Robust hedging strategies

While investing in foreign assets may bring additional benefits in terms of risk diversification, it may also expose the portfolio to a further source of risk derived from changes in the value of the foreign currencies. Hedging strategies for international portfolios have usually focused on the use of forward contracts to mitigate the currency risk. We propose an alternative formulation aimed at the reduction of the overall portfolio risk by assuming the returns are uncertain and maximizing the portfolio return for the worst possible outcome of the returns. This technique known as robust optimization provides a first guarantee on the portfolio value thanks to the non-inferiority property. We further complement our approach with forward contracts on the foreign exchange rates and options on the assets. Because the total return on any asset will be the product of its local return and currency return, the models proposed are bilinear and non convex. A reformulation of both the uncertainty set and the objective function as a semidefinite problem will yield an approximate tractable model. We compare the hedging alternatives proposed with simulated and historical market data and conclude on their relative benefits.     

A decision support system for strategic asset allocation

Strategic asset allocation is a crucial activity for any institutional or individual investor. Given a set of asset classes, the problem concerns the definition and management over time of the best asset mix to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. Although a considerable attention has been placed by the scientific community to address this problem by proposing sophisticated optimization models, limited effort has been devoted to the design of integrated framework that can be systematically used by financial operators. The paper presents a decision support system which integrates simulation techniques for forecasting future uncertain market conditions and sophisticated optimization models based on the stochastic programming paradigm. The system has been designed to be accessed via web and takes advantages of the increased computational power offered by high performance computing platforms. Real-world instances have been used to assess the performance of the decision support system also in comparison with more traditional portfolio optimization strategies.     

Dynamic option hedging with transaction costs: A stochastic model predictive control approach

This paper proposes stochastic model predictive control as a tool for hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. The methodology combines stochastic scenario generation for the prediction of asset prices at the next rebalancing interval with the minimization of a stochastic measure of the predicted hedging error. We consider 3 different measures to minimize in order to optimally rebalance the replicating portfolio: a trade‐off between variance and expected value of hedging error, conditional value at risk, and the largest predicted hedging error. The resulting optimization problems require solving at each trading instant a quadratic program, a linear program, and a (smaller‐scale) linear program, respectively. These can be combined with 3 different scenario generation schemes: the lognormal stock model with parameters recursively identified from data, an identification method based on support vector regression, and a simpler scheme based on perturbation noise. The hedging performance obtained by the proposed stochastic model predictive control strategies is illustrated on real‐world data drawn from the NASDAQ‐100 composite, evaluated for a European call and a barrier option, and compared with delta hedging.     

基于微分进化算法的多阶段投资组合优化

投资组合优化问题就是决定每个具有特定风险和回报的投资资产在总投资价值中的分配比例。在不断变化的金融市场中,多阶段投资组合优化就是通过周期性重新平衡投资资产比例管理投资组合以达到投资风险最小或投资回报最大。研究了基于微分进化算法在多阶段投资组合优化中制定投资决策的方法,目标函数是最大化个人经济效益或最大化周期结束时个人财富。通过比较用微分进化算法和遗传算法(GA)优化同样的资产对象所得到的期望收益率均值与方差,该文所提出的方法的优越性被美国标准普尔指数100的不同股票和现金分配优化所证实。     

Performance of a Hedged Stochastic Portfolio Model in the Presence of Extreme Events

Classical methods for computing the value-at-risk(VaR) do not account for the large price variationsobserved in financial markets. The historical methodis subject to event risk and may miss some fundamentalmarket evolution relevant to VaR; thevariance/covariance method tends to underestimate thedistribution tails and Monte Carlo simulation issubject to model risk. These methods are therebyusually completed with analyses derived fromcatastrophe scenarios.We propose a special case of the extreme-valueapproach for computing the value-at-risk of a stochasticmulticurrency portfolio when alternative hedgingstrategies are considered. This approach is able tocover market conditions ranging from the usual VaRenvironment to financial crises.We implement a multistage portfolio model with anexchange rate dynamic with stochastic volatility. Theparameters are estimated by GARCH-t models. Thesimulations are used to select multicurrencyportfolios whose exchange rate risk is hedged andrebalanced each ten days, accounting for VaR. Wecompare the performances of the two most classicalinstitutional options strategies – protective puts andcovered calls – to that of holding an unhedgedportfolio in presence of extreme events.     

