Non-separation in the mean–lower-partial-moment portfolio optimization problem

With a number of advantages, lower partial moments (LPM) serve as alternatives to variance as measures of portfolio risk. For two specific targets, a separation property holds in the context of mean–LPM portfolio optimization that allows investors to separate the decision about investment proportions among risky assets from the decision about how much to invest in risky versus risk-free assets. For other targets, however, separation is not guaranteed, and this case has not received much attention in the literature. We show in the case of non-separation that investment curves are not common to all optimizing investors, but that they are convex in (mean, LPM) space and their lower envelope is the efficient frontier. We consider the interesting behavior of investment curves and optimal risky portfolios. We also show empirically that an investor who mistakenly assumes separation holds will not experience significant excess portfolio risk in all practical cases.     

Fuzzy portfolio model with different investor risk attitudes

We propose a fuzzy portfolio model designed for efficient portfolio selection with respect to uncertain or vague returns. Although many researchers have studied the fuzzy portfolio model, no researcher has yet attempted a behavioral analysis of the investor in the fuzzy portfolio model. To address this problem, we examined investor risk attitudes—risk-averse, risk-neutral, or risk-seeking behaviors—to discover an efficient method for fuzzy portfolio selection. In this study, we relied on the advantages of possibilistic mean–standard deviation models that we believed would fit the risk attitudes of investors. Thus, we developed a fuzzy portfolio model that focuses on different investor risk attitudes so that fuzzy portfolio selection for investors who possess different risk attitudes can be achieved more easily. Finally, we presented a numerical example of a portfolio selection problem to illustrate ways to address problems presented by a variety of investor risk attitudes.     

Optimal portfolio choice and stochastic volatility

In this paper we examine the effect of stochastic volatility on optimal portfolio choice in both partial and general equilibrium settings. In a partial equilibrium setting we derive an analog of the classic Samuelson–Merton optimal portfolio result and define volatility‐adjusted risk aversion as the effective risk aversion of an individual investing in an asset with stochastic volatility. We extend prior research which shows that effective risk aversion is greater with stochastic volatility than without for investors without wealth effects by providing further comparative static results on changes in effective risk aversion due to changes in the distribution of volatility. We demonstrate that effective risk aversion is increasing in the constant absolute risk aversion and the variance of the volatility distribution for investors without wealth effects. We further show that for these investors a first‐order stochastic dominant shift in the volatility distribution does not necessarily increase effective risk aversion, whereas a second‐order stochastic dominant shift in the volatility does increase effective risk aversion. Finally, we examine the effect of stochastic volatility on equilibrium asset prices. We derive an explicit capital asset pricing relationship that illustrates how stochastic volatility alters equilibrium asset prices in a setting with multiple risky assets, where returns have a market factor and asset‐specific random components and multiple investor types. Copyright © 2011 John Wiley & Sons, Ltd.     

考虑红利支付与提前退休的最优投资组合

研究了在经济代理人通过不可逆退休时间选择来调整劳动时间框架下的最优消费和投资问题,主要考虑风险资产派发红利的情形.运用随机控制方法,求解使得消费-闲暇预期效用最大化的最优策略.最优投资组合及最优退休时刻表明,代理人在为提前退休积累财富的同时,也能最佳享受消费和闲暇所带来的快乐.     

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.     

On the impact of conditional expectation estimators in portfolio theory

In this paper, we investigate the implications for portfolio theory of using conditional expectation estimators. First, we focus on the approximation of the conditional expectation within large-scale portfolio selection problems. In this context, we propose a new consistent multivariate kernel estimator to approximate the conditional expectation and it optimizes the bandwidth selection of kernel-type estimators. Second, we deal with the portfolio selection problem from the point of view of different non-satiable investors, namely risk-averse and risk-seeker investors. In particular, using a well-known ordering classification, we first identify different definitions of returns based on the investors preferences. Finally, for each problem, we examine several admissible portfolio optimization problems applied to the US stock market. The proposed empirical analysis allows us to evaluate the impact of the conditional expectation estimators in portfolio theory.     

