Portfolio selection with probabilistic utility

Inspired by statistical physics, we present a probabilistic approach to portfolio selection. Instead of seeking the global extremum of some chosen utility function, we reinterpret the latter as a probability distribution of ‘optimal’ portfolios, and select the portfolio that is given by the mean value with respect to that distribution. Compared to the standard maximization of expected utility, this approach has several attractive features. First, it significantly reduces the excessive sensitivity to external parameters that often plague optimization procedures. Second, it mitigates the commonly observed concentration on too few assets; and third, it provides a natural and consistent way to account for the incompleteness of information and the aversion to uncertainty. Supportive empirical evidence is derived by using artificial data to simulate finite-sample behavior and out-of-sample performance.     

Equal Risk Bounding is better than Risk Parity for portfolio selection

Risk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification for portfolio selection. RP is based on the principle that the fractions of the capital invested in each asset should be chosen so as to make the total risk contributions of all assets equal among them. We show here that the Risk Parity approach is theoretically dominated by an alternative similar approach that does not actually require equally weighted risk contribution of all assets but only an equal upper bound on all such risks. This alternative approach, called Equal Risk Bounding (ERB), requires the solution of a nonconvex quadratically constrained optimization problem. The ERB approach, while starting from different requirements, turns out to be strictly linked to the RP approach. Indeed, when short selling is allowed, we prove that an ERB portfolio is actually an RP portfolio with minimum variance. When short selling is not allowed, there is a unique RP portfolio and it contains all assets in the market. In this case, the ERB approach might lead to the RP portfolio or it might lead to portfolios with smaller variance that do not contain all assets, and where the risk contributions of each asset included in the portfolio is strictly smaller than in the RP portfolio. We define a new riskiness index for assets that allows to identify those assets that are more likely to be excluded from the ERB portfolio. With these tools we then provide an exact method for small size nonconvex ERB models and a very efficient and accurate heuristic for larger problems of this type. In the case of a common constant pairwise correlation among all assets, a closed form solution to the ERB model is obtained and used to perform a parametric analysis when varying the level of correlation. The practical advantages of the ERB approach over the RP strategy are illustrated with some numerical examples. Computational experience on real-world and on simulated data confirms accuracy and efficiency of our heuristic approach to the ERB model also in comparison with some state-of-the-art local and global optimization codes.     

Minimal-Variance Hedging in Large Financial Markets: Random Fields Approach

We study a large financial market where the discounted asset prices are modeled by martingale random fields. This approach allows the treatment of both the cases of a market with a countable amount of assets and of a market with a continuum amount. We discuss conditions for these markets to be complete and we study the minimal variance hedging problem both in the case of full and partial information. An explicit representation of the minimal variance hedging portfolio is suggested. Techniques of stochastic differentiation are applied to achieve the main results. Examples of large market models with a countable number of assets are considered according to the literature and an example of market model with a continuum of assets is taken from the bond market.     

Constructing banking networks under decreasing costs of link formation

The structure of networks plays a central role in the behavior of financial systems and their response to policy. Real-world networks, however, are rarely directly observable: banks’ assets and liabilities are typically known, but not who is lending how much and to whom. This paper adds to the existing literature in two ways. First, it shows how to simulate realistic networks that are based on balance-sheet information. To do so, we introduce a model where links cause fixed-costs, independent of contract size; but the costs per link decrease the more connected a bank is (scale economies). Second, to approach the optimization problem, we develop a new algorithm inspired by the transportation planning literature and research in stochastic search heuristics. Computational experiments find that the resulting networks are not only consistent with the balance sheets, but also resemble real-world financial networks in their density (which is sparse but not minimally dense) and in their core-periphery and disassortative structure.

     

Market neutral portfolios

In this paper we consider the problem of constructing a market neutral portfolio. This is a portfolio of financial assets that (ideally) exhibits performance independent from that of an underlying market as represented by a benchmark index. We formulate this problem as a mixed-integer nonlinear program, minimising the absolute value of the correlation between portfolio return and index return. Our model is a flexible one that incorporates decisions as to both long and short positions in assets. Computational results, obtained using the software package Minotaur, are given for constructing market neutral portfolios for eleven different problem instances derived from universes defined by S&P international equity indices. We also compare our approach against an alternative approach based on minimising the absolute value of regression slope (the zero-beta approach).     

