Search results for "Modern portfolio theory"

A fuzzy ranking strategy for portfolio selection applied to the Spanish stock market

2007

In this paper we present a fuzzy ranking procedure for the portfolio selection problem. The uncertainty on the returns of each portfolio is approximated by means of a trapezoidal fuzzy number. The expected return and risk of the portfolio are then characteristics of that fuzzy number. A rank index that accounts for both expected return and risk is defined, allowing the decision-maker to compare different portfolios. The paper ends with an application of that fuzzy ranking strategy to the Spanish stock market.

A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection

2012

This paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality. The uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor's aversion to risk. The fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return. The soft-computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem. We …

Fuzzy portfolio optimization under downside risk measures

2007

This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form.

Optimal Dynamic Portfolio Risk Management

2016

Numerous econometric studies report that financial asset volatilities and correlations are time-varying and predictable. Over the past decade, this knowledge has stimulated increasing interest in various dynamic portfolio risk control techniques. The two basic types of risk control techniques are: risk control across assets and risk control over time. At present, the two types of risk control techniques are not implemented simultaneously. There has been surprisingly little theoretical study of optimal dynamic portfolio risk management. In this paper, the author fills this gap in the literature by formulating and solving the multi-period portfolio choice problem. In terms of dynamic portfoli…

Mean‐Variance Portfolio Optimization

2010

Grading investment diversification options in presence of non-historical financial information

2021

Modern portfolio theory deals with the problem of selecting a portfolio of financial assets such that the expected return is maximized for a given level of risk. The forecast of the expected individual assets’ returns and risk is usually based on their historical returns. In this work, we consider a situation in which the investor has non-historical additional information that is used for the forecast of the expected returns. This implies that there is no obvious statistical risk measure any more, and it poses the problem of selecting an adequate set of diversification constraints to mitigate the risk of the selected portfolio without losing the value of the non-statistical information owne…

Value preserving portfolio strategies in continuous-time models

1997

We present a new approach for continuous-time portfolio strategies that relies on the principle of value preservation. This principle was developed by Hellwig (1987) for general economic decision and pricing models. The key idea is that an investor should try to consume only so much of his portfolio return that the future ability of the portfolio should be kept constant over time. This ensures that the portfolio will be a long lasting source of income. We define a continuous-time market setting to apply the idea of Hellwig to securities markets with continuous trading and examine existence (and uniqueness) of value-preserving strategies in some widely used market models. Further, we discuss…

Portfolio optimisation with strictly positive transaction costs and impulse control

1998

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…

Discrete Time Portfolio Selection with Lévy Processes

2007

This paper analyzes discrete time portfolio selection models with Lévy processes. We first implement portfolio models under the hypotheses the vector of log-returns follow or a multivariate Variance Gamma model or a Multivariate Normal Inverse Gaussian model or a Brownian Motion. In particular, we propose an ex-ante and an ex-post empirical comparisons by the point of view of different investors. Thus, we compare portfolio strategies considering different term structure scenarios and different distributional assumptions when unlimited short sales are allowed.

Cluster analysis for portfolio optimization

2005

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.