心理账户、损失厌恶与行为资产配置实证研究

基于前景理论和三参照点理论,建立了单心理账户和三心理账户下的线性损失厌恶行为投资组合模型,并利用中证基金指数数据构建了不同市场状态下的行为投资组合,实证研究不同损失厌恶系数、不同参照点、不同心理账户资金配置条件下模型的最优资产配置策略和投资组合绩效,研究发现线性损失厌恶模型更关注下侧损失,损失厌恶系数影响资产配置,注重安全性的投资者偏好低风险资产,而寻求实现抱负水平的投资者更偏好高收益资产。     

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.     

60 Years of portfolio optimization: Practical challenges and current trends

The concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making. In light of the 60 year anniversary of Harry Markowitz’s paper “Portfolio Selection,” we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice, including the inclusion of transaction costs, portfolio management constraints, and the sensitivity to the estimates of expected returns and covariances. In addition, we selectively highlight some of the new trends and developments in the area such as diversification methods, risk-parity portfolios, the mixing of different sources of alpha, and practical multi-period portfolio optimization.     

Asset portfolio securitizations and cyclicality of regulatory capital

This paper analyzes the level and cyclicality of regulatory bank capital for asset portfolio securitizations in relation to the cyclicality of capital requirements for the underlying loan portfolio as under Basel II/III. We find that the cyclicality of capital requirements is higher for (i) asset portfolio securitizations relative to primary loan portfolios, (ii) Ratings Based Approach (RBA) relative to the Supervisory Formula Approach, (iii) given the RBA for a point-in-time rating methodology relative to a rate-and-forget rating methodology, and (iv) under the passive reinvestment rule relative to alternative rules. Capital requirements of the individual tranches reveal that the volatility of aggregated capital charges for the securitized portfolio is triggered by the most senior tranches. This is due to the fact that senior tranches are more sensitive to the macroeconomy. An empirical analysis provides evidence that current credit ratings are time-constant and that economic losses for securitizations have exceeded the required capital in the recent financial crisis.     

What do robust equity portfolio models really do?

Most of previous work on robust equity portfolio optimization has focused on its formulation and performance. In contrast, in this paper we analyze the behavior of robust equity portfolios to determine whether reducing the sensitivity to input estimation errors is all robust models do and investigate any side-effects of robust formulations. Therefore, our focus is on the relationship between fundamental factors and robust models in order to determine if robust equity portfolios are consistently investing more in the factors opposed to individual asset movements. To do so, we perform regressions with factor returns to explain how robust portfolios behave compared to portfolios generated from the Markowitz’s mean-variance model. We find that robust equity portfolios consistently show higher correlation with the three fundamental factors used in the Fama-French factor model. Furthermore, more robustness among robust portfolios results in a higher correlation with the Fama-French three factors. In fact, we show that as equity portfolios under no constraints on portfolio weights become more robust, they consistently depend more on the market and large factors. These results show that robust models are betting on the fundamental factors instead of individual asset movements.     

Use of stochastic and mathematical programming in?portfolio theory and practice

Standard finance portfolio theory draws graphs and writes equations usually with no constraints and frequently in the univariate case. However, in reality, there are multivariate random variables and multivariate asset weights to determine with constraints. Also there are the effects of transaction costs on asset prices in the theory and calculation of optimal portfolios in the static and dynamic cases. There we use various stochastic programming, linear complementary, quadratic programming and nonlinear programming problems. This paper begins with the simplest problems and builds the theory to the more complex cases and then applies it to real financial asset allocation problems, hedge funds and professional racetrack betting. This paper is based on a keynote lecture at the APMOD conference in Madrid in June 2006. It was also presented at the London Business School. Many thanks are due to APMOD organizers Antonio Alonso-Ayuso, Laureano Escudero, and Andres Ramos for inviting me and for excellent hospitality in Madrid. Thanks are also due to my teachers at Berkeley who got me on the right track on stochastic and mathematical programming, especially Olvi Mangasarian, Roger Wets and Willard Zangwill, and my colleagues and co-authors on portfolio theory in finance and horseracing, especially Chanaka Edirishinge, Donald Hausch, Jarl Kallberg, Victor Lo, Leonard MacLean, Raymond Vickson and Yonggan Zhao.     