Direct data-driven portfolio optimization with guaranteed shortfall probability

This paper proposes a novel methodology for optimal allocation of a portfolio of risky financial assets. Most existing methods that aim at compromising between portfolio performance (e.g., expected return) and its risk (e.g., volatility or shortfall probability) need some statistical model of the asset returns. This means that: (i) one needs to make rather strong assumptions on the market for eliciting a return distribution, and (ii) the parameters of this distribution need be somehow estimated, which is quite a critical aspect, since optimal portfolios will then depend on the way parameters are estimated. Here we propose instead a direct, data-driven, route to portfolio optimization that avoids both of the mentioned issues: the optimal portfolios are computed directly from historical data, by solving a sequence of convex optimization problems (typically, linear programs). Much more importantly, the resulting portfolios are theoretically backed by a guarantee that their expected shortfall is no larger than an a-priori assigned level. This result is here obtained assuming efficiency of the market, under no hypotheses on the shape of the joint distribution of the asset returns, which can remain unknown and need not be estimated.     

A fuzzy modeling for fuzzy portfolio optimization

Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately predicted by historical data. However, no matter how accurate the past data is, this premise will not exist in the financial market due to the high volatility of market environment. This paper discusses the fuzzy portfolio optimization problem where the asset returns are represented by fuzzy data. A mean-absolute deviation risk function model and Zadeh’s extension principle are utilized for the solution method of portfolio optimization problem with fuzzy returns. Since the parameters are fuzzy numbers, the gain of return is a fuzzy number as well. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the return of the portfolio optimization problem. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a pair of ordinary one-level linear programs so they can be manipulated. It is found that the calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on, the greater the potential return. An example, which utilizes the data from Taiwan stock exchange corporation, illustrates the whole idea on fuzzy portfolio optimization problem.     

An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem

In this paper, a novel multi objective model is proposed for portfolio selection. The proposed model incorporates the DEA cross-efficiency into Markowitz mean–variance model and considers return, risk and efficiency of the portfolio. Also, in order to take uncertainty in proposed model, the asset returns are considered as trapezoidal fuzzy numbers. Due to the computational complication of the proposed model, the second version of non-dominated sorting genetic algorithm (NSGA-II) is applied. To illustrate the performance of our model, the model is implemented for 52 firms listed in stock exchange market of Iran and the results are analyzed. The results show that the proposed model is suitable in compared with Markowitz and DEA models due to considering return, risk and efficiency, simultaneously.     

Multiobjective portfolio optimization of ARMA–GARCH time series based on experimental designs

The modern portfolio theory has been trying to determine how an investor might allocate assets among the possible investments options. Since the seminal contribution provided by Harry Markowitz’s theory of portfolio selection, several other tools and procedures have been proposed to deal with return-risk trade-off. Furthermore, diversification across sources of returns and risks based on entropy indexes is another pivotal aspect in portfolio management. An efficient approach to model these portfolio properties with the proportion of each asset can be obtained according to mixture design of experiments. Desirability method can be applied to optimize this nonlinear multiobjective problem. Nevertheless, a tuning procedure is required, since preference articulation parameters in desirability algorithm are unknown a priori. As a result, a computer-aided desirability tuning method is proposed to find an optimal portfolio with time series of returns and risks modeled by ARMA–GARCH models. To assess the proposal feasibility, the method is tested with a heteroskedastic dataset formed by weekly world crude oil spot prices and returns. Computer-aided desirability tuning was able to enhance the global desirability by 79% in relation to the result with no tuning procedure.     

