遗传算法在投资组合模型中的应用

均值-VaR模型是比较复杂的非线性规划问题，传统的算法不能保证得到全局最优值。鉴于此，引入遗传算法求解资产配置比例。对基于均值-VaR的单目标优化问题，设计了限定搜索空间和惩罚函数的遗传算法；而对多目标优化问题，应用并行选择遗传算法，并以沪深300行业分类指数构建投资组合，分析了行业资产配置的投资组合问题。结果表明，算法取得了良好的效果，解的结果既满足了投资的目标和约束条件，又反映了投资者之间不同的收益风险需求，且具有较好的实践性。     

Time-consistent strategies for multi-period mean-variance portfolio optimization with the serially correlated returns

Abstract

In this paper, we discuss several different styles of multi-period mean-variance portfolio optimization problems under the serially correlated returns. We derive the time-consistent strategies for the classical multi-period mean-variance optimization with and without risk-free asset using a backward induction approach. We also propose an alternative multi-period mean-variance model, and the corresponding time-consistent strategies are derived. Whereafter, we provide some portfolio evaluation indexes and perform extensive empirical studies based on real data, aiming to provide useful advice for investors. To a large extent, the empirical results answer one important and practical question: in actual investment situations, which strategy is preferred by different investors?     

Large Dynamic Covariance Matrices

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroscedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present article marries these two strands of literature to deliver improved estimation of large dynamic covariance matrices. Supplementary material for this article is available online.     

Comparison of different estimation techniques for portfolio selection

The main problem in applying the mean-variance portfolio selection consists of the fact that the first two moments of the asset returns are unknown. In practice the optimal portfolio weights have to be estimated. This is usually done by replacing the moments by the classical unbiased sample estimators. We provide a comparison of the exact and the asymptotic distributions of the estimated portfolio weights as well as a sensitivity analysis to shifts in the moments of the asset returns. Furthermore we consider several types of shrinkage estimators for the moments. The corresponding estimators of the portfolio weights are compared with each other and with the portfolio weights based on the sample estimators of the moments. We show how the uncertainty about the portfolio weights can be introduced into the performance measurement of trading strategies. The methodology explains the bad out-of-sample performance of the classical Markowitz procedures.     

An application of a minimax Bayes rule and shrinkage estimators to the portofolio selection problem under the Bayesian approach

This paper shows that a minimax Bayes rule and shrinkage estimators can be effectively applied to portfolio selection under the Bayesian approach. Specifically, it is shown that the portfolio selection problem can result in a statistical decision problem in some situations. Following that, we present a method for solving a problem involved in portfolio selection under the Bayesian approach.     

Dependence between oil and commodities markets using time-varying Archimedean copulas and effectiveness of hedging strategies

The aim of this work is to study in a first step the dependence between oil and some commodity prices (cotton, rice, wheat, sucre, coffee, and silver) using copula theory, and then in a second step to determine the optimal hedging strategy for oil–commodity portfolio against the risk of negative variation in commodity markets prices. The model is implemented with an AR-GARCH model with innovations that follow t distribution for the marginal distribution and the extreme value copula for the joint distribution and parameters and dependence indices are re-estimated in each new day which allow taking into account nonlinear dependence, tails behavior, and their development over time. Various copula functions are used to model the dependence structure between oil and commodity markets. Empirical results show an increase in the dependence during the last 6 years. Volatility for commodity prices registered record levels in the same time with the increase in uncertainty. Optimal hedging ratio varies over time as a consequence of the change in the dependence structure.     

Multiple Regression Model Averaging and the Focused Information Criterion With an Application to Portfolio Choice

ABSTRACT

We consider multiple regression (MR) model averaging using the focused information criterion (FIC). Our approach is motivated by the problem of implementing a mean-variance portfolio choice rule. The usual approach is to estimate parameters ignoring the intention to use them in portfolio choice. We develop an estimation method that focuses on the trading rule of interest. Asymptotic distributions of submodel estimators in the MR case are derived using a localization framework. The localization is of both regression coefficients and error covariances. Distributions of submodel estimators are used for model selection with the FIC. This allows comparison of submodels using the risk of portfolio rule estimators. FIC model averaging estimators are then characterized. This extension further improves risk properties. We show in simulations that applying these methods in the portfolio choice case results in improved estimates compared with several competitors. An application to futures data shows superior performance as well.     