Concentrated portfolio selection models based on historical data

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Risk-Sensitive Dynamic Asset Management

This paper develops a continuous time portfolio optimization model where the mean returns of individual securities or asset categories are explicitly affected by underlying economic factors such as dividend yields, a firm's return on equity, interest rates, and unemployment rates. In particular, the factors are Gaussian processes, and the drift coefficients for the securities are affine functions of these factors. We employ methods of risk-sensitive control theory, thereby using an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk-aversion parameter. Even with constraints on the admissible trading strategies, it is shown that the optimal trading strategy has a simple characterization in terms of the factor levels. For particular factor levels, the optimal trading positions can be obtained as the solution of a quadratic program. The optimal objective value, as a function of the risk-aversion parameter, is shown to be the solution of a partial differential equation. A simple asset allocation example, featuring a Vasicek-type interest rate which affects a stock index and also serves as a second investment opportunity, provides some additional insight about the risk-sensitive criterion in the context of dynamic asset management. Accepted 10 December 1997     

国际多元化下投资组合优化研究:动态Copula方法

国际多元化需要对投资组合的相关结构进行动态性测度,这样才能提供更有效的资产配置策略和资金的理想避险场所。当前资产组合相关结构的Copula分析中考虑变结构和时变性不足,在此基础上构建了包含变结构和时变的诊断方法——分布函数距离法和Vuong-Clarke法在内的Copula动态性诊断方法,同时将二维诊断问题推广至多维情形,接着利用模拟仿真验证了上述方法的有效性。最后将动态Copula应用于金砖国家和西方成熟市场的最优投资组合中,利用标准差、CVaR和DVaR并结合样本预测外推法对最优投资组合进行了评价分析。实证结果表明,最优投资组合策略受Copula动态性影响明显,金砖国家市场在国际金融危机影响下能发挥良好的风险规避作用,实时的动态性诊断方法也能帮助投资者更快速地调整投资策略。     

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.     

Portfolio optimization with a neural network implementation of the coherent market hypothesis

Capital market research seems to be widely governed by traditional static linear models like arbitrage pricing theory and capital asset pricing model, though there is some evidence that better results can be achieved using nonlinear approaches. In this study we described a portfolio optimization model based on artificial neural networks embedded in the framework of a nonlinear dynamic capital market model, the coherent market hypothesis. The main advantage of this theory is that it drops the premise of rational investors and therefore relaxes the precondition of approximately normally distributed stock returns. Neural networks are used to estimate the return distributions in order to forecast the fundamental situation and the level of group behavior of the specific stocks. On the basis of these forecasts the relative stock performance is predicted and used to manage stock portfolios, In a simulation with out-of-sample data from 1991–1994 a portfolio constructed from the eight best ranked stocks achieved an annual return rate about 25% higher than that of the market portfolio and one built from the eight worst ranked stocks attained a return about 25% lower than the market portfolio's return rate. A hedging strategy based on the two aforementioned portfolios leads to a consistently positive annual return of about 25% regardless of the movements of the market portfolio with only 41% of the risk of a buy and hold strategy in the market portfolio.     

随机模糊的等比例-最小方差投资组合优化研究

Markowitz的均值-方差模型在投资组合优化中得到了广泛的运用和拓展,其中多数拓展模型仅局限于对随机投资组合或模糊投资组合的研究,而忽略了实际问题同时包含了随机信息和模糊信息两个方面。本文首先定义随机模糊变量的方差用以度量投资组合的风险,提出具有阀值约束的最小方差随机模糊投资组合模型,基于随机模糊理论,将该模型转化为具有线性等式和不等式约束的凸二次规划问题。为了提高上述模型的有效性,本文以投资者期望效用最大化为压缩目标对投资组合权重进行压缩,构建等比例-最小方差混合的随机模糊投资组合模型,并求解该模型的最优解。最后,运用滚动实际数据的方法,比较上述两个模型的夏普比率以验证其有效性。     

Capital adequacy and risk management in banking industry

The present paper deals with the issue of bank capital adequacy and risk management within a stochastic dynamic setting. In particular, an explicit risk aggregation and capital expression is provided regarding the portfolio choice and capital requirements special context. Such a framework leads to a nonlinear stochastic optimal control problem whose solution may be determined by means of dynamic programming algorithm. The pertaining analysis relies heavily on the stochastic dynamic modeling of such balance sheet items as securities, loans, and regulatory capital with stochastic interest rates. In this respect, the special Kalman filter approach is used for the purpose of estimating the model parameters. The reached findings reveal well that the Tunisian bank, subject of study, generally exceeds the minimum requirements and is adequately capitalized to maintain the appropriate capital amount level commensurate with the aggregate risk. Besides, empirical evidence on the regulations' impact on driving bank capitalization and risk‐taking behavior has also been highlighted. Copyright © 2015 John Wiley & Sons, Ltd.     

Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature

Since the pioneering work of Harry Markowitz, mean–variance portfolio selection model has been widely used in both theoretical and empirical studies, which maximizes the investment return under certain risk level or minimizes the investment risk under certain return level. In this paper, we review several variations or generalizations that substantially improve the performance of Markowitz’s mean–variance model, including dynamic portfolio optimization, portfolio optimization with practical factors, robust portfolio optimization and fuzzy portfolio optimization. The review provides a useful reference to handle portfolio selection problems for both researchers and practitioners. Some summaries about the current studies and future research directions are presented at the end of this paper.     