Robust portfolio optimization via solution to the Hamilton–Jacobi–Bellman equation

We consider a problem of dynamic stochastic portfolio optimization modelled by a fully non-linear Hamilton–Jacobi–Bellman (HJB) equation. Using the Riccati transformation, the HJB equation is transformed to a simpler quasi-linear partial differential equation. An auxiliary quadratic programming problem is obtained, which involves a vector of expected asset returns and a covariance matrix of the returns as input parameters. Since this problem can be sensitive to the input data, we modify the problem from fixed input parameters to worst-case optimization over convex or discrete uncertainty sets both for asset mean returns and their covariance matrix. Qualitative as well as quantitative properties of the value function are analysed along with providing illustrative numerical examples. We show application to robust portfolio optimization for the German DAX30 Index.     

基于量子行为粒子群优化方法的随机规划算法

在不断变化的金融市场中,多阶段投资组合优化通过周期性地重组投资对象来追求回报最大,风险最小。提出了使用基于量子化行为的粒子群优化算法（Quantum-behaved Particle Swarm Optimization,QPSO）解决多阶段投资优化问题,并使用经典的利润风险函数作为目标函数,通过算法对标准普尔指数100的不同股票和现金进行投资组合的优化研究。根据实验得出的期望收益率与方差表明,QPSO算法在寻找全局最优解方面要优于粒子群算法（Particle Swarm Optimization,PSO）和遗传算法（Genetic Algorithm,GA）。     

Using genetic algorithm to support clustering-based portfolio optimization by investor information

A clustering-based portfolio optimization scheme that employs a genetic algorithm (GA) based on investor information for active portfolio management is presented. Whereas numerous studies have investigated trading behaviors, investor performance, and portfolio investment strategies, few works have developed investment strategies based on investor information. This study is conducted in two phases. First, a basket of portfolio (i.e., a collection of stocks held in individual portfolios) is developed through a cluster analysis of investor information. A GA is then employed to optimize the weights of the selected stocks. And the optimized portfolio is rebalanced to get excess return. It is concluded that the proposed multistage portfolio optimization scheme for active portfolio management generates superior results than previously proposed methods for the Korean stock market.     

An adaptive portfolio trading system: A risk-return portfolio optimization using recurrent reinforcement learning with expected maximum drawdown

Dynamic control theory has long been used in solving optimal asset allocation problems, and a number of trading decision systems based on reinforcement learning methods have been applied in asset allocation and portfolio rebalancing. In this paper, we extend the existing work in recurrent reinforcement learning (RRL) and build an optimal variable weight portfolio allocation under a coherent downside risk measure, the expected maximum drawdown, E(MDD). In particular, we propose a recurrent reinforcement learning method, with a coherent risk adjusted performance objective function, the Calmar ratio, to obtain both buy and sell signals and asset allocation weights. Using a portfolio consisting of the most frequently traded exchange-traded funds, we show that the expected maximum drawdown risk based objective function yields superior return performance compared to previously proposed RRL objective functions (i.e. the Sharpe ratio and the Sterling ratio), and that variable weight RRL long/short portfolios outperform equal weight RRL long/short portfolios under different transaction cost scenarios. We further propose an adaptive E(MDD) risk based RRL portfolio rebalancing decision system with a transaction cost and market condition stop-loss retraining mechanism, and we show that the proposed portfolio trading system responds to transaction cost effects better and outperforms hedge fund benchmarks consistently.     

Robust optimal decisions with imprecise forecasts

A robust minimax approach for optimal investment decisions with imprecise return forecasts and risk estimations in financial portfolio management is considered. Single-period and multi-period mean-variance optimization models are extended to worst-case design with multiple rival risk estimations and return forecasts. In multi-period stochastic formulation of classical mean-variance portfolio optimization problem, an investor makes an investment decision based on expectations and/or scenarios up to some intermediate times prior to the horizon and, consequently, rebalances or restructures the portfolio. Multi-period portfolio optimization entails the construction of a scenario tree representing a discretized estimate of uncertainties and associated probabilities in future stages. It is well known that return forecasts and risk estimations are inherently inaccurate and there are different rival estimates, or scenario trees. Robust optimization models are presented and imprecise nature of moment forecasts to reduce the risk of making a decision based on the wrong scenario is addressed. The worst-case performance is guaranteed in view of all rival risk and return scenarios and will only improve when any scenario other than the worst-case is realized. The ex-ante performance of minimax models is tested using historical data and backtesting results are presented.     