Estimation of the optimal portfolio weights by shrinking the mean vector towards a linear subspace

To obtain estimators of mean-variance optimal portfolio weights, Stein-type estimators of the mean vector that shrink a sample mean towards the grand mean have been applied. However, the dominance of these estimators has not been shown under the loss function used in the estimation problem of the mean-variance optimal portfolio weights, which is different than the quadratic function for the case in which the covariance matrix is unknown. We analytically give the conditions for Stein-type estimators that shrink towards the grand mean, or more generally, towards a linear subspace, to improve upon the classical estimators, which are obtained by simply plugging in sample estimates. We also show the dominance when there are linear constraints on portfolio weights.     

投资组合动态VaR风险度量

投资组合的VaR风险度量依赖于投资组合中金融资产间联合分布函数的确定，随着投资组合规模的扩大，其VaR的计算难度也不断加大。利用ICA可以将多元联合概率分布函数转化为一元概率分布函数乘积实现简化计算的特点，基于ICA的投资组合动态VaR风险度量方法和计算步骤，克服了多元非正态条件下VaR测算上的困难。实证研究表明，与EWMA模型法、MGARCH模型法相比，ICA法能够准确地度量投资组合动态VaR。     

ON OPTIMIZING MULTI-LEVEL DESIGNS: POWER UNDER BUDGET CONSTRAINTS

This paper derives a procedure for efficiently allocating the number of units in multi‐level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A method is also described for optimizing designs when variance component estimates are not available. Case studies are provided to demonstrate the method.     

基于模糊概率的Markowitz投资组合分散风险的理论及实证研究

在分析Markowitz模型不足的基础上，提出了一个修正模型。该模型采用模糊概率的方法对投资组合里各资产的权重进行合理调整，更准确地显现投资组合分散风险的效果，并利用实际数据对该模型进行了实证研究，验证了资产数量与组合风险之间关系的理论学说，表明在近年来的上海股票市场中适宜的投资规模不超过20种。     

A generalized pivotal quantity approach to portfolio selection

The major problem of mean–variance portfolio optimization is parameter uncertainty. Many methods have been proposed to tackle this problem, including shrinkage methods, resampling techniques, and imposing constraints on the portfolio weights, etc. This paper suggests a new estimation method for mean–variance portfolio weights based on the concept of generalized pivotal quantity (GPQ) in the case when asset returns are multivariate normally distributed and serially independent. Both point and interval estimations of the portfolio weights are considered. Comparing with Markowitz's mean–variance model, resampling and shrinkage methods, we find that the proposed GPQ method typically yields the smallest mean-squared error for the point estimate of the portfolio weights and obtains a satisfactory coverage rate for their simultaneous confidence intervals. Finally, we apply the proposed methodology to address a portfolio rebalancing problem.     

Analysis of mutual funds’ management styles: a modeling,ranking and visualizing approach

A method to rank mutual funds according to their investment style measured with respect to the returns of a reference portfolio (benchmark) is introduced. It is based on a style analysis model estimating a mutual fund portfolio composition as well as the benchmark one. Starting from such compositions, it computes a proximity measure based on the L ₁ or L ₂ norm to assess the similarity between each mutual fund portfolio returns and the benchmark returns as well as between the returns of each benchmark constituent and that of the corresponding mutual fund constituent. To this purpose the mean integrated absolute error and the mean integrated squared error are computed to derive both a global ranking of mutual fund management styles and partial rankings expressing the over- (under-) weighting of each portfolio constituent. A visual inspection of the results emphasizing main differences in management styles is provided, using a parallel coordinates plot. Since a modeling, a ranking and a visualizing approach are integrated, the method is named MoRaViA. From the practitioners’ point of view, it allows the identification of a specific management style for each mutual fund, discriminating active management funds from passive management ones. To evaluate the effectiveness of MoRaViA, many sets of artificial portfolios are generated and an application on a set of equity funds operating in the European market is presented.     

High-dimensional Markowitz portfolio optimization problem: empirical comparison of covariance matrix estimators

We compare the performance of recently developed regularized covariance matrix estimators for Markowitz's portfolio optimization and of the minimum variance portfolio (MVP) problem in particular. We focus on seven estimators that are applied to the MVP problem in the literature; three regularize the eigenvalues of the sample covariance matrix, and the other four assume the sparsity of the true covariance matrix or its inverse. Comparisons are made with two sets of long-term S&P 500 stock return data that represent two extreme scenarios of active and passive management. The results show that the MVPs with sparse covariance estimators have high Sharpe ratios but that the naive diversification (also known as the ‘uniform (on market share) portfolio’) still performs well in terms of wealth growth.     

