Particle Swarm Optimization with non-smooth penalty reformulation for a complex portfolio selection problem

In the classical model for portfolio selection the risk is measured by the variance of returns. It is well known that, if returns are not elliptically distributed, this may cause inaccurate investment decisions. To address this issue, several alternative measures of risk have been proposed. In this contribution we focus on a class of measures that uses information contained both in lower and in upper tail of the distribution of the returns. We consider a nonlinear mixed-integer portfolio selection model which takes into account several constraints used in fund management practice. The latter problem is NP-hard in general, and exact algorithms for its minimization, which are both effective and efficient, are still sought at present. Thus, to approximately solve this model we experience the heuristics Particle Swarm Optimization (PSO). Since PSO was originally conceived for unconstrained global optimization problems, we apply it to a novel reformulation of our mixed-integer model, where a standard exact penalty function is introduced.Portfolio selection, coherent risk measure, fund management constraints, NP-hard mathematical programming problem, PSO, exact penalty method, SP100 index's assets.

An application of Markowitz theorem on Tehran Stock Exchange

During the past 65 years, there have been tremendous efforts on portfolio selection problem. The standard Markowitz mean–variance model to portfolio selection includes tracing out an efficient frontier, a continuous curve demonstrating the tradeoff between return and risk. This frontier can be often detected via standard quadratic programming, categorized in convex optimization. Traditional Markowitz problem has been recently extended into a new form of mixed integer nonlinear problems by considering various constraints such as cardinality constraints, industry limitation, etc. This paper proposes a mixed integer nonlinear programming to determine optimal asset allocation on Tehran Stock Exchange. The results have indicated that a petrochemical firm named Farabi has gained 44% of the portfolio followed by a drug firm named Kosar Pharmacy gaining 28%. In addition, banking sector was the third winning firm where Eghtesad Novin bank gained nearly 10% of the portfolio. Minerals and mining firms were the next sector in our portfolio where Gol Gohar Iron Ore and Tehran Cement collected 0.73% and 0.57% of the portfolio, respectively. In our survey, auto industry gained only 0.26% of the portfolio, which belonged to Saipa group

Heuristic algorithm for portfolio selection with minimum transaction lots

Portfolio selection problem was first formulated in a paper written by Markowitz, where investment diversification can be translated into computing. Mean-variance model he introduced has been used and developed because of it’s limitations in the larger constraints found in the real world, as well as it’scomputational complexity which found when it used in large-scale portfolio. Quadratic programming model complexity given by Markowitz has been overcome with the development of the algorithm research. Theyintroduce a linear risk function which solve the portfolio selection problem with real constraints, i.e. minimum transaction lots. With the Mixed Integer Linear models, proposed a new heuristic algorithm that starts from the solution of the relaxation problems which allow finding close-to-optimal solutions. This algorithm is built on Mixed Integer Linear Programming (MILP) which formulated using nearest integer search method

Оптимизация финансового портфеля на основе принципа безопасности

Вдосконалюється підхід А.Д. Роя до безпечної оптимізації фінансових портфелів. Безпечний портфель має мінімальну ймовірність небажаних, наприклад від’ємних, доходностей. Вдосконалення стосується кращого оцінювання ймовірності небажаних доходностей за допомогою нових порогових функцій ризику. Оптимальний безпечний портфель відшукується аналогічно геометричному методу Роя, але з відмінною ефективною границею. У разі скінченого числа сценаріїв пошук безпечного портфеля зводиться до лінійного частково булевого програмування.A.D. Roy’s safety first (SF) approach to financial portfolio selection is improved. Safety first means the minimization of the probability of negative returns. The improvement concerns a better estimation of the negative return probabilities by means of mean excess return risk functions. The search for the optimal SF-portfolio is similar to Roy’s geometric method but the efficient frontier is different. In case of a finite number of scenarios, SF-portfolio selection problem is reduced to a linear mixed Boolean programming problem

Mean–Variance portfolio selection in presence of infrequently traded stocks

This paper deals with a mean-variance optimal portfolio selection problem in presence of risky assets characterized by low frequency of trading and, therefore, low liquidity. To model the dynamics of illiquid assets, we introduce pure-jump processes. This leads to the development of a portfolio selection model in a mixed discrete/continuous time setting. In this paper, we pursue the twofold scope of analyzing and comparing either long-term investment strategies as well as short-term trading rules. The theoretical model is analyzed by applying extensive Monte Carlo experiments, in order to provide useful insights from a Önancial perspectiv

A Reference Point Approach to Bi-Objective Dynamic Portfolio Optimization

The portfolio selection problem presented in this paper is formulated as a biobjective mixed integer program. The portfolio selection problem considered is based on a dynamic model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to dynamically allocate the wealth on different securities to optimize by reference point method the portfolio expected return and the probability that the return is not less than a required level. In computational experiments the dataset of daily quotations from the Warsaw Stock Exchange were used

Optimal Credit Swap Portfolios

This paper formulates and solves the selection problem for a portfolio of credit swaps. The problem is cast as a goal program that entails a constrained optimization of preference-weighted moments of the portfolio value at the investment horizon. The portfolio value takes account of the exact timing of protection premium and default loss payments, as well as any mark-to-market profits and losses realized at the horizon. The constraints address collateral and solvency requirements, initial capital, position limits, and other trading constraints that credit swap investors often face in practice. The multimoment formulation accommodates the complex distribution of the portfolio value, which is a nested expectation under risk-neutral and actual probabilities. It also generates computational tractability. Numerical results illustrate the features of optimal portfolios. In particular, we find that credit swap investment constraints can have a significant impact on optimal portfolios, even for simple investment objectives. Our problem formulation and solution approach extend to corporate bond portfolios and mixed portfolios of corporate bonds and credit derivatives