Portfolio Risk Measures: The Time’s Arrow Matters

The traditional ex post risk measure associated to a portfolio, a fund or a market performance, is the standard deviation of a series of past returns, called volatility. We propose an alternative risk measure, that turns out to better quantify the risk actually supported by an investor or asset manager with respect to a portfolio or a fund. This alternative measure is computed from the actual dispersion of successive cumulated returns relative to the corresponding successive cumulated returns produced by an accrued performance of null volatility, which better reflects the dynamics of the risk-return relationship over time. Hence, the proposed name of “accrued returns variability”, for such a risk measure that incorporates the passage of time. Applications are presented, to enlighten the advantage of this risk measure.     

基数约束投资组合问题的一种混合元启发式算法求解

针对资产数目和投资资金比例受约束的投资组合选择这一NP难问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法。该算法能很好地平衡开发能力和勘探能力,有效抑制了算法早熟收敛现象。标准测试函数的测试结果表明混合算法与标准的粒子群优化和引力搜索算法相比具有更好的寻优效率;实证分析进一步对混合算法与遗传算法及粒子群优化算法在求解这类投资组合选择问题的性能进行了比较。数值结果表明,混合算法在搜索具有高预期回报的非支配投资组合方面表现更好,取得了更为满意的结果。     

Improving Portfolio Efficiency: A Genetic Algorithm Approach

In this paper, I present a decision-making process that incorporates a Genetic Algorithm (GA) into a state dependent dynamic portfolio optimization system. A GA is a probabilistic search approach and thus can serve as a stochastic problem solving technique. A Genetic Algorithm solves the model by forward-looking and backward-induction, which incorporates both historical information and future uncertainty when estimating the asset returns. It significantly improves the accuracy of expected return estimation and thus improves the overall portfolio efficiency over the classical mean-variance method. In addition a GA could handle a large variety of future uncertainties, which overcome the computational difficulties in the traditional Bayesian approach.I thank for Russell Cooper, David Kendrick, Douglas Dacy for their helpful comments.     

An adaptive neuro‐fuzzy system for stock portfolio analysis

We propose an adaptive neuro‐fuzzy inference system (ANFIS) for stock portfolio return prediction. Previous work has shown that portfolio optimization can be improved by using predicted stock earnings rather than historical earnings. We show that predicted portfolio returns can be improved by using ANFIS and taking as input a variety of technical and fundamental attributes about various indices of the stock market. To generate membership functions, we use a robust noise rejection‐clustering algorithm. The neuro‐fuzzy model is tested on portfolios constituted from the Tehran Stock Exchange. In our experiments, the proposed method performs better in predicting the portfolio return than the classical Markowitz portfolio optimization method, a multiple regression, a neural network, and the Sugeno–Yasukawa method. © 2010 Wiley Periodicals, Inc.     

Robust multiperiod portfolio management in the presence of transaction costs

We study the viability of different robust optimization approaches to multiperiod portfolio selection. Robust optimization models treat future asset returns as uncertain coefficients in an optimization problem, and map the level of risk aversion of the investor to the level of tolerance of the total error in asset return forecasts. We suggest robust optimization formulations of the multiperiod portfolio optimization problem that are linear and computationally efficient. The linearity of the optimization problems is an advantage when complex additional requirements need to be imposed on the portfolio structure, e.g., limitations on positions in certain assets or tax constraints. We compare the performance of our robust formulations to the performance of the traditional single period mean-variance formulation frequently employed in the financial industry.     

Automating test generation for discrete event oriented embedded systems

A method for the automatic generation of test scenarios from the behavioral requirements of a system is presented in this paper. The generated suite of test scenarios validates the system design or implementation against the requirements. The approach proposed here uses a requirements model and a set of four algorithms. The requirements model is an executable model of the proposed system defined in a deterministic state-based modeling formalism. Each action in the requirements model that changes the state of the model is identified with a unique requirement identifier. The scenario generation algorithms perform controlled simulations of the requirements model in order to generate a suite of test scenarios applicable for black box testing. Measurements of several metrics on the scenario generation algorithms have been collected using prototype tools.