Cointegration and Long-Run Asset Allocation

We show that economic restrictions of cointegration between asset cash flows and aggregate consumption have important implications for return dynamics and optimal portfolio rules, particularly at long investment horizons. When cash flows and consumption share a common stochastic trend (i.e., are cointegrated), temporary deviations between their levels forecast long-horizon dividend growth rates and returns, and consequently, alter the term profile of risks and expected returns. We show that the optimal asset allocation based on the error-correction vector autoregression (EC-VAR) specification can be quite different relative to a traditional VAR that ignores the cointegrating relation. Unlike the EC-VAR, the commonly used VAR approach to model expected returns focuses on short-run forecasts and can considerably miss on long-horizon return dynamics, and hence, the optimal portfolio mix in the presence of cointegration. We develop and implement methods to account for parameter uncertainty in the EC-VAR setup and highlight the importance of the error-correction channel for optimal portfolio decisions at various investment horizons.     

New characteristics for portfolio surveillance

This paper elaborates the tools for the surveillance of the global minimum variance portfolio weights. Golosnoy and Schmid [V. Golosnoy and W. Schmid, EWMA control charts for optimal portfolio weights, Sequential Anal. 26 (2007), pp. 195–224] introduced exponentially weighted moving average-type control charts for this task based on the processes of the estimated weights as well as of their first differences. This paper proposes the new approximations to these processes exhibiting better stochastic properties for sequential monitoring purposes. The control schemes for the new processes are compared for different types of economically relevant changes using Monte Carlo simulations. The suggested procedures appear to be superior for the considered performance measures.     

A descent algorithm for constrained LAD-Lasso estimation with applications in portfolio selection

To improve the out-of-sample performance of the portfolio, Lasso regularization is incorporated to the Mean Absolute Deviance (MAD)-based portfolio selection method. It is shown that such a portfolio selection problem can be reformulated as a constrained Least Absolute Deviance problem with linear equality constraints. Moreover, we propose a new descent algorithm based on the ideas of ‘nonsmooth optimality conditions’ and ‘basis descent direction set’. The resulting MAD-Lasso method enjoys at least two advantages. First, it does not involve the estimation of covariance matrix that is difficult particularly in the high-dimensional settings. Second, sparsity is encouraged. This means that assets with weights close to zero in the Markovwitz's portfolio are driven to zero automatically. This reduces the management cost of the portfolio. Extensive simulation and real data examples indicate that if the Lasso regularization is incorporated, MAD portfolio selection method is consistently improved in terms of out-of-sample performance, measured by Sharpe ratio and sparsity. Moreover, simulation results suggest that the proposed descent algorithm is more time-efficient than interior point method and ADMM algorithm.     

基于投资者异质性的投资组合选择与证券市场价格

 马科维茨给出了风险规避型投资者最优投资组合的解,并论证了组合投资的风险分散功能。然而组合投资是否只是风险规避型投资者的“专利”呢？本文依据马科维茨均值-方差模型的研究范式,在充分讨论不同风险偏好投资者投资组合选择最优解的基础上,分别剖析了风险规避、中性、追求型三类投资者投资组合选择行为,以此为依据来探讨均衡条件下证券市场运行特征,并相应给出我国证券市场的经验证据。分析结果表明：无论哪类风险偏好型投资者,其都存在可供选择的最优投资组合方案,只是风险追求型投资者的最优解复杂一些罢了,风险中性型投资者将选择ETF工具代替市场组合,且他们的选择行为对市场运行不产生影响,市场运行完全由风险规避和风险追求型投资者的行为决定,虽然我们从投资组合选择的差异上无法区分个体投资者的风险偏好类型,但我国证券市场整体却表现出明显的风险追求型特征。     

Penalized optimal scoring for the classification of multi-dimensional functional data

Many fields of research need to classify individual systems based on one or more data series, which are obtained by sampling an unknown continuous curve with noise. In other words, the underlying process is an unknown function which the observed variables represent only imperfectly. Although functional logistic regression has many attractive features for this classification problem, this method is applicable only when the number of individuals to be classified (or available to estimate the model) is large compared to the number of curves sampled per individual.To overcome this limitation, we use penalized optimal scoring to construct a new method for the classification of multi-dimensional functional data. The proposed method consists of two stages. First, the series of observed discrete values available for each individual are expressed as a set of continuous curves. Next, the penalized optimal scoring model is estimated on the basis of these curves. A similar penalized optimal scoring method was described in my previous work, but this model is not suitable for the analysis of continuous functions. In this paper we adopt a Gaussian kernel approach to extend the previous model. The high accuracy of the new method is demonstrated on Monte Carlo simulations, and used to predict defaulting firms on the Japanese Stock Exchange.