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.     

Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization.     

Risk management strategies via minimax portfolio optimization

Recent extreme economic developments nearing a worst-case scenario motivate further examination of minimax linear programming approaches for portfolio optimization. Risk measured as the worst-case return is employed and a portfolio from maximizing returns subject to a risk threshold is constructed. Minimax model properties are developed and parametric analysis of the risk threshold connects this model to expected value along a continuum, revealing an efficient frontier segmenting investors by risk preference. Divergence of minimax model results from expected value is quantified and a set of possible prior distributions expressing a degree of Knightian uncertainty corresponding to risk preference determined. The minimax model will maximize return with respect to one of these prior distributions providing valuable insight regarding an investor’s risk attitude and decision behavior. Linear programming models for financial firms to assist individual investors to hedge against losses by buying insurance and a model for designing variable annuities are proposed.     

An exact solution to a robust portfolio choice problem with multiple risk measures under ambiguous distribution

This paper proposes a unified framework to solve distributionally robust mean-risk optimization problem that simultaneously uses variance, value-at-risk (VaR) and conditional value-at-risk (CVaR) as a triple-risk measure. It provides investors with more flexibility to find portfolios in the sense that it allows investors to optimize a return-risk profile in the presence of estimation error. We derive a closed-form expression for the optimal portfolio strategy to the robust mean-multiple risk portfolio selection model under distribution and mean return ambiguity (RMP). Specially, the robust mean-variance, robust maximum return, robust minimum VaR and robust minimum CVaR efficient portfolios are all special instances of RMP portfolios. We analytically and numerically show that the resulting portfolio weight converges to the minimum variance portfolio when the level of ambiguity aversion is in a high value. Using numerical experiment with simulated data, we demonstrate that our robust portfolios under ambiguity are more stable over time than the non-robust portfolios.     

Mean-chance model for portfolio selection based on uncertain measure

This paper discusses a portfolio selection problem in which security returns are given by experts’ evaluations instead of historical data. A factor method for evaluating security returns based on experts’ judgment is proposed and a mean-chance model for optimal portfolio selection is developed taking transaction costs and investors’ preference on diversification and investment limitations on certain securities into account. The factor method of evaluation can make good use of experts’ knowledge on the effects of economic environment and the companies’ unique characteristics on security returns and incorporate the contemporary relationship of security returns in the portfolio. The use of chance of portfolio return failing to reach the threshold can help investors easily tell their tolerance toward risk and thus facilitate a decision making. To solve the proposed nonlinear programming problem, a genetic algorithm is provided. To illustrate the application of the proposed method, a numerical example is also presented.     

基于均值-熵的机构投资者行为投资组合模型

考虑决策者的有限理性,利用相对财富和习惯形成效用函数描述了机构投资者的投资组合决策行为;在SHEFRIN和S TATM AN行为投资组合理论(BPT)框架下,引入均值-熵度量证券投资组合风险;由此,建立了一种机构投资者行为投资组合决策模型,算法释例进一步验证了其有效性.     

A note on portfolio selection with restrictions on leverage

This note focuses on a mean–variance asset allocation framework having restrictions on leverage, namely where investors are constrained either to hold funds in a risk-free asset (i.e. to lend) or to hold debt (i.e. to borrow). It is shown that the optimal portfolio in a constrained leverage situation will not have the same composition as the optimal portfolio in an unconstrained situation. We give formal justification for the intuitive notion that the more debt an investor is constrained to hold, the more the investor should tilt the remaining investments towards a portfolio of less risky assets. Conversely, the greater the proportion an investor is constrained to hold in a risk-free asset, the more the investor should tilt remaining investment towards a portfolio of more risky assets.     