Robust portfolios that do not tilt factor exposure

Robust portfolios reduce the uncertainty in portfolio performance. In particular, the worst-case optimization approach is based on the Markowitz model and form portfolios that are more robust compared to mean–variance portfolios. However, since the robust formulation finds a different portfolio from the optimal mean–variance portfolio, the two portfolios may have dissimilar levels of factor exposure. In most cases, investors need a portfolio that is not only robust but also has a desired level of dependency on factor movement for managing the total portfolio risk. Therefore, we introduce new robust formulations that allow investors to control the factor exposure of portfolios. Empirical analysis shows that the robust portfolios from the proposed formulations are more robust than the classical mean–variance approach with comparable levels of exposure on fundamental factors.     

改进的Atlas模型下市场的稳定分布

Atlas模型在随机投资组合理论中有广泛的应用,但它的假定具有一定的局限性．我们对该模型进行了改进,证明了满足改进的Atlas模型的市场是渐进稳定的;在改进的Atlas模型下我们得到了市场稳定分布的确定性等价近似以及不同投资组合的渐近增长率与渐近超额增长率,这些结果与Atlas模型的类似结果相比有很大的优点;同时我们使用中国股票市场的交易数据对资本的稳定分布以及某些投资组合的长期平均增长率进行了实证研究,对比市场平均资本分布以及Atlas模型的相应结果,我们改进的Atlas模型在实证上比Atlas模型具有更好的适用性．     

Robust portfolio selection involving options under a “ marginal+joint ” ellipsoidal uncertainty set

In typical robust portfolio selection problems, one mainly finds portfolios with the worst-case return under a given uncertainty set, in which asset returns can be realized. A too large uncertainty set will lead to a too conservative robust portfolio. However, if the given uncertainty set is not large enough, the realized returns of resulting portfolios will be outside of the uncertainty set when an extreme event such as market crash or a large shock of asset returns occurs. The goal of this paper is to propose robust portfolio selection models under so-called “ marginal+joint” ellipsoidal uncertainty set and to test the performance of the proposed models. A robust portfolio selection model under a “marginal + joint” ellipsoidal uncertainty set is proposed at first. The model has the advantages of models under the separable uncertainty set and the joint ellipsoidal uncertainty set, and relaxes the requirements on the uncertainty set. Then, one more robust portfolio selection model with option protection is presented by combining options into the proposed robust portfolio selection model. Convex programming approximations with second-order cone and linear matrix inequalities constraints to both models are derived. The proposed robust portfolio selection model with options can hedge risks and generates robust portfolios with well wealth growth rate when an extreme event occurs. Tests on real data of the Chinese stock market and simulated options confirm the property of both the models. Test results show that (1) under the “ marginal+joint” uncertainty set, the wealth growth rate and diversification of robust portfolios generated from the first proposed robust portfolio model (without options) are better and greater than those generated from Goldfarb and Iyengar’s model, and (2) the robust portfolio selection model with options outperforms the robust portfolio selection model without options when some extreme event occurs.     

Introduction to convex optimization in financial markets

Convexity arises naturally in financial risk management. In risk preferences concerning random cash-flows, convexity corresponds to the fundamental diversification principle. Convexity is a basic property also of budget constraints both in classical linear models as well as in more realistic models with transaction costs and constraints. Moreover, modern securities markets are based on trading protocols that result in convex trading costs. The first part of this paper gives an introduction to certain basic concepts and principles of financial risk management in simple optimization terms. The second part reviews some convex optimization techniques used in mathematical and numerical analysis of financial optimization problems.     

Regulatory capital decisions in the Context of consumer loan portfolios

A topic of interest in recent literature is regulatory capital requirements for consumer loan portfolios. Banks are required to hold regulatory capital for unexpected losses, while expected losses are to be covered by either provisions or future income. In this paper, we show the set of efficient operating points in the market share and profit space for a portfolio manager operating under Basel II capital requirement and under capital constraints are a union of single-cutoff-score and double-cutoff-score operating points. For a portfolio manager to increase market-share beyond the maximum allowable under a single-cutoff score policy (eg, with binding capital constraints) requires granting loans to higher than optimal risk applicants. We show this result in greater portfolio risk but without an increase in regulatory capital requirement amount. The increase in forecasted losses is assumed to be absorbed by provisions or future margin income. Given portfolio managers take on higher risk under the same regulatory capital amount, our findings call for greater focus on provision amounts and future margin income under the supervisory review pillar of Basel II. This research raises the issue of whether the design of the regulatory formula for consumer loan portfolios is flawed.