A general approach to Bayesian portfolio optimization

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm. The portfolio optimization is done using the first two moments of the predictive discrete asset return distribution. For illustration purposes we apply our method to empirical stock market data where daily asset log-returns are assumed to follow an orthogonal MGARCH process with t-distributed perturbations. Our results are compared with other portfolios suggested by popular optimization strategies.     

Elasticity approach to portfolio optimization

We study investment problems in a continuous-time setting and conclude that the proper control variables are elasticities to the traded assets or, in the case of stochastic interest rates, (factor) durations. This formulation of a portfolio problem allows us to solve the problems in a kind of two-step procedure: First, by calculating the optimal elasticities and durations we determine the optimal wealth process and then we compute a portfolio process which tracks these elasticities and durations. Our findings are not only interesting in itself, but the approach also proves useful in many varied applications including portfolios with (path-dependent) options. An important application can be the solution of portfolio problems with defaultable bonds modelled by a firm value approach.     

Particle swarm optimization approach to portfolio optimization

The survey of the relevant literature showed that there have been many studies for portfolio optimization problem and that the number of studies which have investigated the optimum portfolio using heuristic techniques is quite high. But almost none of these studies deals with particle swarm optimization (PSO) approach. This study presents a heuristic approach to portfolio optimization problem using PSO technique. The test data set is the weekly prices from March 1992 to September 1997 from the following indices: Hang Seng in Hong Kong, DAX 100 in Germany, FTSE 100 in UK, S&P 100 in USA and Nikkei in Japan. This study uses the cardinality constrained mean-variance model. Thus, the portfolio optimization model is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. The results of this study are compared with those of the genetic algorithms, simulated annealing and tabu search approaches. The purpose of this paper is to apply PSO technique to the portfolio optimization problem. The results show that particle swarm optimization approach is successful in portfolio optimization.     

A stochastic programming approach to multicriteria portfolio optimization

We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random walk model to generate scenarios on the possible values of the index return. We consider expected return, Conditional Value at Risk and liquidity as our criteria. With stocks from Istanbul Stock Exchange, we make computational studies for the two and three-criteria cases. We demonstrate the tradeoffs between criteria and show that treating these criteria simultaneously yields meaningful efficient solutions. We provide insights based on our experiments.     

A polynomial optimization approach to constant rebalanced portfolio selection

We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers.     

A unified approach to portfolio optimization with linear transaction costs

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.     

A stochastic programming approach for multi-period portfolio optimization

This paper extends previous work on the use of stochastic linear programming to solve life-cycle investment problems. We combine the feature of asset return predictability with practically relevant constraints arising in a life-cycle investment context. The objective is to maximize the expected utility of consumption over the lifetime and of bequest at the time of death of the investor. Asset returns and state variables follow a first-order vector auto-regression and the associated uncertainty is described by discrete scenario trees. To deal with the long time intervals involved in life-cycle problems we consider a few short-term decisions (to exploit any short-term return predictability), and incorporate a closed-form solution for the long, subsequent steady-state period to account for end effects.     

Fuzzy portfolio optimization a quadratic programming approach

The topic of this paper is as, the title shows, to introduce the formulation of fuzzy portfolio optimization problem as a convex quadratic programming approach and then give an acceptable solution to such problem. A numerical example included in the support of this paper for illustration.     

Robust portfolio optimization: a conic programming approach

The Markowitz Mean Variance model (MMV) and its variants are widely used for portfolio selection. The mean and covariance matrix used in the model originate from probability distributions that need to be determined empirically. It is well known that these parameters are notoriously difficult to estimate. In addition, the model is very sensitive to these parameter estimates. As a result, the performance and composition of MMV portfolios can vary significantly with the specification of the mean and covariance matrix. In order to address this issue we propose a one-period mean-variance model, where the mean and covariance matrix are only assumed to belong to an exogenously specified uncertainty set. The robust mean-variance portfolio selection problem is then written as a conic program that can be solved efficiently with standard solvers. Both second order cone program (SOCP) and semidefinite program (SDP) formulations are discussed. Using numerical experiments with real data we show that the portfolios generated by the proposed robust mean-variance model can be computed efficiently and are not as sensitive to input errors as the classical MMV??s portfolios.     