基于Multi-Agent的机构投资者行为投资组合模型

从人的有限理性角度研究了机构投资者的投资组合决策问题．基于Multi-Agent构建了多心理账户情景下,机构投资者的两级行为投资组合模型；并且,利用两状态Markov链和管理熵函数描述了该模型中的关键参数；仿真算法释例验证了该模型能够逼近实际决策情景．     

Time-invariant portfolio strategies in structured products with guaranteed minimum equity exposure

We introduce a new exotic option to be used within structured products to address a key disadvantage of standard time-invariant portfolio protection: the well-known cash-lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option-based structure with a dynamic allocation logic as underlying. We provide an in-depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek-type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time-invariant portfolio protection strategies, meanwhile being also afraid to experience a cash-lock event triggered by market turmoils.     

Suitable-portfolio investors,nondominated frontier sensitivity,and the effect of multiple objectives on standard portfolio selection

In standard portfolio theory, an investor is typically taken as having one stochastic objective, to maximize the random variable of portfolio return. But in this paper, we focus on investors whose purpose is to build, more broadly, a “suitable portfolio” taking additional concerns into account. Such investors would have additional stochastic and deterministic objectives that might include liquidity, dividends, number of securities in a portfolio, social responsibility, and so forth. To accommodate such investors, we develop a multiple criteria portfolio selection formulation, corroborate its appropriateness by examining the sensitivity of the nondominated frontier to various factors, and observe the conversion of the nondominated frontier to a nondominated surface. Furthermore, multiple criteria enable us to provide an explanation as to why the “market portfolio,” so often found deep below the nondominated frontier, is roughly where one would expect it to be with multiple criteria. After commenting on solvability issues, the paper concludes with the idea that what is the “modern portfolio theory” of today might well be interpreted as a projection onto two-space of a real multiple criteria portfolio selection problem from higher dimensional space. M. Hirschberger: Research conducted while a Visiting Scholar at the Department of Banking and Finance, Terry College of Business, University of Georgia, October 2003–March 2004.     

Inverse portfolio problem with mean-deviation model

A Markowitz-type portfolio selection problem is to minimize a deviation measure of portfolio rate of return subject to constraints on portfolio budget and on desired expected return. In this context, the inverse portfolio problem is finding a deviation measure by observing the optimal mean-deviation portfolio that an investor holds. Necessary and sufficient conditions for the existence of such a deviation measure are established. It is shown that if the deviation measure exists, it can be chosen in the form of a mixed CVaR-deviation, and in the case of n risky assets available for investment (to form a portfolio), it is determined by a combination of (n + 1) CVaR-deviations. In the later case, an algorithm for constructing the deviation measure is presented, and if the number of CVaR-deviations is constrained, an approximate mixed CVaR-deviation is offered as well. The solution of the inverse portfolio problem may not be unique, and the investor can opt for the most conservative one, which has a simple closed-form representation.     

Robust ranking and portfolio optimization

The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets’ ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts.     

投资组合模型的改进研究:基于企业社会责任视角的实证分析

在尊重和借鉴前人对企业社会责任研究,尤其是在企业社会责任评价研究基础之上,本文从投资者的角度在投资组合过程中研究企业社会责任。在Markowitz(均值—方差)理论模型上添加企业社会责任的三个一级指标期望作为目标函数,由此将传统的投资组合模型扩展为五个目标函数的投资组合选择模型,而且我们根据经济学中经典的效用函数理论证明了此模型的正确性。本文引入主流的企业社会责任评价标准,并对一些典型公司进行打分量化。在此基础之上建立了以期望回报率、回报率的方差、核心利益相关者期望、蛰伏利益相关者期望和边缘利益相关者期望为目标函数的投资组合选择模型,在最小方差曲面上选取10个点构造投资组合,并以样本外的数据验证了模型的有效性。研究发现:根据此模型计算出来的部分投资组合回报率显著高于同期的市场指数。研究结果表明,这种关注企业社会责任的多目标投资组合选择模型,不仅让投资者可以直接控制企业社会责任,而且实际数据证明了此模型的优势之处,从而为关注企业社会责任的投资者提供一种投资的方法和思路。