Short sales in Log-robust portfolio management

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case portfolio wealth over that set in a one-period setting. The degree of the manager’s aversion to ambiguity is incorporated through a single, intuitive parameter, which determines the size of the uncertainty set. The presence of short-selling requires the development of problem-specific techniques, because the optimization problem is not convex. In the case where assets are independent, we show that the robust optimization problem can be solved exactly as a series of linear programming problems; as a result, the approach remains tractable for large numbers of assets. We also provide insights into the structure of the optimal solution. In the case of correlated assets, we develop and test a heuristic where correlation is maintained only between assets invested in. In computational experiments, the proposed approach exhibits superior performance to that of the traditional robust approach.     

具有不完全信息的内部交易动态博弈

在Kyle模型中的线性均衡假设进行了修正的基础上,针对内部交易者只具有资产价值不完全信息情况,建立两期风险厌恶型内部交易均衡模型,并求得该模型的子博弈纳什均衡解.由此发现资产价值不完信息中噪音对市场干扰程度愈小(波动程度愈小),就愈有利于内部交易者的收益;内部交易者的交易就愈活跃;交易均衡价格包含资产价值信息就愈多.     

A mixed integer programming model for multistage mean–variance post-tax optimization

In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

A new defined benefit pension risk measurement methodology

Defined benefit pension plan sponsors have taken on greater risks for sponsoring these plans in the last several years. Due to ever increasing concerns of longevity risk and the weak economic environment, sponsors are eager to understand their pension-related risks to facilitate optimal enterprise decision-making. Borrowing an analytical framework from the life insurance and annuity industry where the amount of risk is framed in terms of the total assets required to remain solvent over a one-year period with a high level of confidence, i.e., the economic capital approach, this paper develops a benchmark risk measure for pension sponsors by obtaining a total asset requirement for sustaining the pension plan. The difference between the total asset requirement and the actual trust assets thus provides a measure of sponsor assets at risk due to plan sponsorship. Two factor-based approaches are proposed for this calculation. The first approach develops a set of pension-specific factors as if the pension plan were a group annuity. The second approach directly simulates the risk drivers of the pension plan and develops a framework for obtaining factors and calculating the pension risk given a desired confidence level. Our approach is very easy to implement and monitor in practice.     

Portfolio performance measurement using differential evolution

The basic problem in finance theory is the selection of an appropriate mix of assets in a portfolio in order to maximize portfolio expected return and subsequently to minimize portfolio risk. Another approach takes into account portfolio performance expressed by various measurement techniques e.g. Sharpe ratio, Treynor ratio, Jensen’s alpha, Information ratio, Sortino ratio, Omega function and Sharpe Omega ratio that are focused on determine the allocation of the available resources in the selected group of assets. This paper presents the alternative approach computing the weights of assets in portfolio assets based on the nonlinear measure techniques: Sortino ratio and Omega function. The proposed alternative includes principle of differential evolution from the group of evolutionary techniques. The experiments are set up on assets included in Dow Jones Industrial Average. Presented original approach enables using also other evolutionary algorithms in the area of portfolio selection based on different measurement techniques.     

A systems approach to identifying decisive information for sustainable development

Many governments are striving to implement sustainable development programs. While there are many definitions of `sustainability', most agree that a more comprehensive information infrastructure including economic, social, environmental, and cultural measures is required to assess courses of action and evaluate progress. Also critical is the development of information about the structure and behavior of the systems in which decisions are made. Most of the efforts toward the identification of information to support sustainable development decision making have focused on developing measures of progress toward sustainability. The Pressure-State-Response framework has been suggested as a method for capturing perceptions of causality. This framework fails to capture important information about complex causal relationships and system behavior. A systems approach to identifying decisive information is discussed as an alternative. This approach supports the identification of relationships among the indicators, learning about the behavior of the system, and provides a common language for interdisciplinary communication.     

An intensity‐based approach for equity modeling

This paper analyzes an intensity‐based approach for equity modeling. We use the Cox–Ingersoll–Ross (CIR) process to describe the intensity of the firm's default process. The intensity is purposely linked to the assets of the firm and consequently is also used to explain the equity. We examine two different approaches to link assets and intensity and derive closed‐form expressions for the firms' equity under both models. We use the Kalman filter to estimate the parameters of the unobservable intensity process. We demonstrate our approach using historical equity time series data from Merrill Lynch. Copyright © 2011 John Wiley & Sons, Ltd.     

