1,720,981 research outputs found
Risk disparity is better than risk parity for portfolio selection
No full textThe Risk Parity approach to portfolio selection 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 asset
equal among them. We show that this approach is theoretically dominated by
an alternative similar approach that does not require such equality but only appropriate
inequalities
Does Greater Diversification Really Improve Performance in Portfolio Selection?
No full textOne of the fundamental principles in portfolio selection models is minimization
of risk through diversification of the investment. This seems to require that in
a given working universe, or market, the investment should be spread among all
(or almost all) the available assets. Indeed, this is what some classical investment
strategies, like Equally-Weighted portfolios, or more recent and refined ones, like
Risk Parity, actually recommend.
The purpose of this work consists in giving some empirical evidence of the fact
that diversifying through the use of larger portfolios is not the best way to achieve an
improvement in out-of-sample performance. More precisely, we investigate the role
of the restriction on the number of assets in a portfolio (a cardinality constraint) on
the in-sample and out-of-sample outcomes of the Equally-Weighted approach and
of some well-known portfolio selection models that minimize risk through the use
of Variance, Semi-Mean Absolute Deviation, and Conditional Value-at-Risk.
Our empirical analysis is based on some new and on some publicly available
benchmark data sets often used in the literature
MINLP models for portfolio selection
No full textStarting with the seminal work by Markowitz, a large number of optimization models
have been proposed to find an ideal allocation of capital among several available
assets to achieve the investor’s objectives.
Here we propose a new framework for portfolio selection that explicitly takes into
account assets selection, risk diversification and utility maximization. This new
framework leads to several hard MINLP models, including some (black box) nonlinear
pseudoBoolean optimization problems. We present some theoretical and
computational results for the solution of the proposed models and we compare the
selected portfolios with the classical Mean-Variance approach
A New LP Model for Enhanced Indexation
No full textEnhanced Indexation is the problem of selecting a portfolio that should produce excess return
with respect to a given benchmark index. In this work we propose a linear bi-objective
optimization approach to Enhanced Indexation that maximizes average excess return and
minimizes underperformance over a learning period. This can be formulated as a simple
Linear Programming problem that is solved to optimality by standard LP codes. Moreover,
we investigate conditions that guarantee or forbid the existence of a portfolio strictly
outperforming the index. We present extensive computational analysis of the results on
publicly available real-world financial datasets, including comparison with previous results,
performance and diversification analysis, and empirical verification of some of the proposed
theoretical results
Risk Bounding is better then Risk Parity for portfolio selection
No full textRisk Parity (RP), also called equally weighted risk contribution, is a recent approach to risk diversification in 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. We call it the Equal Risk Bounding (ERB) approach.
This alternative approach might, and actually does in some cases, select portfolios that do not contain all assets and where the risk contributions of all assets is strictly smaller than in the RP portfolio.
We prove some relations between the solutions of the ERB and of the RP models and we use such relations to provide a finite method for finding an ERB portfolio. In the case of equal correlation, a closed form solution to the ERB model is also provided.
Some numerical examples illustrate the advantages of the ERB approach over the RP approach
Portfolio selection problems in practice: a comparison between linear and quadratic optimization models
No full textSeveral risk-return portfolio models take into account practical limitations on the number of assets to be included in the portfolio and on their weights. We present here a comparative study, both from the efficiency and from the performance viewpoint, of the Limited Asset Markowitz (LAM), the Limited Asset mean semi-absolute deviation (LAMSAD), and the Limited Asset conditional value-at-risk (LACVaR) models, where the assets are limited with the introduction of quantity and of cardinality constraints.The mixed integer linear LAMSAD and LACVaR models are solved with a state of the art commercial code, while the mixed integer quadratic LAM model is solved both with a commercial code and with a more efficient new method, recently proposed by the authors. Rather unexpectedly, for medium to large sizes it is easier to solve the quadratic LAM model with the new method, than to solve the linear LACVaR and LAMSAD models with the commercial solver. Furthermore, the new method has the advantage of finding all the extreme points of a more general tri-objective problem at no additional computational cost.We compare the out-of-sample performances of the three models and of the equally weighted portfolio. We show that there is no apparent dominance relation among the different approaches and, in contrast with previous studies, we find that the equally weighted portfolio does not seem to have any advantage over the three proposed models. Our empirical results are based on some new and old publicly available data sets often used in the literature. © 2014 Springer-Verlag Berlin Heidelberg
A new method for mean-variance portfolio optimization with cardinality constraints
No full textSeveral portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM) model, where the assets are limited with the introduction of quantity and cardinality constraints.
We propose a completely new approach for solving the LAM model based on a reformulation as a Standard Quadratic Program, on a new lower bound that we establish, and on other recent theoretical and computational results for such problem. These results lead to an exact algorithm for solving the LAM model for small size problems. For larger problems, such algorithm can be relaxed to an efficient and accurate heuristic procedure that is able to find the optimal or the best-known solutions for problems based on some standard financial data sets that are used by several other authors. We also test our method on five new data sets involving real-world capital market indices from major stock markets. We compare our results with those of CPLEX and with those obtained with very recent heuristic approaches in order to illustrate the effectiveness of our method in terms of solution quality and of computation time. All our data sets and results are publicly available for use by other researchers
A Linear Programming Model for Enhanced Indexation based on Strong Stochastic Dominance
No full textIn the field of Portfolio Optimization, Enhanced Indexation is the problem
of selecting a portfolio that generates excess return with respect to
a benchmark index. In this work, we propose a linear programming
model for Enhanced Indexation that selects an optimal portfolio according
to a generalization of strong stochastic dominance. Since our
model has an exponential number of constraints, we solve it through
a constraint generation procedure. Some experimental results are presented
for well-known financial data sets showing good out-of-sample
performance of our model
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