diversified portfolio, mutual funds charge fees for their services. Our results show that the fee levels that make private investors indifferent between direct and indirect stock investments vary heavily according to risk aversion, the amounts invested, correlations between assets, transaction costs, and the length of investment horizon. In particular, our results suggest that for a wide range of actively managed mutual funds, the fees charged are too high for these mutual funds to appeal to a wide range of informed investors. However, accounting for search costs, such as costs for financial advice, can facilitate an understanding of the levels of management fees charged by mutual funds existing in the market.     

Project Portfolio Selection: A Newsvendor Approach

We consider the problem of balancing the penalties associated with budgetary slack (being underbudget) and cost overruns in the project portfolio selection problem by addressing randomness in project costs and making individual project budgets decision variables. Setting the budget for a single project is shown to be analogous to the newsvendor problem. For related versions of the project portfolio selection problem we provide optimal and heuristic procedures. Numerical experiments are used to test the procedures and provide managerial guidelines. We show project budgets should be set so that each project in the portfolio has the same probability of running over budget, it is better to have a larger number of projects with less than ideal funding compared to a smaller number of projects with ideal funding, and substantial opportunities to select more projects with a higher expected profit are available if an aggregate portfolio budget is used.     

Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry

We study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of non-divisible projects when the risk is measured by the semivariance of the portfolio׳s Net-Present Value (NPV) and the reward is measured by the portfolio׳s expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from the PSPLIB library of project scheduling problems.     

THE EFFECTS OF VARIABLE AND FIXED TRANSACTION COSTS ON OPTIMAL INVESTMENT DECISIONS

This paper studies the impact of variable and fixed transaction costs on investment decisions under conditions of risk. The decision model is first formulated as a mixed-integer nonlinear program. The following subjects are then examined: the structure of the investment frontier facing the investor and the effects of transaction costs on this frontier, the impact of transaction costs on the investor's optimal investment strategy, and the conditions for the equilibrium structure of risky asset prices and risk-return relationships. The main finding is that the relaxation of the assumption of the absence of transaction costs eliminates some of the most unattractive implications of the classic capital asset pricing model (CAPM) while preserving the more attractive implications of this model. Also, our model provides explanations for some discrepancies between the theoretical CAPM and empirical findings and, therefore, is a step toward narrowing the gap between theory and practice.     

基于在线算法的改进指数梯度投资组合策略

弱集成算法是对专家意见进行动态加权平均的在线学习算法。近年来,机器学习和人工智能等方法被用来研究在线投资组合问题。该文从弱集成算法的在线学习及其序列决策性角度出发,设计改进的指数梯度在线投资组合策略,以弥补指数梯度在线投资组合策略不能结合交易费用进行分析的缺陷。首先根据指数梯度在线投资组合策略的更新方法构建代表投资策略的专家意见池,并以此为基础应用弱集成算法加权集成专家意见得到改进的指数梯度在线投资组合策略,证明了该策略可与最优专家策略(基准策略)相媲美。其次将交易费用引入到改进的指数梯度在线投资组合策略中,进一步给出对应的投资策略,重要的是理论上证明了该策略实现的平均累积收益与最优专家策略实现的平均累积收益之间的差值存在渐进式下界,从而提高了指数梯度在线投资组合策略的实用性。最后利用国内外股票市场的历史数据进行实证分析,说明了改进的指数梯度在线投资组合策略的可行性和有效性。     

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。     

Do individual investors learn from their mistakes?

Based on recent empirical evidence which suggests that as investors gain experience, their investment performance improves, we hypothesize that the specific mechanism through which experience translates into better investment returns is closely related to learning from investment mistakes. To test our hypotheses, we use an administrative dataset which covers the trading history of 19,487 individual investors. Our results show that underdiversification and the disposition effect do not decline as investors gain experience. However, we find that experience correlates with less portfolio turnover. We conclude that compared to other investment mistakes, it is relatively easy for individuals to identify and avoid costs related to excessive trading activity. When correlating experience with portfolio returns, we find that as investors gain experience, their portfolio returns improve. A comparison of returns before and after accounting for transaction costs reveals that this effect is related to learning from overtrading.     

不确定终止时间的多阶段最优投资组合

研究了当终止时间不确定时的多阶段最优投资组合问题.假定终止时间是个服从某分布的随机变量,将不确定终止时间的问题转化为确定时间的问题,应用动态规划求解模型,得到最优投资策略以及有效边界的解析形式.实例证明所得的结论是对确定终止时间情形的推广,最优投资策略受终止时间分布的影响.     

改进区间可接受度的证券投资组合区间二次规划模型

本文首先基于Markowitz的经典均值方差模型，针对不确定环境下的投资组合问题，把证券的收益率、风险损失率和流动性用区间数描述，建立了一种新的含交易成本的证券投资组合区间二次规划模型。其次，为求解该模型，提出了改进的区间可接受度确定性转换方法，通过引入优化水平α与可接受水平η将不确定二次规划转化为确定型规划。最后，通过数值实验将提出的方法与传统方法进行比较，结果表明本文所提出的方法与模型具有相对较好的可行性与实用性。     