A fuzzy goal programming approach to portfolio selection

Portfolio selection is a usual multiobjective problem. This paper will try to deal with the optimum portfolio for a private investor, taking into account three criteria: return, risk and liquidity. These objectives, in general, are not crisp from the point of view of the investor, so we will deal with them in fuzzy terms. The problem formulation is a goal programming (G.P.) one, where the goals and the constraints are fuzzy. We will apply a fuzzy G.P. approach to the above problem to obtain a solution. Then, we will offer the investor help in handling the results.     

A mean-absolute deviation-skewness portfolio optimization model

It is assumed in the standard portfolio analysis that an investor is risk averse and that his utility is a function of the mean and variance of the rate of the return of the portfolio or can be approximated as such. It turns out, however, that the third moment (skewness) plays an important role if the distribution of the rate of return of assets is asymmetric around the mean. In particular, an investor would prefer a portfolio with larger third moment if the mean and variance are the same. In this paper, we propose a practical scheme to obtain a portfolio with a large third moment under the constraints on the first and second moment. The problem we need to solve is a linear programming problem, so that a large scale model can be optimized without difficulty. It is demonstrated that this model generates a portfolio with a large third moment very quickly.Presently at Mitsubishi Trust Bank Co., Ltd.     

A clustering approach for scenario tree reduction: an application to a stochastic programming portfolio optimization problem

This paper deals with the problem of scenario tree reduction for stochastic programming problems. In particular, a reduction method based on cluster analysis is proposed and tested on a portfolio optimization problem. Extensive computational experiments were carried out to evaluate the performance of the proposed approach, both in terms of computational efficiency and efficacy. The analysis of the results shows that the clustering approach exhibits good performance also when compared with other reduction approaches.     

A global optimization problem in portfolio selection

This paper deals with the issue of buy-in thresholds in portfolio optimization using the Markowitz approach. Optimal values of invested fractions calculated using, for instance, the classical minimum-risk problem can be unsatisfactory in practice because they lead to unrealistically small holdings of certain assets. Hence we may want to impose a discrete restriction on each invested fraction y _i such as y _i >  y _min or y _i =  0. We shall describe an approach which uses a combination of local and global optimization to determine satisfactory solutions. The approach could also be applied to other discrete conditions—for instance when assets can only be purchased in units of a certain size (roundlots).     

A portfolio theory approach to crop planning under environmental constraints

This paper presents a multiobjective model for crop planning in agriculture. The approach is based on portfolio theory. The model takes into account weather risks, market risks and environmental risks. Input data include historical land productivity data for various crops, soil types and yield response to fertilizer/pesticide application. Several environmental levels for the application of fertilizers/pesticides, and the monetary penalties for overcoming these levels, are also considered. Starting from the multiobjective model we formulate several single objective optimization problems: the minimum environmental risk problem, the maximum expected return problem and the minimum financial risk problem. We prove that the minimum environmental risk problem is equivalent to a mixed integer problem with a linear objective function. Two numerical results for the minimum environmental risk problem are presented.     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

A note on portfolio optimization with path-dependent utility

This paper considers the portfolio selection with preferences depending on the history of the wealth process. The maximization problem of the expected terminal utility consisting of the combination of two kinds of preferences is discussed in a continuous trading setting. Especially we focus on the relationship between the portfolio risk and the goal seeking behavior of the financial agent. The numerical example shows how the risk sensitivity affects the optimal portfolio and the corresponding expected path-dependent utility. Finally, we provide a criterion to choose buy and hold or buy and sell strategies.     

Convex optimization approaches to maximally predictable portfolio selection

In this article we propose a simple heuristic algorithm for approaching the maximally predictable portfolio, which is constructed so that return model of the resulting portfolio would attain the largest goodness-of-fit. It is obtained by solving a fractional program in which a ratio of two convex quadratic functions is maximized, and the number of variables associated with its nonconcavity has been a bottleneck in spite of continuing endeavour for its global optimization. The proposed algorithm can be implemented by simply solving a series of convex quadratic programs, and computational results show that it yields within a few seconds a (near) Karush–Kuhn–Tucker solution to each of the instances which were solved via a global optimization method in [H. Konno, Y. Takaya and R. Yamamoto, A maximal predictability portfolio using dynamic factor selection strategy, Int. J. Theor. Appl. Fin. 13 (2010) pp. 355–366]. In order to confirm the solution accuracy, we also pose a semidefinite programming relaxation approach, which succeeds in ensuring a near global optimality of the proposed approach. Our findings through computational experiments encourage us not to employ the global optimization approach, but to employ the local search algorithm for solving the fractional program of much larger size.