Large deviations theorems for optimal investment problems with large portfolios

The thrust of this paper is to develop a new theoretical framework, based on large deviations theory, for the problem of optimal asset allocation in large portfolios. This problem is, apart from being theoretically interesting, also of practical relevance; examples include, inter alia, hedge funds where optimal strategies involve a large number of assets. In particular, we also prove the upper bound of the shortfall probability (or the risk bound) for the case where there is a finite number of assets. In the two-assets scenario, the effects of two types of asymmetries (i.e., asymmetry in the portfolio return distribution and asymmetric dependence among assets) on optimal portfolios and risk bounds are investigated. We calibrate our method with international equity data. In sum, both a theoretical analysis of the method and an empirical application indicate the feasibility and the significance of our approach.     

A hybrid optimization approach to index tracking

Index tracking consists in reproducing the performance of a stock-market index by investing in a subset of the stocks included in the index. A hybrid strategy that combines an evolutionary algorithm with quadratic programming is designed to solve this NP-hard problem: Given a subset of assets, quadratic programming yields the optimal tracking portfolio that invests only in the selected assets. The combinatorial problem of identifying the appropriate assets is solved by a genetic algorithm that uses the output of the quadratic optimization as fitness function. This hybrid approach allows the identification of quasi-optimal tracking portfolios at a reduced computational cost.     

Multivariate option pricing using copulae

The complexity of financial products significantly increased in the past 10 years. In this paper, we investigate the pricing of basket options and more generally of complex exotic contracts depending on multiple indices. Our approach assumes that the underlying assets evolve as dependent GARCH(1, 1) processes. The dependence among the assets is modeled using a copula based on pair‐copula constructions. Unlike most previous studies on this topic, we do not assume that the dependence observed between historical asset prices is similar to the dependence under the risk‐neutral probability. The method is illustrated with US market data on basket options written on two or three international indices. Copyright © 2012 John Wiley & Sons, Ltd.     

An extension of Sharpe's single-index model: portfolio selection with expert betas

This paper presents an approach to the portfolio selection problem based on Sharpe's single-index model and on Fuzzy Sets Theory. In this sense, expert estimations about future Betas of each financial asset have been included in the portfolio selection model denoted as ‘Expert Betas’ and modelled as trapezoidal fuzzy numbers. Value, ambiguity and fuzziness are three basic concepts involved in the model which provide enough information about fuzzy numbers representing ‘Expert Betas’ and that are simple to handle. In order to select an optimal portfolio, a Goal Programming model has been proposed including imprecise investor's aspirations concerning asset's proportions of both, high-and low-risk assets. Semantics of these goals are based on the fuzzy membership of a goal satisfaction set. To illustrate the proposed model a real portfolio selection problem is presented.     

资产剥离对风险溢价的影响研究

资产剥离会通过改变在位资产的构成而影响总资产风险收益特征。区别于已有研究将资产剥离看作看跌期权的通常做法,本文考虑企业剥离非核心资产并将资源重新聚焦于核心资产的一般情形,将资产剥离决策视作一种交换期权。运用实物期权方法和定价核技术,本文在连续时间框架下分析了资产剥离影响资产风险溢价的理论机理,并利用沪深A股上市公司数据进行实证检验。研究结果表明:资产剥离对资产风险溢价的影响方向取决于非核心和核心两类资产风险溢价的相对大小,影响程度则由两类资产价值占比的差异和交换期权的价值占比共同决定;进一步,等待剥离的决策灵活性会削弱资产剥离的影响;年轻阶段的资产剥离更加可能对风险溢价具有提升作用。     

基于矩匹配的、多标的实物期权估值方法研究

实物期权能够恰当地反映管理的灵活性价值,但是实际应用中往往对应多个标的物,现有的方法不能很好的求解其价值及变量的敏感性,从而限制了其应用.本文将多个标的资产视为一篮子资产组合,通过矩匹配方法求得组合资产的近似分布,从而可求解多标的实物期权的解析解,并通过案例分析了该方法的优势和便利性.     

A multicriteria decision support tool for modelling bank credit ratings

We introduce an application of the SMAA-Fuzzy-FlowSort approach to the case of modelling bank credit ratings. Its stochastic nature allows for imprecisions and uncertainty that naturally surround a decision-making exercise to be embedded into the proposed framework, whilst its output complements the ordinal nature of a crisp classification with cardinal information that shows the degree of membership to each rating category. Combined with the SMAA variant of GAIA that offers a visual of a bank’s judgmental analysis, both recent approaches provide a holistic multicriteria decision support tool in the hands of a credit analyst and enable a rich inferential procedure to be conducted. To illustrate the assets of this framework, we provide a case study evaluating the credit risk of 55 EU banks according to their financial fundamentals.