Optimal market timing strategies under transaction costs

In this paper, we consider optimal market timing strategies under transaction costs. We assume that the asset's return follows an auto-regressive model and use long-term investment growth as the objective of a market timing strategy which entails the shifting of funds between a risky asset and a riskless asset. We give the optimal trading strategy for a finite investment horizon, and analyze its limiting behavior. For a finite horizon, the optimal decision in each step depends on two threshold values. If the return today is between the two values, nothing needs to be done, otherwise funds will be shifted from one asset to another, depending on which threshold value is being exceeded. When investment horizon tends to infinity, the optimal strategy converges to a stationary policy, which is shown to be closely related to a well-known technical trading rule, called Momentum Index trading rule. An integral equation of the two threshold values is given. Numerical results for the limiting stationary strategy are presented. The results confirm the obvious guess that the no-transaction region increases as the transaction cost increase. Finally, the limiting stationary strategy is applied to data in the Hang Seng Index Futures market in Hong Kong. The out-of-sample performance of the limiting stationary strategy is found to be better than the simple strategy used in literature, which is based on an 1-step ahead forecast of return.     

Absolute return portfolios

In this paper we consider the problem of selecting an absolute return portfolio. This is a portfolio of assets that is designed to deliver a good return irrespective of how the underlying market (typically as represented by a market index) performs. We present a three-stage mixed-integer zero-one program for the problem that explicitly considers transaction costs associated with trading. The first two stages relate to a regression of portfolio return against time, whilst the third stage relates to minimising transaction cost.We extend our approach to the problem of designing portfolios with differing characteristics. In particular we present models for enhanced indexation (relative return) portfolios and for portfolios that are a mix of absolute and relative return. Computational results are given for portfolios derived from universes defined by S&P international equity indices.     

基于非参数估计框架的期望效用最大化最优投资组合

本文基于期望效用最大化和非参数估计框架研究了最优投资组合选择问题。和以往大多文献假定资产收益率服从某些特定分布不同资产收益率的分布类型无需作任何假设。首先在一般效用函数下,利用组合收益率密度函数的非参数核估计给出了期望效用的基本非参数估计公式,并建立了期望效用最大化投资组合选择问题的基本框架。然后,在投资者具有幂效用函数的假定下,给出了期望效用具体的非参数计算公式,并给出了求解最大期望效用的数值算法。最后,利用中国证券交易所11支股票日收益率的真实数据给出了一个数值算例。本文提出的非参数估计框架具有一般性,还可以进一步用来研究各种现实条件下（如各种现实不等式约束和具有交易成本）的投资组合管理问题。     

Stationary Equilibria in Asset‐Pricing Models with Incomplete Markets and Collateral

We consider an infinite‐horizon exchange economy with incomplete markets and collateral constraints. As in the two‐period model of Geanakoplos and Zame (2002), households can default on their liabilities at any time, and financial securities are only traded if the promises associated with these securities are backed by collateral. We examine an economy with a single perishable consumption good, where the only collateral available consists of productive assets. In this model, competitive equilibria always exist and we show that, under the assumption that all exogenous variables follow a Markov chain, there also exist stationary equilibria. These equilibria can be characterized by a mapping from the exogenous shock and the current distribution of financial wealth to prices and portfolio choices. We develop an algorithm to approximate this mapping numerically and discuss ways to implement the algorithm in practice. A computational example demonstrates the performance of the algorithm and shows some quantitative features of equilibria in a model with collateral and default.     

AN ANALYSIS OF PORTFOLIO REVISION STRATEGIES UTILIZING VARIABLE REVISION INTERVALS*

This paper investigates portfolio revision with an emphasis on the decision of when to revise. A statistical technique based on the sequential analysis of the time series of portfolio return relatives determines when revision is to occur. The technique detects changes in the time series which are an indication that the underlying generating process of the time series has changed and that the portfolio should be, if necessary, revised. Thus, the length of the revision interval is variable and a function of the data. The statistical technique is utilized in conjunction with three portfolio revision strategies. These three revision strategies are compared to a buy and hold policy over three nonoverlapping, 12-year investment horizons. The basis of comparison is the net terminal values which include adjustments for transaction costs and taxes. The sensitivity of the statistical technique to its parameters is also analyzed.     

含流动性约束及保证金购买的多空投资组合选择模型

本文在基于风险资产的价格服从梯形可能性分布的基础上,引入流动性约束、保证金限制、交易成本和存贷利差等因素,建立了多空投资组合模型。利用非线性规划理论和极大熵方法,给出了求解该模型的一种方法。最后,通过实例验证了主要结果并分析了流动性约束、保证金、交易费和存贷利差等因素对投资组合有效前沿的影响。     

Application of the Fuzzy Weighted Average in Strategic Portfolio Management*

We propose a systematic approach that incorporates fuzzy set theory in conjunction with portfolio matrices to assist managers in reaching a better understanding of the overall competitiveness of their business portfolios. Integer linear programming is also accommodated in the proposed integrated approach to help select strategic plans by using the results derived from the previous portfolio analysis and other financial data. The proposed integrated approach is designed from a strategy‐oriented perspective for portfolio management at the corporate level. It has the advantage of dealing with the uncertainty problem of decision makers in doing evaluation, providing a technique that presents the diversity of confidence and optimism levels of decision makers. Furthermore, integer linear programming is used because it offers an effective quantitative method for managers to allocate constrained resources optimally among proposed strategies. An illustration from a real‐world situation demonstrates the integrated approach. Although a particular portfolio matrix model has been adopted in our research, the procedure proposed here can be modified to incorporate other portfolio matrices.